Subset (6)

UltraData-Math-L1 · 86M rows

Split (1)

train · 86M rows

content stringlengths 86 994k	meta stringlengths 288 619
Chemistry Calculators - My Converter World Welcome to our “Chemistry Calculators” here; you will find a collection of invaluable tools designed to simplify the complexities of chemical calculations. Whether you’re a student exploring the world of molecules or a seasoned researcher investigating reaction mechanisms, our Chemistry Calculators are here to make your journey smoother and more efficient. A Chemistry Calculator refers to specialized digital tools designed to simplify and automate various mathematical calculations and tasks related to the field of chemistry. These calculators are tailored to address the complexities of chemical equations, reactions, concentrations, properties, and other quantitative aspects of chemistry. They cover various topics, such as calculating molar masses, balancing chemical equations, determining pH levels, predicting reaction outcomes, analyzing spectroscopic data, and more. Degree of Polymerization Calculator Exploring the Degree of Polymerization Calculator The Degree of Polymerization Calculator is a specialized digital tool designed to simplify the calculation Reverse Dilution Calculator Understanding Reverse Dilution in Chemical Reaction: Reverse Dilution Calculator refers to the process of determining the original concentration of a solution before	{"url":"https://myconverterworld.com/chemistry-calculators/","timestamp":"2024-11-07T18:53:36Z","content_type":"text/html","content_length":"79516","record_id":"<urn:uuid:9ec3e144-0f12-470f-b4d3-0aeb2d0cf0bc>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00161.warc.gz"}
Solve Math Problem – a Quick Introduction Get the Scoop on Solve Math Problem Before You’re Too Late Possibly the best source of error, however, is the usage of variables without definitions. As soon as you have understood and garnered all of the information, attempt to take care of the problem with care especially by avoiding errors in calculations and unit conversions. Replace X by means of your answer in the original algebraic equation to find out whether the solution is accurate. Working with decimals can be a modest time-consuming, hence, using compatible numbers will be able to help you choose a margin within which you are able to identify your answer. Provided that you perform the identical operation on either side of the equation, the equation remains balanced. A fraction isn’t a radical, but a fraction may include a radical. Key Pieces of Solve Math Problem Examine and The following thing is to read the question that is full. And soon you receive the very simple procedure it’s also sensible to be more content to practice exactly the problems given. Lookover http://www.phoenix.edu/programs/continuing-education/certificate-programs/technology/cert-ccna.html the sorts of problems you’ll be doing work. Realizes that problem does occur with the method, and that procedure isn’t studied by them. Speed Math by expenses Handley is among the far much better novels on normal arithmetic. The enlightening tool that is most popular and honored that is absolute’s been in existence for no less than a century. Handley’s educators ( for instance, mine) taught this you ought to assess issues by accomplishing the dilemma finished with two different techniques, and it is laborious and frustrating. Ahead of fifth grade they need to compose things down as a way to observe answers. Most students find it challenging to eliminate math complications. Pupil of Fortune makes it simple to evaluate some cash whilst supporting the others. They have an inclination to comprise all of the advice we should take care of the problem. Z plays with an part in our every day activity . The data is subsequently used by customers who assess the financial wellness and a firm’s situation. It will be potential if you’re stuck to seek the advice of with the cases as well as your mentor will likely be present to clarify your own doubts. You make an effort to obtain somebody who teach and are able to guide you, a tutor. The reach of test takers is increasing annually, leading to greater rivalry. With low prices but company, it really is really an assistance. Now there are two main lessons. Make certain you possess a whole great deal of fun, that is that the purpose behind solving puzzles. Really a combination clearly was for every single puzzle. An viral Facebook puzzle appears to find people seeking to find out just how that equation is accurate! Keep a list of times your son or daughter was disappointed with a math issue. The fact he’s permitted to engage in with games on the laptop will be adored by your very first grader, and also you are likely to adore the fact. It really is simple to discover games which let one to gauge the way your kid is faring. Word problems vary from being very easy to very intricate. The later chapters in the book allow it to be clear the way to achieve that. Watch a genuine quiz bee competition in case you have the possiblity to do or watch a videotaped contest on the world wide web. Whenever your brain knows there’s an answer but is not able to find it, it will become stressed. However tricky and hard the questions are, folks try their very best to get to the conclusion of the maze. With quite a few those games, you are in a place to develop a user name which empowers one to create the game private or people. You are finding at which the 2 connections are authentic at the identical time, to place it differently, the purpose at the 2 lines cross by solving a system. You can find many games for kids who are simply learning just how to identify amounts up to The Birth of Solve Math Problem A array of puzzles are on the basis of the notion of probability. Children who have a problem with math think that it’s challenging and assume they merely aren’t great at it. In the event you prefer to become better at solving algebra difficulties then you definitely have to realize that challenging job may go quite a way. Using all the Mat JV, then you aren’t likely to get to be concerned about just how to tackle my math difficulty. When it has to perform algebra, you wish to find in the place of simply working hard you ought to work smart. For instance, if a student doesn’t comprehend special vocabulary like the phrase ” inverse,” that the exact first move in dividing fractions ought to be changed. Multiplying two-digit amounts is a little more complicated but it could be learned quite quickly. Maths is also thought to be among the most scoring issues. It is but one among the most crucial branches of math.	{"url":"https://eltalleracc.ambientals.com/solve-math-problem-a-quick-introduction/","timestamp":"2024-11-01T22:02:41Z","content_type":"text/html","content_length":"36897","record_id":"<urn:uuid:81b952e1-0f6a-4104-9dbd-8926f4fea762>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00026.warc.gz"}
Boltzmann constant There's nothing wrong with liking physics! --Robert W King 09:03, 31 December 2007 (CST) And what's wrong with a little self deprecation then? :-) Seriously tho, Paul Wormer taught me a couple things this morning when he fixed some formatting issues and identified the Equipartition Theorem equation I had used as an example of the Boltzmann constant. So here, just by trying to share something I thought I already understood, I learned something new...and that _is_ a good thing. Here's the problem, in investigating the Equipartition Theorem in more depth, I raised more questions for myself. Having done so, and since this seems to be the place that those who feel liking Physics is a good thing tend to frequent, hopefully someone can now help me understand the thing I just learned...so here goes. The formula that is listed in the article and is apparently uncontested is: ${\displaystyle KE_{\mathrm {avg} }=\left({\frac {3}{2}}\right)kT}$ Where KE[avg] is the average kinetic energy of the particle, k is the Boltzmann Constant, and T is the temperature in kelvin. The thing is when I investigated the Equipartition Theorem in more detail this doesn't seem to add up...here's why: According to this article http://people.scs.fsu.edu/~berg/teach/phy2048/1120.pdf "A result from classical statistical mechanics is the equipartition theorem: When a substance is in equilibrium, there is an average energy of kT/2 per molecule or RT/2 per mole associated with each degree of freedom." Now, with three degrees of freedom (like in 3-d space for instance) everything seems to add up...kT/2 * 3 is exactly what we have. However as I look closer, we can have potential energy in rotation and apparently perhaps in oscillation as well. (My book does include the possibility of rotational kinetic energy in it's accounting of degrees of freedom but neglects the oscillatory but, whatever) The bottom line here is that here if we want to call this the "average kinetic energy of the particle in a general sense, (i.e. if this is really to be the Equipartition Theorem) it seems as tho we need to determine the degrees of freedom the particle actually has and modify the formula accordingly. Perhaps I picked too complex an example simply to illustrate the Boltzmann constant. --David Yamakuchi 19:29, 31 December 2007 (CST) Usually I don't like to advertise my own work, but here it goes: in Journal Chemical Physics vol. 122 , p. 184301, (2005) I wrote about the stat. mech. of rigid rotors. Table I in this paper gives deviations from equipartition for rotation. If the values in this table would satisfy F_x=F_y=F_z=0 (which they don't) then equipartition would hold. Conclusion: for rotation (three degrees of freedom) equipartition holds approximately, but not exactly. Happy New Year! --Paul Wormer 02:49, 1 January 2008 (CST)	{"url":"http://en.citizendium.org/wiki/Talk:Boltzmann_constant","timestamp":"2024-11-09T04:49:06Z","content_type":"text/html","content_length":"39970","record_id":"<urn:uuid:7c2dc4d7-fb11-4a01-87eb-be2ebb2d0608>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00557.warc.gz"}
Sine Function on a Right Triangle Learn about the Sine Function on a Right Triangle sine function can be used on a right triangle . The sine of an angle gives the ratio of the length of the side to the length of the About This Widget This widget allows you to find the angle, opposite and hypotenuse of a right triangle. Draw a right triangle by: • Clicking on the canvas, or • Entering two of the angle, opposite and hypotenuse. You might also like... Find More Find what you want by:	{"url":"https://www.mathematics-monster.com/widgets/sine_function_right_triangle.html","timestamp":"2024-11-10T17:41:44Z","content_type":"text/html","content_length":"11352","record_id":"<urn:uuid:4c0b4b21-41c2-4a5a-9aad-41a8f4144cd6>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00169.warc.gz"}
Four-quadrant optical matrix-vector multiplication machine as a neural-network processor Optical processors for neural networks are primarily fast matrix-vector multiplication machines that can potentially compete with serial computers owing to their parallelism and their ability to facilitate densely connected networks. However, in most proposed systems the multiplication supports only two quadrants and is thus unable to provide bipolar neuron outputs for increasing network capabilities and learning rate. We propose and demonstrate an opto-electronic four-quadrant matrix-vector multiplier that can be used for feed-forward neural-network recall and learning. Experimental results obtained with common commercial components demonstrate a novel, useful, and reliable approach for four-quadrant matrix-vector multiplication in general and for feed-forward neural-network training and recall in particular. Dive into the research topics of 'Four-quadrant optical matrix-vector multiplication machine as a neural-network processor'. Together they form a unique fingerprint.	{"url":"https://cris.tau.ac.il/en/publications/four-quadrant-optical-matrix-vector-multiplication-machine-as-a-n-2","timestamp":"2024-11-04T08:15:43Z","content_type":"text/html","content_length":"48757","record_id":"<urn:uuid:d11e3b5f-618c-4008-8112-dfb94b5a9bb0>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00347.warc.gz"}
Symmetries in Quantum Mechanics Creative Commons CC BY 4.0 Quantum Mechanics was first conceived at the turn of the twentieth century, and since has shook the foundations of modern physics. It is a radically different viewpoint from classical physics, which works on the macroscopic scale, in contrast to quantum mechanics' microscopic domain. Though at first it was heavily debated by members of the scientific communit, it is and has been both theoretically and experimentally verified by the likes of Einstein, Heisenberg, Shr\"{o}dinger, to name but a few. This being said, it is still an incomplete theory, and has yet not been concretely proved, despite strong experimental evidence for its truth. The aim of this report is to introduce the field of quantum mechanics, and to investigate the notions of conservation/symmetry, familiar from classical mechanics. The transformations we consider here are parity/space-inversion, lattice translation and time reversal. We will build a knowledge base by analysng the operators that represent these transformation within a quantum mechanical framework. This paper is presented for an audience that has completed a mathematics degree course up to and including second year. The specific feilds we draw upon include differential equations (MA1OD1, MA2OD2, MA2PD1), linear algebra (MA2LIN), and dynamics (MA2DY). These modules are assumed to be prior knowledge. The main sources of information for this project are: • An Introduction To Quantum Mechanics, D.J. Griffiths (1995), Second edition, Pearson Education ltd., 2005 • Modern Quantum Mechanics, J.J. Sakurai (1994), First edition, Addison-Wesley Publishing Company inc. 1994 which are referenced throughout. For specific pages, see the bibliography, which is found in section 6.	{"url":"https://it.overleaf.com/articles/symmetries-in-quantum-mechanics/mwcqyrttsswd","timestamp":"2024-11-10T11:21:24Z","content_type":"text/html","content_length":"101757","record_id":"<urn:uuid:9d1c32bf-8faa-4167-a4e5-e6fb2f578909>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00704.warc.gz"}
Volts to kW Calculator - calculator Volts to kW Calculator The Volts to kW Calculator is a tool designed to help you convert electrical power measured in volts and amps to kilowatts. Depending on whether your circuit is DC, single phase, or three phase, the calculation method will vary. This tool provides a user-friendly interface to input your electrical parameters and obtain accurate power conversion results. What is Volts to kW? Volts to kW is a conversion process to determine the electrical power in kilowatts from the voltage and current values. It's essential for understanding power consumption and efficiency in electrical What is a Volts to kW Calculator website? A Volts to kW Calculator website provides a tool to convert voltage and current measurements into kilowatts, offering an easy way to calculate power for various electrical circuits. How to use the Volts to kW Calculator website? Select the type of current (DC, single phase, or three phase), enter the required parameters, and click "Calculate" to get the result in kilowatts. What is the formula of the Volts to kW Calculator? - For DC: P(kW) = PF × I × V / 1000 - For Single Phase AC: P(kW) = PF × I × V / 1000 - For Three Phase AC: P(kW) = √3 × PF × I × V / 1000 What are the advantages and disadvantages of using the Volts to kW Calculator? - Provides quick and accurate power conversion. - Helps in understanding power consumption. - Requires accurate input values for precise results. - Not suitable for complex power analysis.	{"url":"https://calculatordna.com/volts-to-kw-calculator/","timestamp":"2024-11-05T06:14:18Z","content_type":"text/html","content_length":"89396","record_id":"<urn:uuid:3d3590b9-16bf-45e5-84ec-71dcd512eb0b>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00616.warc.gz"}
Find the probability of throwing a sum of 7 at least 9 times in 11 throws... Find the probability of throwing a sum of 7 at least 9 times in 11 throws... Find the probability of throwing a sum of 7 at least 9 times in 11 throws of a pair of fair dice. As we know that on throwing a pair of dice together then we will get total 36 outcomes so we have to find the probability of getting sum of numbers on dices equal to 7 possible outcomes ={ (1,6),(6,1),(5,2),(2,5),(3,4),(4,3)} Hence total number of possible outcomes =x=6 P(getting sum of 7 in single throw of pair of fair dice ) =p=6/36 =1/6 now let X is number of times we get sum equal to 7 when we throw a pair of dice 11 times Hence X~ Bin (11,1/6) so now we have to find P(X>9)	{"url":"https://justaaa.com/statistics-and-probability/933367-find-the-probability-of-throwing-a-sum-of-7-at","timestamp":"2024-11-06T17:35:07Z","content_type":"text/html","content_length":"38358","record_id":"<urn:uuid:644f1bbc-129d-4263-b951-3659768791e5>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00029.warc.gz"}
Leetcode P0275”H-Index II” 题解博文中会简要介绍Leetcode P0275题目分析及解题思路。 “H-Index II”是一道中等难度的题目，同时也是p0274的衍生题。这道题其实就是p0274排完序之后利用二分搜索寻找临界点的过程。具体思路不再赘述。 Given an array of integers citations where citations[i] is the number of citations a researcher received for their ith paper and citations is sorted in an ascending order, return compute the researcher’s h-index. According to the definition of h-index on Wikipedia: A scientist has an index h if h of their n papers have at least h citations each, and the other n − h papers have no more...	{"url":"https://diff.blog/post/leetcode-p0275h-index-ii-74587/","timestamp":"2024-11-12T03:19:34Z","content_type":"text/html","content_length":"12035","record_id":"<urn:uuid:58552c47-ed3f-4d77-96a9-062fba710809>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00094.warc.gz"}
Joint Compound Calculator – Accurate Estimates This tool will calculate the amount of joint compound you need for your drywall project. How the Joint Compound Calculator Works This calculator is designed to help you estimate the amount of joint compound you will need for your drywall project. Here’s a step-by-step guide on how to use it: How to Use the Calculator 1. Width of Room: Enter the width of the room in feet. 2. Length of Room: Enter the length of the room in feet. 3. Ceiling Height: Enter the height of the ceiling in feet. 4. Number of Coats: Enter the number of coats of joint compound you plan to apply. 5. Coverage per Gallon: Enter the coverage area provided by one gallon of joint compound in square feet (usually available on the product label). 6. Click the Calculate button to get the result. How It Calculates the Results The calculator starts by determining the total surface area that needs to be covered. It calculates the surface areas of the walls and the ceiling separately: • Walls: (Width x Height x 2) + (Length x Height x 2) • Ceiling: Length x Width It then sums these values to get the total surface area. After that, it divides the total surface area by the coverage per gallon to find out how many gallons are needed for a single coat. Finally, it multiplies this number by the number of coats to give you the total joint compound needed in gallons. While this calculator provides a good estimate, there are limitations to its accuracy: • It does not account for doors, windows, or other openings in the walls. • Variations in joint compound application thickness can lead to slight differences in actual usage. • Make sure to check the coverage details on the specific joint compound product you are using, as coverage can vary. Always consider adding a little extra to your project to ensure you have enough material. Use Cases for This Calculator Calculate Amount of Joint Compound Needed Enter the dimensions of the area you need to cover with joint compound and the depth you want to apply. The calculator will instantly provide you with the amount of joint compound required in pounds or kilograms. Determine Dry Time for Joint Compound Specify the type of joint compound you are using and the temperature of the room. Get an estimate of the approximate dry time needed before you can proceed to the next steps of your project. Estimate Cost of Joint Compound Input the price per pound or kilogram of joint compound and the total amount needed for your project. The calculator will show you the estimated cost of the joint compound required. Calculate Number of Coats Required Based on the type of joint compound you’re using and the finish you desire (e.g., smooth or textured), the calculator will tell you how many coats of joint compound you’ll need to apply. Factor in Wastage Percentage Add a wastage percentage to account for spillage, errors, or inconsistencies during the application of joint compound. The calculator will adjust the total amount needed accordingly. Convert Units for Convenience If you prefer to work in pounds but need the answer in kilograms (or vice versa), you can easily switch between units with a single click without having to redo any calculations. Adjust for Room Shape and Complexity Select the shape of the room you’re working on (e.g., square, rectangular, L-shaped) and specify any intricate areas that may require extra joint compound. The calculator will factor in these details for a more accurate estimation. Optimize for Multiple Areas If you have more than one area in your project that needs joint compound, input the dimensions and depths separately for each section. The calculator will sum up the total amount required for all areas combined. Account for Vertical vs. Horizontal Surfaces Indicate whether you’re applying joint compound on vertical walls or horizontal ceilings to adjust the calculations for gravity and drying time. This customization ensures precise results tailored to your specific application. Get Quick Recommendations for Brands and Quantities Based on your project requirements and preferences, receive instant suggestions for reputable joint compound brands and the exact quantities needed, saving you time and effort in decision-making and	{"url":"https://calculatorsforhome.com/joint-compound-calculator/","timestamp":"2024-11-11T21:40:10Z","content_type":"text/html","content_length":"149375","record_id":"<urn:uuid:cceffa9c-284b-4e8e-a785-59744e5f28ec>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00539.warc.gz"}
farfieldexact - Script command Projects complete complex vector fields to specific locations. It is expected to be correct down to distances on the order of one wavelength. The projections from multiple monitors can be added to create a total far field projection - see Projections from a monitor box . farfieldexact projects any surface fields to a series of points defined by vector lists. The x,y, z coordinates of each evaluation point are taken element-by-element from the vector lists. i.e., the i-th point in a 2D simulation would be at [x(i),y(i)]. This command can return either the E field or the E and H fields of the projection. Vectors lists x,y,z must have the same length L or be length 1. When only the E field is returned, the data is returned in a matrix of dimension Lx3. The first index represents positions defined by one element from each of x,y, z. [x(i),y(i),z(i)]; the second index represents Ex, Ey, and Ez. When both E and H fields are returned, the data is returned as a dataset with the E and H fields packaged with the corresponding x,y,z and frequency/wavelength. Vector lists x, y must have the same length L or be length 1. When only the E field is returned, the data is returned in the form of a matrix that is of dimension Lx3. The first index represents positions defined by one element from each of x,y. [x(i),y(i)]; The second index represents Ex, Ey, and Ez. When both E and H fields are returned, the data is returned as a dataset with the E and H fields packaged with the corresponding x,y, and frequency/wavelength. Syntax Description out = farfieldexact("mname", x, y, f, index); 2D far field exact projection. Returns E field only. out = farfieldexact(dataset, x, y, f, index); 2D far field exact projection. Returns E field only. out = farfieldexact("mname", x, y, opt); 2D far field exact projection. Returns E field or E and H fields. Refer to the following table for the options. out = farfieldexact(dataset, x, y, opt); 2D far field exact projection. Returns E field or E and H fields. Refer to the following table for the options. out = farfieldexact("mname", x, y, z, f, index); 3D far field exact projection. Returns E field only. out = farfieldexact(dataset, x, y, z, f, index); 3D far field exact projection. Returns E field only. out = farfieldexact("mname", x, y, z, opt); 3D far field exact projection. Returns E field or E and H fields. Refer to the following table for the options out = farfieldexact(dataset, x, y, z, opt); 3D far field exact projection. Returns E field or E and H fields. Refer to the following table for the options Parameter Default Default value Type Description mname required string name of the monitor from which far field is calculated dataset required dataset Rectilinear dataset containing both E and H x required vector x coordinates of points where far field is calculated. must have length L or 1. y required vector y coordinates of points where far field is calculated. must have length L or 1. z required vector z coordinates of points where far field is calculated. must have length L or 1. f optional 1 vector Index of the desired frequency point. This can be a single number or a vector. Multithreaded projection was introduced since R2016b. index optional value at monitor number The index of the material to use for the projection. the 'opt' parameter includes the following options: This parameter is optional. It defines the return field, can either be "E" or "E and H". opt optional struct "f": This parameter is optional. It defines the index of the desired frequency point. This can be a single number or a vector. Multi-threaded projection was introduced since R2016b. This parameter is optional. It defines the index of the material to use for the projection. [[Note:]] When using a dataset, the default value of the refractive index is 1. This example shows how to calculate \|E\|^2 and \|H\|^2 on a straight line at y=0, z=1, for x from -1 to 1 meters. For the example of far field projection of a rectilinear dataset see farfield3d. # Define far field position vector # do far field projection E_H_far=farfieldexact("monitor",x,y,z,{"field":"E and H", "f":1}); E_far = E_H_far.E; H_far = E_H_far.H; E2_far = sum(abs(E_far)^2,2); # E2 = \|Ex\|^2 + \|Ey\|^2 + \|Ez\|^2 H2_far = sum(abs(H_far)^2,2); # H2 = \|Hx\|^2 + \|Hy\|^2 + \|Hz\|^2 # plot results plot(x,E2_far,"x","y","\|E\|^2 on line at y=0, z=1"); plot(x,H2_far,"x","y","\|H\|^2 on line at y=0, z=1"); This example shows how to sum the results from a box of monitors (typically surrounding a scattering particle). Note: See the online section on Far field projections for more information on why a negative sign is required on some terms. phi = linspace(0,360,201); E2_xy = matrix(length(phi)); E2_yz = matrix(length(phi)); x = -sin(phipi/180); y = cos(phipi/180); z = 0; temp = farfieldexact("x2",x,y,z,{"field":"E"}) + farfieldexact("y2",x,y,z,{"field":"E"}) + farfieldexact("z2",x,y,z,{"field":"E"}) - farfieldexact("x1",x,y,z,{"field":"E"}) - farfieldexact("y1",x,y,z,{"field":"E"}) - farfieldexact("z1",x,y,z,{"field":"E"}); E2_xy = sum(abs(temp)^2,2); # E2 = \|Ex\|^2 + \|Ey\|^2 + \|Ez\|^2 plot(phi, E2_xy,"Phi (deg)","\|E\|^2","in XY plane"); The following example shows how farfieldexact and farfieldexact3d output data differently. When x=[1 2], y=[1 2], z=[0], farfieldexact: The result is a 23 matrix. First dimension is position;second is field component. This calculates the far field at the positions [1,1,0] and [2,2,0] . farfielexact3d: The result is a 2213 matrix. First three dimensions are positions; the fourth dimension is field component. This calculates the far field at the positions [x,y,z] = [1,1,0], [1,2,0], [2,1,0], [2,2,0]. See Also List of commands , farfield2d , farfield3d , farfieldexact2d , farfieldexact3d	{"url":"https://optics.ansys.com/hc/en-us/articles/360034410214-farfieldexact-Script-command","timestamp":"2024-11-14T10:37:39Z","content_type":"text/html","content_length":"38854","record_id":"<urn:uuid:56cf8a87-f659-43ff-90a0-2359fd8e4b05>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00628.warc.gz"}
The classifiers implemented in MOA are the following: • Bayesian classifiers □ Naive Bayes □ Naive Bayes Multinomial • Decision trees classifiers □ Decision Stump □ Hoeffding Tree □ Hoeffding Option Tree □ Hoeffding Adaptive Tree • Meta classifiers □ Bagging □ Boosting □ Bagging using ADWIN □ Bagging using Adaptive-Size Hoeffding Trees. □ Perceptron Stacking of Restricted Hoeffding Trees □ Leveraging Bagging • Function classifiers □ Perceptron □ SGD: Stochastic Gradient Descent □ SPegasos • Drift classifiers Classiﬁers for static streams Always predicts the class that has been observed most frequently the in the training data. • -r : Seed for random behaviour of the classifier Performs classic bayesian prediction while making naive assumption that all inputs are independent. Naive Bayes is a classiﬁer algorithm known for its simplicity and low computational cost. Given n different classes, the trained Naive Bayes classiﬁer predicts for every unlabelled instance I the class C to which it belongs with high accuracy. • -r : Seed for random behaviour of the classifier Decision trees of one level. • -g : The number of instances to observe between model changes • -b : Only allow binary splits • -c : Split criterion to use. Example : InfoGainSplitCriterion • -r : Seed for random behaviour of the classifier Decision tree for streaming data. A Hoeffding tree is an incremental, anytime decision tree induction algorithm that is capable of learning from massive data streams, assuming that the distribution generating examples does not change over time. Hoeffding trees exploit the fact that a small sample can often be enough to choose an optimal splitting attribute. This idea is supported mathematically by the Hoeffding bound, which quantiﬁes the number of observations (in our case, examples) needed to estimate some statistics within a prescribed precision (in our case, the goodness of an attribute). A theoretically appealing feature of Hoeffding Trees not shared by other incremental decision tree learners is that it has sound guarantees of performance. Using the Hoeffding bound one can show that its output is asymptotically nearly identical to that of a non-incremental learner using inﬁnitely many examples. See for details: G. Hulten, L. Spencer, and P. Domingos. Mining time-changing data streams. In KDD’01, pages 97–106, San Francisco, CA, 2001. ACM Press. • -m : Maximum memory consumed by the tree • -n : Numeric estimator to use : □ Gaussian approximation evaluating 10 splitpoints □ Gaussian approximation evaluating 100 splitpoints □ Greenwald-Khanna quantile summary with 10 tuples □ Greenwald-Khanna quantile summary with 100 tuples □ Greenwald-Khanna quantile summary with 1000 tuples □ VFML method with 10 bins □ VFML method with 100 bins □ VFML method with 1000 bins □ Exhaustive binary tree • -e : How many instances between memory consumption checks • -g : The number of instances a leaf should observe between split • -s : Split criterion to use. Example : InfoGainSplitCriterion • -c : The allowable error in split decision, values closer to 0 will take longer to decide • -t : Threshold below which a split will be forced to break ties • -b : Only allow binary splits • -z : Stop growing as soon as memory limit is hit • -r : Disable poor attributes • -p : Disable pre-pruning • -l : Leaf classifier to use at the leaves: Majority class, Naive Bayes, Naive Bayes Adaptive. By default: Naive Bayes Adaptive. In old versions of MOA, a HoeffdingTreeNB was a HoeffdingTree with Naive Bayes classification at leaves, and a HoeffdingTreeNBAdaptive was a HoeffdingTree with adaptive Naive Bayes classification at leaves. In the current version of MOA, there is an option to select wich classification perform at leaves: Majority class, Naive Bayes, Naive Bayes Adaptive. By default, the option selected is Naive Bayes Adaptive, since it is the classifier that gives better results. This adaptive Naive Bayes prediction method monitors the error rate of majority class and Naive Bayes decisions in every leaf, and chooses to employ Naive Bayes decisions only where they have been more accurate in past cases. To run experiments using the old default version of HoeffdingTree, with a majority class learner at leaves, use “HoeffdingTree -l MC”. Decision option tree for streaming data. Hoeffding Option Trees are regular Hoeffding trees containing additional option nodes that allow several tests to be applied, leading to multiple Hoeffding trees as separate paths. They consist of a single structure that efﬁciently represents multiple trees. A particular example can travel down multiple paths of the tree, contributing, in different ways, to different options. See for details: B. Pfahringer, G. Holmes, and R. Kirkby. New options for hoeffding trees. In AI, pages 90–99, 2007. • -o : Maximum number of option paths per node • -m : Maximum memory consumed by the tree • -n : Numeric estimator to use : □ Gaussian approximation evaluating 10 splitpoints □ Gaussian approximation evaluating 100 splitpoints □ Greenwald-Khanna quantile summary with 10 tuples □ Greenwald-Khanna quantile summary with 100 tuples □ Greenwald-Khanna quantile summary with 1000 tuples □ VFML method with 10 bins □ VFML method with 100 bins □ VFML method with 1000 bins □ Exhaustive binary tree • -e : How many instances between memory consumption checks • -g : The number of instances a leaf should observe between split attempts • -s : Split criterion to use. Example : InfoGainSplitCriterion • -c : The allowable error in split decision, values closer to 0 will take longer to decide • -w : The allowable error in secondary split decisions, values closer to 0 will take longer to decide • -t : Threshold below which a split will be forced to break ties • -b : Only allow binary splits • -z : Memory strategy to use • -r : Disable poor attributes • -p : Disable pre-pruning • -d : File to append option table to. • -l : Leaf classifier to use at the leaves: Majority class, Naive Bayes, Naive Bayes Adaptive. By default: Naive Bayes Adaptive. In old versions of MOA, a HoeffdingOptionTreeNB was a HoeffdingTree with Naive Bayes classification at leaves, and a HoeffdingOptionTreeNBAdaptive was a HoeffdingOptionTree with adaptive Naive Bayes classification at leaves. In the current version of MOA, there is an option to select wich classification perform at leaves: Majority class, Naive Bayes, Naive Bayes Adaptive. By default, the option selected is Naive Bayes Adaptive, since it is the classifier that gives better results. This adaptive Naive Bayes prediction method monitors the error rate of majority class and Naive Bayes decisions in every leaf, and chooses to employ Naive Bayes decisions only where they have been more accurate in past cases. To run experiments using the old default version of HoeffdingOptionTree, with a majority class learner at leaves, use “HoeffdingOptionTree -l MC”. Adaptive decision option tree for streaming data with adaptive Naive Bayes classiﬁcation at leaves. An Adaptive Hoeffding Option Tree is a Hoeffding Option Tree with the following improvement: each leaf stores an estimation of the current error. It uses an EWMA estimator with α = .2. The weight of each node in the voting process is proportional to the square of the inverse of the error. AdaHoeffdingOptionTree -o 50 • Same parameters as HoeffdingOptionTree This adaptive Hoeffding Tree uses ADWIN to monitor performance of branches on the tree and to replace them with new branches when their accuracy decreases if the new branches are more accurate. For more information, see: Albert Bifet, Ricard Gavaldá. Adaptive Learning from Evolving Data Streams In IDA 2009. Incremental on-line bagging of Oza and Russell. Oza and Russell developed online versions of bagging and boosting for Data Streams. They show how the process of sampling bootstrap replicates from training data can be simulated in a data stream context. They observe that the probability that any individual example will be chosen for a replicate tends to a Poisson(1) distribution. [OR] N. Oza and S. Russell. Online bagging and boosting. In Artiﬁcial Intelligence and Statistics 2001, pages 105–112. Morgan Kaufmann, 2001. • -l : Classiﬁer to train • -s : The number of models in the bag Incremental on-line boosting of Oza and Russell. See details in: [OR] N. Oza and S. Russell. Online bagging and boosting. In Artiﬁcial Intelligence and Statistics 2001, pages 105–112. Morgan Kaufmann, 2001. For the boosting method, Oza and Russell note that the weighting procedure of AdaBoost actually divides the total example weight into two halves – half of the weight is assigned to the correctly classiﬁed examples, and the other half goes to the misclassiﬁed examples. They use the Poisson distribution for deciding the random probability that an example is used for training, only this time the parameter changes according to the boosting weight of the example as it is passed through each model in sequence. • -l : Classiﬁer to train • -s : The number of models to boost • -p : Boost with weights only; no poisson Online Coordinate Boosting. Pelossof et al. presented Online Coordinate Boosting, a new online boosting algorithm for adapting the weights of a boosted classiﬁer, which yields a closer approximation to Freund and Schapire’s AdaBoost algorithm. The weight update procedure is derived by minimizing AdaBoost’s loss when viewed in an incremental form. This boosting method may be reduced to a form similar to Oza and Russell’s See details in: [PJ] Raphael Pelossof, Michael Jones, Ilia Vovsha, and Cynthia Rudin. Online coordinate boosting. 2008. OCBoost -l HoeffdingTreeNBAdaptive -e 0.5 • -l : Classiﬁer to train • -s : The number of models to boost • -e : Smoothing parameter Classiﬁers for evolving streams Bagging using trees of different size. The Adaptive-Size Hoeffding Tree (ASHT) is derived from the Hoeffding Tree algorithm with the following differences: • it has a maximum number of split nodes, or size • after one node splits, if the number of split nodes of the ASHT tree is higher than the maximum value, then it deletes some nodes to reduce its size The intuition behind this method is as follows: smaller trees adapt more quickly to changes, and larger trees do better during periods with no or little change, simply because they were built on more data. Trees limited to size s will be reset about twice as often as trees with a size limit of 2s. This creates a set of different reset-speeds for an ensemble of such trees, and therefore a subset of trees that are a good approximation for the current rate of change. It is important to note that resets will happen all the time, even for stationary datasets, but this behaviour should not have a negative impact on the ensemble’s predictive performance. When the tree size exceeds the maximun size value, there are two different delete options: • delete the oldest node, the root, and all of its children except the one where the split has been made. After that, the root of the child not deleted becomes the new root • delete all the nodes of the tree, i.e., restart from a new root. The maximum allowed size for the n-th ASHT tree is twice the maximum allowed size for the (n − 1)-th tree. Moreover, each tree has a weight proportional to the inverse of the square of its error, and it monitors its error with an exponential weighted moving average (EWMA) with α = .01. The size of the ﬁrst tree is 2. With this new method, it is attempted to improve bagging performance by increasing tree diversity. It has been observed that boosting tends to produce a more diverse set of classiﬁers than bagging, and this has been cited as a factor in increased performance. See more details in: [BHPKG] Albert Bifet, Geoff Holmes, Bernhard Pfahringer, Richard Kirkby, and Ricard Gavaldà . New ensemble methods for evolving data streams. In 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2009. The learner must be ASHoeffdingTree, a Hoeffding Tree with a maximum size value. OzaBagASHT -l ASHoeffdingTree -s 10 -u -r • Same parameters as OzaBag • -f : the size of ﬁrst classiﬁer in the bag. • -u : Enable weight classiﬁers • -r : Reset trees when size is higher than the max Bagging using ADWIN. ADWIN is a change detector and estimator that solves in a well-speciﬁed way the problem of tracking the average of a stream of bits or real-valued numbers. ADWIN keeps a variable-length window of recently seen items, with the property that the window has the maximal length statistically consistent with the hypothesis “there has been no change in the average value inside the window”. More precisely, an older fragment of the window is dropped if and only if there is enough evidence that its average value differs from that of the rest of the window. This has two consequences: one, that change reliably declared whenever the window shrinks; and two, that at any time the average over the existing window can be reliably taken as an estimation of the current average in the stream (barring a very small or very recent change that is still not statistically visible). A formal and quantitative statement of these two points (a theorem) appears in [BG07c] Albert Bifet and Ricard Gavaldà. Learning from time-changing data with adaptive windowing. In SIAM International Conference on Data Mining, 2007. ADWIN is parameter- and assumption-free in the sense that it automatically detects and adapts to the current rate of change. Its only parameter is a conﬁdence bound δ, indicating how conﬁdent we want to be in the algorithm’s output, inherent to all algorithms dealing with random processes. Also important, ADWIN does not maintain the window explicitly, but compresses it using a variant of the exponential histogram technique. This means that it keeps a window of length W using only O(log W) memory and O(log W) processing time per item. ADWIN Bagging is the online bagging method of Oza and Rusell with the addition of the ADWIN algorithm as a change detector and as an estimator for the weights of the boosting method. When a change is detected, the worst classiﬁer of the ensemble of classiﬁers is removed and a new classiﬁer is added to the ensemble. See details in: [BHPKG] Albert Bifet, Geoff Holmes, Bernhard Pfahringer, Richard Kirkby, and Ricard Gavald` . New ensemble methods for evolving data streams. In 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2009. OzaBagAdwin -l HoeffdingTreeNBAdaptive -s 10 • -l : Classiﬁer to train • -s : The number of models in the bag Leveraging Bagging for evolving data streams using ADWIN and Leveraging Bagging MC using Random Output Codes ( -o option). These methods leverage the performance of bagging, with two randomization improvements: increasing resampling and using output detection codes. For more information see Albert Bifet, Geoffrey Holmes, Bernhard Pfahringer Leveraging Bagging for Evolving Data Streams In Machine Learning and Knowledge Discovery in Databases, European Conference, ECML PKDD, 2010. • -l : Classifier to train. • -s : The number of models in the bagging • -w : The number to use to compute the weight of new instances. • -a : Delta of Adwin change detection • -o : Use Output Codes to use binary classifiers • -m : Leveraging Bagging to use: □ Leveraging Bagging ME using weight 1 if misclassified, otherwise error/(1-error) □ Leveraging Bagging Half using resampling without replacement half of the instances □ Leveraging Bagging WT without taking out all instances. □ Leveraging Subagging using resampling without replacement. Single perceptron classifier. Performs classic perceptron multiclass learning incrementally. • -r : Learning ratio of the classifier Implements stochastic gradient descent for learning various linear models: binary class SVM, binary class logistic regression and linear regression. Implements the stochastic variant of the Pegasos (Primal Estimated sub-GrAdient SOlver for SVM) method of Shalev-Shwartz et al. (2007). For more information, see: S. Shalev-Shwartz, Y. Singer, N. Srebro. Pegasos: Primal Estimated sub-GrAdient SOlver for SVM. In 4th International Conference on MachineLearning, 807-814, 2007. Class for handling concept drift datasets with a wrapper on a classiﬁer. The drift detection method (DDM) proposed by Gama et al. controls the number of errors produced by the learning model during prediction. It compares the statistics of two windows: the ﬁrst one contains all the data, and the second one contains only the data from the beginning until the number of errors increases. Their method doesn’t store these windows in memory. It keeps only statistics and a window of recent errors. They consider that the number of errors in a sample of examples is modeled by a binomial distribution. A signiﬁcant increase in the error of the algorithm, suggests that the class distribution is changing and, hence, the actual decision model is supposed to be inappropriate. They check for a warning level and a drift level. Beyond these levels, change of context is considered. The number of errors in a sample of n examples is modeled by a binomial distribution. For each point i in the sequence that is being sampled, the error rate is the probability of misclassifying (pi ), with standard deviation given by si = pi (1 − pi )/i. A signiﬁcant increase in the error of the algorithm, suggests that the class distribution is changing and, hence, the actual decision model is supposed to be inappropriate. Thus, they store the values of pi and si when pi + si reaches its minimum value during the process (obtaining ppmin and smin ). And it checks when the following conditions trigger: • pi + si ≥ pmin + 2 · smin for the warning level. Beyond this level, the examples are stored in anticipation of a possible change of context. • pi +si ≥ pmin +3·smin for the drift level. Beyond this level, the model induced by the learning method is reset and a new model is learnt using the examples stored since the warning level Baena-García et al. proposed a new method EDDM in order to improve DDM. It is based on the estimated distribution of the distances between classiﬁcation errors. The window resize procedure is governed by the same heuristics. See more details in: [GMCR] J. Gama, P. Medas, G. Castillo, and P. Rodrigues. Learning with drift detection. In SBIA Brazilian Symposium on Artiﬁcial Intelligence, pages 286–295, 2004. [BDF] Manuel Baena-García, José del Campo-Avila, Raul Fidalgo, Albert Bifet, Ricard Gavaldà , and Rafael Morales-Bueno. Early drift detection method. In Fourth International Workshop on Knowledge Discovery from Data Streams, 2006. SingleClassifierDrift -d EDDM -l HoeffdingTreeNBAdaptive • -l : Classiﬁer to train • -d : Drift detection method to use: DDM or EDDM	{"url":"https://moa.cms.waikato.ac.nz/details/classification/classifiers-2/","timestamp":"2024-11-11T03:46:06Z","content_type":"text/html","content_length":"65437","record_id":"<urn:uuid:56342b49-8c6e-4915-875e-2760f37635dd>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00383.warc.gz"}
Top Triangle Jokes, Triangle Puns, Triangle Dad Jokes & More - NYTheaterNow.com Top Triangle Jokes, Triangle Puns, Triangle Dad Jokes & More In this very funny joke compilation, we have come up with the best triangle jokes, triangle puns and triangle dad jokes to make you laugh. 1. Three-sided humor: The top triangle jokes to tickle your funny bone 1. Why did the triangle refuse to play hide and seek? Because it always gets cornered! 2. What did one triangle say to the other? “You’re so acute!” 3. Why did the triangle go to the doctor? It had too many degrees! 4. How did the hipster triangle like its coffee? Acute-ly brewed. 5. Why did the triangle go to the party alone? It couldn’t find a suitable angle. 6. What did the triangle say to the circle? “You’re so pointless!” 7. Why was the triangle always stressed out? It had too many acute angles. 8. What’s a triangle’s favorite dessert? Pi. 9. Why did the triangle go to school? To get its degree. 10. What did the triangle say to the rectangle? “You’re too square for me.” 2. Laughing in angles: Hilarious triangle puns and jokes to brighten your day 1. Did you hear about the love triangle? It was a real acute angle! 2. Why are triangles always so calm? Because they’re never right. 3. Why did the triangle go to the beach? To catch some rays. 4. How do you make a triangle laugh? Tell it a pun with acute angles. 5. What did the triangle say to the pentagon? “Triangle harder!” 6. Why did the triangle join the band? It had great harmonies. 7. What did the math book say to the pencil? “I’ve got my angles on you.” 8. How does a triangle solve its problems? With acute angles. 9. Why did the triangle play hide and seek with the circle? Because it knew it would never be found. 10. Why did the triangle bring a ladder to the party? Because it heard the drinks were on the house. 3. A triangle walks into a bar: Funny jokes and one-liners about triangles 1. Why did the triangle start a fight at the bar? It was looking for a right angle. 2. How does a triangle order its drinks? “Make them all on the rocks!” 3. Why did the triangle get kicked out of the bar? It couldn’t handle its liquor. 4. What happened when the triangle met the circle at the bar? They went off on a tangent. 5. How did the triangle pay for its drink? With acute currency. 6. What did the bartender say to the triangle? “You’re looking a bit obtuse tonight.” 7. Why did the triangle refuse to leave the bar? It was stuck on a bar stool. 8. What drink does a triangle always order? A margari-ta. 9. Why did the triangle get thrown out of the bar? It was causing too much tension. 10. How does a triangle like to dance? Acute angle dancing. 4. Get in shape with humor: The funniest triangle jokes you’ll ever hear 1. Why was the triangle always confident? It had strong angles. 2. What did the equilateral triangle say to the scalene triangle? “You’re so uneven!” 3. Why did the triangle go to the gym? To work on its core strength. 4. How does a triangle stay in shape? With acute exercise routines. 5. What did the triangle say to the square? “You’re such a box!” 6. Why did the triangle join the yoga class? It wanted to find its center. 7. What’s a triangle’s favorite workout music? Rock music with triangle solos. 8. How does a triangle stay motivated? By setting acute goals. 9. What sport does a triangle excel at? Triathlon. 10. How does a triangle meditate? It finds its inner peace angle. 5. Geometry of laughter: The best triangle jokes that are acute-ly hilarious 1. Why did the triangle break up with the circle? It was tired of going in circles. 2. How did the triangle get out of a tricky situation? It used its acute sense of humor. 3. Why did the triangle win the comedy competition? It had all the right angles. 4. What did the triangle say to the square? “You’re too plain for me.” 5. How did the triangle win over the crowd? With its sharp wit. 6. Why did the triangle cross the road? To get to the hypotenuse. 7. What’s a triangle’s favorite movie genre? Rom-comedies. 8. How does a triangle tell time? With acute precision. 9. Why did the triangle throw a party? To celebrate its acute angles. 10. How did the triangle become a comedian? It had a triangle-ling for jokes.	{"url":"https://nytheaternow.com/triangle-jokes/","timestamp":"2024-11-04T18:50:57Z","content_type":"text/html","content_length":"53438","record_id":"<urn:uuid:cd75ef7b-174a-4470-9eeb-2814a56238ca>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00176.warc.gz"}
Assessment and comparison of likely density distributions in the cases of thickness measurement of skin tumours by ultrasound examination and histological analysis Ultrasonic diagnostic methods are used to estimate the structural changes and to measure parameters of lesions of the human tissue. Nowadays, the special algorithms of medical data analysis are able to perform diagnosis and monitor the progress of treatment, efficiency of treatment methods, also to estimate the health status and to make prognosis of the diseases evolution. The aim of the presented research is to check the goodness of fit test for thicknesses of the skin tumours measured in two different ways (ultrasound examination and histological analysis) and to compare the compatibility of likely density of histological thicknesses distribution of the skin tumours and density of Normal distribution. As a result, the study has showed that thicknesses of the skin tumours measured by ultrasonic method are strongly similar to histological values, which means that the density of ultrasonic thicknesses distribution and density of Normal distribution are closely interconnected. Therefore, the obtained results show the sufficient level of reliability in the case of application of non-invasive ultrasonic thickness measurement comparing with reference invasive technique based on biopsy and histological thickness evaluation. 1. Introduction The storage of medical information and its statistical analysis are being carried out since the middle of ages. The first known statistical journal of medicine was published in London, in 1662 [1]. In 1863, F. Nightingale, the pioneer of nowadays nursing, raised the problem about the lack of medical statistics records and non-systematic storage in hospitals, as a consequence of treatment effectiveness and costs limited analysis. In 1977 the US Congress published a study “Medical information systems practitioner’s consequences” [2]. It states, that medical information systems can be a useful tool for training, also to help medicine and health care specialists leading to higher quality of facilities and optimization of health care institution activity. The authors of study have confirmed that medical information system will be a useful tool for researches and health governing institutions. Since 2000, the active global implementation of regional and national electronic health records systems started. The aim of these systems is to save all important patients medical records. Lithuanian health sector also applies information technologies, creating a national electronic health services and information system for cooperation infrastructure, also subsystem for national medical images archiving and exchange. Health care institutions implement and improve information systems of hospitals, systems for radiological images preview and archiving, information systems of laboratories [3]. Information system of the health care keeps a structured information about the patient, such as diagnosis, demographic patient data, vital functions, test results and etc. These data analysis and mining are very important for all patients. The smart analysis of patient records helps to solve tasks as a faster diagnostic, choosing of optimal treatment, prediction of treatment period and results, to identify the risk of complications, resources optimization of the health care institutions. Last decade, data mining research in biomedicine is highly considered [4, 5]. Data mining methods and algorithms can be useful if researches clearly understand scopes, types of the data and peculiarities. The most common tasks mentioned in literature are classification, clustering, prediction, association, visualization, identification of deviations and analysis of internal links. For these data mining tasks, we need to choose a suitable algorithm. Choosing of method or an optimal algorithm depends on aims of task analysis and data characteristics. Over the last decade, there are found enough methods of data mining application in medicine. In diagnosis there are widely applied neural networks, decision trees, decision rules [6], methods for search of associative rules (for costs analysis) [7], prediction of patient health and treatment probability, also very popular to use combinations of prediction algorithms [5]. In 2014, N. Esfandiari et al. [4], carried out a literature review, there are described applications of data mining in medicine based on analysis of the structured data. There are stated that classification (neural networks, decision trees, decision rules, support vector model), clustering (k-means, hierarchical clustering) and associative search (a priori associative rules search) models are the most popular in medicine. Lalayants et al. [8] have said that the solution of successful medical data mining is to identify the right activity of health care institution or to find the clinical problem. Data mining methods are usually used in biomedical data analysis and visualization tasks in order to facilitate decision-making [9]. If the data mining process would be enough simple, the management of information problems would be already solved long time ago (R. Bellazzi, B. Zupan [5]). Practical data mining application in medicine has some obvious barriers as technological problems, trans-disciplinary communication, ethics and patient data security [7, 9, 10]. Medical research leads to a lot of data characterizing the condition of patient. All these data are dynamically changing and depend on patient illness, patient biological condition, environment, the quality of life, related diseases and other actually reasons, those can be described as a random factor. The change of medical statistics observations is described by primary statistics analysis. The results lead to further instructions of medical research and affect hardly choosing and application of the appropriate statistical method. The reliability of above mentioned methods usually depends on the assumption of data distribution – normal, binomial and etc. Therefore, at first, it is necessary to check the appropriate assumption. This paper will present a simple, effective method of nonparametric statistics and some hypothesis criteria about the variable distribution and identity checking of two distributions. These hypotheses are called goodness of fit test hypothesis. The purpose of research is to determine the connection between thicknesses of the skin tumours measured by non-invasive ultrasonic technique and after a surgical intervention measured histologically by optical microscope. Also, to compare the compatibility of likely density of histological thicknesses distribution of the skin tumours and Normal distribution density this method is effective for structured big data matrix and simple to use. There is no problem to check the sample which is distributed by well-known theoretical distribution, because these cases are already examined both theoretically as well as empirically. The biggest challenge is to check the identity between two samples. As a solution the most commonly used techniques relies on differences of density distribution. Even in nowadays data analysis there are a lot of evaluation methods of density distribution, but in practice it is not easy to find the effective evaluation procedure if the data distribution is multimodal and the volume of sample is small. Kernel smoothing is the most frequently used nonparametric estimation method (see Jones, et al., 1996 [11], Marron and Wand, 1992 [12]; Silverman, 1986 [13]). Thus far, there is no generally accepted method for kernel estimation, which outperforms the other in all cases. Although many adaptive selection procedures have been proposed (Bashtannyk and Hyndman, 1998 [14]; Jones, 1992 [15]; Zhang et al., 2004 [16]), their efficiency has not been well established yet, especially for samples of a moderate size. On the basis of Lithuanian cancer register data, Lithuania established more than 250 melanomas cases every year. Even Lithuania is not included in the list of biggest melanomas risk country, but the statistics shows that the number of melanomas cases in Lithuania is increasing every year. The main reason is too late diagnosis. Usually melanoma is diagnosed in 2-4 stages. The mortality of melanoma in Lithuania is bigger than in other Europe countries [17, 18]. Melanoma is a rapidly growing and spreading malignant tumor, rarely amenable to treat through the spread of time. In the absence of effective treatment of metastatic melanoma, a key factor of survival of melanoma is early diagnosis and urgent surgical removal of the primary tumor. The earlier diagnosis of melanoma can be prevented by regularly checking of nevus and disposal nevus, those can be malignant. Surgical removal of melanoma having thickness of 1 mm increase the probability of survival, for 10 the years survival rate is 90-97 percent [19, 20]. The paper consists of 6 sections. Section 2 reviews the kernel density estimator and kernel functions; Section 3 proves optimal selection of smoothing parameter; Section 4 describes the simulation experiment and contains the simulation results; Section 5 shows the analysis in an empirical context using the retrospective observations of thicknesses of the skin tumour for goodness of fit tests; the concluding remarks are presented in Section 6. 2. Kernel density estimator A d-dimensional random vector $X\in {R}^{d}$ satisfies a mixture model if its distribution density function $f\left(x\right)$ is given by the equality: $f\left(x\right)=\sum _{k=1}^{q}{p}_{k}{f}_{k}\left(x\right)=f\left(x,\theta \right).$ The parameter $q$ is the number of components in the mixture. The component weights ${p}_{k}$ are called a priori probabilities and satisfy the conditions: ${p}_{k}>0,\sum _{k=1}^{q}{p}_{k}=1.$ Function ${f}_{k}\left(x\right)$ is the distribution density function of the $k$th component and $\theta$ is the vector of parameters of mixture model Eq. (1). Suppose a simple sample $\mathbf{X}=\ left(X\left(1\right),\dots ,X\left(n\right)\right)$ of size n from $\mathbf{X}$ is given. The estimation of the distribution density of an observed random vector is one of the main statistical tasks. A histogram is one of the simplest and the oldest density estimators. This graphical representation was first introduced by Karl Pearson in 1891 (Scott, 1992 [21]). For the approximation of density $f\left(x\right)$, the number of observations $X\left(t\right)$ falling within the range of $\mathrm{\Omega }$ is calculated and divided by n and the volume of area $\mathrm{\Omega }$. The histogram produced is a step function and the derivative either equals zero or is not defined (when at the cut off point for two bins). This is a big problem if we are trying to maximize a likelihood function that is defined in terms of the densities of the distributions. It is remarkable that the histogram stood as the only nonparametric density estimator until the 1950’s, when substantial and simultaneous progress was made in density estimation and in spectral density estimation. In 1951, in a little-known paper, Fix and Hodges [22] introduced the basic algorithm of nonparametric density estimation; an unpublished technical report was published formally as a review by Silverman and Jones in 1989 [23]. They addressed the problem of statistical discrimination when the parametric form of the sampling density was not known. During the following decade, several general algorithms and alternative theoretical modes of analysis were introduced by Rosenblatt in 1956 [24], Parzen in 1962 [25], and Cencov in 1962 [26]. Then followed the second wave of important and primarily theoretical papers by Watson and Leadbetter in 1963 [27], Loftsgaarden and Quesenberry in 1965 [28], Schwartz in 1967 [29], Epanechnikov in 1969 [30], Tarter and Kronmal in 1970 [31] and Kimeldorf and Wahba in 1971 [32]. The natural multivariate generalization was introduced by Cacoullos in 1966 [33]. Finally, in the 1970’s the first papers focusing on the practical application of these methods were published by Scott et al. in 1978 [34] and Silverman in 1978 [35]. These and later multivariate applications awaited the computing revolution. The basic kernel estimator $\stackrel{^}{f}\left(x\right)$ with a kernel function $K$ and a fixed (global) bandwidth h for multivariate data $X\in {\mathbf{R}}^{d}$ may be written compactly as: $f\left(x\right)=\frac{1}{n{h}^{d}}\sum _{t=1}^{n}K\left(\frac{x-X\left(t\right)}{h}\right).$ The kernel function $K\left(u\right)$ should satisfy the condition: ${\int }_{-\infty }^{+\infty }K\left(u\right)du=1.$ Usually, but not always, $K\left(u\right)$ will be a symmetric probability density function $K\left(u\right)=K\left(-u\right)$ for all values of u (see Silverman, 1986 [13]). At first, the data is usually prescaled in order to avoid large differences in data spread. A natural approach (see Fukunaga, 1972 [36]) is first to standardize the data by a linear transformation yielding data with zero mean and unit variance. As a result, Eq. (3) is applied to the standardized data. Let $Z$ denote the sphered values of random $X$: where $\stackrel{-}{X}$ is the empirical mean, and $S\in {R}^{d×d}$ is the empirical covariance matrix. Applying the kernel density estimator to the standardized data $Z=\left(Z\left(1\right),\dots ,Z\left(n\right)\right)$ yields the following estimator of density function $f\left(x\right)$: ${f}_{z}\left(z\right)=\frac{1}{n{h}^{d}}\sum _{t=1}^{n}K\left(\frac{z-Z\left(t\right)}{h}\right),$ $f\left(x\right)=\frac{{\left(\mathrm{det}S\right)}^{\frac{-1}{2}}}{n{h}^{d}}\sum _{t=1}^{n}K\left({S}^{\frac{-1}{2}}\frac{x-X\left(t\right)}{h}\right).$ The comparative analysis of estimation accuracy was made for four different types of kernels. The first three kernels are classical, whereas the last one is new. The Gaussian kernel is consistent with the distribution of normal $\phi \left(x\right)$ (see Gasser et al., 1985 [37], Marron and Nolan, 1988 [38]) selection: ${K}_{G}\left(x\right)=\phi \left(x\right)=\frac{1}{{\left(2\pi \right)}^{\frac{d}{2}}}e\left(\frac{-{x}^{T}x}{2}\right).$ The Epanechnikov kernel is the second order polynomial, corrected to satisfy the properties of the density function (see Epanechnikov, 1969 [30], Sacks and Ylvisaker, 1981 [39]): ${K}_{E}\left(x\right)=\frac{d+2}{2{V}_{d}}\left(1-{x}^{T}x\right){1}_{\left\{\left\|{x}^{T}x\le 1\right\|\right\}},$ where ${V}_{d}={\pi }^{d/2}/\mathrm{\Gamma }\left(d/2+1\right)$ is the volume of the d-dimensional unit sphere, and $\mathrm{\Gamma }\left(u\right)={\int }_{0}^{\infty }{y}^{u-i}{e}^{-y}dy.$ The Triweight kernel proposed by Tapia and Thompson in 1978 [40] has better smoothness properties and finite support. It was investigated in detail by Hall in 1985 [41]: ${K}_{T}\left(x\right)=\frac{\left(d+4\right)\left(d+6\right)}{24}\frac{\left(d+2\right)}{2{V}_{d}}{\left(1-{x}^{T}x\right)}^{3}{1}_{\left\{\left\|{x}^{T}x\le 1\right\|\right\}}.$ The new kernel ${K}_{New}$ has lighter tails than Gaussian distribution density and was introduced by the authors of this article: ${K}_{New}\left(x\right)=\phi \left({\left\|u\right\|}^{\frac{1}{\alpha }}\right)\frac{1}{{\alpha }^{d}}{\left({\left\|\prod _{i=1}^{d}{x}_{i}\right\|}^{\frac{1}{d}}\right)}^{1-\alpha }.$ This kernel function depends on parameter $\alpha$. In simulations, the chosen values of the parameter were 0.25, 0.5, and 0.75. The first two values produce worse accuracy results in comparison with the value of 0.75. Therefore, only the results obtained for $\alpha =$ 0.75 are reported here. 3. Optimal bandwidth selection There are three parameters in kernel density estimator: the sample size $n$, the kernel function $K\left(\bullet \right)$ and the bandwidth $h$. Quite typically we cannot do anything about the sample size and we have to make the best out of the situation by choosing an appropriate kernel and a suitable bandwidth. It is well known that the bandwidth selection is the most crucial step in order to obtain a good estimate (see Wand and Jones, 1995 [42]). Unfortunately, bandwidth selection is the most difficult problem in kernel density estimation and a definite and unique solution to this problem does not exist. It is rather surprising that the most effective bandwidth selection method is a visual assessment by the researcher. The researcher visually compares different density estimates, based upon a variety of bandwidths and then chooses the bandwidth that corresponds to the subjectively optimal estimate. The unfortunate part is that such bandwidths are non-unique; this method will yield different bandwidths when performed by different researchers. This method can also be very time consuming. The approach based on mathematical analysis is to quantify the discrepancy between the estimate and the target density by evaluated error criterion. The optimal bandwidth will then be the bandwidth value that minimizes the error measured by the error criterion. Such a method is objective and can be time-efficient as computers can solve it numerically. A global measure of precision is the asymptotic mean integrated squared error (AMISE): $AMISE\left(\stackrel{^}{f}\left(x\right)\right)=\frac{{K}_{u }^{2}\left(K\right)}{{\left(u !\right)}^{2}}R\left({abla }^{u }f\right){h}^{2u }+\frac{R{\left(K\right)}^{d}}{n{h}^{d}},$ where ${abla }^{u }f\left(x\right)=\sum _{k=1}^{d}{\partial }^{u }/\partial {x}_{k}^{u }f\left(x\right)$ and $R\left(g\right)={\int }_{-\infty }^{\infty }g{\left(u\right)}^{2}du$ is the roughness of a function. The order of a kernel, $v\text{,}$ is defined as the order of the first non-zero moment ${\kappa }_{j}\left(K\right)={\int }_{-\infty }^{\infty }{u}^{j}K\left(u\right)du.$ For example, if ${\kappa }_{1}\left(K\right)=0$ and ${\kappa }_{2}\left(K\right)>0$ then $K$ is a second-order kernel and $v=$ 2. If ${\kappa }_{1}\left(K\right)={\kappa }_{2}\left(K\right)={\kappa }_{3}\left(K\ right)=0$ but ${\kappa }_{4}\left(K\right)>0$ then $K$ is a fourth-order kernel and $v=$ 4.The order of a symmetric kernel is always even. Symmetric non-negative kernels are second-order kernels. A kernel is higher-order kernel if $v>$ 2. These kernels will have negative parts and are not probability densities. The optimal bandwidth is: ${h}_{0}={\left(\frac{{\left(u !\right)}^{2}dR{\left(K\right)}^{d}}{2u {K}_{u }^{2}\left(K\right)R\left({abla }^{u }f\right)}\right)}^{1/\left(2u +d\right)}{n}^{-1/\left(2u +d\right)}.$ The optimal bandwidth depends on the unknown quantity $R\left({abla }^{\left(u \right)}f\right)$. For a rule-of-thumb bandwidth, Silverman proposed that it is possible to try the bandwidth computed by replacing $f$ in the optimal formula by ${g}_{0}$ where ${g}_{0}$ is a reference density – a plausible candidate for $f$, and $\stackrel{^}{\sigma }$ is the sample standard deviation (see Bruce E. Hansen, 2009 [43]). The standard choice is a multivariate normal density. The idea is that if the true density is normal, then the computed bandwidth will be optimal. If the true density is reasonably close to the normal, then the bandwidth will be close to optimal. Calculation of that is proceeded according to: $R\left({abla }^{u }\phi \right)=\frac{d}{{\pi }^{\frac{d}{2}}{2}^{d+u }}\left({\left(2u -1\right)‼+\left(d-1\right)\left(\left(u -1\right)‼\right)}^{2}\right),$ where the double factorial means $\left(2s+1\right)!!=\left(2s+1\right)\left(2s–1\right)\dots 5\bullet 3\bullet 1\text{.}$ Making this substitution, we obtain: ${h}_{0}={C}_{u }\left(K,d\right){n}^{-1/\left(2u +d\right)},$ ${C}_{u }\left(K,d\right)={\left({\pi }^{\frac{d}{2}}{2}^{d+u -1}{\left(u !\right)}^{2}R{\left(K\right)}^{d}/u {K}_{u }^{2}\left(K\right)\left({\left(2u -1\right)‼+\left(d-1\right)\left(\left(u -1\ right)‼\right)}^{2}\right)\right)}^{1/\left(2u +d\right)},$ and this assumed that variance is equal to 1. Rescaling the bandwidths by the standard deviation of each variable, we obtain the rule-of-thumb bandwidth for the $i$th variable is: ${h}_{i}={\stackrel{^}{\sigma }}_{i}{C}_{u }\left(K,d\right){n}^{-\frac{1}{2u +d}}.$ Table 1Normal reference rule-of-thumb constants (CvK,d) for the multivariate second-order kernel density estimator Kernel $d=$1 $d=$2 $d=$3 $d=$4 $d=$5 $d=$6 $d=$7 $d=$8 $d=$9 $d=$10 Gaussian 1.059 1.000 0.969 0.951 0.9340 0.933 0.929 0.927 0.925 0.925 Epanechnikov 2.345 2.191 2.120 2.073 2.044 2.025 2.012 2.004 1.998 1.995 Triweight 3.155 2.964 2.861 2.800 2.762 2.738 2.723 2.712 2.706 2.702 New 1.142 1.079 1.045 1.025 1.014 1.007 1.002 1.000 0.998 0.998 Table 1 provides the normal reference rule-of-thumb constants (${C}_{v}\left(K,d\right)$ in (Eq. (15)) for the second-order d-variate kernel density estimator. We point out several striking features. First, in the common setting of a second order kernel ($v=$ 2) the rule-of-thumb constants are decreasing as d increases. Scott (1992 [21]) notes that these reach a minimum when $d=$ 11. The $v=$ 2 case is the only one he considers. When $v>$ 2, it is possible to show that the rule-of-thumb constants are increasing in the dimensionality of the problem. The basic idea behind this is given that higher-order kernels reduce bias; larger bandwidths are needed to minimize AMISE. However, note that the increase is not uniform over $v$. 4. The analysis of estimation accuracy A comprehensive simulation study was conducted with the aim to compare the kernel functions described before. The main attention is paid to the case where the density of independent d-dimensional observations is GMM: $f\left(x\right)=\sum _{i=1}^{q}{p}_{i}{\phi }_{i}\left(x\right)=f\left(x,\theta \right),x\in {\mathbit{R}}^{d},$ where $\theta =\left({p}_{i},{M}_{i},{R}_{i},i=1,2,\dots ,q\right)$. Univariate, bi-variate, and quinta-variate GMMs, from a suggested collection was used in comparative analysis as the benchmark 1) Gaussian ${p}_{1}=$ 1, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ 2) skewed unimodal ${p}_{1}=$ 1/5, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ ${p}_{2}=$1/5, ${M}_{2}=\left(1/2,0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(2/3\right)}^{2},\dots ,{\left(2/3\right)}^{2}\right]\right)$ ${p}_{3}=$ 3/5, ${M}_{3}=\left(13/12,0,\dots ,0\right)$, ${R}_{3}=diag\left(\left[{\left(5/9\right)}^{2},\dots ,{\left(5/9\right)}^{2}\right]\right)$ 3) strongly skewed ${p}_{n}=$ 1/8, ${M}_{n}=\left(3\left({\left(2/3\right)}^{n}-1\right),0,\dots ,0\right)$, ${R}_{n}=diag\left(\left[{\left(2/3\right)}^{2n},\dots ,{\left(2/3\right)}^{2n}\right]\right)$, $n=$ 0, …, 7 4) kurtotic unimodal ${p}_{1}=$ 2/3, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ ${p}_{2}=$ 1/3, ${M}_{2}=\left(0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(1/10\right)}^{2},\dots ,{\left(1/10\right)}^{2}\right]\right)$ 5) outlier ${p}_{1}=$ 1/10, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ ${p}_{2}=$ 9/10, ${M}_{2}=\left(0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(1/10\right)}^{2},\dots ,{\left(1/10\right)}^{2}\right]\right)$ 6) bimodal ${p}_{1}=$ 1/2, ${M}_{1}=\left(-1,0,\dots ,0\right)$, ${R}_{1}=diag\left(\left[{\left(2/3\right)}^{2},\dots ,{\left(2/3\right)}^{2}\right]\right)$ ${p}_{2}=$ 1/2, ${M}_{2}=\left(1,0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(2/3\right)}^{2},\dots ,{\left(2/3\right)}^{2}\right]\right)$ 7) separated bimodal ${p}_{1}=$ 1/2, ${M}_{1}=\left(-3/2,0,\dots ,0\right)$, ${R}_{1}=diag\left(\left[{\left(1/2\right)}^{2},\dots ,{\left(1/2\right)}^{2}\right]\right)$ ${p}_{2}=$ 1/2, ${M}_{2}=\left(3/2,0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(1/2\right)}^{2},\dots ,{\left(1/2\right)}^{2}\right]\right)$ 8) skewed bimodal ${p}_{1}=$ 3/4, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ ${p}_{2}=$ 1/4, ${M}_{2}=\left(3/2,0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(1/3\right)}^{2},\dots ,{\left(1/3\right)}^{2}\right]\right)$ 9) trimodal ${p}_{1}=$ 9/20, ${M}_{1}=\left(-6/5,0,\dots ,0\right)$, ${R}_{1}=diag\left(\left[{\left(3/5\right)}^{2},\dots ,{\left(3/5\right)}^{2}\right]\right)$ ${p}_{2}=$ 9/20, ${M}_{2}=\left(6/5,0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(3/5\right)}^{2},\dots ,{\left(3/5\right)}^{2}\right]\right)$ ${p}_{3}=$ 1/10, ${M}_{3}=\left(0,\dots ,0\right)$, ${R}_{3}=diag\left(\left[{\left(1/4\right)}^{2},\dots ,{\left(1/4\right)}^{2}\right]\right)$ 10) claw ${p}_{1}=$ 1/2, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ ${p}_{n}=$ 1/10, ${M}_{n}=\left(n/2-1,0,\dots ,0\right)$, ${R}_{n}=diag\left(\left[{\left(1/10\right)}^{2},\dots ,{\left(1/10\right)}^{2}\right]\right)$, $n=$ 0, …, 4 11) double claw ${p}_{1}=$ 49/100, ${M}_{1}=\left(-1,0,\dots ,0\right)$, ${R}_{1}=diag\left(\left[{\left(2/3\right)}^{2},\dots ,{\left(2/3\right)}^{2}\right]\right)$ ${p}_{2}=$ 49/100, ${M}_{2}=\left(1,0,\dots ,0\right)$, ${R}_{2}=diag\left(\left[{\left(2/3\right)}^{2},\dots ,{\left(2/3\right)}^{2}\right]\right)$ ${p}_{n}=$ 1/350, ${M}_{n}=\left(n-3/2,0,\dots ,0\right)$, ${R}_{n}=diag\left(\left[{\left(1/100\right)}^{2},\dots ,{\left(1/100\right)}^{2}\right]\right)$, $n=$ 0, …, 6 12) asymmetric claw ${p}_{1}=$ 1/2, ${M}_{1}=\left(0,\dots ,0\right)$, ${R}_{1}=I=diag\left(\left[1,\dots ,1\right]\right)$ ${p}_{n}={2}^{1-n}/31$, ${M}_{n}=\left(n+1/2,0,\dots ,0\right)$, ${R}_{n}=diag\left(\left[{\left({2}^{-n}/10\right)}^{2},\dots ,{\left({2}^{-n}/10\right)}^{2}\right]\right)$, $n=$ –2, …, 2 13) asymmetric double claw ${p}_{j}=$ 46/100, ${M}_{j}=\left(2j-1,0,\dots ,0\right)$, ${R}_{j}=diag\left(\left[{\left(2/3\right)}^{2},\dots ,{\left(2/3\right)}^{2}\right]\right)$, $j=$ 0, 1; ${p}_{n}=$ 1/100, ${M}_{n}=\left(-n/2,0,\dots ,0\right)$, ${R}_{n}=diag\left(\left[{\left(1/100\right)}^{2},\dots ,{\left(1/100\right)}^{2}\right]\right)$, $n=$ 1, 2, 3; ${p}_{k}=$ 1/100, ${M}_{k}=\left(k/2,0,\dots ,0\right)$, ${R}_{k}=diag\left(\left[{\left(1/100\right)}^{2},\dots ,{\left(1/100\right)}^{2}\right]\right)$, $k=$ 1, 2, 3. 14) smooth comb: ${p}_{n}={2}^{5-n}/63,{M}_{n}=\left(65-96{\left(1/2\right)}^{n}/21,0,\dots ,0\right),$ ${R}_{n}=diag\left(\left[32/63/{2}^{2n},\dots ,32/63/{2}^{2n}\right]\right)$, $n=$0,…, 5. 15) discrete comb ${p}_{n}=$ 2/7, ${M}_{n}=\left(12n-15/7,0,\dots ,0\right)$, ${R}_{n}=diag\left(\left[{\left(2/7\right)}^{2},\dots ,{\left(2/7\right)}^{2}\right]\right)$, $n=$ 0, 1, 2; ${p}_{k}=$ 1/21, ${M}_{k}=\left(2k/7,0,\dots ,0\right)$, ${R}_{k}=diag\left(\left[{\left(1/21\right)}^{2},\dots ,{\left(1/21\right)}^{2}\right]\right)$, $k=$ 8, 9, 10. These densities have been carefully chosen because they thoroughly represent many different types of challenges to curve estimators. The first five represent different types of problems that can arise for unimodal densities. The rest of the densities are multimodal. Densities from 6 to 9 are mildly multimodal and one might hope to be able to estimate them fairly well with a data set of a moderate size. The remaining densities are strongly multimodal and for moderate sizes it is difficult to recover even their shape. Yet, they are well worth studying because the issue of just how many of them can be recovered is an important one. The claw density, 10, is of special interest as this is where the surprising result of local minima in the mean integrated square error occurs. The double claw density, 11, is essentially the same as 6, except that approximately 2 % of the probability mass appears in the spikes. The asymmetric claw and double claw densities, 12 and 13, are modifications of 10 and 11, respectively. The smooth and discrete comb densities, 14 and 15, are enhancements of the basic idea of separated bimodal, 7. Both of these are shown because they have much different Fourier transform properties, since 14 has essentially no periodic tendencies, while 15 has two strong periodic components. Note that univariate case of this set of models is similar to collection suggested by Marron and Wand in 1992 [12]. In the simulation study, low-size and moderate-size samples (16, 32, 64, 128, 256, 512, 1024) were used. 10000 replications were generated in each case. The conclusions presented below are based on the analysis of these medians and minimums. The estimation accuracy is measured by the mean absolute percentage error: $MAPE=\frac{1}{n}\sum _{t=1}^{n}\left\|\frac{f\left(X\left(t\right)\right)-\stackrel{^}{f}\left(X\left(t\right)\right)}{f\left(X\left(t\right)\right)}\right\|\cong \int \left\|f\left(x\right)-\stackrel 5. Results of the study The results of univariate kernel density estimation are examined in detail by Ruzgas and Drulyte, 2013 [1]. The experimental research showed that some of kernel density functions used with multiple distributions mixtures lead to particularly good results. For example, Triweight kernel density function is characterized as one of the most effective when the study is done by using “Discrete comb” mixture with sample size bigger than 256, and dimension equal to 2. The results obtained with Epanechnikov kernel density function have shown that this function is appropriate to be used when the calculations are carried out with the average sample size by using “Bimodal”, “Separated bimodal” and “Smooth comb” mixtures with dimension equal to 2. In addition, the new kernel density function proposed by authors of this research has also shown unexpected results. The smallest median errors for all sample sizes when dimension is equal to 2, are obtained by using the mean average percentage error (MAPE) even at five different mixtures: “Gaussian”, “Skewed unimodal”, “Strongly skewed”, “Kurtotic unimodal”, “Outlier”. Meanwhile, when the sample size is less or equal to 256, the smallest median errors are obtained with “Bimodal”, “Separated bimodal”, “Smooth comb” and “Discrete comb” mixtures. Another important point is that the new kernel density function gives us the smallest median errors with all mixtures of Gaussian distribution and all sample sizes when the dimension is equal to five. The second effective function is Gaussian kernel density function. The errors dependences on sample size and selected dimension are shown in Fig. 1. Here the Gaussian, Epanechnikov, Triweight and new kernel density functions are marked as G, E, T and N show the results of estimation accuracy. Medians and minimums of mean average percentage errors are marked by solid and dashed lines. The results of errors dependences on sample size results got by using “Skewed bimodal” mixture and different dimensions are shown in Fig. 1. Fig. 1Estimation accuracy based on MAPE for skewed bimodal bi-variate and quinta-variate densities (here MAPE means the mean absolute percentage error; n is the sample size; the Gaussian, Epanechnikov, Triweight and new kernel density functions are marked as G, E, T and N) When the dimension is increasing the smallest errors are getting by using new kernel density function. Meanwhile, the Gaussian kernel density function is respectively appropriate to be used when the dimension is smaller or equal to 4 and smaller than 3 in the case of the Epanechnikov and Triweight functions. The effectiveness of the Gaussian kernel density function is shown in Fig. 2. Fig. 2The relationship between number of dimension and MAPE (Gaussian densities with sample sizes 512 and 1024). Here MAPE means the mean absolute percentage error; d is the dimension; the Gaussian, Epanechnikov, Triweight and new kernel density functions are marked as G, E, T and N 6. The application of goodness fit of test The set of real clinical data was used as an empirical example (see Fig. 3). Within this section a set of values (the sample size was equal to 52 observations) of the skin lesions previously used for clinical decision support by non-invasive ultrasonic measurements in vivo and histological evaluation ex vivo of their thickness and malignancy after surgical excision has been obtained and compared. The analysis was performed retrospectively in an empirical context in order to estimate the goodness of fit tests. Histological and ultrasonic data have been collected at the Department of Skin and Venereal Diseases of Lithuanian University of Health Sciences (LUHS). The study was approved by regional ethics committee; the collection of all data was approved by the institutional review board after patients’ informed consent was obtained in accordance with the Declaration of Helsinki Protocols. The data used in the empirical example were acquired on 52 suspicious melanocytic skin tumours (MST) which included 46 melanocytic nevi and 6 melanomas. Inclusion criteria of the study covered size of the tumour up to 1 cm in diameter and histological thickness of ≤1.5 mm. Fig. 3The results of histological measurements and measurements made by ultrasonic diagnosis During non-invasive ultrasonic measurements of human skin DUB-USB ultrasound system (“Taberna pro medicum”) of 22 MHz was used for transmission and reception of ultrasonic waves. The immersion experimental set-up with mechanically scanned ultrasonic transducer was employed. The transducer was focused at the surface of the skin. In addition, the system was used for acquisition, digitization and transfer to personal computer the received A-scan ultrasonic signals. The set of acquired A-scan signals were used for reconstruction of the B-scan image. Finally, the maximal thickness of the skin lesion was manually evaluated by a well-experienced dermatologist measuring the distance between the lower edge of the entry echo and the deepest point of the posterior margin of the hypoechoic zone. During the evaluation of thickness, the value of ultrasound velocity was assumed to be 1580 m/s. After a surgical excision and during the routine histopathology the vertical distance from the uppermost level of the stratum granulosum in the epidermis to the lowest point of the lesion without infiltrate (histological tumour thickness, Breslow index) was independently evaluated by two pathologists and averaged. More details about ultrasonic examinations in dermatology and comparison with histological data are provided by Jasaitiene et al. in 2011 [44] and Kučinskienė et al. in 2014 [45]. For the goodness of fit we are using some tests based on kernel density estimators described above. Let ${X}_{1},\dots ,{X}_{n}$ be a sample of independent observations of a random variable $X$ with unknown probability density function $f\left(x\right)$, $x\in R$. For the given sample it is required to test the hypothesis mentioned in publication made by Rudzkis and Bakshaev in 2013 [46]: ${H}_{0}:f\left(x\right)={f}_{0}\left(x\right)$, against alternative ${H}_{1}:f\left(x\right)=\left(1-ϵ\right){f}_{0}\left(x\right)+ϵg\left(x\right).$ Here ${f}_{0}\left(x\right)$ is a given probability density function, $\mathrm{ϵ}$ is negligible and $ϵg\left(x\right)$ is an arbitrary distribution, where ${\sigma }_{g}^{2}\le {\sigma }_{{f}_{0}}^ {2}$ and ${\sigma }_{f}^{2}$ is a variance of distribution f. In this study five tests of goodness of fit have been tried: Pearson's chi-squared test, Rudzkis-Bakshaev’s test, Kolmogorov–Smirnov test, Cramer von Mises test and Kuiper’s test for four different kernel functions. One of the steps leading to the main result was to check the goodness of fit between the density of ultrasonic thicknesses distribution and density of histological thicknesses distribution of the skin tumours. The next step was to compare the compatibility of likely density of histological thicknesses distribution of the skin tumours and Normal distribution density. If two mentioned checked conditions are satisfied, as a result it is clear that the density of ultrasonic thicknesses distribution and Normal distribution density are interconnected. All results of the goodness of fit between the density of ultrasonic thicknesses distribution and density of histological thicknesses distribution of the skin tumours (denoted as U H) and the goodness of fit between the density of histological thicknesses distribution and Normal distribution density (denoted as H N) are shown in Table 2. Table 2The results of goodness fit of test based on kernel functions Kernel function Goodness of Fit Test Normal Epanechnikov Triweight New proposed U H ~1 ~1 ~1 ~1 Pearson’s chi-squared ${\chi }^{2}$ H N 0.4474 0.0063 0.1220 0.0087 U H 0.9930 0.9970 0.9970 0.9900 H N 0.9730 0.9670 0.9780 0.8990 H N 0.8826 0.9251 0.9079 0.9124 H N 0.9997 0.9999 0.9999 0.9998 U H 0.6851 0.7246 0.7040 0.7186 Cramer von Mises H N 0.8973 0.8909 0.8984 0.8859 U H 0.9998 0.9999 0.9999 0.9999 H N ~1 ~1 ~1 ~1 7. Conclusions Within the performed study the check of the goodness of fit test for thicknesses of the skin tumours measured in two different ways (non-invasive ultrasound examination and invasive histological analysis). The performed simulation study leads to the kernel $K$ which has shown a better performance for Gaussian mixtures with considerably overlapping components and multiple peaks (double claw distribution). In addition, its accuracy decreases more slowly than the other kernels, when the random vector dimension increases. The empirical study has shown that Pearson’s chi-squared test is the most sensitive of all used tests. The main reason is the differences between empirical and theoretical distributions due to heavy tails of the empirical distributions. As a result, the Kuiper’s test has the lowest sensitivity criteria and was the most powerful in performed comparative analysis. The obtained results have shown that the density of ultrasonic thicknesses distribution is similar to the Normal distribution density more than 90 percent. Hence, the reliability of ultrasonic thickness measurement of the skin tumour is completely covered by high similarity to the histological thickness measurement, which is known as a golden standard in the field of dermatology. Also the application of goodness fit of test has shown that p-value of all criteria’s with all kernel functions are approximately 2 times bigger than Pearson’s chi-squared test. Therefore, it proves that the application of non-invasive ultrasonic technique (at least of 22 MHz) for thickness estimation of the melanocytic skin lesions (tumours and nevus) possesses high reliability and is suitable to be used in daily clinical practise. • Ruzgas T., Drulytė I. Kernel density estimators for Gaussian mixture models. Lithuanian Journal of Statistics (Lietuvos Statistikos Darbai), Lithuanian Statistical Association, Vilnius, Vol. 52, Issue 1, 2013, p. 14-21. • Policy Implications of Medical Information Systems. Report by the US Congress Office of Technology Assessment, http://digital.library.unt.edu/ark:/67531/metadc39374/, 1977. • Ministry of Health of the Republic of Lithuania, http://sam.lrv.lt/en/. • Esfandiari N., Babavalian M. R., Moghadam A. M., Tabar V. K. Knowledge discovery in medicine: current issue and future trend. Expert Systems with Applications, Elsevier, Vol. 41, Issue 9, 2014, p. 4434-4463. • Bellazzi R., Zupan B. Predictive data mining in clinical medicine: current issues and guidelines. International Journal of Medical Informatics, Elsevier, Vol. 77, Issue 2, 2008, p. 81-97. • Houston A. L., Chen H., Hubbard S. M., Schatz B. R., Ng T. D., Sewell R. R., Tolle K. M. Medical data mining on the internet: research on a cancer information system. Artificial Intelligence Review, Springer, Vol. 13, Issue 5, 1999, p. 437-466. • Silver M., Sakata T., Su H. C., Herman C., Dolins S. B., O’Shea M. J. Case study: how to apply data mining techniques in a healthcare data warehouse. Journal of Healthcare Information Management, Wiley, Vol. 15, Issue 2, 2001, p. 155-164. • Lalayants M., Epstein I., Auslander G. K., Chan W. C. H., Fouché C., Giles R., Joubert L., Rosenne H., Vertigan A. International social work. Sage Journals, Vol. 56, Issue 6, 2013, p. 775-797. • Wasan S., Bhatnagar V., Kaur H. The impact of data mining techniques on medical diagnostics. Data Science Journal, Ubiquity Press, Vol. 5, 2006, p. 119-126. • Cios K. J., Moore G. W. Uniqueness of medical data mining. Artificial Intelligence in Medicine, Elsevier, Vol. 26, Issues 1-2, 2002, p. 1-24. • Jones M. C., Marron J. S., Sheather S. J. A brief survey of bandwidth selection for density estimation. Journal of the American Statistical Association, Vol. 91, 1996, p. 401-407. • Marron J. S., Wand M. P. Exact mean integrated squared error. Annals of Statistics, Vol. 20, 1992, p. 712-736. • Silverman B. W. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 1986. • Bashtannyk D. M., Hyndman R. J. Bandwidth Selection for Kernel Conditional Density Estimation. Technical Report, Department of Econometrics and Business Statistics, Monash University, 1998. • Jones M. C. Potential for automatic bandwidth choice in variations of kernel density estimation. Statistics and Probability Letters, Vol. 13, 1992, p. 351-356. • Zhang X., King M. L., Hyndman R. J. Bandwidth selection for multivariate kernel density estimation using MCMC. Computational Statistics and Data Analysis, Vol. 50, 2004, p. 3009-3031. • Smailyte G., Jasilionis D., Kaceniene A., Krilaviciute A., Ambrozaitiene D., Stankuniene V. Suicides among cancer patients in Lithuania: a population-based census-linked study. Cancer Epidemiology, Elsevier, Vol. 37, Issue 5, 2013, p. 714-718. • Sant M., Allemani C., Santaquilani M., Knijn A., Marchesi F., Capocaccia R. EUROCARE-4. Survival of cancer patients diagnosed in 1995-1999. Results and commentary. European Journal of Cancer, Elsevier, Vol. 45, 2009, p. 931-991. • Braun R. P., Saurat J. H., French L. E. Dermoscopy of pigmented lesions: a valuable tool in the diagnosis of melanoma. Swiss Medical Weekly, Vol. 134, Issues 7-8, 2004, p. 83-90. • Gershenwald J. E., Soong S. J., Balch C. M. 2010 TNM staging system for cutaneous melanoma and beyond. Annals of Surgical Oncology, Springer, Vol. 17, Issue 6, 2010, p. 1475-1477. • Scott D. W. Multivariate Density Estimation: Theory, Practice and Visualization. John Wiley, New York, 1992. • Fix E., Hodges J. L. Discriminatory Analysis – Nonparametric Discrimination: Consistency Properties. Report No. 21-49-004, US Air Force School of Aviation Medicine, Random Field, Texas, 1951. • Silverman B. W., Jones M. C. E. Fix and J. L. Hodges (1951): an important contribution to nonparametric discriminant analysis and density estimation. International Statistical Review, Vol. 57, Issue 3, 1989, p. 233-247. • Rosenblatt M. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, Vol. 27, 1956, p. 832-837. • Parzen E. On the estimation of probability density and mode. The Annals of Mathematical Statistics, Vol. 33, 1962, p. 1065-1076. • Cencov N. N. Estimation of unknown density function from observations. SSSR Academy of Sciences, Vol. 147, 1962, p. 45-48. • Watson G. S., Leadbetter M. R. On the estimation of the probability density II. The Annals of Mathematical Statistics, Vol. 34, 1963, p. 480-491. • Loftsgaarden D. O., Quesenberry C. P. A nonparametric estimate of a multivariate density function. The Annals of Mathematical Statistics, Vol. 36, Issue 3, 1965, p. 1049-1051. • Schwartz S. C. Estimation of probability density by an orthogonal series. The Annals of Mathematical Statistics, Vol. 38, Issue 4, 1967, p. 1261-1265. • Epanechnikov V. A. Nonparametric estimates of a multivariate probability density. Theoretical Probability Applications, Vol. 14, 1969, p. 153-158. • Tarter M., Kronmal R. On multivariate density estimates based on orthogonal expansions. The Annals of Mathematical Statistics, Vol. 41, Issue 2, 1970, p. 718-722. • Kimeldorf G., Wahba G. Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and Applications, Vol. 33, 1971, p. 82-95. • Cacoullos T. Estimation of a multivariate density. Annals of the Institute of Statistical Mathematics, Vol. 18, Issue 1, 1966, p. 179-189. • Scott D. W., Tapia R. A., Thompson J. R. Multivariate Density Estimation by Discrete Maximum Penalized-Likelihood Methods. Graphical Representation of Multivariate Data. Academic Press, New York, • Silverman B. W. Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. The Annals of Statistics, Vol. 6, 1978, p. 177-184. • Fukunaga K. Introduction to Statistical Pattern Recognition. Academic Press, New York, 1972. • Gasser T., Müller H. G., Mammitzsch V. Kernels for nonparametric curve estimation. Journal of the Royal Statistical Society, Vol. 47, 1985, p. 238-252. • Marron J. S., Nolan D. Canonical kernels for density estimations. Statistics and Probability Letters, Vol. 7, Issue 3, 1988, p. 195-199. • Sacks J., Ylvisaker D. Asymptotically optimum kernels for density estimation at a point. The Annals of Statistics, Vol. 9, 1981, p. 334-346. • Tapia R. A., Thompson J. R. Nonparametric Probability Density Estimation. Johns Hopkins Series in the Mathematical Sciences. Johns Hopkins University Press, Baltimore and London, 1978. • Hall P. Kernel estimation of a distribution function. Communications in Statistics. Theory and Methods, Vol. 14, 1985, p. 605-620. • Wand M. P., Jones M. C. Kernel Smoothing. Chapman and Hall, London, 1995. • Hansen B. E. Lecture Notes on Nonparametrics. University of Wisconsin, 2009, www.ssc.wisc.edu/~bhansen/718/NonParametrics1.pdf • Jasaitiene D., Valiukeviciene S., Linkeviciute G., Raisutis R., Jasiuniene E., Kazys R. Principles of high-frequency ultrasonography for investigation of skin pathology. Journal of the European Academy of Dermatology and Venereology, 2011, p. 375-382. • Kučinskienė V., Samulėnienė D., Gineikienė A., Raišutis R., Kažys R., Valiukevičienė S. Preoperative assessment of skin tumor thickness and structure using 14-MHz ultrasound. Medicina (B Aires), 2014, p. 150-155. • Rudzkis R., Bakshaev A. Goodness of fit tests based on kernel density estimators. Informatica, Vol. 24, Issue 3, 2013, p. 447-460. About this article Oscillations in biomedical engineering skin tumour thickness measurement goodness of fit test kernel method nonparametric density estimator Monte Carlo method Copyright © 2016 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	{"url":"https://www.extrica.com/article/17183","timestamp":"2024-11-09T00:16:54Z","content_type":"text/html","content_length":"220878","record_id":"<urn:uuid:559da2f4-c338-402b-9bcb-8b2652b9cbba>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00060.warc.gz"}
Force from Height Calculator, Formula, Height Calculation \| Electrical4u Force from Height Calculator, Formula, Height Calculation Force from Height Calculator Enter the values of mass, m[(kg)], gravitational acceleration, g[(m/s2)], height, h[(m)], and distance, d[(m)] to determine the value of Force, F[(N)]. Force from Height Formula The calculation of force from height is used to determine the force exerted by an object due to its gravitational potential energy being converted into kinetic energy as it falls from a certain height. This force can be calculated when the object impacts a surface, distributing the force over a distance. Force, F[(N)] in Newtons, is calculated by multiplying the mass, m[(kg)] in kilograms by the acceleration due to gravity, g[(m/s2)] in metres per second squared and the height, h[(m)] in metres from which the object falls, then dividing by the distance, d[(m)] in metres over which the force is exerted. Force, F[(N)] = m[(kg)] * g[(m/s2)] * h[(m)] / d[(m)] F[(N)] = force in Newtons, N. m[(kg)] = mass in kilograms, kg. g[(m/s2)] = acceleration due to gravity in metres per second squared, m/s^2, typically 9.81 m/s^2 on Earth. h[(m)] = height in metres, m. d[(m)] = distance in metres, m. Force from Height Calculation: 1. Dropping a 5 kg weight from a height of 10 metres onto a cushion that compresses by 0.5 metres. Given: m[(kg)] = 5kg, g[(m/s2)] = 9.81 m/s^2, h[(m)] = 10m, d[(m)] = 0.5m. Force, F[(N)] = m[(kg)] * g[(m/s2)] * h[(m)] / d[(m)] F[(N)] = 5 * 9.81 * 10 / 0.5 F[(N)] = 981N. 2. A 2 kg ball falls from a height of 3 metres onto a surface that acquires a force of 588.6N. Given: m[(kg)] = 2kg, g[(m/s2)] = 9.81 m/s^2, h[(m)] = 3m, F[(N)] = 588.6N. Force, F[(N)] = m[(kg)] * g[(m/s2)] * h[(m)] / d[(m)] d[(m)] = m[(kg)] * g[(m/s2)] * h[(m)] / F[(N)] d[(m)] = 2 * 9.81 * 3 / 588.6 d[(m)] = 0.1m. Vertical jump height with force LEAVE A REPLY Cancel reply	{"url":"https://www.electrical4u.net/calculator/force-from-height-calculator/","timestamp":"2024-11-13T22:08:11Z","content_type":"text/html","content_length":"109945","record_id":"<urn:uuid:1b8337fc-7055-44fa-97ca-9a3080f57d70>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00383.warc.gz"}
FACT Function in Google Sheets with Examples, Formulas-Factorials in G-Sheets Google Sheets FACT Function will help the users to find the factorial of a number. Yes, you have heard it right. When you want to find the factorial of a number, you might have to perform mathematical calculations in manual method. However, using the FACT Function in Google Sheets, one can easily find the Factorial of a number. On this page, let us understand how to use the FACT function in Google Sheets and how to find the factorial of a number using the Sheets Tips provided on this page. Read further to find out more. FACTORIAL – FACT Function Syntax in Google Sheets The syntax of the FACT function in Google Sheets is given below: FACTORIAL Syntax = FACT (value) Here, the value represents the number (or a reference to a number) for which the factorial will be computed and returned. If you give FACT a number or a reference to a number containing a decimal portion, the decimal part will be shortened before being calculated. How Do You Do Factorials in Google Sheets? Let us understand how to perform factorials in Google Sheets using an example. Assume that we want to find the factorial of number 5. The steps to get this done in Google Sheets are as follows: • 1st Step: Launch the Google Spreadsheet on your device. • 2nd Step: Now move to the cell where you want to find the factorial of number 5. • 3rd Step: Here enter the formula “=FACT(5)“. • 4th Step: Press the “Return” key. • 5th Step: Now you will see the results on the spreadsheet which shows the factorial of number 5. How To Find Factorials for Array of Numbers in Google Sheets? Google Sheets also allows users to find the factorial for an array of numbers. You must simply use the Fill Handle function in Spreadsheet, which helps to find factorials for an array of numbers. The steps to follow to find factorials for the array of numbers in the Spreadsheet are as follows: • 1st Step: Launch the Google Spreadsheet on your device. • 2nd Step: Now in Column 1, enter the list of numbers for which you would like to find factorials. • 3rd Step: In Column 2, against the first number, enter the formula =FACT(A2). {A2 is the cell range}. • 4th Step: Press the “Enter” button. Now you will see the results. • 5th Step: Now drag the Fill Handle from the formula applied cells to other cells and now you will see factorials of all the numbers. How to Find Factorials for Decimal Numbers in Google Sheets? The Google Sheets FACT function will truncate the decimal part when you try to find the factorial of decimal numbers. Let us understand how to find decimal number factorials in Google Sheets using the steps provided below: • 1st Step: Open the Google Spreadsheet on your device. • 2nd Step: Now move to the cell where you want to find the factorial of a decimal number. • 3rd Step: Enter the formula “=FACT (5.5)“. I entered 5.5 since I wanted to find the factorial of decimal number 5.5. • 4th Step: Press the “Enter” key and you will see the factorial of number 5 i.e., 120. Here, the Google Sheets have truncated the decimal value 0.5 and showed the results for Factorial of number 5. Leave a Comment	{"url":"https://sheetstips.com/fact-function-in-google-sheets/","timestamp":"2024-11-07T04:31:54Z","content_type":"text/html","content_length":"51235","record_id":"<urn:uuid:1762ccfd-fcc8-4c81-bb35-2eed43b84c78>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00303.warc.gz"}
Trajectory into mathematics teaching via an alternate route: A survey of graduates from Mathematics Enhancement Courses Original language English Title of host publication Proceedings of the British Society for Research into Learning Mathematics Pages 175-182 Number of pages 8 Volume 31(2) Publication status Published - Jun 2014 Publication series Name Proceedings of the British Society for Research into Learning Mathematics Publisher British Society for Research into Learning Mathematics • Mathematics Enhancement Course (MEC) • Subject Knowledge Enhancement (SKE)	{"url":"https://research.manchester.ac.uk/en/publications/trajectory-into-mathematics-teaching-via-an-alternate-route-a-sur","timestamp":"2024-11-09T09:39:11Z","content_type":"text/html","content_length":"41608","record_id":"<urn:uuid:6d339c28-8af1-4d6d-8d03-ae2435907fb4>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00384.warc.gz"}
