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https://www.aakash.ac.in/book-solutions/rd-sharma-solutions/class-9-maths/chapter-14-quadrilaterals
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math
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"Quad" in quadrilateral means four. Quadrilaterals are the type of polygons having four sides, four vertices. The interior angles of the quadrilateral on summation provide a value of 360°. For example, a quadrilateral ABCD has four sides AB, BC, CD and DA. The four angles ∠A, ∠B, ∠C, ∠D contained by these four sides always add up to 360°.
There are several types of quadrilaterals we will come across, Convex Quadrilaterals, Concave Quadrilaterals and Intersecting Quadrilaterals. Convex Quadrilaterals are the ones whose interior angles are always less than 180°. The diagonals of the figure join the opposite vertex, and in some cases, it bisects the angles at these vertices. Some examples of convex quadrilaterals are
The trapezium or Trapezoid is a quadrilateral having 4 sides, and two sides are parallel to each other. Isosceles Trapezoid is a trapezoid having 2 equal and opposite sides. Therefore, the angles contained by these sides, commonly known as the base angle, are also equal. A parallelogram is a quadrilateral whose opposite sides are parallel to each other. These sides are also equivalent, along with the opposite angles being equal. Rhombus is a type of parallelogram with all 4 sides of equal length. A rectangle is a quadrilateral with equal opposite sides and all angles measuring 90° A Square is a rectangle with all sides equal.
Concave Quadrilaterals have at least one angle more than 180°, and one of its diagonals lies outside the figure. Intersecting quadrilaterals are the ones having two non-adjacent intersecting sides.
This chapter further deals with the questions regarding all kinds of quadrilaterals that are important for exams. The chapter also includes several formulas to determine perimeter, area or other factors of the quadrilaterals.
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http://slashdot.org/~DRJlaw
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math
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The Elmegreens examined 269 spirals in the Hubble Ultra Deep Field and discarded all but 41 because of factors such as an inability to discern a clear spiral structure or the lack of redshift data which gives a galaxyâ(TM)s age.
They divided these 41 spiral galaxies into five different types, based on features such as the number and clarity of arms, whether well-defined or clumpy and so on.
It sounds like they only found a few of each type, seems more like a good hypothesis than "the answer". It also makes you wonder if they cherry picked some of their data.
Imagine that you're attempting to determine when spiral structure typically arose.
1. You throw out all non-spirals: not relevant.
2. You throw out proto-spirals where there's mushy arm-sh structures: potential bias, yes but
2a. You also throw out other spirals where you cannot objectively classify them as grand (2) or multi-armed (>2) spirals or... to one of the five types -- not an inherent time bias.
3. You throw out all data where you have no redshift to determine age: potential bias, yes but
3a You're attempting to determine a relationship with age. If you have no age data, how is that cherry picking?
There is a difference between objectively screening data based on logical considerations and cherry picking. Cherry picking typically involves biased selections or the use of supposedly objective selection criteria to obtain a directed result. I say supposedly because the true objectivity depends upon how the selection criteria actually relate to the hypothesis or analytical method.
As for the rest, I don't see how the paper claims to have "the answer." You're also incorrect that it's a good hypothesis -- the hypothesis is what you test against the data, not the conclusion that your observations are consistent with the hypothesis. They have a decent conclusion of consistency. Now they could use independent confimation, hopefully with a larger population of samples.
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http://www.princeton.edu/engineering/events/viewevent.xml?id=1581
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math
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Histograms, Graph Limits, and the Asymptotic Behavior of Large Networks
Speaker: Patrick J. Wolfe, University College London
Department: Electrical Engineering
Location: Sherrerd Hall 101
Date/Time: Thursday, April 3, 2014, 4:30 p.m. - 5:30 p.m.
In this talk - which will be accessible to a general audience - we show how the asymptotic behavior of large networks can be exploited for nonparametric statistical inference, using recent developments from the theory of graph limits and the corresponding analog of de Finetti's theorem. We introduce the notion of a network histogram, obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins, and community sizes that of histogram bandwidths or bin sizes.
Working within the framework of exchangeable arrays subject to bond percolation, we prove consistency of network histogram estimation under general conditions, giving rates of convergence which include the important practical setting of sparse networks. Joint work with David Choi (http://arxiv.org/abs/1212.4093) and Sofia Olhede (http://arxiv.org/abs/1309.5936/, http://arxiv.org/abs/1312.5306/).
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http://hydrofrac.com/hfc_home.html
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math
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in situ state of stress in the earth's crust has been widely
recognized as a basic parameter necessary in the engineering
design of underground openings. Quantitative evaluation of
horizontal in situ stresses in rock at a specific site cannot
be made since gravitational forces are practically the only
one clearly understood. Therefore, these horizontal stresses
require direct measurements in the field. Presently the most
common method of measuring in situ stress from near-surface
to considerable depths is hydraulic fracturing (or hydrofrac).
hydraulic fracturing is conducted in vertical boreholes.
A short segment of the hole is sealed off using an straddle
packer. This is followed by the pressurization of the fracture-free
segment of the hole by pumping in water. The pressure is
raised until the rock surrounding the hole fails in tension
at a critical pressure. Following breakdown, the shut-in
pressure, the lowest test-interval pressure at which the
hydrofrac closes completely under the action of the stress
acting normal to the hydrofrac. In a vertical test hole
the hydrofrac is expected to be vertical and perpendicular
to the minimum horizontal stress.
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https://mathematicalcrap.com/2022/12/13/new-cur-13-a-probable-grand-slam/
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math
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A project upon which we spent a lot of time was listing all the “awful” lines in the new mathematics Curriculum. Readers have not paid much attention, but that’s understandable, and readers were not really the point. Compiling the list has given us a clearer sense of the absurd nature of the Curriculum, the list has been and will be the basis for more specific posts, and the list is there ready for the future: next year, when the Curriculum kicks in and people start to realise just how bad it is, we’ll be ready with the “We told you so”.
Compiling the list was not just tiring, it was tricky. Determining what to include or exclude, and why, was difficult. We decided to aim for comprehensiveness: if a line seemed faulty for even a minor reason then it would be listed. As a consequence, many lines listed are not truly “awful”; they are merely “bad” or “wonky”. Given that standard, it resulted in a lot of lines being listed. The vast majority of curriculum lines are, at minimum, wonky.
Nonetheless, although we didn’t look to excuse bad lines, we also attempted to give proper respect to the OK lines, and the rare good lines. So, for each Year-Stream section, there were at least a few lines that seemed acceptable or better, and so were not listed. Except for one: Year 5 Probability.
For Year 5 Probability, we wound up listing both content descriptors and all twelve elaborations. We looked again, and again, and could not see how to do otherwise. We could not find a single line that didn’t make us cringe. Here it is, in full.
Year 5 Probability
list the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely (AC9M5P01) (21/11/22)
discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card (AC9M5P01) (21/11/22)
discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn (AC9M5P01) (21/11/22)
commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning (AC9M5P01) (21/11/22)
investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5; responding to the questions, “Is this game fair?”, “Are some differences more likely to come up than others?” and “How can you work that out?” (AC9M5P01) (21/11/22)
comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers (AC9M5P01) (21/11/22)
discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them (AC9M5P01) (21/11/22)
conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results ; use frequency to compare outcomes and estimate their likelihoods (AC9M5P02) (22/11/22)
discussing and listing all the possible outcomes of an activity and conducting experiments to estimate the probabilities; for example, using coloured cards in a card game and experimenting with shuffling the deck and turning over one card at a time, recording and discussing the result (AC9M5P02) (22/11/22)
conducting experiments, recording the outcomes and the number of times the outcomes occur, describing the relative frequency of each outcome; for example, using “I threw the coin 10 times, and the results were 3 times for a head, so that is 3 out of 10, and 7 times for a tail, so that is 7 out of 10” (AC9M5P02) (22/11/22)
experimenting with and comparing the outcomes of spinners with equal-coloured regions compared to unequal regions; responding to questions such as “How does this spinner differ to one where each of the colours has an equal chance of occurring?”, giving reasons (AC9M5P02) (22/11/22)
comparing the results of experiments using a fair dice and one that has numbers represented on faces more than once, explaining how this affects the likelihood of outcomes (AC9M5P02) (22/11/22)
using spreadsheets to record the outcomes of an activity and calculate the total frequencies of different outcomes, representing these as a fraction; for example, using coloured balls in a bag, drawing one out at a time and recording the colour, replacing them in the bag after each draw (AC9M5P02) (22/11/22)
investigating First Nations Australian children’s instructive games; for example, Diyari koolchee from the Diyari Peoples near Lake Eyre in South Australia, to conduct repeated trials and explore predictable patterns, using digital tools where appropriate (AC9M5P02) (22/11/22)
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https://www.physicsforums.com/threads/engineering-crane-math-problem-like-hell.515221/
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math
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crane: http://tinypic.com/view.php?pic=2ywiidh&s=7 Lifting: http://tinypic.com/view.php?pic=309ok06&s=7 Determine the length of each chain sling that will hold the transformer, if the safe working load in each sling is not to exceed 150 kN. (H3.1) Calculate the maximum stretch in the lifting cable when the transformer is just being lifted off the barge 40 m below the bridge deck (i.e. static load) and the boom is at 60°, using a Ø15 mm steel cable (if young’s Modulus for steel is 210 Gpa’s). Calculate the maximum acceleration of the lifting operation, if the maximum breaking stress in the cable was not to exceed 1.867 Gpa’s [Remember F = m (g + a)] Calculate the pressure in the two hydraulic ram pistons, when the boom is stationary at 45°. The pistons are mounted 3m forward of the boom and 2.12 m up the boom and they have a diameter of Ø100 mm.
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CC-MAIN-2019-04
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http://essayslibrary.com/paper-detail/?paper_id=351006
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math
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New solution updates
Help with measurements
Measurements.docx Download Attachment
Question Set 2 will consist of two questions from your AYL questions in Lesson 2 (see
below). Essay-type questions should be written in complete sentences. If the question is
a mathematical problem, make sure to show all your work to receive full credit. Click on
the link above to be taken to your submission box and answer the following questions.
1. Write an explanation to someone who does not know how to make proper measurements on
how to measure the following line with the ruler.
2. Explain how you would gather data and calculate the density of an irregularly shaped rock.
Solution ID:351006 | This paper was updated on 26-Nov-2015Price : $40
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https://gmyd-china.com/qa/question-what-is-a-simple-hypothesis.html
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math
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- How do you write a simple hypothesis?
- How do you construct a hypothesis?
- What is simple and composite hypothesis?
- What is a good hypothesis example?
- Which hypothesis is written correctly?
- Is a hypothesis a prediction?
- What must you do before you make a hypothesis?
- Why do we use a hypothesis?
- What are the 3 types of hypothesis?
- What are some good hypothesis questions?
- What is a hypothesis for kids?
- What is hypothesis and its types?
- What is a hypothesis in research?
- How do you identify a hypothesis?
- How do you write the null and alternative hypothesis?
- What are the 2 kinds of hypothesis?
- What are examples of hypothesis?
How do you write a simple hypothesis?
However, there are some important things to consider when building a compelling hypothesis.State the problem that you are trying to solve.
Make sure that the hypothesis clearly defines the topic and the focus of the experiment.Try to write the hypothesis as an if-then statement.
Define the variables..
How do you construct a hypothesis?
A guide to constructing a hypothesisDo some research into the topic. … Analyse your current knowledge and that in the field. … Generate some questions that you might be interested in knowing more about. … Look for information about what the answer might be. … Determine your independent variable. … Determine your dependent variable. … Generate a simple hypothesis.More items…
What is simple and composite hypothesis?
In general, a simple hypothesis reflects that where shows the parameters’ specified value, wherein reflects etc. Composite hypothesis, on the other hand, refers to the hypothesis that does not stand to be simple. For instance, if it is assumed that and or and then such hypothesis tends to become a composite hypothesis.
What is a good hypothesis example?
Here’s an example of a hypothesis: If you increase the duration of light, (then) corn plants will grow more each day. The hypothesis establishes two variables, length of light exposure, and the rate of plant growth. An experiment could be designed to test whether the rate of growth depends on the duration of light.
Which hypothesis is written correctly?
A good hypothesis will be written as a statement or question that specifies: The dependent variable(s): who or what you expect to be affected. The independent variable(s): who or what you predict will affect the dependent variable. What you predict the effect will be.
Is a hypothesis a prediction?
The only interpretation of the term hypothesis needed in science is that of a causal hypothesis, defined as a proposed explanation (and for typically a puzzling observation). A hypothesis is not a prediction. Rather, a prediction is derived from a hypothesis.
What must you do before you make a hypothesis?
Before you make a hypothesis, you have to clearly identify the question you are interested in studying. A hypothesis is a statement, not a question. Your hypothesis is not the scientific question in your project. The hypothesis is an educated, testable prediction about what will happen.
Why do we use a hypothesis?
The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter.
What are the 3 types of hypothesis?
Types of HypothesisSimple hypothesis.Complex hypothesis.Directional hypothesis.Non-directional hypothesis.Null hypothesis.Associative and casual hypothesis.
What are some good hypothesis questions?
When trying to come up with a good hypothesis for your own research or experiments, ask yourself the following questions:Is your hypothesis based on your research on a topic?Can your hypothesis be tested?Does your hypothesis include independent and dependent variables?
What is a hypothesis for kids?
A hypothesis is an educated guess, or a guess you make based on information you already know. After you make a hypothesis, then comes the really fun part: doing the science experiment to see what happens!
What is hypothesis and its types?
A hypothesis is a formal tentative statement of the expected relationship between two or more variables under study. … • • A hypothesis helps to translate the research problem and objective into a clear explanation or prediction of the expected results or outcomes of the study.
What is a hypothesis in research?
A research hypothesis is a statement of expectation or prediction that will be tested by research. Before formulating your research hypothesis, read about the topic of interest to you.
How do you identify a hypothesis?
Keep your language clean and simple. State your hypothesis as concisely, and to the point, as possible. A hypothesis is usually written in a form where it proposes that, if something is done, then something else will occur. Usually, you don’t want to state a hypothesis as a question.
How do you write the null and alternative hypothesis?
In a hypothesis test, we:Evaluate the null hypothesis, typically denoted with H0. … Always write the alternative hypothesis, typically denoted with Ha or H1, using less than, greater than, or not equals symbols, i.e., (≠, >, or <).More items...
What are the 2 kinds of hypothesis?
A hypothesis is an approximate explanation that relates to the set of facts that can be tested by certain further investigations. There are basically two types, namely, null hypothesis and alternative hypothesis. A research generally starts with a problem.
What are examples of hypothesis?
Examples of Hypothesis:If I replace the battery in my car, then my car will get better gas mileage.If I eat more vegetables, then I will lose weight faster.If I add fertilizer to my garden, then my plants will grow faster.If I brush my teeth every day, then I will not develop cavities.More items…
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CC-MAIN-2021-10
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| 53
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https://e-vocable.com/60462567-2/
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math
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string(54) ‘ length M of unlimited occupied is minimized \[ one particular \] \. ‘
Packing task is considered since an NP-hard job. Costly optimisation task of going on an optimum arrangement of a group of points within a larger box with the aim of minimising the spread on the packing nation or maximising the textbox use. This type of job takes place in different industrial sectors and is crucial in mechanised design and industry, transportation and in the development of a good layout design of a great endeavor [ 9 ]#@@#@!.
This job have been studied and various algorithms have been completely applied to develop an optimum wadding agreement. A lot of optimisation methods that were found in work outing were family algorithm and atom drove algorithm.
Furthermore, another optimisation and swarm-based algorithm named the Manufactured Bee Nest ( ABC ) algorithm is offered in this daily news. It is an formula that is depending on the scrounging behavior of bees.
Through this survey, the investigation worker is going to utilize the Artificial Bee Colony Algorithm in happening an optimum agreement of jammed rectangles.
Packing jobs consider a group of points and a trash can that will maintain your points which usually aim to pack points every bit dumbly as it can be with actually optimum to no distributes. Packing careers are helpful and widely used in several Fieldss just like in architecture and in state of affairss like make fulling up containers, lading burden, ship edifice, building and schmuck layout and so on [.. ]#@@#@!.
Packing jobs are classified depending on the task , t application and aim. Some of the most of transfer jobs such as cutting inventory, backpack and bin providing [ 4 ] are defined beneath.
The trimming stock job is about reducing various-sized pieces out on specific stock bedding. The job can either be a trim-loss job or an blend job.
Trim-loss job is definitely the allotment on stock bedding of pieces of different sizes required by the clientele with the purpose of minimising the price tag on waste.
The mixture task is concerned to find the size of the pieces or points to end up being kept in stock of sheets such that the best choice of points is used so spend is minimized.
The bookbag job explains the procedure of packing the most valuable factors into a fixed-sized storage for example a backpack. The task consists of details with matching weights and values and a back pack of limited capacity. The goal of the bookbag job should be to find which points that maximize the significance should be inside the backpack considering the fact that the entire pounds of the details is at most of the weight of the backpack.
Extracted from [ 12 ]
Figure. 1: Example on the back pack job
Rubbish bin Packing
Trash can wadding work has a crowd of points of different sizes and a determine of containers holding a similar horizontal and perpendicular dimensions. There are different sorts of rubbish bin packing including 2D wadding, 3D wadding, additive wadding, battalion simply by weight and more [ 14 ]#@@#@!. The essence the job is always to merely load up the details into the bins minimising the figure of bins applied.
Taken from [ 13 ]
Figure. a couple of: Bin wadding of different forms
Loading careers deal with rectangle-shaped boxes which can be to be loaded into a rectangle-shaped palette. These jobs could be classified in maker , s and distributer , s burden jobs [ 5 ]#@@#@!. Manufacturer , s and distributer , s burden jobs happen to be chiefly focused on the wadding of indistinguishable and nonidentical rectangular parts severally. The essence lading jobs is to happen an optimum wadding form so that the determine of bins to be put in a certain palette or pot is strengthened.
Taken from [ 15 ]
Figure. a few: Illustration in palette burden jobs pertaining to indistinguishable bins
Other Discrepancies of Providing Problems
There are lots of sorts of packing jobs. The followers couple of packing jobs that specialize in ” occurring the maximal figure of a certain form that could be packed to a larger, quite possibly different type ” [ a few ]#@@#@!.
Sphere in Cuboid , a ball wadding job that involves in happening the best possible agreement of given a couple of spherical objects with size vitamin D become packed right into a cuboid using a size of a ten B x degree Celsius
Providing Circles , are some group of friends packing jobs that try to pack a set of indistinguishable groups into a group or another contact form
Taken from [ 5 ] , A, [ 6 ]
Determine. 4: ( a ) Circles in circle, ( B ) Circles in square ( degree C ) Circles in equilateral trigon and ( calciferol ) Groups in standard hexagon
Providing Squares , shows a collection of indistinguishable squares packed in an exceedingly form like the square and circle
Taken from [ 5 ] , A, [ 6th ]
Figure. 5: ( a ) Pieces in sq . and ( B ) Squares in circle
Rectangular shape Packing Complications
Rectangle Packaging Problem Explanation
Rectangle wadding job can be an optimisation job of apportioning a set of rectangle points into a much larger rectangle, the container with the aim of reducing the providing country or the country wasted [ 8 ]#@@#@!. The set of rectangular shape points offers different measurements of width tungsten and tallness H and the whole country with the points should non surpasse the country of the container thickness W and height They would. The set up of the details is explained by the undermentioned set of vices [ 8 ] [ 10 ] [ 11 ]#@@#@!.
Zero imbrication of rectangle items.
No points must be wider or higher than the scale the pot.
Edges of the points has to be parallel to the container , s border
Taken from [ 7 ]
Figure. 6th: Illustration of the authoritative rectangular shape wadding work process
Taken from [ 1 ]
Number. 7: An example wadding of 9 square points , 90o rotary motion allowed
Taken from [ 1 ]
Figure. 8: A sample providing , set orientation, simply no rotary motion allowed
Different Rectangle Packaging Problems
Taking Into An Open-ended Rectangular shape
The job is usually described as layout, without overlapping, a set of rectangular shape points of different sizes in an open-ended rectangular container of size W. A rotary motion of 90A is allowed every bit long as no points terme conseillé. All the rectangular shape points needs to be pack in manner the entire size L of infinite busy is minimized [ 1 ]#@@#@!.
You read ‘Bee Colony Formula For Rectangle Packing Problems Design Essay’ in category ‘Essay examples’
Taken from [ you ]
Figure. 9: A possible arrangement of 8-10 points
Extracted from [ 1 ]
Physique. 10: Packing into a great open-ended rectangles with 3 different breadths.
Packing In Rectangles of Fixed Size
The thought behind this job is similar to normal bin packing jobs. This consists of rectangle points of several horizontal and perpendicular dimensions and a couple of rectangular bedsheets of fixed length and breadth. The goal is to inches happen an agreement of the bits that minimizes the physique of bedding needed ” [ 1 ]#@@#@!.
Taken from [ 1 ]
Determine. 11: Packaging into set sized rectangles
Swarm intelligence is defined as ” any work to plan algorithms or perhaps distributed problem-solving devices motivated by the corporate and business behavior of societal pest settlements and other carnal communities ” [ nineteen ]#@@#@!. What makes drove based methods an interesting mechanism for function outing careers particularly NP-complete jobs is a two cardinal constructs within just, self-organisation and division of labor. Some drawings of swarm-inspired algorithms and surveies happen to be Particle Swarm Optimization ( PSO ), ant pay out, bee arrangement, flock of birds and more [ 19 ]#@@#@!.
The Artificial Bee Colony Criteria
The Man-made Bee Colony ( HURUF ) formula is a nature-inspired optimisation formula defined by simply Dervis Karaboga in 2005 [ 2 ]#@@#@!. Based upon the scrounging behavior of bees, the purpose of the formula is to happen nutrient origins with substantial nectar sums and finally take the 1 together with the highest quantity.
In the FONEM algorithm, bees are arranged into employed bees, looker-on bees and lookout bees. The applied bees are definitely the 1 that exploit and keep the information of your peculiar nutritional beginning. The information on a specific nutrient starting is so distributed by each employed bees to the looker-on bees through a shake party. Then, chemical choice is done by the looker-on bees. These bees determine the quality of the nutrient beginnings and acquire to take the best nutritional beginning. If a nutrient starting of an utilized bee has become abandoned, this bee becomes a lookout bee. Scout bees are responsible pertaining to researching and seeking possible nutrient origins around the country.
The Waggle Dance
Bees need to spread with other bees in order for them to happen and achieve nutrient vital for the endurance with their settlement. One of the interesting and challenging components of discoursing around the sensual land peculiarly Apis melliferas is moving. Information on a particular nutrient start off from their very own hive can be passed on to other bees through a move dance.
A shake dance is performed by a lookout bee informing his hive friends the exact way and range to the chemical beginning. Through the shake move, the bee performs a great eight-figure kind dance exactly where it main walks in a consecutive range while waggling his tail back and Forth. After that looping is completed in jumping waies and travels the consecutive series over and over all over again capable to just how and the range being relayed. Walking in the consecutive collection indicates just how and figure of mixtures refers to the length of the chemical beginning [ 18 ] [ 17 ]#@@#@!.
Obtained from [ 16 ]
Physique. 12: The shake party
The chief stairss of the HURUF algorithm by [ 19 ] including the used bees, the looker-on bees and the lookout bees has below.
Number. 13: Main stairss of ABC
Pseudocode of HURUF
The intricate pseudocode in the ABC algorithm shown in [ 20 ] is given below:
Run the population of solutions Xi
Measure the inhabitants
Produce new solutions ( nutrient beginning places ) Vi in the vicinity of Xi to get the applied bees.
Apply Greedy Collection
Calculate the opportunity values Pi for the solutions Xi by organizations of their fittingness values making use of the formula
Normalize Professional indemnity values in to [ 0, one particular ]
Produce the newest solutions ( new areas ) Vi for the looker-ons from your solutions Xi
Apply Greedy Selection Process intended for the looker-ons between Xi and Mire
Determine deserted Solutions, and replace it with new arbitrarily produced alternatives Xi pertaining to the lookout
Memorize the best nutrient start place accomplished so far
rhythm = cycle+1
UNTIL ( rhythm sama dengan Maximum Cycle Number )
Initially, randomly executable alternatives ( nutritious beginnings ) are produced and evaluated. Then, the employed bees will look for new alternatives in the area out of the current solutions as well as the greedy options are applied. Picking out much stronger solutions is done by the looker-on bees which is dependent on the fittingness benefit. The nutritious beginnings which in turn non better after a series of loop are abandoned plus the bee associated to it eventually turns into a lookout. The lookout will seek for a brand new nutrient beginning once more. The entire procedure proceeds until the expiry standard is satisfied.
Neighbourhood looking is the method of provide forthing better solutions through the current executable solutions. A brand new solution is definitely generated utilizing the formula below:
( 1 )
where XAij is the benefit of cellular in remedy XAi ( current option ) which is indiscriminately chosen
XAkj is the value of cell M in XAk, a arbitrary solution non equal to XAi
O is known as a random value in the opportunity of [ zero, 1 ]#@@#@!.
The greedy choice is responsible of doing and taking optimum answer at each stage of the method.
A fittingness map decides the quality of a nutrient start ( option ). The bigger the health value from the equation under, the better the solution can be.
( 2 )
exactly where is the cost map
The chance map establishes the chance that the peculiar nutritional beginning will probably be preferred by looker-on bees. The chance worth is calculated utilizing the expression below:
( 3 )
where I actually is the current nutrient start and Sn is the complete figure of nutrient origins.