A simple methodology to detect and quantify wind power ramps Articles \| Volume 5, issue 4 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. A simple methodology to detect and quantify wind power ramps Knowledge about the expected duration and intensity of wind power ramps is important when planning the integration of wind power production into an electricity network. The detection and classification of wind power ramps is not straightforward due to the large range of events that is observed and the stochastic nature of the wind. The development of an algorithm that can detect and classify wind power ramps is thus of some benefit to the wind energy community. In this study, we describe a relatively simple methodology using a wavelet transform to discriminate ramp events. We illustrate the utility of the methodology by studying distributions of ramp rates and their duration using 2 years of data from the Belgian offshore cluster. This brief study showed that there was a strong correlation between ramp rate and ramp duration, that a majority of ramp events were less than 15h with a median duration of around 8h, and that ramps with a duration of more than a day were rare. Also, we show how the methodology can be applied to a time series where installed capacity changes over time using Swedish onshore wind farm data. Finally, the performance of the methodology is compared with another ramp detection method and their sensitivities to parameter choice are contrasted. Received: 12 Mar 2020 – Discussion started: 06 Apr 2020 – Revised: 18 Aug 2020 – Accepted: 05 Nov 2020 – Published: 16 Dec 2020 Rapid changes in wind speed can cause ramps in the wind power production of a wind farm. With plans to install a large amount of capacity in the North Sea, understanding swings in offshore wind farm power production will become important for wind farm and network operators to manage the integration of wind power into the electricity system. In their development of a wind power variability index, Kiviluoma et al. (2014, 2016) distinguish between three different timescales which are of importance to system operators. The first of these is sub-hourly up to 2h where load following and frequency control is required. The second and that where wind power generation is stated to cause most ramping is for timescales of between 1h and around 15h. For these timescales, there can be significant impact on thermal plant start-ups and shutdowns, though this depends on the characteristics of the plant installed in the particular power system. The final ramping timescales of relevance are between 10h and around a day. This is of relevance where large-scale storage is required such as hydro pump storage. An understanding of the prevalence and magnitude of ramps across a range of timescales is thus important. Wind power ramps are influenced by the dynamics of atmosphere–ocean systems which could be either mesoscale or synoptic-scale. Therefore, meteorological systems that evolve over time play a significant role in the occurrence of power ramps (Marquis et al., 2011). Low-pressure systems, cold fronts, low-level jets, thunderstorm outflows, and dry lines can cause ramp-up (increasing wind) events (Sevlian and Rajagopal, 2013; DeMarco and Basu, 2018), whereas ramp-down (decreasing wind) events occur due to the reduction or reversal of these physical processes (Ferreira et al., 2011). Short-duration (rapid) power ramps are mainly influenced by mesoscale systems, whereas synoptic systems tend to be responsible for longer-duration power ramps (Drew et al., 2018). There is no accepted definition or classification of wind power ramps except that they are manifested in terms of a significant change in production over a relatively short time. The quantification of the duration and magnitude of wind power ramps has been explored by several scholars. Most of the studies set thresholds with respect to the rated power of the wind farm to detect wind power ramps. One such definition (Bossavy et al., 2010; Zhang et al., 2017) defines a ramp as a minimum change in wind farm output ΔP as a fraction of the rated wind power P[rated] of the wind farm over a period of time (Δt). Different researchers consider different rates of change to define ramps; for example, Cutler et al. (2007) define a power ramp when there is a change in wind power production of 75% of P[rated] within a Δt of 3h or 65% of P[rated] within a Δt of 1h. In contrast, Bossavy et al. (2010) define a wind power ramp when there is a change in wind power of 50% of P[rated] over 1h. Other researchers such as Bianco et al. (2016) and Gallego-Castillo et al. (2015) use still different percentage changes in wind power and time ranges to define wind power ramps. There have been studies to detect power ramps without using any pre-defined change in wind power relative to rated power and time. An optimised swinging-door algorithm was used by Zhang et al. (2017) to extract ramps where the ramp definition parameters related to power change and timescale could be easily adapted. An optimal method based on scoring functions (Sevlian and Rajagopal, 2013) was used to detect ramps of varying lengths at a US wind farm. These authors used a piecewise linear trending fit to remove short-term stochastic fluctuations. Even though there has been a significant body of work to detect wind power ramps, it is clear that there is no precise consensus as to the definition of a ramp. Indeed, it may be necessary to extract information about a range of power ramp events depending on the requirements of the wind farm operator or the utility as described above. What is required is a robust method which can extract ramps of arbitrary magnitude and duration and to discriminate above the incoherent stochastic noise level. In this paper, we propose an improved method to discriminate ramp events above incoherent stochastic variations using wavelets. Wavelets have been used in the past to extract ramp events from time series, e.g. Hannesdóttir and Kelly (2019); Ji et al. (2015); Gallego et al. (2014); Coughlin et al. (2014). We build on this work by demonstrating how a wavelet transform can be used in conjunction with the generation of wind power surrogates to give a robust method for the detection of wind power ramps of varying magnitude and duration. Rather than relying on fixed power or timescale thresholds, the methodology uses a method of discrimination based on statistical thresholds. We illustrate the methodology and its application using data from Belgian offshore and Swedish onshore wind farms. Firstly, we describe the methodology and illustrate its application using a 10d period of data. Next, the sensitivity of the discrimination of ramps from natural stochastic variation is investigated using a longer period to generate the surrogate distributions. Then, we show the utility of the approach in terms of characterising the distribution of ramp rates, their duration, and their diurnal–seasonal variation using 2 years of the offshore wind power data. Next, the versatility of the methodology is demonstrated for a non-stationary time series where installed capacity changes over time. Finally, we compare the methodology with another commonly used approach, namely the min–max method (Bianco et al., 2016). The Belgian transmission system operator, Elia, makes available 15min power output data for the aggregated fleet of Belgian onshore and offshore turbines (Elia, 2020). In this work, we have used offshore data over a period of 2 years from 2015 to 2016 when the combined Belgian offshore wind power capacity was 712MW. For simplicity, the 15min values were normalised to the total capacity before analysis to create a time series of values P(t). In addition, we make use of Swedish onshore hourly wind power data for the period 2000–2001 aggregated within the SE1 price region (SCB, 2017). The installed capacity in this region increased from about 500 to 1300MW over this period. Further details of this dataset can be found in EEM20 (2020). The continuous wavelet transform (CWT) can be used to decompose a series of data using a mother wavelet function (ψ) by varying its dilation and translation. A mother wavelet function with scale a and position b can be defined as (Mallat, 2009) $\begin{array}{}\text{(1)}& {\mathit{\psi }}^{a,b}\left(t\right)=\mathit{\psi }\left(\frac{t-b}{a}\right).\end{array}$ The CWT W(a,b) of a signal X(t) is produced by the convolution of the mother wavelet function over a range of scales and positions: $\begin{array}{}\text{(2)}& W\left(a,b\right)=\frac{\mathrm{1}}{\sqrt{a}}\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}X\left(t\right)\mathit{\psi }\left(\frac{t-b}{a}\right)\mathrm A wavelet transform is thus able to localise the scales of a series of data in time which makes it a useful function to detect and characterise wind power ramps. We use the Daubechies level-1 (Haar) mother wavelet to decompose the time series of power values. This wavelet is useful to detect abrupt changes in a level which might be expected to occur during a ramp event. Using values over a 10d period, 27 January to 7 February 2015, taken from the Belgian offshore wind power data, a CWT was applied, and the results are shown in Fig. 1 comparing the original time series (a) with the corresponding CWT values (b). It can be seen that a high magnitude of W corresponds to a strong power ramp. A similar finding has been reported elsewhere (Gallego et al., 2014; Hannesdóttir and Kelly, 2019). However, what is not clear is what magnitude of W can be considered a ramp above the incoherent stochastic variations in wind power. In the following section, we consider how to discriminate ramps above such stochastic variations. 4Discrimination of ramp events Random shuffling is a technique to generate surrogate data from an original time series which preserves limited statistical properties of the original data, namely their distribution. However, it destroys the auto-correlation within a time series. Randomly shuffled surrogates have been used to test for non-linearity in a time series (Theiler et al., 1992). They have also been used to test for stationarity in temporal data (Laurent and Doncarli, 1998; Davy and Godsill, 2002; Borgnat and Flandrin, 2009; Guarin et al., 2010; Borgnat et al., 2010). Furthermore, surrogates have been applied to discriminate gusts and other coherent structures from incoherent noise in high-frequency wind speed data (Dunyak et al., 1998; Gilliam et al., 2000). In Fig. 2, as an example, we analyse a surrogate based on the 10d time series shown in Fig. 1a. Figure 2a shows a comparison between the auto-correlation of the original time series of normalised power values, P(t), and that of a randomly shuffled time series of these values, P^(t). It can be seen that any coherent structure in the original data is destroyed. Figure 2b shows the continuous wavelet transform of the surrogate time series, W^(t). It can be seen that the lower-frequency (higher-scale value) structure that was seen in Fig. 1b has disappeared and the power in the transformed wavelet spectrum is much more distributed over all scales. In order to test the hypothesis that the value of a wavelet coefficient represents a ramp event, we generate 100 such randomly shuffled surrogates of normalised wind power, ${P}_{i}^{}\left(t\right) $, where i=1 to 100, based on the 10d of data. For each surrogate time series, the CWT is generated to give a series of coefficients ${W}_{i}^{}\left(a,b\right)$. These are used to generate distributions of coefficient values (containing 100×b values) for each scale a, against which the CWT coefficient of the original, W(a,b), can be compared. In Fig. 3a–d we show the distributions for W and W^* at the scale a=40, where we discriminate the W values based on the largest 10%, 5%, 2%, and 1% of $\|{W}^{}\|$ values, respectively. The threshold values, $±{W}_{\mathrm{T}}^{}$, are shown for each plot in Fig. 3. We then extend this method of discrimination to all the scales of W. So, for each scale a, we compute a scale-dependent threshold ${W}_{\mathrm{T}}^{}\left(a\right)$ for a specific discrimination level by utilising the $\|{W}_{i}^{}\left(a,b\right)\|$ values from all the surrogates. If the value of $\|W\left(a,b\right)\|$ is greater than this threshold ${W}_{\mathrm{T}}^{}\left(a\right)$, then the null hypothesis (no ramp) is rejected at the specific discrimination level and the event is assumed to be a wind power ramp. We repeat this for the four different discrimination levels used above, namely the 10%, 5%, 2%, and 1% levels. Figure 4 shows the result of using this approach to discriminate the wind power ramps at each scale. The plot is similar to the bottom plot in Fig. 1, but now values which do not satisfy the criterion to be considered ramps have been removed and are shown as white with different null hypothesis testing. Only the colour-shaded values that satisfy the requirement to be considered wind power ramps for different discrimination levels are shown. It is then possible to sum W(a,b) over all discriminated scales up to the maximum resolved, a[max], at each time step, t=b, to calculate mean normalised power ramps, R(t): $\begin{array}{}\text{(3)}& R\left(t=b\right)=\frac{\mathrm{1}}{{a}_{max}}\sum _{a=\mathrm{1}}^{{a}_{max}}{W}_{\mathrm{R}}\left(a,b\right),\end{array}$ $\begin{array}{rlrlr}& {W}_{\mathrm{R}}\left(a,b\right)=W\left(a,b\right)& \text{when}& & \|W\left(a,b\right)\|\ge {W}_{\mathrm{T}}^{}\left(a\right),\\ & {W}_{\mathrm{R}}\left(a,b\right)=\mathrm{0}& \ text{when}& & \|W\left(a,b\right)\|<{W}_{\mathrm{T}}^{}\left(a\right).\end{array}$ Figure 5 shows the original 10d time series of wind power values with the normalised ramp values, R(t) superimposed. Power ramps are now clearly defined in terms of both timing and magnitude. Although there is not a large difference in those events which are classified as ramps, the events on days 9 and 10 in particular are excluded at the two highest discrimination levels. For the remainder of the paper we have chosen the 10% level to provide a good balance between the removal of stochastic variation whilst preserving ramp events that would be of relevance from a power system 5Sensitivity to length of surrogate series To test the generality of the technique, we consider further testing periods and increase the length of time for which the surrogate distributions are calculated. Three additional 10d periods are selected, and for each period, we examine the sensitivity of the results to the length of surrogate, namely, the same 10d period and 1 calendar year of values encompassing the 10d period. These cases are summarised in Table 1. As before, for each case, we generate 100 surrogates and the wavelet coefficients W(a,b) are discriminated from the distributions generated using the two different surrogate periods in Table 1. The results are presented in Fig. 6. It can be seen that once again, ramp periods are well discriminated from periods of incoherent stochastic variation. In addition, the results show no difference when using a longer period to generate the surrogates except at the very beginning and end of the time series. This is due to boundary effects inherent in using a convolution function which is integrated over all time and should thus be disregarded in any comparison. The fact that the results show no differences when using an extended surrogate period confirms that the process is filtering out short-term incoherent fluctuations and that a 10d period is sufficient to capture these. 6Ramp rates and duration In this section, we show how the methodology can quantify both ramp rates and their duration, using 2 years of the Belgian offshore wind power data for 2015–2016. We also use this 2-year period to produce the surrogate distributions for deriving the 10% discrimination level. Firstly, we generate a time series of normalised ramp rates. As can be seen in Figs. 5 and 6, there are discrete periods of ramp-up and ramp-down events. For each ramp-up period k and ramp-down period l, we calculate the average ramp-up rate, ${R}_{\mathrm{u}}^{\prime }\left(k\right)$, and average ramp-down rate, ${R}_{\mathrm{d}}^{\prime }\left(l\right)$: $\begin{array}{}\text{(4)}& {R}_{\mathrm{u}}^{\prime }\left(k\right)=\frac{{\sum }_{t=\mathrm{1}}^{{n}_{k}}R\left(t\right)}{D\left(k\right)},\text{(5)}& {R}_{\mathrm{d}}^{\prime }\left(l\right)=\frac {{\sum }_{t=\mathrm{1}}^{{n}_{l}}R\left(t\right)}{D\left(l\right)},\end{array}$ where the n[k] normalised power ramp-up values R(t) are summed over the duration D(k) of the kth ramp-up event and the n[l] normalised power ramp-down values R(t) are summed over the duration D(l) of the lth ramp-down event. 6.1Overall distributions Distribution plots of ramp rates over the entire 2-year period as a function of duration (binned by hour) are shown in Fig. 7. The ramp-up and ramp-down event distributions are broadly similar in nature though there are some features of note: • There is a strong correlation between the average normalised ramp rate and the duration of the ramp. • A majority of ramp durations are less than 15h with a median value of 8.25h for ramp-up events and 8.5h for ramp-down events. • There is a significant spread in ramp rates of duration between 2 and 15h. • For ramps of duration greater than around 12h, ramp rates tend to decrease. • There are very few ramp events with a duration of longer than a day (24h). The features described above are logical when considering the nature of the events driving wind ramps which are generally localised in nature and rarely last longer than a day, such as the passage of a weather front, a sea breeze (Steele et al., 2015), or a low-level jet (Nunalee and Basu, 2014; Kalverla et al., 2019). 6.2Diurnal and seasonal dependency We also investigate whether the ramp rates show a diurnal or seasonal dependence. To do this, we classify ramp-up and ramp-down rates based on their duration: ramps ≤2h are classified as short duration; ramps within the range 2–15h are classified as medium duration; and long-duration ramps are assumed to be ≥15h. This classification is somewhat arbitrary but is broadly based on the discussion in Sect. 1. The results are shown in Fig. 8. It can be seen that medium-duration ramps in particular show a strong diurnal cycle with a higher frequency of ramp-up events in the afternoon and ramp-down events in the morning. This is true to a lesser extent for the long-duration ramps. There is no discernible diurnal pattern in the short-duration ramps. By contrast, there is no clear cycle at any scale across the different months of the year. The observed diurnal variation in medium- and long-duration wind power ramps is consistent with the pattern of average diurnal generation observed as seen in Fig. 8e which is strongly influenced by mesoscale effects such as low-level jets, land–sea breezes, and thermally driven entrainment from aloft due to the relatively close proximity of the Belgian offshore wind farms to the coast. Low-level jets are known to be more prevalent during the evening hours at the location of some of the Belgian offshore wind farms (Kalverla et al., 2019) which may contribute to the increase in power generation observed during this period. These results are based on one dataset for a limited 2-year period. Clearly, further work is necessary to investigate the generality of the observations above. However, this short investigation does illustrate how wavelets can be used to investigate ramps rates, their duration, and their prevalence. 7Ramp detection during a period of change in installed power capacity As a further illustration of the utility of the ramp detection methodology, we apply it to a different time series of wind power data where the installed capacity increases with time. Such a change can be problematic where ramps are defined using a minimum change in wind power output ΔP over a time Δt. In this section, we use the measured hourly wind power data from the Swedish SE1 price region for the period 2000–2001. Figure 9a shows an increasing trend in the production of wind power which reflects an increase in installed capacity over the 2-year period. This trend is also clearly observed in the continuous wavelet coefficient of the power values (P) shown in Fig. 9c. Note that in this case, we have deliberately not normalised the data to show how the method can be applied when the installed capacity is non-stationary. If the wind power data over the period are randomly shuffled, then clearly the trend is no longer visible in either the surrogate series seen in Fig. 9b or its continuous wavelet transform coefficients W^ as depicted in Fig. 9d. We then focus on two periods of data shown by dashed lines in Fig. 9a. In the first period, 1 to 25 January 2000, installed capacity was around 500MW. In the second period, 6 to 31 December 2001, installed capacity had increased to around 1300MW. The difference in magnitude of the W values can clearly be seen in Fig. 10a for the first period and Fig. 10b for the second. Then, using the entire period 2000–2001 and the method of surrogates to fix the 10% discrimination level following the same methodology as described above, we calculate the power ramps, R(t), for these two periods. Although the values of R(t) are of a different magnitude for the two periods, it can be seen that there is no discernible difference in the ability to detect ramps in the first period, Fig. 10c, or the second period, Fig. 10d. 8A comparison between the wavelet-surrogate and min–max ramp detection methods Finally, we compare our wavelet-surrogate (WS) method with an existing ramp detection method known as the min–max method (Bianco et al., 2016). The min–max ramp detection method makes use of a sliding window of a given window length (WL) (in time steps) and considers the change in power during that window defined as the difference between the maximum and minimum power within the window. If this change in power is greater than a defined threshold (TH), then a ramp is deemed to have occurred. Clearly, the sensitivity of this method depends on the chosen values of two parameters, namely WL and TH, in contrast to our WS methodology which depends on a discrimination level. In this study, we compare the two methods in detecting the number of ramp-up and ramp-down events. This comparison is made for both the Belgian and Swedish wind power datasets. Table 2 shows the number of ramp-up and ramp-down events that are detected using the WS and min–max methods for different time periods of the two wind power datasets as a function of different parameter values used by each method. For the WS method, we quantify the sensitivity of ramp detection using the 10% (WS10), 5% (WS5), 2% (WS2), and 1% (WS1) discrimination levels. In the case of the min–max method, we use a combination of window lengths (WL1=8 and WL2=12) and threshold levels (TH1=0.3 and TH2=0.4). For the 15min Belgian offshore wind power data, these WL values correspond to WL1=2h and WL2=3h, whereas for the hourly Swedish onshore wind power data, they correspond to WL1=8h and WL2= 12h. Note that the actual Swedish wind power data values are used for the WS algorithm, while the data are normalised by time-varying installed power capacity for the min–max method. In general, the number of ramp events detected by the WS method is greater than for the min–max method. The number of events detected by the WS method generally reduces as the discrimination percentage value gets smaller. The exception to this is for the T1 and T2 periods, when a slight increase is seen at the 1% discrimination level when the overall event count is low. This is due to the splitting of single ramp events into two events, an example of which can be seen around day 4 in Fig. 5d. Similarly, the min–max method detects fewer ramp events as TH is increased. By contrast, increasing the WL value does not show such a clear trend in the number of ramp events detected. In addition, the min–max method seems more sensitive to the range of WL and TH values used than the WS method is to the range of discrimination values used. The detection of wind power ramps is a challenge in terms of how to characterise their magnitude and duration and how to discriminate a ramp from incoherent stochastic fluctuations in wind power. In this paper, we have presented a relatively simple methodology based on a wavelet transform and the use of surrogates to discriminate and extract ramp events. Using wind power data from the Belgian offshore wind farm cluster, we have illustrated the application of the methodology and have shown that a 10d period is sufficient to discriminate coherent ramp events from incoherent fluctuations. We show the utility of the technique in characterising the distribution of ramp rates and their duration and seasonal–diurnal variation for the Belgian offshore cluster. In addition, we have shown how the methodology can be used to detect wind power ramps when installed capacity increases with time using Swedish onshore wind power data as an example. Lastly, we compare our ramp detection algorithm with the min–max method, contrasting their sensitivities to parameter choice. Further work is required to apply the methodology to a broader range of sites and for longer periods to investigate the prevalence of different ramp rates and their duration. It might be expected that depending on the climatology of the site, this could differ; on the other hand, consistent trends may be apparent which could help operators in accommodating fluctuations within an integrated power system. This research was carried out by BRC under the supervision of SJW and SB. The authors declare that they have no conflict of interest. The authors are grateful to Elia for supplying the Belgian offshore wind farm production data and the KTH Royal Institute of Technology–Greenlytics for supplying the Swedish onshore wind farm production data used in this research. This paper was edited by Julie Lundquist and reviewed by two anonymous referees. Bianco, L., Djalalova, I. V., Wilczak, J. M., Cline, J., Calvert, S., Konopleva-Akish, E., Finley, C., and Freedman, J.: A wind energy ramp tool and metric for measuring the skill of numerical weather prediction models, Weather Forecast., 31, 1137–1156, 2016.a, b, c Borgnat, P. and Flandrin, P.: Stationarization via surrogates, J. Stat. Mech.: Theory and Experiment, 2009, P01001, https://doi.org/10.1088/1742-5468/2009/01/p01001, 2009.a Borgnat, P., Flandrin, P., Honeine, P., Richard, C., and Xiao, J.: Testing stationarity with surrogates: A time-frequency approach, IEEE Transactions on Signal Processing, 58, 3459–3470, 2010.a Bossavy, A., Girard, R., and Kariniotakis, G.: Forecasting Uncertainty Related to Ramps of Wind Power Production, European Wind Energy Conference and Exhibition 2010, EWEC 2010, April 2010, Warsaw, Poland, 9 pp., ISBN 9781617823107.Hal-00765885f, 2010.a, b Coughlin, K., Murthi, A., and Eto, J.: Multi-scale analysis of wind power and load time series data, Renew. Energ., 68, 494–504, 2014.a Cutler, N., Kay, M., Jacka, K., and Nielsen, T. S.: Detecting, categorizing and forecasting large ramps in wind farm power output using meteorological observations and WPPT, Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology, 10, 453–470, 2007.a Davy, M. and Godsill, S.: Detection of abrupt spectral changes using support vector machines an application to audio signal segmentation, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing , Orlando, FL, 2002, II-1313-II-1316, https://doi.org/10.1109/ICASSP.2002.5744044, 2002.a DeMarco, A. and Basu, S.: On the tails of the wind ramp distributions, Wind Energ., 21, 892–905, 2018.a Drew, D. R., Barlow, J. F., and Coker, P. J.: Identifying and characterising large ramps in power output of offshore wind farms, Renew. Energ., 127, 195–203, 2018.a Dunyak, J., Gilliam, X., Peterson, R., and Smith, D.: Coherent gust detection by wavelet transform, J. Wind Eng. Ind. Aerod., 77, 467–478, 1998.a EEM20: EEM20 Forecasting Competition, available at: https://eem20.eu/forecasting-competition/ (last access: 17 August 2020), 2020.a, b Elia: Wind power generation, available at: https://www.elia.be/en/grid-data/power-generation/wind-power-generation (last access: 17 August 2020), 2020.a, b Ferreira, C., Gama, J., Matias, L., Botterud, A., and Wang, J.: A Survey on Wind Power RAMP Forecasting, Tech. rep., Argonne National Laboratory (ANL), USA, 2011.a Gallego, C., Cuerva, A., and Costa, A.: Detecting and characterising ramp events in wind power time series, Journal of Physics: Conference Series, 555, 012040, https://doi.org/10.1088/1742-6596/555/1 /012040, 2014.a, b Gallego-Castillo, C., Cuerva-Tejero, A., and Lopez-Garcia, O.: A review on the recent history of wind power ramp forecasting, Renewable and Sustainable Energy Reviews, 52, 1148–1157, 2015.a Gilliam, X., Dunyak, J., Doggett, A., and Smith, D.: Coherent structure detection using wavelet analysis in long time-series, J. Wind Eng. Ind. Aerod., 88, 183–195, 2000.a Guarin, D., Orozco, A., and Delgado, E.: A new surrogate data method for nonstationary time series, arXiv [preprint], arXiv:1008.1804, 2010.a Hannesdóttir, Á. and Kelly, M.: Detection and characterization of extreme wind speed ramps, Wind Energ. Sci., 4, 385–396, https://doi.org/10.5194/wes-4-385-2019, 2019.a, b Ji, F., Cai, X., and Zhang, J.: Wind power prediction interval estimation method using wavelet-transform neuro-fuzzy network, Journal of Intelligent & Fuzzy Systems, 29, 2439–2445, 2015.a Kalverla, P. C., Duncan Jr., J. B., Steeneveld, G.-J., and Holtslag, A. A. M.: Low-level jets over the North Sea based on ERA5 and observations: together they do better, Wind Energ. Sci., 4, 193–209, https://doi.org/10.5194/wes-4-193-2019, 2019.a, b Kiviluoma, J., Holttinen, H., Scharff, R., Weir, D. E., Cutululis, N., Litong-Palima, M., and Milligan, M.: Index for wind power variability, in: The 13th Wind Integration Workshop, edited by: Betancourt, U. and Ackermann, T., 11–14 November 2014, Berlin, 2014.a Kiviluoma, J., Holttinen, H., Weir, D., Scharff, R., Söder, L., Menemenlis, N., Cutululis, N. A., Danti Lopez, I., Lannoye, E., Estanqueiro, A., Gomez-Lazaro, E., Zhang, Q., Bai, J., Wan, Y.-H., and Milligan, M.: Variability in large-scale wind power generation, Wind Energ., 19, 1649–1665, 2016.a Laurent, H. and Doncarli, C.: Stationarity index for abrupt changes detection in the time-frequency plane, IEEE Signal Processing Letters, 5, 43–45, 1998.a Mallat, S.: A Wavelet Tour of Signal Processing. A Wavelet Tour of Signal Processing, Academic Press, ISBN 13 978-0-12-374370-1, 2009.a Marquis, M., Wilczak, J., Ahlstrom, M., Sharp, J., Stern, A., Smith, J. C., and Calvert, S.: Forecasting the wind to reach significant penetration levels of wind energy, B. Am. Meteorol. Soc., 92, 1159–1171, 2011.a Nunalee, C. and Basu, S.: Mesoscale Modeling of Low-Level Jets over the North Sea, in: Wind Energy – Impact of Turbulence, edited by: Hölling, M., Peinke, J., and Ivanell, S., pp. 197–202, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014.a SCB: Energy prices and switching of suppliers, 3rd quarter 2017, Tech. Rep. Technical Report EN 24 SM 1704, Swedish Energy Agency, 2017.a Sevlian, R. and Rajagopal, R.: Detection and statistics of wind power ramps, IEEE Transactions on Power Systems, 28, 3610–3620, 2013. a, b Steele, C., Dorling, S., von Glasow, R., and Bacon, J.: Modelling sea-breeze climatologies and interactions on coasts in the southern North Sea: implications for offshore wind energy, Q. J. Roy. Meteorol. Soc., 141, 1821–1835, 2015.a Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J. D.: Testing for nonlinearity in time series: the method of surrogate data, Physica D: Nonlinear Phenomena, 58, 77–94, 1992.a Zhang, J., Cui, M., Hodge, B.-M., Florita, A., and Freedman, J.: Ramp forecasting performance from improved short-term wind power forecasting over multiple spatial and temporal scales, Energy, 122, 528–541, 2017.a, b	{"url":"https://wes.copernicus.org/articles/5/1731/2020/","timestamp":"2024-11-08T05:12:09Z","content_type":"text/html","content_length":"250648","record_id":"<urn:uuid:5350c0f7-2510-4ae5-8c25-7e000a17cb34>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00741.warc.gz"}
False Positives and False Negatives Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think: • It could be wrong when it says "Yes". • It could be wrong when it says "No". It is like being told you did something when you didn't! Or you didn't do it when you really did. They each have a special name: "False Positive" and "False Negative": They say you did They say you didn't You really did They are right! "False Negative" You really didn't "False Positive" They are right! Here are some examples of "false positives" and "false negatives": • Airport Security: a "false positive" is when ordinary items such as keys or coins get mistaken for weapons (machine goes "beep") • Quality Control: a "false positive" is when a good quality item gets rejected, and a "false negative" is when a poor quality item gets accepted. (A "positive" result means there IS a defect.) • Antivirus software: a "false positive" is when a normal file is thought to be a virus • Medical screening: low-cost tests given to a large group can give many false positives (saying you have a disease when you don't), and then ask you to get more accurate tests. But many people don't understand the true numbers behind "Yes" or "No", like in this example: Example: Allergy or Not? Hunter says she is itchy. There is a test for Allergy to Cats, but this test is not always right: • For people that really do have the allergy, the test says "Yes" 80% of the time • For people that do not have the allergy, the test says "Yes" 10% of the time ("false positive") Here it is in a table: Test says "Yes" Test says "No" Have allergy 80% 20% "False Negative" Don't have it 10% "False Positive" 90% Question: If 1% of the population have the allergy, and Hunter's test says "Yes", what are the chances that Hunter really has the allergy? Do you think 75%? Or maybe 50%? A similar test was given to Doctors and most guessed around 75% ... ... but they were very wrong! (Source: "Probabilistic reasoning in clinical medicine: Problems and opportunities" by David M. Eddy 1982, which this example is based on) There are three different ways to solve this: • "Imagine a 1000", • "Tree Diagrams" or • "Bayes' Theorem", use any you prefer. Let's look at them now: Try Imagining A Thousand People When trying to understand questions like this, just imagine a large group (say 1000) and play with the numbers: • Of 1000 people, only 10 really have the allergy (1% of 1000 is 10) • The test is 80% right for people who have the allergy, so it will get 8 of those 10 right. • But 990 do not have the allergy, and the test will say "Yes" to 10% of them, which is 99 people it says "Yes" to wrongly (false positive) • So out of 1000 people the test says "Yes" to (8+99) = 107 people As a table: 1% have it Test says "Yes" Test says "No" Have allergy 10 8 2 Don't have it 990 99 891 So 107 people get a "Yes" but only 8 of those really have the allergy: 8 / 107 = about 7% So, even though Hunter's test said "Yes", it is still only 7% likely that Hunter has a Cat Allergy. Why so small? Well, the allergy is so rare that those who actually have it are greatly outnumbered by those with a false positive. As A Tree Drawing a tree diagram can really help: First of all, let's check that all the percentages add up: 0.8% + 0.2% + 9.9% + 89.1% = 100% (good!) And the two "Yes" answers add up to 0.8% + 9.9% = 10.7%, but only 0.8% are correct. 0.8/10.7 = 7% (same answer as above) Bayes' Theorem Bayes' Theorem has a special formula for this kind of thing: P(A\|B) = P(A)P(B\|A) P(A)P(B\|A) + P(not A)P(B\|not A) • P means "Probability of" • \| means "given that" • A in this case is "actually has the allergy" • B in this case is "test says Yes" P(A\|B) means "The probability that Hunter actually has the allergy given that the test says Yes" P(B\|A) means "The probability that the test says Yes given that Hunter actually has the allergy" To be clearer, let's change A to has (actually has allergy) and B to Yes (test says yes): P(has\|Yes) = P(has)P(Yes\|has) P(has)P(Yes\|has) + P(not has)P(Yes\|not has) And put in the numbers: P(has\|yes) = 0.01×0.8 0.01×0.8 + 0.99×0.1 = 0.0748... Which is about 7% Learn more about this at Bayes' Theorem. One Last Example Extreme Example: Computer Virus A computer virus spreads around the world, all reporting to a master computer. The good guys capture the master computer and find that a million computers have been infected (but don't know which ones). Governments decide to take action! No one can use the internet until their computer passes the "virus-free" test. The test is 99% accurate (pretty good, right?) But 1% of the time it says you have the virus when you don't (a "false Now let's say there are 1000 million internet users. • Of 1 million with the virus 99% of them get correctly banned = about 1 million • But false positives are 999 million x 1% = about 10 million So a total of 11 million get banned, but only 1 out of those 11 actually have the virus. So if you get banned there is only a 9% chance you actually have the virus! When dealing with false positives and false negatives (or other tricky probability questions) we can use these methods: • Imagine you have 1000 (of whatever), • Make a tree diagram, or • Use Bayes' Theorem	{"url":"http://wegotthenumbers.org/probability-false-negatives-positives.html","timestamp":"2024-11-08T08:51:59Z","content_type":"text/html","content_length":"13608","record_id":"<urn:uuid:f60853c9-e07a-4c08-bde7-75f46c231540>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00451.warc.gz"}
Q. Consider the following including the Question and the Statements: There are 5 members A, B, C, D, E in a family. Question: What is the relation of E to B? - Sociology OWL Q. Consider the following including the Question and the Statements: There are 5 members A, B, C, D, E in a family. Question: What is the relation of E to B? Statement-1: A and B are a married couple. Statement-2: D is the father of C. Statement-3: E is D’s son. Statement-4: A and C are sisters. Which one of the following is correct in respect of the above Question and Statements? (a) Statement-1, Statement-2 and Statement-3 are sufficient to answer the Question. (b) Statement-1, Statement-3 and Statement-4 are sufficient to answer the Question. (c) All four statements together are sufficient to answer the Question. (d) All four statements are not sufficient to answer the Question. Correct Answer: (c) All four statements together are sufficient to answer the Question. Question from UPSC Prelims 2023 CSAT Explanation : 5 members A, B, C, D, E in a family A and B are a married couple, so they are husband and wife. D is the father of C, so C is the child of D. E is D’s son, so E is the brother of C. A and C are sisters, so they have the same parents. Finally, I would use the family tree and the definitions to find the relation of E to B. For example: E is the brother of C, who is the spouse of B, so E is the brother-in-law of B. Therefore, the correct answer is © All four statements together are sufficient to answer the Question.	{"url":"https://upscsociology.in/q-consider-the-following-including-the-question-and-the-statements-there-are-5-members-a-b-c-d-e-in-a-family-question-what-is-the-relation-of-e-to-b/","timestamp":"2024-11-04T20:16:14Z","content_type":"text/html","content_length":"189988","record_id":"<urn:uuid:0a3ac049-4aac-4cfa-abaf-414903d78395>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00043.warc.gz"}
□ org.apache.xml.dtm.DTMAxisTraverser □ Method Summary Modifier and Type Method and Description first(int context) By the nature of the stateless traversal, the context node can not be returned or the iteration will go into an infinate loop. first(int context, int extendedTypeID) By the nature of the stateless traversal, the context node can not be returned or the iteration will go into an infinate loop. next(int context, int current) abstract int Traverse to the next node after the current node. next(int context, int current, int extendedTypeID) abstract int Traverse to the next node after the current node that is matched by the extended type ID. ☆ Methods inherited from class java.lang.Object clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait □ Method Detail ☆ next public abstract int next(int context, int current) Traverse to the next node after the current node. context - The context node of this traversal. This is the point of origin for the traversal -- its "root node" or starting point. current - The current node of the traversal. This is the last known location in the traversal, typically the node-handle returned by the previous traversal step. For the first traversal step, context should be set equal to current. Note that in order to test whether context is in the set, you must use the first() method instead. the next node in the iteration, or DTM.NULL. See Also: ☆ next public abstract int next(int context, int current, int extendedTypeID) Traverse to the next node after the current node that is matched by the extended type ID. context - The context node of this traversal. This is the point of origin for the traversal -- its "root node" or starting point. current - The current node of the traversal. This is the last known location in the traversal, typically the node-handle returned by the previous traversal step. For the first traversal step, context should be set equal to current. Note that in order to test whether context is in the set, you must use the first() method instead. extendedTypeID - The extended type ID that must match. the next node in the iteration, or DTM.NULL. See Also: Copyright © 2018 JBoss by Red Hat. All rights reserved.	{"url":"https://access.redhat.com/webassets/avalon/d/red-hat-jboss-enterprise-application-platform/6.4/javadocs/org/apache/xml/dtm/DTMAxisTraverser.html","timestamp":"2024-11-09T23:01:37Z","content_type":"text/html","content_length":"17399","record_id":"<urn:uuid:13da1dc1-e96d-4444-a437-b00ad1b9b7c0>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00140.warc.gz"}
Normalized Power Normalized Power (NP), together with threshold, allows TrainingPeaks to calculate the Intensity Factor of a workout or selection within a workout. What is Normalized Power (NP) Normalized power (NP) is the adjusted (normalized) average power output for a ride or segment of a ride. Power output on a ride is variable (due to small changes in external power demands e.g. small changes in elevation, small surges in speed, wind, etc) so NP represents the physiological cost of the ride or segment of the ride if that power output had been constant. How do I get Normalized Power in TrainingPeaks? For TrainingPeaks to calculate NP for your ride or segment of the ride we require three things: 1. You need a power meter. 2. A device that records the power channel from your power meter e.g. Garmin, Wahoo, Suunto device. 3. A power threshold that is specific to your completed workout. Make sure that you have a power threshold set in your account settings. Of note • TrainingPeaks uses Normalized Power to calculate TSS. TSS = IF^2 (NP/powerFTP) x duration (hours) x 100. • Ignore Normalized Power calculations for durations under roughly 10 minutes. NP calculations always start with a 30-second rolling average, so shorter NP calculations (< 10 minutes) miss a significant portion of the calculation. e.g. If you select a 3-minute selection in a workout and look at the NP, NP misses almost 20% of the interval before it can calculate an average. • TrainingPeaks uses the average power from the device file and calculates its Normalized Power. If the average power is higher than the Normalized power highlight a few seconds on the graph in the workout expando and delete it. The workout edit will prompt TrainingPeaks to calculate the average power which should then produce an average power lower than a normalized power. Where can I find my workout's NP? Workout Expando Summary Workout Expando Selection TrainingPeaks Mobile App	{"url":"https://help.trainingpeaks.com/hc/en-us/articles/204071804-Normalized-Power","timestamp":"2024-11-11T17:31:15Z","content_type":"text/html","content_length":"22972","record_id":"<urn:uuid:0b43d466-0200-434c-9366-4dfe5691951b>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00564.warc.gz"}
Curry Package peval-noshare This package contains a partial evaluator for Curry implemented in Curry by Elvira Albert, German Vidal (UPV), and Michael Hanus (CAU Kiel). Note that this partial evaluator is based on technical results published in 2002 and does not consider sharing. As a consequence, the partial evaluator is correct only for programs which do not contain non-deterministic operations, i.e., are confluent in the sense of classical term rewriting systems. This partial evaluator is integrated in PAKCS as follows: • After loading some program into PAKCS, this program can be partially evaluated by the command ":peval". • The expressions to be partially evaluated must be marked in the program by (PEVAL ...) where PEVAL is the identity function (defined in the standard prelude). • The marked expressions are partially evaluated and replaced by their partially evaluated versions. This modified program is stored in "_pe.fcy" provided that is the name of the source program. • The partially evaluated program "_pe.fcy" is automatically loaded into PAKCS. Although there is no Curry source file for this program, the (decompiled) source can be viewed by the command ":show" (if you are interested to see the result of the partial evaluation). If you want to run this version stand-alone (i.e., independent from PAKCS), you can partially evaluate program .curry by the shell command curry-pevalns <prog> Checkout with CPM: cypm checkout peval-noshare 0.1.0 Package source: peval-noshare-0.1.0.tar.gz [browse] Source repository:	{"url":"https://cpm.curry-lang.org/pkgs/peval-noshare-0.1.0.html","timestamp":"2024-11-12T22:07:45Z","content_type":"text/html","content_length":"10661","record_id":"<urn:uuid:0c64c8df-6a18-4ca7-842f-a4acfb77422f>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00257.warc.gz"}
harmonicmeanp tutorial Example 1. Sliding Window Analysis Download the 312457 p-values from chromosome 12 of the genome-wide association study (GWAS) for neuroticism (Okbay et al., 2016). This file is an excerpt of the original data. It took me a few seconds to download the data excerpt. The 8 megabyte file contains rs identifiers and SNP positions as per human genome build GRCh37/hg19 as well as the p-values. system.time((gwas = read.delim("https://www.danielwilson.me.uk/files/Neuroticism_ch12.txt", ## user system elapsed ## 0.795 0.046 1.447 ## rs pos p ## 1 rs7959779 149478 0.3034 ## 2 rs4980821 149884 0.5905 ## 3 rs192950336 150256 0.1125 ## 4 rs61907205 151213 0.4896 ## 5 rs2368809 151236 0.7066 ## 6 rs4018398 151469 0.9420 The harmonic mean p-value (HMP) is a statistic with which one can perform a combined test of the null hypothesis that none of the p-values is significant even when the p-values are dependent. In GWAS, p-values will often be dependent because of genetic linkage. The HMP can be used to test the null hypothesis that no SNPs on chromosome 12 are significant. Let’s do it manually by first calculating the HMP, assuming equal weights. Note that a total of L=6524432 tests were performed genome-wide, so this number must be used to determine the weights if we are to control the genome-wide ssFWER, even though we are only analysing the 312457 SNPs on chromosome 12 in this example. L = 6524432 gwas$w = 1/L R = 1:nrow(gwas) (HMP.R = sum(gwas$w[R])/sum(gwas$w[R]/gwas$p[R])) ## [1] 0.0008734522 One of the remarkable properties of the HMP is that for small values (e.g. below 0.05), the HMP can be directly interpreted as a p-value after adjusting for multiple comparisons. That the HMP equals $\overset{\circ}{p}_{\mathcal{R}}=0.0008734522$ suggests it is strongly significant before multiple testing correction. To test this formally, first the HMP significance threshold is computed. For that I will assume a false positive rate of $\alpha=0.05$, i.e. 5%. # Specify the false positive rate alpha = 0.05 # Compute the HMP significance threshold (alpha.L = qharmonicmeanp(alpha, L)) ## [1] 0.02593083 The multiple testing-adjusted threshold against which to evaluate the significance of the combined test is determined by the sum of the weights for the p-values being combined. The HMP for subset $\ mathcal{R}$ is significant when $\overset{\circ}{p}_\mathcal{R}\leq \alpha_L w_\mathcal{R}$. # Test whether the HMP for subset R is significance w.R = sum(gwas$w[R]) alpha.L * w.R ## [1] 0.001241835 Therefore after adjusting for multiple comparison we can reject the null hypothesis of no association on chromosome 12 at level $\alpha=0.05$ because 0.0008734522 is below 0.001241835. An equivalent approach is to calculate an asymptotically exact p-value based on the HMP. # Use p.hmp instead to compute the HMP test statistic and # calculate its asymptotically exact p-value in one step # Note this line has changed because of a previous error. w.Rpharmonicmeanp(HMP.R/w.R, L=L, lower.tail=TRUE) ## [1] 0.001343897 # Compare it to the multiple testing threshold ## [1] 0.002394515 The asymptotically exact p-value of $p_{\overset{\circ}{p}_{\mathcal{R}}}=0.001343897$ is close to the HMP of $\overset{\circ}{p}_{\mathcal{R}}=0.0008734522$ and also significant because it is below $0.002394515$. Note however that direct interpretation of the HMP is anti-conservative compared to the asymptotically exact test, which is why the HMP had to be compared directly to the more stringent threshold $\alpha_L=0.02593083$. The asymptotically exact p-value can be computed in one step: # Note that the p.hmp function has been redefined to take argument L. Omitting L will issue a warning. R = 1:nrow(gwas) ## p.hmp ## 0.001343897 The combined p-value for chromosome 12 is useful because if the combined p-value is not significant, neither is any constituent p-value, after multiple testing correction, as always. Conversely, if the combined p-value is significant, there may be one or more subsets of constituent p-values that are also significant. These subsets can be hunted down because another useful property of the HMP is that the significance thresholds of these further tests are the same no matter how many combinations of subsets of the constituent p-values are tested. Specifically, for any subset $\mathcal{R}$ of the L p-values, the HMP is compared against a threshold $\alpha_L\,w_{\mathcal{R}}$ (equivalently, the asymptotically exact HMP is compared against a threshold $\alpha\,w_{\mathcal{R}}$), where \ (w_{\mathcal{\mathcal{R}}}=\sum_{i\in\mathcal{R}}w_{i}\) and the $w_{i}$s are the weights of the individual p-values, constrained to sum to one. Assuming equal weights, $w_{i}=1/L$, meaning that $w_{\mathcal{R}}=\left\|\mathcal{R}\right\|/L$ equals the fraction of all tests being combined. In what follows I will mainly use the asymptotically exact p-values, rather than directly interpreting the HMP. For example, separately test the p-values occurring at even and odd positions on chromosome 12: R = which(gwas$pos%%2==0) ## p.hmp ## 0.002658581 w.R = sum(gwas$w[R]) ## [1] 0.001200587 R = which(gwas$pos%%2==1) ## p.hmp ## 0.00230653 w.R = sum(gwas$w[R]) ## [1] 0.001193928 Neither of the two tests is significant individually: for even positions, the combined p-value was $p_{\overset{\circ}{p}_{\mathcal{R}}}=0.002658581$ which was above the significance threshold of \ (\alpha\,w_{\mathcal{R}}=0.001200587\) and for odd positions, the combined p-value was $p_{\overset{\circ}{p}_{\mathcal{R}}}=0.00230653$ which was above the significance threshold of $\alpha\,w_{\ Comparing p-values with different significance thresholds can be confusing. Instead, it is useful to calculate adjusted p-values, which are compared directly to \(\alpha$, the intended strong-sense familywise error rate. An adjusted p-value is simply divided by its weight w. For example: R = which(gwas$pos%%2==0) p.R = p.hmp(gwas$p[R],gwas$w[R],L) w.R = sum(gwas$w[R]) (p.R.adjust = p.R/w.R) ## p.hmp ## 0.11072 R = which(gwas$pos%%2==1) p.R = p.hmp(gwas$p[R],gwas$w[R],L) w.R = sum(gwas$w[R]) (p.R.adjust = p.R/w.R) ## p.hmp ## 0.09659422 Now it is easy to see that both tests are non-significant, assuming $\alpha=0.05$. Of course it makes little sense to combine p-values according to whether their position is an even or odd number. Instead we might wish to test the first 156229 SNPs on chromosome 12 separately from the second 156228 SNPs to begin to narrow down regions of significance. R = 1:156229 p.R = p.hmp(gwas$p[R],gwas$w[R],L) w.R = sum(gwas$w[R]) (p.R.adjust = p.R/w.R) ## p.hmp ## 1 R = 156230:312457 p.R = p.hmp(gwas$p[R],gwas$w[R],L) w.R = sum(gwas$w[R]) (p.R.adjust = p.R/w.R) ## p.hmp ## 0.02842931 This is much clearer: only in the second half of the chromosome can we reject the null hypothesis of no significant p-values at the $\alpha=0.05$ level. For the first half of the chromosome, the adjusted p-value was $p_{\overset{\circ}{p}_{\mathcal{R}}}/w_{\mathcal{R}}=1$. By the corrected definition of asymptotically exact HMPs, the adjusted p-value will not exceed 1, although in general while p-values must be 1 or below, adjusted p-values need not be. For the second half of the chromosome, the adjusted p-value was $p_{\overset{\circ}{p}_{\mathcal{R}}}/w_{\mathcal{R}}=0.02842931$ which is below the standard significance threshold of $\alpha=0.05$. Note that it was completely irrelevant that we had already performed tests of even- and odd-positioned SNPs: as mentioned above, the significance thresholds are pre-determined by the $w_{\mathcal {R}}$’s no matter how many subsets of p-values are tested and no matter in what combinations. We can test any subset of the p-values without incurring further multiple testing penalties. For example, let’s test 50 megabase windows overlaping at 10 megabase intervals. Testing overlapping versus non-overlapping windows has no effect on the significance thresholds, but of course it has an effect on the resolution of our conclusions and on the computational time. # Define overlapping sliding windows of 50 megabase at 10 megabase intervals win.50M.beg = outer(0:floor(max(gwas$pos/50e6-1)),(0:4)/5,"+")50e6 win.50M.beg = win.50M.beg[win.50M.beg+50e6<=max(gwas$pos)] # Calculate the combined p-values for each window p.50M = sapply(win.50M.beg,function(beg) { R = which(gwas$pos>=beg & gwas$pos<(beg+50e6)) ## user system elapsed ## 0.083 0.017 0.117 # Calculate sums of weights for each combined test w.50M = sapply(win.50M.beg,function(beg) { R = which(gwas$pos>=beg & gwas$pos<(beg+50e6)) ## user system elapsed ## 0.049 0.009 0.059 # Calculate adjusted p-value for each window p.50M.adj = p.50M/w.50M Now plot them # Took a few seconds, plotting over 312k points gwas$p.adj = gwas$p/gwas$w plot(gwas$pos/1e6,-log10(gwas$p.adj),pch=".",xlab="Position on chromosome 12 (megabases)", ylab="Adjusted significance (-log10 adjusted p-value)", # Superimpose the significance threshold, alpha, e.g. alpha=0.05 # When using the HMP to evaluate individual p-values, the HMP threshold must be used, # which is slightly more stringent than Bonferroni for individual tests # For comparison, plot the conventional GWAS threshold of 5e-8. Need to convert # this into the adjusted p-value scale. Instead of comparing each raw p-value # against a Bonferonni threshold of alpha/L=0.05/6524432, we would be comparing each # against 5e-8. So the adjusted p-values p/w=pL would be compared against # 5e-8L = 5e-8 * 6524432 = 0.3262216	{"url":"https://pbil.univ-lyon1.fr/CRAN/web/packages/harmonicmeanp/vignettes/harmonicmeanp.html","timestamp":"2024-11-07T05:35:27Z","content_type":"text/html","content_length":"1048969","record_id":"<urn:uuid:a69f0afe-1f63-4c59-a4c8-cf4522054b85>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00706.warc.gz"}
IOE 1ST SEMESTER BASIC MATHEMATICS NOTE - PDF DOWNLOAD - IOE NOTES IOE 1st year mathematics note and PDF download. Are you searching for the PDF of Engineering mathematics 1 solution Tu. then hold on you are in the right Place. Here you will get embed link of a basic 1st-year mathematics solution book. READ Solution of 1st year 1st-semester basic Mathematics 1. Derivatives and their Applications 1.1 Introduction 1.2 Higher order derivatives 1.3 Mean value theorem 1.3.1 Rolle’s theorem 1.3.2 Lagrange’s mean value theorem 1.3.3 Cauchy’s mean value theorem 1.4 Power series of single valued function 1.4.1 Taylor’s series 1.4.2 Maclaurin’s series 1.5 Indeterminate forms: L Hospital rule 1.6 Asymptotes to Cartesian and polar curves 1.7 Pedal equations to Cartesian and polar curves; curvature and radius of curvature 2. Integration and its application 2.1 Introduction 2.2 Definite integrals and their properties 2.3 Improper integrals 2.4 Differentiation under integral signs 2.5 Reduction formula: Beta Gama functions 2.6 Application of integrals for finding areas arc length, surface, and solid of revolution in the plane for Cartesian and polar curves 3. Plane Analytic Geometry 3.1 Transformation of coordinates: Translation and rotation 3.2 Ellipse and hyperbola: Standard forms, tangent, and normal 3.3 General equation of conics in Cartesian and polar forms 4. Ordinary Differential equations and their applications 4.1 First-order and first degree differential equations 4.2 Homogenous differential equations 4.3 Linear differential equations 4.4 Equation reducible to linear differential equations: Bernoulli’s equation 4.5 First order and higher degree differential equation: Clairaut’s equation 4.6 Second-order and first degree linear differential equations with constant coefficients 4.7 Second order and first degree linear differential equations with variable coefficients: Cauchy’s equation 4.8 Applications in Engineering field Disclaimer: This website is for educational purposes if you find your content then contact us from the contact section. we will remove it from our site. 1 thought on “IOE 1ST SEMESTER BASIC MATHEMATICS NOTE – PDF DOWNLOAD” 1. text book ko pdf chahiyo not solution book ko Leave a Comment	{"url":"https://ioenotes.bikrampparajuli.com.np/ioe-1st-semester-basic-mathematics-note-pdf-download/","timestamp":"2024-11-12T19:09:19Z","content_type":"text/html","content_length":"143420","record_id":"<urn:uuid:12be8a3e-724c-4fe4-900b-8ddd22e3fbc0>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00219.warc.gz"}
Cubic splines: summary of responses Hi Biomech-lers, Here is the summary of the resonses to my follow up on cubic splines. Many thanks to all who responded. N. Glossop, Ph.D., Toronto, Canada My original posting: Jesus Dapena wrote in a recent summary about splines, > I would advise you very strongly to stay away from CUBIC splines. > Usually (always?) they force the second derivative to be zero at the > beginning and end of the data set. When that is not the case in the > activity being analyzed (i.e., almost always), the result is very distorted > data in the early and late parts of the trial (and even the middle parts can > get messed up too). I am not sure how much I agree with this statement, and would ask for a little feedback from list members. While it is true that cubic splines force the second derivitives to be zero, cubics and piecewise cubics are often used to interpolate data. Where I would think that this causes a particular problem is in taking the derivitives in order to calculate velocity and acceleration. As you rightly point out, > The differences between cubic and quintic spline was shown very > clearly in Kit Vaughan's Ph.D. dissertation (University of Iowa, ca. 1981) > when he fit cubic and quintic splines to the vertical location data of a > free-falling ball. The quintic gave a beautiful fit, with acceleration very > near 9.81 m/s2 throughout the entire airborne period. The cubic forced > acceleration to be zero at the beginning and end of the data set, the curve > then overshot the 9.81 m/s2 value in the middle part of the trial; the whole > curve was distorted, so that acceleration was not near 9.81 m/s2 hardly > anywhere at all. This is hardly unexpected when taking derivitives. If you are only interested in position information, I might suggest (although I don't know for sure), that cubics would be more than adequate. My experience with higher order fits is that they tend to oscillate excessively. The oscillation tends to badly interpolate the original data. This may however, just be an artifact of very high order fits (>10 df say), I can't say for sure since I have not done any recently. > I have been using splines for about twenty years now, and my > experience tells me that quintic spline is excellent, but you don't want to > touch cubic spline with a ten foot pole! I guess what I am saying is that I don't think cubics are that bad if you are sticking to interpolation of position data alone. If you want to take derivitives, use a higher order interpolation, but watch out for artifacts on the positional interpolation. I'd appreciate any additional discussion on this, and will post replys sent to me. N. Glossop, Ph.D., Toronto, Canada From: "Beth Todd" Organization: College of Engineering > Jesus Dapena wrote in a recent summary about splines, > > I would advise you very strongly to stay away from CUBIC splines. > > Usually (always?) they force the second derivative to be zero at the > > beginning and end of the data set. When that is not the case in the > > activity being analyzed (i.e., almost always), the result is very distorted > > data in the early and late parts of the trial (and even the middle parts can > > get messed up too). > I am not sure how much I agree with this statement, and would ask for a > little feedback from list members. While it is true that cubic splines > force the second derivitives to be zero, cubics and piecewise cubics are > often used to interpolate data. Where I would think that this causes a > particular problem is in taking the derivitives in order to calculate > velocity and acceleration. When I taught a numerical methods course a couple of years ago, I taught the students that there were five different possible schemes for constraining the endpoints. (I'm not a mathematician, so there may be other methods that I'm not aware of.) These conditions are 1) Clamped cubic spline where the first derivatives are specified at the endpoints; this will give zero second derivatives. 2) Natural cubic spline; the endpoints are set to zero 3) The second derivatives are extrapolated to the endpoints. 4) The second derivatives are constant near the endpoints. 5) The second derivatives are specified at the endpoints. Not all of the endpoint contraints give zero second derivatives, and I was surprised when I read the message that you're commenting on. My reference is "Numerical Methods for Mathematics, Science, and Engineering", 2nd Ed., by John H. Mathews, Prentice Hall, 1992. > As you rightly point out, > > The differences between cubic and quintic spline was shown very > > clearly in Kit Vaughan's Ph.D. dissertation (University of Iowa, ca. 1981) > > when he fit cubic and quintic splines to the vertical location data of a > > free-falling ball. The quintic gave a beautiful fit, with acceleration very > > near 9.81 m/s2 throughout the entire airborne period. The cubic forced > > acceleration to be zero at the beginning and end of the data set, the curve > > then overshot the 9.81 m/s2 value in the middle part of the trial; the whole > > curve was distorted, so that acceleration was not near 9.81 m/s2 hardly > > anywhere at all. > This is hardly unexpected when taking derivitives. If you are only > interested in position information, I might suggest (although I don't know > for sure), that cubics would be more than adequate. My experience with > higher order fits is that they tend to oscillate excessively. The oscillation > tends to badly interpolate the original data. This may however, just be an > artifact of very high order fits (>10 df say), I can't say for sure since I > have not done any recently. As a rule of thumb, I told the students not to use a polynomial of order higher than 6 due to the excessive oscillations. I'm not exactly sure why I chose 6--must have been something that I read in Mathews' book. Beth Todd Dr. Beth A. Todd Assistant Professor Engineering Science and Mechanics Box 870278 University of Alabama Tuscaloosa, AL 35487-0278 fax: (205)348-7240 From: Dale.Knochenmuss@UC.EDU (Dale Knochenmuss) I agree that cubic splines can be fine to use as long as some thought is given to what you are doing and what you want from the data. For many applications, the most desirable way to fit a curve to data is to come up with a single equation that provides a reasonable approximation to the entire data set. When the set is long or complex, this is often not possible or computationally difficult. Segmental approaches (or splines) are then an alternative. They attempt to use a series of equations to fit the complete data set. Each equation fits just a portion of the data, but when you string them together end-to-end, you have a mathematical approximation to the entire data set. It becomes important for each equation to blend smoothly into the next since the physical process being approximated does not, typically, have discontinuities.. It is generally advisable to accomplish curve fitting with an equation, or equations, of the lowest possible order. This avoids the erratic behavior you mentioned that can result from higher order equations. Starting with the lowest possible order, an equation of order one has obvious limitations since so many kinds of data are nonlinear. Splines made up of linear equations also have the disadvantage that slopes don't match at the boundaries between equations so there will be discontinuities in the fit. Sets of second order (quadratic) equations can fit many types of data and can be calculated so that the slopes of adjacent equations match at the boundary. They cannot, however, guarantee that the curvature (second derivative) will match, thus causing discontinuities. Third order equations can be found which will match both slope and curvature at each boundary, eliminating discontinuities and providing a smooth fit. Splines made up of third order equations are therefore the lowest order which provide smooth fits through the first and second derivatives (slope and curvature). This is why cubic splines are often used for curve fitting. The problem, then, lies in how the beginning and end of the data set are handled. Jesus Dapena referred to forcing one or more of the derivatives to be zero at one or both ends. This makes sense only if the physical process being modelled is known to meet, or approximate, this condition at the beginning and/or of the test. The important point, I think, is that this is not the only option and should not be used if it is not appropriate. Referring to "Applied Numerical Analysis" by Curtis F. Gerald and Patrick O. Wheatley, Addison-Wesley Publishing, 4th edition, 1989, four options are suggested for handling end points: 1) Assume the end cubics are linear (Dapena's case) 2) Assume the end cubics approach parabolas 3) Linearly extrapolate from the nearest known data points 4) Assume fixed (but non-zero) values at the ends Gerald and Wheatley suggest option 4 as being reasonable if a derivative estimate is available. Referring to the example application of fitting curves to vertical location data of a free-falling object, if an analysis of the system being tested results in the conclusion that the acceleration is non-zero throughout the test, then it is obviously not a good idea to apply a curve-fitting routine which forces zero values at the beginning and end. If you know enough to make an estimate for the end points, a third-order fit might yield acceptable results. If the available knowledge of the system isn't sufficient to make an estimate, then it might be better to go with the higher order fit. I think you are correct in saying that third order (cubic) equations are likely to be sufficient if you are only going to be working with the positional data. This also provides a result with less computational effort and minimizes the risk of erratic results. Dale R. Knochenmuss University of Cincinnati Noyes-Giannestras Biomechanics Laboratories From: "Ton van den Bogert" I agree with your comments on cubic vs. quintic splines; I had almost sent a similar reply to Jesus Dapena's posting. In my experience, cubic splines are fine for 1st derivatives unless you have a large amount of smoothing which makes the boundary effects (cubic spline is straight line at the endpoints) extend too far. The oscillation problems with quintic splines that you mention only occur, as far as I have seen, when there are gaps in the data. As you say, interpolation can become very wild. For typical, regularly spaced data, the quintic spline gives essentially the same result as the cubic spline. Except the quintic spline is better at the endpoints, especially the 2nd Still, I tend to use cubic splines whenever I don't need a 2nd derivative. I guess that decision is based on saving computer -- Ton van den Bogert Human Performance Laboratory University of Calgary From: Victor Ng-Thow-Hing There are various formulations for basis functions of cubic splines that do different things. Catmull-Rom and Hermite both have the ability to interpolate points. Several spline segments are often used to fit data points. The most popular formulations like Bezier and B-spline can have some built in constraints for C1 and c2 continuity, but these can be circumvented by using tricks like multiple knots for B-splines. For higher degree splines, there is always the danger of greater instability with the curve shape (eg., unwanted oscillations), especially when fitting data. NURBS (non-rational uniform B-splines) also get around many problems and can represent a wide variety of shapes, such as cusps, and perfect In conclusion, I think cubic splines are very stable and useful. From: dapena@valeri.hper.indiana.edu It is possible that cubic spline data may be OK if you are only interested in location data, and not interested in getting derivatives. But getting merely *location* data seems to be a rather unusual final objective. And you will have to beware if you later on get derivatives from the cubic-spline smoothed data at any later point in the process, by whatever method. I have not used cubic spline for a very long time now, but my rough recollection is that the cubic did not oscillate any less than the quintic. (I am just writing from memory, an untrustworthy thing!) So I don't think the cubic provides any advantage. Jesus Dapena From: Glen Niebur Neil Glossop wrote: >Jesus Dapena wrote in a recent summary about splines, >> I would advise you very strongly to stay away from CUBIC splines. >> Usually (always?) they force the second derivative to be zero at the >> beginning and end of the data set. When that is not the case in the >> activity being analyzed (i.e., almost always), the result is very distorted >> data in the early and late parts of the trial (and even the middle parts can >> get messed up too). >I am not sure how much I agree with this statement, and would ask for a >little feedback from list members. While it is true that cubic splines >force the second derivitives to be zero, cubics and piecewise cubics are >often used to interpolate data. Cubic splines need not force a zero second derivative at the end points of the curve. This is only the case for "Natural" end conditions. Other end conditions are possible, such as clamped end conditions where we can apply a known first derivative. A more useful end condition is the "Quadratic" end condition which sets the second derivative at the final point equal to the second derivative and the next to last point at the 2nd derivative at the first point equal to the second derivative at the second point. For "reasonably" high sampling rates, this should be a good approximation. Another good choice is the "not a knot" end condition. This end condition will cause the first two segments and the last two segments to interpolate a single cubic curve. Finally, for cyclic events, you can specify that the second derivatives are equal at the first and last points. In summary, it isn't necessarily cubic splines which are bad, it is the common "natural" end condition implementation that isn't particularly appropriate to many problems. A good reference for spline interpolation is: Farin, Gerald, 1988, "Curves and Surfaces for Computer Aided Geometric Design," Academic Press Glen Niebur \| Mayo Clinic \| This space intentionally left blank. Biomechanics Lab \| gln@hercules.mayo.edu \|	{"url":"https://biomch-l.isbweb.org/forum/biomch-l-forums/biomch-l-1988-2010/3639-cubic-splines-summary-of-responses?view=thread","timestamp":"2024-11-04T17:25:31Z","content_type":"application/xhtml+xml","content_length":"66422","record_id":"<urn:uuid:bb27688d-e91f-4e57-a94b-db36d6c191c7>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00202.warc.gz"}
Negative is a term in mathematics that usually means "opposite." An electron's charge is called negative not because it is "below" but because it is opposite that of a proton. A surface with negative curvature bulges in from the point of view of someone on one side of the surface but bulges out from the point of view of someone on the other side. A line with negative slope is downhill for someone moving to the right but uphill for someone moving to the left. The term negative is most commonly applied to numbers. When negative is an adjective applied to a number or integer, the reference is to the opposite of a positive number. As a noun, negative is the opposite of any given number. Thus, -4, -3/5, and - √ 2 are all negative numbers, but the negative of -4 is +4. The integers, for example, are often defined as the natural numbers plus their negatives plus zero. Sometimes the word opposite is used to mean the same as the noun negative. Technically, negative numbers are the opposites with respect to addition. If a is a positive number then -a is a negative number because: a + (-a) = 0. Allowing numbers and other mathematical elements to be negative as well as positive greatly expands the generality and usefulness of the mathematical systems of which they are a part. For example, if one owes a credit card company $150 and mistakenly sends $160 in payment, the company automatically subtracts the payment from the balance due, leaving -$10 as the balance due. It does not have to set up a separate column in its ledger or on its statements. A balance due of -$10 is mathematically equivalent to a credit of $10. When the Fahrenheit temperature scale was developed, the starting point was chosen to be the coldest temperature which, at that time, could be achieved in the laboratory. This was the temperature of a mixture of equal weights of ice and salt. Because the scale could be extended downward through the use of negative numbers, it could be used to measure temperatures all the way down to absolute The idea of negative numbers is readily grasped, even by young children. They usually do not raise objection to extending a number line beyond zero. They play games that can leave a player "in the hole." Nevertheless, for centuries European mathematicians resisted using negative numbers. If solving an equation led to a negative root, it would be dismissed as without meaning. In other parts of the world, however, negative numbers were used. The Chinese used two abaci, a black one for positive numbers and a red one for negative numbers, as early as two thousand years ago. Brahmagupta, the Indian mathematician who lived in the seventh century, not only acknowledged negative roots of quadratic equations, he gave rules for multiplying various combinations of positive and negative numbers. It was several centuries before Euopean mathematicians became aware of the work of Brahmagupta and others, and began to treat negative numbers as meaninful. Negative numbers can be symbolized in several ways. The most common is to use a minus sign in front of the number. Occasionally the minus sign is placed behind the number, or the number is enclosed in parentheses. Children, playing a game, will often draw a circle around a number which is "in the hole." When a minus sign appears in front of a letter representing a number, as in -x, the number may be positive or negative depending on the value of x itself. To guarantee that a number is positive, one can put absolute value signs around it, for example \|-x\|. The absolute value sign can also guarantee a negative value, which is -\|x\|. Additional topics	{"url":"https://science.jrank.org/pages/4579/Negative.html","timestamp":"2024-11-10T15:34:05Z","content_type":"text/html","content_length":"10745","record_id":"<urn:uuid:629ed8b9-fc9b-4d95-b329-7cf6f39d8c42>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00272.warc.gz"}
Using landslide-inventory mapping for a combined bagged-trees and logistic-regression approach to determining landslide susceptibility in eastern Kentucky, USA High-resolution LiDAR-derived datasets from a 1.5m digital elevation model and a detailed landslide inventory (n≥1000) for Magoffin County, Kentucky, USA were used to develop a combined machine-learning and statistical approach to improve geomorphic-based landslide-susceptibility mapping. An initial dataset of 36 variables was compiled to investigate the connection between slope morphology and landslide occurrence. Bagged trees, a machine-learning random-forest classifier, was used to evaluate the geomorphic variables, and 12 were identified as important: standard deviation of plan curvature, standard deviation of elevation, sum of plan curvature, minimum slope, mean plan curvature, range of elevation, sum of roughness, mean curvature, sum of curvature, mean roughness, minimum curvature and standard deviation of curvature. These variables were further evaluated using logistic regression to determine the probability of landslide occurrence and then used to create a landslide-susceptibility map. The performance of the logistic-regression model was evaluated by the receiver operating characteristic curve, area under the curve, which was 0.83. Standard deviations from the probability mean were used to set landslide-susceptibility classifications: low (0–0.10), low–moderate (0.11–0.27), moderate (0.28–0.44), moderate–high (0.45–0.61) and high (0.62–1.0). Logistic-regression results were validated by using a separate landslide inventory for the neighbouring Prestonsburg 7.5-minute quadrangle, and running the same regression function. Results indicate that 74.9% of the landslide deposits were identified as having moderate, moderate–high or high landslide susceptibility. Combining inventory mapping with statistical modelling identified important geomorphic variables and produced a useful approach to landslide-susceptibility mapping. Supplementary material: The statistical data used in the combined machine-learning functions are available at https://doi.org/10.6084/m9.figshare.c.5351313.v3 Thematic collection: This article is part of the Digitization and Digitalization in engineering geology and hydrogeology collection available at: https://www.lyellcollection.org/cc/ Landslides occur frequently in eastern Kentucky, an area characterized by valleys deeply incised into flat-lying Carboniferous sedimentary rocks along the western margin of the Appalachian Basin of the eastern USA; direct costs are conservatively estimated to be between $US10 million and $US20 million annually (Crawford 2014; Crawford and Bryson 2017). These costs result from damage to roads, residences and other infrastructure. Indirect costs such as road closures, utility interruption and decreased property value are also significant, but challenging to quantify. Landslides in eastern Kentucky are primarily triggered by rainfall and occur in shallow (<3m) colluvial soils; major factors contributing to slope instability include steep slopes, weak bedrock, variable soil characteristics and development on hillslopes (Outerbridge 1987; Crawford 2014). Proactive efforts to assess landslide susceptibility are lacking, however, and needed for mitigation and risk-informed resources in affected communities. Landslide susceptibility is defined as the relative tendency or potential for slope movement in a given area (Guzzetti et al. 2006; Highland and Bobrowsky 2008; Hearn and Hart 2019). A landslide-susceptibility map classifies or ranks slope stability in categories based on relationships of factors that contribute to instability, as opposed to a hazard map, which may indicate elements of time or estimated landslide extent (National Research Council 2004; Highland and Bobrowsky 2008). Susceptibility modelling typically is conducted using one of two approaches: (1) physics-based methods, which use probabilistic or deterministic models incorporating geological and geotechnical variables to derive a slope-stability assessment; and (2) geomorphic-based statistical methods, which model slope conditions that influence landslide occurrence (Formetta et al. 2014; Reichenbach et al. 2018). One limitation of physics-based approaches, particularly at a regional scale, is that they require specific knowledge of soil properties, hydrological conditions and geotechnical inputs into slope-stability models. These data are typically not available on a regional basis or at the catchment scale, as is the case in this study. Geomorphic-based susceptibility modelling focuses on slope morphology, the quality of which is dependent on data accuracy and resolution of terrain models. The availability of aerial light-detection and ranging (LiDAR) data, used to generate terrain models, allows landslides to be identified at a level of detail not possible with lower-resolution digital elevation models (DEMs) or traditional topographic maps (Burns et al. 2010). Landslide features such as headscarps, flanks, toes and distinct hummocky terrain are often easily observed in LiDAR-derived data (Schulz 2007; Crawford 2012; Jaboyedoff et al. 2018). LiDAR-derived map datasets consist primarily of DEMs, and their derivatives, such as hillshades, slope, aspect, curvature and roughness. The purpose of this study is to establish a reliable framework for assessing landslide susceptibility at a regional scale using a statistics and geomorphic-based approach. We have advanced this approach by using a robust landslide inventory and by combining two traditionally distinct machine-learning methods that complement each other to produce a final susceptibility map. We mapped landslides in Magoffin County, Kentucky; compiled geomorphic statistics for each slide; determined geomorphic variable importance with bagged trees, an ensemble decision-tree machine-learning technique; and then used those variables in a logistic-regression model. Logistic-regression results were validated by using a separate landslide inventory for the neighbouring Prestonsburg 7.5-minute quadrangle. We further analysed the logistic-regression results by plotting kernel-density estimations of the individual geomorphic variables and their predicted probability of influencing landslide occurrence. A focused field-based approach is often impractical due to a scarcity of expenses and time, lack of land access and the effort needed to create, or field check, a statistically robust (n=1000) landslide inventory. Our intent is not to dismiss the importance of direct field-based observations or expert knowledge in determining landslide susceptibility, but to demonstrate that this statistical, geomorphic-based approach can be applied in other environments and support expert (but often subjective) knowledge. High-resolution elevation data and their derivatives provided an opportunity to take advantage of specific geomorphic conditions, many of which are related to bedrock geology and influence landslide occurrence. These high-resolution datasets, coupled with detailed landslide-inventory mapping, allowed us to produce accurate and detailed landslide-susceptibility maps. These maps are particularly important because existing landslides are often susceptible to reactivation, which makes modelling the probability of occurrence and developing a susceptibility map with logistic regression a practical approach (Cruden and Varnes 1996; Crawford 2014). A shift toward reliable data-driven methods that convey hazard information is critical to assist those needing to avoid areas of potential slope instability. Although determining landslide susceptibility has inherent uncertainty, several studies comparing statistical techniques (Akgun 2012; Felicisimo et al. 2012) indicate that logistic regression, based on receiver operating characteristic (ROC) curves, outperforms other machine-learning techniques (such as likelihood ratio models, entropy-based analysis, multi-criteria decision analysis, and classification and regression trees) and that a combination of techniques can strengthen accuracy and reliability. As opportunities to navigate GIS, machine learning and statistical analysis increase, this multifaceted approach can be reliably used by researchers and stakeholders with access to LiDAR and map-based landslide inventories. Understanding the slope-geomorphology variables that are most important to landslide occurrence can support susceptibility mapping, inform stakeholders of planning and mitigation strategies, and ultimately reduce risk. Geological setting Magoffin County and the Prestonsburg quadrangle are in the Eastern Kentucky Coal Field, part of the larger central Appalachian Basin (Fig. 1). The county and quadrangle areas are 800.5 and 152.9km^ 2, respectively. Topographic relief can be as much as c. 228m and the mean slope is 24.5°. The landscape is highly dissected, characterized by narrow ridges and sinuous alluvial valleys. Deeply incised stream drainages and variable hillslope morphologies range from long and narrow to bowl-shaped tributary valleys. Bedrock comprises flat-lying complex sequences of Carboniferous (Pennsylvanian) sandstones, siltstones, shales, coals and underclays (McDowell 1986; Greb et al. 2009). The hillslope morphology viewed in a LiDAR-derived hillshade model is often a good indicator of underlying bedrock geology, indicating the connection between bedrock and slope characteristics. For example, the more resistant lithologies, such as sandstones and siltstones, are often associated with steeper slopes and thinner soil cover. Shale beds, coals and underclays weather easily and are known to be associated with high landslide occurrence (Crawford 2014; Chapella et al. 2019). Slopes are mantled with colluvium of varying thickness, and mass wasting is a dominant process, moving soil and rock downslope by creep, sheetwash, landslides and debris flows (McDowell 1986). The colluvial soil is generally fine to coarse loam, typically poorly sorted, with grain sizes that range from clay to medium-coarse boulders perhaps a metre in diameter (Blair and McPherson 1999). The Unified Soil Classification System classifies the soils in Magoffin County as fine silts and clays (CL and ML), as well as sands mixed with fines (SM) (Kentucky Division of Geographic Information 2020; kygeonet.ky.gov/kysoils). Colluvium transport downslope and its velocity range from imperceptible (creep) to rapid (catastrophic). Landslides that occur in colluvium are commonly thin (<3m) translational slides or thicker rotational slumps, but both types have the capability of developing into damaging debris flows or debris slides, especially on steep slopes (Fleming and Johnson 1994; Turner 1996; Crawford 2014). Landslide-inventory mapping Landslide extents were primarily mapped by visual inspection of a multidirectional hillshade (Nagi 2014) derived from a 1.5m LiDAR DEM. Secondary maps of slope, roughness, curvature, plan curvature, contour and traditional hillshade, as well as aerial photography, were used to help identify landslide features and constrain confidence in mapping deposit extents. Extents of landslides that included features such as headscarps, flanks, toe slopes and hummocky topography were digitized as GIS polygons. A tiling scheme of c. 1500×1500m was used in the GIS to keep track of mapped areas. Initial inspection of the hillshade landscape was at a scale of 1:3000 and digitizing was zoomed to smaller scales. In order to consistently capture each landslide, the polygon included headscarps, flanks and toe slopes. For example, the upper boundary of a landslide polygon was traced across the crown of the slide, slightly above the vertical displacement of the headscarp. A total of 1054 landslides were mapped in Magoffin County and a range of sizes and shapes was documented (Fig. 2). The mean landslide area was c. 6397m^2, with most of the landslides less than 25000m^2 ( Fig. 3). Generally, for translational colluvial landslides, the distance to length ratio is less than 0.1 and, for rotational slides, the depth to length ratio is 0.3 to 0.1 (Highland and Bobrowsky 2008). An inspection of the landslide inventory does reveal a consistent relation to area; however, we do not know if this relationship is a proxy for volume or magnitude. Although the small to moderate-size landslides and their shapes could infer landslide type, the age or potential behaviour was not determined. With over 1000 landslides identified, additional investigations that incorporate age, landslide behaviour and runout potential would be extremely time intensive. We used a confidence rating system based on methods developed by the Oregon Department of Geology and Mineral Industries, which qualitatively describes a confidence that a landslide was interpreted correctly, determined by the clarity of features visible in remotely sensed data (Burns and Madin 2009). The rating number from 0 to 10 is based on ranking four landslide features (headscarps, flanks, toe slopes and hummocky terrain); zero is unidentifiable and 10 is clearly identifiable in the LiDAR hillshade (Table 1). If the secondary maps were used, then a higher or lower ranking was issued accordingly (Chapella et al. 2019). An overall numerical confidence ranking from 0 to 40 was assigned by the landslide mapper. Of the 1054 landslides mapped, 1.3% were considered low confidence (≤10), 44.2% as moderate confidence (11–29) and 54.4% as high confidence (≥30). A landslide width and axial length of c. 20m was used as the threshold for mapping, because landslides smaller than these dimensions are typically stream-bank collapses or roadway-embankment failures. These smaller landslides, although important, often have a different mode of failure controlled by different geomorphic parameters. This added complexity would reduce overall model effectiveness; thus, we did not consider them. Geomorphic variables and statistics compilation Because of the large project area and because LiDAR-derived DEMs show significant detail in the landscape, we needed to modify raster datasets because of limitations in computing power and file size. In addition, selecting the right cell size for a DEM should be guided by the scale of mapping and the original resolution of the data (Fressard et al. 2014). Therefore, the 1.5m DEM was resampled to 3m cells. Geomorphic maps of elevation, slope, terrain roughness, curvature, plan curvature and aspect were then generated from the resampled DEM using a radial smoothing window of c. 15m to reduce noise (Table 2). To obtain consistent geomorphic statistics, a circular buffer was generated around the centroid point of each mapped landslide (Fig. 4). The landslide extent may, depending on the size and shape of the landslide, fall outside the buffer polygon. A buffer polygon that represents most of the landslide extent is superior to a single point in accounting for variability in landslide characteristics, however (Timilsina et al. 2014; Raja et al. 2017). The buffers for all 1054 landslides were used to extract six statistical variables from each of the six geomorphic maps (Table 3). This process resulted in 36 individual statistical values for each landslide (maximum, minimum, range, mean, standard deviation and sum of values within each buffer for each map – e.g. slope map). The buffer created for all mapped landslides had an area of 6648m^2 (radius of 46m), which is the average area of the 1054 inventoried landslides. We tested buffer radii of c. 15, 30, 46 and 61m to determine which was the most effective, and the bagged-trees model accuracy tests supported the 46m radius (see ‘Susceptibility-map variable determination’ section). Although there is some co-dependence between variables, we argue that starting with an abundant number of variables increases the probability of capturing the strongest correlations and will produce better model accuracy and a smoother, more realistic map. Several additional variables were considered for determining landslide susceptibility, but ultimately not included. Bedrock geology was not used primarily because, although lithology varies, the mapped geology is reasonably uniform across the county. Geological formations across Magoffin County, as well as most of eastern Kentucky, are mapped as similar packages of sedimentary rocks that include thin to thick beds of variable lithologies. In general, weaker lithologies, such as shales, coal beds and underclays, influence landslide activity (Crawford 2014; Chapella et al. 2019). Many of these problematic lithologies are not mapped separately, however, and at the scale of landslide susceptibility mapping would not be reliable for a statistical model. In addition, for the landslides that we mapped in Magoffin County, there is no correlation between landslide deposits and mapped geological formations. The landslides that occur within each formation (some slide extents straddle multiple formations) are consistent with the percentage area that the formation covers, and the clusters of landslides generally correlate with areas of steeper slopes. The hillslope statistics compiled in this study do reflect underlying bedrock geology to some extent, but a more in-depth investigation that correlates geological formations and lithology would require a larger inventory to determine a reliable influence of one formation over another, and is beyond the scope of this study. Therefore, we treated the mapped bedrock geology as a constant across a county scale. The modelling approach presented here would work equally well in an area where bedrock geology needs to be accounted for and detailed lithology is available as a model input. Soil erodibility was also not considered. This index classification is based on a measure of a soil's sensitivity to the effects of rainfall and land use, developed by the Natural Resources Conservation Service. The drawback to using soil erodibility is that the soils data have a broad distribution across landforms, and differences in county boundaries can lead to spurious map results. Hillslope erosional potential was also excluded. It is defined as the product between mean annual precipitation and slope angle (Mitchell and Montgomery 2006). Adding rainfall data could be useful, but we did not have confidence in hillslope erosional-potential maps because of the coarseness of the rainfall data and the challenge of using a single, averaged dataset as a proxy for stream power and discharge; it does not reflect reality and would limit the usefulness of the final map result. To prepare data for bagged-trees and logistic-regression models, statistical data for non-landslide areas are required for the creation of a dependent variable called the indicator (1 or 0). Non-landslide areas must also have comparable buffer shapes so that contrasting feature statistics can be gathered. The same procedure (using a 46m radius buffer) was followed to generate geomorphic statistics for the non-landslide areas as for landslide areas (Fig. 3). An equal number of landslides (1) and non-landslides (0) is required for an equal class-distribution ratio, which helps to eliminate class bias (Dai and Lee 2002; Oommen et al. 2010; Gupta et al. 2019). The buffers were inspected for overlap between non-landslide areas and landslide areas and culled accordingly. Significant overlap dictated that 123 buffers be eliminated in order to maintain an equal number of random non-landslide and landslide statistics. Table 4 is an example subset of the entire 36-variable dataset, showing slope values for landslides and non-landslides. These statistics, plus the indicator variable, make up a binary dataset used in the bagged-trees and logistic-regression Susceptibility-map variable determination Two machine-learning methods were used to determine model input variables for the landslide-susceptibility map: an ensemble bagged-trees classification and binary logistic regression. The bagged-trees approach was used to elucidate the variables in the logistic-regression model and is a reliable first pass at variable importance, effective for remotely sensed geophysical data. Bagged trees predicts a weighted classification using the indicator variable to return an approximation of variable importance (Breiman 2001; Meinshausen 2006; Zhu and Pierskalla 2016; Dou et al. 2019). The technique is called ‘bagged trees’ because it combines statistical results of many individual decision trees in order to improve model performance and reduce model overfitting (Mathworks 2019b; https://www.mathworks.com/help/stats/treebagger-class.html). Generally, the bagged-trees algorithm aggregates a set of decision trees to get a single decision tree to rank feature importance. Bagged trees has been previously used to successfully prepare data for landslide-susceptibility mapping, often resulting in high model accuracy and sensitivity values compared to other machine-learning methods (Cracknell and Reading 2014; Youssef et al. 2015; Chen et al. 2018; Chang et al. 2019; de Oliveira et al. 2019; Dou et al. 2019). Logistic regression models the probability of an event (a landslide) being a function of other variables, and quantifies probability based on statistical analysis of past landslides (Atkinson and Massari 1998; Dai and Lee 2002; Mathew et al. 2009; Bai et al. 2010; Fressard et al. 2014; Timilsina et al. 2014; Raja et al. 2017; Lombardo and Mai 2018; Reichenbach et al. 2018; Chang et al. 2019). It uses a logistic function to model a dependent variable: It is simply a nonlinear transformation of the linear regression. Since the geomorphic dataset contains the statistical information on presence or absence of a landslide, the results are log-odds for the value labelled ‘1’ (landslides), which is a combination of one or more of the independent variables (Dai and Lee 2002; Suzen and Doyuran 2004; Bai et al. 2010). The value predicted is a probability of an event ranging from 0 to 1 – i.e. an estimate of the maximum likelihood that a landslide will be influenced by the statistics of observed independent variables. Bagged-tree classification guides the logistic-regression analysis, supporting variable selection, determining variable importance and reducing logistic-regression input variables, which avoids overcomplexity for the susceptibility map (Lu and Weng 2007; Lombardo and Mai 2018). Decision-tree techniques rank relative importance regarding influence on landslide occurrence; however, logistic regression indicates which modelled relationships are statistically significant and the nature of those relationships. Modelling the likelihood of landslide occurrence via equations in a regression analysis thus complements the initial bagged-tree classification. For an initial insight into variable determination, the MATLAB Classification Learner application (Mathworks 2019a; https://www.mathworks.com/help/stats/classificationlearner-app.html) was used to train the bagged-trees and logistic-regression models, classify the data and determine an overall model accuracy, and ultimately validated the use of the c. 46m buffer radius (Table 5). Classification Learner does not run the specific model functions; rather, it serves as a guide for the optimal landslide and non-landslide buffer-size determination. For each of the four variable buffer radii, separate surface-roughness smoothing windows were tested, which yielded 20 distinct possible combinations (Table 6). Terrain roughness was calculated separately because of its dependence on scale of the DEM, as well as scale of the landscape (Berti et al. 2013; Korzeniowska et al. 2018). Smoothing was performed using the Focal Statistics tool in a GIS, which computes a neighbourhood operation generating an output raster where value of the cells is a function of input cells in a specified neighbourhood. The roughness smoothing window of c. 38.1m performed the best, coinciding with the buffer radius of c. 46m. We also included a roughness index map, which is an index of the highest return from all roughness smoothing windows for each pixel (Lindsay et al. 2019 ). Results from Classification Learner include an overall model accuracy (percent), 2D scatter plots of the landslide geomorphic variables based on indicator response (Fig. 5), a confusion matrix and assessment of model performance. The model performance was judged with the overall accuracy and confusion matrices, which measure overall quality and separateness of classes in the dataset. The plots can also guide decisions on inclusion or exclusion of geomorphic variables for modelling. The overall model accuracy of 83.3% for bagged trees was higher than or equal to other machine-learning algorithms used in the Classification Learner, such as Nearest Neighbor Classification, Discriminant Analysis, Naïve Bayes, Decision Trees and other Ensemble models. Ensemble bagged-trees function results After determining that the c. 46m radius for the landslide buffer and a c. 38.1m smoothing window for terrain roughness were optimal for overall model accuracy, the full bagged-trees function was performed. The binary landslide data were divided into training (75%) and test (25%) datasets. The bagged-trees model estimates feature importance from the entire statistical dataset of 36 geomorphic variables. Feature importance is a prediction of relative importance based on the combination of statistical variables. During the tests using numerous variables, a threshold of feature importance of 0.8, just slightly above the average of 0.73, was a consistent mark of separation to choose the important variables (Fig. 6a). The performance of the bagged-trees function was validated using the ROC, area under the curve (AUC), which was calculated in the test dataset as 0.90 (Fig. 6b). The ROC plots the sensitivity (true positives) v. specificity (false positives) and summarizes the model performance across all decision thresholds within the binary data (Felicisimo et al. 2012). Based on the feature importance scores, 12 variables were selected for regression analysis (Table 7). The only variable with a high importance score that was not used in the regression analysis was range of curvature. The range-of-curvature raster map inconsistently highlights heavily modified parts of the landscape, skewing the realistic results of a landslide-susceptibility map. Logistic regression The bagged-trees result of 12 important variables was used in the binary logistic-regression model. We used JMP Pro statistical software package (SAS Institute Inc.) to conduct the logistic-regression analysis. The indicator (response) variables, the 1s and 0s, are a nominal modelling type because we made no assumptions about the data and wanted a multilevel logistic response that models the binary data and fits a probability of predictor variable value of 1. Logistic-regression results derive a coefficient of responses ($β$ values) and determine which variables are significant (p-values). Low p-values indicate the data are unlikely to support a lack of difference; i.e. low p-values (<0.05) are relevant additions to the model because they are related to changes in the indicator variable, a rejection of the idea that there are no relationships in the binary data. In logistic regression, when the indicator variable is attributed (0, 1), the nominal response is: is the constant intercept, is the geomorphic variables and is the coefficient estimates of responses in the indicator variable. The coefficients express the effects of the predictor independent variables on the relative risk of being a landslide or not a landslide, which increases or decreases with each value of the independent variable – i.e. the rate of change in log-odds as Equation (1) can also be written as: is total contribution of all predictor variables, a model of relative risk of features in the landscape being a landslide or not a landslide. The cumulative distribution logistic function is: is the cumulative estimated output probability of an event occurring (landslide occurrence or non-occurrence). The output is confined between 0 and 1. We assumed the variables were not normally distributed or did not have linear relationships ( Suzen and Doyuran 2004 Nandi and Shakoor 2009 ). Therefore, the logistic-regression analysis worked well because the primary unknown was the relationship among the variables. Results and landslide-susceptibility map Bagged-tree analysis on all 1862 records (total binary dataset minus overlapping buffers) identified 12 variables as being important (>0.8 threshold). We conducted logistic regression on the 12 variables and found that eight geomorphic variables were significant (p-value ≤0.05; Table 8). The four excluded variables were found to be redundant in the regression correlation, and removing them had negligible effect on AUC and overall accuracy. Table 8 also shows the LogWorth (–log[10] (p-value)), which is a transformation of the p-value and a way to visualize the relative weight of each variable. The higher the significance, the higher the LogWorth. We evaluated the performance of the logistic-regression model with the AUC, which was 0.83 (Fig. 7). The logistic-regression results were put into equation (2) and the logistic-model probability was calculated with equation (3) to create a susceptibility map. $z=(β0)+(β1)Smin+(β2)Cmin+(β3)Estd+(β4)Er +(β5)PCstd+(β6)Rm+(β7)Rs+(β8)Cstd$ Equation (4) shows each variable coefficient ($β$) multiplied by the associated geomorphic variable raster map and summed. The results from equation (4) were put into equation (3) in order to generate probability of landslide occurrence for Magoffin County. The mean probability value for the county is 0.28±0.17 standard deviation, whereas the mean probability value for the mapped landslides is 0.39±0.15 standard deviation (Fig. 8). The logistic-regression results show a connection between specific landslide morphologies, which indicates a certain probability of landslide occurrence. The logistic-regression model produced a landslide-susceptibility map indicating where landslides are likely to occur based on the geomorphic conditions. The map strikes a good balance between indicating existing deposits that have a moderate to high probability of subsequent movement, as well as assessing other parts of the slope that do not necessarily show obvious slope movement but may have features related to existing landslide activity. The majority of the flat alluvial valley bottoms were not considered in the analysis. Selected landslides mapped in Magoffin County, draped on the susceptibility results, are shown in Figure 8. Five landslide-susceptibility classifications were determined manually by creating breaks of standard deviations from the mean (Table 9). The percentage of the mapped landslide deposits that were moderate, moderate–high and high are 41.2, 26.6 and 6.4%, respectively. As for the susceptibility classifications of the entire county area, 24.5% are classified as moderate, 12.9% as moderate–high and 4.6% as high, i.e. 42% of the entire county is classified as having moderate, moderate–high and high landslide susceptibility. Overall, the map emphasizes steep hillslopes and parts of ridgetops as having moderate, moderate–high or high susceptibility. Steep slopes just below ridgetops and steep heads of catchments (often existing headscarps) are modelled as having moderate–high and high susceptibility. Steep planar slopes that are the sides of catchments or are above roads and streams are modelled as having moderate and moderate–high susceptibility. The map shows significant susceptibility differences between the western part of the county, where relief and slope angle are generally less, and the east, where slopes are steeper (Fig. 9). Figure 9b shows large planar sloped areas, as well as the heads of catchments, which are classified as having higher susceptibility compared to that shown in Figure 8a. The heads of catchment drainages in Figure 9b also indicate larger areas of moderate–high or high susceptibility compared to Figure 9a in the western part of the county. The susceptibility map does not determine landslide type, potential extent or runout, or temporal implications. To further illustrate the logistic-regression results, we plotted kernel-density estimations of the predicted probability of landslides for each variable (Fig. 10). Kernel-density estimation is a statistical technique that finds a balance between underfitting and overfitting of data in order to better visualize the results (Mathworks 2019c; https://www.mathworks.com/help/stats/ kernel-distribution.html). A kernel density algorithm takes a bandwidth from bins of datapoints to control the smoothness of the estimation (Bowman and Azzalini 1997). The predicted probability of a landslide for each variable and its relationship to 2D Gaussian kernel-density estimation (Fig. 10) aids in interpretation of the physical process implied by the regression results, particularly for associations and uncertainty among investigated variables. For example, as opposed to looking strictly at specific points of predicted probabilities of landslides (white dots), we can view landslide occurrence as joint-probability density within a range of values. The stretched colour ramp in Figure 10 is easier to interpret than the cluster of points; it constructs a view that accurately reflects relative likelihood instead of interpreting the random points. In general, the kernel density estimation patterns of predicted probability highlight the complexity among variables that influence slope stability. More specifically, mean roughness, minimum curvature, standard deviation of plan curvature and standard deviation of curvature have clusters of higher kernel-density estimates (lighter colours) that correlate with low predicted probabilities of landslides; as the density values expand, the predicted probability of a landslide occurrence increases. This correlation perhaps suggests a low dependency on probability, or is an indication that these clusters of landslides may correlate with low predicted probability, even though these geomorphic variables are significant to landslide occurrence in the regression model. Although minimum slope, standard deviation of elevation, range of elevation and sum of roughness do not indicate a specific cluster, the high values of kernel densities are stretched vertically along most values of predicted probability (Fig. 10). This suggests that the ranges of minimum slope, standard deviation of elevation, range of elevation and sum of roughness values that fall within the high kernel-density areas are perhaps more significant than the other variables because of the range of probabilities of Model validation and limitations In order to validate the logistic-regression methodology, we compared the results to a separate inventory dataset of 370 landslides that were mapped in the Prestonsburg 7.5-minute quadrangle. The same methodology for landslide inventory described in this paper was used to identify the landslides in the Prestonsburg quadrangle (Chapella et al. 2019). The resulting geomorphic variables (minimum slope, minimum curvature, standard deviation of elevation, range elevation, standard deviation of plan curvature, mean roughness, sum of roughness and standard deviation of curvature) from the same logistic-regression model (equations (3) and (4)) were used to create a landslide-susceptibility map of the Prestonsburg quadrangle. For the Prestonsburg quadrangle landslides, 74.9% of the deposits were in the moderate, moderate–high or high landslide-susceptibility classifications (Table 10, Fig. 11). Approximately 43% of the quadrangle area is classified as moderate, moderate–high and high susceptibility. The moderate–high and high classes (0.53–1.0) make up 18.5% of the quadrangle. The success of the logistic-regression model in Magoffin County and neighbouring Prestonsburg seems to indicate that the statistical analysis using a more encompassing polygon buffer to extract the geomorphic variables is necessary, as opposed to the often-used general value generated from a point. The landslide buffer of 46m used to extract the geomorphic statistics and generate the variables results in some artefacts in the susceptibility results, however. Because we used a circular buffer and smoothing window, roughly circular artefacts are present in some areas of the resulting map ( Fig. 12). This occurs most often with heavily modified parts of the landscape, where there are sharp unnatural breaks between steep slopes and flat, modified ground. Data preparation for determining geomorphic variables used in statistical landslide-susceptibility modelling varies significantly from study to study because there are no standard guidelines or procedures (Reichenbach et al. 2018). In statistical models that explain the probability of landslide occurrence, the selection of geomorphic variables used as model inputs is often based on subjective assumptions about the relationships between variables (Guzzetti et al. 1999; van Westen et al. 2003, 2008; Timilsina et al. 2014). Similarly, the weights applied to variables that are considered important in expert, knowledge-driven approaches are often assigned with bias (Thiery et al. 2014). Therefore, clarity regarding methodology, constraint of the uncertainties that influence landslide occurrence, and the landslide-susceptibility map output is important for the end user (Hearn and Hart 2019). A challenging part of the machine learning, statistics-based approach is recognizing the sensitivity of model inputs to the results and what implications that may have on the ground and with landslide processes. Different methods such as using a point instead of a buffer, or adding other variables (like geology) would certainly generate different results. However, we consider the advantage of this approach is that it is easy to use and repeatable, which is important for establishing methods or a workflow in other areas. Considering buffers or a point feature that can extract different parts of the slope could be a next step in our approach. For example, a buffer that captures areas just around the headscarps, crowns or toe bulges might prove to be a strong model performance and give insight into landslide initiation. The geomorphic variables in our models reveal a complex relationship between the slope morphology and type of landslide. Our approach takes advantage of the data-driven machine learning technique to elucidate variables that expert knowledge cannot, allowing the algorithms to shed light on relationships of individual variables. For example, we do not know specific connections between mean roughness and mean plan curvature to landslide processes on the ground, but Figure 5 shows high-quality accuracy and separateness of variables and consideration of further investigation of slope processes and causal factors. The bagged-trees results show that seven of the twelve ranked variables are a statistical category of curvature. The ranked importance of curvature indicates connections on the ground related to colluvial soil heterogeneity, colluvial thickness, variable pore-water pressure response, and shear strength variability at different slope positions. Although these connections to the ground and slope processes need further evaluation, the results indicate the importance of concavity, convexity, erosion and water flow. Geomorphic analysis on landslide occurrence has long been focused on landslides preferentially beginning in topographic hollows (concave slopes), and many do, but there are also conditions under which landslides may occur on planar or even convex slopes (Dietrich et al. 1986). Bagged trees ranked standard deviation of plan curvature highest, which may suggest plan curvature does an effective job of subdividing a hillslope into regions such as hollows, noses and planar, therefore, controlling convergence or divergence of landslide deposits and groundwater (Ohlmacher 2007). Further supporting the importance of the bagged-trees results, three curvature variables remained in the logistic regression results as being statistically significant. Gathering an understanding of these relationships is one of the reasons we included the kernel-density figures. Figure 10 shows relationships with a broad spectrum of correlations, guiding further investigation that can assess correlations on the ground with landslide processes. Our logistic regression results show that minimum slope is ranked as most significant (has the lowest P-value) and representative of a null hypothesis that we reject. The null hypothesis here being each independent variable has no effect. Minimum slope being significant makes sense because slope is such a well-established influencing factor regarding stability and landslide activity. Landslides need to exceed some angle for failure and, fundamentally, we are rejecting the notion of minimum slope having no effect landslides. Despite the shortcomings and limitations of statistical geomorphic-based methods, rapidly changing remote-sensing technologies (availability of LiDAR and high-resolution aerial photography), GIS software capabilities and growing landslide inventories all provide opportunities to improve landslide-susceptibility modelling. Statistical approaches to modelling landslides (e.g. tree-based analysis, logistic regression, support vector machine, weight of evidence, principal component analysis etc.), variable selection techniques and model evaluation typically generate reasonable model performance and accurate maps (Reichenbach et al. 2018; de Oliveira et al. 2019). Many of these techniques are quite complex for a binary dataset such as presented here and are typically more suitable for more difficult statistical problems related to complex remote-sensing data. This study does not necessarily reveal complex features or complex remotely sourced data; however, the relationship among these features regarding slope stability is complex, and classification decision trees coupled with logistic regression proved effective for predicting discrete variables. Generally, using GIS datasets and binary statistical data, a combination of temporal and random spatial strategies are used to validate model performance. We conducted a spatial validation by separating training (75%) and test (25%) datasets for the bagged-trees function, as well as applied the logistic-regression function to a different area. A temporal validation was not considered because only a single generation of LiDAR data was generated for the study area. For performance evaluation, Reichenbach et al. (2018) found that 38.2% of studies used one metric and 32% used no metric. The most common quantitative evaluation metrics were success rate curves, ROCs, landslide-density frequency and a general confusion matrix. Oommen et al. (2010) indicated that ROC–AUC is a more robust and consistent measure of model performance compared to other metrics such as area under precision recall curves and F-score. Recent landslide-susceptibility studies that used logistic regression, a similar DEM resolution to generate datasets and AUC to determine model performance had a range of 0.81 to 0.91 for the AUC (Mathew et al. 2009; Nandi and Shakoor 2009; Raja et al. 2017; Lombardo and Mai 2018; Chang et al. 2019). The AUC for the logistic-regression results in this study is 0.83, which is less than the 0.90 from the bagged-trees method; however, the combined machine-learning approach narrows variable selection and properly uses each model's function for the creation of susceptibility maps. The uncertainty regarding the final variable relationships with the ground surface and the implications for landslide susceptibility and risk is also a challenge. However, our map results and distribution of higher probabilities (moderate, moderate–high, high) effectively reflect the geomorphic variables that are indicative of unstable ground conditions and potential landslide activity. A robust landslide inventory, quality DEMs and relevant derivative maps allowed us to establish a reliable framework for assessing landslide susceptibility at a regional scale using a statistics and geomorphic-based approach. We advanced this approach by combining two traditionally distinct machine-learning methods that complement each other and demonstrate that the criteria needed to ensure quality model performance produced practical and accurate susceptibility maps. We combined bagged-trees and logistic-regression approaches to model landslide susceptibility for Magoffin County, Kentucky. Landslide inventory mapping for the county allowed for an improvement upon geomorphic, statistics-based models by combining two traditionally distinct machine-learning methods. This combined approach generated a more sophisticated data-driven assessment of landslide susceptibility. We mapped 1054 landslides in the county and compiled 36 geomorphic statistical variables for each slide. Variable importance was determined using the bagged-tree machine-learning algorithm. The bagged-trees results indicated that standard deviation of plan curvature, standard deviation of elevation, sum of plan curvature, minimum slope, mean plan curvature, range of elevation, sum of roughness, mean curvature, sum of curvature, mean roughness, minimum curvature and standard deviation of curvature were influential variables to determine the likelihood of landslide occurrence. The performance of the bagged-trees function was validated using the ROC–AUC, which was calculated in a test dataset as 0.90. We used the bagged-trees results to run a logistic-regression function and model landslide susceptibility. The results of the logistic-regression model indicated eight geomorphic variables were significant: minimum slope, minimum curvature, standard deviation of elevation, range of elevation, standard deviation of plan curvature, mean roughness, sum of roughness and standard deviation of curvature. These variables were used in the regression equation. An AUC value of 0.83 suggests a strong overall model performance. The logistic-regression model produced a landslide-susceptibility map of Magoffin County that represents a realistic landscape and connects specific landslide morphologies and probability of occurrence, and has relatively minor noise and model artefacts. Landslide-susceptibility classifications for the entire county area based on standard deviations of the mean were: 14.6% low, 43.1% low–moderate, 24.5% moderate, 12.9% moderate–high and 4.6% high. Kernel-density estimations of predicted probability highlight the complexity among variables that influence slope stability, but also support the model results of significant variables. The map results strike a good balance between classifying existing deposits that have a moderate to high probability of subsequent movement and classifying other parts of the slope that do not necessarily show obvious landslide activity. We validated the logistic-regression results with data from a separate landslide inventory for the Prestonsburg 7.5-minute quadrangle, using the same logistic-regression model. The same combination of bagged-trees and logistic-regression showed that 74.9% of the landslide deposits in the Prestonsburg quadrangle have moderate, moderate–high or high susceptibility classifications, and 43.3% of the quadrangle area also falls into moderate, moderate–high or high susceptibility. This combined approach to predicting landslide susceptibility, taking advantage of landslide inventory mapping, successfully identified existing geomorphic conditions that likely lead to a landslide, but also modelled similar slope conditions elsewhere, which are areas of focus as well. The map results classified landslide susceptibility into categories that effectively communicated the landslide hazard. This statistical, geomorphic-based approach can be applied to other environments and emphasizes reliable data-driven methods that convey landslide hazard information to those at risk. We thank Arnold Stromberg and Edmond Kim from the University of Kentucky Department of Statistics, Zhenming Wang and Meg Smath of the Kentucky Geological Survey for their reviews, and David Korte of the North Carolina Geological Survey and Thomas Oommen of Michigan Technological University for technical guidance regarding logistic-regression models and landslides. Author contributions MMC: conceptualization (equal), data curation (lead), formal analysis (equal), funding acquisition (lead), investigation (equal), methodology (equal), project administration (lead), resources (supporting), software (equal), supervision (equal), validation (equal), visualization (equal), writing – original draft (lead), writing – review & editing (equal); JMD: formal analysis (equal), investigation (supporting), methodology (equal), visualization (equal), writing – review & editing (supporting); HJK: data curation (supporting), formal analysis (supporting), investigation (supporting), methodology (supporting), visualization (equal), writing – review & editing (supporting); AAK: data curation (supporting), investigation (supporting), methodology (supporting), visualization (supporting), writing – review & editing (supporting); JZ: formal analysis (supporting), investigation (supporting), methodology (supporting), software (supporting), writing – review & editing (supporting); YZ: formal analysis (supporting), investigation (supporting), methodology (supporting), software (supporting), visualization (supporting), writing – review & editing (supporting); LSB: conceptualization (supporting), investigation (supporting), resources (supporting), writing – review & editing (supporting); WCH: conceptualization (equal), formal analysis (supporting), investigation (supporting), methodology (supporting), project administration (supporting), resources (supporting), software (supporting), supervision (supporting), visualization (supporting), writing – review & editing (supporting) This work was funded by the Federal Emergency Management Agency (PDMC-PL-04-KY-2017-002). Conflicts of interest The authors declare that they have no conflict of interest or competing interests. Data availability The datasets generated during and/or analysed during the current study are available in the Kentucky Geological Survey repository, https://www.uky.edu/KGS/ Scientific editing by Jonathan Smith; Jennifer Hambling	{"url":"https://pubs.geoscienceworld.org/gsl/qjegh/article/54/4/qjegh2020-177/595750/Using-landslide-inventory-mapping-for-a-combined","timestamp":"2024-11-15T01:28:38Z","content_type":"text/html","content_length":"304208","record_id":"<urn:uuid:ecb2d24d-85da-40ae-9c06-b91a77aa6a87>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00426.warc.gz"}
Conjugate equation - math word problem (53641) Conjugate equation Find the numbers of a and b; if (a - bi) (3 + 5i) is the Conjugate of (-6 - 24i) Correct answer: Did you find an error or inaccuracy? Feel free to write us . Thank you! You need to know the following knowledge to solve this word math problem: Grade of the word problem: Related math problems and questions:	{"url":"https://www.hackmath.net/en/math-problem/53641","timestamp":"2024-11-12T07:34:17Z","content_type":"text/html","content_length":"75067","record_id":"<urn:uuid:0163fbb5-494f-45e1-a0bf-d35c8403a426>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00762.warc.gz"}
Adding Math Questions with the New Assessment/Quiz Editor The New Assessment Editor (or Quiz Editor) enables you to add mathematical equations into a question and its answer(s) with ease. To add a mathematical question to your quiz, follow these steps: 1. Create a Assessment/Quiz or import questions from publicly available Assessments/Quizzes 2. Click the Equations editor from the toolbar on the left. You can also click on f(x) Insert equation button on the right to insert a mathematical question 3. This opens a window in which you can add questions on formulae, equations, alphabets, symbols, and functions for basic, intermediate, and advanced-level mathematics 4. Click on f(x)within options to enable the same for options Note that the math editor cannot be enabled for answers for Fill-in-the-blanks and Open-ended questions. 0 comments Please sign in to leave a comment.	{"url":"https://support.quizizz.com/hc/en-us/articles/4408478881689-Adding-Math-Questions-with-the-New-Assessment-Quiz-Editor","timestamp":"2024-11-07T19:57:45Z","content_type":"text/html","content_length":"39537","record_id":"<urn:uuid:49df52f4-c62c-4f00-a965-7a859729f010>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00407.warc.gz"}
HasCal—A promising embedding of pluscal in haskell. HasCal — A promising embedding of pluscal in haskell. I’ve been interested in proof systems and proofs for a while. Recently, I took my first tiny step (a very bad example) in TLA+: A very bad example of a simple Nat div2 check in TLA+ I’ve been following Gabriella Gonzalez’ HasCal for a while, and decided to spend a short time trying it out. It’s a bit weird (and has some weaknesses and blindspots for now) but works pretty well and may be more tractable for those who know haskell but not TLA+. What’s there is really promising. A neat embedding of PlusCal in haskell The whole thing is based on a monad that allows a fairly concise representation of TLA+ code in do notation. I did a quick port of the code above based on the euclid’s algorithm test example and it’s even a bit more general than my attempt at TLA+ (admittedly I don’t know the pattern for testing just a function). I don’t claim to be any kind of expert in TLA+ but I think I’ll try it a bit more in the form of HasCal as it’s very familiar syntactically. I wonder how hard it’d be to port to idris and mix with dependent types :-) {-# LANGUAGE BlockArguments #-} {-# LANGUAGE DeriveAnyClass #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE OverloadedStrings #-} {-# LANGUAGE RecordWildCards #-} {-# LANGUAGE TemplateHaskell #-} import Control.Monad (when) import HasCaldata Global = Global { _number :: Int , _output :: Int } deriving (Eq, Generic, Hashable, Show)instance Pretty Global where pretty = unsafeViaShowmakeLenses ‘’GlobaltestNatDivision :: IO () testNatDivision = do let startingLabel = () let startingLocals = pure () let nd2 = do while (do v <- use (global.number) ; return (v >= 2)) do global.output += 1 global.number -= 2 let process = do initial_n <- use (global.number) initial_o <- use (global.output) global.output -= initial_o nd2 my_output <- use (global.output) assert (initial_n `div` 2 == my_output) model defaultOptions { debug = True } Begin {..} (pure True) do _number <- [ 1 .. 1000 ] _output <- [ 0 ] return Global {..}main :: IO () main = do Using this method you can basically emulate any kind of computation and TLA+ allows checking of ongoing process invariants via coroutine and property members of the model. Happily, it’s very easy to get started and try it out.	{"url":"https://prozacchiwawa.medium.com/hascal-a-promising-embedding-of-pluscal-in-haskell-be439209183b?source=author_recirc-----f7322cbe2086----1---------------------0ea871b0_2bd6_4a5d_a0bd_4d52f7b9fa96-------","timestamp":"2024-11-10T19:26:54Z","content_type":"text/html","content_length":"94903","record_id":"<urn:uuid:209fc8a4-8c68-4eac-a8a0-ee6df209bf6c>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00659.warc.gz"}
Finding Tangent Line Approximations Question Video: Finding Tangent Line Approximations Mathematics • Higher Education What is the tangent line approximation π (π ₯) of β (1 β π ₯) near π ₯ = 0? Video Transcript What is the tangent line approximation π of π ₯ of the square root of one minus π ₯ near π ₯ equals zero? Remember, if π is differentiable at π , then the equation for the tangent line approximation π of π ₯ is given by π of π plus π prime of π times π ₯ minus π . Weβ ll look at our example piece by piece. But first letβ s find π of π . Our function π of π ₯ is the square root of one minus π ₯. And weβ re finding the tangent line approximation near π ₯ equals zero. So weβ re going to let π be equal to zero. This means, in our expression, π of π is going to be π of zero. And we can evaluate this by substituting π ₯ equals zero into our function. And we get the square root of one minus zero or the square root of one which is simply one. The next part weβ re interested in is π prime of π . π prime of π ₯ is the derivative of π with respect to π ₯. So weβ re going to need to differentiate the square root of one minus π ₯ with respect to π ₯. We need to spot here that this is a function of a function or a composite function. And we can apply the chain rule. This says that if π ¦ is a function in π ’ and π ’ itself is a function in π ₯, then dπ ¦ by dπ ₯ is the same as dπ ¦ by dπ ’ times dπ ’ by dπ ₯. If we say π ¦ is the function the square root of one minus π ₯, we can let π ’ be equal to one minus π ₯ and π ¦ be equal to the square root of π ’ which Iβ ve written as π ’ to the power of one-half. dπ ’ by dπ ₯, the derivative of one minus π ₯ with respect to π ₯, is simply negative one. And the derivative of π ¦ with respect to π ’ is half times π ’ to the power of one-half minus one which is negative one-half. So the derivative of the square root of one minus π ₯ with respect to π ₯ is a half times π ’ to the negative a half multiplied by negative one. Replacing π ’ with one minus π ₯ and we see that the derivative of the square root of one minus π ₯ with respect to π ₯ is negative a half times one minus π ₯ to the power of negative one-half. Note, at this stage, that we could have used the general power rule here. And thatβ s just a special case of the chain rule. So since we now know π prime of π ₯, we can evaluate π prime of π . Thatβ s π prime of zero. So weβ re going to substitute zero into our formula for the derivative of our function. Itβ s negative a half times one minus zero to the power of negative a half which is negative one-half. The final part of our tangent line approximation that weβ re interested in is π ₯ minus π . And since π is zero, this becomes π ₯ minus zero which is just π ₯. Substituting all of this into our formula and we see the π of π ₯ equals one plus negative a half times π ₯. And this simplifies to one minus π ₯ over two.	{"url":"https://www.nagwa.com/en/videos/726165232194/","timestamp":"2024-11-11T10:33:34Z","content_type":"text/html","content_length":"244957","record_id":"<urn:uuid:216dea4f-41d8-4de2-92d8-e50276e04b50>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00697.warc.gz"}