In the paper ” An Improved Genetic Algorithm for the Packing of Rectangles inch by Ming Le
Stefan Jakobs [ twenty-two ] in his daily news entitled inch On familial algorithms pertaining to the wadding of polygons ” implemented a intercrossed attack to familial criteria. Jakobs utilized the bottom-left-condition to cut down the figure of possible wadding forms. The first population is composed of width-sorted pattern of negotiating based on the bottom-left rules. A rectangular piece is moved get downing from the rightmost top corner corner of the country and moving just far for the bottom so allotment is done every bit significantly as to the still left corner in the bounding rectangular shape. This construct of a intercrossed familial criteria was besides used in wadding of polygons job.
Chen Zhao, ain al [ 23 ] introduced the construct of Discrete Molecule Swarm Optimization ( DPSO ) criteria. In this method, a. For any elaborate treatment on the explained method, observe [ 23 ]#@@#@!.
Declaration of the Difficulty
Packing jobs such as rectangle packing belongs to the category of NP-hard jobs because there is no easy way to find the ideal solution for each and every instance. Purchasing the best manner of suiting a figure of rectangles into a much larger rectangle is known as a clip devouring repeating undertaking and entails a really big solution unlimited.
The ABC algorithm, a brand new swarm-based methodological analysis, has become proven to be an effective attack that solves optimisation jobs in various countries. Some research surveies besides present that DASAR outperforms additional optimisation tactics such as family algorithm. In this survey, the ABC criteria will be implemented to work out rectangular shape packing careers.
Therefore , this kind of paper is going to prove the efficiency from the ABC formula in occurring the best possible contract of packaging rectangles.
The tabular array beneath shows the undertakings and the corresponding video periods i intend to started to efficiently finish this kind of research.
Commencing No .
Period of time
Dec 13 , Dec nineteen, 2010
Analysis and examining of msn documents and published surveies sing rectangle wadding careers and the FONEM algorithm.
Making of the initial bill of exchange of the Thesis Pitch.
December 21, 2010 , January 04, 2011
Execution from the proposed protocol.
Making with the Proposed Approach portion of the thesis.
Jan 05, 2011 , Feb 2011
Testing and debugging. Testing stage.
Producing of the 10-page conference paper and 5-page URS daily news.
Feb , Mar 2011
Finalizing of papers and other important demands
Submission 24 hours
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CC-MAIN-2024-18
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https://www.hindawi.com/journals/ijanal/2014/793709/
|
math
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Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator
Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.
1. Introduction and Preliminaries
A continuous function is a complex-valued harmonic function in a complex domain if both and are real and harmonic in . In any simply connected domain , we can write , where and are analytic in . We call the analytic part and the coanalytic part of . A necessary and sufficient condition for to be locally univalent and orientation preserving in is that in (see ).
Denote by the family of functions which are harmonic, univalent, and orientation preserving in the open unit disc so that is normalized by . Thus, for , the functions and are analytic in and can be expressed in the following forms: and is then given by We note that the family of orientation preserving, normalized harmonic univalent functions reduces to the well-known class of normalized univalent functions if the coanalytic part of is identically zero; that is, .
For functions , Jahangiri et al. defined Salagean operator on harmonic functions given by where
In 1975, Silverman introduced a new class of analytic functions of the form and opened up a new direction of studies in the theory of univalent functions as well as in harmonic functions with negative coefficients . Uralegaddi et al. introduced analogous subclasses of star-like, convex functions with positive coefficients and opened up a new and interesting direction of research. In fact, they considered the functions where the coefficients are positive rather than negative real numbers. Motivated by the initial work of Uralegaddi et al. , many researchers (see [6–9]) introduced and studied various new subclasses of analytic functions with positive coefficients but analogues results on harmonic univalent functions have not been explored in the literature. Very recently, Dixit and Porwal attempted to fill this gap by introducing a new subclass of harmonic univalent functions with positive coefficients.
Denote by the subfamily of consisting of harmonic functions of the form
Motivated by the earlier works of [11–14] on the subject of harmonic functions, in this paper an attempt has been made to study the class of functions associated with Salagean operator on harmonic functions. Further, we obtain a sufficient coefficient condition for functions given by (3) and also show that this coefficient condition is necessary for functions , the class of harmonic functions with positive coefficients. Distortion results and extreme points, inclusion relations, and convolution properties and results on partial sums are discussed extensively.
2. Coefficient Bounds
In our first theorem, we obtain a sufficient coefficient condition for harmonic functions in .
Theorem 1. Let be given by (3). If where and , then .
Proof. We let (8) hold for the coefficients of . It suffices to show that
Substituting for and in (9), we get
The above expression is bounded above by 1 if which is equivalent to But (8) is true by hypothesis. Hence, , , and the theorem is proved for and is given by (10) and (11), respectively.
Theorem 2. For and , if and only if
Proof. Since , we only need to prove the “only if” part of the theorem. To this end, for functions of the form (6), we notice that the condition Equivalently, The above required condition must hold for all values of in . Upon choosing the values of on the positive real axis where , we must have If condition (15) does not hold, then the numerator in (18) is negative for sufficiently close to 1. Hence, there exists in for which the quotient of (18) is negative. This contradicts the required condition for . This completes the proof of the theorem.
3. Distortion Bounds and Extreme Points
Theorem 3 (distortion bounds). Let . Then for , we have
Corollary 4 (covering result). If , then
Next we state the extreme points of closed convex hulls of denoted by .
Theorem 5. A function if and only if where , , , and , also , and . In particular, the extreme points of are and .
Theorem 6. The family is closed under convex combinations.
4. Inclusion Results
Now, we will examine the closure properties of the class under the generalized Bernardi-Libera-Livingston integral operator which is defined by , .
Theorem 7. Let . Then .
Theorem 9. Let be given by (6). Then .
Proof. Since , then by Theorem 1 we must have To show that , by virtue of Lemma 8 we have to show that where . For this, it is sufficient to prove that or equivalently , and , which is true and the theorem is proved.
Corollary 10. .
5. Convolution Properties
For functions given by (3) and given by we recall the Hadamard product (or convolution) of and by Let be given by then the convolution is defined by
Theorem 11. Let , then , where
Proof. We use the principle of mathematical induction in our proof. Let , and . By using Theorem 2, we have
Thus, by applying Cauchy-Schwarz inequality, we have
Then, we get
that is, if
then . By (30) we have
Hence we get
That is, if
then . Then we see that
Since for and for are increasing,
Next, we suppose that , where
We can show that , where Since we have
Corollary 12. Let , then , where
6. Partial Sums Results
In 1985, Silvia studied the partial sums of convex functions of order . Later on, Silverman and several researchers studied and generalized the results on partial sums for various classes of analytic functions only but analogues results on harmonic functions have not been explored in the literature. Very recently, Porwal and Porwal and Dixit filled this gap by investigating interesting results on the partial sums of star-like harmonic univalent functions. Now in this section we discussed the partial sums results for the class of harmonic functions with positive coefficients based on Salagean operator of order on lines similar to Porwal .
Let denote the subclass of consisting of functions of the form (3) which satisfy the inequality where and , unless otherwise stated.
Now, we discuss the ratio of a function of the form (6) with being
We first obtain the sharp bounds for .
Proof. Define the function by It suffices to show that . Now, from (56), we can write Hence we obtain Now if From condition (50), it is sufficient to show that which is equivalently to To see that the function given by (55) gives the sharp result, we observe that for
We next determine bounds for .
Proof. Define the function by Hence we obtain The last inequality is equivalent to Making use of (50) and the condition (64), we obtain (61). Finally, equality holds in (63) for the extremal function given by (65).
We next turns to ratios for and .
Proceeding exactly as in the proof of Theorem 14, we can prove the following theorem.
We next determine bounds for and .
Proof. Define the function by We omit the details of proof, because it runs parallel to that from Theorem 14.
Concluding Remarks. By choosing (or ) and (or ), the various results presented in this paper would provide interesting extensions and generalizations of the subclasses of harmonic star-like functions with positive coefficients of order based on Salagean operator and similarly for convex functions. The details involved in the derivations of such specializations of the results presented in this paper are fairly straight-forward and hence omitted.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
We record our sincere thanks to the referees for their valuable suggestions.
K. Vijaya, Studies on certain subclasses of Harmonic functions [Ph.D. thesis], VIT University, Vellore, India, 2007.
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CC-MAIN-2023-50
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http://www.mathpop.com/bookhtms/cal.htm
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math
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Spivak, Calculus and Answer Book to Calculus
4th ed. xvi + 680 pages.
Combined Answer Book to Calculus, Third and Fourth editions.
ii + 448 pages.
Click here for selections from the Preface Return to book list Return to home page
Written as a textbook, Calculus is used both for theoretical calculus courses and for "Introduction to Analysis" courses in several U.S. universities. It is also used (in rather larger numbers) in quite a few Canadian universities, as well as in a few universities overseas. Because of this, sales of the Answer Book, which are intended for instructors of the courses, are normally restricted.
Calculus has also found an audience among individuals learning, or
relearning, the material on their own.
(Some reader reviews may be found on the Amazon.com website.)
For errata for the 4th edition, send an email to email@example.com. Type Errata in the subject line; no message necessary.
Part I Prologue
1 Basic Properties of Numbers
2 Numbers of Various Sorts
Part II Foundations
Appendix. Ordered Pairs
Appendix 1. Vectors
Appendix 2. The Conic Sections
Appendix 3. Polar Coordinates
6 Continuous Functions
7 Three Hard Theorems
8 Least Upper Bounds
Appendix. Uniform Continuity
Part III Derivatives and Integrals
11 Significance of the Derivative
Appendix. Convexity and Concavity
12 Inverse Functions
Appendix. Parametric Representation of Curves
Appendix. Riemann Sums
14 The Fundamental Theorem of Calculus
15 The Trigonometric Functions
*16 Pi is Irrational
*17 Planetary Motion
18 The Logarithm and Exponential Functions
19 Integration in Elementary Terms
Appendix. The Cosmopolitan Integral
Part IV Infinite Sequences and Infinite Series
Approximation by Polynomial Functions
*21 e is Transcendental
22 Infinite Sequences
23 Infinite Series
24 Uniform Convergence and Power Series
25 Complex Numbers
26 Complex Functions
27 Complex Power Series
Part V Epilogue
29 Construction of the Real Numbers
30 Uniqueness of the Real Numbers
From the preface:
Every aspect of this book was influenced by the desire to
present calculus not merely as a prelude to but as the first real encounter with
mathematics. Since the foundations of analysis provided the arena in which
modern modes of mathematical thinking developed, calculus ought to be the place
in which to expect, rather than avoid, the strengthening of insight with logic.
In addition to developing the students' intuition about the beautiful concepts
of analysis, it is surely equally important to persuade them that precision and
rigor are neither deterrents to intuition, nor ends in themselves, but the
natural medium in which to formulate and think about mathematical questions.
Return to top
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http://www.jiskha.com/members/profile/posts.cgi?name=tenesha
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math
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A plate glass window measures 5 ft by 7 ft. If glass costs $7 per square foot, how much will it cost to replace the window.
covert to a decimal and round to the nearest hundreth 8\11
Write fraction in lowest terms 0.05
Bill needs to buy 24 bottles of soda. Each bottle is $ 1.75 including tax. If he has a hundred dollar bill how much change will he get?
If gas cost $ 2.20 per a gallon and you drive 130 miles at 10 miles per a gallon how much will your trip cost?
I want to be able to buy a car with cash in 4 years. I have $5,000 that I can invest today. I can get a bond earning 6.5%. How much will I have for the purchase?
i have a paper due on what is critical thinking and how i think this will help me pass the ged
no because they werent patient enough to wait!!!
in the gun powder plot ,wre the catholics to be blamed?
|
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CC-MAIN-2014-23
| 827
| 9
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https://www.projecteuclid.org/euclid.aos/1176324625
|
math
|
The Annals of Statistics
- Ann. Statist.
- Volume 23, Number 3 (1995), 836-854.
Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data
Consider a statistical procedure (Method A) which is based on $n$ observations and a less effective procedure (Method B) which requires a larger number $k_n$ of observations to give equal performance under a certain criterion. To compare two different procedures, Hodges and Lehmann suggested that the difference $k_n - n$, called the deficiency of Method B with respect to Method A, is the most natural quantity to examine. In this article, the performance of two kernel quantile estimators is examined versus the sample quantile estimator under the criterion of equal covering probability for randomly right-censored data. We shall show that the deficiency of the sample quantile estimator with respect to the kernel quantile estimators is convergent in infinity with the maximum rate when the bandwidth is chosen to be optimal. A Monte Carlo study is performed, along with an illustration on a real data set.
Ann. Statist., Volume 23, Number 3 (1995), 836-854.
First available in Project Euclid: 11 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Xiang, Xiaojing. Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data. Ann. Statist. 23 (1995), no. 3, 836--854. doi:10.1214/aos/1176324625. https://projecteuclid.org/euclid.aos/1176324625
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CC-MAIN-2019-39
| 1,566
| 12
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https://www.onereed.com/books/acalc.php
|
math
|
|One Reed Publications|
|Home||Journal||Maya-Aztec Report||Books||Articles||Services||Events||Software||Divination||2012||Links||Contact Us|
2018 Edition: A new edition of Astrological Chart Calculations is now available. The original 2001 edition has been expanded to 240 pages of information on the astronomy and mathematics of astrology.
One Reed Publications - (c) 2001, 2018
6 x 9, 240 pages, paperback
$23.45 (free shipping)
Astrological Chart Calculations preserves and teaches the methods of the most basic astrological chart calculations and tells the story of its history. It addresses the disconnect between the actual process of mapping the sky and the simple arithmetic that is required by astrological exams.
Astrological Chart Calculations is presentation of the key concepts behind the celestial sphere, the keeping of time, the development of trigonometry and nature of house systems. It is a general reference useful to any student of astrology. Anyone who has passed high school algebra and geometry should be able to follow the explanations and worked calculations in this book.
It is hoped that a deeper knowledge of this traditional part of astrology, that is the challenge of mapping the sky and the mathematical ritual of preparing a chart, will allow students to not only glean deeper insights into the subject, but also to allow for a unique contact with astrologys long history.
Table of Contents
Chapter I: Coordinate Systems: Astronomical and Temporal Frames of Reference...9
Chapter 2: Space and Time Measurement...27
Chapter 3: Using Triangles to Measure the Sky: A Short History of Trigonometry...39
Chapter 4: Systems of House Division...75
Chapter 5: Calculating the Astrological Chart...93
Chapter 6: Chart Calculations using Interpolation Tables...113
Chapter 7: Chart Calculations using Algebraic equations (Proportions)...129
Chapter 8: Chart Calculations using Logarithms...143
Chapter 9: Chart Calculations using a calculator with trigonometric functions...153
Chapter 10: Other Astrological Chart Calculations...163
Chapter 11: Calculations and Certification...201
Tables for Calculations...207
References ... 235
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https://www.newgrounds.com/art/view/fornoreason/chicken-of-one
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math
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In my findings I have found something interesting.
That is a chicken.
haha.. thats pretty good... i mean its very good :) awsum chicken o.O....would it like to be fried? ( im not fat... i promise )
You are free to copy, distribute and transmit this work under the following conditions:
* Please consider sharing revenue!
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https://www.climatecolab.org/contests/2012/profitably-reducing-emissions-from-cement/c/proposal/1304622/tab/COMMENTS
|
math
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Nov 9, 2012
Interesting idea, which perhaps has some parallels with the proposal entitled "Smarter Binder Technology for Concrete" at https://www.climatecolab.org/web/guest/plans/-/plans/contestId/15/planId/1000113 (though I'm not a technical expert in this field, so perhaps I am missing some subtle differences). If in fact there are parallels between these two proposals, perhaps the two teams might benefit from working together?
Jul 4, 2013
Reducing the energy needed to produce cement is certainly a laudable idea, and there is mention of using geo-polymers. Though that is not a novel approach, it opens up many possibilities. But the proposal does not give enough detail on how energy requirements and emissions would actually be reduced.
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CC-MAIN-2021-25
| 746
| 4
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https://quizlet.com/gb/240368545/set-theory-flash-cards/
|
math
|
Terms in this set (20)
What does ~A mean?
Not A. The universal set take away A.
What is a natural number?
A positive whole number
What does ∀ mean?
What does <=> mean?
If and only if
What does A∩B mean
Intersection of A and B
What does intersection mean?
Objects that belong to A AND B
What does A∪B mean?
Union of A and B
What does A⊆B mean?
A is a subset of B
What does ∈ mean?
What does ∅ mean?
What is the compliment of A?
Everything that is not in A.
What is the relative compliment?
represented as A \ B, it is all the numbers in set A not in set B.
What does a∆b mean?
What is the symmetric difference?
The symmetric difference of A and B is everything in A and B but not in both.
What is the cardinallity of a set?
How many elements are in a set
What does |a| mean?
The cardinality of A
What does R denote in mathematics?
What does N denote in mathematics?
What does Q denote in mathematics?
What does Z denote in mathematics?
All the integers
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https://advantagetrading.net/rsi-50-level.html
|
math
|
RSI demystified: part 1 part 2 part 3
The idea to write an article on Relative Strength Index was born long ago. To show what it really is, what it isn’t and what are the strengths and weaknesses of using it. Most of the insights were meant to be described and shared. And they are. But to a surprise, some new and unexpected discoveries also occurred in the process. So instead of one article, I will be three of them… Or even more in the future. One thing is sure – what you are about to read was never published before, and I never even stumbled on any similar ideas. Hopefully, you will equally enjoy reading it as I enjoyed writing it.
Let me make one thing clear: I like working with RSI. RSI is not a bad indicator. Nor it is the best answer to trader’s problems.
It is just a product of mathematical operations derived from price data, that can be interpreted by a trader or used as a part of a trading strategy.
To start the dive into the RSI world, we have to go back to the basics. RSI is constrained between 0 and 100 points. Probably 99% of traders use 14-period setting and 99% of them look for reversals below 30 or above 70. Another thing are divergences between indicator and price behavior. But here, we will not discuss any of this, because it is a domain of discretionary,
not systematic trading.
OK, if RSI is constrained in (0,100) zone it is not that hard to calculate, that the middle of this bracket is 50 point level. Sticking to RSI(14) we get:
Sometimes RSI(14) is well above the 50 point level, sometimes it is well below it, and sometimes it crosses it frequently. If we create a simple strategy that holds long position (1) when RSI(14) > 50 and short position (-1) when RSI(14) < 50 than we will get:
Now, it gets interesting... Zooming in the period of choppy market when RSI(14) crossed the 50 point line frequently, and comparing it with how price behaved in relation to 27-period exponential moving average (RSI is calculated using Wilder Moving Average (more here), so the TRUE period for exponential moving average smoothing is 2*14 – 1 = 27 bars), we can see that the RSI above/below 50-points signals take place at the same time as the crossovers of price and exponential moving average.
Is this coincidence? How close is the 50-point line to the exponential moving average of the corresponding period length? Can we calculate the difference? Can we calculate the 50-point level in terms of price value… ?
To get the answers we have to get a little crafty. RSI indicator can be reversed, so we can create RSI Predictor. The idea is quite simple:
Dear RSI Predictor,
Please tell me, (at the end of the bar) what price has to be reached (next bar close) for my RSI indicator to read (next bar close) the desired number.
Using RSI Predictor to calculate the desired price for RSI(14) to read 50 points, and comparing it to the exponential moving average (27) we notice something very interesting:
Wow! They both look the same... The only difference is the 1-bar offset between RSI Predictor and Exponential Moving Average, which means that RSI 50-point level IS the exponential moving average! So, any other number that RSI shows has to be interpreted as a distance from it.
Making long story short: if RSI(14) is above 50-points than price (close) is above ExpMA(27), and if RSI(14) is below 50-points than price (close) is below ExpMA(27). It is not a magnificent discovery, but without it, we will not be able to properly understand the information we get from our charts, and will fall prey to charlatans telling the fairy tells about magical properties that Relative Strength Index supposedly has.
In the next articles we will check why 14-period setting is the most popular, will compare RSI with histogram of distance from ExpMA, will investigate why short period RSIs reach 5/95 zones really quickly, and why long period RSIs never get there, plus we also will come up with a solution to all the problems that will be diagnosed along the way.
RSI demystified: part 1 part 2 part 3
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https://math.stackexchange.com/questions/401122/explaining-the-derivative-of-xx/401130
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math
|
The $g(a) = a^x$ is invalid, because the argument is $a$ and $x$ appears as a free variable. If a function's body has a free variable, that has to be defined somewhere as a constant or a globally understood parameter.
A function cannot have a free variable that refers to the argument of another function.
The correct version of $g$ is $g(a) = a^a$.
The function $g$ raises the argument to itself; it does not raise its argument to $x$. $x$ is a dummy variable in the definition of $f(x)$, which is another function. And what if the dummy variable in $f(x)$ is some thing else, like $f(b) = b$?
Think about how this would work in some functional programming language in computing:
return pow(a, x)
g is referring to
x, but the only
x that we see is local in another function's scope! There is no visible binding for
x in the scope of
g's body, so it is a free variable. Moreover, we can edit
without changing the meaning of the program. So now there isn't an
In mathematics, functions can often be regarded as macros! But they are not blind, textual macros; they are hygienic macros. Substitution in math formulas is on structure not text, and it obeys scoping rules by maintaining lexical transparency.
For instance consider this following student reasoning error. Let $f(x) = x\times x$ and let $g(y) = y + y$. Therefore, since manipulation of mathematic formulas is just dumb textual substitution like preprocessor macros in the C language, $f(g(3)) = 3 + 3 * 3 + 3$, and so the value is $f(g(3)) = 3 + 9 + 3 = 15$. And in general $f(g(z)) = z^2 + 2z$. What is wrong?
Since substitution in math formulas follows structure, $f(g(z))$ cannot be $z^2 + 2z$. $f$ multiplies whatever object comes out of $g$ without breaking apart its syntax, and so the necessary parentheses have to be shown when it is all put together: $f(g(z)) = (z + z)(z + z) = 4z^2$.
The rule of lexical transparency is this: that when we substitute a formula $\alpha$ as a replacement for some symbol in another formula $\beta$, all of the symbols in $\beta$, all of the symbols in $\alpha$ continue to have exactly the same meaning. Even if $\beta$ has symbols which have the same names, those symbols do not capture any of the references in $\alpha$.
To prevent confusion, if such a situation arises where there is a confusion between symbols in an inserted formula and in the target of insertion, we should perform a variable renaming.
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https://paper-design.wonderhowto.com/how-to/make-3d-diamond-topped-card-320105/
|
math
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Watch this video to learn how to make a stunning diamond topped 3d card from a single sheet of A4 paper! 1. You'll need one A4 sheet of paper and some printed papers to decorate. 2. Score at 10. 5cm across length and 10. 5cm from one end. 3. Crease both scores in the same direction (mountain folds). 4. Turn card over mark 13cm from top on centre line an 17. 5cm from top on both edges. 5. Score from central 13cm mark to 17. 5cm mark on each edge. All printed papers used in this tutorial are available for you to print on Paper Printables.
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http://www.exo.net/~pauld/summer_institute/summer_day10waves/slowwavesonaphonecord2.html
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math
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Send waves down a spring and watch them travel.
Sending waves down a phonecord.
This exploration begins by observing how pulses travel along a stretched spring. Then it continues by measuring the speed of the pulses and how the speed depends on the length and height of the pulse and the tension in and mass per unit length of the spring. Finally, two pulses are observed as they pass through each other.
Optional, paper, pencil, and a calculator
a spring scale able to read up to 10 N
a scale to weigh the cord
(You can also use a snaky spring in place of the phone cord. If you use a snaky spring you will need to attach a carabiner to the metal loops at each end to serve as a handle, if you use a metal coil spring you MUST use a safety wrist loop, a piece of cord tying the end of the spring to each participants wrist.)
To Do and notice
Make pulses on the cord and watch them move.
One person sends a pulse down a phone cord.
Have your partner hold one end of the phone cord
or attach it firmly in place at about waist height.
Stretch the phone cord to a length between 3 and 5 meters.
Jerk the hand holding the cord to the right about one handspan, about 25 cm, then immediately return your hand to its original position.
Notice that a rightward pulse travels down the cord.
A leftward pulse returns down the cord after bouncing at the far end.
What's Going On?
What moves down the cord?
Motion moves down the cord, the motion of bits of the cord to the right and back.
Energy, moves down the cord. The kinetic energy of the parts of the cord moving side to side plus the potential energy of the deformed cord. Your partner could absorb the energy of the pulse and use it to do work.
Momentum moves down the cord. When the pulse reaches the end of the cord it exerts a force on the end to the right and then back to the left because the pulse carries sideward momentum.
The official scientific name for what moves down the cord is displacement. The displacement of the coils from their rest position moves down the cord.
Two pulses adding together
Lay the cord on the ground and stretch it to 4
meters. Place an empty paper or styrofoam cup next to the center of
Send a pulse down the cord that will hit the cup and knock it over.
While you send a pulse toward the cup (move your hand to the right) have your partner send an identical pulse away from the cup (They move their hand toward your left). The pulses will arrive at the center at the same time, the rightward pulse will add to the leftward pulse canceling it. The sum of the waves will be zero the waves will miss the cup, and the cup will remain standing.
Two people can send pulses in opposite directions so that the pulses cancel just as they pass an object located in the center of the cord.
Just like waves on the cord, two sound waves can add together and cancel. Arthur C. Clark once wrote a story of a machine which produced sound waves which canceled other sound waves to create quiet. The pilots aboard the Voyager aircraft wore headphones which created sound waves which added to the sounds of the aircraft and canceled them. Sounds which cancel noise are called anti-noise.
Measuring wave speed
Measure the speed of the pulse, v.