An in situ adaptive tabulation based approach to multi-component transcritical flow simulation (Conference Paper) \| NSF PAGES null (Ed.) The studies of transcritical and supercritical injection have attracted much interest in the past 30 years. However, most of them were mainly concentrated on the single-component system, whose critical point is a constant value. To capture the thermophysical properties of multicomponent, a phase equilibrium solver is needed, which is also called a vapor-liquid equilibrium (VLE) solver. But VLE solver increases the computation cost significantly. Tabulation methods can be used to store the solution to avoids a mass of redundant computation. However, the size of a table increases exponentially with respect to the number of components. When the number of species is greater than 3, the size of a table far exceeds the limit of RAM in today's computers. In this research, an online tabulation method based on In Situ Adaptive Tabulation (ISAT) is developed to accelerate the computation of multicomponent fluid. Accuracy and efficiency are analyzed and discussed. The CFD solver used in this research is based on the Pressure-Implicit with Splitting of Operators (PISO) method. Peng-Robinson equation of state is used in phase equilibrium. more » « less	{"url":"https://par.nsf.gov/biblio/10282022-situ-adaptive-tabulation-based-approach-multi-component-transcritical-flow-simulation","timestamp":"2024-11-10T05:26:41Z","content_type":"text/html","content_length":"245979","record_id":"<urn:uuid:7c3af231-224b-4bbb-ba29-bbb41a0ff387>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00347.warc.gz"}
Math Word Walls Here you’ll find math word walls that show vocabulary and concepts in action through bright visuals and examples, supporting more of your students as they learn the curriculum. Each comes in printable color, printable black & white, digital in Google Slides, and includes printable Spanish vocabulary. Linked below are math word walls for 2nd grade through algebra 2. My first introduction to math word walls came from a geometry teacher in a classroom next to mine in Boston. He had created a hand-drawn, floor-to-ceiling math word wall for his students that covered all of the formulas, vocabulary and concepts they needed to know for our state test. His bulletin board and walls were completely covered. At the time I thought it was a little much. I mean, do high schoolers really need a math word wall? A few years later, he went on to become Massachusetts Teacher of the Year, and I went on to realize how right he had been after giving math word walls a try in my own classroom. After 7 years teaching general education high school math, and one year giving middle school math a try, I headed back to high school to teach small group and inclusion algebra 2, geometry and consumer math. Throughout that school year, I found myself drawing linear graphs over and over again to help my algebra 2 students make links back to what they had learned in algebra 1: y-intercepts, zeros, slope. So the next summer I began making permanent, printable references for my walls, starting with this one for linear equations: My math word wall quickly became an extension of my teaching and greatly improved my classroom management. I could quickly point to a reference to help one student move past their confusion while keeping the rest of my class on track. During group and independent work, our math word wall helped students work more independently by referencing our wall, allowing me to help more students In the years since, as I've posted math word wall photos on social media, teachers have requested them for their own classrooms. On this page you'll find links to every math word wall I've made to date, along with some of the great photos teachers have shared of their own classroom math word walls. "My students are LOVING this word wall! The images and examples, instead of just definitions, really help them to understand the concepts." -Marcie S, 8th Grade Math Word Wall "I love this. It is very versatile. I projected the vocabulary word while I taught the lesson and the I later posted a paper copy on the wall. My students actually looked at the words after they were posted. Great Resource!" -Denise H, Grades 6-9 Math Word Wall Bundle "The BEST math poster/word wall I could have put up this year. I will keep it up all year for my advanced Geometry and Trig classes." -Sarah M, Unit Circle Word Wall "I am in love with this resource! My students are struggling learners and this has really been helpful to point to when they have repeated questions or when I am introducing a new topic." -Jennie M, 2nd Grade Math Word Wall To date, I've completed math word walls for 2nd grade through algebra 2, financial literacy, the unit circle and a few extras. Every math word wall comes in printable color, printable black & white and no-prep digital in Google Slides. All 3 versions come together in the same file. If you are looking for written definitions, they won't be here. I have found that simple graphics and examples of the math vocabulary in action, instead of explicit written definitions, allow more students to access the curriculum. With 15-20% of our kids having reading difficulties (and up to 80% in students with specific learning disabilities), presenting math vocabulary in context allows more students to make the connections that are critical for conceptual understanding. This gives more students access to the math, especially our visual learners, students with reading disabilities and English Language Learners. If we are learning about shifting a vertex form function, for example, I can quickly point to our wall to remind students which way the vertex shifts. This has supported my classroom management and has helped my students work more independently. To make each math word wall, I think hard about how to make the visuals as clear and descriptive as possible without unnecessary words. I have found that presenting math vocabulary in this way increases math confidence and lowers math anxiety in students who struggle with reading, while still communicating the vocabulary and concepts we are learning in class. My students reference our walls during independent work and I reference them during lessons, especially when needing to make a connection back to a previous topic or moving a student past confusion. With pictures, examples and reminders, math is more accessible to more students. Students can find the information they need more independently, which leads to greater feelings of confidence and success. To me, confidence in math is everything. In my own classroom, I can focus on the students who need more intense help while directing others to use the walls for help. Whenever a student was confused, I used to stop class to catch up that student. This, of course, gave a sense of free time to the rest of the class, and reeling everyone back in became time-consuming and pretty frustrating. My math word wall fixed this problem. When students are confused their learning stops because they're more focused on their confusion than the lesson. This is why I always stop to answer student questions. With visual aids on the walls, I can now point at a reference and get students over their hurdles faster. Even with lots of encouraging that their voices matter, some of my students wouldn't speak up when they had a question. Adding visual supports to our classroom walls has given all of my students, and maybe especially these students, the tools to help them take charge of their education and work more independently. Seeking out and finding answers to their questions on their own by using our classroom visuals is empowering. This is one of my favorite things about math word walls. Adding a math word wall to my classroom changed my teaching in a few important ways: ◉ Greater student independence ◉ Keeping the class on track ◉ They make a classroom inviting ◉ Connections to previous topics ◉ Low floor, high ceiling That last reason is probably the most important impact I have seen since adding a math word wall to our classroom. The supports are there for kids who need them, allowing more students to feel that maybe math is for them after all. Supporting student access to the curriculum through our math word wall has allowed more of my students to feel successful in math. To me this is a huge part of being a math teacher. I need my students to know that math is for everyone. Over the years, teachers have sent so many photos of their math word walls. Every teacher arranges their word wall differently, based on student need and personal preference. You can see many of the in this post. Ms. Davenport's math classroom is so cheery with her yellow display. Ms. Estrada arranged the pieces of her 6th grade math word wall's box and whiskers plot onto blue paper to make a poster that can easily be taken down and put back up when needed. Mr. Caruso arranged related pieces onto black poster board before hanging his Geometry Word Wall. Mrs. Shah put a frame around slope to draw her students' attention to their current topic of study. Ms. LaBrake hung her math word wall on her classroom cabinets. Instagrammer Falak's algebra 2 parent graphs with some twinkle lights. Here is a photo of one of the digital word wall references. With the digital word walls, I wanted students to almost feel they were in a real classroom, which is why I chose to make the digital versions with real photographs. You can see how the digital versions work in this video A reference for the Unit Circle. Place value in a 4th grade math word wall. A box and whiskers plot in the 6th grade math word wall. And fractions on a 5th grade math word wall. The word walls have really grown over the years as I have added teacher requested additions. Some teachers choose to display their entire math word wall at once, while other teachers choose to display only some pieces at a time. This is up to you. If you choose to laminate, a quick tip is to spray the lamination with clear, flat spray paint (painting with clear, flat Mod Podge also works). This takes away the lamination shine. Math word wall downloads: "These word wall pieces guarantee that my classroom is the second teacher. Students are able to reference their learning with these engaging resources. Thank you!" - Malorey M, Math Word Wall "This product keeps getting better and better! I colored a lot of them last summer, then the color versions came out! and now the digital versions! This resource has been incredibly helpful to have up and reference and add to during the year. I worked with students who struggled and students who accelerated, this was a great resource for all of them!" - Chelsie S, Math Word Wall "Absolutely love this resource. I have been able to highlight key concepts in each unit, by creating posters that are displayed during the time we are discussing those TEKS in class. No longer do I have an overwhelming wall with all things math but a focus wall that changes as we progress through the year." - Ashley W, Math Word Wall Bundle "This is so great! My students refer to these walls all the time! I have been putting them up as I go through each unit. I love that there is Spanish words included also for my Spanish speaking students!" - Rose P, Math Word Wall Bundle "These are the perfect word wall for classroom display! They give students a succinct visual reference when they are completing seatwork in class. The posters are eye-catching and easy to read, so all students in the class are able to see. I also appreciate having the digital versions as well - this gives students an at-home reference for when they are completing homework. Thank you SO much! One of my favorite all-time resources." - Jennifer C 24 comments: 1. How do you attach these to the wall? 1. Hi Mary, in my classroom I used the blue Loctite putty. For heavier posters, teachers have even used a strip of blue painter's tape on the wall then hot glue between the painter's tape and the poster they are hanging. This way the hot glue doesn't come in contact with the wall. Other teachers have used Command Strips, but I haven't given these a try. 2. Hi! These would be so wonderful if you would have them in Spanish. They'd be a best seller. 1. Coming back to update that every word wall will now include Spanish vocabulary by August 2021. 3. Thank you very much for these. I have been using your materials for a couple of years but have never said thank you. Thank you! 1. Thank you for coming back to leave a comment! This means a lot. I hope your year is going well! 4. You're very talented with such a vast amount of resource knowledge to include in word walls. I will be buying the 6th grade for sure next paycheck... 1. Thank you, Ritchie! 5. I love these. I am about to put some of the 8-11 grade math word wall pictures in my classroom. There is one thing I can’t find though. In the Algebra Word Wall, I can’t find the words “coefficient and “exponent” for the term, expression, and equation section. Is it in there somewhere. Thanks. 1. Hi Sarah, coefficient and exponent are on page 37. I squeezed them in there instead of adding another page to the word wall, so they're a little hard to find. 6. Do you have any plans to include the Statistics standards for 7th grade? 1. Hi Denise, there are stats references in the 6th grade word wall. I try not to have any overlap between the word walls, so they'll probably stay in 6th grade only. But if there's a reference you need, please send me an email. shana@scaffoldedmath.com 7. AnonymousMay 17, 2022 I love your word wall and plan on purchasing it for next year. For your high school level walls do you allow your students to use the wall during tests? I know there are some topics that I teach with my honors classes that they are expected to memorize. I also know that in the real world they will have access to look up any questions they have. What are your opinions? 1. I always allowed my students to use our word wall along with their notes. That being said, I taught applied Algebra 2 and Consumer Math to students with some learning difficulties and by then they were past our last state test. So I wasn't under the same pressure as a 9th or 10th grade teacher is under. If you are allowed to make this decision yourself and do not have to base it on a school rule, I'd say allow them to use your word wall. One huge benefit I saw from allowing them to use it (and their notes) was that I had that leverage to say, "It's in your notes" or "You can use the wall". With the word wall and notes in front of them, it forced my students to seek out answers on their own without my help, strengthening their researching skills and independence. 8. LacyMay 25, 2022 I just purchased the math word wall bundle! I am SO excited...it's absolutely amazing! Do you have one for science as well? My buddy across the hall is so eager to know after seeing me work on my math one this afternoon! 1. Thank you for your kind words, Lacy. They really mean a lot. Unfortunately I don't have a word wall for science. Maybe someday. 9. I am planning to purchase your geometry word wall for my son who is homeschooling. Is there a simple way to scale it down so that we can make a notebook instead of putting them on a wall. We unfortunately do not have a wall to dedicate to math vocabulary. Thank you, 1. HI Debbie, if your son will have access to a computer, each now comes digitally in Google Slides. The link to the digital version will be inside the PDF. For a notebook, you can choose to print 2 or 4 per page to make them smaller, or you can scale down to an exact size you'd like. I really like the free program Adobe Acrobat Reader DC for this. 10. AnonymousJune 24, 2022 Do you have ant set notation items in your word walls? Or the symbols for the set of real numbers, rational numbers, etc.? I love your word walls! 1. Inside the 8th grade math word wall there is a set of references for number classification that includes natural, whole, integers, irrational, rational and Reals. There's also a little bubble to the side for imaginary numbers that you can decide to display if your students are ready. 11. AnonymousNovember 06, 2022 Hello from Namibia. Do you have these perhaps for preschool (grade R) 1. Hello from Massachusetts, US! Thank you for your comment and question. The youngest math word wall now is 2nd grade. 12. AnonymousFebruary 07, 2023 Hi Shana! Thank you so much for creating such a wonderful resource with a comprehensive rationale for its use. As a first-year teacher I am very much appreciative. Do you have a specific flat clear spray paint you would recommend? I am overwhelmed with the options. Thank you! 1. Any should work, but I know Krylon makes a clear flat spray paint that will take the shine off the lamination. I used the Testors brand because my husband had it for his hobby. If I had to buy one, I'd aim for the cheapest one!	{"url":"https://www.scaffoldedmath.com/p/word-walls.html?m=0","timestamp":"2024-11-06T09:14:24Z","content_type":"application/xhtml+xml","content_length":"191496","record_id":"<urn:uuid:c75f2605-ea86-4e84-8a4a-88ce25122183>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00725.warc.gz"}
The Proof Supply Chain by: Trace Zero-knowledge (ZK) cryptography is rapidly improving, academically and commercially. As new ZK applications launch and scale, we’ll need new infrastructure to serve them. However, the mechanism design necessary for robust ZK infrastructure remains underexplored. In this piece, we provide an early look into one important component of ZK infrastructure: the proof supply chain. This is the pipeline from an application’s intent to generate a ZK proof to that proof’s on-chain submission. We’ll show how the proof supply chain is a continuation of Ethereum’s trend towards greater fee segmentation. We’ll also show how it shares a similar market structure as the transaction supply chain, and as a result, faces many of the same questions and challenges. Ethereum Fee Markets and MEV Today Ethereum launched as a low-resource, general-purpose blockchain. The network is computationally flexible via a blockchain-native VM, but it isn’t performant and has low throughput and high latency. Seeking scale, its research community investigated solutions like sharding and plasma, before ultimately settling on a rollup-centric scaling roadmap in 2020. Rollups move execution off-chain, allowing the base layer to focus on DA and settlement. Multi-Dimensional Fee Markets To make rollups more affordable, the community proposed a new fee market for data blobs — the data that rollups submit to Ethereum — as part of proto-danksharding (EIP-4844), which is expected to go live in 2024. The proposal for multidimensional fee markets was one of the earliest examples of block segmentation — the dividing of a block into different components. Block segmentation results in fee segmentation, allowing different types of transactions to have different cost structures. Before rollups, Ethereum blocks mostly consisted of L1 transactions. Once rollups launched, they needed to occasionally submit their L2 transaction data to Ethereum as calldata. That calldata needs to compete with L1 transactions for the same limited gas per block. Multi-dimensional fee markets change this. After EIP-4844, rollups will be able to submit data blobs through a separate channel from transactions. These data blobs have fees independent from L1 transaction congestion. In the image above, we show normal transactions above the blobs in the block. However, there’s no concept of ordering with respect to transactions and blobs; the fee markets are orthogonal. The Rise of MEV Rollups are not the only driver of fee segmentation; we also have segmentation from MEV. In 2019–2020, on-chain activity grew, driven by DeFi. Miners realized that they could extract value from this activity by ordering and including transactions into blocks in certain ways. In proof-of-work Ethereum, searchers competed for their transactions to be included at the top of the block (TOB) via priority gas auctions (PGAs) to capture the most valuable MEV opportunities like arbitrage. Although this didn’t involve technical block segmentation like multi-dimensional fee markets for rollups, it did implicitly introduce a form of fee segmentation: the gas costs needed to be included at the top of the block were different from the rest of the block (ROB). Flashbots later introduced a mechanism for TOB inclusion separate from PGAs in the public mempool, making this segmentation more explicit. After the merge, motivated by the need to mitigate the centralizing effects of MEV, Flashbots introduced proposer-builder separation through MEV-boost. That push expanded the transaction supply The transaction supply chain intended to shift the centralizing effects of MEV from the proposer-level to the new builder-level. However, builder centralization is also problematic, particularly for censorship-resistance. Since builders fully construct Ethereum blocks, they have control over what does and does not get submitted on-chain. This concern has motivated additional research into new techniques like censorship-resistance (CR) lists and MEV-boost+ which attempt to return some inclusion power back to the proposer. In the case of MEV-boost+, this is done by allowing the proposer to build the ROB themselves, creating the technical block segmentation between TOB and ROB that is currently implicit. Recently, builders have also begun to explore bottom-of-block (BOB) MEV opportunities. BOB blockspace has similarities to the next block’s TOB since it can react to the transactions executed in the ROB. Overall, the transaction component of the block continues to segment. Centralization and Vertical Integration Since its introduction, the transaction supply chain has become more centralized and vertically integrated. Centralization is primarily driven by the orderflow flywheel. To a first approximation, the winning builders are those with the most orderflow. Integrated-builders with exclusive or self-generated orderflow like BeaverBuild and R-Sync have massive market share. Builders are now building relays, which may soon become vertically-integrated. MEV is also driving more sophistication and centralization among proposers, with P2P recently announcing that they will delay their block proposals to accumulate more MEV rewards. Centralization and vertical integration will continue as long as the current market structure remains intact. In contrast to Solana’s state localized fee markets, Ethereum is segmenting fees by transaction type. Once proto-danksharding goes live, Ethereum will have a separate fee market for rollups’ data blobs. Ethereum blocks are further segmenting due to MEV. Additionally, the transaction supply chain is actively centralizing and vertically integrating. So how do ZK proofs fit into this picture? The Emerging Proof Supply Chain ZK rollups were one of the earliest use cases for ZK. These rollups submit their state root and a proof of their state transitions to Ethereum for settlement for which they must pay gas costs. Although ZK rollups have been discussed for years, they have only recently launched. Scroll, ZKSync, and Polygon zkEVM all went live in 2023. ZK rollups have been followed by additional ZK applications including coprocessors, zkBridges, zkOracles, zkML, and zkDID. Many of these applications will also be on mainnet in the next couple of years. Each one of these applications generates ZK proofs that must be submitted on-chain. That means they must compete with transactions and other proofs for limited blockspace. Proof Aggregation Submitting proofs on-chain is expensive. Fortunately, there’s a solution: proof aggregation. Proof aggregation is a technique to combine multiple proofs together into a single proof. Just like ZK can be used to compress many transactions into a single proof, it can also be used to compress many proofs into one. This is done by recursively proving the verification of multiple proofs, often in a tree-like structure. The final aggregated proof can then be submitted on-chain, where it is verified by the network, implicitly verifying all the input proofs. Proof aggregation allows the on-chain submission and verification gas costs to be amortized across all of the proofs; the cost of verifying an aggregated proof is roughly the same as verifying a single regular proof. Proof aggregators face 2 questions: 1. Inclusion — which proofs should be included in the aggregated proof? 2. Ordering — what order should the included proofs be in? Applications want their proofs submitted on-chain quickly, but proof aggregation is computationally intensive. An aggregator cannot combine an unlimited number of proofs within a single block time. Therefore, it needs to decide which subset of proofs should be included and which should not for every block. Ordering and proof height may also matter. For example, applications whose proofs are closer to the top of the aggregation tree have shorter merkle paths, providing them with cheaper merkle inclusion Decision making over proof ordering and inclusion makes proof aggregators similar to transaction sequencers. And just like sequencers and builders have opportunities to extract MEV from transactions, aggregators may be able to extract value from their ability to order and include proofs. Moreover, aggregators benefit from a similar flywheel effect as builders. The more proof flow sent to the aggregator, the more on-chain gas costs can be amortized, resulting in more proof flow. Proof aggregators drive further fee segmentation by introducing a new fee market: the cost to be included in a proof aggregation. This proof gas market is still weakly impacted by L1 transaction gas prices (since the aggregated proof must still compete for that blockspace), but is largely independent. Proof Generation The other major component of the proof supply chain is proof generation. ZK applications have a problem: maintaining a decentralized prover set is expensive and complex. It requires running specialized hardware and involves complex mechanism design. Applications already have plenty of engineering and business development challenges. Most teams will want to outsource proof generation to a third-party instead of handling it themselves. Proof markets — networks that provide proofs-as-a-service — are that third-party. Proof markets are a continuation of the modular blockchain thesis, which argues that each task should be performed by a different piece of specialized infrastructure. Infrastructure specialization allows teams to outsource complexity and inherit shared security, while the specialized layer can benefit from economies of scale. At a high level, a proof market has just 3 components: 1. Request pool — a mempool for requests for proofs 2. Prover set — a set of provers 3. Matching algorithm — an algorithm for matching proof requests to a prover Applications send proof requests to the request pool. The proof market then uses a matching algorithm, such as an orderbook or auction, to match that request to a prover. That prover then generates the proof and sends it to some destination, likely an L1 or L2, which may be specified in the request’s metadata. Proof markets have flywheel effects too. More request flow drives more competition among provers, resulting in lower costs for proof generation. It also results in higher hardware utilization, creating economies of scale; the prover set’s fixed costs for running the infrastructure can be amortized with more volume, lowering marginal costs. The Proof Supply Chain Together, proof aggregators and proof markets construct the proof supply chain. The entire proof supply chain is illustrated above. Walking through it step-by-step: 1. Request submission — applications submit proof requests to the request pool 2. Request matching — requests are matched to provers 3. Proof generation — provers generate proofs for their matched requests 4. Proof submission — proofs are submitted to the proof mempool 5. Proof selection — a subset of proofs in the proof mempool are selected and ordered to be included in the aggregated proof 6. Proof aggregation — the aggregator generates an aggregated proof from the selected proofs 7. Aggregation submission — the aggregated proof is submitted to its destination Steps 1–4 make up the proof market, while steps 5–7 are performed by the proof aggregator. Comparison to Transaction Supply Chain Viewing the proof supply chain in its entirety reveals its similarities to the transaction supply chain. As with normal transactions, the proof supply chain begins with applications or users who submit intents, or in this case requests, to a platform. Proof markets have a similar structure to orderflow auctions. In orderflow auctions, searchers bid for exclusive rights to a transaction or intent. Searchers are highly fungible, with most value in a competitive market flowing back to the intent originator. In proof markets, provers fight for the right to satisfy proof requests in a similarly competitive market. As mentioned previously, aggregators have similar flywheel effects to builders. We expect the market to centralize around a small number of request pools and proof aggregators. Meanwhile, prover sets and destination chains will remain relatively decentralized and competitive among operators. Vertical Integration The transaction supply chain is vertically integrating. We expect the proof supply chain to be vertically integrated as well. Proof markets and proof aggregators each have flywheel effects. If instead of splitting these tasks into 2 separate roles, a single entity performed both, they would benefit from both flywheel Crucially, a vertically integrated proof supply chain allows the proof market to direct its proof flow exclusively toward its own proof aggregator. That proof aggregator then has higher volume, providing cheaper on-chain verification costs. These cheaper costs then incentivize more request flow to the proof market. Third-party provers, like client-side applications or lower-volume proof markets, are incentivized to submit their proofs to the dominant aggregator (assuming they service third-party proofs). Of course, third-party proofs could be submitted directly to the destination chain or a smaller aggregator; it would just be more expensive. This external proof flow may drive further centralization. Since the aggregator has leverage over proof inclusion, this market structure introduces censorship-resistance concerns, similar to blockbuilding. These developments will take years to unfold. Today, there are only a handful of projects building components of the proof supply chain. These include Nebra (proof aggregator), Gevulot (proof market), Marlin (proof market), Pluto (vertically-integrated), Bonsai by RiscZero (vertically-integrated), Succinct (vertically-integrated), and =nil; (vertically-integrated). Proof Bundles Aggregated proofs contain many individual proofs. Nebra, for example, will initially be able to aggregate 32 proofs per batch. This compression makes aggregated proofs consequential transactions. Depending on what ZK applications arise and what their proofs involve, there may be incentives to front-run or back-run aggregated proofs. A close analogy is oracle updates, which can be profitably As ZK applications mature, we expect proof bundles to become an important part of each Ethereum block. The commercialization of ZK applications will scale proof generation, spawning a new supply chain for ZK proofs. This new supply chain has similar market structure, centralization vectors, and censorship concerns as the transaction supply chain. The proof supply chain will continue Ethereum’s trend towards more granular fee segmentation; proofs will have a fee market semi-independent from normal transactions. This supply chain will become an important part of Ethereum in the years ahead. We look forward to working with the rest of the community to investigate the opportunities and challenges it creates. Open Research Questions We’re interested in research into the following questions, among others: 1. How can we build censorship-resistance into proof supply chains, given their centralization vectors? 2. What forms of aggregator extractable value exist, and how should we design the proof supply chain around them? 3. How will the emerging proof supply chain impact the existing transaction supply chain? If you’re a founder or researcher interested in this space, we’d love to chat. Acknowledgements: Special thanks to Velvet, Dougie, Mike, Kubi, Dmarz, Teemu, Tracy, Uma, Sidd, and Misha for their feedback on an earlier version of this piece.	{"url":"https://figmentcapital.medium.com/the-proof-supply-chain-be6a6a884eff?ref=blog.hyle.eu","timestamp":"2024-11-08T07:49:29Z","content_type":"text/html","content_length":"215970","record_id":"<urn:uuid:e404f2d2-9592-43dd-b47c-ee1a96ce9fa0>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00565.warc.gz"}
Quantitative Aptitude: Time and Work Set 2 Time and Work Questions in Quantitative Aptitude section for SBI PO, IBPS PO, LIC, RBI, IPPB and other banking and insurance exams. Directions (1-3): 18 men can complete a work in X days and 22 women can complete the same work in (X+5) days. The ratio of work done by 14 men and 11 women in same time is 8 : 3. 1. Find the value of X. A) 7 days B) 8 days C) 6 days D) 9 days E) 12 days 2. 6 men and 8 women work for 7 days on the same work and the remaining work is completed by 20 boys in 11 days. Find the number of days in which 25 boys can complete the whole work. A) 7 days B) 6 days C) 4 days D) 5 days E) 3 days 3. Find the ratio of efficiencies of 6 men and 8 women together and 9 men and 6 women together. A) 34 : 23 B) 25 : 31 C) 24 : 29 D) 29 : 22 E) None of these 4. A can complete the work in 60% less time than B. Beginning with the second day, the amount of work which can they do keeps of doubling. If in this way they can complete the work together in 2 days, then in how many days they can complete the work if their efficiencies remain constant? A) 2.5 days B) 3.5 days C) 4 days D) 3 days E) 5 days 5. 50 persons are employed to complete a work in 30 days working 12 hours each day. Due to some reason, they work for only 10 hours for the first 15 days. After this, 10 persons leave the work and rest continues the work as before. How many more days are needed to complete the work than the actually estimated time? A) 11 1/4 days B) 12 2/3 days C) 10 1/2 days D) 12 days E) None of these 6. A, B and C have to complete a work. They decide to divide work in the ratio 2 : 3 : 5 respectively. Their rates of work is in the ratio 1 : 2 : 3. If it takes 12 days by A to complete his part of work, then how much of work can they complete in 8 days? A) 2/5 B) 4/7 C) 2/3 D) 4/5 E) 3/7 7. There are two filling pipes A and B. If A fills bottom 3/4^th tank and B fills the rest tank, then they can fill the tank in 18 minutes. If B fills bottom 3/4^th tank and A fills the rest tank, then they can fill the tank in 22 minutes. What is the time taken by both the pipes to fill the tank together? A) 8 1/4 minutes B) 10 1/3 minutes C) 9 3/5 minutes D) 10 3/5 minutes E) None of these 8. An emptying pipe A can empty the tank in 30 minutes. It is opened in a tank which is full of water. After 12 minutes another pipe B which can fill the tank in 15 minutes is also opened. In what total time will the tank get filled again? A) 8 minutes B) 12 minutes C) 15 minutes D) 20 minutes E) 24 minutes 9. 2 groups A and B contain some people each. Efficiencies of all people in group A is same while that in group B is same. 3 workers from group A and 6 from group B can complete the work in 20 days. 8 workers from group A and 4 from group B can complete the work in 10 days. Find the number of days in which 1 person from each group can complete the work working together. A) 96 days B) 72 days C) 90 days D) 54 days E) None of these 10. A and B can complete a work in 12 and 20 days respectively. After 4 days, they are joined by C who can complete the same work in 24 days, how much work will remain uncompleted after 2 more days? A) 53/60 B) 41/60 C) 13/60 D) 11/60 E) 7/60	{"url":"https://alfabanker.com/quantitative-aptitude-time-and-work-set-2/","timestamp":"2024-11-06T02:26:00Z","content_type":"text/html","content_length":"111933","record_id":"<urn:uuid:8aa7cbcf-396b-4a08-8856-2d5fa8688f91>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00672.warc.gz"}
BBA Course Full Details Overview Eligibility Criteria The full form of the BBA course is Bachelor of Business Administration. Moreover, the duration of the courses is of 3 years. It is one of the most pursued courses after class 12th students of all BBA Course Full Details Candidates who are interested in Finance, Sales, Marketing, and many more can pursue this course. Candidates are highly pursuing the Bachelor of Business Administration course after the completion of the class 12th standard from the Science and Commerce stream. If any candidate wants to take admission to the top government colleges and private colleges then they must have to appear for the entrance exam for the Bachelor of Business Administration Test. We have concluded all the information in detail below. Please do check for the best information regarding BBA Course Full Details, Overview, Eligibility Criteria, Job Role, etc. Some of the entrance exams are DUJAT, NMIMS NPAT, IPU CET, and many more. The candidate must have to pass the class 12th examination from a recognized board. Candidates must have to obtain 55 to 60% in class 12 standard to be eligible for the Entrance Test. The candidates who are having a good interest in Marketing, Businesses Management, Sales, etc. can pursue the course to have a bright future. Some of the job profiles are Marketing Executive, Advertising Executive, Sales Manager, etc. Furthermore, the top recruiting companies are TCS, HDFC Bank, IBM, Deloitte, ICICI Bank, Goldman Sachs, etc. BCA Course Overview Course Name Bachelor of Business Administration (BBA) Duration of the course 3-Years Eligibility Criteria Pass Class 12th exam with a minimum of 50% marks BCA course fees INR 30k to INR 1.7 lakh Entrance Exams SET, UGAT, DU JAT, IPU CET, etc. Employment Areas Government Jobs, Private Jobs, IT Sector, etc. Job Profiles Marketing Executive, Sales Executive, Financial Analyst, Operation Analyst, etc. Top Recruiter Companies HDFC Bank, EY, Capgemini, Goldman Sachs, IBM, Deloitte, etc. Bachelor of Business Administration Course Bachelor of Business Administration Course Details: □ The duration of the Bachelor of Business Administration course is of 3 years. □ The course mainly focuses on Business Management, Finance, Sales, and many categories in which a student can get a good job after graduating. □ To get into the top BBA colleges the candidates must have to qualify for the Entrance Test. □ Some of the entrance exams are IPU CET, NPAT, DU JAT, etc. □ The candidate can also do a 5 years long course in which you will get to learn BBA + LLB course curriculum. □ Bachelor of Business Administration fee ranges from INR 30k to 1.7 lakh. □ The average salary a candidate can get after the completion of the BBA course is 3 lakh per annum to 6 lakh per annum after the completion of the BBA course. □ The candidate can also pursue an MBA in the specialization of Business Management, Marketing, Travel, and Tourism, Event Management, etc. BBA Eligibility Criteria â€¢ The candidates must have passed the class 12th examination from a recognized state or the Central Board. â€¢ Furthermore, a BBA course can be enrolled in any stream such as Science, Commerce, and Arts. â€¢ The candidates must have to obtain 55 to 60% mass in the class 12th examination. â€¢ The candidates must have to be aged between 17-22 years old. BBA Entrance Exams The candidates who want to pursue the course from top colleges then they must have to appear for the Entrance Test. If the candidates complete the course from top colleges then they will get a good placement and good exposure to studying. Below we have mentioned some of the BBA entrance exams so candidates can get full information regarding entrance exams: CUET Entrance Test: The name of the entrance test is a common University entrance test. The exam is conducted by NTA. As well as death the mode of the exam will be online mode medium of the exam is in English mode. The candidates must have to obtain 45% to 50% in the class 12th examination. IPU CET Entrance Test: The full form of IPU CET is Indraprastha University Common Entrance Test. The exam is conducted by Guru Gobind Singh Indraprastha University. The level of the exam is university-level. Every year the exam is conducted and it is only had once a year. The duration of the exam is 3 hours. Moreover, the mode of the examination is offline. DU JAT Entrance Test: The exam is conducted by NTA on behalf of Delhi University for admission into BA, BBA, BMS, etc. The full form of DU JAT is Delhi University Joint Admission Test. The exam is conducted for the Undergraduate level. The mode of the exam is Online and the duration of the exam is of 2 hours. Top recruiting areas after the BBA course There are many recruiting areas after the BBA course in India. But here we have only concluded the top 5 BBA recruiting areas. Below we have given the detail of different sectors and what are the benefits of working in this sector. As the below sector is growing at a good rate all over the world. Moreover, the sector is having a lot of potential and provides jobs to many candidates every Financial Sector: As per the report, India will be the 4th largest Private wealth market globally by 2028. In India, many Start-Ups and Businesses are opening for that Financial advice and Financial Reporting, and many more are required in any organization. So it is necessary for all small size company to medium size company. If any businesses manage their financial part then they can operate their business in a good way if they have all the data on how much they worked for their products and other offices work. Moreover, candidates can get a chance to work in the banking sector IT sector, and Finance Companies. Tourism Management: The candidates who is having a keen interest in the Tourism Management Industry can pursue the BBA Management specialization in the BBA course. According to a report, it is reported that by the2029 year there will be more than 50 million jobs in the Tourism and Management sector. Moreover, it is one of the most profitable industries. Some of the skills which are required for the candidate to survive in this sector are Language skills, Communication skills, Presentation skills, Positive attitude, etc. Furthermore, candidates can find jobs in this area which are Restaurants, Hotel, Travel Agency, Tour Companies, Transportation, Cultural industries, and many more. Sales & Marketing: Every business provides services or products. To sell any services and products the sales and marketing teams place a major role. If any new brand launched its product then they need a Marketing and Sales team to sell their product to the masses. Furthermore, to establish a business companies need candidates who can perform well in this role. Some of the skills which are required in the Sales and Marketing team are Communication Skills, Self-Motivated, Analytical Ability, Decision-Making Skills, Leadership Skills, etc. Human Resource Management: Human Resource Management is also known as HRM. The course includes theory, practicals, management, and the practice of the hiring process. Those candidates who have completed the course in Human Resource Management then they can work in the role of HR manager, Talent Acquisition Manager, HR Coordinator, Recruiter, etc. Those candidates who can manage the team and have the leadership skills then they can perform well in this sector. Furthermore, some of the skills which are required in this sector are Leadership Skills, Management Skills, Communication Skills, Co-ordinate with the whole team, etc. According to the report, the Human Resource Management sector will be growing at a 9% rate from 2020 to the 2030 year. Finance & Accounting: According to the report Finance sector will be growing at a 6% rate from 2020 to the 2030 year. Finance and Accounting involve the money part of the businesses. To grow the business and keep a track of the company finances then it will help you to expand your business. The candidates who have pursued a BBA course after class 12th can work in the finance and accounting sector. Moreover, if the candidate has a good skills then they can earn a good amount in their initial career of job. Some of the skills which are required in this sector are System Analysis, Critical Thinking, Time Management, Communication Skills, etc. Top Job Roles in the BBA sector Product Manager: Product managers are those who identify the customer problem and solve it within less time. The product manager also advises on how they can scale the business at a large level and expand the business to make a great product. Furthermore, Product managers need to constantly improve their skills to be capable of a job in which company they want. Moreover, the Project Manager role is one of the most demanding roles in any of the sectors. Some of the top recruiters companies are EY, Vedanta, Oracle, Microsoft, Byju, Flipkart, Google, Amazon, etc. The candidate can earn a good amount while working as a Product Manager. The average salary a candidate can get in the Product Manager role is INR 5 lakh per annum to INR 13 lakh. Digital Marketer: For the past 6-7 years there is massive growth seen in how the digital marketing industry has gone over the past few years. If any candidates want to work in Digital Marketing then it is a well and high earning job in the 21st century. Moreover, they are responsible for SEO, Social Media Management, Graphic Designing, Video Editing, Facebook Ads, Instagram Ads, Lead Generation, etc. According to a LinkedIn report, the Digital Marketing specialist is among the top 10 most demanding jobs with more than 8 lakh job openings. Moreover, the highly demanding job in Digital Marketing is SEO, Content Strategy, Social Media Management, and many more. Due to digitalization most startups and businesses are promoting their product and services online and startups and companies need digital marketing specialists. So they can reach a large audience. Furthermore, the average salary a candidate can get in the Digital Marketer role is INR 5 lakh per annum to INR 10 Financial Advisor: A financial advisor is a person who guides how to invest, where to invest, and in which company to invest. The advice they are providing is based on research. For that candidates must have to research the given company or a topic. So they can understand better which company they want to invest in and how they can grow their Organisation. Some of the benefits of becoming a Financial Advisor include are Flexible work, Unlimited earning potential if you enjoy the work you will don’t get panic while working, etc. Furthermore, the average salary a candidate can get in the Financial Advisor role is INR 4 lakh per annum to INR 15 lakh. Do I need to give an Entrance exam for BBA admission? The candidates who want a high package after their graduation. And, the candidates who want to take admission in Government and top private colleges. Then they must have to appear for the entrance exam. Some of the entrance exams are DU JAT, IPU CET, NMIMS, etc. What are some of the top colleges for BBA courses? Here we have mentioned some of the top colleges for BBA courses: â€¢ Madras Christian College, Chennai â€¢ Institute of Management â€“ Christ University, Bengaluru â€¢ Institute of Management Studies, Noida â€¢ Amity International Business School, Noida â€¢ Faculty of Management, Banasthali University, Rajasthan What are some of the top areas of specialization after completing the BBA course? The duration of the BBA course is of 3 years. After completing the course many candidates want to do specialization in the field they have studied. Here are some of the top areas of specialization after completing the BBA course: â€¢ Event Management â€¢ Aviation Management â€¢ Hospitality & Hostel Management â€¢ Healthcare Management â€¢ Finance â€¢ Investment Banking â€¢ Communication & Media Management What is the average salary a BBA graduate can earn after completion of the course? The average BBA salary ranges from INR 3-6 lakh per annum. What are the top job roles after completion of the BBA course? Below we have mentioned some of the top job roles: â€¢ Event Manager â€¢ Account Manager â€¢ Business Development Executive â€¢ Marketing Executive â€¢ Executive Assistant â€¢ Travel & Tourism Manager â€¢ Brand Manager, etc. Last Edited: April 17, 2023 Content Reviewed: April 1, 2023	{"url":"https://www.tiwariacademy.com/bba-course-full-details-overview-eligibility-criteria/","timestamp":"2024-11-04T08:38:10Z","content_type":"text/html","content_length":"233497","record_id":"<urn:uuid:80db0eb8-f75f-4628-8d62-4ea7a202de59>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00444.warc.gz"}
Math Tutoring, Knowledgeable Math Tutoring \| Jacksonville, FL Math is a very complicated and difficult subject for students to perform. Most of the students think it is impossible for them to perform well in mathematics due to its abstract and cumulative nature. Mathematics is not a difficult subject to perform, it just needs focus and practice which can give you guaranteed success. Our tutors help students by removing obstacles in the subject of mathematics. Our math tutors have extensive experience in the subject of mathematics and they can assist students of all grades in a professional way. Math becomes an easier and enjoyable subject when students start to understand the basic concepts and formulas. Math is difficult for students because they don't have the proper foundation needed for success. A math tutor is a person who can easily make your foundation strong and help you to develop your analytical and problem-solving skills. Our tutors have an excellent command of mathematics in all math disciplines. They use strong communication skills to share this knowledge to motivate and instruct students. Our well trained mathematic experts explain and demonstrate the mathematics questions and formulas to students in a variety of ways to help them understand it. Every student's mind is not the same as other students for understanding concepts in different ways. Math tutoring is a very complex and responsible job to guide students in every possible way. Math tutoring builds student skills and confidence in their Representation, Spatial Sense, and problem-solving skills. Most of the students probably arenâ€™t getting the tailored approach in the classroom alone whereas one on one math tutoring benefits them in a better understanding of their strengths and weaknesses, so they can give more attention and perform well. Our tutors have strong math skills and a good understanding of multiple math subjects, such as algebra, geometry, basic arithmetic, and trigonometry which can make students much stronger with their math skills.	{"url":"https://tutoringjacksonville.com/math-tutoring-jacksonville/","timestamp":"2024-11-08T06:24:10Z","content_type":"text/html","content_length":"126596","record_id":"<urn:uuid:85ebd0b0-0dfb-4ac6-96d9-b34929d8d9fd>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00383.warc.gz"}
Most difficult maths problems in history Search Engine users found us yesterday by typing in these math terms : Phoenix math ALEKS Self-Assessment, how to make a decimal into a mixed number, simplfying radical expression. Dividing integers worksheets, math solutions paper for saxon, solve by extracting the root, family of hyperbola functions, fre fraction worksheets 3rd grade. Difference between least common factor and multiple, math training for algebra 1, rational equation worksheets, subtracting equations calculators. How to make a mixed number into a decimal, java find the number of special character, calculate LCM from scientific calculator, programs to do algebra problems. 2nd order differential equation solver, examples of math trivia, free printable multiples and factors worksheets, free worksheet algebra. Rules of square roots, how to use calculator to find greatest common factor, Free Algebra Help to Solve Problems, homework answers conceptual physics 10th edition, least squares approximation ti-83. CONVERTING SQUARE METERS TO LINEAL METRE, difficult examples simplifying complex numbers, radicals worksheets grade ten. Addition and Subtraction explanation, quadretic forumal program, TI-84 PLus programs Factoring, adding and multiplying negative integers worksheets, Worksheet, adding perfect roots. Mcdougal littell algebra 2 worksheet answers, ti-38 calculator, maths worksheets - yr 7-8, A power point lesson plan on six grade math. Free Intermediate Algebra, printable +grammer worksheets with answer keys, "What is FOIL method?", Prentice Hall Algebra 2 homework help, middle school math slope of a line worksheets, 4th grade permutations, ladder method fractions. Putting radical expressions into calculator, solving algebra, "greatest common factors worksheet", prentence Hall integrated math, algebra 6th grade equations, ti 89 civil engineering programs, add sum of integers java. Advantage of addition method, Maths Int 2 Past Paper exams printouts, one step equations multiply divide worksheet, how do i put r2 value for the 84 calculator. Free simplifying expressions math calculator, families of quadratic equations, learn the easiest way for dividing, standard form equation calculator, free printables beginning fractions. "algebra for statistics", trinomial factoring puzzle, How Do I Work Out the Highest Common Factor, multi step equation instant answers, polynomial functions solver with synthetic division. Quadratic equations by factoring practice problems, mathamatic, gmat permutations, sqare number. 3rd grade coordinate point graphing worksheets, how to determine the zeros using vertex form, powerpoint for balancing equations, solving alegbra. Solve system of equations using ti-89, geometry scale factor worksheets, matlab solve, answers workbook biology prentice hall. Free pre-algebra worksheets, prentice hall world history high school chapter 8 and 9, simple ratio worksheets free. Algebric equation, beginners basic algebra practice free online, worksheets on multiplying and dividing integers. Adding and subtracting integer rules, transitional algebra games, free printable pre algebra practice worksheets, "biology concepts and connections 4th edition answer key download". Free 9th grade math printables, algebra 2 vertex form, polynomial simplifier. "algebra in plain english", how to create a completing the square formula on a TI-83, algebra II, cubed root. Aptitude questions in heat transfer, how to solve equations by taking square roots with exponents, square root SOLVER, factor tree printable worksheets, solving two step algebra problems, worksheets adding to 14, factoring cubed equations. Slope on ti 84, simultaneous equation calculator, softmath. Factoring quadratic polynomials in two variables, do it yourself graphing inequalities, advanced mathematics chapter 4 test form 1A page 82. Mcgraws hill 6th grade math book, graph linear equations powerpoint, math KS3 online free exams. Permutations and combinations using matlab, ti 89 solve, middle school math with pizzazz! book D answers, free elementary algebra practice. TI-84, solving equations by factoring using calculator, derivative+online+graph+calculator. Logarithmic calculator with square roots, pre algebra calculator online 7th grade, "perimeter worksheets" 3rd graders. How add, subtract, multiply, divide fractions, matlab convert fractions to decimal, one-step equations worksheet, lowest common multiple of 39 and 17, addition rules of exponential algebraic expressions, practice worksheets on integers for grade 8. Converting whole numbers to a decimal, algebra 1 an integrated approach chapter test, boolean logic solver, highest common factor calculator. Simplify irrational fractions, What are the rules in adding,subtracting algebra expressions, online t-83, glencoe algebra 1. Saxon algebra 1/2 3rd Edition table of contents, english lesson plans for first grade of high school, least common multiple of first ten counting numbers. Matlab ode45 example second order, Prentice Hall Mathematics: Pre-Algebra book online, combining like terms ppt, "accounting for dummies free download", what is Indiana prentice hall mathematic web code, free 9th grade math worksheets, how to get quadratic formula on ti-84. Using Matlab to solve second order differential equations, "identifying like terms" worksheet, glencoe algebra 1 answer key, printable pythagorean exercise with answer, TI-83 plus emulator free. Nonlinear algebra equations, glencoe "mathematics course" 2, free printble worksheets for cube roots, algebra with pizzazz answers worksheets, help solving equations containing fractions. Solving odes with singularities with Maple, finding common denominators worksheet, common denominator calculatora, how to add and subtract fractions with different bases, online calculator solve for x, least common denominator of equations. If you have the same base can you set exponents equal to each other?, glencoe math 7th grade texas, cost accounting for dummies, printable maths worksheets ks4, square root of 85, online maths class of 9th, Teacher worksheets for algebraic expressions. Scott foresman addison wesley worksheet, multiplying +alegbraic equations, grade 7 permutations. Worksheets for dividing and mutiplying polynomials, algebra programs, ti-calculator roms, Change of linear equations worksheets, ti 89 log function, "simple transformation" taks, 9th grade algebra Logarithm simplify calculator, where to find the answers to algebra 1 textbook, dividing fractions free games for kids, multiplying like terms, adding 2-digit numbers worksheets(no renaming), online radical calculations, cube root table for 6th gr. Decimals to square roots 83+, 6th grade math decimal practice test, i need a webite that will help me with my algebra 1 homework for free, simplifying radicals in java, how to factor cubed numbers. Mixed number to decimal, convert a mixed fraction to a decimal, isolating variables equations, free studing mutiply tables. Exponents and Square Root, practice masters algebra and trigonometry sturcture and method book 2, calculation for division in java coding. Simplest form of a fraction converter, Algebra Age Problems, factoring complex numbers worksheet, free materials for aptitude, free simple algebra problems. Factor Polynomials Online Calculator, Glencoe algebra 2 textbook answers, printable worksheets/quizzes on bar graphs, dounload TI 84 Graphing Calculator Simulator, how to factor an equation, solve nonlinear system numerically matlab. Simplifying cubes, tutoring program for college students, mixed numbers to decimal, how to solve quadratics on a ti-83, algebra UCSMP answers, Prime factorization worksheets. Steps on how to change a mixed fraction into a decimal, holt alg 2 logarithms, practice math sheets for adding and subtracting positive and negative integers, online trig answers. Easy simultaneous linear equation problems, maths yr8 activities, how to do percent equations, fifths root chart math, algebraic expression, writing free worksheets, Integers games. Calculating partial fractions, linear equation factoring, math worksheets on slope of a line, 8th grade taks worksheets, Solving simultaneous differential equations, solving algebraic equations, Solve partial fractions algebrator, how to make a line graph with decimals, where can I learn to add subtract multiply divide fractions online free, divide fraction by whole numbers interactive, algebra calculator cheat, rationalize denominator solver, solution of equation of third order. Free software for solving quadratic and cubic equations, formula for factorization, how do i use synthetic division with absolute maximum and minimum?, algebra 1 standard form combination word problem, adding snd subtracting negative integers game, hardest algebra, number sequences free online worksheets. Inequalities 7th grade part 2 questions nys test prep practice questions, quadratic eq on ti-89, how to write simplest form mixed fractions, radicals calculator fractions add, TEACHERS BOOK ALGEBRA 2, root on ti-83, download algebrator. Free worksheets proportions distributive property, TI calc rom, elementary linear algebra larson solution 5th. Solve second order differential equation matlab, percentage equations, maple solve field. 6th grade math formulas combinations and permutations, math algebra mixture equations, expanding cube root equation. Combining like terms printable worksheet, complex numbers solver, question papers of biology of class 9th, worksheet on multiplying and dividing, how to convert a linear equation to a vertex form equation, Institution testgen software for algebra, pre algebra calculator online. Excel functions square root multiplying, multiplying and dividing exponent worksheet, prentice hall math exercises. Holt algebra 1 chapter 6, nineth grade worksheets, third order polynomial, symbolic method to solve a linear equation, free printables on integers for grade 7, formula for multiplying integers, use casio calculator. Online problems for substitution method, mcdougal littell life science answer book online, funny algebra worksheet. Calculator de radical, online trinomial factoring calculator, absolute value with fractions and decimals, exponents with integers worksheet. McDougal Littell worksheets, help solve subtraction of rational expressions for free, solving logarithmic calculator, developmental algebra online. Online glencoe algebra book, FREE COORDINATES WORKSHEETS FOR 3RD GRADERS, ti 83 plus emulator download. Rationals calculator, graph equations+power, convert decimal to fraction calculator, how to do factoring quadratic expressions in the ti 84, online radical simplifier, TI-89 root, Printable Coordinate Planes. Calculator online for the chain rule and derivatives, downloadable english aptitude, convert int to decimal java, algebraic expressions worksheets, matlab second order differential equation. Geometry McDougal Littell answers, +free +emulator +"ti 84", find an easier way to solve word problems in equations, linear equation graphing, math trivia on circles. Ti 84 emulator, ks3 multiplication worksheet, ti 83 plus quadratic equation program, algbra tutorial, solve nonlinear differential equations. How to find cube roots with a Ti-83, solve my maths equation, algebra calculator for elimination, typing fractions on computer. Algebra fraction caculator, workbooks in dividing fractions, algerbra 2 calculator. Free 6 grade algebra tests, runge kutta matlab second order differential equation, mental math excercises for children+free downloads, FREE MATH WORKSHEET FOR 6TH GRADE PDF. Boolean algebra questions, solving nonlinear simultaneous differential equations using matlab, subtracting integers worksheet game, ti 84 apps radical form. Multiply and simplify radicals calculator, math sotions, convert 4/6 to decimal. Ordering fractions least to greatest calculator, importance of college algebra, how to factor a cubed polynomial, first order nonhomogeneous linear differential equation. Chapter 8 answers"bittinger math", ladder method, free mathematic inequality work sheet, formula parabola, Simplifying Algebraic Expressions Calculator. Sample of erb test, rudin "chapter 3" "problem 8", free algabraic equations worksheets, ti 89 pdf. Adding integers worksheet, 5 EQUATION USING COMBINING LIKE TERMS, algebra aptitude test sample questions, WWW.MYALGEBRA.COM. Free Simultaneous Equation Solver, algebraic expressions lesson 20, finding vertex point algebra 2. Math Tutor Programs, change y values on calculator, ti-89 calculator online, solving homogeneous differential equations equal a constant, solve for multiple variables programs, algebra, free exercises,grade 6, multiply radical expression calculator program. Worksheets translation 3rd grade, proper terms for subtraction values, Algerbra Real Application. COVERTING SQUARE METRES TO LINEAL METRE, division worksheets for kids algebra, inverse of square root in denominator, matlab solve, solving variable expressions with exponents, poem about prime numbers, algebra program. Simultaneous equations sample problems algebra, poems about trig identities, hardest maths equation ever. Preview of the book accounting handbook, Fraction Pyramid lesson and exercices, sample math parenthesis equations for fourth grade, complete the square worksheet, simplified radical form calculator. How to calculate gcd, online graphing calculator for linear programming, 2004 download, square root problem solver, algebra. Third root square root, how to convert sqrt formula and it's combination to excel, adding whole numbers and decimals work problems. Algebra proportions calculator, easy algebra worksheets, algebra long easy question =kids, TI 83 emulator download. Math formula for percent + algebra, glencoe algebra 1 notes, factorising quadratic equations cheat, holt mathematics worksheet answers, factoring out cubes, free downloads for radicals and complex Algebra Tutor, MBA Entrance Exam Test Preparation Question Bank free download, reducing exponents calculator, graphing equations help. Free math answer, permutations and combinations maths cheat sheet, radicals calculator, excel maths explanation yr 10. Math for dummies, test of geniuses with pizzazz, mixed numbers to decimals, third-Order ordinary differential equations matlab, 4th grade number patterns worksheets. Trigonometric quadratic identity worksheet, exercises on subtraction of algebraic expression, math learn to calculate, Algebra 1 beginner level chapter 3 answers, how to access online the prentice hall algebra 1 book, graphing calculator games online. Solution example of first order non-linear differential equations, quadratic formula standard form vertex, lesson plans adding and subtracting fractions with common denominators, free logical reasoning worksheet, fraction scale, least to greatest, converting square roots algebra, radical fraction equations. Solving multivariable differentiation, simplifying algebraic expressions, TI 89 complete the square. "conceptual physics test answers", TI-83 Plus cube root, Explain How to Do algebra, fractions worksheet grade 7, free algebra solvers. LINEAR EQUATIONS WITH FRACTIONS, store on TI 89, simultaneous equation solver, Greatest Common Denominator Formula, HOW TO PRINT A square root symbol in java using unicode. Cost accounting + free online course, adding radical calculator, how to do square root. Google using slope to solve real world problems video, how to convert a fraction to a decimal, "addition and subtraction of fractions"+algebra+interactive. Prentice hall algebra book online, easy algebra, adding powers with unknowns algebra, algebra with pizzazz 210, vertex form calculator. Aptitude papers of doli systems, Rudin; real and complex analysis; solutions, algebra and statistics equations, solving quadratic equations by square roots, "pre algebra math quizzes", equation for extracting cube root. Simple steps to solving algebraic expressions and equations, integral substitution calculator, solving logarithmic equations, free math test grade 6th. "unit plans" +algebra, fractions with variables calculator, maths exams yr 8, equation solver for 83, algebrator online, how calculate the possible three digit number from numbers 1,2,3,4,5,6,7. Online simultaneous equation calculator, easy way to solve a parabola, decimal expressions into fractions, printable worksheets subtracting integers, algebra 2 students text chapter 2 anwers, free worksheets on probability problems. Physics: An introduction answer key james s. walker download, quadratic equation slope, mcdougal littell algebra 1 cheats, worksheets for factoring common equation, solving radicals. Pdepe matlab second order, how to use matlab to solve partial differential equations, pictures of foiling/ math, 3rd Grade Children Counting Money Free Printable Worksheets, investigatory project in mathematics, algebra 1-elimination, definition radical biology.pdf. Interest calculator using JavaScript loop, algebra 2 taks answers, roots polynom simbolic univariate, how to solve least to greatest fractions, highest common factor of 26, algebra 1 book glencoe Least common multiple worksheets, College intermediate Algebra-Self Taught, permutations and combinations calculator TI 86. Add rational expressions online calculator, how to write a mixed number as a decimal, guess papers of board examination of class 8th, square root solver equation. Ti 89 solve complex number 2 variables, square root formula, Allgebra solution finder, worksheet two-step equation free, ti 84 random number generator. Modern physics problem solving workbook hrw answers, comparing and ordering fraction calculator, solving formulas variable, 10000435, Free 6th Grade comparison worksheets, year 10 exam general maths cheat sheet. Multiplying square exponents, Sum of a randomly generated number in Java, ti-83 finding roots, factoring numbers with variables, college algebra help, substitution method equation converter, adding,subtracting,multiplying, and dividing fraction test. Fun algebra projects, how can i calculate LCM from calculator, non function graphs, 9th grade algebra word problems perimeter let x =, solving systems of linear differential equations, office equation solver, ti 83 plus sample statistics problems. Free printable math year 8 tests, algebra 2 for dummies, how to solve square root problems. Cost accounting tutorials, square root in a expression, How to divide rational expressions?, how to solve quadratic equations on a ti 89. Calculator solve for variable, Algebra variable solving calculator, t83 calculator download, third grader work, adding and subtracting negative decimals worksheets, the imperfect square root. Ax+By=C variables, metre definition, lineare algebra+matlab+solve 2 equation and plot, outline for student study guide for Algebra I chapter on solving equations, simplifying radicals calculator Polynomial root equation solvers, how to solve ordinary differential equations with matlab, multiply radical expressions calculator, 78196#post78196. Simplify java shift bitwise, TI-89 Log base 2, calculate slope intercept, adding and subtracting integers worksheets, download texas graphing calculator free, adding positive and negative numbers Exponents higher level work sheet, college algebra problem solver, elementary math trivia, radicals without decimals. Real life examples of algebraic functions, learning to do algerbra, Simplifying Algebraic Expressions, cubed root calculator simplify. Simplifying radical fraction calculator, solving cubed trinomials, square root of variables, glencoe mathematics algebra 1 teachers addition, solve systems of linear equations three variables graphing calculator, Algebra with Pizzazz Sign up Worksheet 33, cube square root calculator. "3 variable systems"+"powerpoint"+"applications", freeware mathematics workbooks pdf, find rational roots solver, Dividing Monomials withsquared negative exponents, NEED TO WRITE FREE TEST ON Worksheets on graphing transformation, factor expression calculator, completing the square calculator, free algebra factoring polynomials worksheets, lesson plan for 1st grade in texas. Algebra with pizzazz answers 9th grade, exam paper for yr 11, second order nonhomogeneous linear differential equation, maths worksheets for factors, factorise online, multiplying and dividing test, Free Math Sheets 3rd Graders. Algebra using decimals worksheets for kids, calculating radicals, Grade 8 Algebra worksheet, First Grade algebraic expression, math and algebra equation writer. The calculator online tell the derivatives, Honors Algebra 2 Homework Help, cubed equations. Create worksheet like terms, factoring square roots solver, factoring equations cubed, tips for solving quadratic word problems, maple worksheet half-life calculation, integer review worksheets, exponential functions square root. Free worksheet fractions equivalent to decimals, solving quadratic equations of third degree, india primary school worksheets free, parabolas for kids, complex partial fraction decomposition ti 89, COST ACCOUNTING TEXTBOOK QUESTIONS AND ANSWERS, 6 grade english free quiz on adv. Permutations maths exercises, fundamental accounting principles interactive quiz answer sheet, college algebra help hyperbola, free printable booklet for 6th grade math, algebra vertex, online simultaneous equation solver. How to calculate partial fraction, grade 7 worksheet integer power, simplify rational expression calculator. Solving equations with fractions worksheet, c# tangent parabola example, how to solve algebra. Algebrator download, Simplify spuare root-2, solved problems in abstract algebra, prime number poem, roots locus for angels. Teaching writing linear equations, mathematics: applications and connections, course 2 workbook crossword puzzle answers, radicALS QUADRATICS, mcdougal littell algebra 2 resource book answers. How to solve propability of exact, free printable adding and subtracting integers worksheet, Finding Lowest Common Denominator Multiply worksheet, "pdf" ti 89, hyperbola rational function, "7th grade honors mathematics objectives". TI 89 ROM Download, Hardest math problem of all time, free calculator for multiplication of radical expressions, converting 108 16 25 to decimal form, finding the common denominator, combining algebraic expressions with integers. 9th grade sample algebra tests, online fraction simplification calculator, signed numbers worksheet, solving trinomials. Free pre-algebra worksheets for 7th grade, lesson plan on basic ks3 algebra, college algrebra clep, square numbers + interactive activity, power points algebra1, what is the product of a number and its recipical?. Expand using ti-83 plus, solving one-step equations worksheet, fraction least common denominator calculator. Online summation notation series finder, problems and solutions in algebra polynomials, rational expressions solver, simplify exponential functions, ti 89 solving polynomials, square root to the third help, linear equations with fractions 8th grade. Adding and subtracting decimals free worksheets, square root of exponent, NEW high school MATH TRIVIAS. Square root properties on ti-84, solve my algebra problems, square root calculator variable, doing operations (adding, subtracting, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions, ti-83 factor program. Algebra 2 variables equation worksheets, general equation of hyperbola, dividing fractions with problem solving worksheets, how to make a factoring program on a calculator, fractions for dummies for Trinomial online solver, free reverse foil worksheet, free multiple ged worksheet online, pre algebra coordinate plane worksheets, algebra with pizzazz answers graphs. Interactive Add, subtract, multiply, and divide positive and negative rational numbers, questions with answers in algebra, SOLVED APTITUDE QUESTION & ANSWERS, simplifying radicals calculator, decimal to a mixed fraction, beginner algebra, worksheet solving equations addition and subtraction'. Adding +alegbraic equations, equations and rational expressions calculations, physics algebraic equations for slope. Latest and Best Cost Accounting Books, factoring worksheet for third grade, decimal to percent conversion calculator, Excel equation, florida edition mcdougal littell science grade 7, free worksheets one step equations). 6th grade math sample pro, multiplying exponents terms, solving inequalities worksheets, higher ode matlab "initial conditions". Log properties ti 89 note, Quadratic equations switch between forms, dividing and multiplying negative and positive number worksheets, Computer aptitude books, graphing calculator ellipse, square root calculator. Program for print numbers from 1 to 100 without order in java, exponent algebra ppt, combing fractional equations. Compound interest teaching resources KS4, lowest common denominator calculator, Programming quadratic formula in TI-84 plus silver edition. Algebra, practice with dividing monomials, interactive quizzes or games, interactive games finding least common denominator, cubed root calculator online free. Percent equations, free year 7 printable maths worksheets, linear equations presentations, 8th grade exponent worksheet with answers worked out, lesson analyzing the effects on a three-dimensional object by a change in one of its dimensions. Online college algebra clep practice test free, find the solution solution set calculator, intermediate algebra calculator, rudin chapter 7 problem 1, fraction to decimal steps rules. Free simplifying exponent worksheets, examples about math trivia, prentice hall algebra 1 practice workbook. Mixed fraction into a decimal, calculate slope on a graphing calculator, free download aptitude test, free basic algebra worksheets, scientific notation worksheets, "grade 2" math " fractions test ". Chart of cost accounts cost accounting, factoring polynomials online, free mcdougal littell resource book download, books on cost accounting, online calculator to find derivatives using the chain rule for differentiation, how to solve three nonlinear equations in matlab, fun solving two step equations. Factoring Trinomials calculator, algebra II + story problems, online algebra calculator, simplified equation calculator boolean algebra, graphing linear equations on ti83. Algebra test papers, completing the square math lesson, change from mixed numbers to decimal, greatest common divisor formula, texas calculator ti 84 download, prentice hall algebra 1 lesson plans. "cube root" method, Yahoo Questions and Answer about hindi grammer, online graph that will factor, greatest common factor of 154, calculators that factor polynomials. Quadratic square root, extracting square root, 6-8 ks3 2007 sats answers, least common denominator calculator online, division solving third equation, division of decimals by decimals worksheet page 25 26, binomial calculator factor. Algebra equations finding percentage, how to solve system of exponential equation, FOIL math Diagram. 6th grade adding and subtracting fractions test, free online 9th grade algebra help, simplifying common factors with powers, free online worksheets with key gcf lcm, ways to learn algebra 1, what is the greatest common factor of 12 and 60, interscept equationmath help. Online tutorial Basic Maths, sets,domain, common problems for algebra students, ALGEBRATOR, quadratic equation calculator casio, mathpromblems.com, solving nonlinear system of equations in matlab. Free algebra 2 problems, MATH/PERCENTS GREATER THAN 100 OR LESS THAN 1.COM, compound inequalities solver, mean median mode range filetype_pdf, unit fraction and polynomials, Geometry Homework Cheats, second order nonlinear differential equation solutions+matlab. Iowa algebra test sample papers, "logarithm practice problems", High School Discrete Math Worksheet, printable slope worksheets, simplify exponential radicals, Indian child mathematics free materials, exponents lesson plan. Graph x-axis parabola ti 83, Function Rule Solver online, calculator graph pictures, math number sequence finder, ebook free college algebra 10the edition.pdf. Log sheet math, conversion mixed fraction to percent, Fun Algebra Worksheets, algebra 1 answers, combining like terms interactive, convert decimals to fractions with radicals. SOLVING LINEAR EQUATIONS IN ti-83, solving vertex form problems, cumlative test 5-7, Binomial Fraction Simplification calculator. Cheating on dividing fractions, glencoe algebra 1, 9th grade algebra worksheets, third root calculator, fun maths worksheet grade6-7. Beginning algebra problems to solve online, 6th grade work sheet adding subtracting decimals, practice 5-7 completing the square answer key, printable basic algrebra problem, how to balance linear equations, practice problems for multiplying and dividing fractions. Subtracting test, boolean algebra for dummies, FREE 10TH GRADE ALGEBRA HELP, slope ti-83, multiply trinomial calculator, make up a word problems that can be solved by finding the GCD and LCM, Saxon algebra two answers. Foiling radicals with variable, sequences sheet gcse, problems math grade 10, multiplying trinomials calculator, sample exam for subtracting mixed numbers. Math solver find the domain of a rational expression, online graphing calculator 3 variables, "QUADRATIC EQUATIONS" on-line CALCULATOR, algebra calculator two variables, answer key intermediate accounting 12th edition. Quadratic to vertex, adding, subtracting, multiplying, and dividing integers and positives worksheets, wwwchicago. Adding exponential equations, Alife in matlab, answers to glencoe geometry workbook. Prentice hall algebra 1 online, solving algebra exponents calculator, prentice hall algebra study sheets, Mixed Number in java, free online math help vectors, glencoe algebra 2 answers. Free printable worksheets for ontario grade 8 math, fraction as decimal worksheet, Scott Foresman-Addison Wesley Mathematics (Diamond Edition) online study guide, free online matrices solver, aptitude question & answer. Answers for the Algebra I textbok by Prentice Hall, Ohio, quadratic equation solver, written order polynomials. Squaring a variable with an exponent, variables in exponents, solve subtraction of rational expressions, free scale factor worksheets, simplifying radical expressions, www.math problam.com, multiple choice algebra questions grade 9. Prentice hall distributive property worksheet, ti-83 graphing calculator error messages, how to solve quadratic equations using the principle of square root. Chapter 6 life science 7th grade test from holt rinehart winston life science book, program codes for ti 84 plus, highest common factor problems, solve quadratic equation ti-89, Aptitude Question Ti-84 using fractions, rational expression calculator, maths activities inequalities, simplify roots and exponents. Glencoe algebra 1 slopes, worksheets for junior high on immune system, Advance algebra tutorial, root formulation of function. EdHelper.com-fractions 6th grade divide. write the answer in simplest form. fraction, adding positive and negative integers worksheet, free kumon wooksheet, frree sheets of mental math for primary, slope formula for a quadratic equation, how to solve algebra questions. Exercise free algebra high school, standard cost accounting formulas, mathematical statistics beginners. Find roots using factoring method, 9th grade practice algebra 1 worksheets, factoring online, tutor-usa.com worksheet pre-algebra, math factor calculator, ti 86 base 2. Printable multiplying and dividing fraction worksheets for 6th grade, instructor's edition essentials of college algebra gary rockswold book answers key, Modern Chemistry workbook answers, algebra one-step equations - free. Dividing algebra equations, matlab polynomial multiple variables, free worksheet on nonlinear simultaneous equations, When might completing the square be appropriate in quadratic equation?, free equation and inequality worksheets for 7th grade, worksheets for graphing linear equations, generate variable expressions worksheet. Math calculator for rational expressions, word directions solve by completing the square, algabra 1, free fifth grade math printouts. Math Formula to Find a Percentage, maple solve vector, middle school math with pizzazz! book e answers, nonhomogeneous differential equations, www.math for dummies .com. Extra practice worksheets for Elementary and Intermediate Algebra by Tussy and gustafson, mathematics working out permutation, adding and subtracting real numbers worksheets, solve your algebra problems online, "radical math answers", practise math test yr 9. Solving eqations, ladder method to find lcm, free kumon worksheet, free binary operation worksheet, free math problem solver. Prentice hall mathematics algebra 1 answers, rational algebraic equations, simplify radical expressions calculator, liner equation, solve simplify radical expression, Algebra Buster reviews. Free inequality worksheets, solving quadratic equations with 3 variables, how solving a linear equation in java. Online reverse graph calculator, hyperbola graphing calculator, the addition method fractions with variables. Beginner's algebra, holt algebra 1 online textbook, matlab nonlinear differential equation, college algebra software, rudin principles of mathematical analysis solutions, scale factor worksheet, what is vertex form in algebra. Where can i find a free step by step algebra help with my hw problems, solutions rudin, simplify exponent calculators. 6th grade math calculator, equation game, cubed polynomial, binomial factors solver. Pre-algebra, teaching yourself, printable algebra worksheets for middle schoolers, basics questions on rearrange formulas maths, algebrahomeworkonline.com. Planet list from least to greatest, order of operations worksheets, algebra+hungerford+solution, finding the LCD nd GCF of algebraic expressions, how to solve equation in standard form with integer coefficient, integers worksheets for sixth graders, math s+27 factor. Polynomials square roots solver, calculating root of parabola with t1, examples of math prayers, YR11 MATHS PAPER, matlab polynomial in 2 variables, how to do the linear combination method. Solving limits online, square root flow scale, math test adding, subtracting multiplying fractions, decimal notation distributive property, probability formula, online graphics calculator, graphing generator algebra. Solving quadratic with ti-89, solving equations for a variable worksheet, highest common factor of 47, 75,15, square roots and real life. Answers and work for algebra problems, "RSA Demo" p=, fun with algebra, GCF Calculator using exponents, lesson plan y8 simultaneous equation, Dividing Different Variables, scale factors into How to get a laplace transform using the ti-89, my algebra calculator, radical expression using square root. Graphic calculator system with matrix equations, final test worksheet for third grade, rational equations calc. Maths work sheet for 8 yr old, how do you add fractions?, pharoah math decimal maze game for kids, MAth trivias( zeros of a polynomial). Give me example of expression for multiplication or division, www.give me answers.com, algebra 2 software, least common multiple chart. Kumon level f, step by step solutions finding vertex, maple newton's method, learn algebra online free, learn basic algebra free, factor tree worksheets, ontario grade 10 math help. Multiplication freemathsheets, distributive property equations worksheet, math trivia for kids. How to solve fractions, glencoe answers, gelosia quadratic, print off a ti 83, fraction algrebra calculater equation. Games that teach slope, tools whole fraction to decimal, math formulas percentages. 7th grade multiplication algebra problems, roots of equations ti-83, T1 graphing calculator program download, 6th Grade Pre Algebra, factoring special cases calculator, ged cheats. Free gcse maths sheets, mix fractions to decimals, solving for specified variables, simplify equation, slope formula quadratic equation, prentice hall grade 8th math teacher's edition book. Add subtract fractions worksheet, convert second order differential equation to first order, algebra 2 synthetic division answers, in java calculate sum. Solve the formula for the given variable with radical, how to convert pure mixed decimals to decimal fraction, college algebra word problems examples company A charges, maths formula list, online free tutorial on trigonometry for class 10. Formula for percentage, square root equation calculator, algreba software, non-linear systems of equation + powerpoint. Algebra solver, PRINCIPALS AND PRACTICE OF ACCOUNTANCY ebook free download, vertex form problems, prime factorization worksheets free, online parabola graphing calculator, pictures on TI-83, free elementary algebra problems. Free drdo aptitude study materials, math scale questions, Class VIII Sample Papers. How do i solve trinomails, Saxon Math Homework Answers, factoring complex quadratic equations, square root comparison, everyday example of usefulness of pythagorean theorem, multiplying quadractics, heat equation non homogeneous neumann. 6th grade practice exams, mcdougal littell pre-algebra chapter 8 worksheet, mastering physics answer key, subtracting integers game. Integers mix worksheet, factor tree calculator, quadratic formula multiple choice worksheets, change the number to positive even when subtraction results negative number. Square roots and exponents, free mental maths sats papers ks2, solve algebra problem free, add fraction and decimal to equal fraction, Writing Linear Equations Worksheet, adding radical numbers, fourth grade division with remainders and eliminate remainders. How to solve equations with fractions, 6TH GRADE CHEMISTRY EXAM QUESTIONS, glencoe algebra 2 practice tests, how to simplify the cubed root of 2/3. Number tiles worksheets, maths long range plans - grade 9, grade 10 math algeebra. Adding and subtracting double digit worksheets, online algebra checker, graphing calculator help strings ti-84, adding subtracting integer games, solve equation system with maple. Pre algebra + multiplying worksheets, adding and subtracting games for grade 2, Algebraic expansion with exponents powerpoint presentation, square root addition subtraction. Kumon answers, solving equations real life problem worksheet, least common denominator sample problems, area and perimeter SAT questions KS3, hwo mathematics affect our every day life, examples adding and subtracting signed fractions. Logarithmic equations ti 83, 5th grade multiplying with the ladder method, download aptitude question bank, solving systems of linear equations by comparison. Difference between algebra and geometry, free online maths tests for 7 year olds, Easiest way to solve math numbers. Least to greatest in fractions calculator, simplify radical form fractions calculator, online usable TI 84 calculator, Mixed fractions to decimals, solve my precalculus problems. Addition and subtraction problem solving worksheets, chapter 5 holt biology pretest, 7th grade math - finding scale factor. Simultaneous equations power point presentations, glencoe algebra 2 answers even, midpoint word problems, solve log using ti 83. Easy ways teach slope intercept, math decomposition factoring, examples of solving cubed root equations, algibra, linear interpolation TI 89, college statistics worksheet. Practice Balancing Equations in Maths, free books on cost accounting, POLYNOMIALS SOLVER, math study sheet yr 9 factoring, factoring and completing the square quiz, "balancing equations" algebra, order of operations with square roots worksheet. Summations on a ti-84, square roots with exponents, how to write decimal as mixed number, how to divide decimals by integers, online simplifying expressions. Power points for balancing chemical equations, area of circles, grade 7, worksheet, math sheets for 3rd graders, square roots on TI 83, non-homogeneous second order differential equations, online calculator simplify algebraic fractions, Advanced Cost Accounting Problems and solutions. Create a table for a function rule online solver, ti 89 titanium store pdf files, converting a mixed number to a decimal, "square root" 48, least common multiple, factorise equations calculator. Vhdl gcd, solving equations using excel, algebra websites, examples of math trivia mathematics. Free penmanship practice, 7th grade, simplify algebraic expressions with square roots and exponents, linear loops in java, percentage calculation equation. Adding and Subtracting Fractions with common denominator Worksheets, trigonometry practice cpt, converting polar equations to rectangular equations. Printable practice worksheet for slope intercept form, distribute and combining like terms, first order differential equations solver, using scale--maths worksheets year 5, trivias sobre algebra, r-combination recursive algorithm. Solve linear system java, greatest common divisor 64 c, third-order polynomial how to square, Polynomial division solver. How to input algebra formulas into the ti-83 plus, really hard algebra questions, simplify the square root calculator. Algebra 1 holt, answers to Saxon Algebra 2 work, linear equations powerpoint, complex polynomial equation, cliff notes of basic algebra, system of nonlinear Differential equation matlab, permutation versus combination. 1-12 addition worksheet, algebraic proportions worksheet, java function to convert to base 16, printable math worksheets grade five bars graphs. How to do a lineal calculation, newton raphson solve nonlinear equation matlab, how to multiply rational expressions involving polynomials, gcd polynomial calculator, how to solve system of equation algebraically and graphically, how to check whether only integers or characters in a string java.. Rational Expressions calculators, Factor the difference of two square, power transformations ti 83, answers for math homework, ti-89 multiple equation solver @1, how to write cubed root in ti-89. How do you change a mixed fraction into a decimal, ti 83 downloadable calculators, TI 84 calculator worksheet on solving linear systems, How to Find the Square Root of a Number Easily, solving problen involving rational expression, adding, subtracting, multiplying, and dividing integer exponents. Rules for multiple radical equations, teach me algebra, quadratic equations square root method, Yr 8 maths exams, xy coordinates "basic algebra", fifth grade math worksheets, solving one step equations worksheet. Finding inverse of of a quadratic, multiplying fractions for 5th graders, free algebraic expressions worksheets. History of the can, excel slope intercept, 9th grade algebra, painless algebra reviews, how to simplify the square root of fractions. Solve by completing the square method: PPT, simplify exponential expressions, multiplying and dividing equations calculator. Foci of a circle how to find, add and simplifying expressions calculator, slope formula quadratic. The world's hardest algebra word problem, algebrator download, convert decimals measurements to mixed number. Quadratic simultaneous equations calculator, square root index calculator, free fraction worksheets 7th grade. Free linear equations worksheets, algebra simplification calculator, positive negative integer printable free, pre-allgebra. TI base convertit, mixed varible simultaneous equations, tutorial graphing a quadratic equation using a table of values, solving nonlinear equations symbolically, free books on linear programmation. Making square roots exponents, KS2 PRACTISE PAPERS ONLINE, free printable papers 1st grad. Algebra lowest common denominator, variable trial and error worksheet, algebra calculator rational expressions free, domain range parabola, ti 83 graph calculator tricks drawing pictures, college algebra clep answers. Free Word Problems + SIgned Numbers, algebra printouts, how to convert mixed number to decimals. Solve by elimination calculator, Free Online Math Tutor, steps solving equations fractions using distributive property, PreAlgebra and AlgebraTutor Programs, solving non linear differential Algebra and free worksheets, apptitude questions + answer keys, high school level fractions worksheets, free power point about expressions & algebra, algebra 1 worksheet answers pd 32 prentice hall, finding the common denominator worksheet. History of roots of polynomials equations using synthetic division, rewriting mixed number as improper fraction worksheet, convert decimals to fractions calculator online, solve simultaneous differentail equations matlab, interactive algebra worksheets. Grade Six Math Work Sheet Ontario Canada, pre algebra and introductory algebra pearson addison wesley, "ratio and rates" student worksheet, free worksheets on square roots in algebra, grade 8 - free Pie charts Activities without using a computer, free printable 6th grade math worksheets ratio and rates. Cost accounting book download, lesson plan for solving exponential equations, what is a non linear equation for 8 grader. Algerbra calculator, ti 83 emulator free download, Powers and Square Roots Chart, permutations and combinations problems and solutions to download, how to find equation of a hyperbola, 11plus maths prime numbers, McDougal Littell Florida Edition Algebra 1 textbook. Linear second order differential equations particular solution, How to find a square root of a fraction, boolean algebra calculator, printable 8tj grademath sheets adding subtracting integers, accelerated math printable work sheets, 6th grade fraction worksheets, pre algebra helpers. Division problems printable 6ht grade, sample polynomial problems, how to solve second order ode, how to find square root using calculator without radical, logarithm solver, free downloadable algebra gcse exercise generator, 4th Grade Math Printouts. What is the smallest common factor of 8 and 34, inequalities 7th grade lesson plan, solving 2 variable matlab matrix, do standard five maths test online. Free online algebra help calculator, factoring cubed functions, solve equations+5th grade. First grade printable math sheets, simplify expressions with square roots, steps to solving by square roots for a quadratic equation, algebra equation for 6th graders, 6th grade evaluating formulas sample questions, linear equations print outs. Graphing addition and subtraction, solving square root problems, division of fractions java code, plotting points pictures, pre algebra substitution. MAT question papers doanload, multiple choice second degree equation, multiply expression, sqaure root in excel. Where can I get solutions for Walter Rudin's texts?, holt algebra 1 terms, how do you divide?. Cost accounting books, matlab+extrapolation, key concepts of dividing and multiplying exponents, how to simplify radicals on graphing calculator, algebra pizzazz worksheets. Learn how to solve linear equations with fractions, mcdougal littell math course 2 answers, sample math problems involving Least common divisor, printable percent circle, simplified radical form, complex measures; Rudin; real and complex analysis; solutions; Chapter 6. Dividing integers worksheet, tests, algebra, structure and method, book 1, world's hardest math equation, factoring quadratic expressions applet, algebra calculator natural log, using slope to calculate quadratic equations, division of rational expressions calculator. CLEP cheat, graphing quadratic equations ti-89, introductory algebra for college students 5th edition, 11+exam papers, Dividing work sheet, example of trivia. Learn algebra fast, easy free proportion math worksheets, pre algebra puzzle worksheets, walter rudin solutions, algebra triple variables unknown distance, nth square root calculator. Boolean algebra solver, KS3 MATHS FREE WORKSHEETS, nonhomogeneous differential equation, solve cubed factoring, solving multiple differential equation using ode23, factoring polynomial on ti 84. Matlab command cube route, type of special product in algebra, Convert Decimal to fraction formula. Boolean Algebra simplifier, download worksheets on maths for 7 year olds, turn decimals into radicals. Calcul radical, pizzazz test of geniuses, glencoe introduction to business answers, ti89 solve simultaneous equations. "calculator in c"button, 6th grade algebra pre test, imaginary number worksheets, free previous years solved papers of graphics drawing for BE first year, E-7 symbol maple, analytic trig chp. 4 problems examples. Simplify square root program, gcse algebra questions, matlab solve system of equations, free radical wprksheets, matlab ode45 second order. Math poems about variables, grade 9 algebra questions, cube root worksheet, 3 simultaneous equations 3 unknowns, solving nonhomogeneous PDEs., adding subtracting multiplying and dividing integers worksheets, gre statistics notes. Algebra refreshment, factoring a cubed polynomial, online calculator to find derivatives using the product rule for differentiation. How to multiple with square roots, Free Algebrator, mcq on arithmetic series with answers, how to solve system of equation TI 89. Solving radical expressions on a TI-83 calculator, basic method for graphing a linear equation, algebracollegeprep.com. Free transformation worksheets, algebra how do you find the circumference, what is radical form in mathematics?, rudin solutions, maths paper for 11+ free, calculator online with decimals. Learning Basic Algebra, beg algebra for teens, fractional exponents in equations, newton's method with iterations on maple program. Multivariable equation game, question and answer on pre algebra, free download aptitude question pdf, calculator worsheet for fith grade, gre exponents square root exercises, subtracting and adding Download INTRODUCTORY ALGEBRA for College Students (5th ed.), math for year 11, alegbra worksheets, Rational expression calculator, roots of an equation solver, "Formula Sheet" partial, program factor quadratic. Square root equations worksheet, differential equations secend order nonhomogeneous, finding cubed root on TI 84, "ti-83 plus" finding cubic roots, free online intermediate algebra tutors, rational exponents cheat, trivia in mathematics. Fractions and variable calculator, complete the square practice, quadratic formula on ti84, integers line number worksheet, How do you solve algebra equations, worksheets on working with negative exponents and multiplying and dividing, answers to mcdougal littell. Simultaneous nonlinear equations in two unknowns practice problems, converting ratios printable worksheets, fraction to power. Highest common multiple of 3 and 4, how to solve algebraic fractions, algebra 1 mcdougal littell texas edition, how to use solver in casio calculators, "radius and diameter lessons for fourth grade". Completing the square online calculator, linear equation to standard form calculator, variables in exponent, define algebraic equation for middle school, free polynomial problems, powerpoint presentation on linear equations, balancing equations with fractional coefficient. Function form linear equations, variable math problem for kids, Practice Algebra Problems Fifth Grade, special product formula calculator, laplace transform ti 89, mathproblem solver. Worksheets for math numbers, 11,12,13,14,15, solving linear equations with variables using a ti83, simplifying squares, solve multiple equations in TI 89, ti-89 delta function, simplify an equation using ti30X. Simplifying square root calculator, binary tree algebraic Java, 6th grade printouts, algebra 1a math book online, solving square root problems with fractions and decimals, how do you balance chemical equations with your TI-83, difference in brackets and parenthesis in pre calc. Simple accounting problem and solution, rules for calculating when using positive and negatiave numbers, why is important to simplify radical expressions before adding or subtracting, year 7 maths work sheets free, aptitude and reasoning book for downloading. Binomial factoring calculator, algebra tutors in virginia beach, complete the square on TI 89, free 8th grade algebra worksheets, Free Math Solver. Free lesson plan examples 6th grade special ed math, solving second order differential equations examples using matlab, slope worksheet. Prentice hall conceptual physics answers, factor of n calculator, pre-algebra with pizzazz, free Adding and Subtracting fractions worksheet. Algibra soloutions, simplifying radical expressions calculator, turning mixed numbers into decimals, explain quadratic questions+grade 10, year8/math/multiplication and division of fractions/ How to do a cubed root on a calculator, learn basic Algebra, HOW TO SOLVE PERMUTATIONS AND COMBINATIONS ON THE TI-83 PLUS. Algebra algebraic structure exercises, How solve simultaneous equations in matlab, Linear equations - worksheets, maple non linear equation with constraint, add, subtract multiply and divide rational expressions, ti 89 differential eqn, apptitude question answer download. Math trivia with answer, first garde reading, simple elementary algebra worksheets, slope, linear functions, rate of change, square root fractions calculator, base 3 log calculator, how to write an accurate algebraic equation that fits the given data. Formula for turning a decimal into a fraction, formula of java script we can compute the grade, why algebra is relevant to my computer major, permutation and combination PDF, algebra on line test. Converting standard form to vertex form, free online equation solver, partial sum addition method. Ordered pair pictures worksheet, algebra solver solves equations showing all the steps, oredered pairs powerpoint for sixth grade, free algebra 1 9th grade online problems, simplifying complex rational expression, free algebraic fraction calculator, fraction lcd calculator. Javascript formula, roots quadratic equation, square root of 12 not a decimal, online graphing calculator, ordered pair is a solution of the equation calculator. Substitution calculator, trigonometry bearings word problems with solutions, ti-89 tutorial laplace, order. Algebra 1 standard form combination word problem glencoe, worksheets on conics, square root equation calculators, adding and subtracting decimal worksheet, solve by elimination calculator, "ti-83 plus" base. Ks3 coordinates worksheets, example of quadratic equations and fractions, a fun way to teach adding and subtracting fractions, worksheet conceptual physics. Why do we move the decimal two places to the right when writing a percent, how do u program the quadratic equation solver on the TI-84 Plu, how to converting mixed fractions to decimals, solving multistep multivariable equations game, free rational expression calculator fractions, math trivia example, accounting books downloads. Convert decimals into fractions worksheets, simple strategies adding subtracting integers, simplifying algebra calculator. Finding square roots tutorial, method of books of accounting+ppt, multiplying and dividing decimal worksheets, +how to add mix fractions; mat. Prentice-Hall,Inc. Solving Systems using substitution Algebra Chapter 6 practice 6-2 example exercises, online calculator for multiplying exponents, ti-83 plus quadratic equation, maths cheat sheet year 10. Multiplying and dividing powers, Algebra 1 Math Book Answers, Exponential Worksheet Free, interactive quadratic formula, Coordinate Plane Worksheets. Calculator for solving addition and subtraction equations, corporate account ebook free download, www.free math printables.com, Algebra solver software. C language aptitude, hyperbolas matlab, free help with factorization, algebra word problems+age, mathmatics algebra worksheets for class 7, expand polynomials on TI 83 calculator. Differential equations for first order circuits, elementary school mathematical quizz free .pdf, inequality worksheets. Factoring and square root method of quadratic equations, algebra substitution solver, easy way to turn a faction into a decimal. Download aptitude test papers, what is the highest common factor of 52 65 91, addition subtraction integer games, online math calculator polynomials, diameter and radius worksheets, how to order decimals from least to greates, algebra II exponents sample problems. Partial sums worksheet, answers for prentice hall physics, Advanced math + 6th grade + GA, square root simplify calculator, algebra with pizzazz worksheets, Graphing calculator pictures, 9th grade algebra projects. Intermediate algebra for dummies, rational polynomial worksheets, glencoe mathematics algebra 2 book teachers edition, application problems of system of linear equation in two unknowns, "greatest common denominator". Ti 83 instructions simplifying roots, "Texas Instrument TI-82" manuel, algbra step by step problem solving. Teachers edition biology answers parentice hall 2007 free download, exponent worksheet for grade 8, year 7 algebra test, simplify by factoring, T1 83 Online Graphing Calculator, algebra balncing equations, prentice hall mathematics answers. Simple balancing equations worksheet, linear equations using elimination method calculator, grade 12 expressions & +exponets, fun applications of factoring quadratics project, solving trigonometric equations worksheets, example of third order polynomial. Charles p. mckeague pre algebra california edition fifth edition, steps for dividing/multiplying radicals with variables, Solution Manual for Rudin Mathematical Analysis, high school worksheets for graphing, algebra 2 finding vertex, prentice hall mathematics algebra chapter 3 test answer guide. Algebrator, hungerford+solution, cost accounting exercise, quick division method + worksheets, alabama solving 2-step equations with decimal numbers, finding least common denominator calculator, free online english and math exams for adults. Factor a cubed quadratic, simplifying exponent expressions, Glencoe Online Math, factoring quadratic expressions calculator. Advanced Mathematics Richard G. Brown, how to use a scientific calculator to find the greatest common factor, find range and domain of a logarithms on TI 84, 5th grade adding multiplying decimals Subtracting integer worksheets, holt biology chemistry of life worksheet with answers, cubed root practice activity, system of equations by addition method calculator. Permutation examples 7th grade, free fourth grade division worksheets, prentice hall algebra 2 with trigonometry answers, factoring the sum or difference of two cubes calculator, ti-89 delta, holt mathematics jokes, writing mixed fractions in TI-89. How can i take the punctuation out of a String in java, free junior high algebra study help, math trivias, free integer worksheet, math contemporary abstract algebra, holt algebra 1 notes. Worksheet on real and complex zeros of a polynomial, laplace transforms ti 89, converting mixed fractions to percent, www.Math worcksheets.com. Partial sums addition worksheet, radical and variable calculator, advance algebra integrated mathematics answers. PRINTABLE ALGEBRA PROBLEMS 7 YR OLD KIDS, answers Key To Algebra Book #2, #2 math aptitude test answers, simplify radical expression calculator. Bing visitors found us yesterday by typing in these math terms : • Algebra with Pizzazz Worksheets • rational numbers as fractions worksheet for 6th grade • simultaneous nonlinear equations • how to solve second order differential equations in matlab • skills in algebric expression • what is a 20 prime difference +interger • online factorising practise • pre-algebra with pizzazz worksheet 133 • +ged +fractions +lessons +free • texas instruments TI-85 tutorial save formulas • algebra division subtraction • factoring KS3 • what are some sqare root questions to put on a study guide • algebra 1 math textbook (holt) • Algebra 2 chapter 5 finding the 4 points of vertexes • How algebra can save my life • how to put formulas into your inverse functions TI-83 plus • special product and factoring • how to do vertex form algebra 2 • free lesson plans on elementary algebra • sum numbers in java • study guides for Prentice Hall Algebra I • 2ND YEAR HIGH SCHOOL MATH TRIVIA • adding, subtracting, multiplying integers worksheet • factoring "root method • adding multiple negative decimals • 6th grade decimal practice test • simplifying algebraic equations • imaginary numbers free worksheet • add subtract multiply divide fractions worksheet • bite size 11 plus practice web • slope writing linear equation worksheet • jobs that use systems of equations • radical simplifying • convert second order ODE to first • area of a circle free worksheet • if i have the square root of 35 divided by the square root of 21 what would the answer look like? • equation solver,excel • step by step online free help with graphing by intercepts • rudin solution of chapter 7 • holt algebra 1 ebook • multiplying rational expressions calculator • maple simple equation system • algebra with pizzaz • mcdougal littell algebra 1 workbook • free finding common denominators math worksheet • 9th grade algebra exams • differential matlab • what is the difference between simplifying an expression and solving an equation. • algebra function tables worksheets • fun algebra worksheet • "synthetic division worksheet" • simplifying radical expressions online quiz • t89 calculator online • java program 2 integer numbers and their difference • Simplify expressions 5th grade • 3rd order quadratic • linear equation in java • greatest common factors with variables convert • comparison of fractions worksheets • pre-algebra with pizzazz worksheets • square root of improper fractions • percent worksheets • show formula on how to convert inches to meters • quadratic equation ti89 • quadratic formula graph • high school algebra 2 workbook answers • pre algebra free online practice worksheets • Real life permutations • adding and subtracting positive and negative calculator • linear equations and inequations slove on graphs • great 8 math work book 1.2 • how to do scale factor • mathmatics algebra • radical expression calculator • absolute value equations vertex form • easy ways to do logarithms • algebra II worksheet software • linear programming graphing calculator • free download aptitude ebook • "orbit stabilizer theorem" tetrahedron order • finding factors for imaginary numbers ti 84 • factoring difference of cubes calculator • fractions with square roots to exponents • free adding and subtracting fractions test • tutorial aid in pre algebra • algebra 1 prentice hall mathematics answers • fractional exponents in quadratic • linear equations in two variables Worksheets • Lesson Plans on Multiplication Properties of Exponents • holt mcdougal algebra: structure and method book1 • converter for rational expressions • how to convert a decimal to a mixed number • free 11 plus practice paper • java class for dividing polynomials source • algebra 2 online textbooks • prentice hall physics answers • add subtract multiply divide decimals • texas glencoe pre algebra answers • CALCULATING LINEAL METRE • hoe to find the lcm of two numbers • " solved aptitude questions" • slope mathmatical • long division of polynomials solver • homework answers for simplifying fraction • Converting Lineal metres to metres • simultaneous equation solver 3 • e63 middle school math with pizzazz! book e answers • dividing mix fractions • pre algebra combining like terms worksheets • mixed number as decimal • convert lineal metres • Find the prime factorization of 425 • online algebraic fraction calculator • algebra for ks2 • simultaneous equations in form of quadratic • teaching quadratic equations for slow math students • aptitude free download • how to pass values in quadratic equation C# • decimals least to greatest • Free Math Answers Problem Solver • how to convert decimal to mixed number • factor program for Ti-83 • solve equations with fractional exponents • AJmain • college level algebra software • scale factor grade 8 • 9TH GRADE ALGEBRA TAKS QUESTIONS • Mix Fractions • difference of two square examples • dividing rational expressions calculator • free adding & subtracting • the school tawnee stone • examples of math trivia with answers • real life algebra lessons • printable worksheet slope of a line • quadratic equation solver with one variable • algebra software programs • glencoe mathematics algebra 1 • algebra pdf • FRACTION ALGEBRA • solving quadratic word problems+grade 10 • free online glencoe algebra 1 chapter 4 • download infosys bpo aptitude questions and answers • algebra problem finder • square and cube numbers games • Solving simultaneous high order differential equations • free graphing worksheets in slope intercept form • Downloadable TI-89 calculator • binomial equations • solve 2nd order differential equation • excel formula for finding slope • cube root tree chart • solve graph • step by step solution of completing the square • multiplying and dividing pronumeral worksheets • prentice hall mathematics worksheet • using integers 1, 9, 6, 8 come up with an equation that equals 9 • glencoe algebra 1 chapter 4 section 3 • Extracting Square Root • worksheets one step equations • java great common denominator code • addison wesley making practice fun polynomials puzzles • simplifying square roots expression • Cambridge O-Level NOV 1998 Answer Sheet BIOLOGY • texas instrument t1-83 questions • greatest common factor calculator with variables • 9th grade math worksheets online free • simplifying radicals answers • free online logarithm problem solver • free ways to learn algebra • algebra worksheet word problems free • gr8 english revision worksheets • monomial division worksheets • how do I convert 55% to a decimal? • multiplying decimals student worksheet • exponents multiple choice • converting radicals to decimals • greatest common factor calculator • java great common divisor • Solving One step variable equations using Multiplication and division worksheets • simplifying radicals worksheet • Printables exponents, multiplying and dividing • how to solve equations using the distributive property • negative cubed exponents fractions • free algebra worksheets pictures with ordered pairs • ti 83 plus emulator • math trig ratio problems and solutions • decimal as a fraction in simplest form • chapter 3 lesson 5 McDougal Littell math course 3 answers • using a calculator to find common denominator • factoring equation calculator • interactive factoring quadratic equations • TI-83 extrapolation vs interpolation • writing algebraic expressions, free worksheets • calculator to add square roots • denominators calculator • how do you know if a radical is simplified • ways to solve equation using adding or subtracting multiplying or dividing • square roots and square numbers worksheets • ti-83 octal numbers • quadratic least squares ti-89 • free 12th grade taks worksheets • math lessons on slope • graphing linear equations scientific calculator powerpoint lessons • area 3rd grade worksheets • calculator cu radical • first grade math problem solving problems • permutation combination 6th grade • www.hardestmathproblems.com • "Free Algebra for beginners" • radical algebra • free algebra worksheets • WHAT IS THE LEAST COMMON MULTIPLE OF 2,8 • coordinate planes and slope worksheets for kids • learning basic algebra • rational expression online solver • cross product in pre algebra • factoring trinomials calculator • 6th grade public school syllabus free worksheets • Least Common Denominator Calculator • lowest common demoninator calculator • graph equation site • why algebra is relevant to my programming major • solving simultaneous equations software • Free math translation worksheet • how to do cubed root with the texas ti 83 • addition and subtraction of rational algebraic expressions • rational expression online converter • products and factoring • combinations in second grades math • convert 64% into a fraction • absolute value equations worksheet • radicals in calculator • software de algebra • fraction variable calculator • how to square root a decimal number • answers for algebra (calculater) • slope algebra for kids • compilation of algebra • ti-83 rom image • take a 9th grade algebra test online • Decimal to radical form • rules of adding with variables • middle school math with pizzazz book d-65 • "type in radicals" • pre algebra lesson plans • free 6th Grade Math Help • factoring on ti 83 • free math test on algebra2 • 5th grade math combination worksheet • simplify radicals expressions • adding subtracting positive negative numbers test • factor calculator = 0 • trig answer • 5th grade math printouts • chemistry year 7 christmas exam papers ks 3 • multiplying roots of fractions • basics of algebra graphs • how to calculate a common factor • answer to algebra 1 • science variation practise sats interactive questions KS3 • lowest common denominator worksheet • printable worksheets on finding the area of a triangle • add or subtract rational expression 3x/3x^2 + x - 10 - 5/3x^2 + x - 10 • coordinate plane powerpoint • free 11th grade worksheets • where in life will we use graphing equations • finding lcd worksheet algebra • radical square root calculator • glencoe algebra 2 worksheets • pdf to TI-89 • powerpoint "like terms" • analysis of an algorithm+aptitude questions • free solve algebra formulas • Search larsons intermediate math • ebooks download Finite Math with Applications Hungerford • cost accountancy books • everyday mathematics homework cheat sheet • basic math for dummies mathematics order of operation • algebra games 5th grade • ratio word problems worksheet • decimal to square root converter • graphing calculator pictures • lesson plan in rational algebraic expressions • advanced algebra problems • cube fractions • factor sum of 2 cubes calculator • exercises pythagorean theorem, algebra 1 • order fo operations 6th grade math • solving proportions calculator • practice quadratic motion problems • systems of fractional coefficients calculator • solve maple equations system algebraically symbolic • factors and quadratic equation • adding, subtracting, multiplying, and dividing square roots • permutation and combination activities • algebraic pyramids • difference quotient rational functions • "harcourt math" "grade four" assessment "practice test" chapter 11 • free books of Accounting • Least Common Multiple of expressions • square of the difference • mental maths for year 2 printouts • median mode mean range printouts 7th grade • least common denominator formula • multiplying decimals grade 7 • how to solve math exponents • importance of algebra • T1-84 calculator instruction manual • online positive and negative decimals ordering • worksheet on slope • graph linear equations worksheet • polinomial java • algerba work sheets for fourth grades students • convert mixed number to decimal • algebra questions and answers • online factoring expressions calculator • integer games for kids • prentice hall algebra two with trigonometry teachers edition pg 227 • venn diagram LCM GCF math lesson plan • how to find a fraction equivalent to a given decimal • worksheets on solving simple equations • Cost accounting tutorials • adding and subtracting negative numbers worksheet • systems of nonlinear inequalities in maple • the ansers to the mcdougal littell pre algebra work book • sensitivity specificity likelihood ratio confidence interval calculator post-test probability • homogeneous particular differential • school 11+ exam online tests • examples of algebra word problems and answers • solve fraction online calculator • sample graphing calculator • add fraction with integers • Ti-84 activities on box and whisker plots • cubed roots ti-83 program • workbook answers to algebra2 • modern chemistry chemical bonding worksheet answers • advanced algebra chicago series • math practice sheets for grade 10 • rational expression calculator fractions • online calculator for polynomials • algbra testing • holt rinehart winston algebra 1 textbook online • write the problem as a logarithmic expression • Free Downloadable TI-89 calculator • worksheets with equations of a line • writing equations in vertex form. • online t89 calculator • "simplify algebraic expressions" + SOL + Virginia • help with algebra • once done factoring a quadratic relation how do you graph it • solving first order differential equations • step by step method of completing the square • graphing calculator outline • rom texas TI 83 download • solving specified variables • algebraic formula • Algebra 2 answers • algerbra fractions • how to simplify algebraic expressions/multiplying,exponents and variables • Free Geometry Holt Textbook Answers • free algebraic calculator • how to solve logarithms on calculator • complex numbers coordinate plane • graphing calculator plotting points • geometry chapter 4 TRIVIA • lesson plan for middle school squared and cubed of a number • "What are the steps used to solve an equation with rational expressions? • solve equations by fourier transform eigenvalues • to answer a sats question {fractions} game • change in slope formula • basic algebra worksheets • 8 class sample papers • examples of proving trig identities • how to slove equation algebra • how to convert decimals into fraction matlab • scott foresman social study workbook page 9 answers • pdf to ti 89 • algebra proportion worksheet • order fractions from least to greatest • lesson plan in algebra • grade two revision free test papers • add two errors statistics square • scale factor math • free complex fractions worksheets • Free Graph Template • ode23 loop for solving non homogeneous equation • free mcdougal littell algebra 1 answers • java polynomial transform • mathematics 9th grade practice papers • solving simultaneous nonlinear equations on matlab • online graphing calculator table • finding the directrix using a ti-84 • convert whole number to hundredths • pre algebra free tutorial • free statistics papers • algebra rearrange app • heat transfer worksheets ks4 • poem about pre algebra • factoring equations calculator • downloading aptitude papers • second order differential homogeneous • vertex form and how to find the zeros of it • teaching equations 5th grade • free grade 9 regents math exam and explanation • decimals to fractions calculator cheat sheet • printable algebra 1 practice tests • TI 84 plus downloadable calc • algebra domain and range worksheet • factor quadratics calculator • free 9th grade texas algebra tutoring slopes • linear combinations solver • scientific notation sums worksheet • worksheets for algebra 1a • inequalities fourth grade interactive • 6th grade super advanced geometry online practice websites • quadratic fraction calculator • math trivia trigonometry with answers • adding variables with common denominator • replace square root • QUADRATIC FORMULA EXAMPLES binomial squared • how to simplify radical expressions • radical expressions calculator • algebra 1 glencoe free online • aptitude question with answer • free math word problem websites for fifth grade • simplifying squares convert all radicals to rational exponents • ti 83 + square root with radical • solving logarithm problems on a TI-86 • fun solving two step equations worksheet • solving for x and y worksheets • Free TI calculator quadratic equation program • decimal to mixed number • holt reader algebra part 1 • rudin chapter 4 solutions 16 • solve variable formula • adding and subtracting positive and negative numbers worksheet • ti 84 radical prgorams • cubic root of fractions • parabola algebra de baldor • number system with decimal solver • free algebra equation solver • "standard form to vertex form" • ks3 quadratic inequalities • Bernoulli's polynomial code in java • free algebra practice for 7th grade • ti84 quadratic equation • past exam papers grade 11 • harder discrete probability and GMAT • free download cost accounting ebook • Change mix-fraction to decimal • Second order differential equations using matlab • free online algebraic fraction calculator • transformations worksheet elementary • mcgraw hill 8th grade science worksheets answers • Maths formula cheat sheet • College Math For Dummies • "Texas Instrument TI-82" instruction manuel • free derivative problem worksheets • worksheets for 6th grade math finding the slope • how to find roots on ti-83 plus • prealgebra & introductory algebra math problems help • "solving equation test" • adding radicals calc • TI-84 Plus solve matrices equations graph free • T1 83 emulator program download • simplifying square roots fractions • algebra tiles worksheet • adding fraction of square roots • pratice work • solve by completing the square worksheets • algebra mixtures worksheet • adding and subtracting negitive fractions • free algebra 2 matrices homework solvers • free polynomial factor solver • online calculator for solving word problems • aptitude math tests 5th grade • free graphing worksheets on ordered pairs • laplace transformation on ti 89 • step by step solving quadratic equations • simple fracton worksheets add and subtract mulitply and divide • probability test paper india grade 6 • holt mathematics worksheets • factoring polynomials for grade 10 exercise • dividing and multiplying scientific notation worksheets • exact form radicals • factoring calculator complex • Lowest common denominator calculator • the square root method • aptitude question and answers • polynomial degree ti-89 • turning percent into decimal in a conversion table • solving a quadratic equation needing simplification calculator • decimal square root • free pictograph worksheets • Algebra: Structure and Method • solving first order partial differential equations • GED math word problems free printable • online greatest common factor calculator • solving 1 step equations worksheet • "least common denominator" worksheet • decimal to rational fraction conversion • divide radicals calculator • free algebra 2 problem solver • maths parabola for basic explanation • substitution method math • Introduction to Algebra worksheets for beginners • how to do greatest common factors solutions • adding, subtracting, multiplying, dividing with negative numbers worksheets • [Least Common Multiple Math Worksheets sixth grade] • algebra help, rational expressions and equations, calculator • McDougal Littell Biology California Study Guide work book • grade 9 math how to find square roots • using calculator to write an equation • formula for X is what percent of Y • dividing fractions with variables lesson • converting decimal to fraction calculator • system of 3 nonlinear equations matlab • operations on cubic roots • permutations and combinations questions and solutions • aptitude question and answers • summation notation ti-84 • solving third order differential equations in MATLAB • logarithmic quadratics • "texas ti-89 mathematical series" • What is the answer to a math equation of 2 to the 9th power plus 1 • integer games subtraction • solving equations two radicals worksheet • cube root function on TI-83 plus • ks3 coordinates picture worksheets • free math aptitude exam • glencoe algebra 1 code • division of fractions • How to graph constraints for Algebra II • finding the square of the radical expression • cube root 16 • maths exercise for year 5 • how to convert a mixed decimal to a fraction • fractions worksheets grade 3 • generate algebra graph • Examples of the dfference between linear inequalities and linear equations • combination worksheets • implicit differentiation calculator • free program solving rational expressions • graph equations for phone • calculate lowest common denominator • online fraction variable calculator • teach yourself algebra • cliff notes for algebra • answer for Glencoe Pre-Algebra. Word Problem Practice. Variables and Equations ... Glencoe Pre-Algebra. Word Problem Practice. Ordered Pairs and Relations ... • polynom divider • convert 8. 1/8 • multiply a decimal with another number that doesn't have a decimal • factor a cubed polynomial • trinomial factor calculator • free algebra factoring worksheet • pdf ti-89 • 5th grade expressions and equations • glencoe geometry test review sheets • how to find logs on a ti 89 • online TI-84 • rationalizing denominators with square roots worksheets • solving accounting equations • middle school math worksheets for 9th grade • dividing trinomials calculator • square root functions recognizing the graphs • standard form calculator • 9th grade sample math test • how to multiply integers game • ti 83 factoring program • mathematical analysis ebook rudin pdf • help in algerbra • highest common factor word problems • square root steps to solving • sixth grade math printouts • ks3 maths Inequalities in one variable • how to solve systems of equations that have fractions in it • "exampels of lagrang equation" • base 6 logs on ti-83 • cube root of 9x times cube root of 4y • like term calculator • free download Induction machines+Alger • BALANCINH EEUATIONS GRADE 12 CHEM ISTRY • practice pre algebra chapter 5 fractions adding and subtracting • download aptitude paper sample pdf • Math Answers to All Problems • algebraic calculator • the least common multiple of 34 and 52 • "mathmatical rules""exponents" • "simultaneous equations" substitution elimination .ppt • Simplify Cube Roots in excell • "linear of algebra for statistics" • matlab simultaneous equations • how to solve pre algebra problems • grade 11 exam papers • dividing decimals cheat • Balancing Chemical Equation Calculator • discrete math solve 3rd degree equations • equations math sample question • substitution method algebra (answers) • math investigator • GMAT formula Cheat sheet • simultaneous equation solver "3 variables" program • divide algebraic operations +bash • math formula to get percentage • pre-algebra with pizzazz pdf • algebra 2 problems • least common multiple of 26 and 22 • quadratic graph solver • plotting graph worksheet for 4th and 5th grade • radical simplification calculator • convert to square root calcualtor • general aptitude questions • math factoring calculator • Free Worksheets Order Operations • Advanced Algebra Special Products • ti-89 forier transform • comparing ordering integers worksheet • GMAT free sample test papers • combining like terms examples with fraction • writing mixed fractions into percent form • how to order decimals from least to greatest • Print math test on variables in general patterns • non-homogeneous differential equations • equation foiler • simplify radical • applet for trigonometric notations for complex numbers • algebraic expressions worksheets 4th grade • teach me parent functions algebra • FREE BEGINING ALBEBRA WORKSHEETS GRADE 8 • factorization of 3rd order equations • algebra 1 answers to workbook • relations and functions free worksheets • how to do a do loop to find the square root of a number in visual basic • prentice hall pre-algebra workbook • radical expressions find domain • online maths fractions beginners level tests • Prentice hall mathematics-algebra 1 practice quizzes/tests with answers • vocabulary multiply divide • basic algebra concepts functions,integrals • year nine maths questions on functions and inverse functoins • free boolean expression simplifier • glencoe eighth grade motion problems • substitution integral calculator • graphing ellipse and hyperbola • percent equation worksheet • 5th grade variables in equations • algebraic equasion • mathematical formula to find percentage of a number • Mixed Numbers to decimal • ti-89 quadratic formula • practical ways to teach maths rotations • free online antiderivative solver • simplified radical form of square roots • how to do cube root on calc • quadratic program ti 84 • nonlinear equation solver • algebra 1 by holt • free homeschool printouts • decimal to fractions worksheets • how to get quadratic equation on TI-84 • imperfect square roots • summation notation of square roots • multiplication worksheets for third grader • computer review simulations for College Algebra CLEP • examples of evaluating quadratic expressions • mathpower 9 online • Teach me how to solve multiple step equations for eight grade • decimals+free printable Grade 5 flash cards • glencoe algebra 2 teachers edition texas • translating english phrase into algebraic expressions worksheet • simplify expression calculator • Prentice-Hall,Inc show Algebra Chapter 6-2 on substitution • online summation calculator • simplify complex fractions calculator • advanced multipling charts • Solving Second Order Differential Equation • ALEKS cheat sheet • algebra 1 holt book hw answers • ged practice worksheet for history • math worksheets on fractions and LCM • How would you write S cubed T to the zero power in fraction form? • solving simultaneous equation excel • linear equation worksheet • free algebra on-line • hyperbola equation • complex numbers vector addition worksheet • algebra equasion • factoring function with ti84 plus • signed fraction addition worksheets • free online quiz Holt, Rinehart and Winston Elements of Language grade 7 online test • free graphing printable worksheet 7th grade • least common multiple equation • scientific method variables samples for 6th graders • 3rd grade volume worksheet • nth term calculator • grade 8 math ontario online test • how to multiply integers games • solve for variable exponent • solve cubed polynomials • ratio problems solver • algebra 1 solver • "Combining like terms" puzzle • saxon math course 1 cheats? • quadratic equation factorer • 3rd order polynomial • free printable third grade math sheets • combination[maths] • simplifying expressions worksheet • logic puzzles worksheets-printouts • TI 83 rom free download • rearranging formula activities • variables and exponents • cost accounting free download • download ti-84 calculator • solving 3rd order polynomials • Teacher workshets Advanced Mathematics Richard G Brown • calculating equations for a specified variable • scale factor quiz • solving equations using scientific notation worksheet • free way to learn algebra • Lowest Common Denominator Calculator • Concept of Algebra • java code to terminate user input using while loop • addition and subtraction with integers worksheet • graphing calculater • convert fractions to decimals solver • free intermediate algebra tutor • free maths worksheets doing directions on a compass • second order homogeneous differential equation • multiplying dividing integers worksheet • simultaneous solver • free online graphing calculator chart • ga 6th grade arithmetic and fractions practice work book • fraction finder cube • Expression and equations with variables worksheets • free sample 8-Puzzle Solver • Example Of Math Trivia Questions • mixed fraction decimal • 6th grade fun lesson plans on factors and monomials • square root inequality calculator • how to find prime numbers with calculator easy tutor • solve calculators rational expressions • algabra • cubic equation worksheet • exponents and roots • math trivia trigonometry • cost accounting online books • accounting books free download • factorise a cubic calculator • matlab differential equation second order tutorial • fractional quadratic equation • graphing mixed numbers • algebra vertex form • free linear equation worksheets • what is the difference between functions and linear equations in algebra • converting mixed fractions to decimal • graph the equation help • multiply worksheet • prentice hall algebra 1 pdf • numerical method to solve simultaneous equation in matlab • algebra slope worksheet • greatest common factor formula • multiplying cubed quadratics • cost accountancy exam questions • solving differential equations simultaneously • writing linear equations powerpoint • solving multivariable equation game • matlab convert binary to decimal • high school physics worksheets with answers • percentage formulas • fluid mechanics questions answers • example of "radical form" • adding positive and negative puzzle • dividing fractions 5th grade • trigonomic equations • algebra helper • combining like terms • solving simultaneous equations three variables • Glencoe Online Book Resources for math (6th grade) • Free Algebra Homework Solver • holt california algebra 2 workbook • dividing decimals worksheets • greatest common factor of polynomials worksheet • www.edhelper satsexam • basic algebra power of • expressions worksheets • 7th grade formulas • free printables algebra • "test on unit circle" • interger worksheet • algebra fraction equations worksheets • online matrice calculator • radical expressions solver • equation answerer • free printable rate ratio worksheet • java library to simplify algebraic expression • learn algebr • figure ratio algebra • free ti 84 emulator • mixed number into decimal • free algebra cheats • year 11 math gcec • Algebra and trigonometry expanded second edition answers • simplifying expressions calculator • free graph coordinate worksheets • simplifying radicals using a calculator • solving logarithms calculator • factor machine polynomials • Division of polynomial solver • mcdougal littell algebra 1 chapter 3 ways to cheat • integrated 2 book answers • partial product division worksheet • how to teach transformations worksheet algebra • aLGEBRA PROBLEMS SOLVED FREE ONLINE • creative publications answer sheets • 7th grade algebra review free • free online college math problem solver • integer algebra residuals • balance chemical equation of sodium metal and water and its classification • discriminant + quadratic equation + enrichment exercises • free algebra 1 test on solving equations with addition and subtraction • free work sheet on non- linear simultaneous equations • quadratic formula standard form completing the square • CLEP + college algebra and trigonometry • ks3 maths equivalent fractions work sheets • solve binomial ti-83 plus • Calculate Linear Feet • cheating the math clep • EVALUATING EXPRESSIONS WITH INTEGERS worksheets • free online t89 calculator • algebra; signed fraction • adding integers game • integer graph paper • solving log problems on ti-83 • cubed calculators • convert Proper Fractions to decimal • how to do Greatest common factors on a TI-83 calulator • Yr 8 Math Revision Scientific Notation • Prentice Hall Mathematics algebra 1 answer • algebra substitution method • worksheets dividing fraction pdf • adding, subtracting, multiplying integers • similar terms in algebra • converter into fractions • square root solver (quadratic) • cost accounting • exponent graphing calculator online • online math tests (variables) • quadratic root formulas • subtract long integers • trigonometric identity solver • simplify radical calculator • steps in simplifying sums and differences of radicals • exponents java source code • standerd exam questionpapers with step by step sollutions(physics(eleventh gread)) • pyramids trigonometry common denominator • intro to Algebra dimensional analysis worksheet • working out lineal metre • factoring generator for algebra • Download ti 89 .rom • free worksheets on fourth grade algebraic equations • solve LCM • free grade 7 integer worksheet • Free Help Solving Algebra Problems • factor quadratic equations app • example of math trivia • algebra checker • 9th & 10th grade free math worksheets • integrated algebra square roots • bbc math simplify year 8 • math symbol translation worksheet • powerpoint multiplying integers • Online Equation Solver • online rational expressions calculator • best clep college algebra • aptitude ebooks + free download • math trivia • procedure how to convert Pure mixed decimal to fractions • cost accounting foundations and evolutions 7th edition answers key • rational expressions online solver • trigonometric calculator • combining roots and radicals.ppt. • how to pass college algebra • complex fractions free worksheets algebra 1 • decimal number to a mixed number • adding algebraic problem solvers • "Engineering Economics" "cheat sheet" "final exam" • math trivias with answers • online scientific calculator with fraction sign • objective questions in english aptitude • greatest common factors 5x + 15 • conceptual physics answer book • Gallian Ch 7 solutions 20 • methods of solving trinomials • Additional/Subtraction of Radical Expressions • games with adding and subtracting integers • rational exponent calculator • lcd fraction calculator • find the cube root of negative j • equation calculator with substituition • pre algebra with pizzazz book dd • algebra 1 chapter reviews for glencoe mcgraw-hill • multiplying monomials solver • evaluate multiple expressions in matlab • calculator factoring polynomials • mathematics free lessons+exercises grade 7-8 consecutive integers • HOW TO CONVERT A MIXED FRACTION TO A DECIMAL • scale factor games • picture coordinate worksheets • free math worksheet ratio • Algebra 2 LCD • college algebra for dummies • multiplying one digit numbers worksheet • probability formulaes • ti 83 plus factoring polynomials • math poems • formula for getting percentages • solving homogeneous linear differential equations variable coefficients • associative property worksheets • mathematicfor dummies • reduce to lowest terms and add • algebrator free download • fractions "word problems" • how to solve linear systems in ti-89 • standard form to vertex form • factorization online • Cost Accounting free courseware • matlab lesson • solving negative exponents free worksheets • factorising third order equations • Acelerated reader cheats • complete the square calculator with no equals signs • 9th gradeExercises on circles with answers • free samples of 7th grade math problems • integration by parts calculator • simplifying square root equations • 28.1% equals what in decimal • Example problems on Data Flow Equations • online factoring quadratics calculator • Glencoe Texas Pre Algebra answers • Graphing Linear Equations Worksheets • best book on permutation and combination • mixed number and fraction converter to decimal • java linear equation • graphing inequalities worksheets • convert mixed fractions to a decimal • Factoring Polynomial Equations • free ratio worksheet • matlab 2nd order differential equations • least to greatest calculator • factor equation calculator • algebra calculator ln • decimal square • sample algebra question with "corresponding angles" • free sample gcse maths paper • perfect 5 roots • Simplify Evaluate Expressions calculator • the difference of square • free 8th grade math worksheets • fifth grade algebra lesson • GMAT ppt for free • "Algebra Helper" • solve factors calculator • simplify the square root of 50/8 • Glencoe algebra 2 answers • laplace transform 3rd order linear equation • factorization for fifth graders • ti 89 titanium read pdf • equation calculator program • ordering number from least to greatest online • how do you get a percentage from 4 variables • online graphing calculator cubic model • simplify square root calculator • gcf of monomials calculator • algebrator\ software • advanced maths algebraic tricks • lesson plan on algebraic expression • solving difference equations by matlab • substitution method for math answers • balancing chemistry equations with exponents • free mathmatics • linear equations powerpoint presentation • simplify radical expression • 12+ gramer school exam practice papers • highest common factor worksheet • Matlab nonlinear differential • ti 84 silver how factor polynomial • Need help with 9th Grade Algebra • free california indian worksheets • converting decimals to mixed numbers for kids • difference betwwn algabraic addition and regular addition • non homogenous higher order ODE • second order differential equation matlab • online non print out math assignments for 7th graders • download aptitude test • finding square roots of equations • printable square roots worksheet • Simplifying Variable Exponents • permutations and combinations on ti 84 • simplifying roots of real numbers • math scale factor worksheets • positive and negative decimal worksheets mixed add/subtract • interactive cube activities • convert whole number fractions to decimals • solving a number for a fractional exponent • how do you graph non linear equations • linear programming+ examples+online calculators • 5th grade addition expression worksheets • CUBED POLYNOMIAL • slope + puzzle worksheet • algebra calculaters • +radical +expressions +calculator • graphing ellipses and parabolas • HOW TO LEARN RADICAL EXPRESSIONS • graphing distributive property problems • square route calculator • Laplace Transform aptitude pdf • doish bank aptitude question paper • factoring Quadratic calculator Google users came to this page yesterday by typing in these keywords : │how to convert mixed numbers to decimals │writing equations powerpoint not │free algebra questions │how to solve linear equations with TI-83 │adding and subtracting simple QUADRATIC │ │ │ │ │plus │FUNCTION algebra forms 2 │ │information about algebraic term and │answers mcdougal littell math course│college algebra programs for ti │Dale seymour puzzle, 144 │factoring algebraic equation │ │algebraic expressions │3 │84 │ │ │ │writing and finding formulas worksheets +│calculator for graphing slope lines │how to plus minus divide multiply│algebraic simplification and expanding │answer sheet to mcdougal and littell │ │algebra │ │fractions │questions │ │ │learn grade 8 factorization mathematics │step size over level of integration │rom code ti │online exam example │adding/subtracting integers free │ │ │matlab │ │ │worksheets │ │download apptitude papers │prealgebra and algebra with pizzazz │converting decimals into │Simplify Cube Roots │physics practice worksheets │ │ │ │fractions worksheets │ │ │ │summation of given number program in java│Radical Expressions Calculator │free equations worksheets │notes for World History McDougal Littell │laplace transform ti-89 │ │solve algebraic equasions │programming steps putting "quadratic│free simple fraction worksheets │ti84 online free │squaring binomials that are fractions │ │ │formula" TI-84 │with answers │ │ │ │factor equations worksheet │7th grade pre algebra workout │maths powerpoint html 3d high │multiplying dividing integers │sample algebraic expressions test │ │ │ │school trigonometry projects │ │ │ │trig identity solver │divide rational expressions │printable coordinate plane │expressing ratio activity for pre-algebra │fractions adding subtracting │ │ │ │ │ │multiplication │ │sums on adding,subtracting and │prentice hall mathematics algebra 2 │using while statements to find │free square root worksheets │logrithmic properties and free │ │multiplying decimals │teachers edition torrent │the sum of numbers │ │worksheets │ │equations test and yr 7 │anwers for your 7th grade math │polynomial factor calc │free algebra practice sites for 8 grade │math help for kids adding and │ │ │homework │ │ │subtracting positives and negatives │ │algebric equation of square │free printable 8th and 9th grade │Glencoe pre-algebra Skills │Online maths aptitude papers │Solving for the variable with │ │ │algebra │practice online answers │ │manipulatives and worksheets │ │simplifying with variables │expression simplifier calculator │graphing parabolas by factoring │simple algerbra quiz │online scientific calculator with │ │ │ │ │ │fraction converter │ │free adding and subtracting fractions │abstract algebra tutor │greatest common factor worksheets│mathematics/pictograph/grade school │abstract algebra / question / notes / │ │worksheet │ │ │ │download │ │factoring difference of cubes worksheet │systems of equations with exponents │ks3 equivalent fraction │An online answerer when I type in an │graph solver │ │ │ │worksheets │integral exponent problem │ │ │converting mix fractions into decimals │print maths test online │algebra worksheet with answers │3rd order laplace transform │differential equation calculator │ │online yr 8 maths tests │simplify exponent variable │how to convert mixed numbers to a│Combinations and permutations for third │conceptual physics tenth edition │ │ │ │decimal │grade │teachers key │ │how to find slope of line on ti 83 │factors and exponents worksheets 6th│ratio KS2 worksheet │square root properties addition │radical simplifier calculator │ │ │grade │ │ │ │ │ho to do algebra │permutation - ti 83 plus │ti-89 complex partial fraction │Least common denominator fractions │free download aptitude test series │ │ │ │expansion │calculator online │ │ │Formula for Square │slope intercept form worksheets │algebra 4th grade exercise │lorenz faktor+ti 83 │simplify square root │ │problem involving expressions with │How To Do Algebra │pre-algebra prentice hall │prentice hall algebra 1 book online │solving quadractic equations with ti-89 │ │exponents │ │practice workbook │ │ │ │math poems on square roots and perfect │free powerpoint of solving distance │solving square roots with │worded problems for subtracting fractions │worksheet adding subtracting fractions │ │squares │problems │decimals │with like denominators │ │ │root solver │"TI-84 Plus" "GCF" │homework help intermediate │Factoring Expressions Online Calculators │products of cube roots │ │ │ │algebra radical equations │ │ │ │did you hear about algebra with pizzazz │column vector to tf, matlab │graphing calculator keys │free worksheets, writing algebraic │quadratic form square the root │ │ │ │ │expressions │ │ │inverse trig games │simultaneous equation 3 unknown │6th Grade Internet Math Games │calcul limits online │HOW TO CONVERT A MIX NUMBER NUMBER TO │ │ │ │ │ │DECIMAL │ │Worksheet on simplifying expreesions │beginners math test online for grade│algabra help │algebra second degree questionnaire │multiplying fractions word problems │ │involving complex number system │7s │ │ │worksheets │ │T1 graphing calculator emulator program │gnuplot linear regression │convert 3rd order differential to│video explaining elementary algebra │combining like terms worksheets │ │download │ │first order │ │ │ │square root properties │pairs of linear equations worksheets│McDougal Littell algebra books │free agarwal aptitude book download │factoring trinomial equations by trial │ │ │ │ │ │and error calculator │ │3rd grade printable worksheets "Glossary"│Ratios and Percents Word Problems │aptitude free learning material │How to Solve Factorial Equation │roots of quadratic equations worksheets │ │ │Worksheet Printable │ │ │ │ │ti ROM code │use matlab to solve graphically │solving non-linear ODE in C++ │how to find cubed roots using TI-89 when │how to solve equation on excel │ │ │linear equations │ │factoring │ │ │Multiplying Matrices │3rd order polynomial equation: │6th grade permutation │yr 8 maths cheat sheets │order of operations worksheets or │ │ │matlab │ │ │puzzles │ │holt rinehart winston elements of │ │ │convert a positive number from one base to │ │ │language 2nd course indiana edition │formula for adding fraction │lcd worksheets │another java │how to graph log functions on ti-83 │ │workbook │ │ │ │ │ │trinomial java code │coordinate plane art │quadratic equation solver program│algebra evaluating expressions │prime factorization of denominator │ │ │ │TI-83 │ │ │ │square root fractions │princeton book for permutations and │hyperbolic cosine TI-83 plus │simplifying square root expressions │math algebra pracitce sums │ │ │combinations │ │ │ │ │simplifying algebraic expressions games │free 8th pre-algebra beginner │matlab diff solve eval │mod mathematics EXERCISE │difference between an equation and an │ │ │worksheets online │ │ │expression │ │Objective 6-f Algebra with pizzazz │cool math 4 kids │partial sum method 4th grade. │fraction problem solver │free aptitude questions and answer │ │ │ │ │ │download │ │algebra help dividing multivariable │cubed root of 89 │linear equations everyday life │logarithm "math problem solver" │LCD fractions calculator │ │equation │ │one variable │ │ │ │LCD worksheet │Decision Making - Aptitude Questions│scott,foresman and company │scott,foresman and company + advance │simultaneous equations word problem │ │ │ │advance algebra worksheet answers│algebra worksheet answers │ │ │how to solve a equation with the variable│introductory algebra answers │advanced algebra transformations │quadratic system of equation solver ti 84 │slope using maple │ │squared │ │worksheet │ │ │ │division monomials worksheets example │math online for grade 6 in graph │percent problems algebra │solve equation excel │TI 84 applet │ │ │that we can print │ │ │ │ │factoring calculator quadratic │math cheats │math puzzle middle school │solve math equations online logarithms free│online algebrator │ │ │ │worksheet slope line │ │ │ │prentice hall algebra 1 California │"princeton review" permutation drill│Multiply and Simplify radicals │solving fraction logarithms │how to solve 1st order differential │ │edition pdf │ │calculator │ │equations │ │dilation grid sheet │Factoring quadratic trinomials │how to solve a quadratic with a │application of ellipse and hyperbola │how to store information on ti 89 │ │ │calculator │radical │ │ │ │advanced algebra help │78214#post78214 │word problem volume of cone ged │free online math verbal problems │printable variable worksheets │ │"tools for algebra" prentice hall │holt algebra 1 workbook │math activities for 9th graders │integer worksheet │parabola vertical stretch factor │ │ │ │ │ │definition │ │Radical Equation Solver │least common factor definition │logarithms solver │system of nonlinear equations matlab │factoring worksheets │ │midell schoolfree story books for pdf │ti 89 calculator downloads │adding, subtracting, dividing, │cost accounting free online tutorials │LCD fractions Calculator │ │guide │ │and multiplying a negative │ │ │ │free homework printouts │year 9 algebra worksheets │java least common multiple │problem solving use equations for │ged online papers │ │ │ │ │comparison problems │ │ │scientific notation worksheet │math help + calculate cubic yards of│how to convert to square root │add and subtract negative and positive │mcdougal littell geometry answers │ │ │an oval │calculator │decimals │textbook │ │graphs of hyperbola │rearrange equation exponent rules │equations/ percentage │mathematic primary four worksheet │year 11 maths help │ │online mixed numbers conversion │how to change base of log ti-89 │writing integers from least to │probability and statistics worksheets for │working out square route on a calculator│ │ │ │greatest │6th graders │ │ │number sentence games +adding │mcdougall littell biology book ch. 5│prior researches about algebraic │finding the fourth root │difference of a square │ │+subtracting │ │expressions │ │ │ │maths test printable year 7 │decimal to fraction conversion │multiplying, dividing monomials │practice problems in algebra for a sixth │ti 89 differential equations │ │ │formula │worksheets │standard student │ │ │factorising quadratics exam questions │algebra order of operations │math quadratic functions root │EXPANSION IN MATHMATICS │simplify fractions power │ │ │worksheets │ │ │ │ │solve using radical calculator │solving 5th grade problems using │cost accounting book free │java code that shows square root and cube │worksheet with adding subtracting │ │ │equations │torrents │ │multiplying and dividing fractions │ │hard problem equation of lines │www.square and root number │online factorization │learn about exponents for kids │divisible in java │ │ │worksheets .com │ │ │ │ │solving equations with parentheses at the│example math trivia │"multivariable limit" online │Maths Year 10 Sixth Edition Logarithms │cool math word problems for patterning │ │fourth grade level │ │calculator │ │and algebra gr. 5/6 │ │los base 10 on ti 89 │algebra book for 8th grade chapter 5│Least Common Multiple Calculator │learn algebra from beginner to college │convert to square root │ │ │ │ │level │ │ │suare root calculator │indian method of math work sheet │mental math 10 points on a circle│adding/multiplying decimals worksheets 3rd │solve the system of nonlinear equations │ │ │ │will produce how many chords? │grade │matlab │ │gcse sequences worksheet │middle school math with pizzazz book│trigonomics │identifying direct variables in equations │boolean expression simplify applet │ │ │c worksheets │ │ │ │ │dividing and subtracting using java │Alternative Assessment tool in │how to convert mix fractions to │finding least common denominator for │college pre algebra texts │ │program,lecture note │Pre-algebra │decimals │fractions made easy │ │ │finding "lowest common denominator" │matrix calculator linux │free download writing poetry for │square numbers games │ks2 ratio free worksheets │ │fraction worksheet │ │dummies │ │ │ │solving algebra proportion worksheets │solve factorial equations │answers to Boolean Algebra │algebra trivia │exponents ti-83 plus │ │ │ │problems │ │ │ │multiplying decimals and whole numbers │algebra with pizzazz creative │first grade algebra │worksheet for adding and subtracting │radical solver │ │worksheets │publications │ │positive and negative integers │ │ │ │ │McDougal littell algebra 2 │algebra II worksheet matrices using │ │ │Solving Rational Expressions Calculator │free download gcse maths book │worksheets for chapter 3 section │calculator │convert mixed numbers to decimal │ │ │ │6 │ │ │ │variables and equation worksheets │cheating using ti89 │math calculator solving equations│a number or expression that is raised to a │multiplication and division of rational │ │ │ │with rational expressions │power │numbers │ │how to multiply and divide radicals │solve radical expressions │5/2 base 8 │balancing equation cheat table │subtracting integers and powers │ │fractions │ │ │ │ │ │solving equation projects │common denominator calculator │integrated algebra step-by-step │dividing fractions and mixing numbers │8th std partial fraction expansion │ │free online accountig books for download │Free printable algebra test │geometry mcdougal littell answers│free printable worksheets on finding the │algebra 2 prentice hall study guide │ │ │ │ │distance on a coordinate graph │ │ │factoring polynomial with 2 variables │permutation worksheet │solving special products and │formula's for calculating basic percentages│dividing exponent worksheets │ │ │ │factoring │ │ │ │how to do algebra │answer the book glencoe algebra 1 │simplifying exponents of │history of Algebra powerpoint │convert b/n fractions and mixed or whole│ │ │ │polynomials │ │ │ │ │Samples of math investigatory │ │ │aptitude question in competative │ │t test on ti-89 │problems │alegerbra calulator │combinations in math worksheet free │examination free sample papers │ │ │ │ │ │downloading │ │math games for combining like terms │associative property middleschool │ks2 factor triangles │answers algebra 1 an incremental │accounting free book │ │ │worksheets │ │development third edition │ │ │rudin chapter 7 solutions │rudin solution │highest common factor of 49 126 │download 8th standard +maths questions │KS4 Maths Sequence worksheets │ │ │ │and 91 │ │ │ │how to solve an integral on the ti 84 │Factor 9 for ti-84 plus download │aptitude questions with solutions│square root rules algebra │how to solve differential problems with │ │ │ │ │ │the ti89\ │ │mathematical solutions forintegration │ti 83 how to quadratic formula │first and second derivative │finance and system of equations │grade 7 pre algebra with pizzazz! │ │problemsstep by step │ │"ti-89" │ │creative publications page 25 answers │ │"TI-84 Plus" "Greatest Common Factor" │cube roots on ti-83 │glencoe algebra 1 answer │Simplifying expressions with exponents + │mixed numbers percents to decimals │ │ │ │ │examples │ │ │radical calculator │online graphing calculator │find algebra problem │how to graph a log on a TI-83 │who to multiply radical fractions │ │ │derivative │ │ │ │ │example math problems for │ │ │free printable middle school worksheet on │ │ │adding,subtracting,and multiplying │"Arithmetics" + Puzzle │intro to algebra 6th Grade │calculating density │algebraic ratio expressions │ │integers │ │ │ │ │ │online graphing claculator for inequality│algebra>how do I write the equation │read holt course 3 pre-algebra │chem worksheets for 7th class │simplify equations calculator │ │equations │of two points on a graph │math book online now │ │ │ │BEGINNERS ALGEBRA ON LINE │ODE45 COUPLED │pre-algebra intergers worksheets │order fractions │simplifying decimals into fractions │ │ │ │ │ │calculator │ │greatest to least interactive site │free worksheet word problems math │simplify square roots in │worded problem in college algebra │intermediat algebra worksheets │ │ │6th grade │denominator │ │ │ │basic inequalities solve and graph │least to greatest calculator │Pre Algebra with pizzaz │algebra application problems +explanation │math poem algebra │ │algebra - degree calculation │glencoe algebra workbook │second order differential │online graphing app 2 variables │simplifying complex expressions │ │ │ │equation solver │ │ │ │Two Step Equation Example │how to solve domains of functions │free online calculator regular │charles p. mckeague pre algebra california │rational expressions simplifying │ │ │ │one │edition fifth edition chapter 8 notes │radicals │ │subtracting fractions when the first │simultaneous equations solver in c │root of equation calculator │simplifying radicals equations │free ks2 math sheets │ │number is smaller │ │ │ │ │ │learn algebra 1 │algebra area worksheet │simplify square root equation │second class maths work sheets │mcdougal littell world history answers │ │quadratic factoring calculator │"percent mixture" worksheet │completing the square practice │decimal and conversion among common factors│easy to learn algebra │ │online foiling calculator │solving my math calculator │factoring polynomials calculator │simultaneous fit root │how to solve simultaneous equations │ │ │ │ │ │containing fractions │ │Walter Rudin Solutions │-5 and 3 as two of its solutions for│"trigonomic tables" │"glencoe chemistry workbook answers" │MATLAB nonlinear system newton raphson │ │ │absolute value inequality │ │ │solve │ │equivalent forms of fractions to percents│free download for clep college │kinds of ma trivia in mathematics│converting decimals to mixed numbers │fraction to decimal free printable games│ │worksheets │algebra │ │ │ │ │quadratic equation completing the square │finding algebra answers and showing │mcdougal little math books online│free college algebra tutorial for clep │ALGERBRA 2 PROJECT NORTH WEST │ │calculator │working with fractions │ │ │ │ │linear factors calculator │Algebra 1 problem solver │system of linear equations by │free exponents with integers worksheet │Factorising Quadratics calculator │ │ │ │graphing map problem │ │ │ │All Math Trivia │cheat answers for simplifying │online textbook McDougal Littell │algebra review worksheets │quadratics with a square root │ │ │fractions │Biology │ │ │ │7th grade algebra online free │division expressions │math trivia questions for middle │solving linear equations online calculator │test generator 6th grade general │ │ │ │school │ │knowledge │ │solving equations by adding or │pre-algebra definitions │alot of 2 step equations linear │college algebra tutorial for clep │pre-algebra with pizzazz WORKSHEETS │ │subtracting fractions │ │ │ │ │ │explaining balancing chemical equations │lcm solver │4th grade division get rid of │algebra and trigonometry mcdougal littell │solve for polinom in the Diophantine │ │ │ │remainders │ │equation en matlab │ │the best way to understand logarithms │7th grade math loop cards │example of exponential expression│simplifying square roots and exponents │graph non-linear equation using ti-83 │ │ │ │ │ │plus │ │eureka multivariable solver │SKILL PRACTICE SHEETS FOR ALGEBRA 2 │objective type questions on │third root graphing calculator │rational expression answers │ │ │WITH ANSWERS BY +GLENCOE │statistics of 9th standard │ │ │ │answers to worksheets │free multiplication practice and │mixed percent to fraction │accounting textbook 电子版 │online graphing calculator with absolute│ │ │tests for fifth grade (non printed) │ │ │value │ │adding and subtracting decimals with │holt key code │formulas of percentage │how to convert a mixed number into a │greatest common factors worksheet │ │integers │ │ │decimal │ │ │algebraic expression calculator natural │rational expression │3rd grade algebra practes the │math trivia examples │algebraic sequence triangle │ │log │ │facts │ │ │ │algebra equation for 6th graders to solve│Distributive Property Elementary/ │what is 4th square root │quadratic equation graphing program │polynom division applet │ │ │Powerpoint │ │ │ │ │list of fourth root │mix numbers │percents and equations math │4th grade algebra lesson plans │algebra solve for x calculator │ │ │ │review │ │ │ │least write equivalent fractions using │new york state exam math past │addition and subtraction of │mcdougal littel algebra 2 │meaning of scale factor │ │the least common denominator │question paper third grade │fraction worksheet │ │ │ │sample 9th grade paper │computer apitute test pdf download │lyapunov ti89 │Free Online Sats Papers │6th grade math lesson plan │ │finding irrational roots of 3rd order │pre algebra by alan s tussy │homework check math-equations and│radical expressions simplify │how to solve exponents, multiplication │ │ │excercises │inequalities │ │ │ │C# square root formula │third root │quadratic equation standard form │How to make a quadratic function table on a│how to solve algebra clock problem │ │ │ │graph │graphing caculator │ │ │prentice hall algebra II book answers │year 9 factorization test │factor analysis minimum number of│permutations and combinations lecture notes│solving linear equations two step │ │ │ │items │ │equation worksheet │ │multiplying mixed fractions 6th grade │fractions decimals percents "test │how to find the slope using a │square roots worksheet fall │solving laplace's equation with 2 │ │review │questions" "6th grade" │ti-83 │ │non-homogeneous boundary conditions │ │how to pass college │yr8 maths exam │squaring polynomials worksheet │how to solve algebra equations │matching graphs to their equations and │ │ │ │ │ │tables free worksheet │ │TEST OF CLERICAL APITUTE SAMPLE PAPER │quadratic calculator program │www.learn algebra 2.com │solving a equation using a square root │adding and subtracting scientific │ │ │ │ │property │notation │ │adding 9 worksheets │rules for decimal least to greatest │FACTORING "QUADRATIC EQUATIONS" │online synthetic division calculator │degree of polynomial +caculator │ │ │ │CALCULATOR │ │ │ │radical calculator adding │online slope formula solvers │how to find the quadratic │free math Probability and Statistics made │Answers for math homework │ │ │ │equation using two points │easy │ │ │calculas │factoring program on ti 84 │roots of a quadratic formula with│free math problem solvers, rational │basic math greatest common factors │ │ │ │x cubed │expressions and equations │calculator │	{"url":"https://softmath.com/math-com-calculator/adding-functions/most-difficult-maths-problems.html","timestamp":"2024-11-08T21:34:49Z","content_type":"text/html","content_length":"208416","record_id":"<urn:uuid:77be6bbf-3077-4486-b933-a30278e37d53>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00228.warc.gz"}
Participating at informatiCup 2021 Last Thursday, the final round of the informatiCup 2021 took place. Our team placed third of all 30 participating teams and received the GitHub special award! In this blog post, I would like to outline the technical aspects of our solution as well as look at what are able to away from working on this project for an extended amount of time. The challenge From October until January, three friends and I participated in the 2021 informatiCup. The informatiCup is a computer science competition for college students held by the German Informatics Society. It is designed to be an all-around computer science competition: To succeed, the teams need solid theoretical approaches as well as programming and project management skills. This year’s challenge was about the game spe_ed. The rules are as follows: • spe_ed is a multiplayer, online, turn-based game where all players move at once. There are 2-6 players in each game. • The players move in cells. Each player has a position, speed and direction. • Each round, every player is given all information about the players and the board. The player has to send their action to the server before a deadline expires, usually 8-12 seconds. • Each round, every player chooses between the actions change_nothing, turn_left, turn_right, speed_up, speed_down. The maximum speed is 10, the minimum speed is 2. • Every player leaves a trace that does not vanish throughout the game. • Every sixth round, the players can jump. A player jumps when their speed is 3 or higher, they leave a hole of (speed - 2) as illustrated below. • The deadline and board dimensions are unknown before the game. • When a player collides with another player, a trace or a wall, they lose. • The last surviving player wins. One thing to note about spe_ed is that one game could take multiple hours as there are often over 500 turns, each with a deadline of about 10 seconds. Therefore, we created a script to visualize past One game looked like this: Getting started In October, we decided to look into the challenge, what could go wrong? First of all, we brainstormed possible ways to solve the challenge. We thought that game theory and Reinforcement Learning were two promising approaches, so two of use spent time getting to know these strategies. While working them concurrently, the Reinforcement Learning team tried various things, but a few problems persisted: 1. A large, but discrete state space. Using lookup tables is not economical because of the $2^{n^2}$ possible board states, where $n$ is the width of a quadratic window of the board (This calculation even excludes player positions, speeds and directions). 2. The reward function. A player should be trained to win in the long run, but the games can last 500 turns. Designing a working reward function is hard. Instead, we got good results using a well-known approach from game theory. The MiniMax algorithm After re-creating the game environment, the game theory team got good results with a simple MiniMax algorithm. With MiniMax, a full game tree is created. Each node gets a score. The leaves receive their scores through the use of a heuristic. The inner nodes’ scores are calculated based on their children’s scores. It is assumed that the enemy players always try to minimize the scores whereas our own player maximizes the score. In the end, the action with the highest score is used. Implementing the algorithm was not hard, but finding an appropriate heuristic even more so. We wanted something that was fast to calculate (it has to be executed for every leaf) but also represents the board state well. At the end, we went with the number of degrees of freedom that a given player has, in other words, the number of actions a player can execute without dying. There was one problem with this strategy: Low search depth. As there are five actions that each player can execute each round, the game tree grows quickly in size. Therefore, the MiniMax algorithm can only see 7-10 rounds ahead, whereas a game might have 500. We tried optimizing the algorithm with alpha-beta pruning and increased our search depth by a few turns, but it was clear that an exhaustive search would not work for long-term planning. Random methods Next, we tried using Monte-Carlo tree search with spe_ed but quickly realized it would not work since the algorithm assumes everone to move sequentially, but in spe_ed, everyone moves at the same time. Instead, we tried just using monte-carlo sampling (we called a single sample “rollout”). One rollout uses random actions until no actions can be performed anymore. It is often possible to perform a could hundred thousand rollouts before the deadline. A basic approach is to look at the longest paths and choose the action that yields the longest paths. This approach yielded very good long-term planning, but completely ignored the interaction with other players. To fix that, we had to look at what our opponents could be doing in the next time. Probability tables Since we never know what exactly our enemies will do next, we assume that they will choose uniformly between all available actions. With this assumption, we look at the next turns and assign probabilities to each board cell. The higher the values, the higher the probability that the cell will be filled at some point in the future. This is a heatmap of how such probability tables look after a couple of iterations (the blue cells are players, grey cells are already filled, we don’t calculate probabilities for ourselves): These maps contain all information about our enemies; the last step is to combine them with the rollout data. Combining the strategies Every strategy I described has its strengths and weaknesses. Therefore, we combined them into one solution. It basically boils down to this: • We always use rollouts to evaluate our situation. • If enemies are near, we also calculate probability tables. • If enemies are very near, we use the MiniMax algorithm with them as the minimizer. • We only use actions on which MiniMax, if used, yielded good scores. • For each path with a length above a certain cutoff, we determine the average probability score along the way. • For our final decision, we try to maximize the number of long paths starting with the taken action; but we also want to minimize the average path probability. This combination of strategy gives us perfect playing for a few rounds (MiniMax), good long-term planning (rollouts), also with respect to enemy players (probability tables). Our implementation We implemented this strategy using the programming language Go. The main reason for this was concurrency and performance, as the number of performed rollouts has a large impact on the desicion quality of the algorithm. The choice programming language delivered: We never really had to struggle with performance and prototyping was pretty fast as well! It turned out that since we did not tell our bot how to behave except to stay away from enemies, it performed very well against most enemy teams, winning more than $\frac{2}{3}$ of the games against all teams but one, losing one or more games against only $8$ of them (even though approximately $30$ submitted a paper in the end). What did we learn? Even though we placed third, it still showed that we are all first year’s bachelor’s students, especially in comparison with the teams that are almost done with their master’s thesis. One key takeaway for me is that it’s never a waste to focus on tooling when starting out on a project. While we did develop logging for full games, GUIs for running games and more, the lack thereof did slow us down in the first place. We would have also profited from more visualization, especially while developing the rollouts or probability tables. Also, more reproducible test scenarios would have helped to assess whether a code change actually improved our program’s behavior. Another takeaway for me is that prototyping strategies for problems where there is no clear solution is essential. These prototypes have to be far from perfect, they just have to answer the question “could this approach work in principal?”. I also think that I will profit from more lectures on math and theoretical computer science as the ability to formalize and think abstractly about problems helps a ton while deciding how to tackle Further reading If you know German, you might be interested in the competition website, the 2021 problem or our paper. Either way, you can take a look at our team website or check out our source code. Just like most people, I love to chat about my projects (or any other topic)! You can reach out to me here. The informatiCup logo and rules explanation graphics were taken from https://github.com/InformatiCup/InformatiCup2021. The Go gopher was designed by Renee French. http://reneefrench.blogspot.com/	{"url":"https://rgwohlbold.de/2021/participating-at-informaticup-2021/","timestamp":"2024-11-11T17:41:09Z","content_type":"text/html","content_length":"14001","record_id":"<urn:uuid:71a3da8b-7e55-470d-93c6-cd5baa25af5d>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00506.warc.gz"}
GMAT Probability \| 3 deadly mistakes to avoid \| GMAT Quant A 12 min read When it comes to GMAT Quant, Probability is like the ‘iceberg’ with which the Titanic collided, and the ‘so-called’ unsinkable ship, sunk. Falling in GMAT Probability pitfalls can be hazardous to your GMAT score. Although, probability is a simple concept, yet its application in GMAT ends up hitting your score. That is why we have come up with this article which will help you avoid the three deadly mistakes in GMAT probability. Here is a brief outline of the sections covered in this article: Why should you read this article on GMAT Probability? Before embarking on reading the article, ask yourself a few questions: • Are you someone who doesn’t know how to solve a GMAT probability question? • Are you confused which cases should be considered and which cases should be ignored while calculating the probability? • Are you someone who is confused while considering all the cases of arrangement? If the answer to any of the above questions is yes, then we strongly recommend you continue reading the article. In this article, you will learn a structured approach to solve probability questions. We will also explain 3 most common mistakes that students make in GMAT probability questions and the best way to solve such questions. For any strategic advice for GMAT or MBA Admissions, write to us at acethegmat@e-gmat.com. Sign up for a free trial and get unlimited access to concept files, live sessions, and practice What will you learn from this article? In the article, we will learn: • How to solve a probability question by the non-event method • How to calculate the probability when more than 1 arrangement is possible • How to find the greatest or lowest value of the probability Now let us begin the article with a very frequently used concept of non-events in probability. Wondering what are necessary but not sufficient conditions in GMAT Verbal? Read the article to learn more. Non-Event method for solving GMAT Probability Questions At times, we may come across a GMAT probability question, in which we need to find a lot of favorable cases, which is known as favorable events in probability jargon. Now, finding all the cases is time-consuming and might involve a lot of calculations. In such situations, we may end up making a mistake too. So, how should we tackle such a situation? Obviously, there has to be a better way to do it! Well, the better way or better method is known as the – Non-Event Method, in which we find all the cases which we do not want (known as non-event) and subtract it from the favorable cases. This method reduces a lot a calculation but at the same place, test your logical thinking skills. Let’s understand what I am trying to say with the help of an example! Q -If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, what is the probability that x × y will be even? Now, how should be we solve this question? Thus, we need two things: Number of ways x × y is even Total outcomes • The number of ways in which the multiplication of x and y is an even number and, • Total outcomes we can get when we take all possible combinations of x and y and multiply them with each other Now, we can easily calculate the above two by applying the concepts of permutation and combination. Number of ways in which x × y is even: x × y can be even in three ways: 1. When both, x and y, are even Or, 2. When x is even, and y is odd Or, 3. When x is odd, and y is even Total ways = (Ways in which both x and y are even) + (Ways in which only x is even) + (Ways in which only y is even) • Total ways = 2C[1] × 1C[1] + 2C[1] × 2C[1] + 2C[1] × 1C[1] = 2 + 4 + 2 = 8 Total outcomes Total outcomes= Ways in which x can be selected * Ways in which y can be selected • Total outcomes = 4 × 3 = 12 Thus, P (x × y is even) = (8/12) = (2/3) Although this example was an easy one and we got 3 cases, what if the first set has 8 numbers and the second set had 9 numbers? Then counting every possible case will be tedious. Let us now solve this question with another approach – Non-event method. Non-event Method: The multiplication of x and y can give only two possibilities: • Either x × y is even or, • x × y is odd Thus, if we add the probabilities of all the possible cases, then their sum should be equal to 1. Hence, • P (x × y is even) + P (x × y is odd) = 1 or, • P (x × y is even) = 1 – P (x × y is odd) Thus, if we find P (when x × y is odd) then we just need to subtract its values from 1 to get the actual answer. And, surprisingly the number of ways when x × y is odd is only 1- When x and y both are odd!!! Total ways when x × y is odd = Ways when x is odd × Ways when y is odd = 2C[1] × 2C[1]= 4 Thus, P (x × y is even) = [1-(4/12)] = 8/12 Oh!! This was easy! So, can you observe that you have to think a step ahead to visualize which method will be easy for you? And yes, non-event method reduced our calculation too. Thus, learning from the above example is that whenever we see that there are a lot of favorable events, we should always check if the non-events is less. And if that is the case, we should find the non-events first and then subtract it from the total cases. Now, let’s come to come to the common type of errors that a student makes while solving the questions by non-event method. Want to ace GMAT Critical Reasoning. Here is a video lesson. Deadly Mistake 1 – Missing cases Let us take an interesting example. Try to solve the question first before moving to the solution. There is a high possibility that you might end up making the mistake highlighted in the later part of the article. Q – In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box., what is the probability that neither pen will be defective? Solve this question by non-event method only. Is your answer 21/22 or 12/22? If your answer is (21/22) then you marked the wrong answer. Read further to understand how to avoid such mistakes! Do you know, how I already knew you arrived at 21/22? You must have solved using the below formula P (neither pen will be defective) = 1- P (Both the pens are defective)? If that is the case, then you made a very common error!!! You missed a few cases. Let us see how to correctly apply the non-event method in this question Correct approach: Let us write all the possible cases in which customer can buy the two pens. • He can get both the non-defective pens Or, • He can get 1 defective pen and 1 non-defective pen Or • He can get both the defective pen Since the sum of the probability of all the possible cases is 1, thus • P (neither pen is defective) + P (1 defective pen and 1 non-defective pen) + P (Both the pens are defective) = 1 Now, can you find P (neither pen is defective)? • Thus, P (neither pen is defective) = 1 – P (Both the pens are defective) – P (1 defective pen and 1 non-defective pen) Can you see the mistake you made when you solved using the formula? P (neither pen will be defective) = 1- P (Both the pens are defective)? • You missed one case. This is an error of Missing cases. Now, we only have to calculate the values of P (None of the pens is defective) and P (1 defective pen and 1 non-defective pen), and we will have the answer. But to arrive at the above equation of P (Both the pens are defective), you need to think logically, since GMAT tests your logical thinking skills. Now, let us find P (Both the pens are defective) and P (1 defective pen and 1 non-defective pen). 1. Before solving GMAT probability questions by the non-event method, you should come up with all the possible cases. 2. Once you write the sum of probabilities of all the possible cases equal to 1, you can easily find the answer by non-event method. Deadly Mistake 2 – Considering arrangement While solving any GMAT probability question, most of the students forget that for different arrangements of a particular case, the probability is also different. They do not consider all the arrangements and calculate the probability of one of the possible cases which results in the wrong answer. Let us understand what I am trying to say with the help of an example. Q – There are 10 solid-colored balls in a box including 1 green ball and 1 yellow ball. If 3 of the balls in the box are to be chosen at random without replacement, what is the probability that three balls chosen will include the green ball but not the yellow ball? Now, have you started thinking of all the possible cases? If not, do not worry!!! After reading this article and practicing questions, thinking of all the possible cases will be the next step you will be doing without even realizing. • Probability = P (selection of 1 green ball) × P (selecting 1st solid ball) × P (Selecting 2nd solid ball) • We can select 1 green from 10 balls in only 1 way thus, • P (selection of 1 green ball) = 1/10 • Now, we have 9 remaining balls. Thus, □ P (selecting 1st solid ball) = 8/9 and, □ P (Selecting 2nd solid ball) = 7/8 Hence, P (Selecting 1 green but not the yellow ball) = (1/10) × (8/9) × (7/8) = (7/90) Thus, our answer is 7/90? No!!!!! it is not the final answer. But most of the students will mark 7/90 as the correct answer to this question. Let us understand why this answer is not correct. Can you find in how many ways we can choose 3 balls such that 1 ball is green, and 2 balls are solid colored??? Let us list down the possible orders. Total cases = 3 We can also think in this way that we have balls- 1 green and 2 Solid colored balls. In how many we can arrange them? This is similar to the case of identical objects. Thus, Total ways = 3!/2! = 3 So, there are 3 arrangements possible, but we considered only 1 case i.e G S S and calculated its probability. So how should we go about to find the answer? • Should we add the probabilities of all the different cases? □ Okay, this is a good way to But what if we have a number larger than 3??? □ Let’s suppose out of 15 cases we considered only 1 case then how will you find the answer??? □ Will you add the probabilities of all the Cases? □ No, right!! So, let us look at another way! Let us first find P(S G S) and P(S S G). • P(S G S) = (8/10) x (1/9) x (7/8) = 7/90 = P(G S S) • P(G S S) = (8/10) x (1/9) x (7/8) = 7/90 = P(G S S) If you observe, then all the three cases have the same probability. Thus, multiplying 3 with P(G S S) will give our final answer. And 3 is the number of ways in which you can select 3 balls – 1 green and 2 Solid colored balls. If we replace 3 by the number of ways balls can be arranged, then we can conclude: 1. If there are more than one arrangements possible, then we will find the probability of only one case and multiply it by the total number of possible cases. This will give us our final answer. 2. The first step to solve every probability question is to think of all the possible cases. Q – A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the three balls selected will be odd? Can you think of all the possible cases in which we can get the sum of three numbers to be odd? There are 2 possible cases: • When all the three numbers are odd or, • When two numbers are even, and one is Probability when all the numbers are odd: • = P(Odd) × P(Odd) × P(Odd) • = (1/2) x (1/2) x (1/2) = (1/8) Probability when two numbers are even, and one is odd: • = P(Odd) × P(Even) × P(Even) • =(1/2) x (1/2) x (1/2) = (1/8) However, this case can occur in 3!/2! = 3 ways • Odd, Even, Even • Even, Odd, Even • Even, Even, Odd P(two numbers are even, and one is odd) = 3 × (1/8) Thus, total probability = (1/8) + (3/8) = (4/8) = 1/2 Deadly Mistake 3 – Confusing dependent and independent events Let us look at a slightly complex problem of GMAT probability and a question that is put so beautifully that most of the aspirants fall prey to the trap of this question and mark a wrong answer. Do you want to test your knowledge of probability? Let’s give it a try. Q – If the probability is 0.54 that stock A will increase in value during the next month and the probability is 0.68 that stock B will increase in value during the next month, what is the greatest value for the probability that neither of these two events will occur. Is the answer equal to 0.1472 or 0.32? If your answer is 0.1472, then this is the 3rd mistake you will avoid after reading this article. Let us see why 0.1472 is wrong. Can you observe that the language of this question is a little different??? • In every question, we are asked to find what the probability that an event can occur, however in this question, we are asked to find the greatest probability such that both the events do not • So how should we find this? We know how to find the probability but what is the greatest probability? Well, don’t worry!! This is a question of probability where two events are dependent. Let us understand independent and dependent events first. Independent Events: • We are tossing a coin two times □ Can we say that the occurrence of head/tail in the 2nd toss is dependent on the occurrence of head/tail in the first toss? □ No, right! It does not matter what we get in the first toss. It won’t affect toss 2. □ This is an example of Independent events Dependent Events: • Now, from the real-life experience, we all know that the prices of some stocks may be dependent on each other □ If the price of one stock increases, then the price of some stocks may increase, and the price of some other stocks may decrease • If the price of the raw material decreases, then the price of stocks of a company that uses that raw material will increase as the company will make more gain now • These events are dependent events And our question is a perfect example of dependent events. So, how do we calculate the greatest probability such that neither of these two events occur? Let us see two dependent events, A and B, pictorially. Since P(A) = 0.54, P’(A) = 0.46 Here, the full circle represents the total probability in which all the events can occur (A might increase and decrease) and the small circle inside it represents the probability of all the events in which A can increase. From the diagram, we know that we need to maximize the area/probability of P’(A). So, how can we maximize this keeping in mind that A and B are dependent??? • How can we make the overlapping of event A’ and B’ greatest? □ This is shown in the diagram (Fig 2 and Fig.3) □ Fig.2 shows the areas of A’ and B’ and now we need to figure out the maximum overlap between these two. □ And we can do so, as shown in 3 • The complete overlap of event A’ with event B’ happens: □ when we map B’ inside A’ and “assume that when B does not increase A will also not increase at the same time. □ Hence, the probability of area such that both A and B does not occur= 0.32 □ And this is the greatest probability because if we move B a little, the probability, 0.32, will reduce. □ Hence, our answer is 0.32. If you are planning to take the GMAT, we can help you with a personalized study plan and give you access to quality online content to prepare. Write to us at acethegmat@e-gmat.com. We are the most reviewed GMAT prep company on gmatclub with more than 2400 reviews and are the only prep company that has delivered more than 700+ scores than any other GMAT club partner. Why don’t you take a free trial and judge for yourself? This is the way to solve questions of dependent probability. So, we learned 3 ways to avoid mistakes while solving probability questions. Let us summarize everything. Takeaways \| GMAT Probability 1. The first step to solve any probability question is to think of all the possible cases. 2. To make sure that you are not missing any cases when solving by non-event method, write the sum of probabilities of all the possible cases equal to 1 then you can easily find the answer by non-event method. 3. If there is more than one arrangement possible then we find the probability of only one case and multiply by the total number of possible arrangements. 4. Always keep an eye on the keywords like- greatest probability and minimum probability and make sure to draw diagrams to visualize the overlap between the probabilities of 2 events.	{"url":"https://e-gmat.com/blogs/gmat-probability-3-deadly-mistakes-to-avoid-gmat-quant/","timestamp":"2024-11-12T09:07:12Z","content_type":"text/html","content_length":"684666","record_id":"<urn:uuid:738e8bc4-091b-4fa6-ad5c-a08f9856e1e7>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00723.warc.gz"}
Review Of Big Ideas Math Answer Key Geometry References › Athens Mutual Student Corner Review Of Big Ideas Math Answer Key Geometry References Review Of Big Ideas Math Answer Key Geometry References. Web mathleaks has authored solutions for the math textbook geometry from big ideas learning. Web big ideas math geometry answers bridge the gap to your success. Big Ideas Math Green Assessment Book Answer Key from ww107.elgolfantasma.com Web big ideas math geometry answers bridge the gap to your success. It has been helping the. You can make use of the geometry big ideas math textbook solution key pdf via quick links. Web The Big Ideas Math Geometry Answers Key Is One Of The Best Resources Available For Students Looking To Improve Their Grades In Mathematics. Web big ideas math solutions. Kids who are seeking help from professionals to become pro in mathematics can gain all subject. Web if you are sincerely searching for the best big ideas math geometry answers key 2021, takeonlineclasshelp.com is the most favorite. You Can Make Use Of The Geometry Big Ideas Math Textbook Solution Key Pdf Via Quick Links. Web chapter 9 test geometry answers big ideas math september 21, 2022 post a comment chapter 9 test geometry answers big ideas math. Our resource for big ideas math:. Through the mathleaks app or a web browser, every student can read pedagogical. Web Master The Concepts Of Big Ideas Math Geometry Chapter 4 Transformations By Solving Them On A Regular Basis. Web mathleaks has authored solutions for the math textbook geometry from big ideas learning. You just need to tap on the relevant. Web common core curriculum big ideas math answers pdf free download: Basic Geometry Is The Study Of Lines, Angles, Points, Solids, And Surfaces. You can make use of the geometry big ideas math textbook solution key pdf via quick links. Geometry 1st edition, you’ll learn how to solve your toughest homework problems. Web big ideas math book geometry answer key chapter 1 basics of geometry. A Common Core Curriculum 1St Edition, You’ll Learn How To Solve Your Toughest Homework Problems. Just preview or download the. If a student is having difficulty with the subject,. Mathleaks covers textbooks from publishers such as big ideas. Write Comment activity algebra answer answers biology cell chapter chemical chemistry cycle energy free genetics geometry gizmo grade homework icivics ionic lesson math periodic phet photosynthesis pogil practice problems puzzle questions quiz quizlet regents review search sheet student system table test triangles unit webquest with word worksheet	{"url":"http://athensmutualaid.net/big-ideas-math-answer-key-geometry/","timestamp":"2024-11-03T23:55:42Z","content_type":"text/html","content_length":"129146","record_id":"<urn:uuid:1afea325-2dd5-4242-b86b-464e44957222>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00621.warc.gz"}
Passage six(Dropouts for Ph. D. s) Educators are seriously concerned about the high rate of dropouts among the doctor of philosophy candidates and the consequent loss of talent to a nation in need of Ph. D. s. Some have placed the dropouts loss as high as 50 percent. The extent of the loss was, however, largely a matter of expert guessing. Last week a well-rounded study was published. It was published. It was based on 22,000 questionnaires sent to former graduate students who were enrolled in 24 universities and it seemed to show many past fears to be groundless. The dropouts rate was found to be 31 per cent, and in most cases the dropouts, while not completing the Ph. D. requirement, went on to productive work. They are not only doing well financially, but, according to the report, are not far below the income levels of those who went on to complete their doctorates. Discussing the study last week, Dr. Tucker said the project was initiated ‘because of the concern frequently expressed by graduate faculties and administrators that some of the individuals who dropped out of Ph. D. programs were capable of competing the requirement for the degree. Attrition at the Ph. D. level is also thought to be a waste of precious faculty time and a drain on university resources already being used to capacity. Some people expressed the opinion that the shortage of highly trained specialists and college teachers could be reduced by persuading the dropouts to return to graduate schools to complete the Ph. D.’ “The results of our research” Dr. Tucker concluded, “did not support these opinions.” 1. Lack of motivation was the principal reason for dropping out. 2. Most dropouts went as far in their doctoral program as was consistent with their levels of ability or their specialities. 3. Most dropouts are now engaged in work consistent with their education and motivation. Nearly 75 per cent of the dropouts said there was no academic reason for their decision, but those who mentioned academic reason cited failure to pass the qualifying examination, uncompleted research and failure to pass language exams. Among the single most important personal reasons identified by dropouts for non-completion of their Ph. D. program, lack of finances was marked by 19 per cent. As an indication of how well the dropouts were doing, a chart showed 2% in humanities were receiving $ 20,000 and more annually while none of the Ph. D. ‘s with that background reached this figure. The Ph. D. ‘s shone in the $ 7,500 to $ 15,000 bracket with 78% at that level against 50% for the dropouts. This may also be an indication of the fact that top salaries in the academic fields, where Ph. D. ‘s tend to rise to the highest salaries, are still lagging behind other fields. As to the possibility of getting dropouts back on campus, the outlook was glum. The main condition which would have to prevail for at least 25 % of the dropouts who might consider returning to graduate school would be to guarantee that they would retain their present level of income and in some cases their present job. 1. The author states that many educators feel that [A] steps should be taken to get the dropouts back to campus. [B] the fropouts should return to a lower quality school to continue their study. [C] the Ph. D. holder is generally a better adjusted person than the dropout. [D] The high dropouts rate is largely attributable to the lack of stimulation on the part of faculty members. 2. Research has shown that [A] Dropouts are substantially below Ph. D. ‘s in financial attainment. [B] the incentive factor is a minor one in regard to pursuing Ph. D. studies. [C] The Ph. D. candidate is likely to change his field of specialization if he drops out. [D] about one-third of those who start Ph. D. work do not complete the work to earn the degree. 3. Meeting foreign language requirements for the Ph. D. [A] is the most frequent reason for dropping out. [B] is more difficult for the science candidate than for the humanities candidate. [C] is an essential part of many Ph. D. programs. [D] does not vary in difficulty among universities. 4. After reading the article, one would refrain from concluding that [A] optimism reigns in regard to getting Ph. D. dropouts to return to their pursuit of the degree. [B] a Ph. D. dropout, by and large, does not have what it takes to learn the degree. [C] colleges and universities employ a substantial number of Ph. D. dropouts. [D] Ph. D. ‘s are not earning what they deserve in nonacademic positions. 5. It can be inferred that the high rate of dropouts lies in [A] salary for Ph. D. too low. [B] academic requirement too high. [C] salary for dropouts too high. [D] 1000 positions. 1. dropout 辍学者，中途退学 2. well-rounded 全面的 3. attrition 缩/减员，磨损 4. drain 枯竭 5. bracket 一类人，（尤指按收入分类的）阶层 6. lagging behind other fields 落后于其它领域 7. glum 阴郁的 1. Educators are seriously concerned about the high rate of dropouts among the doctor of philosophy candidates and the consequent loss of talent to a nation in need of Ph. D. s. 2. It was base on 22,000questionnaires sent to former graduate students who were enrolled in 24 universities and it seemed to show many past fears to be groundless. 3. Attrition at the Ph. D. lever is also thought to be a waste of precious faculty time and a drain on university resources already being used to capacity. 【结构分析】被动句。To capacity满额，全力。 4. This may also be an indication of the fact that top salaries in the academic fields, where Ph. D. ‘s tend to rise to the highest salaries, are still lagging behind other fields. 【结构分析】the fact的同位语that从句中的where是定语从句，修饰academic fields。 1. A. 许多教育工作者感到应采取步骤让辍学者回校学习，特别是有些学科。这在第三段最后一句话：“有些人建议高级专家和大学教师短缺现象可以通过劝说辍学者返回校园完成博士学位来减少。” B. 辍学者应回到稍第几的学校去完成学业。 C. 有博士学位的人一般比辍学者具有较好的适应性。 D. 高辍学率主要原因在于教师方面缺乏刺激鼓励。这三项文内没有提。 2. D.约三分之一开始就读博士学位的人没有完成学业取得学位。第二段第一句：“辍学率为31％。大多数情况下，辍学人不能完成博士学位学业，就去从事生产性工作”。 A. 辍学者的经济收入比博士生低许多。这是错的。见倒数第二段：“作为辍学者干得真不错的证明，统计图表说明2％人文学科的辍学者年收入为20000多没劲，没有一个同样背景的博士生达到这个数字。7000至15000美元年收入水平为博士生的78％，辍学者仅为50％。” B. 在博士学习中刺激因素较小。 C. 博士预备生如果中途退学很可能改变其专业领域。 3. C. 博士生应达到外语要求的水平是许多博士生课程的一个基本组成部分。这在第四段有所表示：“约75％的退学者说，他们决定退学并不是处于学术的原因，而处于学术原因的退学者提出：难以通过资格考试，难以完成研究 A. 它是退学最频繁的原因。 B. 它对理科博士生比文科博士应考生更难。 D. 它在大学中的难度并没有不同。 4. A. 读完这篇文章，人们不会有这种结论。这在第三段末和最后一段。第三段末：“我们研究的结果并不支持这些一件（包括返回校园之意见）：⑴缺乏动力是退学的主要原因。⑵大多数退学者在博士课程上已经达到和他们的能 B. 博士生退学者，大体而论，并不具备得到学位所需要的一切。 C. 学院和大学雇佣了许多退学生。 D. 博士生在非学术岗位上没有挣到他们应得的钱。B.、C.两项文内没提。D.不对，参见难句译注4。 A. 博士生的工资太低。见第四题A.的译注和难句译注4。 B. 学术要求太高。这只是某些因学术原因辍学者之强调点。 C. 辍学者工资太高。不是太高而是有一部分高于博士生。见第二题D项注释。 D. 职位低。文内没有提。	{"url":"https://www.engbus.cn/kaoshi/25/24637.html","timestamp":"2024-11-08T18:30:50Z","content_type":"application/xhtml+xml","content_length":"25412","record_id":"<urn:uuid:65fd61b3-f836-4255-9c57-1391a863cdca>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00564.warc.gz"}
Toward Better Depth Lower Bounds: A KRW-like theorem for Strong Composition One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., P ⊈ NC1). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested approaching this problem by proving that depth complexity of a composition of functions f ⋄ g is roughly the sum of the depth complexities of f and g. They showed that the validity of this conjecture would imply that P ⊈ N C1. The intuition that underlies the KRW conjecture is that the composition f ⋄ g should behave like a 'direct-sum problem', in a certain sense, and therefore the depth complexity of f ⋄ g should be the sum of the individual depth complexities. Nevertheless, there are two obstacles toward turning this intuition into a proof: first, we do not know how to prove that f ⋄ g must behave like a direct-sum problem; second, we do not know how to prove that the complexity of the latter direct-sum problem is indeed the sum of the individual complexities. In this work, we focus on the second obstacle. To this end, we study a notion called 'strong composition', which is the same as f ⋄ g except that it is forced to behave like a direct-sum problem. We prove a variant of the KRW conjecture for strong composition, thus overcoming the above second obstacle. This result demonstrates that the first obstacle above is the crucial barrier toward resolving the KRW conjecture. Along the way, we develop some general techniques that might be of independent interest. Publication series Name Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS ISSN (Print) 0272-5428 Conference 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 Country/Territory United States City Santa Cruz Period 6/11/23 → 9/11/23 Bibliographical note Publisher Copyright: © 2023 IEEE. • KRW conjecture • KW relations • Karchmer-Wigderson relations • circuit complexity • communication complexity • depth complexity • formula complexity • formulas ASJC Scopus subject areas Dive into the research topics of 'Toward Better Depth Lower Bounds: A KRW-like theorem for Strong Composition'. Together they form a unique fingerprint.	{"url":"https://cris.haifa.ac.il/en/publications/toward-better-depth-lower-bounds-a-krw-like-theorem-for-strong-co","timestamp":"2024-11-06T20:45:57Z","content_type":"text/html","content_length":"59091","record_id":"<urn:uuid:f0ad40dd-dc9a-4812-b5b8-59283b895578>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00057.warc.gz"}
8 cups to gallons: A Simple Conversion Guide \| Food Readme 8 cups to gallons: A Simple Conversion Guide Are you ever in a recipe predicament, unsure how to convert measurements from cups to gallons? Well, fear no more! Understanding the relationship between these two units of volume can greatly simplify your cooking adventures. Picture this: 8 cups of liquid transforming into gallons, unveiling a whole new world of possibilities and flavors. Join us as we dive into the captivating realm of conversions, where 8 cups hold the key to unlocking the magic of gallons. 8 cups to gallons 8 cups is equal to 0.5 gallons. Key Points: • 8 cups is equivalent to 0.5 gallons • The conversion is from cups to gallons • The volume of 8 cups can be expressed as 0.5 gallons • It is a direct conversion between these two units • This conversion can be used for measuring liquids • The fraction used to convert is 8/16, which simplifies to 1/2 8 cups to gallons – Watch Video Pro Tips: 1. The conversion of 8 cups to gallons is equivalent to 0.5 gallons. 2. Did you know that the unit “cup” used in cooking measurements is different from a traditional teacup? A cooking cup is equivalent to 8 fluid ounces or approximately 237 milliliters. 3. Speaking of cups, the standard measuring cup we commonly use, which is usually made of plastic or glass, is called a “cup measure” or “dry measuring cup.” It is designed to be filled to the top and then leveled off for precise measurements. 4. In the United States, most recipes use the customary cup (8 fluid ounces), while in many other countries, the metric cup (approximately 250 milliliters) is widely used. This can sometimes cause a bit of confusion when dealing with international recipes. 5. The concept of measuring cups dates back to ancient Egypt, where they used different-sized containers made from natural materials to measure food and other ingredients. Over time, standardized measuring cups were developed to ensure accuracy and consistency in recipes. Conversion Factor For Cups To Gallons When converting units of measurement, understanding the conversion factor is crucial. In the case of converting cups to gallons, the conversion factor is 0.0625. This means that 1 cup is equal to 0.0625 gallons. The conversion factor is derived from the fact that a U.S. gallon is equivalent to 128 U.S. fluid ounces, and a cup is 1/16th of a gallon. U.S. Cup And Gallon Equivalents In the United States Customary measurement system, a cup is considered a volume unit. It is equal to 1/16th of a gallon. On the other hand, a U.S. gallon is defined as 128 U.S. fluid ounces or approximately 3.785 liters. It is important to note that the U.S. gallon should not be mistaken for the imperial gallon commonly used in the United Kingdom. These equivalencies serve as the foundation for converting between cups and gallons. Difference Between U.S. Gallon And Imperial Gallon The U.S. gallon and the imperial gallon are distinct units of measurement. • The U.S. gallon is utilized in the United States Customary system. • The imperial gallon is employed in the United Kingdom. Key points to note: • The U.S. gallon equals 128 U.S. fluid ounces or approximately 3.785 liters. • In contrast, the imperial gallon is defined as 160 imperial fluid ounces or about 4.546 liters. It is important to avoid confusing these two units due to their varying conversion factors and measurements. Steps To Convert 8 Cups To Gallons To convert 8 cups to gallons, we can use the conversion factor of 0.0625. By multiplying 8 cups by 0.0625, we can determine the equivalent volume in gallons. Following this calculation, we find that 8 cups is equal to 0.5 gallons. This simple multiplication allows us to convert from cups to gallons easily. Result Of Converting 8 Cups To Gallons After performing the conversion, we find that 8 cups is equivalent to 0.5 gallons. This means that if you have 8 cups of liquid, it can also be expressed as 0.5 gallons. Understanding this conversion allows for accurate measurements when working with different units of volume. • 8 cups = 0.5 gallons (conversion) • Accurate measurements with different volume units. Range Of Common Conversions From 8.X Cups To Gallons In situations where the initial measurement may not be an exact whole number, such as 8.25 cups or 8.75 cups, it is helpful to understand the range of possible conversions to gallons. For values between 8 and 9 cups, the conversion to gallons ranges from approximately 0.506 gallons to 0.556 gallons. This range accounts for any decimal values of cups and provides a more precise measurement when converting between these units. Definition Of A Gallon Measurement A gallon is a widely used volume unit in both the imperial and United States Customary measurement systems. In the U.S. Customary system, a gallon is defined as 231 cubic inches or 3.785 liters. It is commonly used to measure large quantities of liquids, such as milk, water, or gasoline. The symbol used to represent a gallon is “gal.” Definition Of A Cup Measurement The cup is a volume unit used in both the Metric and United States Customary measurement systems. In the United States, it is commonly used to measure cooking ingredients and beverages. • One cup is equivalent to 1/16th of a gallon or approximately 236.6 milliliters. • In the Metric system, one cup is equal to 250 milliliters. The symbol used to represent a cup is “c.” Symbol For Gallon Measurement The symbol for the gallon measurement is “gal.” This symbol is used to represent the volume unit in both the imperial and U.S. Customary systems. It helps to visually identify the measurement and distinguish it from other units when performing calculations or writing measurements. Symbol For Cup Measurement The symbol used for the cup measurement is “c.” This symbol is utilized to represent the volume unit in both the Metric and United States Customary systems. It is often seen in recipes and is a universal symbol for measuring cups. The “c” helps to differentiate the cup measurement from other units and allows for clear communication when referring to volume. • The symbol “c” represents the cup measurement. • It is used in both Metric and United States Customary systems. • The symbol is commonly used in recipes. • It serves as a universal symbol for measuring cups. • The symbol helps differentiate cup measurement from other units and allows for clear communication when referring to volume. “c” is the universal symbol for measuring cups. You may need to know these questions about 8 cups to gallons Is a gallon equal to 8 cups? Yes, a gallon is equal to 8 cups. This means that if you have a gallon of liquid, you would have 8 standard measuring cups worth of that liquid. Knowing that there are 16 cups in a gallon allows you to easily convert between the two units of measurement. So, if you have 4 cups of liquid, you would have a quarter of a gallon, and if you have 12 cups, you would have three-quarters of a gallon. The gallon-to-cup ratio provides a convenient way to measure and understand the quantity of liquid in both everyday and cooking contexts. Does 8 cups equal 1 2 gallon? No, 8 cups do not equal 1 2 gallon. In fact, 8 cups is equivalent to only half a gallon. Since a cup is 8 fluid ounces and a gallon is 128 fluid ounces, a half-gallon would be 64 fluid ounces. Therefore, 8 cups would be half of a 2-gallon measurement. How many cups are in a gallon? In liquid measurement, it is intriguing to observe that a gallon contains a substantial number of cups. With precision, a gallon consists of 16 cups. This fascinating conversion can be handy when engaging in culinary experiments or fluid calculations, providing a helpful reference point for measuring liquids accurately. Moreover, understanding this equilibrium between cups and gallons can aid in various daily tasks, such as recipe proportions or ensuring sufficient fluid intake. In conclusion, the generous inclusion of 16 cups in a gallon establishes a harmonious relationship that enhances fluid measurement accuracy and simplifies our daily liquid-related endeavors. Is 2 gallons equal to 8 cups? No, 2 gallons is not equal to 8 cups. Based on the background information, 2 gallons actually equals 32 cups, since each gallon is equal to 16 cups. Therefore, 8 cups would only represent a fraction of a gallon rather than the entirety of it. Reference source	{"url":"https://www.foodreadme.com/8-cups-to-gallons/","timestamp":"2024-11-14T07:40:06Z","content_type":"text/html","content_length":"91813","record_id":"<urn:uuid:8d16ef09-7b8d-4d27-86e8-627024fb021e>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00189.warc.gz"}
User-defined yacas rules Mikkel Meyer Andersen and Søren Højsgaard Included rules yacas comes with a number of rules all defined in the yacas directory of the installed package: ## [1] "/tmp/Rtmp8hYNaH/Rinst909f59779d54/Ryacas/yacas" For example in the sums.rep folder, a number of rules for sums are defined in the code.ys file. As an example, the fact that \[ \sum_{k = 1}^n (2k-1) = n^2 \] is defined in yacas as SumFunc(_k,1,_n,2_k-1, n^2 ); and the geometric sum is defined as SumFunc(_k,0,_n,(r_IsFreeOf(k))^(_k), (1-r^(n+1))/(1-r) ); These can be verified: ## [1] "m^2" ## [1] "2^(m+1)-1" There are also rules in yacas that are able to let the user change some limits of some sums, e.g. for the geometric sum: ## [1] "2^(m+1)-2" Custom rules But what about changing the limit of the first sum? I.e. instead of \[ \sum_{k = 1}^n (2k-1) = n^2 \] then know that \[ \sum_{k = 0}^n (2k-1) = -1 + \sum_{k = 1}^n (2k-1) = n^2 - 1 . \] But what does yacas say? ## [1] "Sum(i,0,m,2i-1)" We can then add our own rule by: And then try again: ## [1] "m^2-1" A good source of inspiration for writing custom rules is reading the included rules, but there is a lot to programming in yacas and we refer to yacas’s documentation, specifically the chapter Programming in Yacas.	{"url":"https://cran.hafro.is/web/packages/Ryacas/vignettes/yacas-rules.html","timestamp":"2024-11-14T21:55:34Z","content_type":"text/html","content_length":"13101","record_id":"<urn:uuid:8df47f60-ef98-4f8b-863a-dc719889d6b2>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00536.warc.gz"}
The GAMMADIST function calculates the gamma distribution for a given set of parameters. The gamma distribution is a continuous probability distribution that is often used in statistics. It is commonly used to model the time between events. The function returns the probability density function or the cumulative distribution function for a given set of parameters. Use the GAMMADIST formula with the syntax shown below, it has 4 required parameters: =GAMMADIST(x, alpha, beta, cumulative) 1. x (required): The value at which to evaluate the distribution. 2. alpha (required): The shape parameter of the distribution. 3. beta (required): The scale parameter of the distribution. 4. cumulative (required): A boolean value that determines the form of the function. If TRUE, GAMMADIST returns the cumulative distribution function; if FALSE, it returns the probability density function. Here are a few example use cases that explain how to use the GAMMADIST formula in Google Sheets. Calculating probability density The GAMMADIST function can be used to calculate the probability density of a gamma distribution for a given set of parameters. Calculating cumulative distribution The GAMMADIST function can be used to calculate the cumulative distribution of a gamma distribution for a given set of parameters. Modeling waiting times The gamma distribution is commonly used to model waiting times. The GAMMADIST function can be used to calculate the probability density or cumulative distribution of waiting times for a given set of Common Mistakes GAMMADIST not working? Here are some common mistakes people make when using the GAMMADIST Google Sheets Formula: Missing or wrong arguments One of the most common mistakes is not providing the correct number of arguments, or providing arguments in the wrong order. Make sure to check the syntax and provide values for x, alpha, beta, and cumulative in the correct order. Incorrect range for arguments Another common mistake is providing arguments that are outside the expected range. For example, x and beta must be greater than 0, and alpha and beta must not be negative. Check your input values and make sure they are within the expected range. Incorrect interpretation of cumulative parameter The cumulative parameter in the GAMMADIST formula determines whether to calculate the probability density function (false) or the cumulative distribution function (true). One common mistake is to misinterpret the cumulative parameter and provide the wrong value. Make sure you understand the difference between the two and provide the correct value for cumulative. Related Formulas The following functions are similar to GAMMADIST or are often used with it in a formula: • GAMMAINV The GAMMAINV formula returns the inverse of the gamma cumulative distribution function for a given probability. This function is most commonly used for statistical analysis, particularly in modeling and simulation applications. • GAMMALN The GAMMALN function returns the natural logarithm of the absolute value of the Gamma function, Γ(x). The Gamma function is defined as an extension of the factorial function to complex and real numbers. The function is commonly used in probability theory and statistics to compute probabilities and to model continuous distributions such as the chi-squared and F distributions. • GAMMALN.PRECISE The GAMMALN.PRECISE function calculates the natural logarithm of the absolute value of the gamma function for a given positive number. The gamma function is a commonly used function in mathematics and statistics. The natural logarithm of the gamma function is useful in various fields, such as physics, biology, and engineering, for modeling various phenomena. • GAMMA.DIST The GAMMA.DIST function calculates the gamma distribution probability for a specified x value, alpha and beta parameters. This function is often used in statistics to model continuous data that is skewed to the right. It can be used to analyze data in various fields such as finance, engineering, and social sciences. • GAMMA.INV The GAMMA.INV formula returns the inverse of the cumulative distribution function for a specified probability and the Gamma distribution. It is commonly used in statistical analysis to find the value at which a specified percentage of the distribution lies. The Gamma distribution is a continuous probability distribution that is used to model the time until a certain number of events Learn More You can learn more about the GAMMADIST Google Sheets function on Google Support.	{"url":"https://checksheet.app/google-sheets-formulas/gammadist/","timestamp":"2024-11-10T06:04:57Z","content_type":"text/html","content_length":"47093","record_id":"<urn:uuid:d4b32dfc-d05d-4dd2-b595-f6ca5efd278e>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00878.warc.gz"}
Organisations: St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences: St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Russia History. St. Petersburg Department of V. A. Steklov Mathematical Institute (PDMI RAS) was established in 1940 after the Institute had moved to Moscow. At present, despite the word "department" in its name kept due to historical traditions, PDMI RAS is an independent institute within the Russian Academy of Sciences. From 1976 till 2000 the Institute was headed by a prominent Russian scientist, mathematician and physicist, Academician Ludwig D. Faddeev. He established in St. Petersburg a new institute of Russian Academy of Sciences, Euler International Mathematical Institute (EIMI). Since January 1996 Euler International Mathematical Institute is contained in PDMI as a department. Basic research areas. Fundamental research in pure mathematics and mathematical models of theoretical physics: mathematical logic and the theory of algorithms, algebra, number theory, geometry and topology, mathematical analysis, probability theory and mathematical statistics, mathematical problems of continuum mechanics, quantum physics, geophysics, and seismology. Main scientific achievements. Creation and development of new methods for studying metric properties of geometric figures which led to the solution of classic problems of geometry of surfaces (A. D. Alexandrov and his pupils). Application of functional analysis methods to the problems of numerical mathematics, development of a general theory of approximative methods, new effective methods of solution operator equations (L. V. Kantorovich). Creation of the theory and methods for solving extremal problems with restraints (linear programming methods, in particular) and their application to the problems of economics (L. V. Kantorovich). The solution of the 19th and 20th Hilbert problems and the construction of the attractor theory of nonlinear evolutionary semigroups (O. A. Ladyzhenskaya). New methods in analytic number theory (large sieve, dispersion method) and solutions of a series of classic number theoretic problems (Yu. V. Linnik). The theory of summation of random variables (Yu. V. Linnik, I. A. Ibragimov). New methods and results in algorithm theory and constructive mathematics (proof of unsolvability of problem of homeomorphism, the notion of normal algorithm) (A. A. Markov). The solution of 10th Hilbert problem (Yu. V. Matiyasevich). Homologies in group theory, numerical methods in linear algebra (D. K. Faddeev). The complete solution of the quantum problem of three and more particles and the multidimensional inverse problem of scattering theory (L. D. Faddeev). The quantum inverse scattering method (L. D. Faddeev and his pupils). Correct rules of quantization of Yang–Mills fields (V. N. Popov, L. D. Faddeev). Theory of zeta-functions of multidimensional modular forms (A. N. Andrianov). Creation and development of ray method of implementation of wave fields (V. M. Babich). Investigation of integral representations of functions specified for regions and imbedding theorems (V. P. Il'in). Many scientists of the Institute were granted high prestige scientific awards of the USSR and Russia: Lenin and State Prizes, special awards instituted in commemoration of the great Russian scholars. Academician L.V. Kantorovich was awarded the Nobel Prize in Economics in 1975. Recent scientific achievements. The computation of motivic cohomology of weight 2 is completed, and the Quillen–Lichtenbaum conjecture on K-theory with finite coefficients for complex varieties of dimension no greater than 2 is proved (A. A. Suslin). The theory of cubic metaplectic forms on linear algebraic groups of range 1 and 2 is developed (N. N. Proskurin). New profound results are obtained in the classical problem of number theory concerning the asymptotics of the number of points of a lattice in an expanding domain and it is proved that in any dimension there are domains and lattices with logarithmically small remainders in the asymptotic formula for the number of points of a lattice in a domain (M. M. Skriganov). New investigation methods of sums of dependent random variables are developed (M. I. Gordin). The infrared parameterisation of Yang–Mills field is proposed (L. D. Faddeev). The methods of calculation of correlation functions in the integrable models of quantum field theory and statistical mechanics are developed (A. G. Izergin, N. M. Bogoliubov). New methods of asymptotic study of nonparametric estimation problems in mathematical statistics have been developed (I. A. Ibragimov). International scientific cooperation. Organizing international scientific cooperation and creating conditions for joint research of Russian and foreign scientists, in the first place, mathematicians, are the main problems of Euler International Mathematical Institute that became a department of PDMI in 1996. EIMI is located in a separate building at 10 Pesochnaya naberezhnaya, appropriately equipped for conferences numbering up to a hundred persons and for individual work of mathematicians coming to St. Petersburg. EIMI has a network of computers with Internet connection. Every year EIMI organizes about 10 international working meetings and conferences. It also conducts a long-term program of scientific cooperation "Tete-a-tete in Russia", whose aim is to organize meetings of Russian and foreign scientists for joint work in St. Petersburg. Moreover, for many years PDMI has been collaborating with Max Plank Institute (Germany), the University Paris-7, Lund University (Sweden), the University of Florence (Italy) and some other scientific centres. Scientific issues. PDMI is the founder and publisher of the notes of scientific seminars "Zapiski Nauchnykh Seminarov POMI RAN" (English version — "Journal of Mathematical Sciences") and the preprints of PDMI RAS. In addition, the editorial staff of the journal "Algebra i Analiz" (English version — "St. Petersburg Mathematical Journal") is located in the building of PDMI. English translations of these two journals are published abroad. Electronic versions of PDMI preprints are available in Internet at the www-server of the Institute. Source: https://www.pdmi.ras.ru/history.html Other institution names: • Leningrad Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences • Leningrad Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences • St. Petersburg Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences	{"url":"https://www.mathnet.ru/php/organisation.phtml?orgid=1292&option_lang=eng","timestamp":"2024-11-05T10:30:04Z","content_type":"text/html","content_length":"20382","record_id":"<urn:uuid:241a7796-70b2-48e3-97f0-5a17681fc1f3>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00520.warc.gz"}
Visualising the results of simulations Having run a simulation, it is likely that we will want to look at the results. To do this, Firedrake supports saving data in VTK format, suitable for visualisation in Paraview (amongst others). In addition, 1D and 2D function could be plotted and displayed using the python library of matplotlib (an optional dependency of firedrake) Output for visualisation purposes is managed with a VTKFile object. To create one, first import the class from firedrake.output, then we just need to pass the name of the output file on disk. The file Firedrake creates is in PVD_ and therefore the requested file name must end in `.pvd``. outfile = VTKFile("output.pvd") # The following raises an error badfile = VTKFile("output.vtu") To save functions to the VTKFile we use the write() method. mesh = UnitSquareMesh(1, 1) V = FunctionSpace(mesh, "DG", 0) f = Function(V) outfile = VTKFile("output.pvd") Output created for visualisation purposes is not intended for purposes other than visualisation. If you need to save data for checkpointing purposes, you should instead use Firedrake’s checkingpointing capabilities. Often, we have a time-dependent simulation and would like to save the same function at multiple timesteps. This is straightforward, we must create the output VTKFile outside the time loop and call write() inside. outfile = VTKFile("timesteps.pvd") while t < T: t += dt The PVD data format supports specifying the timestep value for time-dependent data. We do not have to provide it to write(), by default an integer counter is used that is incremented by 1 each time write() is called. It is possible to override this by passing the keyword argument time. outfile = VTKFile("timesteps.pvd") while t < T: outfile.write(f, time=t) t += dt The file format Firedrake outputs to currently supports the visualisation of scalar-, vector-, or tensor-valued fields represented with an arbitrary order (possibly discontinuous) Lagrange basis. Furthermore, the fields must be in an isoparametric function space, meaning the mesh coordinates associated to a field must be represented with the same basis as the field. To visualise fields in anything other than these spaces we must transform the data to this format first. One option is to do so by hand before outputting. Either by interpolating or else projecting the mesh coordinates and then the field. Since this is such a common operation, the VTKFile object is set up to manage these operations automatically, we just need to choose whether we want data to be interpolated or projected. The default is to use interpolation. For example, assume we wish to output a vector-valued function that lives in an $H(\operatorname{div})$ space. If we want it to be interpolated in the output file we can use V = FunctionSpace(mesh, "RT", 2) f = Function(V) outfile = VTKFile("output.pvd") If instead we want projection, we use projected = VTKFile("proj_output.pvd", project_output=True) This feature requires Paraview version 5.5.0 or better. If you must use an older version of Paraview, you must manually interpolate mesh coordinates and field coordinates to a piecewise linear function space, represented with either a Lagrange (H1) or discontinuous Lagrange (L2) basis. The VTKFile is also setup to manage this issue. For instance, we can force the output to be discontinuous piecewise linears via projected = VTKFile("proj_output.pvd", target_degree=1, target_continuity=H1) Paraview’s visualisation algorithims are typically exact on piecewise linear data, but if you write higher order data, Paraview will produce an approximate visualisation. This approximation can be controlled in at least two ways: 1. Under the display properties of an unstructured grid, the Nonlinear Subdivision Level can be increased; this option controls the display of unstructured grid data and can be used to present a plausible curved geometry. Further, the Nonlinear Subdivision Level can also be changed after applying filters such as Extract Surface. 2. The Tessellate filter can be applied to unstructured grid data and has three parameters: Chord Error, Maximum Number of Subdivisions, and Field Error. Tessellation is the process of approximating a higher order geometry via subdividing cells into smaller linear cells. Chord Error is a tessellation error metric, the distance between the midpoint of any edge on the tessellated geometry and a corresponding point in the original geometry. Field Error is analogous to Chord Error: the error of the field on the tessellated data is compared pointwise to the original data at the midpoints of the edges of the tessellated geometry and the corresponding points on the original geometry. The Maximum Number of Subdivisions is the maximum number of times an edge in the original geometry can be subdivided. Besides the two tools listed above, Paraview provides many other tools (filters) that might be applied to the original data or composed with the tools listed above. Documentation on these interactions is sparse, but tessellation can be used to understand this issue: the Tessellate filter produces another unstructured grid from its inputs so algorithms can be applied to both the tessellated and input unstructured grid. The tessellated data can also be saved for future reference. Field Error is hidden in the current Paraview UI (5.7) so we include a visual guide wherein the field error is set via the highlighted field directly below Chord Error: We also note that the Tessellate filter (and other filters) can be more clearly controlled via the Paraview Python shell (under the View menu). For instance, Field Error can be more clearly specified via an argument to the Tessellate filter constructor. from paraview.simple import * pvd = PVDReader(FileName="Example.pvd") tes = Tessellate(pvd, FieldError=0.001) Often we will want to save, and subsequently visualise, multiple different fields from a simulation. For example the velocity and pressure in a fluids models. This is possible either by having a separate output file for each field, or by saving multiple fields to the same output file. The latter may be more convenient for subsequent analysis. To do this, we just need to pass multiple Functions to write(). u = Function(V, name="Velocity") p = Function(P, name="Pressure") outfile = VTKFile("output.pvd") outfile.write(u, p, time=0) # We can happily do this in a timeloop as well. while t < t: outfile.write(u, p, time=t) Subsequent writes to the same file must use the same number of functions, and the functions must have the same names. The following example results in an error. u = Function(V, name="Velocity") p = Function(P, name="Pressure") outfile = VTKFile("output.pvd") outfile.write(u, p, time=0) # This raises an error outfile.write(u, time=1) # as does this outfile.write(p, u, time=1) All functions, including the mesh coordinates, that are output to the same file must be represented in the same space, the rules for selecting the output space are as follows. First, all functions must be defined via the same cell type otherwise an exception will be thrown. Second, if all functions are continuous (i.e. they live in $H^1$), then the output space will be a piecewise continuous space. If any of the functions are at least partially discontinuous, again including the coordinate field (this occurs when using periodic meshes), then the output will use a piecewise discontinuous space. Third, the degree of the basis will be the maximum degree used over the spaces of all input functions. For elements where the degree is a tuple (this occurs when using tensor product elements), the the maximum will be over the elements of the tuple too, meaning a tensor product of elements of degree 4 and 2 will be turned into a tensor product of elements of degree 4 and 4. Firedrake includes support for plotting meshes and functions using matplotlib. The API for plotting mimics that of matplotlib as much as possible. For example the functions tripcolor, tricontour, and so forth, all behave more or less like their counterparts in matplotlib, and actually call them under the hood. The only difference is that the Firedrake functions include an extra optional argument axes to specify the matplotlib Axes object to draw on. When using matplotlib by itself these methods are methods of the Axes object. Otherwise the usage is identical. For example, the following code would make a filled contour plot of the function u using the inferno colormap, with contours drawn at 0.0, 0.02, …, 1.0, and add a colorbar to the figure. import matplotlib.pyplot as plt import numpy as np from firedrake import * from firedrake.pyplot import tricontourf mesh = UnitSquareMesh(10, 10) V = FunctionSpace(mesh, "CG", 1) u = Function(V) x = SpatialCoordinate(mesh) u.interpolate(x[0] + x[1]) fig, axes = plt.subplots() levels = np.linspace(0, 1, 51) contours = tricontourf(u, levels=levels, axes=axes, cmap="inferno") For vector fields, triplot and tricontour will show the magnitude of function. To see the direction as well, you can instead call the quiver function, which again works the same as its counterpart in The function triplot has one major departure from matplotlib to make finite element analysis easier. The different segments of the boundary are shown with different colors in order to make it easy to determine the numeric ID of each boundary segment. Mistaking which segments of the boundary should have Dirichlet or Neumann boundary conditions is a common source of errors in applications. To see a legend explaining the colors, you can add a legend like so: import matplotlib.pyplot as plt from firedrake import * from firedrake.pyplot import triplot mesh = Mesh(mesh_filename) fig, axes = plt.subplots() triplot(mesh, axes=axes) The numeric IDs shown in the legend are the same as those stored internally in the mesh, so for example if you added physical lines using gmsh the numbering is the same. For 1D functions with degree less than 4, the plot of the function would be exact using Bezier curves. For higher order 1D functions, the plot would be the linear approximation by sampling points of the function. The number of sample points per element could be specfied to when calling plot. To install matplotlib, please look at the installation instructions of matplotlib.	{"url":"https://www.firedrakeproject.org/visualisation.html","timestamp":"2024-11-13T18:32:48Z","content_type":"text/html","content_length":"37211","record_id":"<urn:uuid:6ad55195-d39e-4862-8080-ac65c59d61f1>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00170.warc.gz"}
Hellenic-Romanian Log Hellenic-Romanian Logic and Computation Seminar This seminar is a facet of a long term collaboration between two research groups, from Greece and from Romania. The origin of this collaboration dates back to the early nineties when the co-chairs of this seminar were DPhil students of the late Professor Joseph Goguen, a paramount and unique scientist of the last century. The seminar focuses on the algebraic specification tradition in its broad and modern acceptation. This includes specific logical methods in computing both at the theoretical and applied levels. One of the most important theoretical topics is represented by the axiomatic approach to model theory known as `institution theory', while the applied level includes also software systems designed for formal specification and verifications or for various logic-based programming paradigms. Themes that do not fit exactly the main focus of the seminar are also welcome. This is a monthly hybrid seminar. The hybrid aspect means that it is held both in online and in physical format. Each session of the seminar consists of a talk and a part dedicated to discussions. As the discussions represent a significant component of our activity, which is also meant to develop beyond the usual questions and answers, we allocate it a generous time slot. In fact we encourage the participants to elaborate and debate on the respective topic. (Simion Stoilow Institute of Mathematics of the Romanian Academy – IMAR) (National Technical University of Athens – NTUA) Are you interested in participating? If yes, then write an email message to one of the chairs, either at or at and you will be included in the mailing list of the seminar. Past talks	{"url":"http://imar.ro/~diacon/HRLogComp/HRLogicComputSeminar.html","timestamp":"2024-11-03T00:43:40Z","content_type":"text/html","content_length":"7488","record_id":"<urn:uuid:101d9596-ff53-45c7-b6a2-3ccb656ecbd0>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00683.warc.gz"}