To do this,
Measure the length of your cord, d,
and the time it takes a pulse to move the length of the cord, t.
The time is best measured with a stopwatch by the person who sends the pulse.
The speed is length divided by time
It will take about half a second for the pulse to travel the length of the cord. If the length is 4 m then the speed will be about 8 m/s. This will be difficult to measure precisely. However, after the next two activities you will be able to measure the speed more accurately.
Measure the speed of the pulse as a function of the length of the pulse. Move your hand 25 cm to the side as rapidly as possible to make a pulse which is short in length as well as in time.
Then move your hand 25 cm to the side and back more slowly.
Long pulses move at the same speed as short pulses
Theoretically, and practically, the speed of your
pulse is independent of the length of your pulse.
How fast you move your hand to the side has nothing to do with how fast the pulse travels along the cord.
Reach out along the cord about 25 cm and pull it to the side 25 cm and hold it.
Pull the cord to the side, make a pulse by releasing it.
Release the cord.
Measure the speed of the pulse.
The pulse which starts from rest travels at the same speed as the pulses which start as jerks.
Measure the speed of the pulse as a function of its height. Make a pulse by moving your hand 10 cm (about a fist width) to the side. Then make a 25 cm high pulse. Then a 50 cm pulse.
Large amplitude pulses travel at the same speed as small amplitude pulses.
The speed of the pulse should be independent of
(It's more complicated than that. For large pulse heights the speed may show a slight increase since pulling the cord far to the side increases the tension in the cord.)
Since the speed of pulses is independent of their size you can improve the accuracy of your timing by sending a pulse and allowing it to travel down the string to your partner and back 5 times. The pulse travels down and back so it travels the length of the cord 10 times. The speed of the pulse is the 10 times the length of the cord, d, divided by the time for 10 one way trips.
v = 10 d/T (for 5 round trips)
To time ten one-way trips start the pulse as you count zero, then count one, two, three, four, five counting once each time the pulse returns.
Note it is really important that when you start the pulse you count ZERO, then on the first return ONE, and so on. Otherwise your count will be off-by-one, and you'll get the wrong speed.
Speed, Tension, and Density
To complete the quantitative part of this activity you will need a spring scale.
Stretch the cord until it is 4 meters long.
Measure the speed of the pulses on the cord. Remember that the speed
does not depend on the amplitude so you can measure the time it takes
the pulse to make 5 round trips or ten lengths of the cord, then get
the time it takes to travel one length, four meters, by dividing the
total time by 10.
Next, stretch the cord to 3 meters long and measure the speed.
Finally, stretch the cord to 5 meters and measure the speed.
(Optional you can measure the speed at 6, 7, and 8 meters.)
The speed increases as the cord is stretched. Theory says that the speed of the wave increases as the tension in the cord increases, and that it also increases as the mass per unit length of the cord decreases. As you stretch the cord you increase the tension and decrease the mass per unit length so that the speed definitely increases.
The theory says that
v is the speed of the pulse on the cord.
T is the tension in the cord.
m/L is the mass per unit length of the cord.
Measure the mass of the cord, m, in kilograms then compute the mass per unit length.
For example our cords have a mass of 0.5 kg and so when stretched to 4 meters they have a mass per unit length of 0.12 kg/m or 1/8 kg/m.
Measure the tension in the cord with a spring scale. To stretch our cords to 4 m requires 8 newtons of tension.
The predicted speed of our pulse is
v = (T/m)0.5 = (8/(1/8))0.5 = 8 m/s
the measured speed is
v = 8 m/s.
Stretching the cord to 6 meters from 3 meters doubles the length of the cord, cuts the mass per unit length in half (it is, after all, the same cord.) and increases the tension to double the original tension (or more.)
If the tension were to double exactly, then the
speed of the pulse would double.
(2 /(1/ 2))0.5 = 2.
The time it takes for a pulse to travel the length
of the cord would remain the same!
The pulse has to travel twice as far, at twice the speed, so the time remains the same.
In reality, the speed more than doubles so that the time it takes the pulse to travel the length of the cord decreases slightly when the cord is stretched.
Return to Day 10
Scientific Explorations with Paul Doherty
25 May 2000
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CC-MAIN-2022-33
| 7,987
| 90
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https://www.encyclopedia-titanica.org/community/threads/titanics-blueprints.16988/
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math
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I need to ask some of your rivet counters a question. Where is the best place to purchase Titanic's original blueprints. I have a smaller copy of them, but the writing is so small I can barely read it. I was also looking for one that had room numbers listed on it, so that I could put into perspective where everyone was. Any help would be greatly appreciated!
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710962.65/warc/CC-MAIN-20221204040114-20221204070114-00173.warc.gz
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CC-MAIN-2022-49
| 360
| 1
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https://www.fosseenergy.co.uk/home-help/will-energy-costs-calculated/
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math
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How will my energy costs be calculated?
Your meter readings will be used to calculate the amount of energy you have used.
All electrical devices have their power measured in watts (W) but for gas, we have to convert it to kilowatt-hours (kWh).
Wattage x Hours x Days ÷ 1000 = kWh
To calculate the costs of the power used by an electrical item, the wattage is multiplied by the number of hours it’s used for each day, and then by the number of days per year. The total is divided by 1,000 to give us the number of kilowatt-hours (kWh).
£ per kWh x Total kWh = your energy cost
The final cost is worked out by multiplying your price per kWh by the amount of kWhs used.
Need help working out the wattage?
You can usually find the wattage label on the appliance or sometimes in the user’s manual. If not, you will need to know the amps or amperes (A) and voltage (V). The amps is the amount of electricity used and voltage measures the force at which the electricity is charged. Multiplying the two will give you your wattage.
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CC-MAIN-2020-45
| 1,028
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http://mathforum.org/library/drmath/view/56681.html
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math
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Odds of Winning the PowerBall Lottery
Date: 08/29/2001 at 17:16:39 From: Joseph Flowers Subject: Odds of winning the lottery Dear Dr. Math, A friend of mine says that a recently published article in the Louisville Courier Journal stating that the odds of winning the 300-million-dollar powerball were just one in 80,089,128 is wrong. He is a math teacher, but has yet to offer his odds on winning. Can you verify the paper's numbers?
Date: 08/29/2001 at 17:49:18 From: Doctor Paul Subject: Re: Odds of winning the lottery The newspaper is correct: There are C(49,5) ways to choose the first five balls and clearly there are 42 ways to choose the powerball. So the odds of winning are: C(49,5) * 42 = 49!/(5! * (49-5)!) * 42 = 42*45*46*47*48*49/120 = 80,089,128 So there are 80089128 possible ways to pick the lottery numbers and there is only one way to win (getting them all correct). Hence the odds are 1:80089128. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/
Date: 08/30/2001 at 22:20:17 From: Joseph W. Flowers Subject: Re: Odds of winning the lottery Dear Dr. Math, Thanks for your reply, and your answer so soon!
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.
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CC-MAIN-2018-05
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https://math.answers.com/Q/When_you_multiply_two_negatives_by_a_positive_will_the_answer_be_a_negative_or_a_positive
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math
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no, negative....if you multiply two negatives it comes out positive
If you multiply a negative number with a positive number, the result will be negative. If you multiply two negatives, the result will be positive.
Yes two negatives do make a positive if you multiply.
If you add two negative numbers, the result is negative.If you multiply two negative numbers, the result is positive.
Actually it does, whenever you mulitply and divide two negative and two positive numbers they always equal a positive number. When you multiply and divide a negative and positive they always equal a negative number.
Since there are two negatives, the answer has to be positive. So, just mulitpl as usual.
There is no such thing as a positive or a negative zero. A negative divided by a positive is a negative, and a positive divided by a negative is a negative. If you have a negative and a positive, the answer will be a negative. But if you have two negatives or two positives as the dividend and divisor, the answer will be a positive. In other words, dividing two positives or two negatives will always give you a positive. But dividing a positive and a negative will always give you a negative.
To help you with future negative multiplications, two negatives= a positive answer. One negative and one positive= a negative. Just multiply like you would normally, but keep those two pointers in mind.
When combining (adding) two negatives you get a negative. When multiplying two negatives you will get a positive.
GenelleBabee: it becomes a positive because when you multiply two negatives it becomes a positive, & it's the same thing with division.
The two negatives cancel out and the number becomes positive.
If the two numbers you are multiplying are both negatives, the answer will be a positive,(two negatives make a positive).If you multiply a negative and a positive the result willbe a negative,(different symbols will result in negative.============================So, if I can squeeze in here for a second and actually answer the question . . .To multiply a negative number by another negative number, throw away bothnegative signs, and proceed just as if both numbers were positive.
Positive x Positive =Positive Positive x Negative= Negative Negative x Positive= Negative Negative x Negative =Positive
For negatives, two negatives equal a positive & all goes for positive
always...whenever u multiply a negative with a negative it gives a positive other rules are: - * - = + -*+ = - +*+=+ -*-*-=- because - * - is positive multiplied by negative is negative
With an odd number of negative numbers included in the equation, the product is always negative; if there is an even number of negatives, it would be positive. This is because it takes two negatives to cancel each other out and make a positive, but with an odd amount, one is left uncancelled.
Only if you multiply or divide them.
No. Two negatives can't make a positive.
Adding two negative numbers will always be negative. Subtracting two negative numbers may be positive or negative. Dividing or multiplying two negative numbers will always be positive.No
A positive number times another positive number will give you a positive answer. If you multiply two negative numbers together, you will also have a positive answer. The only way to get a negative answer is if you multiply a positive by a negative.
No. It is more negative than either of the two negatives.
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CC-MAIN-2021-43
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https://www.nbccomedyplayground.com/how-do-you-calculate-pre-tax-margin/
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math
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How do you calculate pre tax margin?
- 1 How do you calculate pre tax margin?
- 2 What is a pre tax profit margin?
- 3 What is a good operating margin for a nonprofit?
- 4 What is Pbdit margin?
- 5 Is pre tax profit the same as operating profit?
- 6 Is a higher or lower Ebitda better?
- 7 What does a profit margin tell you?
- 8 Do nonprofits have profit margins?
- 9 Can nonprofits have too much in reserve funds?
- 10 What is Pbdit in balance sheet?
- 11 What is a good EV EBIT ratio?
- 12 Is pre tax margin the same as operating margin?
- 13 What does it mean to have a pre tax margin?
- 14 How to calculate the pretax profit margin formula?
- 15 Which is better a high or low pretax margin ratio?
- 16 When to use EBT or pretax margin ratio?
How do you calculate pre tax margin?
Pretax profit margin only requires two pieces of information from the income statement: revenues and income before taxes. The percentage ratio is calculated by deducting all expenses except for taxes, found in the income before taxes figure, dividing it by sales and then multiplying the resulting number by 100.
What is a pre tax profit margin?
The pretax profit margin reflects the level of profit a company generates before it pays its taxes. It is calculated from the information given on a company’s income statement.
What is a good operating margin for a nonprofit?
Operating reserve. Not-for-profit organizations should aim to have an operating reserve ratio of no less than 25 percent, or enough to cover at least three months of their annual expenses.
What is Pbdit margin?
The margin at the level of profit before depreciation, interest and tax (PBDIT), a measure of operational strength, remained at a 3-year high of 19.9%.
Is pre tax profit the same as operating profit?
Profit before tax may also be referred to as earnings before tax (EBT) or pre-tax profit. Gross profit deducts costs of goods sold (COGS). Operating profit factors in both COGS and all operational expenses. Operating profit is also known as earnings before interest and tax (EBIT).
Is a higher or lower Ebitda better?
A low EBITDA margin indicates that a business has profitability problems as well as issues with cash flow. A high EBITDA margin suggests that the company’s earnings are stable.
What does a profit margin tell you?
Profit margin gauges the degree to which a company or a business activity makes money, essentially by dividing income by revenues. Expressed as a percentage, profit margin indicates how many cents of profit has been generated for each dollar of sale.
Do nonprofits have profit margins?
Generally, nonprofit companies do not plan to generate profits through their operations. A good profit margin for a nonprofit will depend on the nature of the organization and its goals.
Can nonprofits have too much in reserve funds?
Yet recent reports suggest that many nonprofits do not have enough saved in their operating reserves. A commonly used reserve goal is 3-6 months’ expenses. At the high end, reserves should not exceed the amount of two years’ budget. At the low end, reserves should be enough to cover at least one full payroll.
What is Pbdit in balance sheet?
PBDIT. Profit Before Depreciation Interest and Taxes.
What is a good EV EBIT ratio?
The enterprise-value-to-EBITDA ratio is calculated by dividing EV by EBITDA or earnings before interest, taxes, depreciation, and amortization. Typically, EV/EBITDA values below 10 are seen as healthy.
Is pre tax margin the same as operating margin?
To calculate operational profit, you must begin with total business revenues and subtract costs and depreciation. To calculate total pre-tax profit, you must start with total income and subtract total expenses.
What does it mean to have a pre tax margin?