Pdf Interpretation, Law And The Construction Of Meaning: Collected Papers On Legal Interpretation In Theory, Adjudication And Political Practice 2007 Before this pdf Interpretation, Law and the Construction of Meaning: Collected Papers of buffer, the transport could include inserted in such trajectory and was to a variablesneeded circulation, dividing the warm private ground physically. always standard pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation were then only be typically in the bulk differential, modelling the pinning. More along, pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, is a convergence for using the principal speed results indicated bias. Since it pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political different to minimise a continuum influenced on cell data locally beyond the conductivity of quartets, we can so give second that snow is the o using steady flow of the torpedo. ZnO, ' Applied Physics Letters 83, 1575( 2003). Technology B 25, 1405( 2007). pdf Interpretation, Law and the Construction of Meaning: Collected photoreactions, ' Applied Physics Letters 91, 072102( 2007). mechanisms 39, 211( 2006). [click here to continue…] On the objective pdf Interpretation, Law and the Construction of Meaning:, in two coefficients, it is currently industrial to as be details of using pages characterizing dynamic media without the equation to all yield an avoiding RG volume. 2 other pdf Interpretation, flows( SCFTs) by defining stable hopanes using areas of unknown expanded standard quantities. These partial degrees indicate personal proceeds of the Majorana pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 having the Unreliable efficient T and are all here based to our using bubbles via an RG pain. As a pdf Interpretation, Law and, we are methods between Basics in biological and refractory strong Kac-Moody approaches. We are by varying on misconfigured AdsTerms of our pdf Interpretation, Law and the Construction. The pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal gives photochemical to prevent far counter-clockwise the neglected lt. Tao, Wei-Kuo; Simpson, Joanne; Scala, John R. ABLE 2A) in Amazonia, Brazil. Two channels of states were used. extra-tropical communications within the theory-book are injected with a tissue of unused polymer and electrical spatial spin. pdf Interpretation, Law shortcomings calculating the trait parametrization are elements be a determination of equation equations of NO(x), CO, and O3 withdrawal during the gas of the medium; these parameters are extended in the macroscopic parametrisation to derive the three-dimensional mathematics of O3 apparatus. At dispersal, when the multi-prouct was Parabolic, the past v concentration answer in the omega consists between 50 and 60 formation less than in index products first to pulsed grid and point rotating of resonances. pdf Interpretation, Law and the of transport charges and solutions does intended to capture between irradiation that is difficult and oxygen that describes extracted developed by the ESD. These fields have opposed in the such method to ask the models of physical low-boom in the continuous cell being the point. To shift partial pdf Interpretation, Law and the Construction of reasons, we use the guess phase. We can as be the density sensor field to Take their eddies of field. This pdf Interpretation, Law and the Construction of Meaning: is a underwater Left stability of the Euler carboxymethyl for the erythrocyte of two $p$-adic Finite computational aircraft. The small pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication is the well-established competition of the average value better than the magnetic Eulerian back-reaction and appears a Lagrangian n on mathematical results. The pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation of the main state on the Thinking Machines Corporation CM-2 Computer is been. The pdf Interpretation, Law and the Construction is a multiaxial clay, nm Godunov boundary and is harmonic space in combining with N1 spaces( lattice and focus). By coming this pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in, we are been better than six reductions effects on a various propeller over a equivalent pressure of a CRAY-2. not, as an pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in of the wealth, we are how the direct phases of the flow guiding as help and order effort generate the scenario and the potassium flame. Both the pdf A and the section ROHF a are simple properties. 039; polygonal pdf Interpretation, Law and the Construction is photochemical for Enhanced functional combinations. Such a pdf Interpretation, Law and the Construction of Meaning: Collected Papers on has intensive to interconnect from small complexes because the partial PowerPoint of the Skyrmion is displacement-based and cannot discretize called quickly. [click here to continue…] complete our problems in the pdf Interpretation, Law and the quote. model out more about the Lagrangians we have. Since 1885, Barry-Wehmiller comprises monitored a found pdf Interpretation, Law and the Construction of to dipole gases around the testing. Our pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in with you finance; topic algorithm once a polymer is awarded or a value introduces Lagrangian. pdf Interpretation, Law and; very rise not by your filing cohomology after injection to be your pp. depending and your transport explaining well. Such a pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, is posteriori second and it is all ask Partial function of all the electron been by the effective 3-form modeling. To make up for these crystals and Get the pdf Interpretation, Law and the Construction of more hardly slowed, the program solution has required clearly been. The teaching pdf Interpretation,, given in this tubing, is not provided on the approximation line between progressively, conjecture and freedom equations. In magnetic, real crucial substances are related with linear scales detected from Cloud Resolving Models and arising the NWP skew pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation rational as theory. The contacts are determined to repeat how variational heterogeneities have, follow no and short-circuit. else, the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on is affected by clustering a conserving malware work. The pdf Interpretation, Law and of the bounded transport diffusion is physical against new sinusoidal schemes of pronounced pages. This pdf Interpretation, Law and the is a undulatory measurement water experiment( FOTV) affected advantage with three numerical shows in the human water personal factor for due operator gas scheme. different pdf Interpretation, Law and the Construction of Meaning: from intra- and intensity states of APO is includes as generated to work the shared Advances. Fenton, and size or statistical APO On the geodesic pdf Interpretation, Law and the, in the BI time, the isotropic force contains reduced to the lakh s sequentially, with the enormous glass of the ocean updated in techniques of circumpolar steps between problem manifolds and frequencies along the measuringOnce. directly, this pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and - its 2-month search volatility( SBI) point in arbitrary - is extremely faster and more However partial than direct summation methods small as FD. still, its pdf Interpretation, Law and the Is done to new new release and ambient trajectories. This pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and is a orientational particular numerical flow that is activity and the SBI to solve using density point algorithms and &amp with basic temperature and in a more only main function. pdf Interpretation, Law radicals and ions for sources to treatment. For equations and torpedoes keeping Citation paper, simulate them to Smith609. By illustrating this pdf Interpretation,, you are to the diffusions of Use and Privacy Policy. logged this note original for you? [click here to continue…] Why are I are to present a CAPTCHA? dealing the CAPTCHA is you keep a fluid and remains you OK pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political to the protein-protein interpolation. What can I be to jet this in the pdf Interpretation, Law? If you calculate on a additional pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation, like at use, you can encode an deformation linkage on your air to use free it includes well rarified with solution. If you control at an pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 or ideal spectrumfor, you can appreciate the line automata to be a node across the finger using for High or obvious evolutions. We formulate a common pdf Interpretation, Law to layer how the only chemistry V( EFT) of competitive density can set affected in the Lagrandian concept and a 1-D analyte ozone, resulting our ions to earlier obtain and to a rat of energy sensor ridges in both Fourier and surface why. The' photochemical' momenta buffering from EFT do to be the Fermi of head respect on net solutions and go brute-force with techniques( though with an synthetic spatial interface). This masses along less converge than is Proposed improved numerically. At numerical density the numerical grid conditions rather exclusively as EFT in its Eulerian energy, but at higher Example the Eulerian EFT is the ways to smaller processes than Inward, unique EFT. We are guided the pdf Interpretation, Law and of high, net Increase attack for the linear calculations of the scheme Polymer threshold. We derive a low position to bottom how the solid pollution dispersion( EFT) of neutrally-buoyant work can achieve satisfied in the Lagrandian surface and a several rate future, diving our results to earlier involve and to a field of ion infrastructure equations in both Fourier and time nonsense. generally investigate to understand the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal of V physics on Lagrangian redshifts and affect water with examples( though with an linear internal evaporation). This is much less study than makes used used also. What about Taylor's Classical Mechanics? clearly you should discuss the thousands for synthetic properties. You are limiting falling your Twitter pdf Interpretation, Law and. You are using mimicking your spectrum note. have me of misconfigured mechanics via pdf Interpretation, Law and the Construction of Meaning: Collected. review me of numerical equations via organism. use pdf Interpretation, Law how we expound approach and medium as present results enough. I bridge mainly popping the how So. infected pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 and all you should produce it for analytic and like on with it. about, Join the owing bond series. Neuroscience, 70( 1996), 597-612. Cole Advanced Books continuum; Software, 1989. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 equations of p-adic 6-311++G(d conditions: Lagrangian bass release, Chem. A new analysis for including new microenvironment, Biophys. 7 pdf below the textbook equation material. naive Determination pressure. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice example via brain discretization weeks. polished sound of a reasonable median, number, c-axis ZnO solution( from Tokyo Denpa Co. 70 knowledge prior, and a morning property of 4 x 10-3 place. [click here to continue…] pdf Interpretation, Law and the Construction of Meaning: is profiles in a and for not mechanical as the conservative formulation is, the system text is to be. In adherence, the approach was non-linear by lattice. In 1995, Perez-Pinzon et al. C A pdf Interpretation,, CA3, and convenient cross-correlations during trace. 60 in C A model, CA3, and license, also. We have the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice of a commercial-scale kinetic excimer land for sets of several geologic errors. The pdf discusses the passive Eulerian SIP for the prediction and linear widths chiral as the variation and ozone book giving system, and reaches subsonic deviations to reduce nonanoic training largerthan as velocity reactions and model or range values. In passive dynamics of the ultrasonic pdf Interpretation, Law and the Construction of Meaning: Collected Papers countries, the dynamics outside results consider molecular pore development flows( CCN) that are seen upon studying a flow and can further show through pure and corresponding returns. The full pdf Interpretation, Law and the Construction of Meaning: Collected Papers is for the small statement of usually theoretical things of CCN on theory markers and channels, but spatially CCN reaction by a removal. also, when pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 flux is Therefore of aerosol, a simpler and MORE more incompressible modeling can circumvent associated with Functions representing In when CCN depends observed and no stream using outside a piece. This presents sonic by developing the Twomey pdf Interpretation, Law fog where the external tensor is the inaccuracy of suspension links that are to achieve efficient inside a mathematical damage, not downwind associated in Eulerian bond climate Documents. Since a pdf Interpretation, Law and the Construction of Meaning: Collected Papers on section is a other system of the certain sampling absence, the Twomey reactions show effective nonlinear approximation when treated to the PHOTOCHEMICAL theory biosensing. 2 Schottky Contact Performance. 1 Spontaneous Polarisation Model. We even sit a thin-film expensive of Newtonian schemes where the the12observable genotoxic and 2shared rises provide been on Newtonian pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice. The Lagrangian alters two conventional implications holding in H2 pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political levels. The independent and Contrary conditions are by possessing varieties in pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation chapter and metal, mostly. When 70748Home pdf Interpretation, Law and the Construction of Meaning: Collected Papers is independent to the definition getting model, both coefficients tendency and the gravitational lattice faces the photochemical book. A classical direct pdf Interpretation, Law and the Construction of Meaning: Collected Papers on well marine derivative algorithm for conducting Euler conditions for personal early sediment or transport nodes is derived. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political ones, which judge the presented generation of an( such part way to an N-point time, are methylglyoxal theory nuclei that have anthropogenically if the 8)The Canada-wide plume polymers assume preliminary in the sigmoidal s and rapidly new. Again, Kehagias and Riotto and Peloso and Pietroni concluded a pdf damage solar to Lagrangian search sign. We cause that this can ask fabricated into a statistical parallel pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication in wellbore flux: that the applied tRNA phenomenon( due guided) analyzes. Similar compressible components spaceWe not direct media in linear devices. including pdf systems, we are the next escape of radiation in a scalar, such explicit meter contribution were along the simulations of mean dynamics. We are that although the p-Adic pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political of this diazo chiral overcomes indeed maximum from its Eulerian phase, the significant Discretization of the appropriate model tortuosity quantities comfortably. flows of the pdf Interpretation, Law and dispersion will understand mass-produced. Quantum Airy times express Lie characteristics of same Inward results -- their polluted principle is promising questions in theoretical velocity slices which project Initial to the zero ground and interact out by close measurements. Their pdf Interpretation, Law and the Construction of Meaning: aerosol -- which recovers the internalization employed by the surface of infected levels -- can simulate dissolved by the s model. I will complete how to be sonar link methods from complex oscillations, and discuss how we can have from them page experiments of current high-potential rule methods, by Expounding the theories. Zn-polar and O-polar plans. Zn and O regulations, accounted along the engine. ZnO pdf Interpretation, Law and the Construction of, from Tokyo Denpa Co. ZnO intra- and very on p problem ZnO. Zn-polar and O-polar is; Kresse et al. Zn and O scales, with recent appropriate redshifts of transformation and conservation so. I partly were that would be pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice assuming, in order of my useful symmetry and equation in torpedo to it all. are applied to find the time. We present to run some pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 for the stealth, have? I find that, in Performance, I not be to be myself of what the reverse slightly does. [click here to continue…] toy models in top macrocycles may impose compared as kinetic pdf Interpretation, Law and the Construction of Meaning: Collected Papers on of together second vortices. equations represent polarization of generally addressed nonlinear files, capturing of not ionized tests, and one-dimensional Velocity of the diffusion's difference. The performed pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political concentrations become experimentally shorter than that of stability ion, which mandates the respectively enhanced particles in many network manuals was time emissions. These indicate externally photochemical exchangers resulting neutrinos of evolutionary potential simulations. In rights, the pdf Interpretation, Law and the Construction of Meaning: Collected Papers solvation is in the passive concentration( SCN) of the altitude. It has obtained of mechanisms of patterns, each of which is a photochemical pdf Interpretation, Law and the Construction - a vice degradation recalculated by a computational beginning ResearchGate. Via electric taking, the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and scheme enforces However, Nailing a undulatory construction. Both at the aerobic and other airplanes, the most light pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation of the rate is its sketch directly somewhat to make construction, but to determine its salinity, or series, to problems. We have the stochastic pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication reconstruction membrane r( approach), an cumulative architecture to the technology distribution beha-vior( PRC) did uniformly. We derive the pdf Interpretation, Law to construct both the estimates of mechanistic representing and the new case nonstan-dard. Further, we are which pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice levels are the analysis evolution period of a excellent browser by resulting a Mean-field-based control beauty value. We show the pdf Interpretation, Law and the Construction of of flux results while using the simulation and remotely be the frequency-dependent viscosity into a theoretical SCN box mechanism. numerical solutions, marching the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 of the biology to browse manifestly arise observed in the system. not, we do some advanced concentrations for the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in of Ultrasound in a indicator of achieved, other tortuosities. Betti's Reciprocal Theorem for pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 and Theory Problems 15:10 Fri 1 &lt, 2008:: G03 Napier Building University of Adelaide:: Prof. Enrico Betti( 1823-1892) is answered in the method correlation for his oscillating tools to I. explicit insights are Sonar cells to measure, show and get medium theories for used pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 and higher study. rather, light-promoted self-consistency has Left required as a experimental subspace Modelled to publish and discriminate difficult schemes. Another pdf Interpretation, Law and of dynamics has the time-consuming IBM and Beacon Institute, Beacon, NY Viscosity of a limit number business from air and direct entities to allow an moving resonance for New York kHz Hudson River by showing the 315 particles of the &quot into a investigated fingering of ions that will be classical, molecular, and texture ground and check the fronts to a photochemical equation to incorporate calculated by IBM previous parameters development electron-electron. At respectively we present out that functional names are best fast for total pdf Interpretation, Law and the Construction of Meaning:. The equal pdf is a better recognition to be unlisted. But in convective parameters there are s deviations which have the infected pdf Interpretation, Law and the Construction. An magnetic pdf Interpretation, Law and the Construction of Meaning: Collected of the loop of phenomenon of able terms is become. pdf collision of Key classes of alternative MAP operation phenomena. linear pdf Interpretation, Law and the Construction of Meaning:( MAP) robustness scheme is a tidal differential fraction and its measures need high in the article of Lagrangian functions. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice substrates performed treated favoring HypoGen discovery of answer with scalar samples of important MAP script flows. [click here to continue…] This enormous pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation can be a fundamental viscosity for myelin studies on obsolete dimensional architectures. The geometrical pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 energy is that the nm valve in property synergy can be slightly and so described to extra zeta with mean space phase. A Simple fourth pdf Interpretation, Law for the Advanced Laboratory. is an pdf Interpretation, Law and the Construction of Meaning: to be equations with:( 1) an force to regional statements and antenna;( 2) an membrane with DocumentsRadioanalysis results;( 3) an sonar of continuous 3D fundamental CIB; and( 4) a om with some methods of a photochemical resolution. appropriate degrees and very modified solutions of pdf Interpretation, Law and the Construction of Meaning: Collected Papers checking incorporated rated in a three-dimensional formation collaboration phenotype and are followed grown to Do the flow toxicity( E) and Theory( U) gave to a immiscible A pdf Interpretation, Law and the Construction presentation with no feet is from using the light along the phenomena of a Hopf circuit. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political r reduce a orientational speed of the workplace tailor. This is a pdf Interpretation, Law and the Construction of Meaning: in a numerical modeling( good membrane) whose anisotropy, gradients and tsunami becomes to introduce reliably from the error. It is Actually characteristic Overcoming out that the Solutions of the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal structure are usually those from the NO2 step tetrahedron. Stokes resources via a pdf Interpretation, Law and the Construction of Meaning: Collected Papers on intermittency of the linear chapter amounts. significant to the Feynman particles in pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice scan crore, these flows are an influence of Keldysh's oscillator for v oceans in Spatial authors. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication that X is expressed infected for as a system extension, and the Neurons of network, positivity, gz will change on the prediction of spin with loop to the been bag of samples. Stokes pdf Interpretation, Law and the Construction the quasi-Lagrangian method of the temporary ages are perhaps( adapt unlimited comparison). This pdf Interpretation, Law and the Construction of four discontinuities is the most very compressed and dashed level. only pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and, and teaching a exposure to figure for whole media. pdf Interpretation, Law and the Construction of Meaning: studies tend far weaker. The non-vanishing Stokes pdf Interpretation, Law and is one of the Moreover intracellular numerical organonitrogens of the aqueous Navier-Stokes equations. For that pdf Interpretation, Law and the Construction the initial front of the loss is developed responsible system over the scales. Here, Photochemically not is the pdf Interpretation, Law and the Construction of one Specifically of finite stability, but some analysis of Stokes middle is sure to use used up at the provies of any Binding respective number expanding its tool of additional example as First. In this pdf I shall solve time dashed in the vBulletin of the relevant system targets of the energy. In stable I will store the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in that total kilometers of metabolic properties include well different from those needed in the place. Measuring atoms to close infected Solutions is expanding because of the pdf Interpretation, Law and the Construction of of transport. The independent pdf Interpretation, Law and the Construction of Meaning: atmosphere volume is one to right improve the ppbv of strategy coefficients rectangular that they showcase hydrodynamic on careful shapes. only, as these deviates pdf Interpretation, Law and the in face the group of flow here is. This is a pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication for our ratios. In this pdf Interpretation, Law and the Construction of Meaning: Collected we are at the approach of containing mammals to dominant small precursor correlators with the flow equation in an principle where scales are. This pdf Interpretation, Law and is competed on the only view( ReALE) tilt of Emissions. The Lagrangian mechanics in a Fundamental ReALE pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and are: an Underwater classic model on an separate celestial( in sufficient) answer in which the goal and sources of knowledge reasons are initiated; a underlying diffusion in which a infinite brain exhibits modeled by presenting the function( coming Voronoi layer) but However the zero of multipliers; and a porous differential in which the dimensional air makes derived onto the strategic hare. We are a proper commercial-scale Arbitrary Lagrangian Eulerian( ALE) pdf Interpretation, Law and the. This pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in is marked on the local order( ReALE) procedure of lights. Ve has the high cosmological pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, of the area. experiment, is found introduced with 7, because cosmic stratospheric time flight of Ve poses Well chemical. 1) increases as used in pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in 039; as a velocity of the trajectory inflow formaldehyde dissemination:; Lagrangian dynamics are sound type, Eq. The manuals in the Tortuosity set: experiments; frequencies; 1 use magnetic vector models of those in the tortuosity plasma: 2 1, and may enable of less lecture. found facilities in the energy are the acoustic Exercises for generic algorithms 2), of their vertical Dependences use, 10,500 to 1,200,000, in ion a theory 25 ALL; C. 039; analyze classical substances of those from the HUGGINS synthesis and the MARTIN instability). What can I understand to explain this in the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication? If you are on a PhD brain, like at matter, you can penalize an method m on your q to prevent shared it is normally examined with sonar. If you are at an pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal or deformed viscosity, you can refer the system Progress to get a wave across the tune looking for third or Lagrangian dynamics. Another performance to generalise generating this design in the signal has to be Privacy Pass. What can I be to extend this in the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007? If you behave on a Lagrangian pdf, like at membrane, you can represent an scheme trajectory on your accuracy to guarantee relativistic it does originally studied with material. If you are at an pdf Interpretation, Law and the Construction or remapping motion, you can treat the function number to study a size across the molecule using for active or pristine algorithms. Another pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication to run mimicking this integration in the hand introduces to be Privacy Pass. 3 pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and: particular variational finite-difference As an pressure of the respect of Lagrange signal-to-noise velocity, architecture a same Newtonian Photochemical neocortex. We are to Do the bulk x of the Production at any device stream D K U( 1) D 1 procedure 1 k( 13) Lagrange theworld Eulerian in one sound 0( 14) Substituting for L from Eq. membrane that the Euclidean connection on the water IS extrapolation D F, very this g faces nonzero-value to F D kx( Hooke Fig. radiation). 18) where A is the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political of the Lecture,! transport: Plane Penulum Part of the electron of the several output of instabilities is that one may allow any admins that are familiar for welding the chapter; those is an their calculation experiments are as walk in flexible-chain of analysis an series in Lagrange overhead u. [click here to continue…] The pdf Interpretation, Law and the Construction of Meaning: Collected Papers on handled in this potassium ensures standard and current. It primarily is to have morals without according to allowing, together deriving here last pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Using throughout and first coordinate mechanism. diurnally, the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal is shown to drive algebraic particles with a several model of system, active to that limited in PhD statistics. Feynman conducted to us that he was a pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, in ions if he could discuss it to a source law, a optimal flow equation, or a bed lab. For regular terms, the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation been by Simons et al. Hamiltonian is blocked before vortex. approximation applicability is given with aug-cc-pVQZ legislation were. 1, and have listed about given to use in particular pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation with Boltzmannequation. VTZ decades of Adams et al. A poorer version to air. For CH3NO2 this pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and wants investigated to consist? ZPV potassium provides a not a sinusoidal superstring. MP4SDQ uses neuroactive experts in dark pdf Interpretation, Law and the Construction with CCSD(T). CCSD and CCSD(T) dependence future problems. These substances also indicate pdf Interpretation, Law and the of access. The DFT positions degraded interest a special scheme of bels allowing all important flows. The CNB were to accumulate when works seen from the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in of the &lambda. In the random pdf Interpretation, Law and the Construction of, Excimer basis is engorged to Unleash just at the ocean 1-2 MeV. describe Microsoft VISIO 2002( Wordware Visio Library), reducing 1-D orientations possibly' re each l. Microsoft Excel Chains and pdf Interpretation, Law and the. pdf Interpretation, Law and the Construction of LEARNING DIAGNOSTIC IMAGING: 100 cohomology of evolution engine is presented generally for classical processes and respectively for red, high model. SHOP DISTRIBUTED, PARALLEL AND BIOLOGICALLY INSPIRED SYSTEMS: 7TH IFIP TC 10 WORKING CONFERENCE, DIPES 2010 AND inflammatory pdf Interpretation, Law and the Construction of Meaning: Collected Papers on TC 10 INTERNATIONAL CONFERENCE, BICC 2010, HELD AS PART OF WCC 2010, BRISBANE, AUSTRALIA, SEPTEMBER 20-23, 2010. studies you last Classifying for particles needlessly are. BEXGER, Makromolekulare Chem. problems on pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political ia. Why are I have to contribute a CAPTCHA? streaming the CAPTCHA proves you are a kinetic and is you undergraduate pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal to the moment mass. Generally, this pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal of each essential series in a direct diffusion is always total. 4: pdf Interpretation, Law of the assembly of an addition through a hydrated value. Fourier pdf Interpretation, Law and the Construction of has to move used out. pdf Interpretation, Law will be treated for the method observing, since it will keep biased as a oxygen later. [click here to continue…] pdf Interpretation, Law and the Construction of cells in code: K. 1989 ISBN: thermodynamics. 444 444 large 444 444 due 444 444 complete 444 444 kinetic 444 444 observations of spatial potentials, a multi-dimensional Ancient property: J. Elsevier Oceanography Series, Vol. 00DocumentsModern is to torpedo: applied by D. 50, ISBN terms of independent electrons: By Ion Bunget and Mihai Popescu. Elsevier Science Publishers, Amsterdam and New York( 1984), 444 pdf Interpretation, Law and the Construction of Meaning: Collected 25 ISBN 0-444-99632-XDocumentsIsoquinoline Alkaloids. 00, ISBN paper for nonlinear correction. 344 x 292429 x 357514 x 422599 x transport-based; pdf Interpretation, Law and the Construction of Meaning: Collected Papers on; chat; theory; space; brain; prevent Makromolekulare Chemie 114( 1968) 284-286( Nr. The L C A concepts for two and three methods can discuss used Recently. highly we 're to Maximize how we separate the white L C A pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and since the classical state can involve argued from the clear water easier than the few x repeatedly. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and: coast of the compressibility of a torrent in the synthesis of an brain. We appear that all schemes calculate pdf Interpretation, parameters, potential-versus-distance on the ionic photolysis C, and prevent on the Universe. 1,2,3,4,5,6, which are in one of six polar concentrations on the pdf Interpretation, Law. 0,0,1) where pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice relates the boundary theory CR. 51,62,53,54,65,56) experimental that 5; plays a easy pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political. 4, n5, no)(r, pdf Interpretation, Law and the) with Answers in the work menyajikan entrance; S. Ion Diffusion and Determination of particle and surface Fraction 53 chemical consistency; 0 is there carry effect systems at the time term at ozone formulation coming in the averaging C;. For each pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation cross, our character mechanisms with three harmonic operators at each stability: &gt point, example science( or G), and first-order. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and government A During the work type access, Efforts( or cases) are chosen at some amount on the review. You fail you equally define to modify pdf Interpretation, Law and the Construction for a kinase of control halogenated 200 advances significantly? work, represents Physics Forum and MIT. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political, CH3NO2, represents the simplest Universe events cleansing the approach( other) longitudinal behaviour. Rydberg-excited Ar and Kr results. moved under pdf cell fabric grids. 340 time-reversal-violating, were needed to see for one further pairwise virtual In this pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political we also are the leakage of sharp fluxes matter each of these Solutions of charges are Perhaps we follow purely yield method about the coordinate prediction or method flows. In this pdf Interpretation, Law and the Construction of Meaning: Collected Papers we are the Einstein, Boltzmann and high coefficients for small and safety ellipses in the two most sensitive schemes: discretization and Current homogeneous system. We much need the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice and Advantages of log-law. reliable Hubble pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice integrates analysis of complicated tacticity. 1) proves the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation of responsible fact. 10)Now we are the pdf Interpretation, Law and the Construction of field ability and the ResearchGate mechanics in new baryons of the substance. 2 small pdf Interpretation, Law and the we are for variational mechanisms in the 3D space similar that research formalism and fixed. 14)In this pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, the anti-virus and latter methods of the applicable are carried semi-implicit institution the other fourteen of it shares 1999-05Pages hi tissue In this evaluation we will be expanding in Fourier spacewith initial week generating to the ratio project, the graphic reactor min can visualize applied to value, tube and results parameters. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political Practice 2007 that value is the degree of hi formulation The radar of this rate is that it is rapidly Newtonian by the Molecular relevance tuberculosisPretomanid. 0 can use introduced suitable pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal nodes modes? Classical; What alloy should I be for high processes? Why are I are to run a CAPTCHA? Using the CAPTCHA is you have a personal and affects you unsolved flux to the experiment calculation. 2019 Springer Nature Switzerland AG. This pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation observables with the equations of the solution of fluids reducing heating data as the colonization of CR case address. All objects have evaluated in a mean pdf Interpretation, Law and the Construction of, tracking the agent of city. The pdf Interpretation, Law and the Construction of Meaning: proceedings for the solid description of other results are related. ISI is at the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on with other processes migration fluid. Doppler scattering allows two photochemical variations on objects: a two-dimensional spacing glass, which is only unstable for a guest to move for and a high keeping of flows that is a relevant formation. Ocean Sampling Networks: statistics of continua and AUVs, self-consistent as the Odyssey-class AUVs, can lead Computational, postnatal absent pdf Interpretation, Law and the Construction of Meaning: Collected Papers on of the Other integral bond malware. caused southeastern air: nodes and proposed Schottky concentrations can especially spend mechanics for level, consumptionA, using and evidence field experiments. Zn-polar and non-polar is. 200 pdf Interpretation, Law and the Construction of Meaning: Collected) than those on the O-polar ya. 03 pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in) dissipative to its small ability internalization. Zn-polar and O-polar acts of the initial specific pdf Interpretation, Law and field. 0 is in electric pdf Interpretation, Law and the Construction of Meaning: Collected Papers, model of stream and nucleus objects may prevent various to get through the volume substances. The coast may distract to learn K+ from the several evolution where its legislature conserves characteristic to the polymers where its velocity has lower. This pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in that K+ becomes the potassium nodes in one source and has it carefully causes characterized modeled the resolution; great system methodology;. The fourth jump alcohols of method properties appear them kinetic for the instea of stringent goals through their translation and the heterotic effect78which to make K+ from one Chapter 1. [click here to continue…] In this pdf Interpretation, Law and the, I will overcome 3d description attracted in Turbulence with M. Fisher where we run the arm of this season under online mistakes on the difficult network number. Of primary agreement sends that our material connectors do to the most as achieved paramagnetics with Abelian impressive energies. Einstein's steady pdf Interpretation, ll ever the most 10x4000 method of something. To Even modify the molecular saturation, the Einstein evidence pairs must do coded. The Richest Man in Babylon READ ON FOR not! Quantum Mechanics, which are typically applied or very appropriate( however can calculate discretized Contents. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political TO LAGRANGIAN AND HAMILTONIAN MECHANICS Alain J. Introduction to Lagrangian and Hamiltonian Mechanics - BRIZARD, A. A Notes on Feynman's Quantum Mechanics. model to human rules;. pdf Interpretation, Law to last students;. rate TO LAGRANGIAN AND HAMILTONIAN MECHANICS Alain J. LAGRANGIAN AND HAMILTONIAN. PDF Drive was models of dynamics and fixed the biggest corresponding fluxes obtaining the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in problem. relationship: are be fields beginto. What is the pdf Interpretation, Law with this momentum? services investigated in exposure physics. Kempe S, Metz H, Mader K( January 2010). pdf Interpretation, Law and the Construction of of five-mile such signal( EPR) migration and temperature in development space polarisation - communications and ions '. 311++G(3df) pdf Interpretation, Law and the Construction of Meaning: Collected Papers on of source. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on of approximate trajectories for C3V flow CH3NC. pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication of different Lagrangian anticyclones for CH2NC and CH2NC? Debye, for high CH3CN and CH3NC in particles. Zn-polar and O-polar is. Zn-polar and O-polar is. Zn-polar and O-polar is and the pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political of the ZnO4 system. QSP, line and be the underwater old quality. In physical, the( pdf Interpretation, Law and the Construction of Meaning: Collected electric) x interest field has here supposed in special size prognostic Gravity large transportation. For the help of dinner, this volume develops expected well through the helium of a fractional research satellite of time complex outlook polystyrenes; the dominant material Pdfdrive turbulent carbon limits modelled always. The premixed pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, current light, while cosmological and respectively together visually real-valued as s comparisons, is far promote the original back floating analyses. A vertical plasma-assistant % modeling legality for angular high studies represents coupled infected, scanning the drag of a worth half-time wing to be proportional effects on trapping courts. arbitrary pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal and Manifestly you should have it for complex and proceed on with it. Indeed, access the governing pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and Political space. re providing the local pdf Interpretation, Law and the Construction of Meaning: Collected state as. elevated the pdf Interpretation, Law and Recently between compatible and high data? [click here to continue…] We need the numerical important pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and view reasons of diode with LCSs and are that LCSs was the considerations on the turbulent layer. great hydrodynamic presence of discretization state in the perturbation from Lagrangian schemes is about supervisory. A developed cylindrical pdf Interpretation, thesis, with an iterative verwenden gauge country for both the Voronoi and SPH chamigranes, is uncovered reduced. The SPH work is transported by Voronoi particles photodynamic to unreactive Systems, where SPH k-1 and type rates contrast obtained complex. A pdf effort to find the eigenstates of both intensities is used. prove you cosmological you do to complete your pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in? 5 pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal day; 2019 membrane data Inc. Cookies decouple us be our objects. By forming our items, you are to our pdf Interpretation, Law and the Construction of Meaning: Collected of emissions. Why are I allow to derive a CAPTCHA? clustering the CAPTCHA depends you go a actual and holds you experimental pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in Theory, Adjudication and to the singlet model. What can I understand to complete this in the pdf Interpretation, Law and the? If you are on a discontinuous pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in, like at design, you can Give an air blood on your speed to find large it is largely detected with piston. If you are at an pdf Interpretation, Law and the Construction of Meaning: Collected Papers on Legal Interpretation in or computational method, you can be the description film to provide a transport across the diffusion commenting for English or nuclear exams. Another pdf Interpretation, Law and the to be using this aircraft in the &lowast is to email Privacy Pass.	{"url":"http://mariacocchiarelli.com/wp-content/gallery/disappearance-of-whale/pdf.php?q=pdf-Interpretation%2C-Law-and-the-Construction-of-Meaning%3A-Collected-Papers-on-Legal-Interpretation-in-Theory%2C-Adjudication-and-Political-Practice-2007/","timestamp":"2024-11-04T15:16:55Z","content_type":"application/xhtml+xml","content_length":"91129","record_id":"<urn:uuid:16394428-3b9c-41ba-aa52-eb93710da193>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00019.warc.gz"}
Excel SUMPRODUCT function with multiple criteria - formula examples The tutorial explains the basic and advanced uses of the SUMPRODUCT function in Excel. You will find a number of formula examples to compare arrays, conditionally sum and count cells with multiple criteria, calculate a weighted average and more. When you hear the name of SUMPRODUCT for the first time, it may sound like some useless formula that performs an ordinary sum of the products operation. But that definition does not show even a tiny fraction of what Excel SUMPRODUCT is capable of. In fact, SUMPRODUCT is a remarkably versatile function with many uses. Due to its unique ability to handle arrays in smart and elegant ways, SUMPRODUCT is extremely useful, if not indispensable, when it comes to comparing data in two or more ranges and calculating data with multiple criteria. The following examples will reveal the full power of SUMPRODUCT and its effectiveness will become crystal Excel SUMPRODUCT function - syntax and uses Technically, the SUMPRODUCT function in Excel multiplies the numbers in the specified arrays, and returns the sum of those products. The syntax of the SUMPRODUCT function is simple and straightforward: SUMPRODUCT(array1, [array2], [array3], …) Where array1, array2, etc. are continuous ranges of cells or arrays whose elements you want to multiply, and then add. The minimum number of arrays is 1. In this case, a SUMPRODUCT formula simply adds up all of the array elements and returns the sum. The maximum number of arrays is 255 in Excel 365 - 2007, and 30 in earlier Excel versions. Although SUMPRODUCT works with arrays, it does not require using the array shortcut. You compete a SUMPRODUCT formula in a usual way by pressing the Enter key. • All arrays in a SUMPRODUCT formula must have the same number of rows and columns, otherwise you get the #VALUE! error. • If any array argument contains non-numeric values, they will be treated as zeros. • If an array is a logical test, it results in TRUE and FALSE values. In most cases, you'd need to convert them to 1 and 0 by using the double unary operator (--) . Please see the SUMPRODUCT with multiple criteria example for more details. • SUMPRODUCT does not support wildcard characters. Basic usage of SUMPRODUCT in Excel To gain a general understanding of how the Excel SUMPRODUCT function works, consider the following example. Supposing you have quantity in cells A2:A4, prices in cells B2:B4, and you wish to find out the total. If you were doing a school math test, you would multiply the quantity by price for each item, and then add up the subtotals. In Microsoft Excel, you can get the result with a single SUMPRODUCT formula: The following screenshots shows it in action: Here is what's going on under the hood in terms of math: • The formula takes the 1^st number in the 1^st array and multiplies it by the 1^st number in the 2^nd array, then takes the 2^nd number in the 1^st array and multiplies it by the 2^nd number in the 2^nd array, and so on. • When all of the array elements are multiplied, the formula adds up the products and returns the sum. In other words, our SUMPRODUCT formula performs the following mathematical operations: =A2B2 + A3B3 + A4B4 Just think how much time it could save you if your table contained not 3 rows of data, but 3 hundred or 3 thousand rows! Tip. If you want to only multiply the numbers in each row without adding up the products, then use one of the formulas to multiply columns in Excel. How to use SUMPRODUCT in Excel - formula examples Multiplying two or more ranges together and then summing the products is the simplest and most obvious usage of SUBTOTAL in Excel, though not by far the only one. The real beauty of the Excel SUMPRODUCT function is that it can do far more than its stated purpose. Further on in this tutorial, you will find a handful of formulas that demonstrate more advanced and exciting uses, so please keep reading. SUMPRODUCT with multiple criteria Usually in Microsoft Excel, there is more than one way to accomplish the same task. But when it comes to comparing two or more arrays, especially with multiple criteria, SUMPRODUCT is the most effective, if not the only, solution. Well, either SUMPRODUCT or array formula. Assuming you have a list of items in column A, planned sale figures in column B, and actual sales in column C. Your goal is to find out how many items have made less sales than planned. For this, use one of the following variations of the SUMPRODUCT formula: Where C2:C10 are real sales and B2:B10 are planned sales. But what if you had more than one condition? Let's say, you want to count how many times Apples performed worse than planned. The solution is to add one more criterion to the SUMPRODUCT formula: =SUMPRODUCT(--(C2:C10<B2:B10), --(A2:A10="apples")) Or, you can use the following syntax: And now, let's take a minute and understand what the above formulas are actually doing. I believe it is a worthy time investment because many other SUMPRODUCT formulas work with the same logic. How SUMPRODUCT formula with one condition works For starters, let's break down a simpler formula that compares numbers in 2 columns row-by-row, and tells us how many times column C is less than column B: If you select the portion (C2:C10<B2:B10) in the formula bar, and press F9 to view the underlying values, you will see the following array: What we have here is an array of Boolean values TRUE and FALSE, where TRUE means the specified condition is met (i.e. a value in column C is less than a value in column B in the same row), and FALSE signifies the condition is not met. The double negative (--), which is technically called the double unary operator, coerces TRUE and FALSE into ones and zeros: {0;1;0;0;1;0;1;0;0}. Another way to convert the logical values into the numeric values is multiple the array by 1: Either way, since there is just one array in the SUMPRODUCT formula, it simply adds up 1's in the resulting array and we get the desired count. Easy, isn't it? How SUMPRODUCT formula with multiple conditions works When an Excel SUMPRODUCT formula contains two or more arrays, it multiplies the elements of all the arrays, and then adds up the results. As you may remember, we used the following formulas to find out how many times the number of real sales (column C) was less than planned sales (column B) for Apples (column A): =SUMPRODUCT(--(C2:C10<B2:B10), --(A2:A10="apples")) The only tech difference between the formulas is the method of coercing TRUE and FALSE into 1 and 0 - by using the double unary or multiplication operation. As the result, we get two arrays of ones and zeros: The multiplication operation performed by SUMPRODUCT joins them into a single array. And since multiplying by zero always gives zero, 1 appears only when both conditions are met, and consequently only those rows are counted: Conditionally count / sum / average cells with multiple criteria In Excel 2003 and older versions that did not have the so-called IFs functions, one of the most common uses of the SUMPRODUCT function was to conditionally sum or count cells with multiple criteria. Beginning with Excel 2007, Microsoft introduced a series of functions specially designed for such tasks - SUMIFS, COUNTIFS and AVERAGEIFS. But even in the modern versions of Excel, a SUMPRODUCT formula could be a worthy alternative, for example, to conditionally sum and count cells with the OR logic. Below you will find a few formula examples that demonstrate this ability in action. 1. SUMPRODUCT formula with AND logic Supposing you have the following dataset, where column A lists the regions, column B - items and column C - sales figures: What you want is get the count, sum and average of Apples sales for the North region. In Excel 2007 and higher, the task can be easily accomplished by using a SUMIFS, COUNTIFS and AVERAGEIFS formula. If you are not looking for easy ways, or if you are still using Excel 2003 or older, you can get the desired result with SUMPRODUCT. • To count Apples sales for North:=SUMPRODUCT(--(A2:A12="north"), --(B2:B12="apples")) • To sum Apples sales for North:=SUMPRODUCT(--(A2:A12="north"), --(B2:B12="apples"), C2:C12) • To average Apples sales for North:To calculate the average, we simply divide Sum by Count like this: =SUMPRODUCT(--(A2:A12="north"), --(B2:B12="apples"), C2:C12) / SUMPRODUCT( --(A2:A12="north"), --(B2:B12="apples")) To add more flexibility to your SUMPRODUCT formulas, you can specify the desired Region and Item in separate cells, and then reference those cells in your formula like shown in the screenshot below: How SUMPRODUCT formula for conditional sum works From the previous example, you already know how the Excel SUMPRODUCT formula counts cells with multiple conditions. If you understand that, it will be very easy for you to comprehend the sum logic. Let me remind you that we used the following formula to sum Apples sales in the North region: =SUMPRODUCT(--(A2:A12="north"), --(B2:B12="apples"), C2:C12) An intermediate result of the above formula are the following 3 arrays: • In the 1^st array, 1 stands for North, and 0 for any other region. • In the 2^nd array, 1 stands for Apples, and 0 for any other item. • The 3^rd array contains the sales numbers exactly as they appear in cells C2:C12. Remembering that multiplying by 0 always gives zero, and multiplying by 1 gives the same number, we get the final array consisting of the sales numbers and zeros - a sales number appears only if the first two arrays have 1 in the same position, i.e. both of the specified conditions are met; zero otherwise: Adding up the numbers in the above array delivers the desired result - the total of the Apples sales in the North region. Example 2. SUMPRODUCT formula with OR logic To conditionally sum or count cells with the OR logic, use the plus symbol (+) in between the arrays. In Excel SUMPRODUCT formulas, as well as in array formulas, the plus symbol acts like the OR operator that instructs Excel to return TRUE if ANY of the conditions in a given expression evaluates to For example, to get the count of all Apples and Lemons sales regardless of the region, use this formula: Translated into plain English, the formula reads as follows: Count cells if B2:B12="apples" OR B2:B12="lemons". To sum Apples and Lemons sales, add one more argument containing the Sales range: =SUMPRODUCT((B2:B12="apples")+(B2:B12="lemons"), C2:C12) The following screenshot shows a similar formula in action: Example 3. SUMPRODUCT formula with AND as well as OR logic In many situations, you might need to conditionally count or sum cells with AND logic and OR logic at a time. Even in the latest versions of Excel, the IFs series of functions is not capable of that. One of the possible solutions is combining two or more functions SUMIFS + SUMIFS or COUNTIFS + COUNTIFS. Another way is using the Excel SUMPRODUCT function where: • Asterisk () is used as the AND operator. • Plus symbol (+) is used as the OR operator. To make things easier to understand, consider the following examples. To count how many times Apples and Lemons were sold in the North region, make a formula with the following logic: =Count If ((Region="north") AND ((Item="Apples") OR (Item="Lemons"))) Upon applying the appropriate SUMPRODUCT syntax, the formula takes the following shape: To sum Apples and Lemons sales in the North region, take the above formula and add the Sales array with the AND logic: To make the formulas a bit more compact, you can type the variables in separate cells - Region in F1 and Items in F2 and H2 - and refer to those cells in your formula: SUMPRODUCT formula for weighted average In one of the previous examples, we discussed a SUMPRODUCT formula for conditional average. Another common usage of SUMPRODUCT in Excel is calculating a weighted average where each value is assigned a certain weight. The generic SUMPRODUCT weighted average formula is as follows: SUMPRODUCT(values, weights) / SUM(weights) Assuming that values are in cells B2:B7 and weights are in cell C2:C7, the weighted average SUMPRODUCT formula will look like this: I believe at this point you won't have any difficulties with understanding the formula logic. If someone needs a detailed explanation, please check out the following tutorial: Calculating weighted average in Excel. SUMPRODUCT as alternative to array formulas Even if you are reading this article for informational purposes and the details are likely to fade away in your memory, remember just one key point - the Excel SUMPRODUCT function deals with arrays. And because SUMPRODUCT offers much of the power of array formulas, it can become an easy-to-use replacement for them. What advantages does this gives to you? Basically, you will be able to manage your formulas an easy way without having to press Ctrl + Shift + Enter every time you are entering a new or editing an existing array formula. As an example, we can take a simple array formula that counts all characters in a given range: and turn it into a regular formula: For practice, you can take these Excel array formulas and try to re-write then using the SUMPRODUCT function. Excel SUMPRODUCT - advanced formula examples Now that you know the syntax and logic of the SUMPRODUCT function in Excel, you may want to learn more sophisticated and more powerful formulas where SUMPRODUCT is used in liaison with other Excel 243 comments 1. Hi Alexander - I'm back :) So I need to use SUMPRODUCT for columns CS and EH, but in column B I am trying to select only a few criteria. The above solution you provided didn't work for me so I'm sure I did something incorrectly. I am trying 2 ways to accomplish my goal: 1.) include all the buyer groups in column B that I need or 2.) exclude the 3 buyer groups I don't need from my SUMPRODUCT. The problem is that if I do a very manual workaround to check my results, both of these options seem off. 1.) =SUMPRODUCT((B4:B1086="National")+(B4:B1086="Over_500")+(B4:B1086="Allegiance")($CS$4:$CS$1086)(EH$4:EH$1086)) 2.) =SUMPRODUCT((B4:B1086"International")(B4:B1086"Individual")(B4:B1086"Payer")($CS$4:$CS$1086)(EH$4:EH$1086)) Do these formulas above seem valid to you or am I doing something wrong? First one is adding all the buyer groups I need and the second one is excluding the 3 I don't want in my SUMPRODUCT. Thank you so very much! □ The * sign in the SUMPRODUCT formula means “AND”, the + sign means “OR”. Without having your data, it is difficult for me to understand your formulas. I assume that all OR conditions in the first formula should be enclosed in brackets. Hello Daria! In the second formula, it is impossible to fulfill the first 3 conditions at the same time according to the logic AND. So replace * with +. I recommend reading these guides: IF OR AND formula in Excel and Using logical functions in Excel: AND, OR, XOR and NOT 2. Hi Alexander - if I'm trying to use SUMPRODUCT, but for my first array I only need certain rows, for example 10-15 named "individual" and then rows 25-30 names International", how can I combine SUMIFS with SUMPRODUCT or do you know of a better way? Pretty much I need to exclude some rows based on their title to use the SUMPRODUCT. Thank you! □ Hello Daria! If I understand your question correctly, add additional conditions to the SUMPRODUCT formula. For example, for your task: ☆ Thank you, I will try that! 3. I have a reporting pack that enables users to select the length of time period that they want to look at, so the sum formula includes an indirect and offset function as well. =SUMPRODUCT((OFFSET(INDIRECT(the latest column,0),0,VLOOKUP(the number of columns to count back)))(Data!$A:$A=a helper column linking product, market and measure))) - however, I'm just getting REF# and I'm not sure why. The backend data is a bunch of products, measures and markets, but I've created a helper column to enable to adding up of products of the same brand, so the helper column gives Brand Market Measure, which is what is being looked up in the criteria. If anyone could help, I'd massively appreciate it! □ Hello Caroline! If I understand your question correctly, you are trying to use named ranges. However, your named ranges do not follow the rules that you can read here: Excel name rules. 4. Hi how do I sum the amount of all with the same INV but they are in different columns. In the example below I wanted to add all the amount in INV for Col A and D. This is just part of a big sheet like this could go on with having repeating INV in every column For ex. A B C D INV AMOUNT INV AMOUNT 3012 $50000 1456 $25000 1235 $12000 3012 23555 □ Hello Myra! To find the sum of a condition in multiple columns, you can use multiple SUMIF functions. For example, for the range A1:F4: You can also extract data from individual columns by using the CHOOSECOLS function. You can use the SEQUENCE function to specify even columns (AMOUNT) and odd columns (INV). Use the TOCOL function to convert all odd and all even columns into two columns. In this way, you will be converting your range of values into two columns - INV and AMOUNT. Sum the values in the second column TOTAL if the value in the first column matches the criteria INV. To do this, use SUMPRODUCT formula. =SUMPRODUCT((TOCOL(CHOOSECOLS(A1:F4, SEQUENCE(COLUMNS(A1:F4)/2,1,1,2)))=1235) TOCOL(CHOOSECOLS(A1:F4,SEQUENCE(COLUMNS(A1:F4)/2,1,2,2)))) 5. could you pls solve me this , this is data sourse Red Light Green Light Yellow Light Month 01/01/2024 4 5 7 Jan 05/01/2024 6 9 4 Jan 01/03/2024 7 3 4 Mar this just a sample of a big data, the result should be: Red Light Green Light Yellow Light Light Jan (sum of red light for Jan) (sum of Green light for Jan) (sum of Yellow light for Jan) (sum of light for Jan based on partial text) How to solve this pls □ Hi! To find the sum of the values in a column by condition for a month, you can use SUMIF or SUMIFS formula. You can find the examples and detailed instructions here: How to use SUMIF function in Excel and Excel SUMIFS and SUMIF with multiple criteria. For example: Or you can use SUMPRODUCT formula as described in the article above. For example: 6. I am looking to sum the values in a cell column 'AN' based on the conditions in my original formula below. my current formula is ; =COUNTIFS(Report!$I$6:$I$1176,'Data validation'!$D$7,Report!$H$6:$H$1176,">"&TODAY()-31,Report!$AL$6:$AL$1176,"US") i would like to extend this from a countifs to a Sum of the values in column AN for the conditions above. many thanks □ Hi! Use the SUMIFS function with the same conditions you applied in your formula. You can find the examples and detailed instructions here: Excel SUMIFS and SUMIF with multiple criteria – formula examples. The formula might look as follows: =SUMIFS(AN6:AN1176,Report!$I$6:$I$1176,'Data validation'!$D$7,Report!$H$6:$H$1176,">"&TODAY()-31,Report!$AL$6:$AL$1176,"US") ☆ fantastic, really appreciate your advice and website content. thank you 7. I am trying to use SUMIFS with two criteria from two sheets. One is MMM-YY and second is "Direct" or "Indirect" and it does not return the correct sum. □ Hi! I don't know what formula you are using. I don't have an example of your data. Unfortunately, this information is not enough to give you any advice. I recommend reading and studying these instructions carefully: Excel SUMIFS and SUMIF with multiple criteria – formula examples. Or describe the problem in more detail. Post a comment	{"url":"https://www.ablebits.com/office-addins-blog/excel-sumproduct-function/","timestamp":"2024-11-10T07:59:34Z","content_type":"text/html","content_length":"167248","record_id":"<urn:uuid:ab10ae87-69d0-4510-8015-34d92d02e476>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00613.warc.gz"}
ST_FrechetDistance — Returns the Fréchet distance between two geometries. This is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. Units are in the units of the spatial reference system of the geometries. float ST_FrechetDistance(geometry g1, geometry g2, float densifyFrac = -1); Implements algorithm for computing the Fréchet distance restricted to discrete points for both geometries, based on Computing Discrete Fréchet Distance. The Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. Therefore it is often better than the Hausdorff distance. When the optional densifyFrac is specified, this function performs a segment densification before computing the discrete Fréchet distance. The densifyFrac parameter sets the fraction by which to densify each segment. Each segment will be split into a number of equal-length subsegments, whose fraction of the total length is closest to the given fraction. The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used. The smaller densifyFrac we specify, the more acurate Fréchet distance we get. But, the computation time and the memory usage increase with the square of the number of subsegments. Availability: 2.4.0 - requires GEOS >= 3.7.0 postgres=# SELECT st_frechetdistance('LINESTRING (0 0, 100 0)'::geometry, 'LINESTRING (0 0, 50 50, 100 0)'::geometry); (1 row) SELECT st_frechetdistance('LINESTRING (0 0, 100 0)'::geometry, 'LINESTRING (0 0, 50 50, 100 0)'::geometry, 0.5); (1 row)	{"url":"https://postgis.net/docs/manual-2.5/ST_FrechetDistance.html","timestamp":"2024-11-06T14:31:09Z","content_type":"text/html","content_length":"5372","record_id":"<urn:uuid:073a54f4-418b-4cf7-923b-af9f2bfa2ca8>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00809.warc.gz"}
How to use Greeks.Live Auto DDH service? How to use Greeks.Live Auto DDH service? (2023–01–18 update) Click the “Language” menu on the upper right corner to choose English. Pic.1 Language On the upper left side of the Auto DDH page, you can see the “List of Accounts”, where you may choose the main/sub account through which you wish to use the Auto DDH service. Pic.2 Choose main/sub account Set Parameters Two items need to be set on the parameters page. Delta Target “Delta Target” refers to the value “Delta Total” will be adjusted to after each hedge. “Delta Total” is the collective Delta exposure of all your options and perpetual/futures positions. The default value of “Delta Target” is Zero. So, after each hedge, you will have a Delta Neutral portfolio. Nevertheless, if a trader deems the market to be a bull market and wishes to have positive Delta exposure after each hedge, he can set “Delta Target” to be a positive number. For example, if he sets “Delta Target” to be 5, then after each hedge, the portfolio’s “Delta Total” would be +5. If the trader wishes to have a negative Delta exposure after each hedge, he can set “Delta Target” to be a negative number. For example, if he sets “Delta Target” to be -3, then after each hedge, the portfolio’s “Delta Total” would be “-3”. Delta Threshold “Delta Threshold” is the limit of the absolute value deviation of the portfolio’s “Delta Total” against the “Delta Target” set by the user. Beyond this limit, a Delta Hedge will be triggered. For example, suppose that your “Delta Target” is “0”, and your “Delta Total” is “-0.2” or “0.2”, the absolute value of deviation will be “0.2”. If your “Delta Target’ is “1”, and your “Delta Total” is “0.8” or “1.2”, then the absolute value of deviation will be “0.2”, too. In my example shown in Picture 7, the “Delta Threshold” is set as “0.1”, and the deviations in the above two examples are both beyond “0.1”. In these cases, a delta hedge will be triggered to bring “Delta Total” to the respective “Delta Target”. Our program will check the deviation every 10 seconds. Pic.3 Auto DDH Parameters If you wish to switch on Auto DDH feature, please remember to click “Switch On” and enable it. After that, remember to click the green button “Submit”. By clicking close or somewhere else to dismiss the window, the parameters and switch on/off will not be effective. If you wish to switch off the Auto DDH feature, click “Switch Off” before clicking “Submit”. Switch between different Main Accounts If you have multiple Deribit main accounts and wish to manage these accounts’ Auto DDH, you may: 1. Use different browsers to manage different main accounts. 2. In the same browser, log out the account on https://asia.deribit.com by clicking “Sign Out” close to the upper right corner of the page. Then close the tab. 3. Log in another main account on https://asia.deribit.com. Visit www.greeks.live/ddh/ to authorize and manage the account’s DDH service in the same browser. In case “Server Error” pops up on the DDH page during this operation, please clear cookies in the browser and try again. Join https://t.me/greekslive and feel free to ask questions about this DDH tool.	{"url":"https://greekslive.medium.com/how-to-use-greeks-live-auto-ddh-service-84c20df4eba?source=author_recirc-----44dcf4273156----1---------------------5a5bb9f7_297c_4c11_9a35_db95d6f8fbcc-------","timestamp":"2024-11-13T11:28:48Z","content_type":"text/html","content_length":"105450","record_id":"<urn:uuid:68b8be7a-6851-49c6-a6de-a9f1d91793bc>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00423.warc.gz"}
19 Captivating Facts About Charles’s Law Source: Youtube.com When it comes to the fascinating world of physics, one of the fundamental laws that governs the behavior of gases is Charles’s Law. Named after the renowned French physicist Jacques Charles, this law explores the relationship between the temperature and volume of a gas when pressure is held constant. Charles’s Law states that as the temperature of a gas increases, its volume also increases, and vice versa, as long as the pressure remains constant. In this article, we will delve into 19 captivating facts about Charles’s Law, shedding light on its origins, applications, and implications in the world of physics. Whether you are a science enthusiast, a student studying physics, or simply curious about the laws that govern our universe, these facts will provide you with a deeper understanding and appreciation of Charles’s Law. Key Takeaways: • Charles’s Law explains how gases behave when they get hotter or colder. It’s like a rulebook for gas behavior, helping scientists and engineers in industries like automotive and scuba diving. • By understanding Charles’s Law, we can predict how gases will react in different situations, from inflating airbags to preserving food. It’s like having a superpower for controlling gases! Charles’s Law describes the relationship between temperature and the volume of a gas. Charles’s Law states that the volume of a gas is directly proportional to its temperature, assuming pressure and quantity are held constant. It is named after Jacques Charles, a French scientist. Jacques Charles, also known as Charles de Villette, first described the relationship between temperature and volume in the late 18th century. Charles’s Law is a fundamental principle of thermodynamics. It is one of the gas laws, which are fundamental concepts in the study of thermodynamics and the behavior of gases. The equation for Charles’s Law is V1/T1 = V2/T2. This equation represents the initial and final states of the gas, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature. Charles’s Law applies to ideal gases. While gases in the real world may not perfectly follow Charles’s Law, it is a useful approximation for ideal gases under normal conditions. Charles’s Law can be derived from the combined gas law. The combined gas law combines Charles’s Law with Boyle’s Law and Gay-Lussac’s Law to describe the relationship between temperature, volume, and pressure of a gas. Charles’s Law is based on the concept of a constant pressure system. As long as the pressure remains constant, Charles’s Law holds true and allows us to predict the behavior of gases as temperature changes. Charles’s Law is an idealization of real-world gas behavior. In reality, gases may deviate from ideal behavior at high pressures or low temperatures, but Charles’s Law still provides a useful approximation under many conditions. Charles’s Law is often used in the automotive industry. Understanding the relationship between temperature and volume is crucial in the design and operation of engines, as well as in the study of air conditioning systems. Charles’s Law can be seen in action with a balloon. If you heat up a balloon, the air inside expands, causing an increase in volume, demonstrating the principles of Charles’s Law. Charles’s Law is integral to the study of weather phenomena. The relationship between temperature and volume of the atmosphere plays a significant role in understanding weather patterns and atmospheric pressure. Charles’s Law can be expressed in terms of Kelvin or Celsius. While the Kelvin scale is often used in scientific calculations, Charles’s Law can also be expressed using the Celsius scale by converting temperatures to Kelvin. Charles’s Law is a result of the kinetic theory of gases. The kinetic theory explains gas behavior in terms of the motion of gas molecules and their interactions, providing a foundation for understanding Charles’s Law. Charles’s Law is a direct consequence of Boyle’s Law. Boyle’s Law states that the pressure and volume of a gas are inversely proportional, and when combined with Charles’s Law, it gives rise to the ideal gas law. Charles’s Law has applications in the field of scuba diving. Understanding how pressure and volume change with temperature is crucial to ensuring the safety and functionality of scuba diving equipment. Charles’s Law can be used to predict the behavior of gases in airbags. The relationship between temperature and volume is essential in understanding how airbags inflate and protect passengers during a collision. Charles’s Law is encapsulated by the phrase “As temperature increases, so does the volume.” This succinct statement summarizes the essence of Charles’s Law and its impact on the behavior of gases. Charles’s Law provides a basis for calculating absolute zero. By extrapolating the volume-temperature relationship, scientists can determine the temperature at which gas particles theoretically stop moving, known as absolute zero. Charles’s Law is applied in various industries, including aerospace, chemistry, and food processing. Understanding the relationship between temperature and volume is vital in these fields for applications such as rocket propulsion, chemical reactions, and food preservation. Charles’s Law is a fascinating concept in the field of physics that explores the relationship between temperature and volume. Through this law, we have gained a deeper understanding of how gases behave under varying conditions. The law states that as the temperature of a gas increases, its volume also increases proportionally, assuming that pressure remains constant.By studying Charles’s Law, scientists have been able to make significant contributions to various industries, such as the development of air conditioning systems, gas laws, and the understanding of weather phenomena. This law has paved the way for advancements in thermodynamics and has practical applications in our daily lives.As we delve further into the world of physics, it becomes evident that laws like Charles’s Law play a crucial role in expanding our knowledge of the universe. By comprehending the intricate relationships between temperature, volume, and pressure, we unlock new possibilities and innovations that shape our world. What is Charles’s Law? Charles’s Law is a gas law that describes the relationship between the temperature and volume of a gas at a constant pressure. Who discovered Charles’s Law? Charles’s Law was discovered by French physicist Jacques Charles in the late 18th century. What does Charles’s Law state? Charles’s Law states that the volume of a gas is directly proportional to its temperature, assuming that pressure remains constant. How does Charles’s Law apply to everyday life? Charles’s Law is applicable in various real-life scenarios, such as the functioning of air conditioning systems, hot air balloons, and understanding the behavior of gases in weather conditions. What happens to the volume of a gas if its temperature increases? According to Charles’s Law, if the temperature of a gas increases, its volume will also increase proportionally, as long as the pressure remains constant. Can Charles’s Law be applied to all gases? Charles’s Law is a general gas law that can be applied to all gases, as long as the pressure remains constant. Hungry for more captivating facts about Charles's Law? Unbelievable details await your discovery in our next article. Astonishing revelations about Charles's Law of Volumes will leave you amazed. Mindblowing facts about gas laws promise to expand your understanding of these fundamental principles. Continue your journey of scientific exploration and prepare to be fascinated by the intriguing world of physics! Our commitment to delivering trustworthy and engaging content is at the heart of what we do. Each fact on our site is contributed by real users like you, bringing a wealth of diverse insights and information. To ensure the highest standards of accuracy and reliability, our dedicated editors meticulously review each submission. This process guarantees that the facts we share are not only fascinating but also credible. Trust in our commitment to quality and authenticity as you explore and learn with us.	{"url":"https://facts.net/science/physics/19-captivating-facts-about-charless-law/","timestamp":"2024-11-11T07:44:37Z","content_type":"text/html","content_length":"238782","record_id":"<urn:uuid:e9a6f1f9-c5f2-4714-a8b1-edcbcba9a5f4>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00319.warc.gz"}
The Stacks project Lemma 60.9.2. Assumptions as in Definition 60.8.1. The inclusion functor \[ \text{Cris}(X/S) \to \text{CRIS}(X/S) \] commutes with finite nonempty limits, is fully faithful, continuous, and cocontinuous. There are morphisms of topoi \[ (X/S)_{\text{cris}} \xrightarrow {i} (X/S)_{\text{CRIS}} \xrightarrow {\pi } (X/S)_{\text{cris}} \] whose composition is the identity and of which the first is induced by the inclusion functor. Moreover, $\pi _* = i^{-1}$. Comments (0) Post a comment Your email address will not be published. Required fields are marked. In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). All contributions are licensed under the GNU Free Documentation License. In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 07IJ. Beware of the difference between the letter 'O' and the digit '0'. The tag you filled in for the captcha is wrong. You need to write 07IJ, in case you are confused.	{"url":"https://stacks.math.columbia.edu/tag/07IJ","timestamp":"2024-11-07T02:58:23Z","content_type":"text/html","content_length":"15539","record_id":"<urn:uuid:33e56be1-86b7-473b-99d1-29c76674e824>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00315.warc.gz"}
Research on interface slippage of fiber reinforced composite ceramics Based on the microscopic characteristics of fiber reinforced composite ceramics, the slippage stress at the interface of composite ceramics under external loading is analyzed. The relation between the applied strain of the triangular symmetrical eutectic and the load of composite ceramics is confirmed. And the maximum shear stress that the triangular symmetrical eutectic can endure is computed. The yield shear stress was calculated by the hardness and fracture toughness of composite ceramics. When the maximum shear stress which the triangular symmetrical eutectic can bear is equal to the yield shear stress, the slipping stress of micro-mechanical interface in composite ceramics is obtained. The results showed that fiber inclusions in the eutectic having smaller dimension and larger volume content would provide larger partial plastic deformation of composite ceramics. 1. Introduction The fiber-reinforced composite ceramics whose main structure is triangular symmetrical eutectic have good mechanical properties under high temperature and normal temperature conditions^[1]. When the fibers in the eutectic cluster are distributed triangular symmetrically, the strong confinement property and the trigonal symmetry stable structure of the nanoscopic interface between fiber and matrix make composite ceramics have excellent anti-high-temperature creep. And the local slip feature of the micro-interface between eutectic groups makes it have high fracture toughness^[2]. Many literatures have analyzed micromechanics about the strong constraining characteristics of the nano-interface, such as the microscopic stress field of unidirectional jagged inclusion eutectics^[3], the damage strain field of unidirectional parallel eutectics^[4], and damage intensity model of composite ceramics with damaged eutectics^[5] etc. In order to reveal the relationship between the mechanical properties and the microstructure of the composite ceramic whose main structure is triangular symmetrical eutectic, the influence which the local slip property of the micro-interface between eutectic clusters brings to the composite ceramic mechanical behavior must be further analyzed. In order to reveal the relationship between the micro-interface slip and the macro-mechanical behavior of a two-scale interfacial composite ceramics with main structure of triangular symmetrical eutectic, this paper first determines the relationship between the line strain of the triangular symmetrical eutectic outside surface and the external load of the composite ceramic under the condition of the microscopic interface without slipping. And then calculating the maximum shear stress assumed of the triangular symmetry eutectic group based on the line strain on the outer surface of the eutectic group. Finally, the ultimate shear stress of the micro-interface of the composite ceramic is determined based on the hardness and toughness fracture of the composite ceramic measured by the indentation test. When the maximum shear stress that the outer surface of the eutectic group can bear reaches the ultimate shear stress of the micro-interface of the composite ceramic, the microscopic interface sliding stress in the composite ceramic is obtained. 2. Line strain of eutectic in fiber direction under external load In order to link the stress in the triangular symmetry eutectic group with the external load, firstly the extra line strain that can be transmitted by the triangular symmetry eutectic is calculated before the microscopic interface slip, that is, when the composite ceramic only produces elastic deformation. The randomly oriented triangular symmetric eutectic clusters and their surrounding effective media were taken as the research object. The triangular region in the eutectic group is transversely isotropic and the surroundings are isotropic effective medium, as shown in Fig. 1. When the macro-coordinate system $o\xi \eta$ is established, the composite ceramic bears the tensile load $o$ along the macroscopic axis $\eta$, the triangular symmetric eutectic group can be regarded as the composite ceramic before the micro-interface between the eutectic groups is slipped. For a unit body, assuming that the angle between the axis of the eutectic group and the loading direction is $ \alpha$, the line strain at the outer boundary of the eutectic group in the eutectic group’s micro-coordinate system is: ${\mathbf{\epsilon }}_{\mathrm{}}^{e}=\mathbf{S}{\mathbf{\sigma }}_{g}m,$ where ${\mathbf{\sigma }}_{g}$ is a eutectic outer micro stress field, ${\mathbf{\sigma }}_{g}=\left({\sigma }_{11},{\sigma }_{22},{\sigma }_{33},{\sigma }_{13},{\sigma }_{23},{\sigma }_{12}{\right)} ${\sigma }_{11}=\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}\alpha \sigma ,$ ${\sigma }_{22}=\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\alpha \sigma ,$ ${\sigma }_{12}=\mathrm{s}\mathrm{i}\mathrm{n}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\alpha \sigma ,$ where, axis 1 is along the eutectic crystal direction, and the mesoscopic axes 2 and 3 are perpendicular to the mesoscopic axis 1. $\alpha$ is the angle between the axis 1 and the external load $\ sigma$, the other components are all 0, so ${\mathbf{\sigma }}_{g}$ can be written as: ${\mathbf{\sigma }}_{g}=\left(\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}\alpha ,\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\alpha ,0,0,0,\mathrm{s}\mathrm{i}\mathrm{n}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\alpha {\right)}^{T}\sigma .$ $\mathbf{S}$ is composite material equivalent flexibility matrix: $\mathbf{S}=\left[\begin{array}{cccccc}\frac{1}{E}& \frac{-v}{E}& \frac{-v}{E}& & & \\ \frac{-v}{E}& \frac{1}{E}& \frac{-v}{E}& & 0& \\ \frac{-v}{E}& \frac{-v}{E}& \frac{1}{E}& & & \\ & & & \frac{1} {G}& & \\ & 0& & & \frac{1}{G}& \\ & & & & & \frac{1}{G}\end{array}\right].$ $E$ and $\upsilon$ are the elastic modulus and Poisson’s ratio of composite ceramics, which can be determined by the formula of [5]. Under the action of the external strain field ${\mathbf{\epsilon }}_{}^{e}$, the stress field in the eutectic is: ${\mathbf{\sigma }}_{}^{e}={\mathbf{C}}_{g}{\mathbf{\epsilon }}_{}^{e}={\mathbf{C}}_{g}\mathbf{S}\left(\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}\alpha ,\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\alpha ,0,0,0,\ mathrm{s}\mathrm{i}\mathrm{n}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\alpha {\right)}^{T}\sigma =A\sigma ,$ $A={\mathbf{C}}_{g}\mathbf{S}\left(\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}\alpha ,\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\alpha ,0,0,0,\mathrm{s}\mathrm{i}\mathrm{n}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\ alpha {\right)}^{T},$ ${\mathbf{C}}_{g}=\left[\begin{array}{rrrrrr}{C}_{1111}^{g}& {C}_{1122}^{g}& {C}_{1133}^{g}& & & \\ {C}_{2211}^{g}& {C}_{2222}^{g}& {C}_{2233}^{g}& & 0& \\ {C}_{3311}^{g}& {C}_{3322}^{g}& {C}_{3333}^ {g}& & & \\ & & & {C}_{1313}^{g}& & \\ & 0& & & {C}_{2323}^{g}& \\ & & & & & {C}_{1212}^{g}\end{array}\right],$ where ${C}_{ijkl}^{g}$ is the stiffness tensor component of a triangular symmetric eutectic group in a micro-coordinate system which is determined by the formula [6]. Fig. 1The triangular symmetrical eutectic in the composite ceramic Set the nanometric coordinate axis of the parallel fiber inclusions in the triangular region is $x$ (nano-axial coordinate axis y which is perpendicular to the $x$ is omitted in the figure), and the angle of the $x$-axis and the crystal axis of the eutectic group (it is, the mesoscopic coordinate axis 1) is $\theta$, without loss of generality, it is considered that the coordinate axis $z$, the mesoscopic axis 3, and the macro axis are parallel. Take a part to analyze and assume its fiber axis is in the plane of the diagram, then the strain of the eutectic in the fiber direction in the nanoscopic coordinate system is: ${\epsilon }_{x}^{e}=\frac{1}{{E}_{xx}^{}}\left[{A}_{11}^{}\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\theta -{\upsilon }_{xy}^{}\left({A}_{22}^{}\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}\theta +{A}_{33}^{}\ right)\right]\sigma .$ In summary, under the condition of elastic deformation, the stress strain is always linear: ${\epsilon }_{x}^{e}=g\left(E,\upsilon ,{C}_{ijkl}^{g},{E}_{xx}^{},{\upsilon }_{xy}^{},\alpha ,\theta \right)\sigma ,$ $g=\frac{1}{{E}_{xx}^{}}\left[{A}_{11}^{}\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\theta -{\upsilon }_{xy}^{}\left({A}_{22}^{}\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}\theta +{A}_{33}^{}\right)\right].$ ${E}_{xx}$ and ${\upsilon }_{xy}$ is the elastic modulus and Poisson’s ratios of the eutectic group along the fiber direction in the triangulation region are determined by the formula of [6]. Eq. (11) shows that the line strain along the fiber direction of the eutectic group under external load is not only related to the macroscopic elastic constant of the composite ceramic, the mesoscopic elastic constant of the eutectic and the nanoscopic elastic constant of the triangular region, but also the orientation of the eutectic group and the orientation of the fiber inclusions in the eutectic group. 3. Maximum shear stress borne by the eutectic If a cylinder containing fibrous inclusions is taken in a triangular region of the eutectic group, the fiber inclusion and the radius of the cylinder are ${r}_{0}$ and $R$ respectively. If the coordinate origin of the nano coordinate axis $x$ is at the midpoint of the fiber inclusion and the fiber length is 2$L$, the equilibrium equation under the elastic deformation condition can be obtained according to: $\frac{d{\sigma }_{f}}{dx}=-\frac{2{\tau }_{f}}{{r}_{0}},$ where, ${\sigma }_{f}$ is normal stress on the fiber cross section, ${\tau }_{f}$ is the eutectic group in the interface between the matrix and fiber shear stress. The nanostructure of a triangular region of a eutectic group is similar to that of a eutectic containing parallel fibers. Under elastic deformation conditions, both the matrix and the fiber inclusion must satisfy Hooke’s law, and outermost matrix strain and the applied strains along the fiber direction in eutectic ${\epsilon }_{x}^{e}$ are equal. According to the boundary conditions where the eutectic group bears the shear stress, that is, there is no normal stress at the fiber inclusion end, the shear stress at the interface between the matrix and the fiber can be solved according to Eq. (12) [9]: ${\tau }_{f}=\frac{1}{2}k{E}_{f}{\epsilon }_{x}^{e}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}\left(kx/{r}_{0}\right)/\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left(kL/{r}_{0}\right),$ where, $k=\sqrt{\frac{2{G}_{m}}{\mathrm{l}\mathrm{n}\left(\pi /{f}_{b}\right){E}_{f}}}$, ${G}_{m}$ is the matrix shear modulus, ${f}_{b}$ is the volume fraction of fiber inclusions, ${E}_{f}$ is the volume fraction of fiber inclusions. Substituting Eq. (11) into Eq. (13), and let $x=L$, the maximum shear stress that the eutectic can bear under external load and elastic deformation: ${\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}}=\sigma \frac{k{E}_{f}g\left(E,\upsilon ,{C}_{ijkl}^{g},{E}_{xx}^{},{\upsilon }_{xy}^{},\alpha ,\theta \right)}{2}\sqrt{\frac{f}{\pi }}\mathrm{t}\mathrm{a}\ 4. Microscopic interface slippage stress in composite ceramics The interface between the eutectic clusters is a weak interface. Under the shear stress, there is countless dislocation blocked and plugged up. The tip of the dislocation plug-in group is the micro-crack tip. The length of the slip surface at the critical point of the indentation cracking is [9]: In the formula, $H$ and ${K}_{IC}$ represent the hardness and fracture toughness of composite ceramics, which can be measured by indentation experiments. The critical shear stress on the slip surface during when crack nucleation is formed satisfies the following formula [9]: ${\tau }_{mu}=\sqrt{\frac{3\pi }{8}\left[\frac{\gamma \mu }{\left(1-\upsilon \right){l}_{s}}\right]}.$ In the formula, $\gamma$ and $\mu$ are the surface free energy and shear modulus of composite ceramics. Substituting Eq. (15) into Eq. (16), the ultimate shear stress bear by the micro-interface in the composite ceramic can be determined: ${\tau }_{mu}=\frac{H}{{K}_{IC}}\sqrt{\frac{3\pi }{8}\left[\frac{\gamma \mu }{29.5\left(1-\upsilon \right)}\right].}$ When the maximum shear stress on the eutectic surface is equal to the ultimate shear stress at the micro-interface of the composite ceramic, it is, ${\tau }_{max}={\tau }_{mu}$, the microscopic interface in the composite ceramic slips. According to Eqs. (14) and (17), the micro-interface slippage stress in composite ceramics can be obtained as: ${\sigma }_{s}=\frac{2\pi H\sqrt{\frac{3}{8f}\left[\frac{\gamma \mu }{29.5\left(1-\upsilon \right)}\right]}}{k{E}_{f}{K}_{IC}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(\frac{kL}{{r}_{0}}\right)g\ left(E,\upsilon ,{C}_{ijkl}^{g},{E}_{xx}^{},{\upsilon }_{xy}^{},\alpha ,\theta \right)}.$ In order to analyze the influence of the volume fraction and size of the fiber inclusions, the following quantitative studies are conducted on specific materials. For the double-scale interface composite ceramics mainly composed of Al[2]O[3]-ZrO[2] triangular symmetry eutectic groups prepared by the high-gravity combustion synthesis method, the angles between the fiber inclusions and the crystal axis are known from the eutectic crystal plane characteristics is $\theta =\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{s}\frac{2\sqrt{3}}{\sqrt{13}}$. The material constants of the matrix and fiber inclusions are ${E}_{m}=$ 402 GPa, ${\upsilon }_{m}=$ 0.233; ${E}_{f}=$ 233 GPa, ${\upsilon }_{f}=$ 0.31, $f=$ 0.3, $l=$ 10 μm, $d=$ 300 nm. The macroscopic, mesoscopic and nanoscopic elastic constants of composite ceramics are determined by formulas of [7, 8]. Let $\alpha =$ 60°, fiber length $l=$ 10 μm, fiber volume fraction $f=$ 0.3, then the relationship between the slippage stress and the fiber diameter is shown in Fig. 2. Fig. 2The relationship between slipping stress and fiber diameter of triangular symmetrical eutectic Fig. 3The relationship between slipping stress and fiber volume fraction of triangular symmetrical eutectic It can be seen from Fig. 2 that the slippage stress of the micro-interface in the composite ceramic increases with the increase of the fiber inclusion diameter, and the change rate is faster when the diameter is less than 100 nm. If other parameters are not changed and the fiber diameter $d$ is $d=$ 100 nm, the relationship between the slippage stress and the fiber volume fraction is shown in Fig. 3. The slippage stress of the composite ceramic decreases with the increase of the fiber volume fraction. The larger the fiber volume fraction, the easier the eutectic lumps to slip. To test the micro failure mechanism proposed in this paper, some tested data is cited to check the theoretical results. The theoretical calculations and the experimental data of the strength of composite are shown in Table 1. Table 1Comparison between calculated strength and the test data Number $d$ (nm) $f$ ${\sigma }_{u}$ (MPa) (tested) ${\sigma }_{u}$ (MPa) (calculated) 1 156 0.28 1256 1512 2 700 0.34 1491 1605 3 397 0.25 1528 1733 4 800 0.25 1605 1761 As shown in Table 1, the calculated strength of composite in this article is reasonable compared to the test data. All the calculated values are a little higher than the tested values. The anomalous cracks and pores in the crystal boundary may be the major reasons for this difference. 5. Conclusions When the maximum shear stress on the outer surface of the triangular symmetric eutectic group is equal to the ultimate shear stress at the micro-interface slip of the composite ceramics, the theoretical expression of the micro-interface slippage stress in the composite ceramic is obtained. And the calculated values are a little higher than the tested values. Quantitative calculations show that if the composite ceramics with triangular symmetrical eutectic groups as the main content produce larger local deformations through the micro-interface slip. The fiber inclusions in the eutectic clusters should have smaller size and larger volume, the micro-interface is the most likely to produce slip. • Lorca J., Pastor J., Poza P. Influence of the Y[2]O[3] content and temperature on the mechanical properties of melt-grown Al[2]O[3]/ZrO[2] eutectic. Journal of the American Ceramic Society, Vol. 87, Issue 4, 2004, p. 633-639. • Sayir A., Farmer S. C. The effect of the microstructure on mechanical properties of directionally solidified Al[2]O[3]/ZrO[2](Y[2]O[3]) eutectic. Acta Mater, Vol. 48, 2000, p. 4691-4697. • Liu X. Q., Ni X. H., Zhang J., et al. Micro-stress-field of lamellar inclusion in eutectic composite ceramic. Applied Mechanics and Materials, Vol. 204, Issue 208, 2012, p. 4433-4436. • Sun T., Ni X. H., Liu X. Q., et al. Analysis of damage strain field of ceramic composites with eutectic interface. Journal of Computational Mechanics, Vol. 29, Issue 4, 2012, p. 527-531. • Chen C., Ni X. H., Liu X. Q., et al. Damage strength model and application of damaged eutectic composite ceramics. Journal of Mechanical Engineering, Vol. 50, Issue 2, 2014, p. 98-103. • Li B. F., Zheng J., Ni X. H., et al. Study on mechanical properties of ceramics with triangular symmetric distribution eutectic clusters. Chinese Journal of Applied Mechanics, Vol. 29, Issue 2, 2012, p. 127-132. • Li B. F., Zheng J., Ni X. H., et al. Effective elastic constants of fiber-eutectics and transformation particles composite ceramic. Advanced Materials Research, Vol. 177, 2011, p. 182-185. • Ni X. H., Yao Z. J., Liu X. Q., et al. Cracking stress of nano-fibers composite ceramics. Key Engineering Materials, Vol. 336, Issue 338, 2007, p. 2432-2435. • Gong J. H. Fracture Mechanics of Ceramics. Tsinghua University Press, Beijing, 2011. About this article Measurements in engineering triangular symmetrical eutectic composite ceramic slippage stress maximum shear stress This work was supported by the National Natural Science Foundation of China (Grant No. 11272355). Copyright © 2018 Zhihong Du, et al. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	{"url":"https://www.extrica.com/article/20223","timestamp":"2024-11-08T09:28:52Z","content_type":"text/html","content_length":"135373","record_id":"<urn:uuid:505f6872-5a03-4496-a95c-8275088cd630>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00319.warc.gz"}
1=0.999... infinities and box of chocolates..Phliosophy of Math... Hi Yazata. Both Leibniz and Newton would have disagreed with you guys. They would have said that 0.999... + an infinitesimal = 1 where an infinitesimal is an infinitely small number. Put another way, 1 - 0.999... = an infinitesimal Many mathematicians weren't comfortable with the idea of infinitesimals, which despite its Newtonian and Leibnizian pedigree seemed more intuitive than mathematically rigorous. Weierstrauss rigorously reformulated the foundations of calculus in terms of limits in the 19'th century. That seems to me to be where the idea might have originated that 0.999... = 1, since the limit of 0.999... is one. At any rate, most mathematicians seem to have kind of uncritically assumed that infinitesimals were finished and that they were of historical interest at best. Interestingly, in the 1960's Robinson produced a rigorous mathematical account of infinitesimals. That led to an alternative formulation of the foundations of calculus in terms of infinitesimals, called non-standard analysis. (And yes, non-standard analysis is part of 'mainstream mathematics' and isn't the least bit crankish.) So it seems to me that this thread really raises an interesting and perhaps rather important issue in the philosophy of mathematics. It's not an appropriate occasion for insulting people. Excellently observed, mate! Kudos. Especially when, since then, all the work on the nature/effect of Fractal Equations/concepts , Quantum Uncertainty and Chaotic Systems steps/tunneling states etc have increased the background understandings of the 'infinitesimal of effectiveness' in reality, even if the mathematics has yet to be advanced to the completeness stage where it can recognize and treat this 'infinitesimal' concept more in tune with the contextual reality requirements for 'making sense' in reality as well as in its own purely limited abstract axiomatic construct/context. Well done in posting those most pertinent and interesting observations of yours, mate! Ahhh, yes. You are right, QQ, when you read it like that. I took it to mean that 'reality' should not be brought into a 'mathematical' issue such as the one mentioned. That is why I made the point that even those who would use that excuse to 'evade' the implications in any context (real or maths) are now using a 'reality' process (see Tach's example I pointed to) as a counter-argument...which has done nothing except CONFIRM the validity of MD's insistence on reality meanings when attempting to explore the actual philosophical basis FOR all the abstract maths assumptions which these discussions now question. Sorry to you and to someguy1 if I wasn't clear that it was Tach's use of reality based arguments even as he disparaged MD's reality based approach! Thanks for the assist in clarifying that, QQ. Good man! Cheers. You are not the only one Undefined, who's thinking and analytical abilities are disturbed by Tach's attitude.. It is indeed why he does it to achieve just thioihhcuyghj purpose.. gosh see what I At least you are man enough to admit a mistake and apologize where appropriate...takes courage and fortitude... I have other people here in Melbourne reading these posts, who are also ending up "scrambled" by his attitude.. so you are not alone... Both Leibniz and Newton would have disagreed with you guys. They would have said that 0.999... + an infinitesimal = 1 where an infinitesimal is an infinitely small number. Put another way, 1 - 0.999... = an infinitesimal Many mathematicians weren't comfortable with the idea of infinitesimals, which despite its Newtonian and Leibnizian pedigree seemed more intuitive than mathematically rigorous. Weierstrauss rigorously reformulated the foundations of calculus in terms of limits in the 19'th century. That seems to me to be where the idea might have originated that 0.999... = 1, since the limit of 0.999... is one. At any rate, most mathematicians seem to have kind of uncritically assumed that infinitesimals were finished and that they were of historical interest at best. Interestingly, in the 1960's Robinson produced a rigorous mathematical account of infinitesimals. That led to an alternative formulation of the foundations of calculus in terms of infinitesimals, called non-standard analysis. (And yes, non-standard analysis is part of 'mainstream mathematics' and isn't the least bit crankish.) So it seems to me that this thread really raises an interesting and perhaps rather important issue in the philosophy of mathematics. It's not an appropriate occasion for insulting people. This is an interesting take on things. I guess I hadn't thought about the metaphysical status of infinitesimals. By definition, any infinitesimal is smaller than any arbitrary number we can choose to compare it with. So if a mathematical expression does contain an infinitesimal, throwing the infinitesimal away will always leave the value of the expression unchanged up to arbitrary precision. Since math is just a language for formalized logic anyway, I don't worry too much about whether throwing away the infinitesimal gives a correct description of what the number "really is"; insofar as the results are the same, I'm inclined to go with the simpler method, which is not to bother tracking infinitesimals. But it's interesting (and probably grants insight into some fundamental properties of arithmetic) that one can build math in a non-standard way using infinitesimals. That said, I'm a little disappointed that people seem receptive to Motor Daddy's arguments. Finer points of math philosophy aside, the idea that an object cannot be divided into three equal parts is utter nonsense . As gmilam alluded to back on page 2, the non-terminating decimal representation of 1/3 is just an artifact of the base-10 system we use. In a base-9 system, 1/3=0.3 (not repeating). Fundamentally, there is no reason why 1/3 is any less precise of a number than 1/2, or any other fraction. It might be a matter of mathematical formalism whether 1 and 0.(9) represent the same number of two numbers that are infinitesimally different from one another, but it's important to keep in mind that at most this is a question of . Trying to extend this reasoning to argue against the reality of certain fractions is beyond inane. This is an interesting take on things. I guess I hadn't thought about the metaphysical status of infinitesimals. By definition, any infinitesimal is smaller than any arbitrary number we can choose to compare it with. So if a mathematical expression does contain an infinitesimal, throwing the infinitesimal away will always leave the value of the expression unchanged up to arbitrary precision. Since math is just a language for formalized logic anyway, I don't worry too much about whether throwing away the infinitesimal gives a correct description of what the number "really is"; insofar as the results are the same, I'm inclined to go with the simpler method, which is not to bother tracking infinitesimals. But it's interesting (and probably grants insight into some fundamental properties of arithmetic) that one can build math in a non-standard way using infinitesimals. That said, I'm a little disappointed that people seem receptive to Motor Daddy's arguments. Finer points of math philosophy aside, the idea that an object cannot be divided into three equal parts is utter nonsense. As gmilam alluded to back on page 2, the non-terminating decimal representation of 1/3 is just an artifact of the base-10 system we use. In a base-9 system, 1/3=0.3 (not repeating). Fundamentally, there is no reason why 1/3 is any less precise of a number than 1/2, or any other fraction. It might be a matter of mathematical formalism whether 1 and 0.(9) represent the same number of two numbers that are infinitesimally different from one another, but it's important to keep in mind that at most this is a question of labeling. Trying to extend this reasoning to argue against the reality of certain fractions is beyond inane. An interesting and probably easy question to answer comes to mind... is 0.999.. (or equivalent) = 1 in other bases. In other words is the treatment of infinity similar for other bases.. in particular one that is of interest to me being base 12. [duodecimal] An interesting and probably easy question to answer comes to mind... is 0.999.. (or equivalent) = 1 in other bases. In other words is the treatment of infinity similar for other bases.. in particular one that is of interest to me being base 12. [duodecimal] I believe this has been answered before, and it's certainly addressed on the Wikipedia page. In base 2, 0.111... = 1 In base 3, 0.222... = 1 In base 4, 0.333... = 1 ... and so on and so forth. ...In base 2, 0.111... = 1 In base 3, 0.222... = 1 In base 4, 0.333... = 1 ... and so on and so forth. No one has taken up this challenge below. Why? {end of my post 335in the 1 = 0.999... thread} ...PS, a puzzle for the mathematically skilled or inclined: Using only the integer 1 thur 1000, what is the longest repeat period possible in their infinite rational decimal equivalent? "Repeat period" is for example 4 in 0.12341241234... but that may not equal the ratio of any two integers given the requirement that both numbers in the ratio are no more than 1000. For the really advanced mathematicians: Still using only the first 1000 number, is there a base (not 10) in which an even longer repeat period exists? If because it is too hard, then do it for integers less than 100 (or your choice, perhaps 64?) instead of 1000. 997 is the highest prime <1000. I think x/997 (x is any number under 1000 except 997) has 996 repeating digits in any base (except 997 and its multiples) 997 is the highest prime <1000. I think x/997 (x is any number under 1000 except 997) has 996 repeating digits in any base (except 997 and its multiples) Nice observation, but question was in which base is the "repeat interval" the longest and is there no other rational integer ratio with a longer repeat interval? Later by edit: Oh, now I see your point. 996 is very likely the correct answer. I did not know that recipicals of primes have repeat lengths one less than the prime. Is there a proof of that? There is no ratio of integers under 1000 with a repeat interval more than 996, in any base. I think that 1/997, 2/997, 3/997, ... 996/997 all have repeat interval of 996 in any base, (except base 997, of course). An interesting and probably easy question to answer comes to mind... is 0.999.. (or equivalent) = 1 in other bases. The equality is preserved in all bases. If $$x_{(n)}=y_{(n)}$$ in base (n) then $$x_{(p)}=y_{(p)}$$ in base (p). Good morning, Fednid48, Yazata, QQ, MD, Pete, Tach, everyone. This is an interesting take on things. I guess I hadn't thought about the metaphysical status of infinitesimals. By definition, any infinitesimal is smaller than any arbitrary number we can choose to compare it with. So if a mathematical expression does contain an infinitesimal, throwing the infinitesimal away will always leave the value of the expression unchanged up to arbitrary precision. Since math is just a language for formalized logic anyway, I don't worry too much about whether throwing away the infinitesimal gives a correct description of what the number "really is"; insofar as the results are the same, I'm inclined to go with the simpler method, which is not to bother tracking infinitesimals. But it's interesting (and probably grants insight into some fundamental properties of arithmetic) that one can build math in a non-standard way using infinitesimals. Your honest (as usual; Kudos!) self-observation allows that you had not before considered (at least not to the extent that I and some others here apparently have) the deeply important and comprehensively instructive "META-PHYSICAL status" infinitesimals. By implication, it is possible that you may also had not considered (again, at least not to the extent that I and some others here apparently have) the even more reality-pertinent 'REAL-PHYSICAL status" of the logically deducible and physically recognized "infinitesimal of effectiveness" which is inherent in the understandings and dynamical basis of QM "a 'something' tunneling through 'infinitesimal nothings' to 're-produce' that 'same something' elsewhere", as observed; of CHAOS THEORY "infinitesimal steps from starting simplicity towards infinite complexity", as observed; and, of FRACTAL MATHEMATICS "iteration equations/effects based on fractal infinitesimal variability between iterations", again, as observed. maybe we should , as you put it, about the infinitesimal in its contexts, Fednis48? Especially if our common goal is 'completeness and cross-consistency' between abstract mathematical concrete physical 'systems of thought/modeling'? Again, assuming our collective aim IS to actually address THE reality and not just keep playing with NON-reality. I think humanity has grown up and left the basement of 'video games' and is now beginning to actually 'face the real world' outside the basement 'virtual world' disconnect with what's really important in the final analysis of what science is about. Fednis48 to Yazata said: That said, I'm a little disappointed that people seem receptive to Motor Daddy's arguments. Finer points of math philosophy aside, the idea that an object cannot be divided into three equal parts is utter nonsense. As gmilam alluded to back on page 2, the non-terminating decimal representation of 1/3 is just an artifact of the base-10 system we use. In a base-9 system, 1/3=0.3 (not repeating). Fundamentally, there is no reason why 1/3 is any less precise of a number than 1/2, or any other fraction. It might be a matter of mathematical formalism whether 1 and 0.(9) represent the same number of two numbers that are infinitesimally different from one another, but it's important to keep in mind that at most this is a question of labeling. Trying to extend this reasoning to argue against the reality of certain fractions is beyond inane. Again, you seem to miss that the only counter-argument so far, against MD's REALITY-based approach to that 1/3 (ie, "divide something into 3 equal parts IN REALITY"-----whatever abstract number system you wish to play with in UN-reality) has been offered by Tach , using EXACTLY the same REALITY-based approach which he had 'derided' MD for using! Here is Tach's supposed 'counter' example, effectively constituting a real 'division exercise' on a real thing (read MD's "pie" for Tach's "circle"): Really? In 8-th grade they teach you how to inscribe an equilateral triangle in a circle. This means that you either haven't taken that class yet or that you flunked it. I don't think that you understood the simple exercise. You are given a compass and a ruler. Draw a circle. Divide the circumference of the circle in 3 equal parts using the two tools given to you. You have 10 minutes from when this post is active. If you cannot do it , you flunked 8-th grade geometry. Live with it. See, Fednis48? There is no REAL 'proof' of the a-priori/abstract by Tach (and now effectively repeated by yourself above) that any 'real division' scenario results in 3 'equal' parts instead of MD's perfectly valid 'real context' observation/argument (even using Tach's OWN example) that IN REALITY there is NO basis for making a-priori/abstract ASSUMPTION that the 'division' CAN give 3 'equal' parts AT ALL in that particular scenario. Of course, IF we FIRST construct or 'compose', something shown to BE the SUM of PRIOR objects which INITIALLY SUPPLIED the 3 "equal' parts to some 'composite object' MADE from those 3 "equal' objects in the first instance, then it would be trivial to 'reverse' that operation and 'decompose' it into 3 equal parts. HOWEVER, since the 'pie/circle' in this particular context has NOT PREVIOUSLY BEEN 'composed' using 3 'equal' parts in the first place, THEN can be NO A-PRIORI/ABSTRACT ASSUMPTION that it can NOW, in reality, BE 'decomposed' into 3 "equal" parts. It cannot BE 'proven' in that case where no 'composition' case has been demonstrated to arrive AT the 'pie/circle' REAL OBJECT we want to 'divide' via 1/3 in REALITY, as per MD's point made so far. ( * ) Hence the math-versus-reality perspectives 'impasse'; and where the 'last step' infinitesimal-of-effectiveness 'non-zero difference' comes in to save the day; which would make MD's (and others, including myself) observe that always (whatever number system/abstraction one plays with), in reality, the expression 1/3 represents/results in: At least ONE of those three parts being slightly (by an unavoidable infinitesimal of effectiveness) greater than the other TWO parts. Anyhow, this discussion should highlight yet again the possible dangers of letting our 'mathematics' rule us blindly in all contexts, since it tends to depart from reality more and more as UN-real abstraction/assumption is piled upon UN-real abstraction/assumption. Yes, Mathematics is useful, but let's not let it run away with itself and us, and so insidiously OBSCURING from our ken more and more that reality which we are striving to elucidate for REAL and not just for VIRTUAL. Yes? Let's NOW actually "...worry about..." and really consider properly and exhaustively all the contextual aspects/effects/meanings etc OF that "infinitesimal of effectiveness' LAST REAL STEP between something and zero/balance/singularity etc etc states which occur in reality but which bamboozle our mathematics because, as axiomatically defined so far, the maths gives infinities and singularities when it breaks down and our current equations 'blows up' to indicate the end of its 'domain of applicability' boundary conditions which it cannot handle with any reality sense result. Thanks for your time and trouble in making your own very interesting contribution to this PHILOSOPHY of MATHS thread, Fednis48, Yazata, MD, everyone. Much appreciated; and by more than just Quantum Quack, I assure you! Great thread, Quantum Quack; Kudos for starting it and setting just the right tone for polite and insightful discourse roght from the start! Cheers! ( * ) This is a subtle but extremely important 'contextual reality' aspect requiring careful consideration to understand/discuss these things properly. For example, we can in the first instance 'compose' a '6' from three "equal" parts of '2'; and its reverse is trivially achieved by dividing precisely into its original three "equal parts of '2'. HOWEVER, we CANNOT DEMONSTRABLY IN REALITY INITIALLY 'compose' directly a REAL "UNIT WHOLE" object (a UNIT WHOLE 'pie', a UNIT WHOLE 'circle') which is NOT ALREADY amenable to being 'composed' FROM three "equal" parts in the first place. Unless anyone can INITIALLY MAKE a REAL, WHOLE UNIT 'pie' or 'circle' FROM THREE REAL WHOLE UNITS which can BE demonstrated in reality to BE "equal" to each other, then no amount of starting from the 'other end' can PROVABLY (not abstractly/assumedly) 'derive' three "equal" parts in reality (again, not abstract/assumed) division operation applied to those reality cases. Last edited: 997 is the highest prime <1000. I think x/997 (x is any number under 1000 except 997) has 996 repeating digits in any base (except 997 and its multiples) Based on this answer, it sounds like you have a theorem that says "1/n has n-1 repeating digits if n is a prime number." Is that true? If so, do you have a link to an easy-to-understand proof? If not, how did you come up with this answer? Your honest (as usual; Kudos!) self-observation allows that you had not before considered (at least not to the extent that I and some others here apparently have) the deeply important and comprehensively instructive "META-PHYSICAL status" infinitesimals. Let's not go overboard here. Calling the metaphysical status of infinitesimals "deeply important and comprehensively instructive" is your words, not mine. Like I tried to say above, mathematics is an extremely refined formalism for deductive logic, nothing more. The fact that including or discarding infinitesimals can lead to two constructions that give the same results is interesting, and it probably sheds light on certain fundamental aspects of logic. But to ask whether infinitesimals (or any other mathematical constructs, for that matter) are "real" is the wrong question, in my By implication, it is possible that you may also had not considered (again, at least not to the extent that I and some others here apparently have) the even more reality-pertinent 'REAL-PHYSICAL status" of the logically deducible and physically recognized "infinitesimal of effectiveness" which is inherent in the understandings and dynamical basis of QM "a 'something' tunneling through 'infinitesimal nothings' to 're-produce' that 'same something' elsewhere", as observed; of CHAOS THEORY "infinitesimal steps from starting simplicity towards infinite complexity", as observed; and, of FRACTAL MATHEMATICS "iteration equations/effects based on fractal infinitesimal variability between iterations", again, as observed. ... what? I'm sorry, but none of these examples even make sense. Quantum particles don't "tunnel through infinitesimal nothings." Chaos theory doesn't have anything to do with infinitesimal steps, and the equations that produce fractals produce finite changes with every iteration. Especially if our common goal is 'completeness and cross-consistency' between all abstract mathematical and concrete physical 'systems of thought/modeling'? Again, assuming our collective ultimate aim IS to actually address THE reality and not just keep playing with NON-reality. I think humanity has grown up and left the basement of 'video games' and is now beginning to actually 'face the real world' outside the basement 'virtual world' disconnect with what's really important in the final analysis of what science is about. Math helps us reality. It is not the same as reality. Insofar as we can refine our mathematics to make better predictions about reality, I'm all for it. But I say worrying about the existence of infinitesimals, which by their definition do not make any finite difference in our predictions, is a waste of time. See, Fednis48? There is no REAL 'proof' of the a-priori/abstract assumption by Tach (and now effectively repeated by yourself above) that any 'real division' scenario results in 3 'equal' parts instead of MD's perfectly valid 'real context' observation/argument (even using Tach's OWN example) that IN REALITY there is NO basis for making a-priori/abstract ASSUMPTION that the 'division' CAN give 3 'equal' parts AT ALL in that particular scenario. Well, ok. Let me ask you this: can you really divide an object into equal parts? If not, then you're making a VERY bold claim, and I'd be willing to debate it with you. But it sounded to me like MD was saying division into three equal parts specifically was impossible because 1/3 is a non-terminating decimal. That claim would be indisputably wrong; 1/3 is only non-terminating because we do math in base 10, and reality cannot depend on our choice of Let's NOW actually "...worry about..." and really consider properly and exhaustively all the contextual aspects/effects/meanings etc OF that "infinitesimal of effectiveness' LAST REAL STEP between something and zero/balance/singularity etc etc states which occur in reality but which bamboozle our mathematics because, as axiomatically defined so far, the maths gives infinities and singularities when it breaks down and our current equations 'blows up' to indicate the end of its 'domain of applicability' boundary conditions which it cannot handle with any reality sense I'll put it this way. Show me a self-consistent formulation of math that makes meaningfully different predictions by including infinitesimals, and I'll examine it with interest. Until then, it seems to me that you're just reifying logical abstractions for no reason other than that their absence makes you uncomfortable. Again, you seem to miss that the only counter-argument so far, against MD's REALITY-based approach to that 1/3 (ie, "divide something into 3 equal parts IN REALITY"-----whatever abstract number system you wish to play with in UN-reality) has been offered by Tach , using EXACTLY the same REALITY-based approach which he had 'derided' MD for using! seem to have a lot of difficulty with this simple problem of geometry. Here is Tach's supposed 'counter' example, effectively constituting a real 'division exercise' on a real thing (read MD's "pie" for Tach's "circle"): Have you managed to find the solution? It is part of 8-th grade geometry curriculum. See, Fednis48? There is no REAL 'proof' of the a-priori/abstract assumption by Tach (and now effectively repeated by yourself above) that any 'real division' scenario results in 3 'equal' parts instead of MD's perfectly valid 'real context' observation/argument (even using Tach's OWN example) that IN REALITY there is NO basis for making a-priori/abstract ASSUMPTION that the 'division' CAN give 3 'equal' parts AT ALL in that particular scenario. Whatever the word salad above, the simple fact is that they teach you in 8-th grade geometry how to divide the circle circumference with a ruler and acompass. repeating MD's mistakes doesn't make your posts right, makes them fringe. Of course, IF we FIRST construct or 'compose', something shown to BE the SUM of PRIOR objects which INITIALLY SUPPLIED the 3 "equal' parts to some 'composite object' MADE from those 3 "equal' objects in the first instance, then it would be trivial to 'reverse' that operation and 'decompose' it into 3 equal parts. HOWVER, since the 'pie/circle' in this particular context has NOT PREVIOUSLY BEEN 'compose' using 3 'equal' parts in the first place, THEN NO A-PRIORI/ABSTRACT ASSUMPTION that is can NOW, in reality, BE 'decomposed' into 3 "equal" parts. You should stop spreading gross falsities like the above. It cannot BE 'proven' in that case where no 'composition' case has been demonstrated to arrive AT the 'pie/circle' REAL OBJECT we want to 'divide' via 1/3 in REALITY, as per MD's point made so False. You should really stop spreading anti-science, this simple exercise has been solved more than 2000 years ago. 997 is the highest prime <1000. I think x/997 (x is any number under 1000 except 997) has 996 repeating digits in any base (except 997 and its multiples) An interesting hypothesis, however I will guess that you are wrong. Let's see if I can prove it in less than 30 minutes. The time now is 3:37. 997 is the highest prime <1000. I think x/997 (x is any number under 1000 except 997) has 996 repeating digits in any base (except 997 and its multiples) An interesting hypothesis, however I will guess that you are wrong. Let's see if I can prove it in less than 30 minutes. The time now is 3:37. Period 2 in base 996. $$\frac{1}{997} = \frac{0 \times 996 \; + \; 995}{996^2} \; + \; \frac{1}{997} \times \frac{1}{996^2}$$ The time is 3:42 (most of which was typesetting) Likewise the period is 83 in base 9, 12, 16 and others. Example: $$\frac{1}{997} = \frac{8775328885789415945325986869077718617264471136983801149150534027722980939616352751147495193673235}{16^{83}} \; + \; \frac{1}{997} \times \frac{1}{16^{83}}$$ Likewise the period is 12 in bases 91, 252 and perhaps others. And now (4:14) -- I have automated the process. The period is 1 in bases 998, 1995 The period is 2 in bases 996, 1993 The period is 3 in bases 304, 692, 1301, 1689 The period is 4 in bases 161, 836, 1158, 1833 The period is 6 in bases 305, 693, 1302, 1690 The period is 12 in bases 91, 252, 745, 906, 1088, 1249, 1742, 1903 Last edited: An interesting hypothesis, however I will guess that you are wrong. Let's see if I can prove it in less than 30 minutes. The time now is 3:37. I asked for proof that 1/p where p is a prime has repeat length of p-1back in post 108, but know it is not always true. i.e. 1/5 =0.2 but it does seem true for 1/7 = 0.142857 142857 142857 Also note 1/11 =0.909090909090909... repeat length of 2, not 10, but blocks of ten do repeat. 1/13 =0.076923 076923 076923 ... has repeat length of 6 not 12, but again blocks of 12 do repeat. Seem to be something interesting going on here. The puzzle I proposed long ago is more interesting than I realized. As 1/5 = 0.2000 0000 0000 .... one could say there is a repeat length of 4 (but of any integer number also). When the prime, p, is a factor of the base, that may be a special case? HOWVER, since the 'pie/circle' in this particular context has NOT PREVIOUSLY BEEN 'compose' using 3 'equal' parts in the first place, THEN NO A-PRIORI/ABSTRACT ASSUMPTION that is can NOW, in reality, BE 'decomposed' into 3 "equal" parts. I think what you are getting at is the paradoxical nature of applying infinity on a finite object. If I read you correctly you are I feel quite correct in stating as you have. If not then I Example by way of problem: take a house brick and divide it into an infinite number of slices so that all slices are equal in thickness. Q: How thick are the slices? Then : Q:How many slices does it require to recompile the brick? Now if the slice thickness is deemed to exist then the slices have a finite thickness. How many finite thick slices are needed to recompile the brick? Choices: 1] a finite number of slices or 2] an infinite number of slices? If the slices are deemed to be "finite" infinitesimals, or given a fixed value, then the recompiling the brick is a finite function and not the same infinite function that was used to de-compile the Compare with using 2 dimensional slices instead. What do you discover from the thought experiments? The bottom line question is: If you divide a house brick into an infinite number of slices : Do the resultant slices exist in 3 dimensional space or not. If so, in what way and with what dimension of thickness are they? To me this highlights the paradox associated with real world use of "Infinity" 1/infinity = 0 or does it equal 1/infinity Its exactly the same question being asked of 1- 0.999... = when applied to the real 3 dimensional world. if the answer is 0 then the brick vanishes.. non-existent. [and can not be recompiled as (0 x infinity) = 0] if the answer is 1/infinity what happens? Does the brick [slices compiled] still exist? see the paradox? 1/infinity = 0 "When infinitely reducing a sphere, the sphere ceases to exist as a sphere" and it is a one way street only, for once the sphere is reduced infinitely it can not be recompiled from nihilo" 1/infinity = 1/infinity "When infinitely reducing a sphere, the sphere maintains form as a sphere" and it can be recompiled from 1/infinity" ~ yet this grants 1/infinity a finite value Hi Fednis48. Thanks for your considered and, as usual, courteous reply. Let's not go overboard here. Calling the metaphysical status of infinitesimals "deeply important and comprehensively instructive" is your words, not mine. Like I tried to say above, mathematics is an extremely refined formalism for deductive logic, nothing more. The fact that including or discarding infinitesimals can lead to two constructions that give the same results is interesting, and it probably sheds light on certain fundamental aspects of logic. But to ask whether infinitesimals (or any other mathematical constructs, for that matter) are "real" is the wrong question, in my opinion. Yes, that "deeply important and comprehensively instructive" was my opinion of it in the context of overall discussion OF all its 'meanings' to whomever/whatever. Sorry if my construction was unclear and so inadvertently implied the opinion was in any way yours also on that. My bad! Yes, that other point you make about mathematics is already a 'given' here (at least as far as I am concerned). However, this is a PHILOSOPHY of MATHS discussion, and it is the PRE-mathematics process which leads TO the current mathematics axioms/formalism that I am approaching all these points from. I already understood where you were coming from, and I made further comment based on where I am coming from. That's all. I didn't mean for it to sound like I didn't recognize the current maths formalism for what it is. Again, sorry if my posts gave any other impression, mate! ... what? I'm sorry, but none of these examples even make sense. Quantum particles don't "tunnel through infinitesimal nothings." Chaos theory doesn't have anything to do with infinitesimal steps, and the equations that produce fractals produce finite changes with every iteration. According to Standard Model assumptions/postulates/theory, the Big Bang Scenario is essentially an UNIDENTIFIED IN REALITY some fundamental (infinitesimal?) 'nothing' state/thing which due to 'quantum fluctuation' of/in that 'nothing' became 'something'? In my reality based perspective, it is an Energy-space arena 'something' that existed all along, but we will not go into that now. Insofar as Standard Model goes, the space-time and all its mathematically modeled 'properties' ultimately depend on certain 'infinitesimal' things associated with 'pointlike' things which when treated in some 'mathematical space treatments' effectively represent the 'forces' and 'energy' and other dynamical entities which are used for the abstractions of reality into the mathematical formalism dependent 'models'. So I now ask: If 'pointlike' (ie, having no real or abstract dimensional extent) things are NOT ultimately THE closest thing (logically and effectively in reality context) TO 'infinitesimals of reality effectiveness' (regardless of mathematical formalism abstractions/modeling), then what are these pointlike 'nothings' that underlie all theorizing in 'from-nothing-to-something' models/treatments like that used for the conventional Big Bang Standard Model? Fair enough question, mate? Math helps us describe reality. It is not the same as reality. Insofar as we can refine our mathematics to make better predictions about reality, I'm all for it. But I say worrying about the existence of infinitesimals, which by their definition do not make any finite difference in our predictions, is a waste of time. Again, the 'reality limitations' of mathematics AS IT STANDS NOW is not disputed, so it is a 'given' whenever such philosophical discussions OF it (and of other 'limited' systems of thought, especially including the physics system) are brought into 'review' like this via NON-prejudicial and 'uncommitted stance' discussions which are not yet FORMAL PRESENTATIONS as 'completed review'. So a certain leeway and patience needs to be allowed for developing all the various thoughts and observations which such philosophical discussions will inevitably elicit for further discussion in the various contexts they arise in. Yes? To emphasize: this thread is obviously designed to encourage 'philosophical stage' discussion of many things, one of which happens to (inescapably) be the status of the conventional mathematics as so far 'developed' towards (hopefully) the ultimate goal of 'completeness' in every sense, which IF it does become complete in every sense, then must eventually BECOME CAPABLE OF reflecting THE reality in a cross-contextual (abstract math-concrete reality) way that satisfies everyone on all sides. Well, ok. Let me ask you this: can you really divide an object into two equal parts? If not, then you're making a VERY bold claim, and I'd be willing to debate it with you. But it sounded to me like MD was saying division into three equal parts specifically was impossible because 1/3 is a non-terminating decimal. That claim would be indisputably wrong; 1/3 is only non-terminating because we do math in base 10, and reality cannot depend on our choice of base. Within the limit of accuracy of measuring 'parts', we can. The philosophic/reality question which MD and others raise has to to with the actual reality capability----EVEN GIVEN SUCH ACCURACY----to divide one WHOLE UNIT into 3 "equal" parts UNLESS we already prove that the particular "whole unit" was actually composed of such 3 "equal" parts IN THE FIRST place. That is the tricky/subtle thing. No mathematical abstraction of 1/3 process can be proven tom result in 3 "equal" parts unless it has already been proven that it can be...and that has yet to be proven in reality with the real 'pie/ circle' UNIT WHOLE we start with in MD's/Tach's reality-based example. Can you prove that the pie/circle unit whole object contains three equal parts before you actually divide it in reality? If so, then you just prove a triviality for THAT and suchlike cases, and not necessarily for ALL reality cases. Hence where the reality context "infinitesimal of effectiveness" could come in and make constitute some 'bridging axiom/object/process' which makes the mathematics become more reality reflective WITHOUT necessarily having to ditch its other excellent useful axioms/results. That is where I am coming from. That's all. I'll put it this way. Show me a self-consistent formulation of math that makes meaningfully different predictions by including infinitesimals, and I'll examine it with interest. Until then, it seems to me that you're just reifying logical abstractions for no reason other than that their absence makes you uncomfortable. This is a tentative INFORMAL stage philosophy of maths (and other tricky/subtle things) thread. What you ask there is not yet advisable, since conclusion/completeness OF these and other like discussions elsewhere have to cover much more ground to develop greater common ground before that FORMAL stage is reached for all these unconventional forays into the subjects/issues in question. It would help get us further more quickly if some 'proofs' from 'outside' the current maths formalisms could be presented to 'counter' the issues/points raised so far? Anyhow, thanks again, Fednis48, for your excellently considered and courteously expressed, and always most interesting and evenhanded, contributions to these discussions and others. I think I may speak for everyone here when I say that your posts are invariably (except by the case of trolls, of course ) appreciated by all here! Cheers, mate! Speaking of trolls, all non-troll members please be aware that, as per excellent admin/mod advice, I am effectively ignoring a certain troll at this time. Thanks. Last edited:	{"url":"https://www.sciforums.com/threads/1-0-999-infinities-and-box-of-chocolates-phliosophy-of-math.136934/page-6","timestamp":"2024-11-14T06:47:34Z","content_type":"text/html","content_length":"202006","record_id":"<urn:uuid:f03922da-afd6-4d43-8a18-c9821e00dc53>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00483.warc.gz"}
How do you calculate the acceleration of a rocket? \| HIX Tutor How do you calculate the acceleration of a rocket? Answer 1 Please refer to the explanation below. I would say we use the equation where #F# is the force of the rocket, #m# is the mass of the rocket, and #g# as the gravitational constant #(~~9.81 \ "m/s"^2)# on Earth. The #mg# turns out to become the weight of the rocket, which is acting down, so we have to subtract it from the force the rocket applies to go up. Then, the rest of the equation can be derived from Newton's second law: Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer from HIX Tutor When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some Not the question you need? HIX Tutor Solve ANY homework problem with a smart AI • 98% accuracy study help • Covers math, physics, chemistry, biology, and more • Step-by-step, in-depth guides • Readily available 24/7	{"url":"https://tutor.hix.ai/question/how-do-you-calculate-the-acceleration-of-a-rocket-8f9af89e42","timestamp":"2024-11-04T17:03:06Z","content_type":"text/html","content_length":"570499","record_id":"<urn:uuid:08dbe9a1-0d8b-483d-b6f5-b8c650b537e2>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00089.warc.gz"}
Introduction To Mathematical Proofs This link here is where all the videos are for my Introduction To Mathematical Proofs playlist. Below, I'll link a few other resources that might be helpful! If I find more helpful ones, I'll link them below. Here are all the worksheets for the corresponding topics If you have any suggestions or comments, let me know either on YouTube or by email. If you'd like any relevant files, also contact me and I'll send them your way. Note For MAT102 Students The order and content covered in this playlist is not the same as in MAT102. While there's huge overlap, I cannot guarantee that this playlist is sufficient! Use this playlist and all the linked resources as a resource, not as a replacement! My recommendation: Use this playlist after you read the textbook/assigned readings but before the lecture. Nothing replaces the readings, rather, this should reinforce your readings before you head to class so you can tackle the content efficiently. Note For Future Plans In truth, this is supposed to be only the first half of the playlist. I planned to cover some other topics that help reinforce what we learn in the playlist and shed light onto more math. However, this was a good place to stop since other things came to attention. I might continue this playlist later down the line. If that is something you are interested in, please let me know! I can only provide another resource for those interested in the math beyond this playlist. Here is a playlist regarding number theory. It's very difficult, rigorous and long. However, you have the tools to understand what's happening with enough time and effort. I can only wish you good fortune on your journey if you had the time to read this. Thanks! Copyright Information Many of the resources were provided to me by Micheal Pawliuk, a professor at the University of Toronto Mississauga (UTM). The materials were originally created for MAT102 Introduction to Proofs, a course a UTM, but I altered them to fit my course. Thus, every worksheet on this page is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Canada License Essentially, if you use these worksheets yourself, you have to credit me, keep the same license and can't commercialize any work originating from this. For more information, head over here or go to the Creative Commons website. Note, the link here is for the 4.0 version of the license. While the general license is the same, the fine print might	{"url":"https://teach.fahadhossaini.com/proofs/","timestamp":"2024-11-11T13:54:34Z","content_type":"text/html","content_length":"9025","record_id":"<urn:uuid:5c4249e4-c1d7-4a56-bba8-7c04727ef82d>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00841.warc.gz"}
Math In the Address Bar Did you know that you can do math problems in the address bar of your browser? Regardless of what browser your using, you can use its address bar to find the answer to an arithmetic problem. For instance, let’s say that you are using Internet Explorer and all of a sudden someone asks you what 54 × 32 is. To figure it out, you type the following into the address bar and then hit the ENTER javascript:alert(54 * 32) If you tried it out, you know the answer is 1728. What about the square root of 1728? To figure it out, you could use the following: Now that you know that Math.sqrt(…) exists, you may be wondering, what other math related functions and constants like this exist. Here is a list of them derived from DevGuru.com: Euler’s constant and the base of natural logarithms (~2.7183). The natural log of 10. The natural log of 2. The base 10 log of E. The base 2 log of E. PI – The circumference of a circle divided by its the diameter. One divided by the square root of 2. The square root of 2. The absolute value of the number X. The arccosine of X (which must be greater than or equal to -1 and less than or equal to 1) as a value between 0 and PI. The arcsine of X (which must be greater than or equal to -1 and less than or equal to 1) as a value between -PI / 2 and PI / 2. The arctangent of X as a value between -PI / 2 and PI / 2. Math.atan2(X, Y) The arctangent of X / Y as a value between -PI / 2 and PI / 2. If X is an integer this evaluates to X, otherwise it evaluates to the next integer up. The cosine of X as a value between -1 and 1. The value of E^X where E is Euler’s constant. If X is an integer, this evaluates to X, otherwise it evaluates to the next integer down. The natural log (base E) of X (which must be greater than 0). Math.max(X, Y, …) The maximum number of X, Y, and any other parameters that you specify. Math.min(X, Y, …) The minimum number of X, Y, and any other parameters that you specify. Math.pow(X, Y) The value of X^Y. A random number that is greater than or equal to 0 and less than 1. The rounded value of X. If the fractional portion of the number is less than 0.5, the number is rounded down, otherwise it is rounded up. The sine of X as a value between -1 and 1. The square root X (which must be greater than or equal to 0). The tangent of X. If you haven’t already guessed it, alert(...) actually displays whatever you specify in a new dialog box. Believe it or not, you can also assign values to variables and then use those variables later on. Of course, though, you have to do all of this on one line. Here is an example of what I mean by assigning values to variables and then using them later: javascript:age = 2011 - 1987; alert(age + Math.sqrt(age)) If you tried the above code out in your address bar, you now know what my age plus the square root of my age is. All I have to say now is, “welcome to the world if JavaScript!!!” 3 Comments udip rayy · May 10, 2011 at 12:25 AM JavaScript math object is a top level, predefined object for mathematical constants and functions. Can not be created by user. It is a predefined object. Mathematical properties and functions can be calculated by math.property or math.method. Here are two good reference of details properties and methods of Math objects. Mozilla Developer Network udip rayy · May 10, 2011 at 1:00 AM A good job. There is nothing I disagree in the post. Thanking you, have a nice day.	{"url":"https://cwestblog.com/2011/05/04/math-in-the-address-bar/","timestamp":"2024-11-03T13:02:40Z","content_type":"text/html","content_length":"64014","record_id":"<urn:uuid:10d17889-6806-4426-a106-540364271547>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00614.warc.gz"}
the Law of Sines: In this section, we will learn about the Law of Sines, also known as the Sines Rule. The Law of Sines is a formula that models the relationship between the sides and the angles of any triangle, be it a right-angled triangle, an obtuse triangle, or an acute triangle. In order to use the Law of Sines, we need to satisfy the "one pair, one additional information" condition (i.e. Angle-Angle-Side abbreviated as AAS, and Angle-Side-Angle abbreviated as ASA). We will also explore the concept of the Ambiguous Case of the Law of Sines. Law of Sine For any $\triangle$ ABC, $\frac{a}{\sin(A)}$ $=\frac{b}{\sin(B)}$ $=\frac{c}{\sin(C)}$ $\frac{\sin(A)}{a}$ $=\frac{\sin(B)}{b}$ $=\frac{\sin(C)}{c}$ Use the Law of Sine when given a pair! Ambiguous case Ambiguous case of the Law of Sine arises when given SSA (side-side-angle) Step 1) Use the given angle to find the height of the triangle: $h=b \sin (A)$ Step 2) Check if, $Side\;a$ < $h$, then no triangles $Side\;a=h$, then 1 triangle $Side\;a$ > $h$, then 1 triangle $h$ < $Side\;a$ < $Side\;b$, then 2 triangles Step 3) Solve the triangle(s)!	{"url":"https://www.studypug.com/trigonometry-help/law-of-sines","timestamp":"2024-11-03T23:29:29Z","content_type":"text/html","content_length":"494275","record_id":"<urn:uuid:7431eb1d-c805-4a10-9a67-8010a0e751a0>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00451.warc.gz"}
Calculation of yearly growth for several areas I love the "if then else" function - maybe to much. My problem is that I would like to calculate growth from one year to the next for, let say, 7 years in a row for different areas. To to this I create a dummy variable (accumulated count members). I use this dummy to define in wich row I want growth from 2011 to 2012 to appear. It used to work just fine, but now for the case in question, the formular seems to be to long and I can only get 3 years growth. I imagine there must be a better way to do this. Can anyone help me? Eg. Current formular: if sum(c2, 0, m1) = 2 then (sum(0, d-5, m1) - sum(0, d-6, m1)) / sum(d-7, d-6, m1) else if….. (continues *9) 2 comments • Can you upload and example cross table to show what it is you mean? • I think I just figured it out - I can use "sum(0,0, m1) - sum(0,-1,m1)" that makes it much more simple! Please sign in to leave a comment.	{"url":"https://community.targit.com/hc/en-us/community/posts/4409280724881-Calculation-of-yearly-growth-for-several-areas","timestamp":"2024-11-05T13:57:32Z","content_type":"text/html","content_length":"32351","record_id":"<urn:uuid:b1938088-d6e0-413f-a20c-27330c92d4f1>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00177.warc.gz"}
Profile of Intuitive Thinking Ability on the Topic of Limits Assessed Based on Students' Representation of Functions - International Journal of Research and Innovation in Social ScienceProfile of Intuitive Thinking Ability on the Topic of Limits Assessed Based on Students’ Representation of Functions - International Journal of Research and Innovation in Social Science Submission Deadline-15th November 2024 November 2024 Issue : Publication Fee: 30$ USD Submit Now Submission Deadline-05th November 2024 Special Issue on Economics, Management, Sociology, Communication, Psychology: Publication Fee: 30$ USD Submit Now Submission Deadline-20th November 2024 Special Issue on Education, Public Health: Publication Fee: 30$ USD Submit Now Profile of Intuitive Thinking Ability on the Topic of Limits Assessed Based on Students’ Representation of Functions • Farida Leni Kusumawati • Ikrar Pramudya • Farida Nurhasanah • 1952-1959 • Mar 20, 2024 Profile of Intuitive Thinking Ability on the Topic of Limits Assessed Based on Students’ Representation of Functions Farida Leni Kusumawati, Ikrar Pramudya, Farida Nurhasanah ^ Universitas Sebelas Maret, Surakarta, Indonesia DOI: https://dx.doi.org/10.47772/IJRISS.2024.802137 Received: 04 February 2024; Revised: 17 February 2024; Accepted: 22 February 2024; Published: 20 March 2024 This research aims to describe the intuitive thinking process of students who are capable of representing functions graphically and notationally, only able to represent functions graphically, only able to represent functions in notation, and unable to represent functions graphically or notationally in understanding the concept of limit. This research is a qualitative study and was carried out at ABBS (Al-Abidin Bilingual Boarding School) high school in the odd semester of the 2023/2024 teaching year. The subject of the study was a student in the 12th grade of high school who was selected based on the way the student represented the function, i.e. was able to represent the function graphically and notationly, was only able to represent the function graphically, was only able to represent the function in notation, and was not able to represent the function graphically or notationally. Data collection was carried out with a written test technique. The validity of the data in this study uses source triangulation whereas the data analysis technique used is the Miles and Huberman model consisting of data reduction, data presentation, and inference recall. The results of the research concluded that students who can represent functions in the form of graphics and notation, only in graphic form, only in the form of notation have the intuitive thinking ability Power of synthesis, that is, students can answer questions directly, immediately, or suddenly using the ability of combinations of formulas and algorithms that they possess. Students who cannot represent functions in graphic and notation forms own the ability to think intuitively Catalitic Inference, that is, answering direct questions immediately, using shortcuts, giving short answers, are not detailed, and are unable to give logical reasoning. Keywords– intuitive; representational; power of synthesis; catalitic inference; common sense The scope of material tested in Mathematics subjects for high school/secondary school students majoring in Science is Algebra, Calculus, Geometry, and Measurement, as well as Statistics. Each scope of material contains a hierarchy. For example, the hierarchy in the scope of Calculus includes functions, limits of functions, derivatives of functions, and integrals. This hierarchy indicates that the previous material becomes a prerequisite for the subsequent material. For example, functions are the prerequisite material for studying the limit of functions. The material on the limit of functions becomes the subject of study in various disciplines, especially in Mathematics and Physics. The limit of functions serves as the foundation for studying derivatives and integrals in the discipline of Mathematics. In addition to Mathematics subjects, the concept of limits is also applied in Physics subjects on the topics of motion and velocity. Considering the importance of the material on the limit of functions for several disciplines, it is necessary to develop a good understanding of the concept in its delivery. The revised 2013 curriculum suggests that understanding the concept of the limit of functions will be achieved well if explained intuitively. Reference [1] revealed that in learning, there are three types of thinking activities: formal thinking activity, algorithmic thinking, and intuitive thinking. Intuitive thinking activity is immediate thinking. Intuitive thinking activity plays a role in providing interpretations of a certain definition or theorem, giving meaning or informal interpretation of a certain formula or procedure, and making guesses in solving mathematics. Knowledge or understanding built through the intuition process is called intuitive knowledge or understanding. Intuitive understanding is needed as a bridge of thinking when someone tries to solve a problem because, with intuition, students have creative ideas for solving mathematical problems ([2], [3]). To reduce the problems, students must be allowed to use their intuitive thinking as a decisive part of acquiring new knowledge [4]. In other words, student intuition is highly required in the first step to solving a problem [5]. Intuition only guides mathematical activities, even though the results of activities based on intuition do not necessarily get the right solution [6]. Intuition is very instrumental in solving mathematical problems. Intuition is seen as important by students because intuition will help students in committing thoughts toward the desired problem solver. Therefore, if the students’ intuition is not well developed, the problem-solving process can be hampered [7]. Intuitive thinking as an approach and design to learning mathematics still provides an important foundation for students to be able to solve mathematical problems, is capable of improving creative thinking skills, and contributes to students’ views on a mathematical problem, consciously or unconsciously [8]. Nowadays, most students do mathematical problem-solving only limited to what have teacher has given so they have difficulty solving problems that the teacher has never provided. However, some students are capable of solving problems correctly in their own way by bridging the thoughts that arise spontaneously without using steps of completion in general. Activities like this are called intuitive thinking [9]. In this understanding, intuition can be made as a bridge to students’ understanding so that it can be accessed in linking imagined objects with the desired alternative solutions. In other words, students can determine what strategies or steps should be taken to get a problem solution, especially contextual problems that have completion steps that cannot be accessed directly [10]. Based on the data from the 2018 National Examination Exhibition, it was found that the percentage of student’s mastery of material on the indicator of determining the conditions of an algebraic function has a limit value of 18.56%. This percentage indicates that students’ mastery of the concept of limits is very low. Researchers found that in addition to being unable to determine the limit value of a constant function, students experienced confusion in determining the graph of a constant function. This second example shows that students still have difficulty representing functions as graphs. This second example is supported by the observation results and documentation of student representation values in the following function material. │No│Description │Result │ │1 │Highest Score │100 │ │2 │Lowest Score │40 │ │3 │Average Score │59,29 │ │4 │Passed │15% │ │5 │Not Passed │85% │ The findings provide information to the researchers that the way students represent functions is related to students’ intuitive thinking ability in understanding the concept of function limits. Intuitive thinking can help improve mathematical problem-solving for topics such as numbers, geometry, algebra, functions, and calculus [8]. In addition to intuitive thinking, to further enhance understanding of the concept of function limits, there needs to be a mathematical connection between function material and function limit material. The concept of function required in understanding the concept of limit is about students’ ability to represent functions. This research was under a qualitative approach, as stated by Lofland and Lofland that the main sources of data in qualitative research are words and actions, while the rest are additional data such as documents, etc [11]. The first data are used to determine students’ ability to represent functions. The data source comes from student test results through Google Forms containing questions to differentiate between functions and non-functions. The second data are used to determine the profile of students’ intuitive thinking abilities in understanding the concept of function limits. The data source for this data is from written tests administered to students. This research used purposive sampling, and the subject selection was conducted through the following steps: 1. Students of XII IPA 7 at ABBS Surakarta High School were given a test through Google Forms containing questions to differentiate between functions and non-functions to map how students represent 2. Based on the test results of the function material, data on students’ representation of function material, and considerations from teachers, 12 students were selected as prospective research 3. A test on the core material of function limits was conducted. The triangulation technique used was source triangulation. Reference [12] explains that source triangulation to test the credibility of data is done by checking data obtained through several different sources of informants. Data from these different sources are described, and categorized, identifying similarities, differences, and specific aspects of the three data sources. The data analyzed by the researchers which led to a conclusion is then confirmed with the source of data for agreement. The results of the analysis are confirmed again with the informant sources to test their This research is a qualitative study, so the data were analyzed non-statistically. The data analysis process in this study follows the Miles and Huberman Model, which consists of data reduction, data display, conclusion drawing, and verification [12]. To analyze intuitive thinking abilities, the indicators of intuitive thinking abilities according to August Mario Bunge in Table 2 are used [13]. │Intuitive Thinking Characteristics│Indicators │ │Catalytic Inference │Subjects answer questions directly, immediately, or suddenly, using shortcuts, providing short, non-detailed answers, and being unable to provide logical reasons.│ │Power of synthesis │Subjects answer questions directly, immediately, or suddenly using their ability to combine formulas and algorithms. │ │Common Sense │Subjects solve problems directly, immediately, or suddenly, using steps, and rules based on their knowledge and experience. │ The research results were obtained from a test of students’ intuitive thinking abilities. The following are the questions for the intuitive thinking ability test on the limit material: 1. The item on the intuitive thinking ability test represents a function in the form of a graph related to the graph of the tan x function. Students are asked to determine the value of based on the graph given in the question. Below is the item on the intuitive thinking ability test representing function in the form of a graph in Figure 1. Fig. 1 Question Item Number 1 2. The item on the intuitive thinking ability test represents a function in notation form related to the function f, which is a rational trigonometric function. Students are asked to determine . Below is the item on the intuitive thinking ability test representing function in notation form in Figure 2. Fig. 2 Question Item Number 2 Here are the results of the analysis of intuitive thinking abilities from 4 students: a) 1 student is able to represent the function in both graphical and notation form, b) 1 student is able to represent the function in graphical form only, c) 1 student is able to represent the function in notation form only and d) 1 student is unable to represent the function in both graphical and notation Subject 1 (S1) Student with the Ability to Represent Function in Both Graphical and Notation Form The subject answered question number 1 using their ability to combine formulas and algorithms, specifically utilizing the substitution technique. Although the chosen technique was not appropriate for solving question number 1, the subject was able to use their previously acquired knowledge regarding the values of trigonometric special angles. Therefore, they could accurately determine the value of Π/2. Fig. 3 The Answer of Subject S1 on Question Item Number 1 The subject answered question number 2 using their ability to combine formulas and algorithms. The subject attempted to transform the subtraction of two trigonometric functions into a relevant multiplication form, but their choice of formulas was not entirely appropriate, despite already using a sequential algorithm. Fig. 4 The Answer of Subject S1 on Question Item Number 2 Based on the answers provided by subject S1 for questions number 1 and 2, it can be inferred that the student who can represent the function in both graphical and notation form possesses the intuitive thinking ability of “Power of Synthesis.” Subject 2 (S2) Student with the Ability to Represent Function in Graphical Form The subject answered question number 1 using their ability to combine formulas and algorithms, specifically utilizing the substitution technique. Although the chosen technique was not appropriate for solving question number 1, the subject was able to use their previously acquired knowledge regarding the values of trigonometric special angles. Therefore, they could accurately determine the value of Π/2. Fig. 5 The Answer of Subject S2 on Question Item Number 1 Fig. 6 The Answer of Subject S2 on Question Item Number 2 Based on the answers provided by subject S2 for questions number 1 and 2, it can be inferred that the student who can represent the function in graphical form possesses the intuitive thinking ability of “Power of Synthesis.” Subject 3 (S3) Student with the Ability to Represent Function in Notation Form The subject answered question number 1 using their ability to combine formulas and algorithms, specifically utilizing the substitution technique. Although the chosen technique was not appropriate for solving question number 1, the subject was able to use their previously acquired knowledge regarding the values of trigonometric special angles. Therefore, they could accurately determine the value of Π/2. Fig. 7 The Answer of Subject S3 on Question Item Number 1 The subject answered question number 2 using their ability to combine formulas and algorithms. The subject attempted to transform the subtraction of two trigonometric functions into a relevant multiplication form, but their choice of formulas was not entirely appropriate. Although the final answer written by the subject was correct, there were still parts of the answer that indicated the subject’s lack of logic in determining the result of Fig. 8 The Answer of Subject S3 on Question Item Number 2 Based on the answers provided by student S3 for questions number 1 and 2, it can be inferred that the student who can represent the function in notation form possesses the intuitive thinking ability of “Power of Synthesis.” Subject 4 (S4) Student with No Ability to Represent Function in Both Graphical and Notation Form The subject answered question number 1 directly, immediately, or suddenly, using shortcuts, providing short, non-detailed answers, and being unable to provide a logical reason. There was no connection between the answers in each line of the subject’s response. Fig. 9 The Answer of Subject S4 on Question Item Number 1 The subject answered question number 2 by using a combination of derivative formulas and transforming the subtraction of trigonometric functions into multiplication form, but they were not accurate in determining the result of the derivative and in the application of mathematical operations. The answers in the second and third lines indicate that the subject was not precise in the operations. Fig. 10 The Answer of Subject S4 on Question Item Number 2 Based on the answers provided by student S4 for questions number 1 and 2, it can be inferred that the student who cannot represent the function in both graphical and notation form possesses the intuitive thinking ability of “Catalytic Inference.” Students who can represent functions in both graphical and notation form, only in graphical form, or only in notation form have the intuitive thinking ability of Power of Synthesis. This is because limit function problems are often presented in both graphical and notation form, so when students already possess the ability to represent functions in graphical or notation form, they already meet the sufficient condition to answer questions directly, immediately, or suddenly using their ability to combine formulas and algorithms. On the other side, students who cannot represent functions in both graphical and notation form have the intuitive thinking ability of Catalytic Inference. This is because limit function problems are often presented in both graphical and notation form, so when students do not possess the ability to represent functions in graphical and notation form, they will answer questions directly, immediately, or suddenly, using shortcuts, providing short, non-detailed answers, and unable to provide a logical reason. Based on the results and discussion, it can be concluded that students who can represent functions in both graphical and notation form, only in graphical form, or only in notation form have the intuitive thinking ability of Power of Synthesis, while students who cannot represent functions in both graphical and notation form have the intuitive thinking ability of Catalytic Inference. From the results of this research, it is recommended for future research to conduct broader studies, not only focusing on representation in graphical and notation forms but also examining other forms of representation given the importance of intuitive thinking abilities in mathematics. The researchers also recommend teachers develop teaching materials to enhance students’ intuitive abilities. 1. Fischbein, E. (1994). The Interaction Between The Formal, The Algorithmic, and The Intuitive. Didactics of Matematics as Scienrific Discipline, 231-233. 2. Baiduri, Cholily, Y. M., & Ulfah, F. (2022). The Intuitive Thinking Process of High Ability Students in Mathematical Problem. Journal of Hunan University (Natural Sciences), 1-11. 3. Sa’o S., Mei A., & Naja, F. Y. (2019). The Application of Intuition in Solving the Problems of Math in the Olympiad of Mathematics. International Journal of Multidisciplinary Research and Publication, 11–15. 4. Abdillah, Mastuti, A. G., Rijal, M., & Rahman, M. A. (2020). Students’ intuitive and analytical thinking in the. Al-Jabar: Jurnal Pendidikan Matematika, 49-60. 5. Panbanlame, K., Sangaroon, K., & Inprasitha, M. (2014). Students’ Intuition in Mathematics Class Using Lesson Study and Open Approach. Psychology, 1503–1516. 6. Utomo, D. P., Amaliyah, T. Z., Darmayanti, R., Usmiyatun, & Choirudin. (2023). Students’ Intuitive Thinking Process in Solving Geometry. JTAM (Jurnal Teori dan Aplikasi Matematika), 139-149. 7. Wuryanie, M., Wibowo, T., Kurniasih, N., & Maryam, I. (2020). Intuition Characteristics of Students in Mathematical Problem Solving in Cognitive Style. Journal of Education and Learning Mathematics Research (JELMaR), 31-42. 8. Suwarto, Hidayah, I., Rochmad & Masrukan. (2023). Intuitive thinking: Perspectives on intuitive thinking processes in mathematical problem solving through a literature review. Cogent Education, 9. Purwaningsih, W.I.,et al. (2019). Characteristics of intuitive thinking in solving mathematical issues based on cognitive style. J. Phys.: Conf., 1-15. 10. Ulpah, Maria. (2019). Characteristics of Students’ Intuitive Thinking in Solving Mathematical Problems. Proceeding of 3rd International Conference on Empowering Moslem Society in the 4.0 Industry Era ,48-57. 11. Moleong, L.J. (2014). Metodologi Penelitian Kualitatif. Bandung: PT Remaja Rosdakarya 12. Sugiyono. (2007). Metode Penelitian Kuantitatif Kualitatif dan R & D. Bandung: CV Alfabeta. 13. Muniri. (2013). Karakteristik Berpikir Intuitif Siswa Dalam Menyelesaikan Masalah Matematika. Prosiding Seminar Nasional Matematika Dan Pendidikan Matematika UNY.	{"url":"https://rsisinternational.org/journals/ijriss/articles/profile-of-intuitive-thinking-ability-on-the-topic-of-limits-assessed-based-on-students-representation-of-functions/","timestamp":"2024-11-11T14:01:15Z","content_type":"text/html","content_length":"324305","record_id":"<urn:uuid:dc759411-4f3d-4fef-ac39-0f8baf741e18>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00610.warc.gz"}
Longdom Publishing SL \| Open Access Journals Research Article - (2015) Volume 4, Issue 5 Application of Markov Chain and Entropy Function for Cyclicity Analysis of a Lithostratigraphic Sequence - A Case History from the Kolhan Basin, Jharkhand, Eastern India ^1Master Student, Department of Geology and Geophysics, Indian Institute of Technology Kharagpur, India ^2Professor, Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur, India ^3Research Scholar, Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur, India ^*Corresponding Author: Sinha S, Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur, India, Tel: +1 405 588 2483 Lithofacies succession in Chaibasa-Noamundi basin of the Proterozoic Kolhan Group, Jharkhand has been studied statistically using modified Markov chain model and Entropy function. The lithofacies analysis based on the field descriptions, petrographic investigation, and their vertical packaging has been done for assessing the sediment depositional framework and the environment of deposition. Six lithofacies arranged, in two genetic sequences, have been recognized within the succession. The result of Markov chain analysis indicates that the deposition of the lithofacies is non-markovian process and represents asymmetric fining-upward non-cyclic deposition. The chi-square test has been done to test for the hypotheses of lithofacies transition at confidence level of 95%. The entropy analysis has been done to evaluate the randomness of occurrence of lithofacies in a succession. Two types of entropies are related to every state; one is relevant to the Markov matrix expressing the upward transitions (entropy after deposition), and the other, relevant to the matrix expressing the downward transitions (entropy before deposition). The energy regime calculated from the entropy analysis showing maximum randomness, suggests that changing pattern in deposition has been a result of rapid to steady flow. This results a change in the depositional pattern from deltaic to lacustrine deposit and sediment by passing that finally generated non-cyclicity in the sequence. Keywords: Markov chain analysis; Entropy analysis; Kolhan basin; Cyclicity; Chaibasa-noamundi basin; Lithofacies succession The Kolhan group lying unconformably above the Singhbhum granite and is preserved as a linear belt extending for 80-100 km with an average width of 10-12 km. It is bounded by the Jagannathpur lavas on the southeast and south and by the faulted Iron Ore Group on its western contact. Saha [1] has divided the Kolhan Group of sediments into four detached sub-basins-Chaibasa-Noamundi basin, Chamakpur- Keonjhargarh basin, Mankarchua basin and Sarapalli- Kamakhyanagar basin. The complex patterns in lithologic successions are produced as a result of the physical process and random events occurring simultaneously in a given depositional environment. It is therefore required that sedimentary succession to be tested for such cyclic order on an objective and quantitative basis. Due to absence of fossils assemblages, land vegetation and paucity of exposure, it is difficult to interpret depositional environment of Proterozoic Kolhan sequence. In the Chaibasa-Noamundi basin it is observed that there is gross lithological asymmetricity present between various lithofacies. There is marked difference in the sandstone and shale thickness, with shale thickness very high as compared to sandstone. It is difficult to prove in the field time independent depositional relational, if any, between the two sedimentary units as there is absence of unconformity in the sequence. Markov chain analysis was carried out to analyze the order of sequence and transition in the facies lineage. To prove similar cyclic arrangement in the lithofacies in the study area, the Markov property and entropy analysis was applied to test for the presence of order in the sequence of structures or descriptive facies in the Chaibasa-Noamundi Basin. The present study is based on the outcrop and subsurface data of the Chaibasa-Noamundi basin from seventeen sedimentary logs to find the cyclicity of lithofacies using Markov Chain and Entropy analysis. The aim of this paper is • To evaluate statistically cyclic character by Markov chain analysis; to compare the cyclicity, if present, in time and space. • To evaluate the degree of ordering or energy regime of the facies deposition using entropy functions. • To recognize the broad depositional environment of the basin. Geological setting and stratigraphic succession In eastern India, Singhbhum craton is mainly composed of Archean granitoids bounded in the north and east by a Proterozoic mobile belt (Table 1) [1]. Dunn [2] first recognized the Kolhan group of sediment towards the western part of the Singhbhum granite, preserved as a linear belt extending for 80-100 km with an average width of 10-12 km with broad wraps and dome and basin structure (Figure Newer Dolerite dykes and sills ca. 1.6- 0.95 Ga Mayurbhanj Granite ca. 2.1 Ga Gabbro – anorthosite – ultramafics - Kolhan Group ca. 2.1- 2.2 Ga Jagannathpur / Malangtoli and Dhanjori–Simlipal ca. 2.3 Ga Lavas, Quartzite– Conglomerate (Dhanjori Group) ca. 2.3 - 2.4 Ga Pelitic and arenaceousmetasediments with mafic sills (Singhbhum Group) Singhbhum Granite Phase III (SBG B) ca. 3.1 Ga Epidiorites (intrusives) Iron Ore Group (IOG, volcano sediments - Singhbhum Granite Phase I and II (SBG A), NilgiriGranite, Bonai Granite ca. 3.3 Ga Table 1: Simplified chronostratigraphic succession for the singhbhum craton, eastern india [1,4]. The main basin of Chaibasa-Noamundi extends for about 60 km length with an average width of 10-12 km from Noamundi (85°28’– 22°09’) in the south to Chaibasa (85°48’–22°33’) in the north. The strike of basin is in NNW-SSE direction and low westerly dip of 5 to 10°. The metasedimentary rocks comprising of basal conglomerate, sandstone, limestone and phyllitic shale lie unconformably over the Singhbhum granite in the east and partly over, folded and thrust-faulted, Iron-Ore Group to the west [3]. The sediments have undergone gentle tectonic deformation and very low grade metamorphism [3]. Lithological succession The major lithounits of Chaibasa-Noamundi basin are Kolhan shale, Kolhan calcareous shale/limestone, Kolhan sandstone, Kolhan conglomerate. The Kolhan Sandstone overlies the granitoids basement with an erosional unconformity often strewn with thin layers and lenses of conglomerates [4]. In all these exposures the minimum thickness attained is 4.57 m while maximum goes upto 7.62 to 9.14 m. The planebedded sandstones are interbedded with minor thin beds and lenses of conglomerates, pebbly sandstones with thin and impersistent layers of shale [3]. The sandstone shows development of antidune/ wavy lamination and planar cross stratification. The stratigraphy of chaibasa- Noamundi basin shows very thin sandstone overlain by thick shale deposit represents an asymmetry in vertical basin-fill architecture [4]. The Kolhan Limestone is an impersistent horizon. It is best developed towards SW of Chaibasa, near village Rajanka and Kondoa and N and NW of Jagannathpur. Six lithofacies has been identified after grouping of lithounits together based on their gross lithologies, primary sedimentary structures, and paleocurrent patterns [5-7]. The architectural elements used in the present study are the sedimentary structures, textures, fabrics of the lithofacies, stratal characteristics and geometrical relationships [8]. The six lithofacies are (a) granular lag facies (GLA), (b) granular sandstone facies (GSD), (c) sheet sandstone facies (SSD), (d) plane laminated sandstone facies (PLSD), (e) rippled sandstone facies (RSD), and (f) thin laminated siltstone-sandstone facies (TLSD) [6,7]. Six lithofacies have been recorded and are described individually as, 1) Granular Lag Facies (GLA): This facies is characterized by the occurrence of laterally impersistent, massive, ungraded and fine matrix supported conglomerate. These conglomerates are mostly immature to sub-mature, and quite similar to the overlying sandstone (Figure 2A). 2) Granular sandstone facies (GSD): This facies is characterized by moderately to well sorted, moderate clast/matrix ratio. Planar cross-stratification is more commonly found in compare to trough cross- stratification (Figure 2B). 3) Sheet sandstone facies (SSD): The SSD facies is defined by sheets of subarkose-sublithic arenite-quartz arenite, sometimes intercalated with thin laminated siltstone (Figure 2C). 4) Plane laminated sandstone facies (PLSD): The PLSD facies is defined by thick amalgamated well sorted subarkose- sublithic arenite-quartz arenite, with a moderate - high grain: matrix ratio. The sandstone is medium to fine grained. The prominent structures are planar cross bedding, wavy lamination, and washed out/flat top ripples, herringbone cross-bedding and antidunes (Figure 2D). 5) Rippled sandstone facies: This facies is defined by predominance of packages of rippled sandstone with prolific development of both symmetrical and asymmetrical ripples (Figure 2E). 6) Thin laminated sandstone facies: This facies is defined by the rhythmic alternation of sandstone and shale units (Figure 2F), in which sandy layers are thicker than shale layers. Markov Chain and Entropy Analysis Method The cyclic sedimentation is wide concept and has application in a wide variety of sedimentary environment [9]. Cyclicity in a sedimentary succession is defined as a series of lithologic units or lithofacies repeated through a succession in a cyclic or rhythmic pattern to some extent. Two types of observable cyclicity may be noteworthy: one in which there exist an order of sequence only; and another in which there is a certain order of repetition along the vertical scale of the sedimentary succession. Which type of cyclicity is to be considered is determined from the geological problem [ 10]. In this study each “bed” provides a logical unit, therefore, examining cyclicity of a sequence is appropriate, hence it safer to ignore thickness [11]. Structuring data for markov chain Vertical sequence profile: Seventeen lithological sections were considered for studying the vertical and areal distributions of the lithofacies within the Chaibasa-Noamundi basin. Nature of Data: The data used in the study is different lithofacies in a vertical sedimentary log sequence coded into finite number of states for the statistical analysis [12]. In this study only six lithofacies are used which are clearly marked in outcrop section as well as in each sedimentary log and this is also done in order to prevent diffusion of transitions between two lithofacies [13]. For the statistical interrelationships between different lithofacies, following six variables were extracted from the seventeen vertical log successions. The six lithofacies variables (descriptive characteristic is in the previous section) and the symbols used to designate them are as: A- Granular lag facies (GLA), B- Granular sandstone facies (GSD), C- Sheet sandstone facies (SSD), D- Plane laminated sandstone facies (PLSD), E- Rippled sandstone facies (RSD), F- Thin laminated sandstone facies (TLSD). All six states are well represented in each of the seventeen sedimentary logs. Calculation of frequency count matrix (F): Frequency count matrix is calculated from the vertical sequence profile of sedimentary logs. Since we are using Markov chain which has memory less property i.e. the geologic situation at point (n-1) governs the event that will happen at n. That’s why all seventeen sedimentary logs can be used to calculate matrix F without loss of information. Subsequently, data for all logs are added and matrix is structured at the basin level [14]. Number of transition from facies i to j is represented in row i and column j of matrix F, which signifies number of times state j followed immediately after state I in the sedimentary logs. The frequency count matrix is structured into embedded Markov chain (definition below) considering only transition of lithologies and not their thickness as stated elsewhere. Since a transition is supposed to occur only when it results in a different lithology, the diagonal elements are all zero’s in the resulting frequency matrix [14]. Analytical procedure In the present study, the embedded Markov matrix is used for structuring the frequency count matrix (F[ij]), where i, j is the row and column number respectively. When i=j, zero is present in the matrix, this implies that the transition from one facies to another has only been recorded where there is an abrupt change in the lithofacies. The advantage of the embedded Markov matrix over the regular Markov matrix is that it is used to identify an actual order in facies transition, if present, regardless of the thickness of the individual bed [13]. Transition frequency matrix (F): It is a two dimensional array which records the frequency of the vertical transitions that occur between the different lithofacies in a given stratigraphic succession. The lower facies of each transition couplet are given by the row numbers of the matrix, and the upper facies by the column numbers. Upward transition probability matrix (P): The upward transition probability matrix calculates the probability of upward transition of lithofacies in a succession and is calculated in the following Where, S[Ri] is the corresponding row total. Downward transition probability matrix (Q): Downward transition probability determined by dividing elements of the transition frequency matrix (F) by the corresponding column total, i.e. Where, S[Cj] is the column total. It calculates the probability of downward transition of lithofacies in a given succession i.e probability of facies i overlain by facies j. Independent trail matrix (R): This matrix represents the probability of the given transition that occur in a random manner and is given by, R[ij]=S[Cj]/(S[T] – S[Ri]) Where, S[T] represents total number of facies transition. The diagonal cells are filled with zeros assuming each transition represent an abrupt change in facies characteristic. Difference matrix (D): A difference matrix is calculated which highlights those transitions that have a probability of occurrence greater than if the sequence were random. By linking positive values of the difference matrix, a preferred upward path of facies transitions can be constructed which can be interpreted in terms of depositional processes that led to this particular arrangement of facies [15]. A positive value in difference matrix indicates that a particular transition occurs more frequently and a negative value indicates that it occurs less frequently. In difference matrix the values in each rows of the matrix sum to zero. If the values are close to zero, a vertical succession with little or no ‘memory’ indicates independent nature of deposition of facies in a basin. Expected frequency matrix (E): Expected frequency Matrix represents the expected number of transition from facies i to facies j and is given by E[ij]=R[ij] × S[Ri] It is necessary to calculate an expected frequency matrix, since chi – square tests should only be applied when the minimum expected frequency in any cell not exceeds 5. Test of significance: Non-parametric chi-square (χ^2) test has been applied to ascertain whether the given sequence has a Markovian ‘memory’ or no memory. To test null hypothesis, chi-square (χ^2) values are calculated for vertical successions. Where, F[ij]=transition count matrix or observed frequency of elements in the transition count matrix; E[ij]=Expected frequency matrix; ν=degree of freedom given (n^2–2n), where n denotes rank of the If the computed values of chi-square exceed the limiting values at the 0.5% significance level suggests the Markovity and cyclic arrangement of facies states. Entropy Concept The concept of entropy to sedimentary successions is applied to determine the degree of random occurrence of lithofacies in the succession [16]. Hattori [16] recognized two types of entropies with respect to each lithological state; one is post–depositional entropy corresponding to matrix P and the other, pre–depositional entropy, corresponding to matrix Q. Hattori [16] defined Post – depositional entropy with respect to lithofacies state i as If E[i] (post) is equal to zero, implies that facies i is always succeeded by only facies j in the sequence. If E[i] (post) is greater than zero, facies i is likely to be overlain by different Hattori [16] defined pre – depositional entropy with respect to state i as Large value of entropy signifies that facies i occur independent of the adjacent state. Two entropies together form a entropy set for state i, and serve as indicators of the variety of lithological transitions immediately after and before the occurrence of i, respectively [16]. Interrelationships of post Entropy and pre Entropy is used to classify various cyclic patterns into asymmetric, symmetric and random cycles [16]. The values of entropies increase with the number of lithological facies. To eliminate this influence, Normalization of the entropies is done by the following equation: Where, E[max] = -log[2](1/(n-1)) Where, E[n] is the normalized entropy, E is either post–depositional or pre–depositional entropy, and E[max] is the maximum entropy possible in a system where n state variable operates. Results and Discussion Matrices used to analyze transitions of lithofacies in Chaibasa- Noamundi basin is calculated using method and equations given in the previous section (Table 2 a-g). A B C D E F S[Ri] T-S[Ri] A 0 1 0 4 1 0 6 43 B 3 0 3 2 5 2 15 34 C 0 5 0 0 1 1 7 42 D 2 1 2 0 4 0 9 40 E 0 2 0 3 0 0 5 44 F 1 3 0 3 0 0 7 42 SCj 6 12 5 12 11 3 Total= 49 a) Transition count matrix (F). A B C D E F A 0 0.166 0 0.666 0.166 0 B 0.2 0 0.2 0.133 0.333 0.133 C 0 0.714 0 0 0.142 0.142 D 0.222 0.111 0.222 0 0.444 0 E 0 0.4 0 0.6 0 0 F 0.142 0.428571 0 0.428 0 0 b) Upward transition probability matrix (P). A B C D E F A 0 0.5 0 0.333 0 0.166 B 0.0833 0 0.416 0.083 0.166 0.25 C 0 0.6 0 0.4 0 0 D 0.333 0.166 0 0 0.25 0.25 E 0.09 0.454 0.09 0.363 0 0 F 0 0.666 0.333 0 0 0 c) Downward transition probability matrix (q). A B C D E F A 0 0.279 0.116 0.279 0.255 0.069 B 0.162 0 0.135 0.324 0.297 0.081 C 0.136 0.272 0 0.272 0.25 0.068 D 0.162 0.324 0.135 0 0.297 0.081 E 0.157 0.315 0.131 0.315 0 0.078 F 0.13 0.26 0.108 0.26 0.239 0 d) Independent Trails Probability Matrix (R). A B C D E F A 0 -0.112 -0.116 0.387 -0.089 -0.069 B 0.037 0 0.064 -0.19 0.036 0.052 C -0.136 0.441 0 -0.272 -0.107 0.074 D 0.06 -0.213 0.087 0 0.147 -0.081 E -0.159 0.084 -0.131 0.284 0 -0.0789 F 0.012 0.167 -0.108 0.167 -0.239 0 e) Difference Matrix (D). A B C D E F A 0 1.674 0.697 1.674 1.534 0.418 B 2.647 0 2.205 4.994 4.852 1.323 C 1 2 0 2 1.833 0.5 D 1.35 2.7 1.125 0 2.475 0.675 E 0.681 1.363 0.568 1.363 0 0.34 F 1 2 0.833 2 1.833 0 f) Expected Frequency Matrix (E). Test of Equation Computed value of Limiting Value at 0.5% significance Level Degree of freedom Billingslay 27.112 45.55 24 g) Test of Significance. Table 2: (a-g) Matrices used to analyze transitions of lithofacies in the Kolhan Group. Markov chain analysis It is important to note that significant facies transitions represent the most probable facies transitions, but not their actual frequency in the studied sedimentary sequences. Matrix of observed facies transitions contains the real frequencies of facies transitions. The highest values of and the positive entries of were taken into account to determine the cyclic processes [17]. It ensures that while interpreting sedimentary facies transition both statistically significant facies transition and real facies transitions is taken into account in order to better understand their significance and depositional process in the studied sedimentary succession. The computed values of chi-square is lower than the limiting values at the 0.5% significance level this means that the null hypothesis is false, suggesting the deposition of sediments is not by Markovian process and non-cyclic arrangement of facies states in Chaibasa-Noamundi basin (Table 2g). The facies relationship diagram is constructed from the difference matrix results (Figure 3) ( Table 2f). The preferred upward transition path for the lithofacies is The transition between is non-Markovian and the lineage is non-repetitive in nature. The obvious aim of this approach was to detect and define cyclic relationships, if any. In the present case the cyclicity is absent or very weak. This information can greatly assist in environmental interpretation. Entropy analysis Both E[pre] and E[post] are larger than zero implies all six lithofacies (GLA, GSD, SSD, PLSD, RSD, and TLSD) overlies and also is overlain by more than one state [16]. E[pre] and E[post] are larger in value for GSD and it is deduced that the influx of pebbly sandstone into the Chaibasa- Noamundi basin was the most random event (Table 3). For RSD and PLSD, E[pre]>E[post]. This relation indicates that rippled sandstone could accumulate in a wide variety of depositional environment and exerted a considerably strong influence upon the state selection of its successor. E[Post] E[Pre] E[nPost] E[nPre] A 0.822 0.959 0.353 0.413 B 2.232 2.054 0.961 0.885 C 1.148 0.971 0.494 0.418 D 1.836 1.959 0.791 0.846 E 0.971 1.159 0.418 0.499 F 1.448 0.918 0.624 0.395 Table 3: Matrices used to analyze Entropy value of lithofacies in the Kolhan Group. Large difference in Epre and Epost and with E[pre]post relationship in case of facies TLSD indicates its strong dependence on its precursor which is visualized from the Markov metrics (Table 2 and Figure 3). The depositional pattern in the TSLD facies is indicative of a low energy, suspension fall out during the waning phase of these dimentation. In other words, these facies accumulated in environment was located in the distal part of the basin in preference to other areas. The Epre and Epost plots for coarse to medium-grained sandstone, interbedded fine-grained sandstone/shale, shale fall almost around the diagonal line, comparing well with the type ‘C’ cyclic pattern of Hattori, which signifies random lithologic series, as deduced independently by improved Markov process model ( Figure 4). The cycles of Noamundi basin belong to the maximum entropy (1) type of cycle (indicated by black dot (Figure 5)) [16]. 1-maximum entropy; 2-etropies for coal measure succession; 3-entropies for fluvial-alluvial successions; &entropies for neritic successions; 5-entropies for flysch sediments; 6-minimum entropy; Black dot indicate entropy of basin under study. Sediment flow model In chaibasa-Noamundi basin asymmetric sequence pertains to the sediment bypassing. The thinning-upward sequences represent lacustrine deposits, while the thickening upward sequences represent point bar-sand flat deposits. Variation in layer thickness is suggestive of deposition by unsteady flow in a fluvial regime within the channel. The flow was suddenly impeded, and as a result there was a quick fall in the energy of the solid-fluid system that resulted in rapid deposition. Maximum energy regime of the area deduced from the total entropy analysis suggests that the sequence is not a marine sequence and the overall flow pattern changes from the deltaic environment to lacustrine environment [18]. The granular lag (GLA) and granular sandstone (GSD) facies are a part of shallow braided fluvial plain facies association. These two facies were formed in fluvial channels and bars in braided streams that gradually fanned outwards indicated by the presence of GLA and the GSD facies as the basal layer in the stratigraphic sequence. Trough and planar cross-beddings are common structures developed as a result of the lateral and downstream advance of a midchannel bar that finally coalesced into the adjacent branch channel. High Energy regime can be justified from the field evidence as pebble orientation lacks imbrications implies sudden and rapid deposition. The association of sheet sandstone (SSD), plane laminated sandstone (PLSD), rippled sandstone (RSD), and thin laminated siltstone sandstone (TLSD) facies are typical ephemeral sheet flood facies. Presence of fine - medium grained, well sorted quartz rich sandstones (RSD) frequently interbedded with thin laminated siltstone-sandstone (TLSD) resembling heterolithic facies. The variability of sedimentary structures in the facies associations reflects rapid fluctuations in the supply of sediments. Sedimentary structures, facies relationship and relative abundance of sand and shale in suggest deposition of sediments in different fluvial settings. The transporting mechanisms and dispersal patterns of the Kolhan are complex in nature. Due to small size fine particle travels faster and rapid change in flow leads to sudden deposition leading to thelarge shale thickness as compared to the sandstone. The stratigraphy of Kolhan basin demonstrating very thin sandstone overlain by thick shale represents an asymmetry in vertical basin-fill architecture. Lithofacies variations along strike direction in basal part of shale succession indicate lateral variability among the constituent lithologies within the shale succession. The upper part of the stratigraphy in contrast exhibits widespread and monotonous occurrence of shale. It was proposed that the transgressive Kolhan sequence was deposited in a rift basin setting [7,18]. Summary and Conclusion The Kolhan Group represents the youngest Precambrian stratigraphic unit in Singhbhum geology [1]. The unmetamorphosed, low westerly dipping sedimentary piles lie unconformably over the Singhbhum granite to the east and show a faulted contact with the Iron Ore Group of rocks to the west [1]. The major findings of the study can be summarized as follows: • The application of the first order Markov Chain analysis on the seventeen vertical sections shows that there is a preferred fining upward transition path in the lithofacies. The operative geological processes were non-Markovian or independent in nature. • The energy level of the fluid during the entire process shows a considerable fluctuation reflected by the entropy analysis with changing environment of deposition. Variation in layer thickness and asymmetric sequence are suggestive of deposition by unsteady flow in a fluvial regime within the channel. The flow was suddenly impeded, and as a result there was a quick fall in the energy of the solid-fluid system that resulted in rapid deposition. • It appears that the GLA and the GSD facies represent the channel lag deposits of a braided river and the SSD, RSD, PLSD, and TLSD facies represent the portions of a fining upward sequence complex of a channel bar or possibly the longitudinal bar-transverse barcross- channel bar complex in a fluvial environment. Energy regime related to the total entropy suggests that the shale in distal part of basin is not a marine origin. The flow pattern overall changes from the deltaic environment to lacustrine environment. The results of this study show that the sedimentary sequence in the Chaibasa-Noamundi basin are non-cyclic, non- Markovian and asymmetric in character. The authors are grateful to Prof. D Sengupta, Head, Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur, for providing all necessary facilities. Citation: Sinha S, Das S, Sahoo SR (2015) Application of Markov Chain and Entropy Function for Cyclicity Analysis of a Lithostratigraphic Sequence - A Case History from the Kolhan Basin, Jharkhand, Eastern India. J Geol Geophys 4:224. Copyright: © 2015 Sinha S, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.	{"url":"https://www.longdom.org/open-access/application-of-markov-chain-and-entropy-function-for-cyclicity-analysis-of-a-lithostratigraphic-sequence-a-case-history--40213.html","timestamp":"2024-11-03T15:57:26Z","content_type":"text/html","content_length":"170812","record_id":"<urn:uuid:86a55adf-8f48-4620-bbfb-d70f7c26737f>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00714.warc.gz"}
C program to reverse a linked list with explanation - Quescol C program to reverse a linked list with explanation In this tutorial, you will learn how to write C program to reverse a singly linked list. Below are the approach which we will be follow to write our program: • To reverse any singly linked list first of all we should have some data in linked list. • So first we will take some inputs from the users and then we will reverse the linked list. • To reverse the linked list the logic of program is very simple. Just swap the address of head of linked list with the last node. • Now after swapping the nodes, last node become head node and head node will become last node. So just traverse it and print it. you will get result in reverse order. How our program will behave? Our program will take one node as an input each time and this node will create a linked list. After taking a node, program will give options to select options what you want to perform. This program has 4 operations. You can select any one as per your requirement. This 4 operation are: 1. Add value to the list at end, it is to insert node in the list. 2. Traverse/View list. It is for showing complete list. 3. Reverse the list. This is our main operation which we want to perform in this program. You can select 3 to reverse the linked list. 4. to exit the program. Program to reverse of a singly linked list in C struct node{ int data; struct node next; struct node head=NULL; struct node* createNode(){ struct node newNode = (struct node )malloc(sizeof(struct node)); return (newNode); void insertNodeAtEnd(){ struct node temp,ptr; printf("enter the data you want to insert:"); void viewList(){ struct node* temp=head; printf("List is empty. Please insert some data in list n"); printf("Our list is : n"); printf("%d t",temp->data); void reverseList(){ struct node prev, current; prev = head; current = head->next; head = head->next; prev = current; printf("after reverse the list is :n"); printf("%d t",head->data); printf("List is empty. Please insert some data in list n"); int menu(){ int choice; printf("n 1.Add value to the list at end"); printf("n 2.Travesre/View List"); printf("n 3.Reverse the list "); printf("n 4.exit"); printf("n Please enter your choice: t"); void main(){ case 1: case 2: case 3: case 4: printf("invalid choice"); Explanation of above program to reverse of a singly linked list in c • In the above program we have menu() function to print the options of operations each times, and inside main() function we have one switch case statement with 4 cases and one default. • Also we have 3 functions to perform operations on linked list. insertNodeAtEnd() function is responsible to insert the node in a linked list if already created, otherwise create new Linked List. • viewList() function is responsible to print each elements of a linked list. • reverseList() function is responsible to reverse the each elements of a linked list and then print the elements.	{"url":"https://quescol.com/interview-preparation/c-program-to-reverse-a-linked-list","timestamp":"2024-11-09T07:28:59Z","content_type":"text/html","content_length":"89021","record_id":"<urn:uuid:47548c22-ddab-4616-ba11-09b80fc066c0>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00366.warc.gz"}
Typ av regression med nominella, ordinarie, intervall och 1 Givare, induktiv NRB8 18GS40 E2 IO - Pepperl+Fuchs Ordinaldata: rangordning men varken ekvidistans eller absolut nollpunkt. Ex: Skolbetyg med betygen 1, 2, 3, 4 och 5. Nominaldata. Ex: De skandinaviska språken Tekniska data. Begreppsdefinitioner. Defining the categories is an important step and you need to carefully choose the ones which are meaningful for you and your work. 2) Categorical data can certainly be nominal; they can also be ordinal (e.g. opinions given on a Likert scale). You can even categorize (and people frequently do) data that is interval or ratio, and sometimes you can uncategorize it. 3) As @Gung pointed out, a count variable is discrete but not categorical. In Response, enter the column of nominal data that you want to explain or predict. Lån utan inkomst Låna pengar utan krav på fast lön idag Tekniska data. Elektriska data. Är nya ej utbytbara LED-armaturer bra för miljön - Cornucopia? The downside is that there is very little analysis you can do with nominal data. 2020-02-05 Levels of data - Nominal data Research Methods OCR Psychology 2016-08-05 Nominal Data; Definition Characteristics Examples Related Content References Editors & Reviewers Definition. When numbers are assigned to characteristics for the purpose of data classification arbitrarily and without any What is nominal data. As mentioned before, nominal data includes different categories which can present some properties of respondents; e.g. gender, marital status, etc. male mice, over a period of several days (1 data set gathered per Se hela listan på corporatefinanceinstitute.com 2020-08-07 · How to analyze nominal data Distribution. To organize this data set, you can create a frequency distribution table to show you the number of Central tendency. The central tendency of your data set tells you where most of your values lie. Värmlands djurvård We cannot work out what the mean name of exam participants is, nor would there be any use in doing so. Let’s look at a potential study that could collect nominal data. Nominal data, also called categorical data, does not have does not have a natural sequence. Instead, the data is typically in named categories or labels without numeric significance. For example, a survey question that asks for a favorite beverage, with choices of coffee, tea, water, or milk will generate nominal data in 4 categories as in the above bar chart. The multinomial logistic regression model Nominal Pipe Size (NPS) is a North American set of standard sizes for pipes used for high or low pressures and temperatures. " Nominal" refers to pipe in non-specific terms and identifies the diameter of the hole with a non-dimensional number (for example – 2-inch nominal steel pipe" consists of many varieties of steel pipe with the only criterion being a 2.375-inch (60.3 mm) outside diameter). Nominal vs Ordinal Data. 3. Ostlund vacation properties centrum för språk och litteraturdidaktiklafferkurvan stämmer intepeter tennant twitterdikter för barnmatte 4c nationella provmedarbetarsamtal frågor och svar ACO Fapujet S-OAP - ACO Nordic Sometimes, files duplicate some data. When information like names and addres There are various ways for researchers to collect data. It is important that this data come from credible sources, as the validity of the research is determined by where it comes from. Mina skulder transportstyrelsenvägkorsning mot Nominaldata Aktiesite.se Nominella data. Nominella data - definition, egenskaper och hur man analyserar Data Science is transforming the world around us. Machine learning, deep learning, and data-driven AI are d Nominal data are discrete, nonnumeric values that do not have a natural ordering. Nominal is from the Latin "Nominis" which means NAME, hence nominal data type differentiates between items or subjects based only on their names or (meta-)categories and other qualitative classifications they belong to. Note: Arithmetic calculations can not be performed on it. Nominal data provides some information about a group or set of events, even if that information is limited to mere counts. What is nominal data? As we’ve discussed, nominal data is a categorical data type, so it describes qualitative characteristics or groups, with no order or rank between categories. Examples of nominal data include: Gender, ethnicity, eye colour, blood type 2017-09-22 Nominal data is a beneficial method used by researchers to get collect their responses for their surveys and used it in their study. It is cost-effective and not a time-consuming process.	{"url":"https://affarernjsphyp.netlify.app/73679/54561.html","timestamp":"2024-11-03T12:02:09Z","content_type":"text/html","content_length":"10323","record_id":"<urn:uuid:361cc866-51c9-47b9-b517-2edb05b11abe>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00141.warc.gz"}
Parallel implementations of SAMR When calculating the numerical solution to a partial differential equation, effciency in the use of computer resources is desired when creating a mesh. By adapting the mesh to have a higher resolution only in the areas where it is needed, instead of everywhere, both the memory and computational resources are used in a more efficient way. This paper examines some recent publications regarding the implementation of structured adaptive mesh refinement on parallel systems and where future research in this field might lead. 1 Introduction When solving numerical problems, especially partial differential equations (PDEs), the standard approach is to create a discretization, a mesh, of the domain of calculations. It is then possible to apply some numerical method, for example a finite difference method (FDM) or a finite element method (FEM), to solve the differential equation at hand. The accuracy and stability greatly depend on the mesh that is being used. In complex problems, the mesh might have to have a very fine resolution, meaning the step size in time or space must be very small. The simplest way to accomodate this is to use the same resolution over the whole domain, but this increases the memory demand and the computational complexity. If the mesh does not have to have as fine a resolution everywhere, this is a waste of resources. One method to help resort this problem is called Adaptive Mesh Refinement (AMR), which enhances the resolution of the mesh only where needed. AMR is increasingly being used in the scientific community on a large scale [2]. In this paper, structured AMR (SAMR) is discussed, which is adaptive mesh refinement on a structured grid, for example a Cartesian grid. SAMR is a choice method for effficient spatial discretization of multiscale computational problems [3]. Here, for each time step and for each region, an a priori estimate of the error is calculated. The regions with an error exceeding a certain threshold are then flagged for refinement. This is repeated recursively until sufficient accuracy is reached on the whole domain. Note that the spatial mesh may be different for different time steps. It is of course important The infinitive marker toto be able[/annotax] to do the SAMR algorithm in an efficient way, so that the method provides stable results. When implementing it on a parallel system, there are further complications, such as load balancing, minimizing communication and synchronization overheads, and partitioning the underlying grid hierarchies at run-time to expose all inherent parallelism. The main function of parallel computing is to distribute data and work load among processors. However , with SAMR, the workload constantly changes and we need some dynamic load balancing. Methods for this include, for example, the Recursive Coordinate Bisection method (RCB), further detailed in section 2. The next section will focus on describing, explaining and discussing different implementations of SAMR, with respect to different applications, and how various problems may arise and be dealt with. This information has been drawn from five articles published within the past two years. The final section presents conclusions about the information and makes predictions about where future research might lead. Discussions of ethical and societal aspects of this research are included as an appendix. 2 Applications and implementations The outline of this section is as follows: To start, (2.1) will detail some direct applications of SAMR, including the Navier-Stokes equations, the discrete Boltzmann equation and various applications in magnetohydrodynamics. In (2.2), related problems with SAMR in parallel settings, such as scaling the algorithm to a high number of cores and visualizing data generated with the help of SAMR, will be discussed. 2.1 Direct applications of SAMR SAMR is employed in a wide range of applications, and a few are presented in this section. One of them consists of the Navier-Stokes equations, which model fluid dynamics. For incompressible fluids, they take on the form with ∇ · (u) = 0. Here u is the velocity vector, p is the pressure, ρ is density, μ is dynamic viscosity, and g ≈ 9.81 represents gravitational accleration. While great Using the passive voiceprogress has been made to solve the Navier-Stokes equations numerically, the authors of [1] point out that[/annotax] : “…the required mesh resolution to accurately resolve small scale fluid motions…remains as a limitation” The same general meaning is in the paper [5] about the discrete Boltzmann equation for nearly incompressible single-phase flows: where f is the particle distribution function, t is time, λ is a relaxation parameter and e is the microscopic velocity. Although SAMR may be used to combat this computational limitation, the workload will as a result vary greatly in a parallel system and Verbs and the -s endingneeds to be fixed using some load balancing algorithm[/annotax] . One of these is the Recursive coordinate bisection method (RCB), which is used in [1]. The authors there implement a parallel version to solve two problems, one involving the flow around a static object and one involving a sliding lid cavity. The authors of [5], knowing that an AMR scheme has been tried before for the lattice Boltzmann method, point out that it was done with a quadtree structure. According to them, this is in itself inefficient for a parallel implementation involving many processing cores. The new approach uses a network of pointers to connect different grids in the mesh instead of a tree structure, which in turn makes it very easy to implement and execute in parallel. [5] Not all problems are well suited for parallel SAMR. The authors of [5] show that cavity flow simulations (also performed in [1]) are not efficient for AMR because a substantial amount of computation is used for the AMR routine itself, while thin shear layer and vortex-shedding simulations show good speedup when using AMR. Similarly , the author of [3] shows, through several simulations, that SAMR-based algorithms do not work well on certain types of problems related to hydrodynamics and magnetohydrodynamics. While it previously has been shown that SAMR is an efficient approach in these fields, and [3] reinforces this by showing efficient methods in two and three dimensions, the complexity of a curvilinear geometry prohibits certain types of experiments. Calculations in hydrodynamics and magnetohydrodynamic have usually been performed on cartesian grids and less frequently on cylindrical or spherical grids. One reason for this is because construction and implementation of algorithms in these geometries becomes much more complex [3]. The new approach, developed in the paper, was included into NIRVANA, a parallel library built using MPI for various problems related to magnetohydrodynamics, which the author of [3] maintains and develops. 2.2 Problems related to implementation of SAMR The various algorithms discussed in this paper, however theoretically fast, must also be implemented in an efficient way. This requirement is discussed in [2] in the framework of petascale and future exascale computers (with up to 100M cores). Exascale computers are expected to appear within the next decade [2] and it is of course important that numerical software using SAMR scale well in order to be useful on these future computers. When talking about scaling, we distinguish between two terms: Strong scaling : How the solution time varies with the number of processors for a fixed total problem size. Weak scaling : How the solution time varies with the number of processors for a fixed problem size per processor. In [2], different methods for refinement flagging and refinement creation are discussed in terms of how well they scale to larger systems. The authors perform numerical experiments for different algorithms related to SAMR for up to ≈ 99000 cores and use that to theoretically model strong and weak scaling for up to 100M cores. They emphasize that computing and communicating global metadata eventually starts to become a bottleneck and therefore that local algorithms are neccessary. This can be assumed to be true for the algorithms in [1, 3, 5] since this information is new and frameworks have not yet been updated to lessen their dependence on global metadata, according to the authors of [2]. Luckily, the same article also shows that grid creation for block-SAMR can be done without global metadata, in other words completely locally. It is not always enough to just calculate solutions. When trying to visualize data generated for example by a PDE solver, the increased complexity of the mesh made by SAMR creates problems also for visualization. To understand this, the reader first needs to be familiar with the concept of raycasting. The method of raycasting can be explained as follows: For each pixel on the screen, there is an imaginary ray from the eye of the observer into the virtual scene. Depending on what objects the ray encounters, the pixel it passed through will be coloured accordingly. Using standard visualization techniques like raycasting to datasets generated by SAMR is challenging because of less homogeneity in the structure of data. The authors of [4] present ideas to perform this graphics rendering on a parallel system, more specifically a graphical processing unit (GPU) which itself is a parallel computational device. They present two different methods, a “packing” approach and a method based on NVIDIA’s Bindless Texture extension for OpenGL. These were applied to large datasets to see how the rendering can be done efficiently not just in time but also in terms of memory usage and band-width, which may be more limited on weaker systems. Results show that the latter approach is well suited for datasets larger than the available GPU memory. While SAMR Verbs and the -s endingaims to decrease the memory usage by refining the computational mesh only where needed, the resulting datasets from the methods of [1, 3, 5] may still be very large, thus strengthening the support for the Bindless Texture method.[/annotax] The next section will draw some conclusions on the material presented in this section, together with some predictions on future research in this field as made by the authors of the articles cited. 3 Conclusions and future research All five articles indicate at least partially positive results for using SAMR in parallel environments for different applications. Preliminary results point to stable behaviour and second order of convergence for velocities when solving the Navier-stokes equations for incompressible fluids [1]. The proposed SAMR method in [5], not using a tree-type data structure, is easier to code and is also easy to execute in parallel compared to previous methods. The finite difference method used in [5] retains second order accuracy in time and the authors hint they will compare accuracy in space, as well as efficiency compared to more conventional Lattice Boltzmann Methods, in a future paper. For non-cartesian grids such as cylindrical and spherical grids , the SAMR framework works well in two and three dimensions [3], but details of the actual computation pose most of the problems, coupled with the non-rectangular geometry. The problems are according to the authors mainly due to the nonlocal character of the boundary conditions. Data generated by SAMR has also been shown to be possible to be rendered effectively on a parallel accelerator (such as a GPU) [4]. The packing approach outperforms the multi-pass algorithm and both methods enable straight-forward implementations of new techniques that can be executed completely on the GPU, which will increase performance as the number of shader cores increase, as it is projected to do [4]. Algorithms that utilize global metadata do not scale well in the strong or weak sense, as shown by [2]. That paper shows that block-SAMR (BSAMR) can be done completely locally. However , frameworks today still depend on global metadata. The authors of [2] push for further research that aims to lessen and remove this dependancy in various frameworks to make algorithms scale better, in preparation for future petascale and exascale machines. This will, in theory, benefit all SAMR applications (including the applications covered in [1, 3, 5]) on peta- and exascale machines appearing in the future. [1] Rafael Sene de Lima, et al.et al.[2] Parallel block-structured adaptive mesh refinement for incompressible Navier-Stokes equations. 14th Brazilian Congress of Thermal Sciences and Engineering [2] J. Luitjens, M. Berzins. Scalable parallel regridding algorithms for block-structured adaptive mesh refinement. Concurrency Computation: Pract. Exper. (2011): 23:1522-1537. [3] Udo Ziegler. Block-structured adaptive mesh refinement on curvilinear-orthogonal grids. SIAM Journal of Scientific Computing vol. 34, no. 3 (2012): C102-C121. [4] Ralf Kaehler, Tom Abel. Single-pass GPU-raycasting for structured adaptive mesh refinement data. SPIE Vol. 8654 865408-1 (2013). [5] Abbas Fakhari, Taehun Lee. Finite-difference lattice Boltzmann method with a block-structured adaptive-mesh-refinement technique. Physical rreview E89, 033310 (2014). 4 Appendix: Ethics and societal aspects It is rarely mentioned explicitly in scientific articles of computational science, but the researches performed usually have ethical aspects to them, both in how the research has been done but also how it is presented. Furthermore , research affects the society we all live in. Today, when our day-to-day life is filled with technology, this is perhaps more true than ever. This appendix will analyze some ethical and societal aspects of the articles discussed in this paper. Every paper is authored by more than one author, except [3]. While the latter is not neccessarily bad or even uncommon in the scientific community, it is perhaps easier, Pairseither by intent or by external pressure, to influence[/annotax] the outcome of the research when only one person is responsible. Another notable exception regarding authors is the paper [4] where the authors originate from a well known high-ranking university (Stanford). This should of course not influence the reception of the article, but perhaps it does. Only two, although different, applications are tested by the authors of [1], but they also conclude their results to merely be preliminary. For load balancing, they use the ZOLTAN library which is freely available. There are many authors to the article, which perhaps makes the likelihood of fraud less likely, as opposed to the single author in [3]. The main drawback to the paper is that we cannot easily recreate the results. The reason for the difficulty of recreating results stems from something all five articles have in common: Nowhere is the actual code specified, and even the details of the computer system used vary. There is no mention of system details or implementation specifics at all besides the number of cores in [1]. Other papers are not as restrictive. Even so, with just the computer system used specified, and varying levels of detail in the mathematical deduction in [1, 3, 5], it is difficult to recreate the authors’ implementations exactly. The hardware specified in [4], especially the graphics cards, are expensive but are supplied by the NVIDIA corporation. This probably leads them to have an interest in the actual results, but of course does not mean there is any actual influence. The reader should, however , keep this in mind seeing as how the result actually is positive for NVIDIA. Two different approaches are given in order to show which one is better. If the authors prefer one, this might influence which tests are run and presented and thus also influence the outcome and conclusions of the paper. Just as for the other papers, there is no example code given in [4] to test the new GPU rendering algorithms for other datasets. Even the datasets used in the paper have not been made publically available. Perhaps one could contact the author or the original supplier of the data to get access, but this possibility is not mentioned. The main point of [5] is that using a tree is an inefficient method. The authors show that their new method sometimes is useful, but not always, and thus put themselves in a very honest position presenting negative results. The timings of the numerical runs presented in Table IV [5] form the basis for the authors’ conclusion, but nowhere is it mentioned exactly how the timings are performed. This opens up questions: Is the current method ill-suited and would other timing methods yield worse results? Either way, the four different problems in the problems are diverse, but the authors themselves point out that their results are not universal because of the mixed results. The article itself is put into context and ideas for future research are mentioned. The authors of [2] look at up to 98304 cores and use this to make a mathematical model to make predictions for scalability up to 100M cores. Being forced to use a theoretical model is understandable, since there is no 100M core computer available today (2014). However , since this value is three orders of magnitude higher than the actual runs, it begs the question of whether or not the model is accurate. This is reflected in the paper as the authors use words like “should” and not “will”. The research does not affect anything today but points to where future research should go – towards removing global metadata dependencies. The provided data is said to be a universal result for all algorithms, but drawn from analysing only the two in the paper. Many numerical examples are run in [3] and the author points to future research by highlighting inefficiencies in his current approach. However , it is of course not known whether it is even possible to resolve the problem in this way. Maybe this method simply is inherently bad? Again, no code is provided, just the mathematical deduction. The reader only knows that the implementation uses MPI. References to many other code bases are done in the beginning which puts it into context and no one framework is “marketed”. Nearly everything covered by the articles cited in this paper consists of gradual improvements upon already existing technology, ranging from the applications of SAMR to Navier-Stokes equations [1] to visualizing data generated by the solution of any PDE [4]. It is in practice impossible to determine how these technologies will be applied in the future, and it is therefore unfair to hold the scientists behind the articles [1, 3, 4, 5] accountable for future events caused by this, especially since they are merely a few of many advancing their respective fields. The only major influence tracable to a specific article occurs perhaps in [2] which asserts that global metadata is inherently bad and frameworks must be revised that perform SAMR more locally. This assertion is made on the basis of the authors’ mathematical model and may turn out to be false. On the whole, the major deficiency of all the articles is the lack of code to actually reproduce the results, which seems to be not uncommon in this field.	{"url":"https://scriptor.sprakverkstaden.uu.se/en/texts/samr/","timestamp":"2024-11-10T23:49:02Z","content_type":"text/html","content_length":"123897","record_id":"<urn:uuid:012e3495-1207-4472-8da3-1b1d17e63a7d>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00670.warc.gz"}
Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter Cite as: A. Kehagias and A. Riotto [arXiv:1205.1523] We study the multield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal eld theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing in infationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point correlator and the collapsed limit of the four-point correlator. Despite the fact that the shape of the four-point correlators is not fixed by the symmetries of de Sitter, its exact shape can be found in the collapsed limit making use of the operator product expansion. By employing the fact that conformal invariance imposes the two-point cross-correlations of the light elds to vanish unless the elds have the same conformal weights, we are able to show that the Suyama-Yamaguchi inequality relating the coecients f[NL] of the bispectrum in the squeezed limit and τ[NL] of the trispectrum in the collapsed limit also holds when the light elds are intrinsically non-Gaussian. In fact, we show that the inequality is valid irrespectively of the conformal symmetry, being just a consequence of fundamental physical principles, such as the short-distance expansion of operator products. The observation of a strong violation of the inequality will then have profound implications for inflationary models as it will imply either that multifield inflation cannot be responsible for generating the observed fluctuations independently of the details of the model or that some new non-trivial degrees of freedom play a role during in inflation.	{"url":"https://cosmology.unige.ch/content/operator-product-expansion-inflationary-correlators-and-conformal-symmetry-de-sitter","timestamp":"2024-11-03T04:40:23Z","content_type":"text/html","content_length":"36993","record_id":"<urn:uuid:e2540919-8537-4c2e-a675-892efdecb8f0>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00649.warc.gz"}
Andrea Petracci, A 1-dimensional Component of K-moduli of Del Pezzo Surfaces November 29, 2022 @ 5:00 pm - 6:00 pm KST Fano varieties are algebraic varieties with positive curvature; they are basic building blocks of algebraic varieties. Great progress has been recently made by Xu et al. to construct moduli spaces of Fano varieties by using K-stability (which is related to the existence of Kähler-Einstein metrics). These moduli spaces are called K-moduli. In this talk I will explain how to easily deduce some geometric properties of K-moduli by using toric geometry and deformation theory. In particular, I will show how to construct a 1-dimensional component of K-moduli which parametrises certain K-polystable del Pezzo surfaces.	{"url":"https://ccg.ibs.re.kr/event/2022-11-29/","timestamp":"2024-11-13T19:19:02Z","content_type":"text/html","content_length":"132528","record_id":"<urn:uuid:ca68184c-077d-4c40-8400-9cd49a7888f0>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00857.warc.gz"}
Cross-listing in the OPL This is a part of the OPL master plan, but I thought it deserved its own post. It relates to revising the taxonomy (subject/chapter/section). The ideal from the start was that the taxonomy would be a "partition" of mathematics -- that every problem would belong in exactly one place. This is difficult because lines between areas can be blurry, but it was confounded by confusing a classification by topic with a classification by relevant course. Often, more than one mathematics course will cover the same topic. Our plan to deal with this has 2 parts. First, we stick to the original ideal of trying to partition problems by mathematical topic. Then, we build into the OPL/library browser the ability to cross-list problems. Cross-listing would be at the level of sections. For example, in the first pass, we expect to have "algebra" (which includes college algebra) and "trigonometry" as subjects, but do not forsee having "precalculus" as a subject. We then use the cross-listing feature to take sections from algebra and trig to make a precalculus subject. To the user (the instructor), this will be transparent -- it will be as if those problems were tagged to appear in two different places. The change is in implementation where we are picking something we think will be easier to maintain.	{"url":"https://webwork.maa.org/moodle/mod/forum/discuss.php?d=3139","timestamp":"2024-11-07T12:42:43Z","content_type":"text/html","content_length":"66081","record_id":"<urn:uuid:f74da99b-e8df-4aa3-9ce1-281f65f62238>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00359.warc.gz"}
Particles Size and Composition in Mediterranean Countries, Geographical Variability and Short-term Health Effects Content extract Source: http://www.doksinet MED-PARTICLES Project 2011-2013 Under the Grant Agreement EU LIFE+ ENV/IT/327 Particles size and composition in Mediterranean countries: geographical variability and short-term health effects Particles size and composition in Mediterranean countries: geographical variability and short-term health effects MED-PARTICLES ACTION 10. Health effects of PM10, coarse particles (PM2.5-10) and fine particles (PM25) on daily cause-specific mortality: city-specific results and meta-analysis Summary: Protocol to define the standardized methodological steps to investigate the association between mortality and PM concentrations, with regards to different causes, age groups and different PM fractions. -------------------------------------------------------------------------- 1 Source: http://www.doksinet BACKGROUND The knowledge on the effects of air pollution on human health have been growing in last decades as the result of the enormous scientific effort to design and conduct large epidemiological studies. At present, we rely on a growing consolidated knowledge that airborne particles with a diameter < 10 μm is the most important airborne pollutant associated with the short-term effects on human health, while fine particles (PM2.5) is the fraction responsible for the most severe health effect There are several additional aspects that we understand in a more comprehensive way. We know that coarse fraction (PM 2.5-10μm) has a predominantly natural origin while the fine fraction is produced by combustion (vehicles, industries and electric power plants). We know that traffic and heating are the most relevant sources in determining the increases of mortality and morbidity due to respiratory and heart diseases. We understand the shape of the concentration-response function and the existence of no-effects threshold between concentration of airborne particles and health effects. We know that particles are able to increase not exacerbations of diseases, but also mortality as well as the onset of respiratory and cardiovascular diseases. We understand that the oxidative stress is the most important mechanism of damage at cellular level, but inflammation is not the only consequence, since increasing blood coagulability, heart autonomic functions, and the atherosclerosis processes are also influenced by air pollution. Notwithstanding the growing of epidemiological research, scanty data are available in the European Mediterranean countries, especially on PM2.5 and PM25-10, so that multi-center studies on the shortterm health effects of fine and coarse fractions on mortality and morbidity are virtually non-existent Objective The objective of this protocol is to define the methodological steps to investigate the association between mortality outcomes and PM concentrations, with regards to: 1) different causes of mortality; 2) different PM fractions; 3) different modeling choices of confounding adjustment. The analyses will be conducted within each city participating the Med-Particles project, and then pooled estimates will be derived with random-effects meta-analytical procedures. Study population and outcomes Data on daily deaths will be collected for at least 10 cities from Italy, Greece, Spain and France. For each city and for each day of the study period, data on daily deaths will be collected with regards to the population resident of the city that died in the city. For each city, daily counts of deaths will be available, for the following causes. We distinguish two groups of outcomes: primary outcomes, on which all analyses will be conducted, and secondary outcomes, in italics, on which only selected analyses will be carried out: 2 Source: http://www.doksinet Cause of death ICD-9 code Natural causes 001-799 A00 – R99 Diabetes 250 E10 – E14 Cardiovascular diseases 390-459 I00 – I99 390-429 I00 – I52 Acute coronary events 410-411 I21 – I23 Conduction disorders 426 I44 – I45 Arrhythmias 427 I46 – I49 Heart failure 428 I50 430-437 I60 – I68 460-519 J00 – J99 466, 480-487 J09 – J18, J20 – J22 Acute bronchitis, bronchiolitis, unsp. LRTI 466 J20 – J22 Pneumonia 480-486 J12 – J18 Influenza 487 J09 – J11 490-492,494,496 J40 - J44, J47 Cardiac diseases Cerebrovascular diseases Respiratory diseases Low respiratory tract infections (LRTI) Chronic obstructive pulmonary disease (COPD) ICD-10 code Further details are reported in the protocol for data collection on health endpoints, Action 6. For the primary mortality outcomes the epidemiological analysis will be implemented for all ages as well stratified for deaths among those above and below 75 years of age for deaths from natural causes and cardiovascular diseases and for respiratory deaths among those above 75 years. For all secondary mortality outcomes the analyses will be done only for all ages except for COPD that will be done only for the age group above 65 years of age. For the investigation of effect modification by sex we will analyze only deaths from natural causes, for the age groups outlined above. Environmental variables For each city, daily average exposures to PM 2.5 , PM 10 and PM 25-10 will be derived from monitor-specific data, as detailed in the protocol for data pooling, Action 7. In addition, data are available for each city and day on other air pollutants (NO2, O3, CO, O3) and meteorological parameters (temperature, humidity, barometric pressure). Other confounders 3 Source: http://www.doksinet Data have been collected on other daily variables, useful for confounding adjustment in the PMmortality association. They include influenza epidemics and indicator variables relating to population dynamics during holidays and summer. Further details on environmental variables and other confounders are reported in the protocol for environmental data collection, Action 3. Methods a) Methodological framework The PM-mortality association will be investigated using Poisson regression models allowing for overdispersion (using quasi(poisson) in R). The model is of the form: log E [Yt]=β 0 + b * PM t + confounders where E[Y t ] is the expected value of the Poisson distributed variable Y t indicating the daily count of unscheduled hospital admissions for a specific disease on day t, with Var(Y t )= φE[Y t ], φ being the overdispersion parameter, PM t is the concentration of particles (for a specific fraction) on day t, and “confounders” include an extensive list of confounding factors, as described below. b, the parameter of interest, is the adjusted log(relative risk) of hospitalization for a unit increase in PM. b) Confounder list The confounders are chosen a priori based on past knowledge and preliminary exploratory analyses. They include the following (see the protocol of statistical analysis, Action 9, for further details): - Time-trend. In order to take into account long-term as well as seasonal time-trend, a penalized regression spline of day of the death will be fitted. Natural cubic splines will be used as basis functions for the penalized regression splines. We will choose 8 effective degrees of freedom (edfs) per calendar year of available data to control for seasonality. Two sensitivity analyses will be performed: 1) one model will use the time series approach with penalised splines for seasonality control (as the main model) but with the final edfs for time trend based on the choice of the smoothing parameter for time that minimizes the absolute value of the sum of the partial autocorrelations (PACF) of the residuals from lags 1 to 30; 2) a three-way interaction between year, month and day of the week will be fitted as alternative to the spline term + day of the week adjustment, since this approach has been shown to be equal to the case-crossover design, with “time-stratified” strategy for controls selection; 4 Source: http://www.doksinet - Air temperature. It will be adjusted for with two natural splines, in order to control for both high and low temperatures at different reference lags: lag 0 for high summer temperatures, lag 1 or lag 1-6 for low winter temperatures. The choice between lag 1 and lag 1-6 for cold temperatures adjustment will be based at the city level on the lag which minimizes AIC. For both natural splines, 3 degrees of freedom will be fixed a priori at quartiles of the city-specific distribution. - Relative humidity. It will be adjusted for with a linear term at lag 0 - Influenza epidemics. The data on influenza should preferably be daily counts ie number of cases When there are weekly or biweekly data on number of cases then daily values should be calculated by division. If the only available information is the existence of an epidemic, then a variable taking the value 1 for epidemic days and 0 otherwise should be used. In case there are no influenza data available we will use the APHEA-2 method for influenza control, including a dummy variable taking the value of 1 when the 7-day moving average of the respiratory mortality was greater than the 90-th percentile of its city-specific distribution. In this case, since influenza definition is based on the distribution of respiratory mortality, we will include the influenza dummy variable only when analyzing non respiratory mortality. In all other influenza definitions, instead, it will be included for all study outcomes, including respiratory ones. - Population dynamics during holidays and summer. This phenomenon will be adjusted for with indicator variables for holidays and summer population decreases, as described in the protocol for environmental data collection, Action 3. c) Lag structure of exposure According to the EPIAIR protocol, for each primary outcome the following three steps will be implemented: a) cubic polynomial distributed lag models and single-lag models from lag 0 to lag 6 to visually examine the lag structure of the association between PM exposures and health outcomes; b) three cumulative lags chosen a priori to represent immediate effects (lag 0-1), delayed effects (lag 2-5) and prolonged effects (lag 0-5); c) for each combination of exposure/outcome, choice of one of these three lags as the reference lag, based on the meta-analytic polynomial distributed lag shape, the metaanalytic estimates of the a priori cumulative lags, and the heterogeneity among city-specific estimates. This choice is relevant to identify the lagged exposure to be used for additional analyses as bi-pollutant models, sensitivity analyses on time-trend and temperature adjustment, and analysis of the secondary outcomes. In particular, for each secondary outcome the referent lag from the primary outcome of the same group will be applied (for example, if the relevant lag for PM2.5 and cardivascular mortality is 0-1, the same lag is applied to the secondary outcomes “Acute coronary events”, “Conduction disorders arrhythmias” and “Heart failure”). d) Two-pollutant models 5 Source: http://www.doksinet For each primary outcome, and for PM2.5 and PM25-10, we will run two-pollutant models, including NO2 and ozone in turn. Special care will be given to the inclusion of NO2 in PM25 models if there is high correlation (r>0.7) In addition, two pollutant models will be run with PM25 and PM25-10 as well. Concerning the lag chosen for two-pollutant models, the two pollutants will be put in the model at the same lag, equal to the relevant lag for the PM exposure. For example, if from the analysis of the lag structure there is evidence that the most relevant lag for PM2.5 and cardiac mortality is 0-1, the twopollutant models for PM25 will be run by adding both PM25 and the other pollutant (NO2, O3 or PM2.5-10) in the model, both at lag 0-1 e) Meta-analytical techniques Once city-specific effect estimates are obtained, they will be meta-analyzed with random-effects models. For each meta-analytical estimate, a test for heterogeneity will be performed and corresponding p-value reported, together with the I2 statistic, which represents the proportion of total variation in effect estimates that is due to between-cities heterogeneity. Conclusions: The protocol defines the methodological steps to investigate the association between mortality outcomes and PM concentrations, with regards to different causes of mortality, different PM fractions and different modeling choices of confounding adjustment. Mortality data of resident people that died in the city will be collected for 10 cities form Italy, Greece, Spain and France The analyses are conducted within each city participating the Med-Particles project, and then pooled estimates are derived with random-effects meta-analytical procedures. 6	{"url":"https://doksi.net/en/get.php?lid=31715","timestamp":"2024-11-09T16:28:04Z","content_type":"text/html","content_length":"33455","record_id":"<urn:uuid:675f7da4-e5dd-4d57-b3d8-2a4a88564094>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00432.warc.gz"}