Pre-tax Margin for any Year means the Income before Taxes of the Company divided by Consolidated Sales of the Company, as reported in the financial statements of the Company for the Year. Pre-tax Margin means the percentage equal to Profit, divided by Revenue. Pre-tax Margin means the ratio of earnings before income taxes to Sales.
How to calculate the pretax profit margin formula?
As the Pretax profit margin is not influenced by tax expenses, investors and lenders generally use the PBT margin to compare companies in different tax jurisdictions. The Pretax profit margin formula is as easy as it can be. We take Pretax Profit or PBT in the numerator and Net Sales in the denominator and multiply with 100.
Which is better a high or low pretax margin ratio?
A higher pretax margin ratio would be indicative of a company with a high degree of operational profitability, whereas a lower ratio would indicate poorer operational profitability (i.e., higher reliance on a low-tax environment to showcase profitability).
When to use EBT or pretax margin ratio?
(EBT) ratio, is an operating profitability ratio used by market analysts and investors. This ratio is useful in analyzing the standalone profitability of a company’s operations, as it excludes tax expense. The pretax margin ratio is also useful in assessing the year-over-year
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662594414.79/warc/CC-MAIN-20220525213545-20220526003545-00155.warc.gz
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CC-MAIN-2022-21
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https://vivo.library.tamu.edu/vivo/display/n71014SE
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math
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Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling ν(p, ·) → + ∞ AS p → + ∞
- Additional Document Info
- View All
Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem. © 2009 Mathematical Institute, Academy of Sciences of Czech Republic.
author list (cited authors)
Bulíček, M., Málek, J., & Rajagopal, K. R.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057524.58/warc/CC-MAIN-20210924110455-20210924140455-00208.warc.gz
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| 963
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https://www.teacherspayteachers.com/Product/Module-1-Application-Problems-Journal-Grade-2-1991629
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math
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Buy the bundle and get all 8 journals for the price of 6!! Click below to purchase.
Application Problems Journal Bundle
This product contains all of the application problems from Engage NY module 1 for grade 2. Note that lesson 6 does not contain an application problem. Some lessons include 2 application problems. I did not label these as problem 1 and problem 2, as some teachers will choose not to copy both problems into the book. All problems remind students to read, draw, and write (check boxes are included at the top). The formatting for each problem is a little different. For some of the multiple step problems I have my students write their answer under the question, but show all their work at the bottom of the page. Whereas for other problems students show their work under each question.
Clipart comes from Graphics from the Pond.
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CC-MAIN-2017-43
| 847
| 4
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http://www.phwiki.com/motivation-outline-difficulties-in-limit-setting-in-addition-to-the-strong-confidence-approach/
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math
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The Above Picture is Related Image of Another Journal
Motivation Outline Difficulties in Limit setting in addition to the Strong Confidence approach
Edison Community College, US has reference to this Academic Journal, Difficulties in Limit setting in addition to the Strong Confidence approach Giovanni Punzi SNS in addition to INFN – Pisa Advanced Statistical Techniques in Particle Physics Durham, 18-22 March 2002 Outline Motivations in consideration of a Strong CL Summary of properties of Strong CL Some examples Limits in presence of systematic uncertainties. Motivation The set of Neyman?s bands is large, in addition to contains all sorts of inferences like: ?I bought a lottery ticket. If I win, I will conclude then donkeys can fly @99.9999% CL? I want so that get rid of those, but keep being frequentist.
Related University That Contributed for this Journal are Acknowledged in the above Image
Why should you care ? Wrong reason: so that make the CL look more like p(hypothesis | data). Right reason: You don?t want so that have so that quote a conclusion you know is bad. If you think harder, you can do better: You are drawing conclusions based on irrelevant facts (like a bad fit). As a consequence, you are not exploiting at best the information you have Your results are counter-intuitive in addition to convey little information. You must make sure your conclusions do not depend on irrelevant information SOLUTION: Impose a form of Likelihood Principle Take any two experiments whose pdf are equal in consideration of some subset c of observable values of x, apart in consideration of a multiplicative constant. Any valid Confidence Limits you can derive in one experiment from observing x in c must also be valid in consideration of the other experiment. If you ask the Limits so that be univocally determined, there is no solution. RESULT Neyman?s CL bands Strong bands Non-coverage land Surprise: a solution exists, in addition to gives in consideration of any experiment a well-defined, unique subset of Confidence Bands
Construction of CL bands Regular Strong Strong CL vs. standard CL A new parameter emerges: sCL. Every valid band @xx% sCL is also a valid band @xx% CL. You can check sCL in consideration of a band built in any other way. sCL requirement effectively amounts so that re-applying the usual Neyman?s condition locally on every subsample of possible results.This ensures uniform treatment of all experimental results, but in a frequentist way. Strong Band definition is not an ordering algorithm in addition to answer is still not unique. You may need so that add an ordering so that obtain a unique solution. Strong CL It is similar so that conditioning, a standard practice in modern frequentist statistics. ?There is a long history of attempts so that modify frequentist theory by utilizing some form of conditioning. Earlier works are summarized in Kiefer(1977), Berger in addition to Wolpert(1988) [?] Kiefer(1977) formally established the conditional confidence approach? ?The first point so that stress is the unreasonable nature of the unconditional test [?] the unconditional test is arguably the worst possible frequentist test [?] it is in some sense true that, the more one can condition, the better? ?It is sometimes argued that conditioning on non-ancillary statistics will ?lose information?, but nothing loses as much information as use of unconditional testing? (J. Berger) Neyman: (CR(x) is the accepted region in consideration of æ given the observation of x. c is an arbitrary subset of x space)
Artificial Life Lecture 6 Coevolution of Pursuit in addition to Evasion Pursuit/Evasion ? gen 200 Coevolution This study of coevolution Sensors Neural Network Control System Evolution Evaluation Random Start ? gen 0 A Successful run ? gen 999 Potential Circular Trap Possible Variations Analysis of behaviour Applications Coevolving Parasites Sorting Networks Picturing Sorting Networks Minimal Sorting Networks How so that check if it works Genetic Representation Diploid encoding Diploid encoding (ctd) Scoring Spatially Distributed GA (Back so that Lec 3 ? Microbial GA) Now alongside Added Demes !!!! FROM LEC 3 Microbial alongside demes FROM LEC 3 Reproduction Results ? without coevolution Inefficiencies – 1 Inefficiencies – 2 2 populations ? sorters in addition to parasites Scoring each population Benefits of Coevolution The End
Summary of sCL properties 100% frequentist, completely general. The only frequentist method complying alongside Likelihood Principle Invariant in consideration of any change of variables No empty regions, in full generality No ?unlucky results?, no need in consideration of quoting additional information on sensitivity. No pathologies. Robust in consideration of small changes of pdf More information gives tighter limits Easier incorporation of systematics Price tag: Overcoverage Heavy computation (see CLW proceedings in addition to hep-ex/9912048) Invariance in consideration of change of the observable All classical bands are invariant in consideration of change of variable in the parameter (unlike Bayesian limits) The CL definition is invariant in consideration of change of variable in the observable, too. But, most rules in consideration of constructing bands break this invariance ! Strong-CL is also invariant in consideration of any change of variable. Likelihood Ratio is also invariant (non-advertised property?), so it is a natural choice of ordering so that select a unique Strong Band. Effect of changing variables Neyman?s CL bands Strong bands Non-coverage land LR-ordered bands
Poisson+background The upper limit on æ decreases alongside expected background in all unconditioned approaches. Often criticized on the basis that in consideration of n=0 the value of b should be irrelevant. LR-ordering upper limit @90%CL in consideration of n=0 background sCL = 90%, or R.-W. Behavior when new observables are added Do you expect limits so that improve when you add extra information ? A simple example shows that neither PO or LRO have this property (conjecture: no ordering algorithm has it !) Example: comparing a signal level alongside gaussian noise alongside some fixed thresholds Problem: the limit loosens dramatically when adding an extra threshold measurement. Example Unknown electrical level æ plus gaussian noise (? =1). Limited so that |æ|< 0.5. Compare alongside a fixed threshold (2.5 ?), get a (0,1) response. Observe > threshold: PO: empty region @90%CL LR: 0.49 < æ < 0.50 @90%CL sCL: -0.34 < æ < 0.50 @90%sCL N.B. you MUST overcover unless you want an empty region. L(æ) LR(æ) Add another threshold Now, add a second independent threshold measurement at 0: limit become much looser ! sCL limit is unaffected Conjecture: no ordering algorithm can provide a sensible answer in all cases. L(æ) LR(æ) 0.27< æ < 0.5 Observations It may be impossible so that get sensible results without accepting some overcoverage. Why blame sCL in consideration of overcoverage ? Ordering algorithms alone seem unable so that prevent very strange results: the inclusion of additional (irrelevant) information may produce a dramatic worsening of limits. Adding systematics so that CL limits Problem: My pdf p(x|æ) is actually a p(x|æ,?), where ? is an unknown parameter I don?t care about, but it influences my measurement (nuisance) I may have some info of ? coming from another measurement y: q(y|?) My problem is: p(x,y|æ,?) = p(x|æ,?)*q(y|?) Many attempts so that get rid of ?: three main routes: Integration/smearing (a la Bayes) Maximization (?profile Likelihood?) Projection (strictly classical) Hybrid method: Bayesian Smearing 1) define a new (smeared) pdf: p?(x|æ) = ? p(x|æ,?)?(?) d ? where ?(?) is obtained through Bayes: ?(?) = q(y| ?)p(?)/q(y) Need so that assume some prior p(?) 2) Use p? so that obtain Conf. Limits as usual GOOD: Simple in addition to fast Used in many places Intuitively appealing BAD: Intuitively appealing Interpretation: mix Bayes in addition to Neyman. Output results have neither coverage nor correct Bayesian probability => waste effort of calculating a rigorous CL May undercover May exhibit paradoxical tightening of limits A simple example + Bayes systematics Introduce a systematic uncertainty on the actual position of the 0 threshold. Assume a flat prior in [-1,1]. Do smearing => get tighter limits ! No reason so that expect a good behavior æ > 0.272 æ > 0.294 LR(æ) LR(æ) Approximate classical method: Profile Likelihood 1) define a new (profile) pdf: p prof(x|æ) = p(x,y0|æ,?best (æ)) where ?best(æ) maximizes the value of a) p(x0,y0|æ,?best) b) p(x ,y0|æ,?best) (?best = ?best(æ,x) !) This means maximizing the likelihood wrt the nuisance parameters, in consideration of each æ 2) Use p prof so that obtain Conf. Limits as usual GOOD: Reasonably simple in addition to fast Approximation of an actual frequentist method BAD: Flip-flop in case a), non-normalized in case b) !! Only approximate in consideration of low-statistics, which is when you need limits after all. You don?t know how far off it is unless you explicitly calculate correct limits. Systematically undercovers
Exact Classical Treatment of Systematics in Limits 1) Use p(x,y|æ,?) = p(x|æ,?)*q(y|?), in addition to consider it as p( (x,y) | (æ,?) ) 2) Evaluate CR in (æ,?) from the measurement (x0,y0) 3) Project on æ space so that get rid of uninteresting information on ? It is clean in addition to conceptually simple. It is well-behaved. No issues like Bayesian integrals Why is it used so rarely ? 1) It produces overcoverage 2) The idea is simple, but computation is heavy. Have so that deal alongside large dimensions 3) Results may strongly depend on ordering algorithm, even more than usual. ?profile method? ?Overcoverage? Projecting on æ effectively widens the CR ? overcoverage. BUT: You chose so that ignore information on ? – cannot ask Neyman so that give it all back so that you as information on æ – the two things are just not interchangeable. ? overcoverage is a natural consequence, not a weakness Q: can you find a smaller æ interval that does not undercover ? (same situation alongside discretization)
Optimization issue You want so that stretch out the CR along ? direction as far as possible. BUT: The choice of band is constrained by the need so that avoid paradoxes (empty regions, in addition to the like) ! No method on the marked allows you so that treat æ in addition to ? in a different fashion Strong CL allows you so that specify æ as the parameters of interest, in addition to so that obtain the narrowest æ interval The solution does not require constructing a multidimensional region Strong CL Band alongside systematics The solution does not require explicit construction of a multidimensional region The narrowest æ interval compatible alongside Strong CL is readily found. Conclusions Strong Confidence bands have all good properties you may ask for. Systematics can be included naturally in addition to rigorously They can even be actually evaluated
Poisson Example: n=5, b=2, A=0.02ñ0.006(gaussian) Strong CL Upper limit ~30% higher than from Bayesian calculations shown by Luc Demortier (arbitrary units)
Gebhart, Fred Midday On-Air Personality
Gebhart, Fred is from United States and they belong to Midday On-Air Personality and work for KPKX-FM in the AZ state United States got related to this Particular Article.