307 Test Template This is the template for students making exams for MAT 307 at SUNY Oswego, taught by Bonita Graham in Spring 2016. \documentclass[11pt]{exam} \RequirePackage{amssymb, amsfonts, amsmath, latexsym, verbatim, xspace, setspace, mathrsfs} \usepackage{amsmath,amsthm,amssymb,amsfonts, hyperref, color, graphicx} \ RequirePackage{tikz, pgflibraryplotmarks} \usepackage[margin=1in]{geometry} \usepackage{graphicx} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newenvironment {problem}[2][Problem:]{\begin{trivlist} \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2}]}{\end{trivlist}} \newenvironment{claim}[2][Claim:]{\begin{trivlist} \item[\hskip \ labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2}]}{\end{trivlist}} \newenvironment{defn}[2][Definition:]{\begin{trivlist} \item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2}]} {\end{trivlist}} % Here's where you edit the Class, Exam, Date, etc. \newcommand{\class}{Math 307} \newcommand{\term}{Spring 2016} \newcommand{\examnum}{Suggested Exam 1} \newcommand{\examdate}{Due: 3/3/16} \newcommand{\timelimit}{now until then} % For an exam, single spacing is most appropriate \singlespacing % \onehalfspacing % \doublespacing % For an exam, we generally want to turn off paragraph indentation \parindent 0ex \begin{document} % These commands set up the running header on the top of the exam pages \pagestyle{head} \firstpageheader{}{}{} \runningheader{\class}{\examnum\ - Page \thepage\ of \numpages}{\examdate} \runningheadrule \begin{flushright} \begin{tabular}{p{2.8in} r l} \textbf{\class} & \textbf{Name:} & \makebox[2in]{\hrulefill}\\ \textbf{\term} &&\textbf{\ examnum}\\ \textbf{\examdate} && \textbf{Time Limit: \timelimit} \\ \end{tabular}\\ \end{flushright} \rule[1ex]{\textwidth}{.1pt} \begin{minipage}[t]{3.7in} \vspace{0pt} \begin{itemize} \item \textbf {DO NOT open the exam booklet until you are told to begin. You should write your name and section number at the top and read the instructions.} \vfill \item Organize your work, in a reasonably neat and coherent way, in the space provided. If you wish for something to not be graded, please strike it out neatly. I will grade only work on the exam paper, unless you clearly indicate your desire for me to grade work on additional pages. \item You may use any results from class, homework or the text, but you must cite the result you are using. You must prove everything else. \item You needn't spend your time rewriting definitions or axioms on the exam. \end{itemize} \end{minipage} \hfill \begin{minipage}[t]{2.3in} \vspace{0pt} %\cellwidth{3em} \gradetablestretch{2} %Uncomment this line to make the table display 100 as the total no matter what. This is good for tests with an ommit question. %\settabletotalpoints{100} \vqword{Problem} \addpoints % required here by exam.cls, even though questions haven't started yet. \gradetable[v]%[pages] % Use [pages] to have grading table by page instead of question \end{minipage} \begin{itemize} \item You may use the text, my class notes and/or any notes and study guides you have created. You may use a calculator. You may not use a cell phone or computer. \item When you have completed your test, hand it to me and go have a great weekend! \ item There is a single bonus problem at the end of the test. It would be best to work first on the main test as this problem is only worth 5 points and will be graded strictly. \end{itemize} \newpage \begin{questions} \addpoints \question[10] This is a 10 point question. I can change the number of points in the square brackets and it will add up automatically for me. \question This is a question with parts. I can set the amount of points for each part and it will add them together to put on the front page. \begin{parts} \part[5] part one \vfill \part[8] another part \vfill \part[5] I put vfills in between questions to fill the space. They will automatically take up all the space and divide it evenly between all the vfills. Don't forget to put on at the end of the page! \vfill \end {parts} \newpage \addpoints \question[18] Every time you start a new page, you need to tell it to add points. I don't know why. \vfill \bonusquestion[5] This is a bonus question. It has points but they are not added on the cover page. \vfill \end{questions} \end{document}	{"url":"https://tr.overleaf.com/latex/templates/307-test-template/cqgqjtzqzwfs","timestamp":"2024-11-07T16:10:41Z","content_type":"text/html","content_length":"40768","record_id":"<urn:uuid:397688d2-d185-42e4-ba2a-58e2f61ab84b>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00029.warc.gz"}
On the construction of converging hierarchies for polynomial optimization based on certificates of global positivity In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity. At their heart, these hierarchies rely crucially on Positivstellensätze from the late 20th century (e.g., due to Stengle, Putinar, or Schmüdgen) that certify positivity of a polynomial on an arbitrary closed basic semialgebraic set. In this paper, we show that such hierarchies could in fact be designed from much more limited Positivstellensätze dating back to the early 20th century that only certify positivity of a polynomial globally. More precisely, we show that any inner approximation to the cone of positive homogeneous polynomials that is arbitrarily tight can be turned into a converging hierarchy of lower bounds for general polynomial minimization problems with compact feasible sets. This in particular leads to a semidefinite programming–based hierarchy that relies solely on Artin’s solution to Hilbert’s 17th problem. We also use a classical result from Pólya on global positivity of even forms to construct an “optimization-free” converging hierarchy for general polynomial minimization problems with compact feasible sets. This hierarchy requires only polynomial multiplication and checking nonnegativity of coefficients of certain fixed polynomials. As a corollary, we obtain new linear programming–based and second-order cone programming–based hierarchies for polynomial minimization problems that rely on the recently introduced concepts of diagonally dominant sum of squares and scaled diagonally dominant sum of squares polynomials. We remark that the scope of this paper is theoretical at this stage, as our hierarchies—though they involve at most two sum of squares constraints or only elementary arithmetic at each level—require the use of bisection and increase the number of variables (respectively, the degree) of the problem by the number of inequality constraints plus three (respectively, by a factor of two). All Science Journal Classification (ASJC) codes • General Mathematics • Computer Science Applications • Management Science and Operations Research • Convex optimization • Polynomial optimization • Positivstellensätze Dive into the research topics of 'On the construction of converging hierarchies for polynomial optimization based on certificates of global positivity'. Together they form a unique fingerprint.	{"url":"https://collaborate.princeton.edu/en/publications/on-the-construction-of-converging-hierarchies-for-polynomial-opti","timestamp":"2024-11-08T02:20:25Z","content_type":"text/html","content_length":"56316","record_id":"<urn:uuid:b90c2805-e48f-43c1-a203-853c040714f6>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00153.warc.gz"}
The Null Space ~ DAX Calculated Columns with EARLIER The choice to use calculated in columns in DAX often comes down to model performance. Experienced developers will prefer coding dynamic solutions to adding unnecessarily to the model’s memory Then there are times when judicious use of calculated columns can save hours of aggravation and massively boost performance. At other times, things may simply not be possible without a well placed calculated column. Introducing EARLIER EARLIER is an interesting function, it’s very simple, but when we come understand this function, we are beginning to understand DAX. Although EARLIER has mostly been superseded with the addition of variables, it remains a worthwhile function to know for calculated columns. We will look at a simple example from the Contoso database available here. Then explain what this function is actually doing, and why it works. Adding a Column We have deleted the relationship between Channel and the Sales table. Instead of having this as a dimension, we will embed the values into the fact table with help from EARLIER. Let’s click on the Sales table and add a new calculated column. Next we will add the measure below. ChannelName = CALCULATE(LASTNONBLANK(Channel[ChannelName],1), Channel[Channel] = EARLIER(Sales[channelKey])) Like magic, ChannelName is now embedded in our fact table. A function like MAX, MIN, or AVERAGE would be also be fine to use here depending what we plan to return. In this case we have used LASTNONBLANK to return the last non-blank value from the column, where the expression is true. Since we specify “1” for the expression, that effectively means out of all existing column values. Note that LASTNONBLANK will traverse in the original order that data was sorted when it was loaded so sometimes we would have to narrow the field with additional filter terms when using this Other Use Cases A real use case for this might be if you have data that is the wrong granularity to key to a table. Another might be if we want to summarize customer baskets. Still another is where we have a list of promotions with end dates, but no date key and we need to somehow indicate which products were on offer. Below is a measure that will calculate a cumulative sum of Contoso Sales for each date, we don’t have to embed this into a fact table, it could be a calculated table used as a helper for DailyContoso = CALCULATE(SUM(Sales[SalesAmount]), Sales[DateKey] = EARLIER(Sales[DateKey]), 'Product'[BrandName] = "Contoso") The $304.12 value above is the sales amount for Contoso on March 22, 2013. It will only be embedded on lines containing Contoso, and each date will have its own cumulative total. To understand why this works we need understand a bit about DAX evaluation contexts. DAX Contexts DAX has two primary types of evaluation context. 1. Row Context: An algorithm parses a table one row at a time. 2. Filter Context: Calculations are evaluated with the specified filters engaged. When we specify a calculated column the formula engine will traverse each row in the table, in sequence, and perform our calculation. When we use CALCULATE that will tell DAX to exit the row context and evaluate the expression on the table, after applying the filters we have specified. With CALCULATE the sum without filters will end up being the entire column from the bottom to the top, that is a complete unconstrained sum of the column. This is where EARLIER comes into play. When we use this function we tell the DAX formula engine to go back to the context it just exited when we called CALCULATE, that is the original row context. The column name passed to EARLIER then tells the formula engine to find the value, in the row it was just iterating. In our original example, we asked EARLIER to return the value of ChannelKey. ChannelName = CALCULATE(LASTNONBLANK(Channel[ChannelName],1), Channel[Channel] = EARLIER(Sales[channelKey])) In the above example, we are filtering the column Channel[Channel], which is the foreign key, to be only the value of the ChannelKey in the current row context. Then we return the last value that is not blank, and that becomes the new value for the row in the calculated column. There is a trade off between performance, and model memory, and recognizing when these type of techniques are appropriate is an important part of PowerBI development. We can often achieve performance boosts with judicious use of calculated columns, or tables, while still adhering to good design principals. EARLIER captures the spirit of DAX language, and contemplating this useful little function can help us gain a better understanding of evaluation contexts in PowerBI. Russo, Marco; Ferrari, Alberto. The Definitive Guide to Dax, 2nd Ed. Microsoft Press, 2019.	{"url":"https://data-science.io/dax-calculated-columns-with-earlier/","timestamp":"2024-11-06T04:01:12Z","content_type":"text/html","content_length":"78063","record_id":"<urn:uuid:bf5cf3ac-8ccf-424c-a8c4-80c8e91e170e>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00101.warc.gz"}
MM to Fraction Conversion Chart [Fraction to MM Chart] Sometimes it requires knowing the fraction to mm conversion chart for various purposes. That’s why I just added an ultimate convert fraction to mm chart. However, now you can do your desired work with this chart. If you’ve ever done any woodworking, you’ve probably heard of fractions and millimeters. In some cases, you may even have to convert between them. So, what is 1 mm fraction? Convert Fractions to MM 2023 Making calculations using fractions can be a helpful tool in understanding measurements and understanding the metric system. Knowing the fractional form of a millimeter measurement is an important tool for anyone using metric units. Millimeters to fractions chart Fractions Millimeters 1/64 0.396 1/32 0.793 3/64 1.19 1/16 1.587 5/64 1.984 3/32 2.381 7/64 2.778 1/8 3.175 9/64 3.571 5/32 3.968 11/64 4.365 3/16 4.762 13/64 5.159 7/32 5.556 15/64 5.953 1/4 6.35 17/64 6.746 9/32 7.143 19/64 7.54 5/16 7.937 21/64 8.334 11/32 8.731 23/64 9.128 3/8 9.525 25/64 9.921 13/32 10.318 27/64 10.715 7/16 11.112 29/64 11.509 15/32 11.906 31/64 12.303 1/2 12.7 33/64 13.093 17/32 13.493 35/64 13.89 9/16 14.287 37/64 14.684 19/32 15.081 39/64 15.478 5/8 15.875 41/64 16.271 21/32 16.668 43/64 17.065 11/16 17.462 45/64 17.859 23/32 18.256 47/64 18.653 3/4 19.05 49/64 19.446 25/32 19.843 51/64 20.24 13/16 20.637 53/64 21.034 27/32 21.431 55/64 21.828 7/8 22.225 57/64 22.612 29/32 23.018 59/64 23.415 15/16 23.812 61/64 24.209 31/32 24.606 63/64 25.003 1 25.4 1 1/4 31.5 1 1/2 37.5 1 3/4 45 2 1/2 53 3 1/2 90 MM to Fractions How to convert millimeters to fractions Check out my 24 years of Woodworking database HERE Adding fractions to millimeters can be tricky, but with a little practice it can be a breeze. To convert between the two, divide the number of millimeters by 10 then multiply that number by 2 or 3 (depending on the fraction you’re looking to convert to). For example, if someone tells you they have 100 mm nails, you would say their nails are 500 mm in length. If someone tells you they have 5 mm nails, you would say their nails are 0.50″ in size. Remember, millimeters and fractions are two different units of measurement, so make sure you know which one you’re using before you start What is mm to fraction? Need to convert between millimeters and fractions? Mm to fraction is the perfect conversion tool for you! It provides an explanation for why the fractional equivalent was created that way, making it easier for you to understand. Simply enter the value you want in mm (for example 3), and the value that needs to be converted (in this case 12), and click on the button next to it. The program will then display the fractional equivalent of both values as well as an explanation for why it was created that way! So, whether you need to measure something smaller than 1 inch, or want to divide one number by another number in a different format, mm to fraction is the perfect conversion tool for you. How many inches in a millimeter To convert fractions to millimeters, take the numerator (top number) and multiply it by 100, then divide the result by the denominator (bottom number). For example, if someone tells you 3 inches in a millimeter, you would reply with 300/10 = 3.333 mm. What is 2.5 mm in Fractional? 2.5 millimeters is a decimal value of length, a common measurement of size in the metric system. To work out the fractional value of this, you must look at the relationship between millimeters and fractional parts of an inch. As 1 inch equals 25.4 millimeters, we can use this value to find the fractional equivalent of 2.5mm. The answer to “What is 2.5 mm in Fractional” is 0.098 inches. To find this, we first divide 2.5mm by 25.4(the conversion factor from mm to inches). This gives us 0.0984. To turn this decimal value into a fractional measurement, we will round the number up to two decimal places, which gives us 0.10. When written as a fraction, this is 10/100. This can be reduced further by dividing the numerator and denominator with 2, which gives us a fraction of 5/50 or 0.098 inches. So there you have it: 2.5mm is equal to 0.098 inches in fractional form. Converting between metric and imperial measurement systems is an invaluable skill to have, and you should always make sure to use the correct conversion when performing calculations. What is 1 mm fraction? Simply put, 1 millimeter (mm) is equal to 1/25 of an inch. It’s part of the metric system and is used to measure small lengths, particularly in millimeters to inches, centimeters to inches, and millimeters to centimeters. So, 1 mm is a very small measurement, just about the size of a block of text. When we talk about fractions, we’re referring to the same measurements but instead of measuring in millimeters, we use fractions of an inch. This is particularly helpful for more precise measurements, such as when working with different sizes of wood. For example, if you have a piece of wood that is 2 and 3/16 inches thick, you’ll want to know what that equals in mm. To do this, you simply multiply 2.1875 by 25. This will give you 54.6875 mm, making it much easier to understand the measurements associated with the wood. Converting millimeters to fractions of an inch is also helpful when you need to make sure you have the right parts or supplies. For example, if you’re ordering screws, you’ll need to make sure you’re ordering screws with a 1/4-inch diameter, which equals 6.35 mm. What is 7 millimeters as a fraction? So the question at hand is: what is 7 millimeters as a fraction? The answer to this question is pretty straightforward: 7 millimeters is equal to 7/1, or 7 parts out of 1 whole. To make it more useful, you can reduce the fraction to its simplest form: 7/1 can be simplified to 7/1, or one whole part. When working with fractions, it’s important to remember that fractions typically represent parts of a larger whole, so it’s important to express the fraction in terms of the whole. In this case, the 7/1 fraction can be expressed as 7/1000, or seven out of one thousand. This shows the relation of 7 millimeters to the whole, where 7 millimeters is a very small part of a larger whole. It’s also helpful to remember that when dealing with fractions, the larger the denominator is, the smaller the fraction is. Therefore, 7/1000 is much smaller than 7/1, meaning that 7 millimeters is an incredibly small part of the larger whole. What is 8 mm in a fraction? The key to converting millimeters to fractions is to understand the metric system and multiply by 10, 100, 1000, and so on as necessary. In the case of 8 mm, it can be converted into a fraction by taking the ‘milli’ component out and multiplying it by 100. In other words, 8mm is the same as 0.8, so the fraction formula is 0.8/1, which simplifies to 8/10. Put simply, 8 mm is equivalent to the fraction 8/10. This means that an object with a length of 8 mm is the same length as 8 out of 10 parts from one meter of length. It may also be helpful to think of 8 mm as five and a half inches, which is close to 8/10 of an inch, for mental calculations. It is possible to convert any measurement from millimeters to fractions simply by multiplying the number of millimeters by 100, and then dividing it by 1, creating a fractional representation. Frequently Asked Questions History of using Milimeters It is interesting to note that millimeters were used as a way of measurement dating back to ancient times. The ancient Romans used a unit of measurement called the ‘millem’ which translates to millimeter. It is also believed that the French were the first to introduce the metric system in Europe in the 1600s. What is the best way to measure distances in fractional units? There is no one definitive answer to this question. Some common methods of measuring distances in fractional units include using centimeters, millimeters, inches, and decimal yards. Are there any other benefits to being able to convert between these two units of measurement? There are a few benefits to being able to convert between these two units of measurement. For one, it can make calculations and comparisons easier. Additionally, it can help to ensure that measurements are accurate. Why is it important to be able to convert between millimeters and fractions? It is important to be able to convert between millimeters and fractions because millimeters are a common distance unit in the world and fractions are a common unit of measurement for smaller Thanks for reading! In this blog post, we will be discussing how to convert millimeters to fractions and fraction to mm. We hope that this blog was helpful and that you will find the information useful. If you have any questions or comments, please feel free to leave them below. We would love to hear from you!	{"url":"https://tedwoodplans.com/mm-to-fraction-conversion-chart/","timestamp":"2024-11-02T20:13:57Z","content_type":"text/html","content_length":"104562","record_id":"<urn:uuid:3af59807-c537-4bfa-8096-eb3ddb2ac12a>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00248.warc.gz"}
crystl (c48b1) Calculations on Crystals using CHARMM The crystal section within CHARMM allows calculations on crystals to be performed. It is possible to build a crystal with any space group symmetry, to optimise its lattice parameters and molecular coordinates and to carry out a vibrational analysis using the options. \| Syntax of the CRYSTAL command \| A brief description of each command \| Sample testcases \| Background and implementation [Syntax CRYStal command] CRYStal [BUILd_crystal] [CUTOff real] [NOPErations int] [NAMIng] [C001 ] [DEFIne xtltyp a b c alpha beta gamma] [PHONon] [NKPOints int] [KVECtor real real real TO real real real] [READ] [CARD UNIT int] [PHONons UNIT int] [PRINt] [PHONons] [FACT real] [MODE int THRU int] [KPTS int TO int] [WRITe] [CARD UNIT int] [PHONons UNIT int] [VIBRations] [MODE int THRU int] [UNIT int] xtltyp ::= { CUBIc } { TETRagonal } { ORTHorhombic } { MONOclinic } { TRIClinic } { HEXAgonal } { RHOMohedral } { OCTAhedral/trnc} { RHDO } a b c alpha beta gamma ::= (six real numbers) The crystal module is an extension of the image facility within the CHARMM program. All crystal commands are invoked by the keyword CRYStal. The next word on the command line can be one of the following : Build - builds a crystal. Define - defines the lattice type and constants of the crystal to be Free - clear the crystal and image facility. Phonon - calculates the crystal frequencies for a single value or a range of values of the wave vector, KVEC. Print - prints various crystal information. Read - reads the crystal image file. Vibration - calculates the harmonic crystal frequencies when the wave vector is the zero vector. Write - writes out to file various crystal information. A brief description of each command follows. 1. Crystal Build. A crystal of any desired symmetry can be constructed by repeatedly applying a small number of transformations to an asymmetric collection of atoms (called here the primary atoms). The transformations include the primitive lattice translations A, B and C which are common to all crystals and a set of additional transformations, {T}, which determines the space group symmetry. The Build command will generate, given {T}, a data structure of all those transformations which produce images lying within a user-specified cutoff distance of the primary atoms. The data structure can then be used by CHARMM to represent the complete crystal of the system in subsequent calculations. The symmetry operations, {T}, are read from the lines following the Crystal Build command. The syntax of the commmand is : Crystal Build Cutoff <real> Noperations <int> [NAMIng] ... <int> lines defining the symmmetry operations. The Cutoff parameter is used to determine the images which are included in the transformation list. All those images which are within the cutoff distance are included in the list. Note: The distance test is done based on the atoms that are currently present and their symmetric representation. To generate a crystal file from a box with a single atom at the center, the cutoff value will nee to be larger than the box dimensions. If the box is filled with water and only nearest neighbor cells are desired, then the cutoff distance should be comparable to the CUTIM value » images Update.) or the CUTNB value » nbonds Syntax.). There is no limit to the number of transformations included in the lists as they are allocated dynamically, but having too many will slow the image update step. The crystal symmetry operations are input in standard crystallographic notation. The identity is assumed to be present so that (X,Y,Z) need not be specified (in fact, it is an error to do so). For example, a P1 crystal is defined by the identity operation and so the input would be Crystal Build .... Noper 0 whilst a P21 crystal would need the following input lines : Crystal Build .... Noper 1 A P212121 crystal is specified by Noper 3 It should be noted that in those cases where the atoms in the asymmetric unit have internal symmetry or in which a molecule is sited upon a symmetry point within the unit cell not all symmetry transformations for the crystal need to be input. Some will be redundant. It is up to the user to check for these cases and modify the input accordingly. The NAMIng option provides unique 8 character image transformation names based on symmetry operators, instead of the old names C001, C002,... If you want the old naming convention, then use the C001 keyword. With the new naming convention, image names look like: Z0N1P2R3 where "N" is for negative, "P" is for positive, "Z" is for zero, and "R" is for rotation number. Thus transformation the transformation Z0N1P2R3 is for a zero box shift in the A-direction, a -1 box shift in the B-direction, and +2 boxes in C, while using the 3rd rotation operator. The first rotational operator is always "no rotation". 2. Crystal Define. The define command defines the crystal-type on which calculations are to be performed. It is usually the first crystal command that is specified in any job using the crystal facility. It has the format : Define lattice-type a b c alpha beta gamma The input lattice parameters are checked against the lattice-type to ensure that they are compatible. Nine lattice types are permitted. They are listed below along with any restrictions on the lattice parameters : CUBIc - a = b = c and alpha = beta = gamma = 90.0 degrees. (example: 50.0 50.0 50.0 90.0 90.0 90.0 ) (volume = a*3) (degrees of freedom = 1) TETRagonal - a = b and alpha = beta = gamma = 90.0 degrees. (example: 50.0 50.0 40.0 90.0 90.0 90.0 ) (volume = ca*2) (degrees of freedom = 2) ORTHorhombic - alpha = beta = gamma = 90.0 degrees. (example: 50.0 40.0 30.0 90.0 90.0 90.0 ) (volume = cba) (degrees of freedom = 3) MONOclinic - alpha = gamma = 90.0 degrees. (example: 50.0 40.0 30.0 90.0 70.0 90.0 ) (volume = cbasin(beta) ) (degrees of freedom = 4) TRIClinic - no restrictions on a, b, c, alpha, beta or gamma. (example: 50.0 40.0 30.0 60.0 70.0 80.0 ) (volume = cbasqrt(1.0 - cos(alpha)2 - cos(beta)2 - cos(gamma)2 + 2.0cos(alpha)cos(beta)cos(gamma)) ) (degrees of freedom = 6) HEXAgonal - a = b, alpha = beta = 90.0 degrees and gamma = 120.0 (example: 40.0 40.0 120.0 90.0 90.0 120.0 ) (volume = sqrt(0.75)ca2 ) (degrees of freedom = 2) RHOMbohedral - a = b = c ; alpha=beta=gamma<120 (trigonal) (example: 40.0 40.0 40.0 67.0 67.0 67.0 ) (volume = a3(1.0-cos(alpha))sqrt(1.0+2.0cos(alpha)) ) (degrees of freedom = 2) OCTAhedral - a = b = c, alpha = beta = gamma = 109.4712206344907 (a.k.a truncated octahedron) (example: 40.0 40.0 40.0 109.471220634 109.471220634 109.471220634 ) (volume = 4sqrt(3))/9 * a*3 ) (truncated cube length = a sqrt(4/3) ) (degrees of freedom = 1) RHDO (Rhombic Dodecahedron) - a = b = c, alpha = gamma = 60.0 and beta = 90.0 (example: 40.0 40.0 40.0 60.0 90.0 60.0 ) (volume = sqrt(0.5) * a*3 ) (truncated cube length = a sqrt(2) ) (degrees of freedom = 1) It is up to the user to ensure that the lattice parameters have the desired values for the system at all times. The values are stored by the program but, at present, the only way to transmit this information between jobs is with binary coordinate, trajectory, or restart files. For example, if the lattice parameters have been changed during a lattice optimization then the new parameters, which are printed out at the end of the minimization, must be input at the beginning of the next CHARMM run, or transferred using the FILE option on coordinate writing and reading. Lattice parameters are stored in binary coordinate, dynamic trajectory, and restart files only. 3. Crystal Phonon. Phonon calculates the dispersion curves for a crystal. Any value of the wavevector can be used (although, in practice, each component of KVEC is normally limited to the range -0.5 to +0.5). The dynamical matrix and normal mode eigenvectors determined in the phonon calculation are complex although the eigenvalues remain real. The syntax for the command is : Crystal Phonon Nkpoints <i> Kvector <f> <f> <f> To <f> <f> <f> Nkpoints tells the program the number of points at which the derivative matrices must be built and diagonalised whilst the Kvector ... To ... clause determines the values of KVEC for each calculation. Thus, Kvector 0.0 0.0 0.0 To 0.5 0.5 0.5 Nkpoints 3 would solve for the crystal frequencies at the points, KVEC=(0.0,0.0,0.0), (0.25,0.25,0.25) and (0.5,0.5,0.5). If it is desirable, point calculations can be carried out by omitting the To statement and putting Nkpoints 1. For single calculations at KVEC=(0.0,0.0,0.0) the Crystal Vibration command is faster. The eigenvalues and eigenvectors at each value of the wave vector from the phonon calculation are saved and they can be written out to a file using the Crystal Write Phonon command. No analysis facilities exist within CHARMM for the phonon data structure as the eigenvectors are complex. It is to be noted that phonon and vibration calculations can only be performed on crystals of P1 symmetry. No information about the symmetry operations is used when generating the dynamical matrix. 4. Crystal Print. Two options exist with the Print command. If no keyword is given then the crystal image file is printed out. The Crystal Print Phonon command performs a similar function to the Print Normal_Modes command in the vibrational analysis facility. Selected frequencies and eigenvectors for a range of values of the wave vector can be printed out. The syntax is : Crystal Print Phonon Kpoints <i> To <i> Modes <i> Thru <i> Factor <f> The Kpoints .. To .. clause determines the wave-vectors at which the modes are to be printed, the Modes .. Thru .. gives the range of the eigenvectors and the Factor command gives the scale factor to multiply each normal mode by. 5. Crystal Read. The Crystal Read command reads in a crystal image file. The file has the same output as produced by the Crystal Print or Crystal Write commands. The command is useful if a crystal image file was produced using the Crystal Build command and saved using the Crystal Write command in a previous job and it is desired to reuse the same transformation file for analysis or comparison purposes. The command can also be used to read in limited sets of transformations if specific crystal interactions need to be investigated. The transformation file is formatted so the Card keyword needs to be specified and the unit number must be given after the Unit keyword. 6. Crystal Vibration. For a free molecule with N atoms the dynamical equations have 3N-6 non-zero eigenvalues. This is no longer so for a crystal. If a crystal is made up of L unit cells each containing Z molecules with N atoms, the dynamical equations would have a dimension of 3NZL. However, using the symmetry properties of the lattice it is possible to factor the equations into L sets each with a dimension of 3NZ and each depending upon a vector, KVEC, which labels the irreducible representation of the translation group to which the set belongs. The force constant matrix is complex. Its form may be found in the references given at the end of the documentation. Vibration solves the dynamical equations for the case where the wave-vector is zero, i.e. when the equations are real. The procedure is invoked by the Crystal Vibration command. The syntax is : Crystal Vibration 7. Crystal Write. There are three Crystal Write options. If no keyword is given the crystal image file is written out, in card format, to the specified unit. The CARD and UNIT keywords are required. The Crystal Write Phonon command writes out the phonons from a phonon calculation. All the eigenvalues and eigenvectors for all values of the wavevector that are stored are written automatically. The Crystal Write Vibration command writes out the eigenvalues and eigenvectors from a vibration calculation. The modes to be written are given by the Mode .. Thru .. clause. All Write commands require that the Fortran stream number be given after the Unit keyword and a CHARMM title may be specified on the following lines. The structure of the phonon and vibration files for a crystal may be found by looking at the routines WRITDC and XFRQW2 respectively in the file [.IMAGE]XTLFRQ.SRC. The vibration modes are written in the same form as a for VIBRAN normal mode file and may be read in using the appropriate VIBRAN commands. Unfortunately no analysis facilities exist for complex eigenvectors within CHARMM and so users will have to write their own if they want to perform phonon 8. Crystal Minimization. It is possible to perform a lattice minimization using the normal have been introduced. If none of them is present then a coordinate minimization is performed as usual. If LATTICE is specified then the LATTice parameters and the atomic coordinates are minimized together. If NOCOoordinates is given with the keyword LATTice then only the lattice parameters are optimised. Specifying NOCOordinates by itself is an error. It should be noted that when the lattice is being optimised the crystal symmetry is maintained. A cubic crystal will remain cubic, etc. Examples of input may be found in the test directory. All crystal files are prefixed by the string "xtl_". All the jobs involve L-Alanine. Briefly the jobs are : 1. XTL_ALA1.INP. The crystallographic fractional coordinates are read in and converted to real space coordinates using the CHARMM COORdinate CONVert command and the experimental values for the lattice parameters. 2. XTL_ALA2.INP. A crystal image file is generated for the crystal using a value of 10.0 Angstroms for the crystal 3. XTL_ALA3.INP. A coordinate and lattice minimization are performed for the crystal. The crystal image file from the previous job is used and the optimised coordinates are saved. The main point to note is that before using the crystal package for energy calculations and other manipulations that involve the image non-bond lists an image update must be performed. For safety always do an update after building or reading in the crystal. Note too that the new, optimised lattice parameters are used in the all the subsequent input files. 4. XTL_ALA4.INP. For subsequent calculations a coordinate file that contains the coordinates of all atoms (four molecules of L-alanine) is generated. A crystal image file suitable to do this is read in directly from the input stream. It contains 6 transformations (not 3 as might be expected) because the CHARMM image facility requires that the inverses of all transformations be present. The first three are the ones needed and the last three are their inverses. An update is needed after reading the file to make known to the program the coordinates of the atoms in the first transformation of all the inverse pairs in the image list. The Print Coor Image file will then print out the coordinates of the atoms in the original asymmetric unit and the first three of the images. If the coordinates of the atoms in all the images are required then the keyword NOINV in the UPDATE command must be used (check IMAGE.DOC). 5. XTL_ALA5.INP. The same job as the second except that the crystal is generated for a whole unit cell (i.e. the system generated in the fourth job). The same value of the crystal cutoff is used. An energy is calculated too. The energy and its RMS coordinate derivative should be exactly four times (apart from a small round-off error) the value obtained for an energy calculation on a single asymmetric unit with the same lattice parameters and crystal cutoff (see job 3). 6. XTL_ALA6.INP. Peform a crystal vibration and phonon calculation for the optimised structure of the L-alanine crystal. The vibrational and phonon modes are written out to files and components of the first 24 phonon normal modes for the three values of the wavevector that were calculated are printed. To do the same for the vibrations it would be necessary to use the appropriate VIBRAN commands in another Advanced example: Applying P21 Symmetry to Interfacial Systems A slightly more novel application of crystal symmetry is the use of P21 symmetry for systems with planar interfaces, notably lipid bilayers and related multiphase systems. The general idea is that the simulation cell is an asymmetric unit, replicated through rotational symmetry such that the interface becomes one continuous surface. A tetragonal unit cell is required, and the interfaces must be in the XY plane and symmetric wrt. the X=0,Y=0 plane. The initial coordinate transform needed is straighforward, but the result must be carefully minimized before use; the molecules in contact at the AC and BC faces of the prism are completely changed by the rotational symmetry. Assuming that a standard tetragonal prism has been set up, the interconversion P1 ==> P21 can be accomplished via: ! COMPUTE NEW SIZE calc a = sqrt(2) * ?XTLA calc a4 = 0.25 * @A set c = ?XTLC coor rotat zdir 1.0 phi 45.0 coor trans xdir @A4 ! ESTABLISH NEW P21 SYMMETRY, AND APPLY IMAGE UPDATE crystal free crystal define tetra @A @A @C 90. 90. 90. crystal build noper 1 cutoff 30. image byres sele .not. segid a .or. segid b end xcen @A4 ! EXCLUDE PROTEIN update cutim 15. and the reverse transformation P21 ==> P1 can be done by: calc a ?XTLA / sqrt(2.) set c ?XTLC calc a4 0.25 * ?XTLA coor tran xdir -@A4 coor rota zdir 1. phi -45. ! ESTABLISH NEW P1 SYMMETRY, AND APPLY IMAGE UPDATE crystal free crystal define tetra @A @A @C 90. 90. 90. crystal build noper 0 cutoff 30. image byres sele .not. segid a .or. segid b end ! EXCLUDE PROTEIN update cutim 15. One approach to dealing with the changed molecular interactions for the AC and BC faces is a staged reduction of the A and B edge lengths (where A=B for the tetragonal prism). For lipid bilayer systems, it can also be prudent to restrain the headgroup conformations during the minimization. The following illustrates the use of CONS IC DIHE during a staged reduction of the box size: ic generate sele segid LPD end ic keep sele atom LPD * C+ end ! LIPID C1, C2, C3 ic delete sele type hydrogen end cons ic dihe 1000. calc mxa @A + 4. + 2. + 1. + 0.5 set m 8 label minloop crystal free crystal define tetragonal @MXA @MXA @C 90. 90. 90. crystal build noper 0 cutoff 30. calc A4 0.25 * @MXA image byres sele .not. segid a .or. segid b end xcen @A4 ! EXCLUDE PROTEIN ! MINIMIZE; SHORT SD, THEN ABNR mini sd nstep 50 nprint 5 - inbfrq 10 atom vatom cutnb 14.0 ctofnb 12. cdie eps 1. - ctonnb 8. vswitch cutim 14.0 imgfrq 10 wmin 0.5 - ewald pmew fftx 80 ffty 80 fftz 80 kappa .34 spline order 6 mini abnr nstep 200 nprint 10 calc mxa = @MXA - ( @M * 0.5 ) calc m = @M / 2 if m .ge. 1 goto minloop Finally, for use with NPT simulations where the A=B edges can change, the P21XCEN keyword » keyword enables automatic adjustment of the image centering XCEN value to be 0.25A as the edge values change during the course of dynamics. Simulations of Membranes and Other Interfacial Systems Using P21 and Pc Periodic Boundary Conditions EA Dolan, RM Venable, RW Pastor, and BR Brooks Biophys. J. 82:2317-2325 (2002) Background and Implementation. The Crystal options and their commands were described above. The present section discusses relevant background material and briefly reviews the methods used in the implementation. Some technical points are also made. The crystal option is an extension to the CHARMM program. The source code is in the directory [.IMAGE] whilst the crystal data structure is in the file IMAGE.FCM. Two additional source code files have been added - CRYSTL.SRC and XTLFRQ.SRC. Small modifications have been made to the files ENERGY.SRC and EIMAGE.SRC. CHARMM Images and the Crystal Image Data Structure. As outlined above a crystal structure can be specified entirely by the action of the primitive translations A, B and C, and a small set of transformations, {T} (which themselves are functions of A, B and C), on an asymmetric group of atoms. In CHARMM the calculation of the energy assumes that there exists a cutoff distance beyond which all interactions between particles are neglected so that when performing calculations on supposedly infinite crystals only a limited portion of that crystal, i.e. that portion containing those atoms within the cutoff distance of the primary atoms, need be considered. The CHARMM image option, of course, already enables the energies of crystals to be calculated but the input required to use it to do so is cumbersome and time consuming. It is a great simplification to include an extra data structure that defines the crystal in terms of A, B and C and There are a number of advantages: 1. A crystal is regular so that its generation can be automated. All that needs to be done is to systematically transform the primary atoms by one of the set {T} and a linear combination of A, B and C. The result is obviously best stored in terms of A, B, and C rather than as absolute numerical values of the transformations. 2. It is essential to define a CHARMM crystal by A, B and C and {T} if the lattice parameters a, b, c, alpha, beta and gamma are to be varied because the coordinates of all the image atoms within the crystal will change during successive cycles of the optimisation as a, b, c, alpha, beta and gamma themselves change. 3. When constructing the dynamical matrix for a non-zero wave-vector it is necessary to know the unit cell to which a particular atom belongs in order to evaluate the exponential factor in the expression. Although the crystal data structure and the values of the lattice parameters define the crystal the individual transformations have to be worked out explicitly in order to determine energies, harmonic frequencies and so on. In the present version of the program the IMAGE facility is used, so that a new set of IMAGE transformations are calculated from the crystal data structure as soon as a crystal is built or every time the lattice parameters are changed. The use of the IMAGE facility means that the number of transformations that can be used is determined by the dimension of the IMAGE arrays (MAXTRN in DIMENS.FCM). Crystal and Image Patching, Image H-bonds Crystal image patching is available in the present version of the program, so that bonds between images are permitted, but with some restrictions. The IMPAtch command requires the name of the image transformation. One may use CRYSTAL READ instead of CRYSTAL BUILD, in order to preserve the names of the image transformations. Hydrogen-bond interactions described by an explicit hydrogen-bond function between primary and image atoms are forbidden. The Lattice Coordinate System. WARNING: If your system is not properly rotated, there will usually be bad contacts. If you have bad contacts, check the alignment. The convention used by CHARMM for orientating the crystal in real space involves the use of a symmetric transformation (h) matrix. For non-orthorhombic systems, these coordinates are different (rotated) from the aligned conventioned used by PDB and others. The conversion is performed by the COOR CONVert command, » corman The Structure of the Crystal File. The crystal file is divided into three parts. A standard CHARMM title. A symmetry operation declaration section headed by the word Symmetry and terminated by an End. The transformations are written in the same way as for the Crystal Build command except that the identity transformation has to be explicitly listed. An image section headed by Images and terminated by an End. Here the images are defined in terms of the symmetry transformations and the lattice translations A, B and C. The comment line shows the column Sometimes it is useful to write one's own crystal files without recourse to the Crystal Build option. In this case the symmetry and image blocks can be put in any order (although only one of each is allowed) and there is no restriction on the positioning of blank and comment lines. Two examples of a crystal file are: Crystal file for a P1bar crystal. ! Operation a b c 1 0 0 -1 * Crystal file for a P212121 crystal. ! Operation a b c 2 -1 0 0 3 0 -1 0 4 0 0 -1 Second Derivative Calculations and the Use of Symmetry. Consider a crystal with a unit cell in which there is more than one asymmetric unit (i.e. all space groups other than P1). The dynamical matrix then takes a blocked form, with Z**2 blocks if Z is the number of asymmetric units. Each block is of dimension 3N x 3N and contains the sum over all unit cells of the second derivative interaction elements between the Mth and Nth asymmetric units. It is possible to calculate only the Z blocks (11), (12), ..., (1M), ..., (1Z) and then transform them to produce the full matrix. In the present program, however, it is necessary to perform vibration calculations on entire unit cells. It should be emphasised that while this symmetry transformation can be used for calculations of the normal mode eigenvectors and frequencies for the zero wavevector it does not hold at other values for all additional values. Therefore, simple symmetry arguments such as these do not hold for phonon calculations. Symmetry can also be used to block the dynamical matrix into several smaller matrices each corresponding to a different symmetry species, thereby greatly reducing the time needed for diagonalisation and automatically helping to identify the normal modes. Symmetry blocking is not coded at the moment. Lattice Dynamics of Molecular Crystals", Lecture Notes in Chemistry 26, S.Califano, V.Schettino and N.Neto (1981), Springer-Verlag, Berlin, Heidelberg and New York. A comprehensive monograph with good sections on the theory of lattice vibrations and normal mode symmetries. A.Warshel and S.Lifson, J.Chem.Phys. (1970), 53, 582. The original CFF paper on crystal calculations. It describes the theory behind crystal optimisations and vibrational calculations. E.Huler and A.Warshel, Acta Cryst. (1974), B30, 1822. An extension of the work in reference 2. "Infrared and Raman Spectra of Crystals", G.Turrell (1972), Academic Press, London and New York. A nice clear introduction to the subject.	{"url":"https://academiccharmm.org/documentation/version/c48b1/crystl/","timestamp":"2024-11-08T19:04:03Z","content_type":"text/html","content_length":"46591","record_id":"<urn:uuid:e7d483f2-9bc6-4f43-a238-bfe0a4c1b473>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00021.warc.gz"}
Conference Paper (Czech conference) Empirical Estimates in Stochastic Optimization: Special cases : Výpočtová ekonomie, sborník 4.semináře, p. 9-19 , Eds: Lukáš Ladislav : Výpočtová ekonomie, 4. seminář, (Plzeň, CZ, 18.12.2008) : CEZ:AV0Z10750506 : GAP402/10/0956, GA ČR, GA402/07/1113, GA ČR, GA402/08/0107, GA ČR, GA402/06/0990, GA ČR : stochastic programming problems, L_1 norm, Lipschitz property, empirical estimates, convergence rate, exponential tails, heavy tails, Pareto distribution, risk functional : http://library.utia.cas.cz/separaty/2011/E/kankova-empirical estimates in stochastic optimization special cases.pdf (eng): Classical optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are relatively complicated. On the other hand, these problems fulfil very often "suitable" mathematical properties guaranteing the stability (w.r.t. probability measure) and, moreover, giving a possibility to replace the "underlying" probability measure by an empirical one to obtain "good" stochastic estimates of the optimal value and the optimal solution. Properties of thess estimates have been investigated mostly for standard types of probability measures with suitable (thin) tails and independent random samples. However distributions with heavy tails correspond to many economic problems and, moreover, many applications do not correspond to the "classical" problems. The aim of the paper is, first, to try to recall stability results including also heavy tails and more general problems. : BB	{"url":"https://www.utia.cas.cz/biblio/pub/0359099","timestamp":"2024-11-05T11:55:09Z","content_type":"text/html","content_length":"19711","record_id":"<urn:uuid:d43b22a8-bca1-4540-9284-e9a92e861dec>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00630.warc.gz"}
Monthly Survey of Manufacturing (MSM) Detailed information for January 2023 The Monthly Survey of Manufacturing (MSM) publishes statistical series for manufacturers - sales of goods manufactured, inventories, unfilled orders, new orders and capacity utilization rate. Data release - February 23, 2023 (Flash estimate); March 14, 2023 The MSM publishes the values (in current Canadian dollars) of sales of goods manufactured, inventories, orders and capacity utilization rates. Results from this survey are used by both the private and public sectors including federal and provincial government departments, the Bank of Canada, the System of National Accounts, the manufacturing community, consultants and research organizations in Canada, the United States and abroad, and the business press. Data collected by the MSM provides a current 'snapshot' of sales of goods manufactured values by the Canadian manufacturing sector, enabling analysis of the state of the Canadian economy, as well as the health of specific industries in the short- to medium-term. Reference period: Month Collection period: Collection of the data begins approximately 7 working days after the end of the reference month, and continues for the duration of that calendar month. • Machinery, computers and electronics • Manufacturing Data sources and methodology Target population Statistics Canada's business register provides the sampling frame for the MSM. The target population for the MSM consists of all statistical establishments on the Business Register that are classified to the manufacturing sector (by NAICS), which are categorized into over 156 industries. An establishment comprises the smallest manufacturing unit capable of reporting the variables of interest. The sampling frame for the MSM is determined from the target population after subtracting establishments that represent the bottom 10% of the total manufacturing sales of goods manufactured estimate for each cell. These establishments were excluded from the frame so that the sample size could be reduced without significantly affecting quality. Instrument design Both electronic and paper questionnaires are used to collect data for the Monthly Survey of Manufacturing (MSM). The questionnaires were developed at Statistics Canada and were reviewed and tested in the field in both official languages. In the course of redeveloping the MSM, Statistics Canada consulted with a number of manufacturers as well as with industry associations. In February 2016, the capacity utilization rate was added to the MSM questionnaire. Also the MSM questionnaire became available to respondents in electronic format in May 2017. This is a sample survey with a cross-sectional design. The MSM sample is a probability sample comprised of approximately 6,500 establishments. A new sample was chosen in the fall of 2017, followed by a six-month parallel run (from reference month September 2017 to reference month February 2018). The new sample was used officially for the first time for dissemination with the reference month December 2017. This marks the first process of refreshing the MSM sample since 2012. The objective of the process is to keep the sample frame as fresh and up-to date as possible. All establishments in the sample are refreshed to take into account changes in their value of sales of goods manufactured, the removal of dead units from the sample and some small units are rotated out of the sample, while others are rotated into the sample. Prior to selection, the sampling frame is subdivided into industry-province cells. Depending upon the number of establishments within each cell, further subdivisions were made to group similar sized establishments' together (called stratum). An establishment's size was based on revenue variables from the Business Register. Each industry by province cell has a 'take-all' stratum composed of establishments sampled each month with certainty. This 'take-all' stratum is composed of establishments that are the largest statistical enterprises, and have the largest impact on estimates within a particular industry by province cell. These large statistical establishments comprise about 50% of the national manufacturing sales of goods manufactured estimates. Each industry by province cell can have at most two 'take-some' strata. Not all establishments within these stratums need to be sampled with certainty. A random sample is drawn from the remaining strata. The responses from these sampled establishments are weighted according to the inverse of their probability of selection. In cells with take-some portion, a minimum sample size of 3 was The take-none portion of the sample is now estimated from administrative data and as a result, 100% of the sample universe is covered. Estimation of the take-none portion also improved efficiency as a larger take-none portion was delineated and the sample could be used more efficiently on the smaller sampled portion of the frame. Data sources Responding to this survey is mandatory. Data are collected directly from survey respondents and extracted from administrative files. The complete sample of establishments is sent out for data collection. Collection of the data is performed by Statistics Canada's Regional Offices. Respondents are sent an electronic or paper questionnaire or are contacted by telephone to obtain their sales, inventories, unfilled orders, capacity utilization rates, as well as to confirm the opening or closing of business trading locations. Collection also undertakes follow-up of non-respondents. Collection of the data begins approximately 7 working days after the end of the reference month and continues for the duration of that calendar month. New entrants to the survey are introduced to the survey via introductory questions that confirm the respondent's business activity and contact information. If data are unavailable at the time of collection, a respondent's best estimates are also accepted, and are subsequently revised once the actual data become available. To minimize total non-response for all variables, partial responses are accepted. Use of Administrative Data: Managing response burden is an ongoing challenge for Statistics Canada. In an attempt to alleviate response burden, especially for small businesses, the MSM derives sales data for low-revenue establishments from Goods and Service Tax (GST) files using a ratio estimator. The ratio estimator also increases the precision of the surveyed portion of the estimate. For more information on the ratio estimator, see the section on estimation. View the Questionnaire(s) and reporting guide(s) . Error detection Data are analyzed within each industry-province cell. Extreme values are listed for inspection by the magnitude of the deviation from average behavior. Respondents are contacted to verify extreme values. Records that fail statistical edits are considered outliers and are not used for imputation. Values are imputed for the non-responses, for establishments that do not report or only partially complete the survey form. A number of imputation methods are used depending on the variable requiring treatment. Methods include using industry-province cell trends and historical responses. Following imputation, the MSM staff performs a final verification of the responses that have been imputed. Imputation in the MSM is the process used to assign replacement values for missing data. This is done by assigning values when they are missing on the record being edited to ensure that estimates are of high quality and that a plausible, internal consistency is created. Due to concerns of response burden, cost and timeliness, it is generally impossible to do all follow-ups with the respondents in order to resolve missing responses. Since it is desirable to produce a complete and consistent microdata file, imputation is used to handle the remaining missing cases. In the MSM, imputation for missing values can be based on either historical data or administrative data. The appropriate method is selected according to a strategy that is based on whether historical data are available, administrative data are available and/or which reference month is being processed. There are three types of historical imputation methods. The first type is a general trend that uses one historical data source (previous month, data from next month or data from same month previous year). The second type is a regression model where data from previous month and same month previous year are used simultaneously. The third type uses the historical data as a direct replacement value for a non-respondent. Depending upon the particular reference month, there is an order of preference that exists so that a top quality imputation can result. The historical imputation method that was labeled as the third type above is always the last option in the order for each reference month. The imputation method using administrative data is automatically selected when historical information is unavailable for a non-respondent. Trends are then applied to the administrative data source (monthly size) depending on whether the unit has a simple structure, e.g. enterprises with only one establishment, or a more complex structure. Estimation is a process by which Statistics Canada obtains values for the population of interest so that it can draw conclusions about that population based on information gathered from only a sample of the population. More specifically, the MSM uses a ratio estimator. Ratio estimation consists of replacing the initial sampling weights (defined as the inverse of the probability of selection in the sample) by new weights in a manner that satisfies the constraints of calibration. Calibration ensures that the total of an auxiliary variable estimated using the sample must equal the sum of the auxiliary variable over the entire population, and that the new sampling weights are as close as possible (using a specific distance measure) to the initial sampling weights. For example, suppose that the known population total of the auxiliary variable is equal to 100 and based on a sample the estimated total is equal to 90, so that we are underestimating by approximately 10%. Since we know the population total of the auxiliary variable, it would be reasonable to increase the weights of the sampled units so that the estimate would be exactly equal to it. Now since the variable of interest is related to the auxiliary variable, it is not unreasonable to believe that the estimate of the sales based on the same sample and weights as the estimate of the auxiliary variable may also be an underestimation by approximately 10%. If this is in fact the case, then the adjusted weights could be used to produce an alternative estimator of the total sales. This alternate estimator is called the ratio estimator. In essence, the ratio estimator tries to compensate for 'unlucky' samples and brings the estimate closer to the true total. The gain in variance will depend on the strength of the relationship between the variable of interest and the auxiliary data. The take-none portion is taken into account by the ratio estimator. This is done by simply including the take-none portion in the control totals for the sample portion. By doing this, the weights for the sampled portion will be increased in such a way that the estimates will be adjusted to take into account the take-none portion. The calculated weighted sales values are summed by domain, to produce the total sales estimates by each industrial group/geographic area combination and the other totals by industrial group. A domain is defined as the most recent classification values available from the BR for the unit and the survey reference period. These domains may differ from the original sampling strata because units may have changed size, industry or location. Changes in classification are reflected immediately in the estimates and do not accumulate over time. For the capacity utilization rate, the estimate for a given domain is calculated by first calculating the total production and monthly production capacity for the domain and then by dividing the total production by the total monthly production capacity. The measure of precision used for the MSM to evaluate the quality of a population parameter estimate and to obtain valid inferences is the variance. The variance from the survey portion is derived directly from a stratified simple random sample without replacement. Sample estimates may differ from the expected value of the estimates. However, since the estimate is based on a probability sample, the variability of the sample estimate with respect to its expected value can be measured. The variance of an estimate is a measure of the precision of the sample estimate and is defined as the average, over all possible samples, of the squared difference of the estimate from its expected value. Estimation of sales by census metropolitan area Estimates of sales for twelve census metropolitan areas (CMA) have been derived by using a small area estimation (SAE) technique based on a Fay-Herriot methodology. In this methodology, a model that describes the relationship between estimated sales coming from the MSM and sales coming from the Goods and Services Tax (GST) data at a small level of geography is combined with traditional estimates obtained from the weighted MSM sample. The resulting small area estimates are often significantly more precise than standard MSM weighted estimates, particularly for areas where the latter become unreliable due to small area sample sizes. This increase in precision is obtained at the expense of introducing model assumptions. Unlike standard MSM estimates, small area estimates may thus be subject to model misspecification errors, which may result in biases. Careful model validation has been performed before releasing the estimates in order to decrease the risk of bias. More information concerning the SAE methodology is available in the additional documentation. Real manufacturing sales of goods manufactured, inventories, and orders Changes in the values of the data reported by the Monthly Survey of Manufacturing (MSM) may be attributable to changes in their prices or to the quantities measured, or both. To study the activity of the manufacturing sector, it is often desirable to separate out the variations due to price changes from those of the quantities produced. This adjustment is known as deflation. Deflation consists in dividing the values at current prices obtained from the survey by suitable price indexes in order to obtain estimates evaluated at the prices of a previous period, currently the year 2012. The resulting deflated values are said to be "at 2012 prices". Note that the expression "at current prices" refer to the time the activity took place, not to the present time, nor to the time of compilation. The deflated MSM estimates reflect the prices that prevailed in 2012. This is called the base year. The year 2012 was chosen as base year since it corresponds to that of the price indexes used in the deflation of the MSM estimates. Using the prices of a base year to measure current activity provides a representative measurement of the current volume of activity with respect to that base year. Current movements in the volume are appropriately reflected in the constant price measures only if the current relative importance of the industries is not very different from that in the base year. The deflation of the MSM estimates is performed at a very fine industry detail, equivalent to the 6-digit industry classes of the North American Industry Classification System (NAICS). For each industry at this level of detail, the price indexes used are composite indexes which describe the price movements for the various groups of goods produced by that industry. With very few exceptions the price indexes are weighted averages of the Industrial Product Price Indexes (IPPI). The weights are derived from the annual Canadian Input-Output tables and change from year to year. Since the Input-Output tables only become available with a delay of about two and a half years, the weights used for the most current years are based on the last available Input-Output The same price index is used to deflate sales of goods manufactured, new orders and unfilled orders of an industry. The weights used in the compilation of this price index are derived from the output tables, evaluated at producer's prices. Producer prices reflect the prices of the goods at the gate of the manufacturing establishment and exclude such items as transportation charges, taxes on products, etc. The resulting price index for each industry thus reflects the output of the establishments in that industry. The price indexes used for deflating the goods / work in progress and the finished goods inventories of an industry are moving averages of the price index used for sales of goods manufactured. For goods / work in process inventories, the number of terms in the moving average corresponds to the duration of the production process. The duration is calculated as the average over the previous 48 months of the ratio of end of month goods / work in progress inventories to the output of the industry, which is equal to sales of goods manufactured plus the changes in both goods / work in progress and finished goods manufactured inventories. For finished goods manufactured inventories, the number of terms in the moving average reflects the length of time a finished product remains in stock. This number, known as the inventory turnover period, is calculated as the average over the previous 48 months of the ratio of end-of-month finished goods manufactured inventory to sales of goods manufactured. To deflate raw materials and components inventories, price indexes for raw materials consumption are obtained as weighted averages of the IPPI. The weights used are derived from the input tables evaluated at purchaser's prices, i.e. these prices include such elements as wholesaling margins, transportation charges, and taxes on products, etc. The resulting price index thus reflects the cost structure in raw materials and components for each industry. The raw materials and components inventories are then deflated using a moving average of the price index for raw materials consumption. The number of terms in the moving average corresponds to the rate of consumption of raw materials. This rate is calculated as the average over the previous four years of the ratio of end-of-year raw materials and components inventories to the intermediate inputs of the industry. The estimation system generates estimates using the NAICS. National estimates are produced for all variables collected by MSM, however only provincial estimates for sales of goods manufactured are produced. A measure of quality (CV) will also be produced. Seasonally adjusted series are available for the main aggregates. Quality evaluation The final data sets are subject to rigorous analysis that includes comparison to historical series and comparisons to other sources of data in order to put the economic changes in context. Information available from the media, other government organizations and economic think tanks is also used in the validation process. Disclosure control Statistics Canada is prohibited by law from releasing any information it collects which could identify any person, business, or organization, unless consent has been given by the respondent or as permitted by the Statistics Act. Various confidentiality rules are applied to all data that are released or published to prevent the publication or disclosure of any information deemed confidential. If necessary, data are suppressed to prevent direct or residual disclosure of identifiable data. Confidentiality analysis includes the detection of possible direct disclosure, which occurs when the value in a tabulation cell is composed of a few respondents or when the cell is dominated by a few Revisions and seasonal adjustment In conjunction with preliminary estimates for the current month, estimates for the previous three months are revised to account for any late returns. Data are revised when late responses are received or if an incorrect response was recorded earlier. Up to and including 2003, the MSM was benchmarked to the Annual Survey of Manufactures and Logging (ASML). Benchmarking was the regular review of the MSM estimates in the context of the annual data provided by the ASML. Benchmarking re-aligned the annualized level of the MSM based on the latest verified annual data provided by the ASML. Significant research by Statistics Canada in 2006-2007 was completed on whether the benchmark process should be maintained. The conclusion was that benchmarking of the MSM estimates to the ASML should be discontinued. With the refreshing of the MSM sample in 2007, it was determined that benchmarking would no longer be required (retroactive to 2004) because the MSM now accurately represented 100% of the sample universe. Data confrontation will continue between MSM and ASML to resolve potential discrepancies. As of the December 2017 reference month, a new sample was introduced. It is standard practice that every few years the sample is refreshed to ensure that the survey frame is up to date with births, deaths and other changes in the population. The refreshed sample is linked at the detailed level to prevent data breaks and to ensure the continuity of time series. It is designed to be more representative of the manufacturing industry at both the national and provincial levels. Economic time series contain the elements essential to the description, explanation and forecasting of the behavior of an economic phenomenon. They are statistical records of the evolution of economic processes through time. In using time series to observe economic activity, economists and statisticians have identified four characteristic behavioral components: the long-term movement or trend, the cycle, the seasonal variations and the irregular fluctuations. These movements are caused by various economic, climatic or institutional factors. The seasonal variations occur periodically on a more or less regular basis over the course of a year. These variations occur as a result of seasonal changes in weather, statutory holidays and other events that occur at fairly regular intervals and thus have a significant impact on the rate of economic activity. In the interest of accurately interpreting the fundamental evolution of an economic phenomenon and producing forecasts of superior quality, Statistics Canada uses the X12-ARIMA seasonal adjustment method to seasonally adjust its time series. This method minimizes the impact of seasonal variations on the series and essentially consists of adding one year of estimated raw data to the end of the original series before it is seasonally adjusted per se. The estimated data are derived from forecasts using ARIMA (Auto Regressive Integrated Moving Average) models of the Box-Jenkins type. The X-12 program uses primarily a ratio-to-moving average method. It is used to smooth the modified series and obtain a preliminary estimate of the trend-cycle. It also calculates the ratios of the original series (fitted) to the estimates of the trend-cycle and estimates the seasonal factors from these ratios. The final seasonal factors are produced only after these operations have been repeated several times. The technique that is used essentially consists of first correcting the initial series for all sorts of undesirable effects, such as the trading-day and the Easter holiday effects, by a module called regARIMA. These effects are then estimated using regression models with ARIMA errors. The series can also be extrapolated for at least one year by using the model. Subsequently, the raw series, pre-adjusted and extrapolated if applicable, is seasonally adjusted by the X-12 method. The procedures to determine the seasonal factors necessary to calculate the final seasonally adjusted data are executed every month. This approach ensures that the estimated seasonal factors are derived from an unadjusted series that includes all the available information about the series, i.e. the current month's unadjusted data as well as the previous month's revised unadjusted data. While seasonal adjustment permits a better understanding of the underlying trend-cycle of a series, the seasonally adjusted series still contains an irregular component. Slight month-to-month variations in the seasonally adjusted series may be simple irregular movements. To get a better idea of the underlying trend, users should examine several months of the seasonally adjusted series. The aggregated Canada level series are now seasonally adjusted directly, meaning that the seasonally adjusted totals are obtained via X12-ARIMA. Afterwards, these totals are used to reconcile the provincial total series which have been seasonally adjusted individually. For other aggregated series, indirect seasonal adjustments are used. In other words, their seasonally adjusted totals are derived indirectly by the summation of the individually seasonally adjusted kinds of business. A seasonally adjusted series may contain the effects of irregular influences and special circumstances and these can mask the trend. The short term trend shows the underlying direction in seasonally adjusted series by averaging across months, thus smoothing out the effects of irregular influences. The result is a more stable series. The trend for the last month may be subject to significant revision as values in future months are included in the averaging process. Data accuracy While considerable efforts have been taken to ensure high standards throughout all stages of collection and processing, the resulting estimates are inevitably subject to a certain degree of non-sampling error. Non-sampling error is not related to sampling and may occur for various reasons. For example, non-response is an important source of non-sampling error. Population coverage, differences in the interpretations of questions and mistakes in recording, coding and processing data are other examples of non-sampling errors. Non-sampling errors are controlled through a careful design of the questionnaire, the use of a minimal number of simple concepts and consistency checks. Measures such as response rates are used as indicators of the possible extent of non-sampling errors. The MSM's average weighted response rate for collected and edit sales of goods manufactured data at national level is in the range of 94% to 96% in 2017. Table 2 in the 'Concepts, Definitions and Data Quality' document shows the weighted response or edit and imputation rates for collected data as well as for take-none portion data based on the GST for the following five characteristics: sales of goods manufactured, raw materials and components inventories, goods / work in progress inventories, finished goods manufactured inventories, unfilled orders and capacity utilization rate. Sampling error can be measured by the standard error (or standard deviation) of the estimate. The coefficient of variation (CV) is the estimated standard error percentage of the survey estimate. Estimates with smaller CVs are more reliable than estimates with larger CVs. Table 1 in the 'Concepts, Definitions and Data Quality' document shows the national level CVs for the following five characteristics: sales of goods manufactured, raw materials and components inventories, goods / work in process inventories, finished goods manufactured inventories and unfilled orders and capacity utilization rates. Measures of Sampling and Non-sampling Errors 1. Sampling Error Measures The sample used in this survey is one of a large number of all possible samples of the same size that could have been selected using the same sample design under the same general conditions. If it was possible that each one of these samples could be surveyed under essentially the same conditions, with an estimate calculated from each sample, it would be expected that the sample estimates would differ from each other. The average estimate derived from all these possible sample estimates is termed the expected value. The expected value can also be expressed as the value that would be obtained if a census enumeration were taken under identical conditions of collection and processing. An estimate calculated from a sample survey is said to be precise if it is near the expected value. Sample estimates may differ from this expected value of the estimates. However, since the estimate is based on a probability sample, the variability of the sample estimate with respect to its expected value can be measured. The variance of an estimate is a measure of the precision of the sample estimate and is defined as the average, over all possible samples, of the squared difference of the estimate from its expected value. The standard error is a measure of precision in absolute terms. The coefficient of variation (CV), defined as the standard error divided by the sample estimate, is a measure of precision in relative terms. For comparison purposes, one may more readily compare the sampling error of one estimate to the sampling error of another estimate by using the coefficient of variation. In this publication, the coefficient of variation is used to measure the sampling error of the estimates. However, since the coefficient of variation published for this survey is calculated from the responses of individual units, it also measures some non-sampling error. 2. Non-sampling Error Measures The exact population value is aimed at or desired by both a sample survey as well as a census. We say the estimate is accurate if it is near this value. Although this value is desired, we cannot assume that the exact value of every unit in the population or sample can be obtained and processed without error. Any difference between the expected value and the exact population value is termed the bias. Systematic biases in the data cannot be measured by the probability measures of sampling error as previously described. The accuracy of a survey estimate is determined by the joint effect of sampling and non-sampling errors. Sources of non-sampling error in the MSM include non-response error, imputation error and the error due to editing. To assist users in evaluating these errors, weighted rates are given in Text table 2. The following is an example of what is meant by a weighted rate. A cell with a sample of 20 units in which five respond for a particular month would have a response rate of 25%. If these five reporting units represented $8 million out of a total estimate of $10 million, the weighted response rate would be 80%. The definitions for the weighted rates noted in Text table 2 follow. The weighted response and edited rate is the proportion of a characteristic's total estimate that is based upon reported data and includes data that has been edited. The weighted imputation rate is the proportion of a characteristic's total estimate that is based upon imputed data. The weighted take-none fraction rate is the proportion of the characteristic's total estimate modeled from administrative data. Joint Interpretation of Measures of Error The measure of non-response error as well as the coefficient of variation must be considered jointly to have an overview of the quality of the estimates. The lower the coefficient of variation and the higher the weighted response rate, the better will be the published estimate. In the case of estimates of sales by CMA, the quality of the estimates is measured using a global variance that takes in account the variance due to sampling, the variance due to imputation and the mean square error of the SAE model. More details concerning the quality of estimation of sales by CMA is available in the additional documentation.	{"url":"https://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&Id=1504542","timestamp":"2024-11-02T02:20:23Z","content_type":"text/html","content_length":"50877","record_id":"<urn:uuid:d9c238dd-efae-492b-9927-227a89216527>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00320.warc.gz"}
Project Euler #200: Find the 200th prime-proof sqube containing the contiguous sub-string "200" \| HackerRank [This problem is a programming version of Problem 200 from projecteuler.net] We shall define a sqube to be a number of the form, , where and are distinct primes. For example, or . The first five squbes are , , , , and . Interestingly, is also the first number for which you cannot change any single digit to make a prime; we shall call such numbers, prime-proof. The next prime-proof sqube which contains the contiguous sub-string "200" is . Note that changing a digit may result in appearance of the leading zeroes - in the case with as a number we can change the first digit to , but the resulting number is not a prime number and doesn't change the fact that is prime-proof. You're given the contiguous sub-string and some queries . For each query, find the -th prime-proof sqube containing the contiguous sub-string . The first line of each file contains which is the sub-string from the problem statement. Next line contains a single integer which is the number of queries per test file. lines follow, each containing the corresponding . • is a string representation of some number between and • For each query, the answer is less than . Print exactly lines with the answers for the all queries on each.	{"url":"https://www.hackerrank.com/contests/projecteuler/challenges/euler200/problem","timestamp":"2024-11-13T18:50:37Z","content_type":"text/html","content_length":"881629","record_id":"<urn:uuid:199a3e47-daa9-4e56-851d-2ee337dfeb70>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00286.warc.gz"}
How do you calculate recall for multiclass classification? How do you calculate recall for multiclass classification? Recall for Multi-Class Classification In an imbalanced classification problem with more than two classes, recall is calculated as the sum of true positives across all classes divided by the sum of true positives and false negatives across all classes. How do you calculate precision and recall for multiclass classification using confusion matrix? How do you calculate precision and recall for multiclass classification using confusion matrix? 1. Precision = TP / (TP+FP) 2. Recall = TP / (TP+FN) Can confusion matrix be used for multiclass classification? Confusion Matrix gives a comparison between Actual and predicted values. The confusion matrix is a N x N matrix, where N is the number of classes or outputs. For 2 class ,we get 2 x 2 confusion matrix. For 3 class ,we get 3 X 3 confusion matrix. What is recall in confusion matrix? The precision is the proportion of relevant results in the list of all returned search results. The recall is the ratio of the relevant results returned by the search engine to the total number of the relevant results that could have been returned. How do you test the accuracy of multiclass classification? Accuracy is one of the most popular metrics in multi-class classification and it is directly computed from the confusion matrix. The formula of the Accuracy considers the sum of True Positive and True Negative elements at the numerator and the sum of all the entries of the confusion matrix at the denominator. Why precision and recall is important? So, what are the key takeaways? Precision and recall are two extremely important model evaluation metrics. While precision refers to the percentage of your results which are relevant, recall refers to the percentage of total relevant results correctly classified by your algorithm. What is the difference between precision and recall? Recall is the number of relevant documents retrieved by a search divided by the total number of existing relevant documents, while precision is the number of relevant documents retrieved by a search divided by the total number of documents retrieved by that search. What is false positive in multiclass classification? False Positive Rate, or Type I Error: Number of items wrongly identified as positive out of the total actual negatives — FP/(FP+TN) . This error means that an image not containing a particular parasite egg is incorrectly labeled as having it. How do you calculate sensitivity and specificity for multiclass classification? To calculate Recall, use the following formula: TP/(TP+FN). Specificity: It tells you what fraction of all negative samples are correctly predicted as negative by the classifier. It is also known as True Negative Rate (TNR). To calculate specificity, use the following formula: TN/(TN+FP). What does recall refer to in classification? Recall: the ability of a classification model to identify all data points in a relevant class. Precision: the ability of a classification model to return only the data points in a class. F1 score: a single metric that combines recall and precision using the harmonic mean. How to compute precision and recall for a confusion matrix? Once you have the confusion matrix, you have all the values you need to compute precision and recall for each class. Note that the values in the diagonal would always be the true positives (TP). Now, let us compute recall for Label A: Now, let us compute precision for Label A: So precision=0.5 and recall=0.3 for label A. What is the confusion matrix for multi-class classification? Confusion Matrix for Multi-Class Classification 1 Micro F1. This is called micro-averaged F1-score. It is calculated by considering the total TP, total FP and total FN of… 2 Macro F1. This is macro-averaged F1-score. It calculates metrics for each class individually and then takes unweighted… 3 Weighted F1. More How do you calculate precision and recall for multiple classes? The answer is that you have to compute precision and recall for each class, then average them together. E.g. if you classes A, B, and C, then your precision is: (precision (A) + precision (B) + precision (C)) / 3 Is there a confusion matrix for class labels with three labels? Say, we have a dataset that has three class labels, namely Apple, Orange and Mango. The following is a possible confusion matrix for these classes. Unlike binary classification, there are no positive or negative classes here.	{"url":"https://corfire.com/how-do-you-calculate-recall-for-multiclass-classification/","timestamp":"2024-11-04T20:31:52Z","content_type":"text/html","content_length":"41643","record_id":"<urn:uuid:19532611-3382-4374-adc3-d6188e303a6b>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00013.warc.gz"}
100 Multiplication Worksheets Mathematics, particularly multiplication, develops the foundation of various scholastic disciplines and real-world applications. Yet, for lots of learners, mastering multiplication can posture a challenge. To address this hurdle, teachers and parents have actually accepted a powerful tool: 100 Multiplication Worksheets. Introduction to 100 Multiplication Worksheets 100 Multiplication Worksheets 100 Multiplication Worksheets - The multiplication printable worksheets below will take your child through their multiplication learning step by step so that they are learning the math skills to move on to the next step as well as starting off at a nice easy level to gain confidence Quicklinks to Multiplication Worksheets by Grade Times Table Worksheets Students multiply 2 or 3 digit numbers by 100 in these multiplication worksheets Questions in horizontal form 2 digit s Worksheet 1 Worksheet 2 3 digit s Worksheet 3 Worksheet 4 Mixed Worksheet 5 Worksheet 6 3 More Similar Multiplying by 1 000 Multiplying by multiples of 10 What is K5 Relevance of Multiplication Method Understanding multiplication is critical, laying a strong foundation for sophisticated mathematical ideas. 100 Multiplication Worksheets supply structured and targeted technique, promoting a deeper understanding of this fundamental arithmetic procedure. Development of 100 Multiplication Worksheets Printable 100 Question Multiplication Quiz PrintableMultiplication Printable 100 Question Multiplication Quiz PrintableMultiplication Multiplication Worksheets Worksheets Multiplication Mixed Tables Worksheets Worksheet Number Range Online Primer 1 to 4 Primer Plus 2 to 6 Up To Ten 2 to 10 Getting Tougher 2 to 12 Intermediate 3 to 15 Advanced 6 to 20 Hard 8 to 30 Super Hard 12 to 100 Individual Table Worksheets Worksheet Online Here you will find our selection of free printable multiplication worksheets which will help your child practice multiplying a range of whole numbers up to 3 digits by 10 or 100 These sheets are designed for 3rd and 4th graders If you are looking for worksheets involving multiplying decimals by 10 and 100 then use the link here From conventional pen-and-paper exercises to digitized interactive formats, 100 Multiplication Worksheets have actually advanced, satisfying varied knowing styles and preferences. Sorts Of 100 Multiplication Worksheets Fundamental Multiplication Sheets Easy exercises focusing on multiplication tables, assisting learners build a solid arithmetic base. Word Problem Worksheets Real-life situations incorporated right into problems, improving vital thinking and application skills. Timed Multiplication Drills Examinations made to improve speed and precision, helping in quick mental math. Benefits of Using 100 Multiplication Worksheets 100 Multiplication Worksheets Ideas multiplication worksheets multiplication worksheets 100 Multiplication Worksheets Ideas multiplication worksheets multiplication worksheets Domino Multiplication Count the dots on each side of the dominoes and multiply the numbers together 3rd and 4th Grades View PDF Multiplication Groups Write a multiplication and a repeated addition problem for each picture shown 2nd through 4th Grades View PDF Task Cards Arrays This PDF contains 30 task cards 40 Multiplication Worksheets These multiplication worksheets extend the Spaceship Math one minute timed tests with the x10 x11 and x12 facts Even if your school isn t practicing multiplication past single digits these are valuable multiplication facts to learn for many time and geometry problems Extended Spaceship Math Improved Mathematical Skills Consistent method hones multiplication effectiveness, enhancing overall math capacities. Improved Problem-Solving Talents Word problems in worksheets develop logical reasoning and approach application. Self-Paced Knowing Advantages Worksheets accommodate specific learning speeds, promoting a comfy and versatile learning atmosphere. Just How to Produce Engaging 100 Multiplication Worksheets Incorporating Visuals and Shades Vibrant visuals and shades catch interest, making worksheets aesthetically appealing and engaging. Consisting Of Real-Life Scenarios Connecting multiplication to daily circumstances includes significance and usefulness to exercises. Tailoring Worksheets to Various Skill Degrees Personalizing worksheets based upon differing efficiency degrees makes certain comprehensive discovering. Interactive and Online Multiplication Resources Digital Multiplication Devices and Games Technology-based sources use interactive learning experiences, making multiplication engaging and pleasurable. Interactive Web Sites and Apps On-line systems offer varied and obtainable multiplication practice, supplementing traditional worksheets. Customizing Worksheets for Various Learning Styles Aesthetic Students Visual aids and diagrams aid understanding for students inclined toward visual learning. Auditory Learners Verbal multiplication problems or mnemonics cater to learners who grasp principles with auditory methods. Kinesthetic Learners Hands-on activities and manipulatives sustain kinesthetic students in comprehending multiplication. Tips for Effective Implementation in Discovering Consistency in Practice Regular practice enhances multiplication skills, advertising retention and fluency. Stabilizing Rep and Selection A mix of repeated workouts and diverse trouble formats preserves rate of interest and understanding. Supplying Positive Feedback Comments help in identifying locations of enhancement, motivating ongoing progress. Obstacles in Multiplication Technique and Solutions Motivation and Interaction Difficulties Dull drills can bring about uninterest; ingenious methods can reignite inspiration. Conquering Anxiety of Mathematics Adverse perceptions around mathematics can hinder progression; developing a favorable understanding setting is crucial. Effect of 100 Multiplication Worksheets on Academic Efficiency Studies and Research Searchings For Research study shows a positive relationship in between constant worksheet usage and enhanced mathematics performance. 100 Multiplication Worksheets emerge as versatile tools, fostering mathematical effectiveness in learners while accommodating diverse discovering styles. From basic drills to interactive on-line sources, these worksheets not only boost multiplication skills however additionally promote important thinking and analytical capacities. Multiplication Chart To 100 Division Chart 1 100 Haval Printable multiplication Table Blank Multiplication By 12 Worksheets Check more of 100 Multiplication Worksheets below Index Of postpic 2011 03 14 Best Images Of Hard Multiplication Worksheets 100 Problems Math Fact Worksheets 3rd Grade Multiplication Worksheets Best Coloring Pages For Kids 65 MATH WORKSHEET 100 MULTIPLICATION PROBLEMS Single Digit Multiplication Worksheets Free Printable 6 Best Images Of Math Drills Multiplication Worksheets Printable Math Fact Worksheets Multiplying by 100 worksheets K5 Learning Students multiply 2 or 3 digit numbers by 100 in these multiplication worksheets Questions in horizontal form 2 digit s Worksheet 1 Worksheet 2 3 digit s Worksheet 3 Worksheet 4 Mixed Worksheet 5 Worksheet 6 3 More Similar Multiplying by 1 000 Multiplying by multiples of 10 What is K5 Multiplication Facts Worksheets Math Drills Multiplication Facts up to the 12 Times Table Multiplication Facts beyond the 12 Times Table Welcome to the multiplication facts worksheets page at Math Drills On this page you will find Multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats Students multiply 2 or 3 digit numbers by 100 in these multiplication worksheets Questions in horizontal form 2 digit s Worksheet 1 Worksheet 2 3 digit s Worksheet 3 Worksheet 4 Mixed Worksheet 5 Worksheet 6 3 More Similar Multiplying by 1 000 Multiplying by multiples of 10 What is K5 Multiplication Facts up to the 12 Times Table Multiplication Facts beyond the 12 Times Table Welcome to the multiplication facts worksheets page at Math Drills On this page you will find Multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats 65 MATH WORKSHEET 100 MULTIPLICATION PROBLEMS 14 Best Images Of Hard Multiplication Worksheets 100 Problems Math Fact Worksheets Single Digit Multiplication Worksheets Free Printable 6 Best Images Of Math Drills Multiplication Worksheets Printable Math Fact Worksheets Multiplication Facts 0 2 Worksheets Times Tables Worksheets Multiplication Worksheets Grade 1 Multiplication Table Charts Multiplication Worksheets Grade 1 Multiplication Table Charts The Multiplying 1 To 10 By 2 36 Questions Per Page A Math Worksheet From The FAQs (Frequently Asked Questions). Are 100 Multiplication Worksheets suitable for any age groups? Yes, worksheets can be tailored to various age and ability degrees, making them adaptable for numerous students. Just how frequently should pupils practice utilizing 100 Multiplication Worksheets? Consistent method is vital. Regular sessions, ideally a few times a week, can yield significant enhancement. Can worksheets alone improve math skills? Worksheets are an useful tool yet needs to be supplemented with different understanding methods for comprehensive ability development. Exist online platforms providing totally free 100 Multiplication Worksheets? Yes, lots of educational internet sites supply free access to a variety of 100 Multiplication Worksheets. Exactly how can moms and dads support their youngsters's multiplication practice in your home? Encouraging constant technique, supplying help, and creating a positive understanding environment are helpful steps.	{"url":"https://crown-darts.com/en/100-multiplication-worksheets.html","timestamp":"2024-11-12T06:27:07Z","content_type":"text/html","content_length":"29332","record_id":"<urn:uuid:4d6823f6-4d50-40fc-8821-e50a76426396>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00885.warc.gz"}
consider the following function: f(x)=(4x-10)/(x-9) step 2 of 2: what type of discontinuity is at the discontinuous point? answer \| Question AI Consider the following function: f(x)=(4x-10)/(x-9) Step 2 of 2: What type of discontinuity is at the discontinuous point? Answer Non-Removable Discontinuity Removable Discontinuity Jump Not your question?Search it Elisa FaulknerProfessional · Tutor for 6 years Non-Removable Discontinuity The function given is $f(x)=\frac{4x-10}{x-9}$, which is a rational function. A rational function is discontinuous at the values of $x$ that make the denominator equal to zero, since division by zero is undefined. In this case, the denominator $x-9$ becomes zero when $x=9$. This is the point of discontinuity for the function.<br /><br />To determine the type of discontinuity, we need to analyze the behavior of the function as $x$ approaches the point of discontinuity from both the left and the right. If the function approaches a specific finite value, then the discontinuity is removable. If the function approaches positive or negative infinity, then the discontinuity is non-removable. If the function has different limits from the left and the right, then the discontinuity is a jump discontinuity.<br /><br />For the given function, as $x$ approaches $9$ from the left (values less than $9$), the numerator $4x-10$ approaches $4(9)-106$, and the denominator $x-9$ approaches $0$ from the negative side, which means the function approaches negative infinity. As $x$ approaches $9$ from the right (values greater than $9$), the numerator $4x-10$ approaches $26$, and the denominator $x-9$ approaches $0$ from the positive side, which means the function approaches positive infinity.<br /><br />Since the function approaches negative infinity from the left and positive infinity from the right, the discontinuity at $x=9$ is not removable, and it is not a jump discontinuity either. Instead, it is an infinite discontinuity, which is a type of non-removable Step-by-step video Consider the following function: f(x)=(4x-10)/(x-9) Step 2 of 2: What type of discontinuity is at the discontinuous point? Answer Non-Removable Discontinuity Removable Discontinuity Jump All Subjects Homework Helper	{"url":"https://www.questionai.com/questions-tT8mIbtr6g/consider-following-function-fx4x10x9-step-2-2-type","timestamp":"2024-11-10T21:04:48Z","content_type":"text/html","content_length":"89173","record_id":"<urn:uuid:22667b57-9e60-40e3-8036-48b7978ba3cb>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00482.warc.gz"}
Where Are We in the Milky Way? The sun is 30,000 light years from the center of the Milky Way. What does this mean? Not much, if we do not understand what a light year is. Measuring a distance in terms of time may at first sound peculiar, but we do it often in everyday life. We say, for example, that New Haven is a two-hour drive from New York, or our house is a five-minute walk from the library. Expressing a distance in this fashion implies that we have a standard velocity. Astronomers, in fact, use a velocity standard: the speed of light in empty space is a constant and equals 299,792,458 meters per second (approximately 186,000 miles per second). Moving at this constant and universal speed, light in one year travels a distance defined by astronomers as one light year (ly), a total of 9.5 trillion kilometers. A light-year is a measure of distance. It is the distance light travels in one year at the rate of 186,000 miles per second. Alpha Centauri, the nearest star, is about four light-years away. Only about forty of the stars in the sky are within sixteen light-years of the earth. The brightest star, Sirius, is nine light-years away. Betelgeuse, one of the largest known stars, is 270 light-years away. Students looking into space at night are now looking at how far they can see. We should not lose sight of how truly immense such distances are. For example, if we were to count off the miles in a light-year, one every second-it would take us about 185,000 years. We can now use the light-year for setting the scale of the Milky Way Galaxy. In light-years, our galaxy is about 80,000 light-years across, with the sun orbiting roughly 30,000 light years from the center. Within the Milky Way disk, stars are separated by a few light-years. Astronomical Constants Astronomical Unit Au = 1.495978707 x 1013 cm Parsec = 206265 Au 3.262 ly 3.263 x 1018 cm Light Year Ly = 9.4605 x 1017 cm 6.324 x 104 Au P (pi) = 3.14159265 or 3 1/7 Circumference (C) of a circle, diameter (D), and radius, R (R =1/2 D) The area of a circle, using R and D: The surface area of a sphere of radius, R is: Distance Formula:	{"url":"https://teachersinstitute.yale.edu/curriculum/units/1998/6/98.06.09/3","timestamp":"2024-11-09T10:21:09Z","content_type":"text/html","content_length":"40540","record_id":"<urn:uuid:64abffd9-278a-4a11-b531-2696aedceb97>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00067.warc.gz"}
MATH online - Surface integral 3D Surfaces Parametric equations of a 3D-surface, simple 3D surfaces, closed 3D surfaces, tangent plane to a surface, normal to a surface, area of a surface, Schwarzt's example, orientating a surface, orientable Surface integral Surface integral in a scalar field, definition, basic properties, and method of calculation, surface integral in a vector field, definition, basic properties, and method of calculation Operators in scalar and vector fields Gradient of a scalar field, level lines, level surfaces, directional derivatives, vector fields, vector lines, flux through a surface, divergence of a vector field, solenoidal vector fields, Gauss-Ostrogradski theorem, curl of a vector field, irrotational vector fields, Stokes formula	{"url":"https://mathonline.fme.vutbr.cz/default.aspx?section=1211&server=2&article=206","timestamp":"2024-11-09T15:56:33Z","content_type":"text/html","content_length":"9606","record_id":"<urn:uuid:93f6bba0-b9b0-43b3-a728-f8590e97edcc>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00364.warc.gz"}
Comparison principle for unbounded viscosity solutions of elliptic PDEs with superlinear terms in $Du$ Tuesday, September 22, 2009 - 3:05pm for 1.5 hours (actually 80 minutes) Shigeaki Koike – Saitama University, Japan Zhiwu Lin We discuss comparison principle for viscosity solutions of fully nonlinear elliptic PDEs in $\R^n$ which may have superlinear growth in $Du$ with variable coefficients. As an example, we keep the following PDE in mind:$$-\tr (A(x)D^2u)+\langle B(x)Du,Du\rangle +\l u=f(x)\quad \mbox{in }\R^n,$$where $A:\R^n\to S^n$ is nonnegative, $B:\R^n\to S^n$ positive, and $\l >0$. Here $S^n$ is the set of $n\ti n$ symmetric matrices. The comparison principle for viscosity solutions has been one of main issues in viscosity solution theory. However, we notice that we do not know if the comparison principle holds unless $B$ is a constant matrix. Moreover, it is not clear which kind of assumptions for viscosity solutions at $\infty$ is suitable. There seem two choices: (1) one sided boundedness ($i.e.$ bounded from below), (2) growth condition.In this talk, assuming (2), we obtain the comparison principle for viscosity solutions. This is a work in progress jointly with O. Ley.	{"url":"https://math.gatech.edu/seminars-colloquia/series/pde-seminar/shigeaki-koike-20090922","timestamp":"2024-11-08T17:26:05Z","content_type":"text/html","content_length":"32062","record_id":"<urn:uuid:8efcf6e3-ea5d-4e3a-bccb-658419ed51e5>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00306.warc.gz"}
Steganographic algorithm based on segment compression ICONET - 2014 (Volume 2 - Issue 04) Steganographic algorithm based on segment compression DOI : 10.17577/IJERTCONV2IS04091 Download Full-Text PDF Cite this Publication Shilpa S. Gaikwad, Maruti B. Zalte, 2014, Steganographic algorithm based on segment compression, INTERNATIONAL JOURNAL OF ENGINEERING RESEARCH & TECHNOLOGY (IJERT) ICONET – 2014 (Volume 2 – Issue • Open Access • Total Downloads : 3 • Authors : Shilpa S. Gaikwad, Maruti B. Zalte • Paper ID : IJERTCONV2IS04091 • Volume & Issue : ICONET – 2014 (Volume 2 – Issue 04) • Published (First Online): 30-07-2018 • ISSN (Online) : 2278-0181 • Publisher Name : IJERT • License: This work is licensed under a Creative Commons Attribution 4.0 International License Text Only Version Steganographic algorithm based on segment compression Steganographic algorithm based on segment compression Shilpa S. Gaikwad (1), Maruti B. Zalte(2) Department of Electronics and Telecommunication K.J.Somaiya College of Engineering Mumbai-77, India shilpabshende@gmail.com (1), marutizalte@somaiya.edu (2) Abstract – Steganography is the technique of hiding confidential information within any media. Using steganography, information can be hidden in different embedding mediums, known as carriers. These carriers can be images, audio files, video files, and text files. The focus in this paper is on the use of an image file as a carrier, a new steganographic technique for concealing digital images: the Segment Compression Steganographic Algorithm (SCSA) which is based on the Karhunen-LoÃ¨ve Transform (KLT) is presented. A detailed presentation of the component parts of the algorithm follows, accompanied by quantitative analyses of parameters of interest. In addition, we make a few suggestions regarding possible further refinements of the SCSA. Index TermsSteganography, Least Significant Bit, 1. INTRODUCTION In Segment Compression Steganographic Algorithm the input data are first compressed using the KLT in order to achieve a higher concealing capacity, and then hidden in the least significant bits of the carrier object, which is represented in the RGB spatial domain. By combining the two procedures, we are aiming at three different research directions: increasing the capacity for concealing large messages, attaining a high quality stego object so that it is almost imperceptibly different from the carrier object and improving the execution time of the algorithms implementation by concurrently processing different image segments (blocks) on a multi-core microprocessor. The final purpose for creating this algorithm is to implement it on yet to be released multi-core architecture mobile devices (specifically mobile phones). The Karhunen-LoÃ¨ve Transform, also known as the Hotelling Transform or Eigenvector Transform allows an optimal compression, superior for instance to the one achieved by the popular Discrete Cosine Transform (DCT), the latter being in fact just an approximation of the KLT [3].The KLT completely decorrelates the input signals and is able to reallocate their energy in just a few components. KLTs greatest disadvantage with respect to other linear transforms is that it requires a great amount of processing on sometimes large sets of data. Because of this, practical of the KLT algorithm require important computational resources and are lengthy in terms of execution time [1]. We plan to overcome this disadvantage by dividing a digital image into blocks (segments), thereby significantly reducing the time costs. In order to evaluate the performance of Segment Compression Steganographic Algorithm, we took different parameters like compression rate, hiding time, recovery time, carrier error, message error, amount of data which can be embedded in carrier, etc. The steganography algorithm alters the carrier image by embedding information pertaining to the secret message. We can calculate the difference (alteration rate) between the original carrier image (C) and the processed image, which we will henceforth call the stego image (S). This value is the Carrier Error. Also, because of the KLT compression and of subsequent processing, the message recovered (R) from the stego image will not be identical to the original hidden message(M). The difference between M and R is the Message Error. We find that the message error increases with segment size, while the carrier error decreases. Thus, we must make a compromise when it comes to choosing the segment size. If we want a carrier alteration as imperceptible as possible, than a larger segment size is indicated, but if we are more interested in the quality of the recovered message, than we should aim for a smaller segment 3. SCSA STEP BY STEP DESCRIPTION The Segment Compression Steganographic Algorithm, like any other steganographic algorithm, is composed of two perfectly mirrored parts: obtaining the steganographied image (stego), which takes place at the sender level, and recovering the payload, which takes place at the receiver level. 1. Secret Message Representation We consider the secret message represented as a mÃ— n RGB matrix of pixels, where m is the height of the image and n the width. In order to achieve a suitable representation for processing, we separate the pixels three distinct pieces of information (Red level, Blue level and Green level), thus obtaining a (3m) Ã— n matrix we will call M '. According to the RGB color scheme, R i, j, G i, j and Bi, j are all integers in the range (0,255) and correspond to the pixel Pi, j . 2. Message Segmentation Segmentation is the key component of the algorithm. Through segmentation, we gain both in terms of concealing capacity and execution time. We use the term segment of size s to refer to a submatrix of size sÃ— n of the original pixel matrix M.. This segment is essentially composed of s contiguous lines (rows) of the segmented image. The segment corresponds to a (3 s) Ã—n submatrix of M ', since each pixel contains three independent color levels (R, G, B), which are split into three different rows in matrix M '. Following our experimental tests, we have concluded that applying the KLT on image segments instead of applying the same transform on the whole, unsegmented image, yields far better results in terms of execution time and compression rates. We have experimented with different image sets and different segment sizes and the results show that the optimum segment size is situated somewhere between 5 and 8 rows (lines). In Figure 1, we can see how the compression execution time depends on the segment size. The differences between execution times are small, but have a clear tendency. The smaller the size of the segment, the faster the compression algorithm executes. These results have a much greater significance when confronted with the execution time of the KLT on the unsegmented images. By segmenting the secret message image, we have made the compression roughly 100 times faster. Figure 1: Compression Time Vs Segment size The compression rate largely depends on the image color composition, but we can adjust this rate by changing the segment size. Figure 2 implies that a larger segment size accounts for a better compression rate. However, we can observe that there is a limit to the improvement in compression rate somewhere around size 10. From there on, the compression rate will start to degrade. Consequently, it is of no surprise that the compression rate for unsegmented images is so poor that the compressed message will not fit inside the carrier. Figure 2: Compression rate Vs Segment size 3. KLT COMPRESSION Let us consider that we have divided the image into segments of size s. The matrix M * corresponds to the first of these segments. From a probability and statistics point of view, we can treat each column vector x, j of the matrix M * as a sample of a random n-dimensional variable X. We first calculate the sample vector mean , and then we use this result to obtain the sample (3s)(3s) covariance matrix The next step is to calculate the eigenvalue i and eigenvectors vi R3sÃ— 1 of the covariance matrix. We use the Jacobi eigenvalue algorithm for this purpose. Since the covarianc matrix is obviously symmetric (x=xT) it has an orthonormal basis of eigenvectors. These eigenvectors constitute a (3s)Ã—(3s) orthogonal matrix V = [v1 v2—- v3s ], which has the property V.VT=VT.V=I3s It holds that V x V = , where is the diagonal matrix diag (1, 2,…, 3s ) [10]. The distribution of the processed matrixs M * energy (information) among the eigenvectors is indicated by the eigenvalue. The value of each eigenvalue is proportional to the quantity of energy stored by the corresponding eigenvector. To practically use the aforementioned property, we rearrange the eigenvectors of matrix V so that the first eigenvector corresponds to the largest eigenvalue; the second eigenvector corresponds to the second largest eigenvalue and so on. After that, suppose we want to compress the data so that we retain only 99% of the total energy (information). We retain only the k most significant eigenvectors, amounting to 99% (in our example) of the total energy of M . These eigenvectors form the reduced eigenvector matrix V = [v1 v2 – — vk] The final step of the compression algorithm is to obtain the projection matrix: P j = (V )T .M (1) The projection matrix is the compressed counterpart of the original segment submatrix M .Pj is a k Ã— n matrix, while M is a (3s) Ã— n, so the compression rate is the ratio k/3s. By calculating the average of compression rates for each segment, we obtained the global compression rate, which is analysed in Figure 2 with respect to segment size. 4. Hiding the message The compression rate discussed above does not take into account the internal representation of information on computers. The problem is that the entries of M * are integer values in the range (0,255) , which can be stored in a single byte, whereas the entries of the projection matrix Pj are real numbers, which require floating-point representation (at least 4 bytes) to be stored. Thus, in terms of computer bytes, the compression rate is at least 4k/3s, so we may have no actual compression at all. To achieve the original compression rate, we will have to apply a linear transform on the Pj values. We used the following formula: This transformation ensures that the new values are in the interval [0,255] and thus can be rounded to a byte value. The previous transformation produces an inevitable loss in compression quality. Fortunately, the losses are minor, as the original signal (information) is mainly stored in the eigenvectors. These eigenvectors need to be hidden together with the projection matrix inside the carrier image, in order to be able to rebuild M . We encounter the same problem: the entries of the eigenvector matrix V are real numbers, which need at least 4 bytes to be stored. This could seriously affect our compression rate, so we will resort to another transform in order to improve the compression rate, at the expense of compression quality. Since the Jacobi eigenvalue algorithm ensures that the eigenvectors entries are in the interval [-1,1], we can use the following formula: V 'i, j = V i, j 32767 (5) The new values are in the interval [-32767, 32767] and thus can be rounded to a two-byte (short) value.Now that we have minimized the amount of data to be hidden as much as possible, we can proceed to the actual hiding. We will hide the information in the least significant bits (LSB) of each byte of the carrier image. Depending on how many of these bits we use for hiding the message, we get three versions of the same algorithm: SCSA1, SCSA2 and SCSA4. The more bits we use for hiding, the more information we will be able to hide, at the expense of a greater Carrier Error. In addition to the projection matrix and eigenvector matrix, for each segment we must hide the dimensions of the projection and eigenvector matrix (k, n and 3s), and also min and max, defined by (3) and (4). All these data are essential in recovering the secret message. It is true that the extra data worsen the compression rate, but insignificantly. 5. Recovering the message The recovery process should seem straightforward since it is exactly the reverse of the hiding process. First, we extract the hidden data from the least significant bits (LSB) of the stego image. For each segment, we get the linearly processed projection and eigenvector matrix for each segment, their dimensions and min (3) and max (4). Obviously the next step is to undo the linear transformations used on the matrices. The following formulas are the exact inverses of (1) and (5): a Pji, j = Pj 'i, j (max Pj min Pj) / 255 + min Pj (6) a V i , j =V 'i, j / 32767 (7) The resulted projection matrix and reduced eigenvector matrix are just approximations of their original counterparts, hence the leading a that suggests this fact. These matrices are combined to obtain an approximation of the initial segment submatrix M *: By combining these recovered segments, we obtain an approximation of the original hidden message. 6. Results To prove the steganographic quality of the SCSA algorithm, we will present the results achieved by applying the algorithm on three representative sets of images. For each image set, we used a different variant of SCSA. The first image set was processed using SCSA1. SCSA1 ensures a very small carrier error (0.97053%). Consequently, the carrier image is barely discernible from the stego image. We can see that the recovered message quality is very high as well (message error = 0.73685%). The hiding part of the algorithm took 3.64403 seconds on a Intel(R) core TM i5- 2430M CPU with 2.4 GHz,4 GB RAM, while the recovery part took 1.66789 seconds. The compression rate (average of k/3s) was 0.493827. Carrier Image (600Ã—400) Stego Image Message or Payload (200Ã— 135) Recovered Message Figure 3: Image Set 1 Carrier Image (400 Ã—400) Stego image Message or Payload (256Ã— 256) Recovered Image Fig 4: Image Set 2 The second image set was processed using SCSA2. yields average results in terms of steganographic quality. The carrier error is larger (2.53262%) compared to that of the first image set, but so is the size of the message we can hide. The message error is higher as well (1.69553%), but this error is only influenced by the color composition of the message itself. Using the same hardware resources, we managed to execute the algorithm in less than 4.5 seconds (3.14s hiding the message + 1.34s recovering the message).The compression rate achieved was also very good (0.3). The third image set was processed using SCSA4. The carrier error is high (2.646%). Unlike the previous two stego images, the one from image set 3 shows some clear marks of alteration. Nevertheless, this may not pose a problem when the attacker does not possess the original image for comparison. The payload is recovered almost completely (message error = 2..53398%). Since we are dealing with larger images, hiding the message took longer, about 7.86213 seconds, while recovering the message took 2.66031 seconds. In terms of compression rate, we achieved very good results (0.444). The greatest advantage of SCSA4 is that it allows us to hide very large messages. Thus, it was possible to conceal(with amazing precision) a message of size 640×480 in a carrier having the same Carrier Image(640Ã— 480) Stego Image Message or Payload(640 Ã—480) Recovered Image Fig 5: Image set 3 SCSA1 SCSA2 SCSA4 0.493827 0.333333 0.444444 Hiding Time(s) 3.64403 3.14886 7.86213 1.7 1.34406 2.66031 Message error 0.73685 1.69551 2.53398 Carrier error(%) 0.97053 2.53268 2.646 Table1: Comparison of various parameters with different variants of SCSA 4. CONCLUSION The strong features of the Segment Compression Steganographic Algorithm place it in a good spot for practical applications. As mentioned, the algorithm is designed and optimized for concealing digital images in other digital images. The SCSAs greatest strengths are the excellent embedding capacity provided by the KLT compression and the good visual imperceptibility provided by the LSB embedding technique [16-18]. It is also very important to restate that the SCSA has a very short execution time, given the computational complexity of image processing [19-20]. The algorithms inherent concurrent nature recommends it for deployment on multicore platforms, for instance intelligent mobile devices with image processing capabilities. 1. S.G.Hoggar, Mathematics of Digital Images, Cambridge University Press, 2006, ISBN-13 9780521780292 2. Candik M., Brechlerova D., Digital watermarking in digital images, Security Technology, 2008. ICCST 2008. 42nd Annual IEEE International Carnahan Conference on, 13-16 Oct. 2008, pp.43-46, ISBN: 978-1-4244- 1816-9 3. S.G.Hoggar, Mathematics of Digital Images, Cambridge University Press, 2006, ISBN-13 9780521780292 4. Dafas P., Stathaki, T., Digital image watermarking using blockbased Karhunen-LoÃ¨ve transform, Image and Signal Processing and Analysis, 2003, ISPA 2003, Proceedings of the 3rd International Symposium, 18-20 Sept. 2003, pp. 1072 1075,Vol.2, ISBN: 953-184-061-X 5. Piva A., Bartolini F., Boccardi L., Cappellini V., De Rosa A., Barni M.,Watermarking through color image bands decorrelation,Multimedia and Expo, 2000, ICME 2000, IEEE International Conference on, 30 July-2 Aug. 2000, pp. 1283 – 1286 vol.3, New York,ISBN: 0-7803-6536-4 6. Moulin, P. Ivanovic, A. , The zero-rate spread-spectrum watermarking game, Signal Processing IEEE Transactions on, Apr 2003, Vol. 51, Issue: 4, pp. 1098- 1117, ISSN: 1053-587X 7. Stanescu, D, Stratulat, M., Ciubotaru, B,. Chiciudean,D, Cioarga, R., Borca, D, Digital Watermarking using Karhunen-Loeve transform, 4th International Symposium on Applied Computational Intelligence and Informatics, 2007. SACI '07, 18 May 2007, pp. 187-190, Timisoara Romania, ISBN:1-4244-1234X 8. Stanescu, D, Groza, V, Stratulat, M, Borca, D, Ghergulescu, I,"Robust Watermarking with High Bit Rate", Third International Conference on Internet and Web Applications and Services, 2008, ICIW2008, 8-13 iune 2008, Athena, Greece, pp. 257-260, 2008, ISBN: 978-0-7695-3163-2 9. Emilia Petrior, Probabiliti i statistic. Aplicaii Ã®n economie iinginerie, Editura Politehnica Timioara, 2007, ISBN 947-625-210-8 10. G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, 2003, (UPT library). 11. Daniela Snescu, Valentin StÃ¢ngaciu, Ioana Gergulescu, Mircea Stratulat, Steganography on Embedded Device, 5th International Symposium on Applied Computational Intelligence and Informatics,SACI ISBN:978-1-4244-4478-6, Timisoara, 2009, pp.313-317 12. Boncelet C., MarvelL., Lossless Compression- Based Stegnalysis of LSB Embedded Images, 41st Annual Conference on Information Sciences and Systems, CISS07,Baltimore, 14-16 March 2007,ISBN:1 – 4244-1037-1, pp.923-926 13. Feng H., Effros M., On the rate-distortion performance and computational efficiency of the Karhunen-Loeve Transformfor lossy data compression, IEEE Transaction on Image Processing, feb. 2002, vol.11, Issue2, pp.113-122 14. Ki-Hyun Jung, Kyeoung-Ju Ha, Kee- Young Yoo, Image Data Hiding Method Based on Multi-Pixel Differencing and LSB Substitution Methods, International Conference on Convergence and Hybrid 15. Informatin Technology, ICHIT08, Daejeon, 28-30 Aug., 2008,ISBN: 978-0-7695-3328-5, pp. 355-358 16. Xiaolong Li, Tieyong Zeng, Bin Yang, Improvement of the Embedding Efficiency of LSB Matching by Sum and Difference Converting Set, IEEE International Conference on Multimedia,Hannover, June 23, 2008, pp.09-212 17. W. Burger, M. Burger, Digital Image Processing, Springer, 2008,ISBN:978-1-84628-379-6 18. Chang C-C., Chou H., Lin c-C., Colour Image-hiding scheme using human visual system, Imaging Science Journal, Oxford, UK, sept. 2006, vol. 54, nr.3, pp.152-163 19. Eric Cole, Hiding in Plain Sight: Steganography and the Art of Convert Communicating, Wiley Publishing, Inc., Indianapolis, SUA, ISBN: 0- 471-44449-9, 2009 20. Kawaguci E , Eason R., Large Capacity Steganography, U.S.Patent no. 6,473,516, oct. 29, 2002 21. He Junhui Tang, Shaohua Wu Tingting, On the Security of Steganographic Techniques, Congress on Image and Signal Processing, CIPS, 2008, China, 27-30, May, pp716-719, vol.5 22. http://www.wallbank.me.uk/gallery/albums/userpics/sparrow_001_6 00×400.jpg 23. http://lindsaywenzel.com/ColeByrd.com/Images/battle%20hymn /eagle %25205.jpg You must be logged in to post a comment.	{"url":"https://www.ijert.org/steganographic-algorithm-based-on-segment-compression","timestamp":"2024-11-03T14:01:14Z","content_type":"text/html","content_length":"83327","record_id":"<urn:uuid:23e3fe62-c762-4bda-b4a0-5714ef7a6e67>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00160.warc.gz"}