Journal Ratings by Edison Community College
This Particular Journal got reviewed and rated by Optimization issue You want so that stretch out the CR along ? direction as far as possible. BUT: The choice of band is constrained by the need so that avoid paradoxes (empty regions, in addition to the like) ! No method on the marked allows you so that treat æ in addition to ? in a different fashion Strong CL allows you so that specify æ as the parameters of interest, in addition to so that obtain the narrowest æ interval The solution does not require constructing a multidimensional region Strong CL Band alongside systematics The solution does not require explicit construction of a multidimensional region The narrowest æ interval compatible alongside Strong CL is readily found. Conclusions Strong Confidence bands have all good properties you may ask for. Systematics can be included naturally in addition to rigorously They can even be actually evaluated and short form of this particular Institution is US and gave this Journal an Excellent Rating.
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https://de.zxc.wiki/wiki/Gro%C3%9Fer_Fermatscher_Satz
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math
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Great Fermatsch sentence
The Great Fermatsche Theorem was formulated in the 17th century by Pierre de Fermat , but only proven in 1994 by Andrew Wiles . The conclusive climax for the proof is the collaboration between Wiles and Richard Taylor , which, in addition to the final proof by Wiles, was reflected in a simultaneous publication of a partial proof by both Wiles and Taylor as joint authors.
with positive integers is only possible for and .
The Great Fermatsche Theorem is considered unusual in many ways. His testimony is easy to understand even for laypeople, despite the difficulties that arose in proving it. It lasted more than 350 years and was a story of the failed attempts in which numerous leading mathematicians such as Ernst Eduard Kummer have participated since Leonhard Euler . Numerous partly romantic, partly dramatic, but also tragic episodes of this story have made him popular far beyond the circle of mathematicians.
The proof finally provided, in whose preparatory work alongside Wiles and Taylor also Gerhard Frey , Jean-Pierre Serre , Barry Mazur and Ken Ribet , is considered the high point of mathematics of the 20th century.
There are different names for this sentence. The most common in German is Großer Fermatscher Satz and derived from it Großer Fermat in contrast to the Little Fermat Sentence or Little Fermat. Since there is no evidence from Fermat himself, it was strictly speaking initially only a conjecture. This is why the term Fermat's conjecture is also used, but Fermat's theorem was used even before the proof . In order to include Wiles, the finder of the proof, the Fermat-Wiles theorem is also mentioned . In English, the sentence is called Fermat's Last Theorem , which in German is sometimes (imprecisely) translated as Fermat's last sentence or Fermat's last theorem .
Probably between 1637 and 1643, an exact year cannot be given due to the circumstances explained below, Fermat wrote while reading the arithmetic of Diophantos of Alexandria next to the 8th task of the second (Greek) “book” the following lines as a marginal note in his hand copy Work:
“Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duas ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. "
“However, it is not possible to divide a cube into 2 cubes, or a biquadrat into 2 biquadrates and generally one power, higher than the second, into 2 powers with the same exponent: I have discovered a truly wonderful proof of this, but this one is Edge here too narrow to hold it. "
Since Fermat's hand copy of the arithmetic was found by his son in his father's estate after his death and the latter did not date his notes in the margin, an exact date cannot be determined. It is plausible to assume, however, that Fermat had at least solved the case and perhaps also the case before he was tempted to make his famous and "reckless" remark. Therefore, the year 1641 is more likely than 1637.
That Fermat had found a proof for the special case , of which he perhaps believed he could generalize, is obvious, because this special case is an easy inference from a theorem that he has explicitly proven: Area trianguli rectanguli in numeris non potest quadratus. (The area of a Pythagorean triangle cannot be a square number.), Which he wrote including the proof in the margin next to the 26th task of the 6th (Greek) “book” of arithmetic. André Weil has also proven convincingly that Fermat had all the means to prove the case with his method.
The theories used in Wiles' proof in 1995 were not even rudimentary developed over 350 years earlier. That does not exclude with certainty that one day an even simpler proof will be found that gets by with more elementary means. But most number theorists today doubt that Fermat could have found one. The surest sign that Fermat soon realized that he had not found any evidence after all is that he had not mentioned the sentence or any proof of it to any of his correspondents. Moreover, Fermat's marginal note was only intended for himself. He could not expect publication by his son Samuel.
After Fermat's death, his number-theoretic discoveries were long forgotten because he had not had his findings printed and his contemporaries among mathematicians were not particularly interested in number theory, with the exception of Bernard Frenicle de Bessy. Fermat's eldest son, Samuel, published a new edition of Arithmetica five years after his father's death , which also included his father's forty-eight remarks. The second of these marginal notes later became known as the Fermat conjecture . Although the notes contained a number of fundamental mathematical theorems, evidence or even simple explanations of how Fermat had arrived at these results were mostly, if not all, missing. One of the most important findings of Fermat's, the famous Area trianguli rectanguli in numeris non potest esse quadratus , is provided with a complete proof in addition to the 26th task of the 6th “book” of arithmetic. Here Fermat uses his method of infinite descent . It was left to the subsequent mathematicians, above all and first to Leonhard Euler , to gradually find the missing evidence.
In this context, in the centuries that followed, the (now so-called) Great Fermat's Theorem in particular developed into a challenge for many mathematicians - there was in fact no one who could prove or disprove it. But because Fermat himself had claimed the existence of a “wonderful proof”, generations of mathematicians, including the most important of their time, tried to find it. Fermat's other remarks, too, turned out to be a source of difficult, long-term work for his mathematician colleagues. All in all, however, these efforts led - almost incidentally - to a large number of significant discoveries.
Exception n = 1, n = 2
For and has an infinite number of solutions . For the equation is simple and any solutions can be chosen. For the solutions are the Pythagorean triples .
Evidence for special cases of the theorem
It is enough to prove the conjecture for prime exponents and exponent 4. It is customary to distinguish two cases in the Fermat problem for a prime exponent . In the first case, solutions are sought that are not divisible by. In the second case the product divides .
Special cases of Fermat's Great Theorem could be proven early on:
n = 3, n = 4 and multiples of these numbers
Bernard Frénicle de Bessy published the first evidence for the case as early as 1676 . His solution came from Fermat himself, of whom in this case a sketch of evidence is known in a marginal note in his Diophant edition on a closely related problem (see Infinite Descent ).
Leonhard Euler published evidence of the case in 1738 . Later, with the help of the complex numbers, he was also able to confirm the claim for the case that he published in 1770 (that he had the proof, he announced in a letter as early as 1753). However, Euler did not succeed in extending his method of proof to other cases.
At least 20 different pieces of evidence have now been found for the case . For there are at least 14 different evidence.
4 and odd prime numbers are sufficient
It soon became clear that it was sufficient to prove Fermat's theorem for all prime numbers greater than 2 and for the number 4. Because every natural number that is not prime is divisible by 4 or an odd prime number. If now either 4 or an odd prime number, a natural number and as well as a solution for the exponent , there is also a solution for the exponent , namely . However, such a solution should not exist if Fermat's theorem applies to the exponent . Thus Fermat's theorem also applies to the exponent .
With the evidence in the cases and Fermat's last theorem was for all that a multiple is 3 or 4, proved.
The problem is that the prime numbers also represent an infinitely large set of numbers and therefore - per se - an infinite set of cases to be proven: With these methods a (further) plausibility check could and can be achieved, but never a conclusive and mathematically exact proof.
n = 5, first case and Sophie Germain primes
In 1825 Peter Gustav Lejeune-Dirichlet and Adrien-Marie Legendre were able to prove the theorem for . They relied on the preparatory work of Sophie Germain . Germain was able to prove that the first case of Fermat's conjecture applies to all Sophie-Germain prime numbers (which also have a prime number). Legendre was able to extend this to the cases in which the exponent is also prime, with . This then provided the validity of the first case of the Fermat conjecture for prime numbers . However, until the work of Wiles and Taylor, no general evidence was known for either the first case ( ) or the second case ( ). However, Roger Heath-Brown , Leonard Adleman and Étienne Fouvry were able to show in 1985 that the first case of Fermat's conjecture applies to an infinite number of prime numbers, and in the first case criteria were derived that made it possible for example for Andrew Granville in 1988 to prove that the first Part of the presumption is true.
n = 14 and n = 7
Dirichlet was able to provide evidence for the case in 1832 . In 1839, Gabriel Lamé showed that the case is also valid. Like Augustin-Louis Cauchy , Lamé was still convinced in March 1847 that complete proof of Fermat's conjecture could be presented to the French Academy of Sciences within weeks (hope was destroyed a little later by a letter from Kummer).
Later, simpler variants of the proof were also found.
Further individual cases
In 1885, GB Matthews presented evidence of the cases and . J. Fell published an article in 1943 in which he a method for setting out, also for and should be applicable.
All regular prime numbers
However, the hope of a quick (and general) proof expressed by Cauchy and Lamé in 1847 was dashed by Ernst Eduard Kummer , who discovered a reasoning error in Lamé and Cauchy's considerations: they had tacitly assumed that in the whole end of the whole numbers in the The expansions of the field of rational numbers considered by them ( fields of circular division of the order ) for the respective Fermat equation for the exponent (it arises from the adjunction of the -th roots of unity) the unambiguous prime factorization still applies.
Kummer developed a theory in which the unambiguous prime factorization could be saved by combining certain sets of numbers of the number field ( ideals ) and examining the arithmetic of these new "ideal numbers". He was able to prove Fermat's great theorem in 1846 for regular prime numbers ; A prime number is called regular if none of the Bernoulli numbers have their numerator divisible by . In this case, the class number - ie the number of non-equivalent ideal classes - the cyclotomic field of order not divisible. It is not known whether there are infinitely many regular prime numbers.
With the help of the computer and further development of Kummer's methods, Harry Vandiver succeeded in proving the theorem for all prime numbers less than 2000 as early as the 1950s. With the help of the computer, the limit could be shifted considerably upwards, but one did not get any closer to proving Fermat's conjecture in this way, it only became more plausible.
At most finitely many coprime solutions for n ≥ 4 with fixed n
From Mordell's conjecture - proved in 1983 by Gerd Faltings - it follows as a special case that if one of Fermat's equations has for a solution, it can only have at most a finite number of coprime solutions.
The search for general evidence was also materially motivated at the beginning of the 20th century by the will of the Darmstadt doctor and mathematician Paul Friedrich Wolfskehl . According to a legend told later , his fate was strangely linked to Fermat's theorem. When his love for a woman was not returned by her, he made up his mind to kill himself. He set the time of his suicide at exactly midnight. In order to bridge the time until his suicide, he reread one of Ernst Eduard Kummer 's relevant works on Fermat's conjecture and believed that he had found a mistake in it. He began to check it out carefully and forgot the time. By the time Wolfskehl finally found out that Kummer hadn't made a mistake, the planned time of his suicide was already over and he decided to give up on his plan. In gratitude that Fermat had effectively saved his life, he changed his will. - But that is an unproven legend.
When he died of natural causes ( multiple sclerosis ) in 1906 , it was announced that in his last will he had offered a price of 100,000 gold marks for whoever would first publish complete evidence in a professional journal . In 1908 the Royal Society of Sciences in Göttingen announced the Wolfskehl Prize . The closing date for this project should be September 13, 2007. In 1997 the prize, which was still worth 75,000 DM, was paid to Andrew Wiles .
In 1993 Andrew Wiles presented a proof of the Taniyama-Shimura conjecture in lectures at the Isaac Newton Institute in Cambridge , which would also prove Fermat's great theorem. However, the evidence he presented was incomplete in one essential point, as only became apparent in the subsequent review . Together with his student Richard Taylor , Wiles was able to close the gap in 1994 and thus also prove Fermat's great theorem.
The core of the 98-page work without appendix and bibliography consists of a two-part proof by contradiction :
- not modular . This was suspected by Gerhard Frey in 1986 and proven by Ken Ribet in a 1990 contribution by Jean-Pierre Serre .
- According to the Taniyama-Shimura conjecture (named after Yutaka Taniyama and Gorō Shimura , sometimes also named after André Weil ), however, all elliptical curves are modular. Wiles and Taylor proved this conjecture in 1994 for a large class of elliptic curves, including the Frey curve.
This is a contradiction to the first part of the proof, the assumed existence of a counterexample to Fermat's great theorem must be wrong.
Conjectures that include the Fermat conjecture
There are a few open conjectures that include the Fermat conjecture as a special case, the most important being the abc conjecture . Others are the Fermat-Catalan conjecture and the Andrew Beal conjecture . Another generalization is Euler's conjecture , which has now been refuted.
- In the episode Hotel Royal of the television series Spaceship Enterprise: The Next Century from 1989 it is claimed that the Fermatsche theorem could not be proven even with computer help until the 24th century. Shortly after the series was discontinued in 1994, the proof was then provided. However, Star Trek generally plays in a different timeline . In 1995 there was a "correction" by the "Star Trek" authors: In the episode Facetten (season 3, episode 25) of the television series Star Trek: Deep Space Nine , the symbiote Dax is an alternative ("more original") proof of gossip And at this point explicitly referred to Andrew Wiles's solution.