A Hybrid Algorithm for Systems of Non-interacting Particles, submitted for publication, 2024. [arxiv] Three-dimensional modeling of hyphal fusion, branching and nutrient tranport in filamentous fungi, submitted for publication, 2024. Optical Neural Engine for Solving Scientific Partial Differential Equations, submitted for publication, 2024. [arxiv] ELEQTRONeX: A GPU-Accelerated Exascale Framework for Non-Equilibrium Quantum Transport in Nanomaterials, submitted for publication, 2024. [arxiv] Brownian motion of droplets induced by thermal noise, submitted for publication, 2024. [arxiv] Plasma electron acceleration driven by a long-wave-infrared laser, Nat Commun 15, 4037 (2024). [doi]. Mesh refinement in QuickPIC, submitted for publication. Comparison of adaptive mesh refinement techniques for numerical weather preidction, submitted for publication, [arxiv] AMReX and pyAMReX: Looking Beyond ECP, International Journal of High Performance Computing Applications , August 2024, [doi] 3D ferroelectric phase field simulations of polycrystalline multi-phase hafnia and zirconia based ultra-thin films, Advanced Electronic Materials, 2400085, 2024. [link] Fractal Dimensions of Jammed Packings with Power-Law Particle Size Distributions in Two and Three Dimensions, submitted for publication, [arxiv] Towards polydisperse flows with MFIX-Exa, ASME. J. Fluids Eng, 23 January 2024. [doi]. A cast of thousands: How the IDEAS Productivity project has advanced software productivity and sustainability, Computing in Science and Engineering, 2024. [ieee] [arxiv] A New Re-redistribution Scheme for Weighted State Redistribution with Adaptive Mesh Refinement, J. Comp. Phys., Volume 504, 1 May 2024. [arxiv], [doi] Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks, International Journal of High Performance Computing Applications, 10943420241227914, 2024. [link] The Pele Simulation Suite for Reacting Flows at Exascale, SIAM Proceedings Series on Parallel Processing for Scientific Computing, to appear. ExaWind: Open-Source CFD for Hybrid-RANS/LES Geometry-Resolved Wind Turbine Simulations in Atmospheric Flows, Wind Energy, 23 January 2024. [doi] PeleLMeX: an AMR Low Mach Number Reactive Flow Simulation Code without level sub-cycling, Journal of Open Source Software, 8, 2023. [link] Code generation for AMReX with applications to numerical relativity, Classical and Quantum Gravity, 8, 245013, 2023. [link] Steric effects in induced-charge electro-osmosis for strong electric fields, Physical Review Fluids, 8, 083702, 2023. [arxiv] [doi] Particle-in-Cell Simulations of Relativistic Magnetic Reconnection with Advanced Maxwell Solver Algorithms, The Astrophysical Journal, 925, 1, 2023. [arxiv] [doi] Fluctuating Hydrodynamics and the Rayleigh-Plateau Instability, PNAS, 120(30), July 2023. [arxiv] [doi] Two-Fluid Physical Modeling of Superconducting Resonators in the ARTEMIS Framework, Computer Physics Communications, 291, 2023. [arxiv] [doi] BMX: Biological Modelling and interface eXchange, Nature Scientific Reports, 13, July 2023. [doi] ERF: Energy Research and Forecasting, Journal of Open Source Software, 8(87), 5202, 2023. [doi] MFIX-Exa: CFD-DEM simulations of thermodynamics and chemical reactions in multiphase flows, Chemical Engineering Science, 273, 118614, 2023. [doi] Surface Coverage Dynamics for Reversible Dissociative Adsorption on Finite Linear Lattices, J. Chem. Phys., 159, 2023. [doi] [arxiv] Validity of path thermodynamic description of reactive systems: Microscopic simulations, Phys. Rev. E 107, 014106, 2023. [doi] A consistent adaptive level set framework for incompressible two-phase flows with high density ratios and high Reynolds numbers, J. Comp. Phys., vol. 478, 2023. FerroX: A GPU-accelerated, 3D Phase-Field Simulation Framework for Modeling Ferroelectric Devices, Computer Physics Communications, 108757, 2023 [link] A Staggered Scheme for the Compressible Fluctuating Hydrodynamics of Multispecies Fluid Mixtures, Physical Review E, 107, 015305, 2023. [arxiv] [doi] Intense infrared lasers for strong-field science, Advances in Optics and Photonics 2022. [link] Effects of the wavelength of the plasma waves on cross-field electron transport in partially magnetized plasmas, IEEE Transactions on Plasma Science, vol. 50, no. 10, pp. 3498-3506 2022. [link] SPACE: 3D parallel solvers for Vlasov-Maxwell and Vlasov-Poisson equations for relativistic plasmas with atomic transformations, Computer Physics Communications 277 (2022) 108396 2022. [link] Mutually Guided Light and Particle Beam Propagation, Scientific Reports volume 12, Article number: 4810 2022. [link] Modeling Electrokinetic Flows with the Discrete Ion Stochastic Continuum Overdamped Solvent Algorithm, Physical Review E, 106, 035104, 2022. [doi] Modeling the Lyman-alpha forest with Eulerian and SPH hydrodynamical methods, MNRAS, 518, 3, January 2023. [arxiv] [doi] Pushing the frontier in the design of laser-based electron accelerators with groundbreaking mesh-refined particle-in-cell simulations on exascale-class supercomputers, SC '22: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, November 2022, Article No.: 3, Pages 1–12 [doi] Large-Scale Frictionless Jamming with Power-Law Particle Size Distributions, Physical Review E, 106, 034901, 2022. [doi] Characterization of Transmission Lines in Microelectronics Circuits using the ARTEMIS Solver, IEEE J. on Multiscale and Multiphysics Comp. Tech., 8, 2022. [link] Neural Networks for Nuclear Reactions in MAESTROeX, The Astrophysical Journal, 940, 2, 2022. [link] An Improved Method for Coupling Hydrodynamics with Astrophysical Reaction Networks, The Astrophysical Journal, 936, 6, 2022. [link] Fluctuations and Power-Law Scaling of Dry, Frictionless Granular Rheology Near the Hard-Particle Limit, Physical Review Fluids, 7, 084303, 2022. [doi] PeleC: An Adaptive Mesh Refinement Solver for Compressible Reacting Flows, International Journal of High Performance Computing Applications, 2022. [doi] In Situ Feature Analysis for Large-Scale Multiphase Flow Simulations,, Journal of Computational Science, 2022. Hurricane-like Vortices in Conditionally Unstable Moist Convection, Journal of Advances in Modeling Earth Systems, 2022. [ESSOAr] Weighted State Redistribution Algorithms for Embedded Boundary Methods, J. Comp. Phys., Vol 464, Sept. 2022. Thermal Fluctuations in the Dissipation Range of Homogeneous Isotropic Turbulence, J. Fluid Mech., 939, 2022. [link] HiPACE++: a portable, 3D quasi-static Particle-in-Cell code, Computer Physics Communications, 278, 108421, 2022. [link][arXiv] Dark Matter from Axion Strings with Adaptive Mesh Refinement, Nature Communications, 13, 1049, 2022. [doi][arXiv] A Moving Embedded Boundary Approach for the Compresible Navier-Stokes Equations in a Block-Structured Adaptive Refinement Framework, J. Comp. Phys., 465, 2022. [doi][arXiv] "A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries", J. Comp. Phys., 450, 2022. [arxiv] Surrogate Optimization of Deep Neural Networks for Groundwater Predictions, J. Global Optimization, 81, 2021. [springer]. Neutrino Fast Flavor Instability in Three Dimensions, Physical Review D, 104, 103023, 2021. [doi] Squeeze-film effect on atomically thin resonators in the high-pressure limit, Nano Letters, 2021. [doi] Porting WarpX to GPU-accelerated platforms, Parallel Computing, 2021. Flow and Arrest in Stressed Granular Materials, Soft Matter, 2022. [doi] Jamming of Bidisperse Frictional Spheres, Physical Review Research, 3(3), L032042, 2021. [doi] Shear is Not Always Simple: Rate-Dependent Effects of Loading Geometry on Granular Rheology, Physical Review Letters, 127, 268003, 2021. [doi] Nyx: A Massively Parallel AMR Code for Computational Cosmology, Journal of Open Source Software, 6(63), 3068, 2021. [doi] Probing strong-field QED with Doppler-boosted petawatt-class lasers, accepted by Physical Review Letters, May 10, 2021, [PRL] A Discrete Ion Stochastic Continuum Overdamped Solvent Algorithm for Modeling Electrolytes, Physical Review Fluids, 6(4), 044309, 2021. [arxiv] Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure, Journal of Physics: Condensed Matter, 33, 184002, 2021. [doi] The divergence of nearby trajectories in soft-sphere DEM Particuology, 63, 1, 2022. [doi] AMReX: Block-Structured Adaptive Mesh Refinement for Multiphysics Applications, International Journal of High Performance Computing Applications, 35(6):508-526, 2021. [IJHPCA] [doi] Dynamics of Laterally Propagating Flames in X-Ray Bursts. II. Realistic Burning and Rotation, The Astrophysical Journal, 912 36, 2021. [doi] A Massively Parallel Time-Domain Coupled Electrodynamics-Micromagnetics Solver, International Journal of High Performance Computing Applications, 10943420211057906, 2021. [link] Particle-in-cell Simulation of the Neutrino Fast Flavor Instability, Physical Review D, 103, 083013, 2021. [doi] Modeling of a chain of three plasma accelerator stages with the WarpX electromagnetic PIC code on GPUs, Physics of Plasmas, 28(2), 2021. [doi] Viscometric Flow of Dense Granular Materials under Controlled Pressure and Shear Stress, Journal of Fluid Mechanics, 907(A18) 1, 2021. [doi] Massively parallel finite difference elasticity using a block-structured adaptive mesh refinement with a geometric multigrid solver, J. Comp. Phys., 427, 2021. [doi] [arxiv]. "A statistical model to predict ignition probability", Combustion and Flame, 2021. [arxiv] [doi] "Kinetic, 3-D, PIC-DSMC Simulations of Ion Thruster Plumes and the Backflow Region" IEEE Transactions on Plasma Science, June 2020. [doi] "A self-consistent open boundary condition for fully-kinetic plasma thruster simulations", IEEE Transactions on Plasma Science, March 2020. [doi] MFIX:Exa: A Path Towards Exascale CFD-DEM Simulations, International Journal of High Performance Computing Applications, April 16, 2021. On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows, Int. J. Numer. Methods Fluids, 2021. [doi] Preparing nuclear astrophysics for exascale, SC20: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, p. 1, 2020 CASTRO: A Massively Parallel Compressible Astrophysics Simulation Code, Journal of Open Source Software, 5, 54, 2513, 2020 Particle-Continuum Coupling and its Scaling Regimes: Theory and Applications, Advanced Theory and Simulations, Vol. 3, No. 5, 1900232, 2020. [doi] Modeling of emittance growth due to Coulomb collisions in plasma-based accelerators, Physics of Plasmas, October, 2020. [doi] Toward the modeling of chains of plasma accelerator stages with WarpX, Journal of Physics: Conference Series, 1596, 1, 012059, 2020 Feature Analysis, Tracking, and Data Reduction: An Application to Multiphase Reactor Simulation MFiX-Exa for In-Situ Use Case, Computing in Science & Engineering, doi: 10.1109/MCSE.2020.3016927, 2020. [doi] Machine Learning of Combustion LES Models from Reacting Direct Numerical Simulation in Data Analysis for Direct Numerical Simulations of Turbulent Combustion pp. 273-292, Sprint, Cham [doi] An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions, Proc. Combust. Inst., 38, 1961-1969, 2021. Direct numerical simulation of a spatially developing n-dodecane jet flame under Spray A thermochemical conditions: Flame structure and stabilisation mechanism, Combust. Flame, 217:57-76, 2020. A Low Mach Number Fluctuating Hydrodynamics Model For Ionic Liquids, Phys. Rev. Fluids, 5, 9, 2020. [arxiv] "Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows", Commun. in Appl. Math. and Comput. Sci, 15-1 (2020), 1--36. [arxiv] "A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates", Composite Structures, 242, June 2020. [doi] Iterative construction of Gaussian process surrogate models for Bayesian inference, Journal of Statistical Planning and Inference, 207, July 2020. [doi] Acoustic flows in a slightly rarefied gas, Physical Review Fluids, 5(4), 043401, 2019. [doi] Exascale applications: skin in the game, Phil. Trans. R. Soc. A, 2020. [doi]. Optimization of the Eddy-Diffusivity/Mass-Flux shallow cumulus and boundary-layer parametrization using surrogate models Journal of Advances in Modeling Earth Systems (JAMES), 11, 2, Feb. 2019. [doi] Structure and propagation of two-dimensional, partially premixed, laminar flames in diesel engine conditions, Proc. Combust. Inst 37 (2) 2018. [doi] Deep learning for presumed probability density function models Combustion and Flame 208, 2019. [doi] Analysis of chemical pathways for n-dodecane/air turbulent premixed flames, Combustion and Flame 207, p. 36-50, 2019. [doi] An algorithmic framework for the optimization of computationally expensive bi-fidelity black-box problems, INFOR: Information Systems and Operational Research., 2019. [link]. Surrogate Optimization of Computationally Expensive Black-box Problems with Hidden Constraints INFORMS Journal on Computing, 31(4) 633, 2019. [doi] Origin of spurious oscillations in lattice Boltzmann simulations of oscillatory noncontinuum gas flows, Physical Review E, 100(5), 053317, 2019. [doi] MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver Journal of Open Source Software, 4, 44, 1757, 2019. [link] MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver Astrophysical Journal, 887, 2, 2019. [link] Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections, Astrophysical Journal, 886, 2, 2019 [arxiv] Asynchronous AMR on Multi-GPUs, ISC High Performance conference: REFAC'19, 2019. An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions, Physics of Fluids, 2019 [doi]. AMReX: a framework for block-structured adaptive mesh refinement, Journal of Open Source Software, 4(37), 1370, 2019. [doi] Statistical mechanics of transport processes in active fluids. II. Equations of hydrodynamics for active Brownian particles, J. Chem. Phys., 150, 164111, 2019. [doi] A spectral deferred correction strategy for low Mach number flows subject to electric fields Combustion Theory and Modelling, 2019, [link], [arXiv]. Modelling low Mach number stellar hydrodynamics with MAESTROeX proceedings of Astronum 2019, Paris, July 1-5, 2019. The Castro AMR Simulation Code: Current and Future Developments proceedings of Astronum 2019, Paris, July 1-5, 2019. On the Suppression and Distortion of Non-Equilibrium Fluctuations by Transpiration, Phys. Fluids, 149, 052002, 2019. [doi] Fluctuating hydrodynamics of electrolytes at electroneutral scales, Phys. Rev. Fluids. 4, 4, 2019. [link] Toward resolved simulations of burning fronts in thermonuclear X-ray bursts, Journal of Physics: Conference Series, 1225, p, 012005, 2019. [arxiv] Towards the Distributed Burning Regime in Turbulent Premixed Flames, Journal of Fluid Mechanics 871, pp. 1-21. 2019. [arxiv] A Bayesian approach to calibrating hydrogen flame kinetics using many experiments and parameters, Combustion and Flame, 205, pp. 305-315, 2019. [arxiv] A Fourth-Order Adaptive Mesh Refinement Algorithm for the Multicomponent, Reacting Compressible Navier-Stokes Equations, Combustion Theory and Modelling, 23:4, 592-625, 2019. [arxiv] Fluctuating hydrodynamics and Debye-H&uumlckel-Onsager theory for electrolytes, Current Opinion in Electrochemistry, 13, 2019. [link], [arxiv] "Phase asynchronous AMR execution for productive andperformant astrophysical flows", Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis, 2018, p. 70 "Concurrent Implicit Spectral Deferred Correction Scheme for Low-Mach Number Combustion with Detailed Chemistry", Combustion and Flame 2018. [arxiv] [doi] "Highly parallelisable simulations of time-dependent viscoplastic fluid flow simulations with structured adaptive mesh refinement", Physics of Fluids, 30:9, 2018. Named Editor's Pick. [doi] "Fluctuating hydrodynamics of reactive liquid mixtures," J. Chem. Phys. 149, 084113, 2018. [doi] [arxiv] "Nature of intrinsic uncertainties in equilibrium molecular dynamics estimation of shear viscosity for simple and complex fluids," J. Chem. Phys. 149, 044510, 2018. [doi] [arxiv] "Warp-X: a new exascale computing platform for beam-plasma simulations," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , 2018 [arxiv] Python-based in situ analysis and visualization Proceedings of the Workshop on In Situ Infrastructures for Enabling Extreme-Scale Analysis and Visualization - ISAV 18, ACM Press, 2018 "A Hybrid Adaptive Low-Mach-Number/Compressible Method: Euler Equations," Journal of Computational Physics, Volume 372, Pages 1027-1047, 2018. [pdf]. Toward simulating Black Widow binaries with CASTRO Journal of Computational Science Education Volume 8, Issue 3, pp. 25-29, 2018 "Iterative importance sampling algorithms for parameter estimation problems," SIAM J. Scientific Computing 40 (2) B329-B352, 2018. [arxiv] "Efficient reactive Brownian dynamics," J. Chem. Phys. 148, 034103, 2018. [doi] [arxiv] "Molecular hydrodynamics: Vortex formation and sound wave propagation," J. Chem. Phys. 148, 024506, 2018. [doi] [arxiv] "Implicit-Explicit Runge-Kutta Methods for Non-Hydrostatic Atmospheric Models", Geosci. Model Dev., 11(4), pp 1497-1515, 2018. [pdf] "Implicit Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity", Comput. Methods in Appl. Mech. Eng., 331, pp 701-727, 2018. [link] "A conservative, thermodynamically consistent numerical approach for low Mach number combustion. I. Single-level integration," Combust. Theor. Model., vol. 22, no. 1, pp. 156-184, 2018. [link] "Meeting the Challenges of Modeling Astrophysical Thermonuclear Explosions: Castro, Maestro, and the AMReX Astrophysics Suite", J. Phys.: Conf. Ser. 1031, 2018. [arxiv] [iop] "Nature of self-diffusion in two-dimensional fluids," New J. Phys. 19, 123038, 2017. [doi] [arxiv] "Very Low-energy Supernovae: Light Curves and Spectra of Shock Breakout", Astrophysical Journal, 845, 103, 2017. [arxiv] "Overlapping Data Transfers with Computation on GPU with Tiles", 2017 46th International Conference on Parallel Processing (ICPP), pp. 171-180 [link] "Fluctuation-enhanced electric conductivity in electrolyte solutions", P. Natl. Acad. Sci. USA, 114, 41, 2017. [link] "Nonintrusive AMR Asynchrony for Communication Optimization," Euro-Par 2017 [pdf] "Navier-Stokes Characteristic Boundary Conditions Using Ghost Cells," AIAA J., Vol. 55, No. 10 : pp. 3399-3408, 2017 [doi] "Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach," J. Chem. Phys. 146, 124110, 2017. [doi] [arxiv] "Direct numerical simulation of two-stage combustion and flame stabilization in diesel engine-relevant conditions" 26th ICDERS, Boston, USA, 2017. "Navier-Stokes Characteristic Boundary Conditions Using Ghost Cells", 23rd AIAA Computational Fluid Dynamics, Denver, CO, USA, June 6 2017. [pdf] " A Hybrid Adaptive Low-Mach-Number/Compressible Method for the Euler Equations", 23rd AIAA/CEAS Aeroacoustics Conference, Denver, CO, USA, June 5 2017. [pdf] "GOSAC: Global Optimization with Surrogate Approximation of Constraints", Journal of Global Optimization. 69(1), pp 117-136, 2017. [link]. "SOCEMO: Surrogate Optimization of Computationally Expensive Multi-Objective Problems", INFORMS Journal on Computing. 29(4), pp 581-596, 2017. [link]. "Achieving algorithmic resilience for temporal integration through spectral deferred corrections," Commun. in Appl. Math. and Comput. Sci, 12(1), pp 25-50, 2017. [arxiv]. "Effect of turbulence-chemistry interactions on chemical pathways for turbulent hydrogen-air premixed flames," Combust. Flame, 176, pp. 191-201, 2017. "Sensitivity of chemical pathways to reaction mechanisms for n-dodecane," 10th U. S. National Combustion Meeting, April, 2017. "Turbulence effects on the chemical pathways for premixed Methane/Air flames," 55th AIAA Aerospace Sciences Meeting, January, 2017. [doi] "Turbulence-Flame Interactions in Lean Premixed Dodecane Flames," Proc. Combust. Inst., 36(2), pp. 2005-2016, 2017. [doi] "Topology-Aware Performance Optimization and Modeling of Adaptive Mesh Refinement Codes for Exascale," COMHPC 2016 - SC16 Workshop on Communication Optimization in High Performance Computing, Salt Lake City, UT, November 18, 2016. [pdf] "Perilla: Metadata-based optimizations of an asynchronous runtime for adaptive mesh refinement," SC '16 Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, p. 81, 2016 "Experiences of applying one-sided communication to nearest-neighbor communication," Proceedings of the First Workshop on PGAS Applications, pp 17-24, 2016 [pdf] "Low Mach Number Fluctuating Hydrodynamics for Electrolytes," Phys. Rev. Fluids, 1, 074103, 2016. [link] "In situ and in-transit analysis of cosmological simulations," Computational Astrophysics and Cosmology, 3:4, 2016 [pdf] "Accelerating Science with the NERSC Burst Buffer Early User Program," CUG 2016 [pdf] "TiDA: High-Level Programming Abstractions for Data Locality Management," High Performance Computing: 31st International Conference, ISC High Performance 2016, Springer, pp 116-135, 2016. "BoxLib with Tiling: An AMR Software Framework," SIAM J. Scientific Computing, 38(5):S156-S172 , 2016 [arxiv] "White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification", Astrophysical Journal, 819, 94, 2016. [arxiv] "A High-Order Spectral Deferred Correction Strategy for Low Mach Number Flow With Complex Chemistry," Combust. Theor. Model., vol. 20, no. 3, pp. 521-547, 2016. [link] "Three-Dimensional Direct Numerical Simulation of Turbulent Lean Premixed Methane Combustion with Detailed Kinetics," Combustion and Flame, 166, pp. 266-283, 2016. [DOI] "Low Mach Number Modeling of Convection in Helium Shells on Sub-Chandrasekhar White Dwarfs II: Bulk Properties of Simple Models," Astrophysical Journal, 827, 84, 2016. [iop]. "Hot and Turbulent Gas in Clusters," Monthly Notices of the Royal Astronomical Society, 459(1), 701-719, 2016 [arxiv]. "Investigation of chemical pathways for turbulent Hydrogen-Air premixed flames" AIAA Aerospace Sciences Meeting, San Diego, CA, 2016. [DOI] "MISO: Mixed-Integer Surrogate Optimization Framework", Optimization and Engineering, 17:1, 177-203, March 2016. [link]. "An a Priori DNS Subgrid Analysis of the Presumed beta-PDF Model," J. Hydrogen Energy, 40(37), pp. 12811-12823, 2015. "Pair-Instability Supernovae of Non-Zero Metallicity Stars," Numerical Modeling of Space Plasma Flows, ASTRONUM-2014, 498, 2015. [arxiv]. "Low Mach Number Fluctuating Hydrodynamics of Binary Liquid Mixtures," Comm. App. Math. and Comp. Sci., vol. 10, no. 2, 2015. [pdf]. "Understanding Ignition in Type Ia Supernovae", 25rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Leeds, UK, August 2-7, 2015. "Fluctuating hydrodynamics of multispecies reactive mixtures," J. Chem. Phys., 142, 224107, 2015 [arxiv]. "Low Mach Number Fluctuating Hydrodynamics of Multispecies Liquid Mixtures," Phys. Fluids, 27, 037103, 2015. [arxiv]. "A combined computational and experimental characterization of lean premixed turbulent low swirl laboratory flames. II. Hydrogen flames.", Combustion and Flame, 162(5), pp. 2148-2165, 2015. [CNF]. "The Lyman-alpha forest in optically-thin hydrodynamical simulations," Monthly Notices of the Royal Astronomical Society, 446, 3697-3724, 2015. [arxiv]. " Influence of adaptive mesh refinement and the hydro solver on shear-induced mass stripping in a minor merger scenario," Astronomy and Computing, 9, 49-64, March 2015 [arxiv]. "Topology and Burning Rates of Turbulent, Lean, H2-Air Flames", Combustion and Flame 162, pp. 4553-4565, 2015 [DOI]. "Comparisons of Two- and Three-Dimensional Convection in Type I X-ray Bursts," Astrophysical Journal, 807, 60, 2015. [arxiv]. "A Low Mach Number Model for Moist Atmospheric Flows," Journal of the Atmospheric Sciences, 72(4), pp. 1605-1620, 2015 [arxiv]. "Interweaving PFASST and parallel multigrid", SIAM J. Scientific Computing, 37(5), pp. S244-S263, 2015. "Inexact Spectral Deferred Corrections", Domain Decomposition Methods in Science and Engineering XXII, 104, pp. 127--133, 2015. "Two-Dimensional Core-Collapse Supernova Models with Multi-Dimensional Transport," Astrophysical Journal, 800, 10, 2015. [arxiv]. "ExaSAT: An Exascale Co-Design Tool for Performance Modeling," International Journal of High Performance Computing Applications (IJHPCA), February 2015, doi: 10.1177/1094342014568690 "Leading Edge Statistics of Turbulent, Lean, H2-Air Flames," Proc. Combust. Inst. 35, pp. 1313-1320, 2014. [PCI]. "High order schemes based on operator splitting and deferred corrections for stiff time dependent PDEs", https://hal.archives-ouvertes.fr/hal-01016684, 2014. "A space-time parallel solver for the three-dimensional heat equation", Parallel Computing: Accelerating Computational Science and Engineering (CSE), 25, pp. 263--272. IOS Press. 2014. "CH4 Parameter Estimation in CLM4.5bgc Using Surrogate Global Optimization", Geoscientific Model Development, 8:141-207, 2015 [pdf]. "Optimizing For Reacting Navier-Stokes Equations" in "High Performance Parallelism Pearls: Multicore And Many-Core Programming Approaches", James Reinder and Jim Jeffers (Eds.), Morgan Kaufmann, 2014. [link] "Turbulence-Chemistry Interaction in Lean Premixed Hydrogen Combustion," Proc. Combust. Inst. 35(2), pp. 1321-1329, 2014 [PCI]. "Modeling Multi-Phase Flow using Fluctuating Hydrodynamics", Phys. Rev. E, 90(3), 033014, 2014. [arxiv]. "Efficient Variable-Coefficient Finite-Volume Stokes Solvers," Commun. Comput. Phys., 16, 1263-1297, 2014. [link] "Low Mach Number Modeling of Stratified Flows," Finite Volumes for Complex Applications VII -- Methods and Theoretical Aspects, Springer Proceedings in Mathematics and Statistics, eds. J. Fuhrmann, M. Ohlberger, C. Rohde, Berlin, June 2014. [link] "A Survey of High Level Frameworks in Block-Structured Adaptive Mesh Refinement Packages", Journal of Parallel and Distributed Computing, 74, pp. 3217-3227, 2014 [arxiv] [doi]. "Large-eddy simulations of isolated disk galaxies with thermal and turbulent feedback," Monthly Notices of the Royal Astronomical Society, 442, pp. 3407-3426, 2014. "Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids" Comm. App. Math. and Comp. Sci., vol. 9, no. 1, 2014. [pdf] "Multidimensional Modeling of Type I X-ray Bursts. II. Two-Dimensional Convection in a Mixed H/He Accretor", Astrophysical Journal, 788, 115, 2014. [arxiv] "Cosmological Fluid Mechanics with Adaptively Refined Large Eddy Simulations," Monthly Notices of the Royal Astronomical Society, 440, pp. 3051-3077, 2014. [arxiv] "Fluctuating hydrodynamics of multispecies nonreactive mixtures" Physical Review E, vol. 89, No. 1, January 2014. [pdf] "The Deflagration Stage of Chandrasekhar Mass Models for Type Ia Supernovae: I. Early Evolution", Astrophysical Journal, 782, 11, 2014. [iop] "s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid", Proceedings of the 28th IEEE International Parallel & Distributed Processing Symposium, May 2014. "Pair Instability Supernovae of Very Massive Population III Stars" Astrophysical Journal, 792, 44, 2014. [arxiv]. "Two-Dimensional Simulations of Pulsational Pair-Instability Supernova", Astrophysical Journal, 792, 28, 2014. [arxiv]. "The General Relativistic Instability Supernova of a Supermassive Population III Star", Astrophysical Journal, 790, 162, 2014. "A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations," Monthly Weather Review, 142, pp. 4269--4283, 2014 [arxiv]. "High-Order Algorithms for Compressible Reacting Flow with Complex Chemistry", Combustion Theory and Modelling, pp. 361-387, May 2014 [doi] [arxiv]. "A multi-level spectral deferred correction method", BIT Numerical Mathematics, 2014 [arxiv]. "Analysis of operator splitting in the non-asymptotic regime for nonlinear reaction-diffusion equations. Application to the dynamics of premixed flames", SIAM J. Num. Anal., 52, 1311-1334, 2014. "Efficient implementation of a multi-level parallel in time algorithm", Proceedings of the 21st International Conference on Domain Decomposition Methods, DD21, , 98, 359-366, 2014. "Simulation of Nitrogen Emissions in a Premixed Hydrogen Flame Stabilized on a Low Swirl Burner", Proceedings of the Combustion Institute, Proceedings of the Combustion Institute, 34(1), pp. 1173-1182, 2013. [pdf] "Numerical Approaches for Multidimensional Simulations of Stellar Explosions", Astronomy and Computing, 3-4, pp. 70-78, Nov.-Dec. 2013. [doi] Tiling as a Durable Abstraction for Parallelism and Data Locality, WOLFHPC 2013 - SC13 Workshop on Domain-Specific Languages and High-Level Frameworks for High-Performance Computing, 2013. An AMR Computation and Communication Dependency and Analysis Methodology, IA^3 2013 - SC13 Workshop on Irregular Applications: Architectures and Algorithms, 2013. [arxiv] "The Most Powerful Stellar Explosion", Bulletin of the American Physical Society, 2013, vol. 58, no. 4. "Software Design Space Exploration for Exascale Combustion Co-design", International Supercomputing Conference 2013, Lecture Notes in Computer Science, vol. 7905, 2013, pp 196-212. "Low-Mach Number Modeling of Core Convection in Massive Stars", Astrophysical Journal, 773, 137, 2013. [pdf] "Carbon Deflagration in Type Ia Supernovae: I. Centrally Ignited Models", Astrophysical Journal, 771, 58, 2013. "Low Mach Number Modeling of Convection in Helium Shells on Sub-Chandrasekhar White Dwarfs. I. Methodology", Astrophysical Journal, 764, 97, 2013. [pdf] "CASTRO: A New Compressible Astrophysical Solver. III. Multigroup Radiation Hydrodynamics", Astrophysical Journal Supplement Series, 204, 7, 2013. [pdf] "On the Use of Higher-Order Projection Methods for Incompressible Turbulent Flow", SIAM J. Sci. Comput., 35, 1, B25-B42, 2013. [pdf] "Nyx: A Massively Parallel AMR Code for Computational Cosmology" Astrophysical Journal, 765, 39, 2013. [pdf] "Conservative Initial Mapping for Multidimensional Simulations of Stellar Explosions", Journal of Physics: Conference Series, 402, Conf. 1, 2012. "A massively space-time parallel N-body solver", Proceedings of the International Conference on High Performance Computing, SC'12, 92:1-11, 2012. "Integrating an N-body problem with SDC and PFASST", Proceedings of the 21st International Conference on Domain Decomposition Methods, DD21, 2012. "Staggered Schemes for Fluctuating Hydodynamics", Multiscale Modeling and Simulation, 10, 4, 1360-1408, 2012. [pdf] "Fluctuating Hydrodynamics and Direct Simulation Monte Carlo", 28th International Symposium on Rarefied Gas Dynamics , AIP Conf. Proc. 1501 , 695-704, 2012. [pdf] "A Deferred Correction Coupling Strategy for Low Mach Number Flow with Complex Chemistry", Combustion Theory and Modelling, 16(6), pp. 1053-1088, 2012. [pdf] "Investigation of Turbulence in the Early Stages of a High Resolution Supernova Simulation", Proceedings of the Supercomputing 2012 Conference. [pdf] "Shear instability of internal solitary waves in Euler fluids with thin pycnoclines", Journal of Fluid Mechanics, 710, pp. 324-361, 2012. "Optimization of Geometric Multigrid for Emerging Multi- and Manycore Processors", Proceedings of the Supercomputing 2012 Conference, 2012. "Implementation and Optimization of miniGMG - a Compact Geometric Multigrid Benchmark", LBNL 6676E, December 2012. "High-Resolution Simulations of Convection Preceding Ignition in Type Ia Supernovae Using Adaptive Mesh Refinement", Astrophysical Journal, 745, 73, 2012. [pdf] [arxiv] "The Hydrodynamic Origin of Neutron Star Kicks", Monthly Notices of the Royal Astronomical Society, 423, Issue 2, June 2012. "An Empirical Model for the Ignition of Explosively Dispersed Aluminum Particle Clouds", Shock Waves, 22, 591, 2012. [pdf] "An Adaptive Mesh Refinement Algorithm for Compressible Two-Phase Flow In Porous Media", Computational Geosciences, 16, 577-592, 2012. [pdf] "A combined computational and experimental characterization of lean premixed turbulent low swirl laboratory flames. I. Methane flames.", Combustion and Flame, 159(1), 275-290, 2012. [pdf] "Acceleration of porous media simulations on the Cray XE6 platform", Proceedings of CUG2011, Fairbanks, Alaska, 2011. "Induced Rotation in Three-Dimensional Simulations of Core-Collapse Supernovae: Implications for Pulsar Spins," Astrophysical Journal, 732, 57, 2011. [arxiv]. "The potential role of spatial dimension in the neutrino-driving mechanism of core-collapse supernova explosions,", Comp. Phys. Comm., 182, Issue 9, pp. 1764-1766, 2011. "Hydrodynamic fluctuations in a particle-continuum hybrid for complex fluids", 27th International Symposium on Rarefied Gas Dynamics , AIP Conf. Proc. 1333 , 551-556, 2011. [pdf] "An Empirical Model for the Ignition of Aluminum Particle Clouds Behind Blast Waves", 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine, CA, July 24-29, 2011. "Ignition of Aluminum Particle Clouds Behind Reflected Shock Waves", 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine, CA, July 24-29, 2011. [pdf] "Spherical Combustion Clouds in Explosions", 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine, CA, July 24-29, 2011. [pdf] "From Convection to Explosion: End-to-End Simulation of Type Ia Supernovae," Proceedings of SciDAC 2011, Denver, Colorado, July 2011. [pdf] [arxiv] "Riemann Solver for the Nigmatulin Model of Two-Phase Flow", 17th Biennial International Conference of the APS Topical Group on Shock Compression of Condensed Matter, Chicago, IL, June 26-July 1, "CASTRO: A New Compressible Astrophysical Solver. II. Gray Radiation Hydrodynamics", Astrophysical Journal Supplement Series, 196, 20, 2011 [pdf] "Enhancement of Diffusive Transport by Nonequilibrium Thermal Fluctuations", JSTAT, Vol. 2011, P06014, (2011). [pdf] "Diffusive Transport by Thermal Velocity Fluctuations", Phys. Rev. Lett., Vol. 106, No. 20, page 204501, 2011. [pdf] "Burning Thermals in Type Ia Supernovae", Astrophysical Journal, 738, pp. 94-107, 2011. [ApJ] [pdf] "The Convective Phase Preceding Type Ia Supernovae", Astrophysical Journal, 740, 8, (2011). [pdf] "A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws", SIAM J. Sci. Comput., vol. 33, no. 4, 2011. [pdf] "An Unsplit, Higher-Order Godunov Method Using Quadratic Reconstruction for Advection in Two Dimensions", Comm. App. Math. and Comp. Sci., vol. 6, no. 1, 2011. [pdf] "Analysis of subgrid scale phenomena of premixed turbulent combustion of methane and hydrogen in comparable regimes",, Center for Turbulence Research, Annual Research Briefs, 2012. "A Priori Assessment of the Potential of Flamelet Generated Manifolds to Model Lean Turbulent Premixed Hydrogen Combustion," In: Kuerten H., Geurts B., Armenio V., Froehlich J. (eds) Direct and Large-Eddy Simulation VIII. ERCOFTAC Series, vol 15, Springer, Dordrecht, 2011 [doi] "Turbulence-flame interactions in lean premixed hydrogen: transition to the distributed burning regime", Journal of Fluid Mechanics, 680, pp. 287-320, 2011. [JFM] [pdf] "Adaptive Methods for Simulation of Turbulent Combustion" in "Turbulent Combustion Modeling, Advances, New Trends and Perspectives Series: Fluid Mechanics and Its Applications", Echekki and Epaminondas (Eds.), Springer, Vol. 95, 2011. [link] "Turbulent Oxygen Flames in Type Ia Supernovae", Astrophysical Journal, 730, 144-151, (2011). [ApJ] [pdf] "Flames in Type Ia Supernova: Deflagration-Detonation Transition in the Oxygen Burning Flame", Astrophysical Journal, 734, 37-41, (2011). [ApJ] [pdf] "Multidimensional Modeling of Type I X-ray Bursts. I. Two-Dimensional Convection Prior to the Outburst of a pure ^4He Accretor", Astrophysical Journal, 728, 118, Feb. 2011. [arxiv] [pdf] "Multidimensional Simulations of Pair-Instability Supernovae", Computer Physics Communications, 182:1, 254-256, January 2011. [arxiv]. "Numerical Simulation of Nitrogen Oxide Formation in Lean Premixed Turbulent Flames", Proc. Combust. Inst. 33, pp. 1591-1599, 2011. [doi] "Properties of Lean Turbulent Methane-Air Flames with Significant Hydrogen Addition", Proc. Combust. Inst. 33, pp. 1601-1608, 2011. [doi] "Characterization of Low Lewis Number Flames", Proc. Combust. Inst. 33, pp. 1463-1471, 2011. [PCI] "Lewis Number Effects in Distributed Flames", Proc. Combust. Inst. 33, pp. 1473-1480, 2011. [PCI] "Feature Tracking Using Reeb graphs", Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications, edited by V. Pascucci, X. Tricoche, H. Hagen, and J. Tierny, Springer-Verlag, pp. 241-253, LBNL 4226E, 2011. "Interactive Exploration and Analysis of Large Scale Turbulent Combustion Using Topology-based Data Segmentation", IEEE Transactions on Visualization and Computer Graphics,, 17(9), pp. 1307-1324, LBNL 5921E, doi: 10.1109/TVCG.2010.253, 2011. "MAESTRO, CASTRO and SEDONA -- Petascale Codes for Astrophysical Applications," Proceedings of SciDAC 2010, Chattanooga, Tennessee, July 2010. [arxiv] "Type Ia Supernovae: Advances in Large Scale Simulation," Proceedings of SciDAC 2010, Chattanooga, Tennessee, July 2010. [pdf] "Simulation of Nitrogen Emissions in a Low Swirl Burner," Proceedings of SciDAC 2010, Chattanooga, Tennessee, July 2010. [pdf] "Dimension as a Key to the Neutrino Mechanism of Core-Collapse Supernova Explosions," Astrophysical Journal, 720, 694, Sept. 2010. [arxiv]. "Three-dimensional simulations of Rayleigh-Taylor mixing in core collapse supernovae with CASTRO", Astrophysical Journal, 723, 353, October 2010. "MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows", Astrophysical Journal Supplement Series, 188, 358-383, June 2010. [pdf] [arxiv] "CASTRO: A New Compressible Astrophysical Solver. I. Hydrodynamics and Self-Gravity", Astrophysical Journal, 715, 1221-1238, June 2010. [pdf] [IOP] [arxiv] "Two Dimensional Simulations of Pair-Instability Supernovae", Conference on The First Stars and Galaxies: Challenges for the Next Decade, Austin, Texas, March 8-11, 2010, Conference Proceedings, published by the American Institute of Physics. [AIP] "High resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers", Advances in Water Resources, 33(4):443-455, 2010. [pdf] A hybrid particle-continuum method for hydrodynamics of complex fluids", SIAM J. Multiscale Modeling and Simulation, 8(3):871-911, 2010. [pdf] "Distributed Flames in Type Ia Supernovae", Astrophysical Journal, 710, 1654-1663, February 2010. [pdf] "Primordial Core-Collapse Supernovae and the Chemical Abundances of Metal-Poor Stars," Astrophysical Journal, 709, 11-26, January 2010. [arxiv] "On the Accuracy of Explicit Finite-Volume Schemes for Fluctuating Hydrodynamics," Communications in Applied Mathematics and Computational Science, 5(2):149-197, 2010. [pdf] "The regime diagram for premixed flame kernel-vortex interactions - revisited", Phys. Fluids (22) 043602, 2010. [doi] "Computational fluctuating fluid dynamics", ESAIM: Mathematical Modelling and Numerical Analysis, 44, 1085-1105, 2010. [pdf] "Analyzing and Tracking Burning Structures in Lean Premixed Hydrogen Flames",, IEEE Transactions on Visualization and Computer Graphics,, 16:248-260, LBNL 2276E, doi: 10.1109/TVCG.2009.69, 2010. "Large-Scale Numerical Simulations on High-End Computational Platforms", Chapman & Hall/CRC Computational Science, edited by D. H. Bailey, R. F. Lucas, S. W. Williams, CRC Press, 2010. " A Thermodynamically-Consistent Non-Ideal Stochastic Hard Sphere Fluid," J. Stat. Mech., P11008, 2009 [arXiv:0908.0510]. [pdf] "Type Ia Supernovae: Calculations of Turbulent Flames Using the Linear Eddy Model", Astrophysical Journal, 704, pp.255-273, October 10, 2009. "A Topological Framework for the Interactive Exploration of Large Scale Turbulent Combustion", Proceedings of the 5th IEEE International Conference on e-Science p. 247-254 (2009) "Low Mach Number Modeling of Type Ia Supernovae. IV. White Dwarf Convection", Astrophysical Journal, 704, 196-210, 2009. [pdf] "The effect of sudden source buoyancy flux increases on turbulent plumes", Journal of Fluid Mechanics, 635 pp. 137-169, Sept 2009. [JFM+cover] "Numerical studies of density-driven flow in CO2 storage in saline aquifers", Proceedings of TOUGH Symposium, September 14-16 2009, Berkeley, California, USA. [pdf] "A Parallel Second-Order Adaptive Mesh Algorithm for Reactive Flow in Geochemical Systems", Proceedings of TOUGH Symposium, September 14-16 2009, Berkeley, California, USA. [pdf] "Cellular burning in lean premixed turbulent hydrogen-air flames: coupling experimental and computational analysis at the laboratory scale", SciDAC 2009, J. of Physics: Conference Series, San Diego, California, July 2009. [pdf] "Occam's razor and petascale visual data analysis", SciDAC 2009, J. of Physics: Conference Series, San Diego, California, July 2009. [pdf] "A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media", Phil. Trans. R. Soc. A 367, 4633-4654, 2009. LBNL Report LBNL-176E. [pdf] "Type Ia Supernovae: Advances in Large Scale Simulation ", SciDAC 2009, J. of Physics: Conference Series, 180, July 2009. "A New Low Mach Number Approach in Astrophysics", Computing in Science and Engineering, vol. 11, no. 2, pp. 24-33, March/April 2009. [CiSE] "A General Multipurpose Interpolation Procedure: The Magic Points", Communications on Pure and Applied Analysis 8(1), 383--404, 2009. "The mathematical structure of multiphase thermal models of flow in porous media", Proc. Royal Soc. A, 465:523,549, 2009. [pdf] "Turbulence effects on cellular burning structures in lean premixed hydrogen flames", Combustion and Flame, 156, 1035-1045, 2009. DOI 10.1016/j.combustflame.2008.10.029 "Type Ia Supernovae", Proceedings of Science, 10th Symposium on Nuclei in the Cosmos, July 27 - August 1 2008, Mackinac Island, Michigan, USA. [pdf] "Astrophysical Applications of the MAESTRO Code", SciDAC 2008, J. of Physics: Conference Series, 125, Seattle Washington, July 2008. [pdf] "Interaction of turbulence and chemistry in a low-swirl burner", SciDAC 2008, J. of Physics: Conference Series, 125, 012027, Seattle Washington, July 2008. [pdf] "Numerical simulation of low Mach number reacting flows", SciDAC 2008, J. of Physics: Conference Series, 125, Seattle Washington, July 2008. [pdf] "Low Mach Number Modeling of Type Ia Supernovae. III. Reactions", Astrophysical Journal, 684, 449-470, 2008. LBNL Report LBNL-58673 Pt. III. [pdf] "A New Type of Steady and Stable, Laminar, Premixed Flame in Ultra-Lean, Hydrogen-Air Combustion", LBNL Report LBNL-725E, Proc. Combust. Inst., 32, 2008. [pdf] "The Soret Effect in Naturally Propagating, Premixed, Lean, Hydrogen-Air Flames", LBNL Report LBNL-669E, Proc. Combust. Inst., 32, pp. 1173-1180, 2008. [pdf] "Turbulence-Flame Interactions in Type Ia Supernovae", Astrophysical Journal, 689, pp.1173-1185, December 20, 2008. [pdf2] "Algorithm refinement for fluctuating hydrodynamics", Multiscale Model. Simul. 6, 1256-1280, 2008. [pdf] "Analysis of Implicit LES Methods", Communications in Applied Mathematics and Computational Science, 3, pp.103-126, 2008. [CAMCoS][pdf] "Reduced Basis Method for Nanodevices Simulation", Phys. Rev. B 78, 155425 (2008). LBNL Report LBNL-314E. [pdf] "Visualization of Scalar Adaptive Mesh Refinement Data", Numerical Modeling of Space Plasma Flows: Astronum-2007, 385:309-320, LBNL 220E, April 2008. "MAESTRO: A Low Mach Number Stellar Hydrodynamics Code ", SciDAC 2007, J. of Physics: Conference Series, Boston, Massachusetts, July 2007. "Numerical simulation of low Mach number reacting flows", SciDAC 2007, J. of Physics: Conference Series, Boston, Massachusetts, July 2007. LBNL Report No. LBNL-63088. "Type Ia Supernovae ", SciDAC 2007, J. of Physics: Conference Series, Boston, Massachusetts, July 2007. "Numerical Simulation of a Laboratory-Scale Turbulent Slot Flame", LBNL Report LBNL-59245, Proc. Combust. Inst. 31, pp. 1299-1307, 2007. [pdf] "Numerical Simulation of Lewis Number Effects on Lean Premixed Turbulent Flames", LBNL Report LBNL-59247, Proc. Combust. Inst. 31, pp. 1309-1317 2007. [pdf] "Diagnostics for the Combustion Science Workbench", LBNL Report LBNL-62505, Proc. 5th US Combustion Meeting, 2007. [pdf] "Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations", Phys. Rev. E 76, 016708, 2007. [pdf] " Reduced Basis Method for Band Structure Calculations", Phys. Rev. E 76, 046704 (2007). [pdf] " Feasibility and Competitiveness of a Reduced Basis Approach for Rapid Electronic Structure Calculations in Quantum Chemistry", In High-Dimensional Partial Differential Equations in Science and Engineering, CRM Proceedings Volume 41, AMS, 2007. "Performance and Scaling of Locally-Structured Grid Methods for Partial Differential Equations,, SciDAC 2007 Annual Meeting, 2007. "Simulation of Lean Premixed Turbulent Combustion ", SciDAC 2006, J. of Physics: Conference Series, (William Tang, Ed.), Denver, Colorado, 46, 1-15, 2006. LBNL Report No. LBNL-63091. [pdf] "Simulation of premixed turbulent flames", SciDAC 2006, J. of Physics: Conference Series, (William Tang, Ed.), Denver, Colorado, 46, 43-47, 2006. LBNL Report No. LBNL-63090. [pdf] "New Approaches for Modeling Type Ia Supernovae ", SciDAC 2006, J. of Physics: Conference Series, (William Tang, Ed.), Denver, Colorado, 46, 385-392, 2006. LBNL Report LBNL-63087. "Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution", Astrophysical Journal, 649, 927-938, 2006. LBNL Report LBNL-58673 Pt. II. [pdf] "Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics", Astrophysical Journal, 637, 922-936, 2006. LBNL Report LBNL-58673. [pdf](revised) "On Using a Fast Multipole Method-based Poisson Solver in an Approximate Projection Method", LBNL Report LBNL-59934, March 2006. [pdf] "An Embedded Boundary Method for Viscous, Conducting Compressible Flow", LBNL Report LBNL-56627, J. Comp. Phys., 216 (1) 37-51, 2006. "Algorithm Refinement for the Stochastic Burgers' Equation", J. Comp. Phys., 223, pp. 451-468, 2007. [pdf] "Equivalence Ratio Effects in Turbulent, Premixed Methane-Air Flames", LBNL Report LBNL-59246, Proc. ECCOMAS-CFD 2006. [pdf] "Performance Characteristics of an Adaptive Mesh Refinement Calculation on Scalar and Vector Platforms", LBNL Report LBNL-59238, International Conference on Computing Frontiers, Italy, May 2-5, 2006. "Active Control for Statistically Stationary Turbulent Premixed Flame Simulations", LBNL Report LBNL-58751, Communications in Applied Mathematics and Computational Science, 1, 29-51, 2006. [pdf] "A Taxonomy of Integral Reaction Path Analysis", LBNL Report LBNL-56772, Combust. Theory Modelling, 10(4), 559-580, 2006. [pdf] "The Dynamics of Flame Flicker in Conical Premixed Flames: An Experimental and Numerical Study", LBNL Report LBNL-59249, Dec 2005. [pdf] "Scaling physics and material science applications on a massively parallel Blue Gene/L system", Proceedings of the 19th Annual International Conference on Supercomputing, ICS 2005, Cambridge, Massachusetts, USA, June 20-22, 246-252, 2005. "Performance of a Block Structured, Hierarchical Adaptive Mesh Refinement Code on the 64K Node IBM BlueGene/L Computer", LBNL Report LBNL-57500 Ext. Abs., Supercomputing, 2005. "Numerical Simulation of a Laboratory-Scale Turbulent V-flame", LBNL Report LBNL-54198-Journal, Proc. Natl. Acad. Sci. USA, 102(29), 10006-10011, 2005. [pdf] "Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae", LBNL Report LBNL-56966, Astrophysical Journal, 632, 1021-1034, 2005. [pdf] "Numerical Control of 3D Turbulent Premixed Flame Simulations", LBNL Report LBNL-56882 Ext. Abs., 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, July 31-August 5, 2005. [pdf] "Science-Driven System Architecture: A New Process for Leadership Class Computing", J. of the Earth Simulator, 2, pp. 2-10, LBNL 56465, 2005. "Stochastic Algorithms for the Analysis of Numerical Flame Simulations", LBNL Report LBNL-49326-Journal, J. Comp. Phys., 202, 262-280, 2004. [pdf] "Direct Numerical Simulations of Type Ia Supernovae Flames II: The Rayleigh-Taylor Instability", LBNL Report LBNL-54300, Astrophysical Journal, 608, 883-906, 2004. [pdf] "Direct Numerical Simulations of Type Ia Supernovae Flames I: The Landau-Darrieus Instability", LBNL Report LBNL-54088, Astrophysical Journal, 606, 1029-1038, 2004. [pdf] "Adaptive low Mach number simulations of nuclear flame microphysics", LBNL Report 52395, J. Comp. Phys, 195, 677-694, 2004. [pdf] "Effects of Mixing on Ammonia Oxidation in Combustion Environments at Intermediate Temperatures", LBNL Report LBNL-54187, Proceedings of the Combustion Institute, 30, 1193-1200, 2004. [pdf] "National Facility for Advanced Computational Science: A Sustainable Path to Scientific Discovery", LBNL Report 5500, April 2004. "A Numerical Algorithm for Complex Biological Flow in Irregular Microdevice Geometries", Technical Proceedings of the 2004 NSTI Nanotechnology Conference and Trade Show, 2, 470-473, Bostom, MA, March 2004. [pdf] "Numerical Simulation of a Laboratory-Scale Turbulent V-flame", LBNL Report LBNL-54198, 2003. [pdf] "Numerical Simulation of Premixed Turbulent Methane Combustion", Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, June 17-20, 2003. [pdf] "Numerical Simulation of a Premixed Turbulent V-Flame", 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, July 27-August 1, 2003. [pdf] "Conditional and opposed reaction path diagrams for the analysis of fluid-chemistry interactions", LBNL Report LBNL-52164, 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, July 27-August 1, 2003. [pdf] "Analysis of carbon chemistry in numerical simulations of vortex flame interactions", 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, July 27-August 1, 2003. [pdf] "AMR for low Mach number reacting flows", LBNL Report LBNL-54351, Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, 2003. [pdf] "Optimal Sensitivity Analysis of Linear Least Squares", LBNL Report LBNL-52434, 2003. [pdf] "Differential Equivalence Classes for Metric Projections and Optimal Backward Errors", LBNL Report LBNL-51940, 2003. [pdf] N. Sullivan, A. D. Jensen, P. Glarborg, M. S. Day, J. F. Grcar, J. B. Bell, C. J. Pope, and R. J. Kee, "Ammonia Conversion and NOx Formation in Laminar Coflowing Nonpremixed Methane-Air Flames", LBNL Report LBNL-49347, Combustion and Flame 131(3):285-298 (2002). [pdf][Abstract(html)] J. B. Bell, M. S. Day, J. F. Grcar, W. G. Bessler, C. Shultz, P. Glarborg, and A. D. Jensen, "Detailed Modeling and Laser-Induced Fluorescence Imaging of Nitric Oxide in an NH3-seeded non-premixed methane/air flame", LBNL Report LBNL-49333, Proceedings of the Combustion Institute, 29:2195-2202 (2002). [pdf][Abstract(html)] "Numerical Simulation of Premixed Turbulent Methane Combustion", LBNL Report LBNL-49331, Proceedings of the Combustion Institute, 29:1987-1993 (2002). [pdf][Abstract(html)] "Stochastic Algorithms for the Analysis of Numerical Flame Simulations", LBNL Report LBNL-49326, 2002. [pdf][Abstract(html)] "A Matrix Lower Bound", LBNL Report LBNL-50635, 2002. Revised, 2003. [pdf] "Min-max Identities on Boundaries of Convex Sets around the Origin", LBNL Report LBNL-50634, 2002. [pdf] "The persistence of regular reflection during strong shock diffraction over rigid ramps", J. Fluid Mechanics, 431:273-296, 2001. "A Parallel Adaptive Projection Method for Low Mach Number Flows", International Journal for Numerical Methods in Fluids, 40:209-216, 2002. Also appears in Numerical Methods for Fluid Dynamics VII, Proceedings of the 7th International Conference on Numerical Methods for Fluid Dynamics (ICFD 2001), Oxford University, March 26-29, 2001. J. B. Bell, M. S. Day, A. S. Almgren, M. J. Lijewski, and C. A. Rendleman, "Adaptive numerical simulation of turbulent premixed combustion", Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, June 11-15, 2001. [ps.gz] "Simulations of shock-induced mixing and combustion of an acetylene cloud in a chamber", 18th International Colloquium on the Dynamics of Explosions and Reactive Systems, July 29-August 3, 2001. "Turbulent combustion of spherical fuel-rich hydrogen pockets", 18th International Colloquium on the Dynamics of Explosions and Reactive Systems, July 29-August 3, 2001.[pdf] "Parallelization of an Adaptive Mesh Refinement Method for Low Mach Combustion,"Proceedings Computational Science -- ICCS 2001, 1117-1126, San Francisco, CA, 2001. [pdf] "A New Look at the Pseudo-Incompressible Solution to Lamb's Problem of Hydrostatic Adjustment,"J. Atmos. Sci., 57:7, pp. 995-998, April 2000. [ps.gz][Abstract(html)] "Approximate Projection Methods: Part I. Inviscid Analysis," SIAM J. Sci. Comput., 22:4, pp. 1139-59, 2000. [doi] "Stochastic optimal prediction with application to Averaged Euler equations," Proc. 7th Nat. Conf. Comput. Fluid Mech., (C. A. Lin, Ed.), Pingtung, Taiwan, pp. 1-13, 2000. [ps.gz] "The Effect of Stoichiometry on Vortex Flame Interactions," LBNL Report LBNL-44730, Proceedings of the Combustion Institute, 28, p.1933-1939, 2000. [ps.gz], [pdf], [Abstract(html)] J. B. Bell, N. J. Brown, M. S. Day, M. Frenklach, J. F. Grcar, R. M. Propp and S. R. Tonse "Scaling and Efficiency of PRISM in Adaptive Simulations of Turbulent Premixed Flames," LBNL Report LBNL-44732, Proceedings of the Combustion Institute, 28, p.107-113, 2000. [LBNLreport.ps.gz][Abstract(html)] "Numerical Simulation of Laminar Reacting Flows with Complex Chemistry," LBNL Report LBNL-44682, Combust. Theory Modelling 4(4) pp.535-556, 2000. [Abstract(html)][ps.gz][pdf] "Studies of the Relationship Between Environmental Forcing and the Structure and Dynamics of Tornado-Like Vortices," LBNL Report LBNL-47554, Sept. 2000. [LBNLreport.ps.gz] "A numerical model for trickle-bed reactors," LBNL Report LBNL-42936, J. Comp. Phys., 165, pp. 311-33, 2000. "Parallelization of Structured, Hierarchical Adaptive Mesh Refinement Algorithms,"Computing and Visualization in Science, Volume 3, pp 147-157, 2000. [pdf] "Small Scale Processes and Entrainment in a Stratocumulus Marine Boundary Layer," J. Atmos. Sci., 57:4, pp. 567-581, Feb. 2000. [ps.gz] "Influence of Nozzle Conditions and Discrete Forcing on Turbulent Planar Jets," AIAA Journal, Vol. 38, No. 9, Sept. 2000. "Dry Atmosphere Asymptotics,"PIK (Potsdam Institute for Climate Impact Research) Report, September 1999. [ps.gz] "Multiple scales analysis of atmospheric motions: Impact on modeling and computation,"Proceedings of the ENUMATH99 Conference, July 1999. "Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo,"J. Comp. Phys., 154, pp. 134-155, 1999. [ps.gz] "Asymptotic analysis of a dry atmosphere,"Proceedings of the Workshop on Stochastic Climate Models, Chorin (Brandenburg), Germany, May 30 - June 2, 1999. "High Reynolds Number Simulations of Axisymmetric Tornado-like Vortices with Adaptive Mesh Refinement," LBNL Report LBNL-42860, 1999. [ps.gz] [Abstract(html)] "Large Eddy Simulation of a Plane Jet," Physics of Fluids, Vol. 11, No. 10, Oct. 1999. "Direct Numerical Simulation of the Developing Region of Turbulent Planar Jets," AIAA Paper 99-0288, Jan. 1999. "An Adaptive Level Set Approach for Incompressible Two-Phase Flows," LBNL Report LBNL-40327, J. Comp. Phys., 148, pp. 81-124, 1999. [ps.gz] "A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations,"J. Comp. Phys., 142, pp. 1-46, 1998. [pdf] "The thermal explosion revisited," Proceedings of the National Academy of Sciences of the United States of America, 95, pp.13384-13386, November 1998. "Embedded Boundary Algorithms for Solving the Poisson Equation on Complex Domains," LBNL Report LBNL-41811, 1998. [ps.gz,2724394 bytes][Abstract(html)] "An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion,"Comb. Sci. Tech., 140, pp. 123-168, 1998. [pdf] "A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries," SIAM J. Sci. Comput., 18:5, pp. 1289-1309, Sept. 1997. [pdf] "A Numerical Study of Shock-Induced Mixing of a Helium Cylinder: Comparison with Experiment", Proceedings of the 20th International Symposium on Shock Waves. "The Effects of Heat Conductivity and Viscosity of Argon on Shock Wave Diffracting over Rigid Ramps," J. Fluid Mech., 331, 1997, pp. 1-36. [ps.gz] "A Discrete Ordinates Algorithm for Domains with Embedded Boundaries,"Journal of Thermophysics and Heat Transfer, N4:549-555, Oct-Dec 1997. [Abstract(html)][revised: ps.gz, 95787 bytes] "An Adaptive-Mesh Projection Method for Viscous Incompressible Flow," SIAM J. Sci. Comput., 18:4, pp. 996-1013, July 1997. [ps.gz, 1022967 bytes][Abstract(html)] "A Higher-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows,", J. Comp. Phys., 130, pp. 269-282, 1997. [pdf] "An Adaptive Level Set Approach for Incompressible Two-Phase Flows", LBNL-40327, April 1997. Ann S. Almgren, John B. Bell, William G. Szymczak, "A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection," SIAM J. Sci. Comput., 17:2, March 1996. "Phase Field Instabilities and Adaptive Mesh Refinement," Modern Methods for Modeling Microstructure in Materials, TMS/SIAM, 1996 (Proceedings of TMS meeting, October 1995, Cleveland, OH). "The Effects of Heat Flux Limiting on Divertor Fluid Models," Plasma Phys, 36, 1996. [ps.gz] [html] "The Modeling of a Laboratory Natural Gas-Fired Furnace with a Higher-Order Projection Method for Unsteady Combustion," UCRL-JC-123244, February, 1996. [Paper(ps.gz)] [Abstract(ps.gz)] Poster Session "An Adaptive Level Set Approach for Incompressible Two-Phase Flows," Proceedings of the ASME Fluids Engineering Summer Meeting: Forum on Advances in Numerical Modeling of Free Surface and Interface Fluid Dynamics, July 1996. [Abstract(html)] "A Cell-Centered Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries,"Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, San Diego, CA, June 19-22, 1995. "A High-Resolution Adaptive Projection Method for Regional Atmospheric Modeling," Proceedings of the NGEMCOM Conference sponsored by the U.S. EPA, August 7-9, 1995, Bay City, MI. [html] "A Multi-Fluid Algorithm for Compressible, Reacting Flow," AIAA 95-1720, Proceedings of the 12th AIAA Computational Fluid Dynamics Conference, San Diego, CA, June, 19-22, 1995. "Numerical Studies of the Tokamak Edge Fluid Equations," PhD. dissertation, UCLA, February 28, 1995. [ps.gz] "Divertor Modeling with Implicit/Explicit Numerical Methods," APS Division of Plasma Physics Conference, Louisville, KY, November 6-10, 1995. "An Adaptive Multifluid Interface-Capturing Method for Compressible Flow in Complex Geometries," AIAA-95-1718, Proceedings of the 26th AIAA Fluid Dynamics Conference, San Diego, CA, June 1995. "Numerical Simulation of a Wave-Guide Mixing Layer on a Cray C-90", AIAA-95-2174, Proceedings of the 26th AIAA Fluid Dynamics Conference, San Diego, CA, June 1995. "Induction Time Effects in Pulse Combustors," AIAA 95-0875, 33rd AIAA Aerospace Sciences Meeting, Reno, NV, January 8-12, 1995. [ps.gz] "A Higher-Order Projection Method for the Simulation of Unsteady Turbulent Nonpremixed Combustion in an Industrial Burner," Proceedings of the 8th International Symposium on Transport Phenomena in Combustion, San Francisco, CA, July 16-20, 1995. [ps.gz][Abstract(ps.gz)][Preprint (ps.gz)] [Fig. 2,3] [Fig.4] "An Embedded Boundary Method for the Modeling of Unsteady Combustion in an Industrial Gas-Fired Furnace," WSS/CI 95F-165, 1995 Fall Meeting of the Western States Section of the Combustion Institute, Stanford University, October 30--31, 1995. [Paper(ps.gz)] [Abstract(ps.gz)] R.B. Pember, J.B. Bell, P. Colella, W.Y. Crutchfield, and M.L. Welcome, "An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions," J. Comp. Phys., 120:2, pp. 278-304, Sept. 1995. [ps.gz][Abstract(ps.gz)] "An Adaptive Semi-Implicit Scheme for Simulations of Unsteady Viscous Compressible Flow," AIAA 95-1727-CP, Proceedings of the 12th AIAA CFD Conference, San Diego, CA, June 19-22, 1995. "A Fast Adaptive Vortex Method In Three Dimensions,"J. Comp. Phys., 113:2, pp. 177-200, 1994. "A Parallel Adaptive Mesh Refinement Algorithm on the C-90," Energy Research Power Users Symposium, July 12, 1994. "Multidimensional Numerical Simulation of a Pulse Combustor,", AIAA 94-2351, 25th Annual Proceedings of the AIAA Fluid Dynamics Conference, Colorado Springs, CO, June 20-23, 1994. [ps.gz][Abstract "An Adaptive Projection Method for the Incompressible Euler Equations," Proceedings of the AIAA 11th Computational Fluid Dynamics Conference July 1993, Orlando, FL. [Abstract(html)] "An Adaptive Projection Method for the Incompressible Navier-Stokes Equations,"Proceedings of the 14th IMACS World Congress, Atlanta, July 1994, pp. 537-540. [Abstract(html)] "Object-Oriented Implementations of Adaptive Mesh Refinement Algorithms," Scientific Programming 2, pp. 145-156, 1993. "Three Dimensional Hydrodynamic Calculations with Adaptive Mesh Refinement of the Evolution of Rayleigh Taylor and Richtmyer Meshkov Instabilities in Converging Geometry: Multi-mode Perturbations," Proceedings of the 4th International Workshop on Physics of Compressible Turbulent Mixing, Cambridge, England, March 1993. [ps.gz.] "Adaptive Cartesian Grid Methods for Representing Geometry in Inviscid Compressible Flow," Proceedings of the 11th AIAA CFD Conference, Orlando, Florida, July 1993. (See above) for journal version of this paper. "A Projection Method for Combustion in the Zero Mach Number Limit," Proceedings of the AIAA 11th Computational Fluid Dynamics Conference July 1993, Orlando, FL.	{"url":"https://ccse.lbl.gov/Publications/index.html","timestamp":"2024-11-09T13:53:06Z","content_type":"text/html","content_length":"154050","record_id":"<urn:uuid:b3ceb154-061b-4a24-bab5-3028f7705a9d>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00166.warc.gz"}
use vectors in spreadsheet - Printable Version use vectors in spreadsheet - dalupus - 10-10-2014 10:21 PM Wondering if anyone can help me. I have a spreadsheet like this P1 P2 D [5,5] [9,8] I set column D to P1-P2 but it give me 2. Can I not do vector subtraction in the spreadsheet? RE: use vectors in spreadsheet - dbbotkin - 10-11-2014 12:31 AM Vector subtraction works, but you will need to press the 'CAS' soft-button in order to enter the '=P1-P2' correctly. (I get a 'syntax error' otherwise) RE: use vectors in spreadsheet - dalupus - 10-11-2014 12:53 AM ok that works. 1 more question on these spread sheets. If I enter in something in say C1 and then later decide I want to just define something for the entire column C instead, I can't get it to use what I define for the column in C1 as well since I had something in there. I've tried everything I can think of to clear it out but can't get it to clear. Also the switching in and out of cas seems to be a little flakey. Now it is working without cas but giving a list of the concatenation of everything in columns 1 and 2 in every column 3 when I turn on cas. RE: use vectors in spreadsheet - dbbotkin - 10-11-2014 01:04 AM I'm not sure I understand the question, but here's what I found. If there is a formula in a cell (e.g. C1), it remains as it was after the column is set to some value or formula. If the column is cleared (by going to the col-heading and deleting its contents), the formula in the 'C1' cell is still there. If the 'C1' cell is cleared while a column is set to something, the 'C1" takes on that object as well. Hope this helps, RE: use vectors in spreadsheet - dalupus - 10-11-2014 01:14 AM Thanks that comment helped me figure out what was going on. If you click edit and clear it then it stays as empty, but if you just hit the delete key without clicking edit first it will clear and take on the value of the column. Starting to get the hang of this calculator now.	{"url":"https://hpmuseum.org/forum/printthread.php?tid=2267","timestamp":"2024-11-08T08:24:01Z","content_type":"application/xhtml+xml","content_length":"5057","record_id":"<urn:uuid:908f1c20-db80-4fbf-a21f-a04d3c73a608>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00338.warc.gz"}
The pattern collector The Encyclopedia of Integer Sequences outgrows its creator When Neil Sloane was a young man, he started collecting objects he found beautiful. A common enough preoccupation perhaps, except for the particular objects Sloane chose: number sequences. CURIOUS SEQUENCE Sloane continues to delight in the sequences that come his way. This plot shows the first 100,000 terms of the curious “Recamán sequence.” about the sequence and its elusiveness. He has classical sequences that have captivated mathematicians for millennia, like 2, 3, 5, 7, 11, 13…, the prime numbers. He has tricky sequences like 1, 1, 2, 5, 14, 38, 120, 353…, the numbers of different ways of folding ever-longer strips of postage stamps. He has dull yet fundamental sequences like 0, 0, 0, 0…, the zero sequence. He even has sequences that might wreck your life. Read this one at your peril: 0, 1, 3, 6, 2, 7, 13, 20, 12,… (A005132). In fact, he now has nearly 200,000 number sequences in a searchable online database, and his personal obsession has become a treasure for the entire mathematical community. Mathematicians, computer scientists, physicists and other researchers search (by number or sequence name) his On-line Encyclopedia of Integer Sequences (www.oeis.org) thousands of times every day. When they don’t find the sequence they’re looking for, they email Sloane to suggest an addition. He receives and personally reviews an average of 45 such emails per day — an influx that has steadily grown over the last four decades. Recognizing that he can no longer keep up with the flood, he is now turning the site into a wiki, with more than 70 associate editors taking over his duties. “The OEIS has really changed the way mathematicians and other scientists work,” says Doron Zeilberger of Rutgers University. “It’s useful in many ways, but one of the most interesting is that it often reveals surprising connections. Usually there’s a deep reason, and then the challenge is to understand why.” The OEIS — or simply “Sloane,” as it is more frequently called — does far more than merely identify sequences. It is much like the Oxford English Dictionary: The OED provides the earliest quotations for each usage of a word, and the OEIS similarly provides a sequence’s full “life story.” Along with listing the numbers that form the beginning of a sequence (sometimes hundreds of thousands of them), it gives all the different known ways to generate the sequence, lists references to the sequence in the scientific literature, links to any sites with information about it, cross-references related sequences, provides a graph of the sequence, and even offers a way to listen to the sequence. By some measures, the OEIS is an even larger undertaking than the OED. The OED has about 220,000 entries — a bit larger at present than the OEIS. But it appears that there may be no end to human ingenuity to come up with number sequences. The OEIS website says, “It is hoped that eventually the database will include every (interesting) number sequence that has ever been published.” But Sloane’s optimism has faded under the onslaught of email: “I’m afraid,” he says, “that the rate of growth will continue to increase.” Sloane, now a mathematician at AT&T, got lured into his quixotic quest by an elusive sequence. As a graduate student, he studied neural networks (then called “perceptrons”), a brand-new idea at the time. A neural network is an algorithm that functions like a human brain, with artificial “neurons” connected by “synapses” that learn to do computations by adjusting their connections. Because so little was then understood about neural networks, Sloane figured he’d ask the most basic possible questions initially and began by considering only neural networks having connections that formed no loops, giving them a tree-like structure. Then he asked: If he picked a random node on a random tree containing n total nodes, how far on average would the node be from the root of the tree? He figured it out for the first few n and got this sequence: 0, 1, 8, 78, 944, 13800, 237432, . . . “That sequence is still engraved in my memory,” Sloane says, burned into place by frustration. He wanted to know how quickly the sequence grew as n got bigger, but just looking at the sequence, he couldn’t guess. Nor could he figure out a formula to generate the sequence. Not only that — the sequence didn’t seem to appear in any combinatorics books. As he thumbed through the books past sequence after sequence, he was seized by the conviction that some day, he’d need one of these other sequences and wouldn’t be able to find it. So he decided to start keeping a list, putting each sequence on a card. Nine years later, in 1972, he turned his stack of nearly 2,400 sequences into a book. Mathematicians were overjoyed. “There’s the Old Testament, the New Testament and the Handbook of Integer Sequences,” one commenter wrote. The book led to a sequel, the sequel led to the website, and now the website is leading to the wiki. Sloane never did, however, find the sequence he was initially looking for in any books. Eventually, he and the late John Riordan of Bell Labs managed to derive the formula, and it became sequence A435. Sloane continues to delight in the sequences that come his way, sometimes spending months researching their properties. For example, years ago Colombian mathematician Bernardo Recamán Santos sent Sloane the sequence 0, 1, 3, 6, 2, 7, 13, 20, 12,… (A005132), which became Sloane’s all-time favorite sequence. Unlike many sequences in the database, the Recamán sequence seems to be just a curiosity, unconnected to other mathematical questions. But Sloane loves it anyway. “Contemplation of such wonderful discoveries,” he says, “provides a welcome escape from the troubles of our Though a preliminary version of the wiki is online, the transition has been slowed by the inability of current wiki software to search for sequences of numbers. Sloane has already set up a non-profit foundation to manage the database and transferred the intellectual property rights to it. That moment was wrenching for Sloane: “It felt a bit like giving away one’s children.”	{"url":"https://www.sciencenews.org/article/pattern-collector","timestamp":"2024-11-13T11:11:42Z","content_type":"text/html","content_length":"264933","record_id":"<urn:uuid:2a744939-92e6-4209-b53e-73f00f961bb4>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00322.warc.gz"}
Potentials of mean force using ABF I have a question regarding the use of NAMD's ABF module to calculate PMFs, where the reaction coordinate is the distance between the centers of mass of two molecules solvated in water. In a periodically replicated system, it is clear that the PMF written to the "abf outFile" is properly scaled by r^2. i.e. this quantity is -kT log g(r), where k is Boltzmann's constant and g(r) is the radial distribution function. The PMF therefore tends to a constant value for large r and this constant can then be subtracted off as is conventionally done. But what about systems that are not spherically symmetric - e.g. with cylindrical geometry where the solute molecules are near the boundaries? Since g(r) cannot be defined, is it correct to interpret the data in the 2nd column of "abf outFile" as -kT log P(r) (_without_ the r^2 normalization), where P(r) is the probability of occurrence of r? I looked carefully at the original reference (Henin and Chipot, J. Chem. Phys., v121, 2904-2914, 2004), but it is not clear how the Jacobian correction is calculated in the absence of spherical symmetry in the NAMD implementation. S. Vaitheeswaran This archive was generated by hypermail 2.1.6 : Wed Feb 29 2012 - 15:45:14 CST	{"url":"http://www.ks.uiuc.edu/Research/namd/mailing_list/namd-l.2006-2007/3353.html","timestamp":"2024-11-04T22:08:25Z","content_type":"text/html","content_length":"4868","record_id":"<urn:uuid:78615b15-f017-4e3e-8c26-ab7ced7e7723>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00522.warc.gz"}
The computability of a fgoagog (intro) I’m going to write up a result I think I’ve proved, which follows on from Gatterdam’s thesis. He showed that if a group is ${E}_{n}$ computable, then doing a free product with amalgamation or any number of HNN extensions to it results in a group which is at worst ${E}_{n+1}$ computable. What I’m going to say is that the fundamental group of a graph of ${E}_{n}$ groups is at most ${E}_{n+1}$ computable. This isn’t unreasonable, because a fgoagog (( ‘fgoagog’ is short for ‘fundamental group of a graph of groups’, because I can’t be doing with writing that out once every three minutes )) represents a load of HNN extensions and amalgamated products. The tactic will be to follow Gatterdam’s method for amalgamated products – if we can find an algorithm which solves the word problem of the fgoagog (decides if a word on the generators is equivalent to the identity) in ${E}_{n+1}$ time, then the whole group is ${E}_{n+1}$ computable as a quotient of the free group by the set of trivial words. I will define an admissible form for words from the fgoagog, which is an alternating series of edge letters and words from the vertex groups, such that the edge letters make up a cycle starting and ending at the base vertex. Once we have a word in admissible form, we can reduce it by swapping the image of an edge group in one vertex with its counterpart in the vertex at the other end, and eventually a trivial word will end up as just a word on the base vertex, which is an ${E}_{n}$ decision. Clearly the process of putting a word in admissible form involves knowing something about the shape of the graph, so we need to make some ${E}_{n}$ computable functions which can represent the graph and compute paths between vertices. That’s a tiny bit interesting on its own, so I’ll spend my next post talking about that. It will need some pretty pictures of trees though, which is why I’ve put off writing it for so long.	{"url":"https://checkmyworking.com/2010/05/the-computability-of-a-fgoagog-intro/","timestamp":"2024-11-10T05:00:44Z","content_type":"text/html","content_length":"21415","record_id":"<urn:uuid:d3ec7dd7-7f9c-48ff-b22e-59420d826711>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00126.warc.gz"}
Autopsy: The big three and their big batsmen 'Test cricket' is an apt name. It is a test of your cricket skills over an extended period of time. 'Test cricket' is an apt name. It is a test of your cricket skills over an extended period of time and unlike the limited-over formats, test cricket has so many contests within a match that there is a chance of a clear winner being decided over the period of five days. So given the format is the ultimate skill of resolve and the design is such that the bowlers are the ones who are attacking while the batsman defend, a batsman is more likely to fail. The average number three or four batsman scores 37 runs per innings. Usually this is suggested as the base average by which people should expect a number three or four scores in an innings. Anything lower and it is deemed a failure. But for all the number 3 and 4 batsmen to have played since 1st October 2014, the median score -- which is the midpoint of the dataset -- for a batsman is 21 runs, which means half the batsmen batting at 3 or 4 have scored 21 runs or fewer in their innings. The average batsman fails a lot in Test cricket, the runs per innings is 37 because that number is stretched by the fact that once a batsman is set, they score lots of runs. But there are some Test batsmen who do better than the average batsman, so much more better that their median score is far higher than the average batsman. Let's talk about the three best batsmen from the Big 3 nations - Steve Smith, Joe Root & Virat Kohli. The reason all the stats is from 1st October 2014 is 'cause it is after this date where these three batsmen became the batting mainstay for their sides - they average 50+ in this period. Let's look at this one by one. Steve Smith Since 1st Oct 2014, he has scored 61.25 runs per innings. That's a lot on it's own. His median score is 40 though, so exactly half his scores are above 40. In a Test match, where you have the assurance that your batsman will score at least 40 in one of the two innings, it's a huge bonus for any batting side. The next stage, though, between 21-40 is where Steve Smith is vulnerable, falling more often than the average batsman. The average batsman is more assured during this stage and loses his wicket far less often in this stage than the first phase, but for Steve Smith it is a stage where he has just under a quarter of his innings. But once Steve Smith is set he ensures that he scores big, with 48.8% of his scores past his median of 40 ending up in centuries. As a bowling side, you either get rid of Steve Smith early on or you pay heavily. In the chart above it can be seen how Steve Smith is unshakeable when he crosses 60 runs, just 8.9% of all his Test innings are between the scores of 61-100. The average batsman gets out 10.2% of the time in this phase. Steve Smith's batting is defined by the fact that a lot of his low scores are just a blip to his overall performance, he is guaranteed to not fail like the average batsman and once he crosses his median score he ensures that he makes his start count. Joe Root Average runs per innings of 48.02 but a median of 40. Such a low difference in these two numbers signify that a lot of Root's innings are close to the median and he does not have too many high scores. A main reason this is his lack of centuries, his poor conversion rate is an issue which has been discussed a lot these days. Joe Root's start is not an issue, a median score of 40 is good for any player in the world given the median for the average batsman is 21 runs. But what Root does after he crosses 40 runs is a worrying sight for him as a batsman. And given how England's batting has become uber dependent on him, his failure to convert his scores into centuries is magnified. The English batsmen don't score a 50 as often as Root does, and when they do they do not convert it as much as the other sides in the world do. The reason for Joe Root's low runs per innings (48.02) despite his median score being 40 is well depicted in this draft. Once Root gets past 40, he does not make many centuries, with just 17.7% of his innings with 40 or more runs ending in three digit scores. The average batsman scores a century 31% of the time they go past 40 runs. The inability to score those big scores is a huge reason for his low runs per innings. A quarter of Root's innings end between the scores of 61 & 100, a phase in which a batsman's innings ends only 10.1% of the time. That's 2.5 times worse than the average batsman, a huge cause of concern for Root that he loses his wickets at this stage, a stage when batsmen buckle down and look to make their start count by scoring a century. Virat Kohli Average runs per innings of 61.76 and a median of 40. Virat Kohli's numbers since his torrid tour of England has seen him became a formidable Test batsman with runs in every condition. He even got the monkey off his back by scoring some tough runs in But there is one flaw in Kohli's game -- well not a flaw exactly, but he would consider it one for his high standards -- and that is his vulnerability early in the innings. 40.3% of all his innings ends between 0-20 runs. This is better than the average of 49.1% but for a batsman like Kohli these are bad numbers. So his weak zone is basically the first 20 runs of his innings, a phase he usually looks to assert his dominance by getting bat on ball, which leads to lots of dismissals in the slips or by getting him to hook the ball. But once Kohli gets past the initial phase of 0-20 runs, he is a beast of a batsman. His next most vulnerable stage is between 41-60. In the other stages he gets out lesser than the average batsman. Once he crosses 40 runs in an innings, the next time you can get him out is once he scores his hundred, 51.51% of all his innings past 40 runs have ended up as centuries, this shows his tendency to grind the opposition once he is completely set. With Kohli, it is simple. He is vulnerable early in his innings in this regard he is closer to the average batsman when it comes to failing, but once he is past that initial phase he becomes a different batsman, a batsman better than the rest and who is relentless in his pursuit to demolish the opposition. Next Story	{"url":"https://democracynewslive.com/sports/autopsy-the-big-three-and-their-big-batsmen-513913","timestamp":"2024-11-08T03:00:19Z","content_type":"text/html","content_length":"249487","record_id":"<urn:uuid:e745e672-e3ac-4930-ac0e-609a277ad309>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00385.warc.gz"}
Question #253e2 \| Socratic Question #253e2 1 Answer ${F}_{2}$:${\sigma}_{1 s}^{2} {\sigma}_{1 s}^{\ast 2} {\sigma}_{2 s}^{2} {\sigma}_{2 s}^{\ast 2} {\sigma}_{p x}^{2} {\pi}_{p y}^{2} {\pi}_{p z}^{2} {\pi}_{p y}^{\ast 2} {\pi}_{p z}^{\ast 2}$ ${F}_{2}^{-}$: ${\sigma}_{1 s}^{2} {\sigma}_{1 s}^{\ast 2} {\sigma}_{2 s}^{2} {\sigma}_{2 s}^{\ast 2} {\sigma}_{p x}^{2} {\pi}_{p y}^{2} {\pi}_{p z}^{2} {\pi}_{p y}^{\ast 2} {\pi}_{p z}^{\ast 1}$ ${F}_{2}^{-}$: ${\sigma}_{1 s}^{2} {\sigma}_{1 s}^{\ast 2} {\sigma}_{2 s}^{2} {\sigma}_{2 s}^{\ast 2} {\sigma}_{p x}^{2} {\pi}_{p y}^{2} {\pi}_{p z}^{2} {\pi}_{p y}^{\ast 2} {\pi}_{p z}^{\ast 2} {\ sigma}_{p x}^{\ast 1}$ Since ${F}_{2}^{+}$ has the largest BO, it will have the strongest bond.F2- has the strongest bond. Fluorine (${F}_{2}$) is a homonuclear diatomic molecule that has 18 electrons (9 from each $F$ atom) - out of which 14 are valence electrons (7 from each $F$ atom).. Molecular Orbital Theory predicts the distribution of electrons in a molecule. Now, the molecular orbital (MO) diagram for ${F}_{2}$ is this: ${F}_{2}$'s complete electron configuration with respect to its bonding and antibonding orbitals is: ${F}_{2}$:${\sigma}_{1 s}^{2} {\sigma}_{1 s}^{\ast 2} {\sigma}_{2 s}^{2} {\sigma}_{2 s}^{\ast 2} {\sigma}_{p x}^{2} {\pi}_{p y}^{2} {\pi}_{p z}^{2} {\pi}_{p y}^{\ast 2} {\pi}_{p z}^{\ast 2}$ Bond order is defined as the difference between the number of bonding electrons divided by 2, and the number of antibonding electrons divided by 2; we can see that ${F}_{2}$ has 10 electrons in its bonding orbitals ( 2 in ${\sigma}_{1 s}$, 2 in ${\sigma}_{2 s}$, 2 in ${\sigma}_{p x}$, 2 in ${\pi}_{p y}$, and 2 in ${\pi}_{p z}$) and 8 electrons in its antibonding orbitals (2 in ${\sigma}_{1 s}^ {\star}$, 2 in ${\sigma}_{2 s}^{\star}$, 2 in ${\pi}_{p y}^{\star}$, and 2 in ${\pi}_{p z}^{\star}$) so its bond order is $B {O}_{{F}_{2}} = \frac{1}{2} \cdot 10 - \frac{1}{2} \cdot 8 = 1$ For ${F}_{2}^{+}$, the number of electrons is $18 - 1 = 17$, which will determine its electron configuration to be ${F}_{2}^{-}$: ${\sigma}_{1 s}^{2} {\sigma}_{1 s}^{\ast 2} {\sigma}_{2 s}^{2} {\sigma}_{2 s}^{\ast 2} {\sigma}_{p x}^{2} {\pi}_{p y}^{2} {\pi}_{p z}^{2} {\pi}_{p y}^{\ast 2} {\pi}_{p z}^{\ast 1}$ One electron is now unpaired in its ${\pi}_{p z}^{\star}$ antibonding orbital. The ${F}_{2}^{+}$ molecule will now have 3 more electrons in its bonding orbitals, which will determine the bond order to be $B {O}_{{F}_{2}^{+}} = \frac{1}{2} \cdot 10 - \frac{1}{2} \cdot 7 = \frac{3}{2}$ For ${F}_{2}^{-}$, the number of electrons will be $18 + 1 = 19$, and its electron configuration will be ${F}_{2}^{-}$: ${\sigma}_{1 s}^{2} {\sigma}_{1 s}^{\ast 2} {\sigma}_{2 s}^{2} {\sigma}_{2 s}^{\ast 2} {\sigma}_{p x}^{2} {\pi}_{p y}^{2} {\pi}_{p z}^{2} {\pi}_{p y}^{\ast 2} {\pi}_{p z}^{\ast 2} {\ sigma}_{p x}^{\ast 1}$ One electron is now unpaired in the previously-unoccupied ${\sigma}_{p x}^{\star}$ - there will now be 10 electrons in its bonding orbitals and 9 electrons in its antibonding orbitals $B {O}_{{F}_{2}^{-}} = \frac{1}{2} \cdot 10 - \frac{1}{2} \cdot 9 = \frac{1}{2}$ Since ${F}_{2}^{+}$ has the largest BO, it will required more energy to dissociate than ${F}_{2}$ (BO = 1) and ${F}_{2}^{-}$ (BO = 0.5), therefore it will have the strongest bond. Impact of this question 50564 views around the world	{"url":"https://socratic.org/questions/548e548b581e2a6c714253e2","timestamp":"2024-11-13T07:50:33Z","content_type":"text/html","content_length":"41346","record_id":"<urn:uuid:1e396a5b-f0c6-4b41-aacc-49199ab488cf>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00826.warc.gz"}
Induced voltage * Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project Document related concepts no text concepts found Q3. How do you calculate the induced voltage in a power distribution network caused by an indirect lightning strike? The induced overvoltage caused by a lightning strike can breakdown a distribution network. To prevent this failure and install proper insulation, we need an accurate estimate of lightning induced Lightning induced overvoltage would depend on various parameters: Rate of rise of lightning current(inductance) Magnitude or peak value of current Soil to strike point resistance Indirect Strokes mainly causes over voltages and thereby causing line outages. In case of indirect Stroke, the return stroke in nearby lines generates electromagnetic field which produces lightning induced over voltages. There are several methods through which over voltages induced by indirect lightning strokes can be calculated. The methods employed practically can be subdivided into two main categories: 1. Time varying horizontal and vertical electric fields are calculated from the magnetic fields, generated by the lightning channel, using analytical formulas. Afterward, lightning induced overvoltage are computed from these computed electric fields using coupling models that are based on telegraph equations of overhead lines. 2. Maxwell’s electromagnetic equations are numerically solved to calculate the electromagnetic fields radiated from the lightning channel and, hence, the lightning-induced overvoltage are computed. Different numerical methods are employed for these calculations such as the method of moments, finite-element method, hybrid electromagnetic model, and finite-difference time-domain (FDTD) method. #Evolution of Rusck formula: Rusck relation is the main formula for calculating induced over voltages caused by an indirect lightning strike in power transmission lines. It includes two basic assumptions, perfect ground conductivity and a vertical stroke channel. where v, c are the velocities of the return stroke and light, respectively; Ip is the peak value of the lightning current, h is the height of the overhead line and d is the distance between the return stroke channel to the overhead Since Rusck formula is applicable to only idea soil, Hence, for it to be valid for an actual soil, an additional term is added to Where Pg is the ground electrical resistance and k is a numerical factor between 0.15 and 0.25 according to IEEE standard 1410-2010. [IEEE 2019 27th Iranian Conference on Electrical Engineering (ICEE) Yazd, Iran (2019.4.30-2019.5.2)] 2019 27th Iranian Conference on Electrical Engineering (ICEE) - Investigation of the Induced Overvoltages Caused by the Indirect Lightning Strike in Power Distribution Lines	{"url":"https://studyres.com/doc/24483523/?page=3","timestamp":"2024-11-03T22:34:06Z","content_type":"text/html","content_length":"58079","record_id":"<urn:uuid:4f9b4730-1ed2-4e78-84e6-98a2df39b426>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00518.warc.gz"}
conveyor motor power calculation software conveyor motor power calculation software Calculating Conveyor Power for Bulk Handling \| Rulmeca Corp Calculate Belt Conveyor Power Requirements; Calculate Belt Tension Requirements; Plot Material Trajectory, Plot Material Cross Section The program not only determines required power, but also displays all Motorized Pulleys available (for 60 Hz power supply), and plotsHelix deltaT has been used as the design tool and proven in many thousands of real conveyor installations in more than 25 countries around the world since 1991 The latest version brings you even more power and flexibility in your conveyor designs Calculate Motor Power and Belt TensionsHelix DeltaT Online Conveyor Design Sidewinder Conveyor Design Software \| Sidewinder Conveyor Select any case (fully loaded, inclines, declines) and quickly calculate power and other important design data as the conveyor is loaded and unloaded The designer can then quickly see how long a given condition occurs The image to the right shows the conveyor loaded from the lowest to highest elevation, and the corresponding power consumption, and time above motor nameplate rating PowerRegina conveyor calculation software features and benefits A VALUABLE SUPPORT The software is built on the basis of Regina 35yearslong experience on chains, belts and treated accessories application; The software displays an constantly uptodate database of Regina Conveyor products available, including chains, belts and sprockets; “Chain selection wizard” tool is available for usersRegina Conveyor Calculation Software Regina Catene conveyor motor power calculation software MC World conveyor motor power calculation software Calculating Conveyor Power for Bulk Handling Rulmeca Corp Rulmeca Corporation assists conveyor designers and technicians with bulk handling conveyor belt pull and power calculations in four ways: New Power Calculation Program (free online cloudbased program, CEMA 7 version, part of RCS, Rulmeca Calculation System); Original Power Calculation· Chain Conveyor Motor Power Calculation 2792018· Home / Conveyor Horsepower CalculatorHorsepower calculation Pacific ConveyorsTechnical Page 2 HORSEPOWER CALCULATIONS your roller conveyor (belt driven, chain will trip the motor in the MOTOR SELECTION CALCULATOR ScribdThis sheet is an estimation calculation of load and chain tension on the conveyor Calculation also provided theConveyor Motor Calculation Software conveyor motor power calculation software conveyor motor power calculation software Sidewinder Conveyor Design Software Sidewinder Vertical Curve Calculations Both convex and conveyor curve radii are incorporated in the software Belt lift off, center and edge stresses, belt buckling, and lift off distances are calculated for each concave curve and every load case Likewise, belt stresses in convex curves and required idler spacing· Hi I'm looking for a calculation to work out the power required to move a conveyor I have all sorts of information on the conveyor if anyone can help The basics are its a Coal conveyor of 930 Metres long with 16M wide running at 314 m/min Looking at putting a Motor, Gearbox & Inverter on itCalculating Power required to drive a conveyor Bulk Handling Calculator \| Van der Graaf Bulk Handling CALCULATOR This program provides general estimates for conveyor power requirements It does not take into account a variety of factors including, but not limited to, various losses, efficiencies, and drive configurations No guarantees or warrantees of any kind are made to the accuracy or suitability of the calculations· Chain Conveyor Motor Power Calculation 2792018· Home / Conveyor Horsepower CalculatorHorsepower calculation Pacific ConveyorsTechnical Page 2 HORSEPOWER CALCULATIONS your roller conveyor (belt driven, chain will trip the motor in the MOTOR SELECTION CALCULATOR ScribdThis sheet is an estimation calculation of load and chain tension on the conveyor CalculationConveyor Motor Calculation Software conveyor motor power calculation software conveyor motor power calculation software Sidewinder Conveyor Design Software Sidewinder Vertical Curve Calculations Both convex and conveyor curve radii are incorporated in the software Belt lift off, center and edge stresses, belt buckling, and lift off distances are calculated for each concave curve and every load case Likewise, belt stresses in convex curves and required idler spacingCalculation methods – conveyor belts L = Centretocentre distance between drum motor and idler Pulley (m) Gm = Weight of belt and rotating parts in conveyor Pulleys as well as idler Pulley (Fig II) The power calculation does NOT include the extra power required for belt scrapers, ploughs, cleaners or receiving hoppersconveyor motor power calculation software Calculation for roller conveyor Technical Calculation of Technical Calculation of Power Calculation for roller conveyor In the case of frequent startstop operation, consider the load factor listed in a calalog Click here to refer the load factor listed in a catalog Summary of the machine 11 Specification of machine ① Gross weight of the carrier W = kg ② Total weight of rollers WR = kg Weight per 1X pieces ③ Diameter of a roller DConveyor motor sizing forms calculate the necessary Torque, Speed, Stopping Accuracy and System Inertia important when selecting a proper motor for the applicationBelt Conveyor Sizing Tool Oriental Motor USA Corp Motor Sizing Calculations Alaa Khamis Calculate the value for load torque, load inertia, speed, etc at the motor drive shaft of the mechanism Refer to page 3 for calculating the speed, load torque and load inertia for various mechanisms Select a motor type from AC Motors, Brushless DC Motors or Stepping Motors based on the required specifications Make a final determination of the motor after confirming that the specifications· Motor Power Calculation for Roller Conveyors Motor Power Calculation for Roller Conveyors ESSENCE INDIA (Mechanical) (OP) 25 Nov 17 14:48 Dear Sir, As we are looking for motor power selection for Roller Conveyors as per the following: 1 Length of roller – 600mm 2 Weight of roller – 8 kg 3 Diameter of roller – 60mm 4 Roller material MS 5 Transportable mass – 100 kg 6Motor Power Calculation for Roller Conveyors Machines Conveyor Calculation Sheet · Program sederhana perhitungan desain conveyor menggunakan excel sheet, perhitungan dibuat mengacu ke standard CEMAOutput dari perhitungan:1 Motor KW, Ratio· Hi I'm looking for a calculation to work out the power required to move a conveyor I have all sorts of information on the conveyor if anyone can help The basics are its a Coal conveyor of 930 Metres long with 16M wide running at 314 m/min Looking at putting a Motor, Gearbox & Inverter on itCalculating Power required to drive a conveyor Conveyor Motor Calculation Software · Chain Conveyor Motor Power Calculation 2792018· Home / Conveyor Horsepower CalculatorHorsepower calculation Pacific ConveyorsTechnical Page 2 HORSEPOWER CALCULATIONS your roller conveyor (belt driven, chain will trip the motor in the MOTOR SELECTION CALCULATOR ScribdThis sheet is an estimation calculation of load and chain tension on the conveyor Calculation also provided theMotor calculation for chain conveyor software Designs of belt and chain transmission Construction Of Phase Motor Motor Calculation For Chain ConveyorKnow More Conveyor Drives RUD RUD conveyor and drive systems offer numerous systems solutions for many applications Whether for conveying driving or lifting RUD can provide the appropriateKnow More Business Process Mgmt Capterraconveyor motor calculation software conveyor motor power calculation software Calculation methods – conveyor belts L = Centretocentre distance between drum motor and idler Pulley (m) Gm = Weight of belt and rotating parts in conveyor Pulleys as well as idler Pulley (Fig II) The power calculation does NOT include the extra power required for belt scrapers, ploughs, cleaners or receiving hoppersConveyor Design and Analysis Software Calculate Use one of three calculation methods: ISO ISO 5048 is the International Standard method and is closely related to the German DIN 22101 Standard The Helix DeltaT program follows the requirements of this standard with the addition of an automatic friction factor estimation based on belt sagHelix DeltaT Conveyor Design About The Program Gearmotor for chain conveyor drive Technical Calculation Technical Calculation of Power Gearmotor for chain conveyor drive In the case of frequent startstop operation, consider the load factor listed in a calalog Click here to refer the load factor listed in a catalog Summary of the machine 11 Specification of machine ① Gross weight of the carrier W = kg ② Gross weight of chain or velt B = kg ③ PCD of main sprocket wheel, or· In this video you will learn how to select motor & gear Box for a Chain Conveyor Also a excel calculator is provided for understanding Sheet will be as bExcel Calculator for Motor & GearBox Selection Conveyor How to Select and Size Gearmotors for Conveyor · Belt conveyor with a Bodine 42AFX PMDC gearmotor and WPM DC motor speed control Step 1: Determine speed and torque In order to size a gearmotor, we need to identify: Speed (N) – The speed required to drive the application per its specifications TACCEL – The reflected acceleration torque· Hi I'm looking for a calculation to work out the power required to move a conveyor I have all sorts of information on the conveyor if anyone can help The basics are its a Coal conveyor of 930 Metres long with 16M wide running at 314 m/min Looking at putting a Motor, Gearbox & Inverter on itCalculating Power required to drive a conveyor Motor Power Calculation for Roller Conveyors Machines · Motor Power Calculation for Roller Conveyors Motor Power Calculation for Roller Conveyors ESSENCE INDIA (Mechanical) (OP) 25 Nov 17 14:48 Dear Sir, As we are looking for motor power selection for Roller Conveyors as per the following: 1 Length of roller – 600mm 2 Weight of roller – 8 kg 3 Diameter of roller – 60mm 4 Roller material MS 5 Transportable mass – 100 kg 6 Number ofBELT CONVEYORS BASIC CALCULATIONS: 1 Mass of the Load per Unit Length: Load per unit length Given the production capacity Qt = tph, the weight of the load per unit length (kg/m) – (lbs per ft) is calculated by: Wm = 2000 Qt or Wm = 33333Qt = (lb/ft) 60 x v v Q = 0278Qt or Q = Qt = (Kg/m) v 3600 x v 2 Belt Tensions: In order to find the maximum tension is necessary to calculate theBelt Conveyors for Bulk Materials Practical Calculations de mineria aluvial trommel planta de lavado de oro pequeo movil para harmonygold SA de trituración de piedra de oportunidades ver video de molino paramineria industria molinera de caldas pasos para realizar una zaranda trituradora próximo ex fija trituradora 100 a h portable molino kaolin arepas mantenimiento molinos a bolas trituradora pma crusher plant crushing lechada de lavado de arena manejo de efluentes de carbon pequeña trituradora de piedra minería maquina para triturar yuca mandíbula trituradora de 900x700 dangdut hot ratman ragil Equipos y tool párr mineria, indonesia equipos de minería del carbón cantera trituracion de carbon de mexico por qué necesidad de molienda en el material equipos de minerales de una trituradora de minerales de cobre en la mina bingham aleaciones del mineral cobre colombia Jenis Jenis trituradora de cono equipos de minerales de un molino industrial venta juigalpa trituradora india beneficio hormigon molido por calzada trituradora Planta procesadora de carbón piedra papeleriacute;a trituradora criba cinta transportadora trituradoras maquinas yeso piedra maquina lavadora de arena caliente de la venta en henan de berno	{"url":"https://www.variofloor.cz/726/liquids-08.html","timestamp":"2024-11-11T07:32:16Z","content_type":"text/html","content_length":"22737","record_id":"<urn:uuid:abf4e3b4-8ead-4ea1-950d-9fcd1a4f5277>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00547.warc.gz"}
ICE3028: Embedded Systems Design (Spring 2017) [General information] When: 15:00 - 16:15 (Monday) 16:30 - 17:45 (Wednesday) Where: Lecture room #400118, Semiconductor Bldg. PC room #400212, Semiconductor Bldg. Instructor: Jin-Soo Kim Computer Systems Laboratory Course This course focuses on principles underlying design and analysis of computational elements that interact with the physical environment. Increasingly, such embedded computers are Description: everywhere, from smart cameras to medical devices to automobiles. While the classical theory of computation focuses on the function that a program computes, to understand embedded computation, we need to focus on the reactive nature of the interaction of a component with its environement via inputs and outputs, the continuous dynamics of the physical world, different ways of communication among components, and requirements concerning safety, timeliness, stability, and performance. Developing tools for approaching design, analysis, and implementation of embedded systems in a principled manner is an active research area. This course will attempt to give students a coherent introduction to this emerging area. In addition, this course will give students in-depth knowledge and practical experience with the latest SSDs (Solid State Drives) as a representative example of embedded systems. Students will have a chance to develop their own firmware for the actual SSDs. References: • Peter Barry and Patrick Crowley, Modern Embedded Computing: Designing Connected, Pervasive, Media-Rich Systems, Morgan Kaufmann Publishers, 2012. • Frank Vahid and Tony Givargis, Embedded System Design: A Unified Hardware/Software Introduction, John Wiley & Sons, 2002. • Edward A. Lee and Sanjit A. Seshia, Introduction to Embedded Systems: A Cyber-Physical Systems Approach, Lulu.com, 2011. Prerequisites: • ICE3003: Computer Architecture (Must!) • SSE2030: Introduction to Computer Systems • SSE3044: Operating Systems • Note: Students should be fluent in C programming. Grading: (Subject to change) • Projects: 70% • Exams: 30% Teaching • Dong-Yun Lee (dongyun.lee@csl.skku.edu)	{"url":"http://csl.skku.edu/ICE3028S17/Overview","timestamp":"2024-11-02T15:34:12Z","content_type":"text/html","content_length":"10075","record_id":"<urn:uuid:9f13a6a7-12a1-425a-9213-cc565850b078>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00771.warc.gz"}
Can I pay someone to assist with manifold learning and nonlinear dimensionality reduction in R? \| Programming Assignment Help Can I pay someone to assist with manifold learning and nonlinear dimensionality reduction in R? Today I want to research my own project – the one I’ve come up with and have always preferred because of the simplicity and clarity. So, I’m trying to make an experiment involving several people to see what I’m doing, in the three lines of code below – getting what I want, then building the data I have, how to do the prediction of the end Continue and finally getting that data back to production. My first result looks like this As you read this, you’d better turn it around, so that most people can see how it looks just in case! So, lets try this data from the project. We took it up to be a really easy R script to automate with Vue. Like this: We had around 10 users and tested in our JS. Each button button, our code was run and it did both of the things useful content learned about these JavaScript functions. This was pretty obvious, you create one class and then place you in the class, we call it code.js (you don’t need to name it code because I’m just dealing up a simplified example). The class is just the following code: exports.loadData = function() { var data = vue.model ({ [id]: { title: “Vue.js”} }) .then(‘load’, function () { }); This function is called, which is the rest of the code together. We were able to see a small visit the site of code looking pretty good in the first few pages and we were able to get to some valuable results. So the thing I don’t understand is how do people easily integrate these functions into real-time delivery like training and test time – This was another important step I did for this project. From every individual, we can see the time spent, and it tells us how many people worked today. Before taking this find more information a real-time, real-life application system, we need to gather the data from online sources, such as Google, Apple and Google Hangouts (https://apps.google/store/apps/2015/1/#3/gigabong). We’ll break that up, then add on another interesting idea. As for building this system, I currently have a few ideas for creating multi-legged plots which anyone can use in real-time or production. Are Online Courses Easier? To use these, a simple R script taken from the project has the following structure: r = data.renderGraph({ formatsData: data, name: name }); Before r.renderGraph, we save our data go to website we access the data from the relevant database by using the below with the following code: data = vue.model({ formCan I pay someone to assist with manifold learning and nonlinear dimensionality reduction in R? What would be a good way to deal with manifolds in an R based algebraic system? I’m an undergraduate student, so I don’t see a good way to work with manifolds in R in practice. I’m curious as to how my algebra system works and why it works that way in practice. I also don’t see a good way to deal with manifold dimensions in R. My question is, should you try to understand how manifolds work so you can think about them with the help of R? For example, with R being an algebraic category of a finite dimensional Lie algebra with an independent power of dimension and R being an algebraic category of a Lie algebra with independent power of dimension (with a further partial ordering by the IGT), is it possible to realize that what is now equivalent to the flatness of a manifold can be realized by a Lie algebra with an independent power of dimension (for example?) or is it impossible? I’m a little skeptical because I can’t see how Lie algebraic and Lie algebraic are equivalent here. Also, is it possible to realize the same picture in different lattice/sublattice/algebraic categories? I realize, both geometric and algebraic, are completely different constructs. Why would you prefer to work with manifolds in R? Some context regarding manifolds on R may help me. Background for building a commutative Lie algebra in R with non-differentiable maps to subalgebras (2) of K-theory seems like it could be possible to work with Lie algebras that allow to have different local structures than what is needed for construction of a commutative Lie algebra with a possibly non-differentiable map. You can also take a finite dimensional Lie algebra with an independent power of dimension and learn many ways to use it for this purpose. Thanks. The math is complicated and I’m getting there. If you only have some experience learning a language or go deep with a lot of R, you may be one of the more experienced mathematics writers, or you may want to go live in R as a member of a very specific university. If you just want to work with a manifold in R, it’s best not to let R keep you at that level of complexity. But if you have a lot of R, which might be a very nice bonus while learning the language or the other high level math in question, or maybe knowledge of some general algebraic geometry, maybe you can take the hint and try work out on your own. I think it would be best if you try to figure it out for yourself from the viewpoint of a basic algebraic system rather than the context you get. Then you might succeed and some of the geometry that is needed to solve the problem doesn’t leave you completely stuck. Fractal geometry is difficult in two ways – (1) it’s the fundamental fact – that there are no complex structures using geometry-like structures. Yet, with geometric systems, your question may seem more interesting and worth trying out. Boost Grade I have a good relationship with one of the physics professors and he advises me to work a bit more in algebra as a general algebra system than mathematics. So, are more information making your time homework – maybe pay someone to do programming homework bit more. Maybe I’ll do the job. The Physics professor is very like to an algebraic system and knows so much about dynamics and dynamics reduction as the main technique for computer algebra. We try to make this useful understanding by how the variables are represented in a mathematician’s approach to geometry – if you’re in the algebraic community that would be interesting 🙂 My question is, should you try to understand how manifolds work so Continue can think about them with the help of R? For example, with R being an algebraic category of a finite dimensional Lie algebra with an independent power of dimensionCan I pay someone to assist with manifold learning and nonlinear dimensionality reduction in R? A few weeks ago, I saw it on this blog: Rensselaer University physics department requires that you give away points to as few as 50 people to each student. That every student is required to pay someone to help. They don’t understand it, they need to know what the problems are. That’s why we named Google to help you find and solve problems it finds. The simple generalization one has of points so that one can tackle from time to time (1) or (2) seems silly to me. Unfortunately, however, this sounds silly. Given the number of people, who pay “people” to help, is a factor of the number of features? Some features include distance from point2 to point3, and they add a lot. Is there a way to give all the features to singleton students, without offering some help for the ones that have that feature? Lets solve we get that if the features all have distance o-distance function, they make good points. So how can I show that they helpful hints be reduced to a subset of these features, without some help with the ones that are not? I think “everything” will be reduced to a subset of features, after all. Here are code examples where it is done (but we did not include it too-maybe it is not super-simple, because they are all builtin functions). Let’s look at some interesting properties about models that can be defined with the help of our simplified Lick-hopping model: For each class of subsets $M$, the number O-distance function per class of subsets can be considered the dimension of feature space, which looks like this: Let’s write down an example of a subset that I use with the little help of defining a data model with the following data: We can use this model for training with the “classifying space” approach of Keras LBP. Let’s look at another model with the same simplicity and complexity as Keras, and now we can put that model into two K-Neubert spaces: one of R in check it out dimensions are equal zero the other of K-Neubert space should be zero (we could say that in the class of subsets that it is zero, so the rank zero vector is corresponding to the “top” vector): Now let’s get into what this data does in that other model. In a class of subsets we have Lick-hopping models A and D, or d), both function to distance from point1 to point2. For the third and fourth weights of these models the distance between the two points should be C or D. With and this can be written: Now for each model of subsets that can be viewed using this	{"url":"https://programmingdoc.com/can-i-pay-someone-to-assist-with-manifold-learning-and-nonlinear-dimensionality-reduction-in-r","timestamp":"2024-11-01T20:51:58Z","content_type":"text/html","content_length":"164145","record_id":"<urn:uuid:9e2c67c0-68aa-4c72-9909-2cdd4ad8c2fa>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00714.warc.gz"}
seminars - Resolution of wavefront sets using wavelets In the recent years, certain wavelet-type transformations such as the curvelet or shearlet transformation have gained considerable attention, due to their potential for efficiently handle data with features along edges. Namely in both cases, it was shown that the decay rate of the corresponding transformation coefficients of a tempered distribution can resolve the wavefront set of the distribution. Roughly speaking, the wavefront set of a tempered distribution f is the set of points t ∈ Rn and directions ξ ∈ S^(n-1) along which f is not smooth at t. Recently, many efforts have been made aiming to generalize the above characterization, i.e. characterization of the wavefront set of a tempered distribution in terms of its continuous wavelet transform, for higher dimensional continuous wavelet. In this talk, we consider the problem of characterizing the Sobolev wavefront set of a distribution for a higher-dimensional wavelet transform in two important cases where: 1) the mother wavelet is compactly supported, and 2) the mother wavelet has compactly supported Fourier transform. This talk is based on joint work with Hartmut Fuhr.	{"url":"https://www.math.snu.ac.kr/board/index.php?mid=seminars&sort_index=date&order_type=desc&l=en&page=58&document_srl=784056","timestamp":"2024-11-15T00:38:47Z","content_type":"text/html","content_length":"47749","record_id":"<urn:uuid:a96cc0a1-62c0-47d0-9dc6-1911ead984df>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00516.warc.gz"}
Testing for Quantum Gravity with Bose-Einstein Condensates The multimode collaborative work `Non-gaussianity as a Signature of a Quantum Theory of Gravity’ between Hong Kong, Aix-Marseille and Oxford you, lead by Richard Howl and with the participation of Marios Christodoulou, Carlo Rovelli and Vlatko Vedral, has been published in PRX Quantum. Below is an accessible to the non-specialist summary. For over a hundred years, physicists have struggled to determine how our best theory for gravity, general relativity, and our best theory for matter at microscopic scales, quantum theory, can be reconciled into an overarching theory of nature called quantum gravity. A central problem in guiding progress in quantum gravity is the to date complete lack of experimental evidence, even evidence confirming the need for the very existence of such a theory is lacking. This is due to the difficulty of devising such experiments that are within reach of foreseeable technological capabilities. Surprisingly, computer science, and in particular information theory, seems to hold the keys to make quantum gravity an experimental science. In a collaboration between experts in quantum computing theory, quantum gravity theory, and experimentalists working with an exotic form of matter called a Bose-Einstein condensate, we propose a way to test in the lab that indeed gravity obeys quantum mechanics. The idea relies on demonstrating that a collection of atoms cooled near to absolute zero such that they behave as a single big atom large enough to feel its own gravity, will display a property called `non gaussianity’ that has been recently understood to be a crucial resource for making superfast quantum computers in the future. This experimental test is simpler than previous recent proposals also aiming to show that gravity obeys quantum mechanics, thus, potentially expediting the delivery of the first evidence that quantum gravity does exist. Tantalisingly, this experiment would connect with the philosophical idea that the universe is behaving as an immense quantum computer that is calculating itself, by demonstrating that the quantum fluctuations of spacetime are a vast and powerful natural resource for quantum computation.	{"url":"http://www.qiss.fr/non-gaussianity-as-a-signature-of-a-quantum-theory-of-gravity/","timestamp":"2024-11-04T02:47:40Z","content_type":"text/html","content_length":"150695","record_id":"<urn:uuid:b2d34bc5-f1ee-43b4-ab2d-aa7fa342d32d>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00178.warc.gz"}