- In the episode In the Shadow of the Genius of the Simpsons , Homer Simpson writes a supposed counterexample for the great Fermat sentence on a blackboard: the expression in which the difference between the two sides appears as zero in simple pocket calculators. However, this is of course not an actual solution, but only a consequence of the limitations of such a pocket calculator: Since all three numbers have the order of magnitude , but the difference between the two sides is only the comparatively small order of magnitude , the calculator can no longer resolve this. The episode Die Panik-Amok-Horror-Show also contains a supposed solution with the equation , in which the difference between the two sides is 10 orders of magnitude smaller than the numbers. Behind these mathematical contributions to the series is the author David X. Cohen , one of several members of the writing staff with a mathematical and scientific background.
- The author Stieg Larsson lets his protagonist Lisbeth Salander recognize the solution to Fermat's theorem in the second volume of the Millennium Trilogy , but after a head injury she cannot remember exactly.
- In the film Teuflisch , the math homework on the blackboard is to prove Fermat's Great Theorem.
- In Arno Schmidt's short novel Schwarze Spiegel , the first-person narrator solves the Fermat problem - long before Andrew Wiles: “ The black dome of the night: from the circular skylight at the zenith it came out poisonously clear and so mockingly that the snow burned eyes and soles. I sat down on the top of my two wooden steps and wrote on a large sheet: Fermat's problem: In , assuming the integer of all sizes, should never be greater than 2. I quickly proved it to myself as follows: (1) […] The symbols swiftly pulled themselves out of the pencil, and I went on muttering cheerfully: you have to imagine that: I solve the problem of Fermat! (But the time passed by in an exemplary manner). “Unfortunately the evidence is flawed.
- Beal's Conjecture (an unproven generalization of Fermat's great theorem)
- Little Fermatsch sentence
- Regular prime number (there is a proof sketch for this special case)
- Wall-Sun-Sun prime
- Wieferich prime number
- Wolstenholme prime number
- Andrew Wiles: Modular elliptic curves and Fermat's Last Theorem. (PDF; 10.7 MB). In: Annals of Mathematics. 142: 443-551 (1995).
- Richard Taylor , Andrew Wiles: Ring-theoretic properties of certain Hecke algebras. In: Annals of Mathematics. 142: 553-572 (1995).
- Kenneth A. Ribet : On modular representations of arising from modular forms. (PDF; 5.0 MB). In: Inventiones Mathematicae . 100: 431-476 (1990).
- G. Frey : Links between stable elliptic curves and certain diophantine equations. In: Annales Universitatis Saraviensis. Series Mathematicae. 1 (1986), pp. 1-40.
Review articles and history
- Solving Fermat. Public Broadcasting Service (PBS) television interview with Andrew Wiles.
- Paulo Ribenboim : 13 lectures on Fermat's last theorem. Springer, New York 1979 (the most important works before Wiles).
- Paulo Ribenboim: Fermat's last theorem for amateurs. Springer 2000, ISBN 0-387-98508-5 .
- Simon Singh : Fermat's last sentence. The adventurous story of a mathematical puzzle. Deutscher Taschenbuch-Verlag, Munich 2000, ISBN 3-423-33052-X .
- The Royal Society of Sciences: Announcement regarding the Wolfskehlsche Prize Foundation. News from the Royal Society of Sciences in Göttingen. Business communications. 16: 1 (1908), pp. 103-104.
- Simon Singh and Kenneth Ribet: Solving Fermat's Riddle. In: Spectrum of Science. 1/98, ISSN 0170-2971, p. 96 ff.
- CJ Mozzochi: The Fermat Diary. In: American Mathematical Society. 2000 (history of the solution from Frey).
- Kenneth A. Ribet: Galois Representations and Modular Forms. In: Bulletin of the AMS . 32 (4/1995), 375-402.
- Gerd Faltings : The Proof of Fermat's last theorem by R. Taylor and A. Wiles. (PDF; 150 kB). In: Notices of the AMS . 42 (7/1995): 743-746. An overview of the proof idea and the most important steps that is easy to understand for “beginners”.
- Peter Roquette : On the Fermat problem. (PDF; 207 kB). Lecture at the Mathematical Institute of the University of Heidelberg, January 24, 1998. Historical development up to the solution.
- Joseph Silverman , Gary Connell, Glenn Stevens (Eds.): Modular Forms and Fermat's Last Theorem. Springer-Verlag, 1997. Mathematical background material on and presentation of Wiles proof.
- Yves Hellegouarch : Invitation to the Mathematics of Fermat-Wiles. Academic Press, 2002.
- Jürg Kramer : About the Fermat conjecture. Part 1, Elements of Mathematics. Volume 50, 1995, pp. 12-25 ( PDF ); Part 2, Volume 53, 1998, pp. 45-60 ( PDF ).
- Klaus Barner: Gerhard Frey's lost letter. Mitt. Dtsch. Math Ver. 2002, No. 2, pp. 38-44.
- Takeshi Saito: Fermat's last theorem (2 volumes), Volume 1 (Basic Tools), Volume 2 (The Proof), American Mathematical Society 2013, 2014.
- Video: The great Fermat theorem Part 1 . Pedagogical University of Heidelberg (PHHD) 2012, made available by the Technical Information Library (TIB), doi : 10.5446 / 19891 .
- Video: The Great Theorem by Fermat Part 2 . University of Education Heidelberg (PHHD) 2012, made available by the Technical Information Library (TIB), doi : 10.5446 / 19890 .
- "Last" here refers to the fact that it was the last unproven of the sentences formulated by Fermat.
- The original is lost, but the comment can be found in an edition of Diophant's Arithmetica with translation and commentaries by Bachet and notes by Fermat, which his son edited, see Paul Tannery , Charles Henry (ed.): Œuvres de Fermat. Tome premier. Gauthier-Villars, Paris 1891, p. 291 , notes p. 434 ; after Samuel de Fermat (ed.): Diophanti Alexandrini Arithmeticorum libri sex. Bernard Bosc, Toulouse 1670, p. 61 ; For translation see Max Miller: Comments on Diophant. Academic Publishing Society, Leipzig 1932, p. 3.
- Pierre de Fermat: Comments on Diophant. Translated from Latin and edited with annotations by Max Miller. Akademische Verlagsgesellschaft, Leipzig 1932, pp. 34–36.
- Catherine Goldstein : Un théorème de Fermat et ses lecteures. Presses Universitaires de Vincennes, Saint-Denis 1995 (French).
- André Weil: Number theory. A walk through history from Hammurabi to Legendre. Birkhäuser, Basel 1992, pp. 120–124.
- Paulo Ribenboim: Fermat's last theorem for amateurs. Springer-Verlag, 2000, ISBN 978-0-387-98508-4 .
- André Weil: Number Theory. An approach through history from Hammurapi to Legendre. Birkhäuser, 1984, p. 76.
- Spectrum of Science , Dossier 6/2009: The Greatest Riddles of Mathematics. ISBN 978-3-941205-34-5 , p. 8 (interview with Gerd Faltings ).
- Klaus Barner: Paul Wolfskehl and the Wolfskehl Prize. (PDF; 278 kB). In: Notices AMS. Volume 44. Number 10, November 1997 (English).
- Peter Roquette : On the Fermat problem. (PDF; 207 kB). Lecture at the Mathematical Institute of the University of Heidelberg, January 24, 1998. Historical development up to the solution. P. 15. Retrieved August 25, 2016.
- Simon Singh: Homer's last sentence. The Simpsons and the Math. Hanser, Munich 2013. pp. 47–54.
- fact that the first sum is incorrect results directly from the checksums : The bases of both summands 3987 and 4365 (like their checksums) are divisible by 3. This means that all of its powers and their sums are divisible by 3 - in contradiction to the fact that the base 4472 of this sum has a cross sum of 17 that is not divisible by 3. The falseness of the second sum can also be recognized almost without calculation, in that one deduces from the equality of the unit digits 2 of the bases 1782 and 1922 that the difference between their powers is divisible by 10, although their base is 1841.
- Arno Schmidt: Black mirrors. In: Arno Schmidt: Brand's Haide. Two stories. Rowohlt, Hamburg 1951, pp. 153-259 (first edition).
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http://bobbyroel.com/forum-forex/american-call-option-delta.php
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math
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In mathematical finance , the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters as are some other finance measures.
Collectively these have also been called the risk sensitivities , risk measures : The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging. The Greeks in the Black—Scholes model are relatively easy to calculate, a desirable property of financial models , and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions.
For this reason, those Greeks which are particularly useful for hedging—such as delta, theta, and vega—are well-defined for measuring changes in Price, Time and Volatility.
Although rho is a primary input into the Black—Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common. The most common of the Greeks are the first order derivatives: The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive.
The use of Greek letter names is presumably by extension from the common finance terms alpha and beta , and the use of sigma the standard deviation of logarithmic returns and tau time to expiry in the Black—Scholes option pricing model. Several names such as 'vega' and 'zomma' are invented, but sound similar to Greek letters.
The names 'color' and 'charm' presumably derive from the use of these terms for exotic properties of quarks in particle physics. For a vanilla option, delta will be a number between 0. The difference between the delta of a call and the delta of a put at the same strike is close to but not in general equal to one, but instead is equal to the inverse of the discount factor. These numbers are commonly presented as a percentage of the total number of shares represented by the option contract s.
This is convenient because the option will instantaneously behave like the number of shares indicated by the delta. For example, if a portfolio of American call options on XYZ each have a delta of 0. The sign and percentage are often dropped — the sign is implicit in the option type negative for put, positive for call and the percentage is understood. Delta is always positive for long calls and negative for long puts unless they are zero.
The total delta of a complex portfolio of positions on the same underlying asset can be calculated by simply taking the sum of the deltas for each individual position — delta of a portfolio is linear in the constituents. Since the delta of underlying asset is always 1. This portfolio will then retain its total value regardless of which direction the price of XYZ moves. Albeit for only small movements of the underlying, a short amount of time and not-withstanding changes in other market conditions such as volatility and the rate of return for a risk-free investment.
The absolute value of Delta is close to, but not identical with, the percent moneyness of an option, i. For example, if an out-of-the-money call option has a delta of 0. At-the-money puts and calls have a delta of approximately 0. The actual probability of an option finishing in the money is its dual delta , which is the first derivative of option price with respect to strike.
Given a European call and put option for the same underlying, strike price and time to maturity, and with no dividend yield, the sum of the absolute values of the delta of each option will be 1 — more precisely, the delta of the call positive minus the delta of the put negative equals 1. This is due to put—call parity: If the value of delta for an option is known, one can calculate the value of the delta of the option of the same strike price, underlying and maturity but opposite right by subtracting 1 from a known call delta or adding 1 to a known put delta.
For example, if the delta of a call is 0. Vega measures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset. Vega is not the name of any Greek letter. Presumably the name vega was adopted because the Greek letter nu looked like a Latin vee , and vega was derived from vee by analogy with how beta , eta , and theta are pronounced in American English.
Another possibility is that it is named after Joseph De La Vega, famous for Confusion of Confusions , a book about stock markets and which discusses trading operations that were complex, involving both options and forward trades. All options both calls and puts will gain value with rising volatility. Vega can be an important Greek to monitor for an option trader, especially in volatile markets, since the value of some option strategies can be particularly sensitive to changes in volatility.
The value of an option straddle , for example, is extremely dependent on changes to volatility. The mathematical result of the formula for theta see below is expressed in value per year. By convention, it is usual to divide the result by the number of days in a year, to arrive at the amount an option's price will drop, in relation to the underlying stock's price. Theta is almost always negative for long calls and puts, and positive for short or written calls and puts. An exception is a deep in-the-money European put.
The total theta for a portfolio of options can be determined by summing the thetas for each individual position. The value of an option can be analysed into two parts: The time value is the value of having the option of waiting longer before deciding to exercise. Even a deeply out of the money put will be worth something, as there is some chance the stock price will fall below the strike before the expiry date.
However, as time approaches maturity, there is less chance of this happening, so the time value of an option is decreasing with time.
Thus if you are long an option you are short theta: Except under extreme circumstances, the value of an option is less sensitive to changes in the risk free interest rate than to changes in other parameters. For this reason, rho is the least used of the first-order Greeks. Rho is typically expressed as the amount of money, per share of the underlying, that the value of the option will gain or lose as the risk free interest rate rises or falls by 1.
Gamma is the second derivative of the value function with respect to the underlying price. Most long options have positive gamma and most short options have negative gamma. Long options have a positive relationship with gamma because as price increases, Gamma increases as well, causing Delta to approach 1 from 0 long call option and 0 from -1 long put option.
The inverse is true for short options. Gamma is important because it corrects for the convexity of value. When a trader seeks to establish an effective delta-hedge for a portfolio, the trader may also seek to neutralize the portfolio's gamma, as this will ensure that the hedge will be effective over a wider range of underlying price movements. Vanna , also referred to as DvegaDspot and DdeltaDvol , is a second order derivative of the option value, once to the underlying spot price and once to volatility.
It is mathematically equivalent to DdeltaDvol , the sensitivity of the option delta with respect to change in volatility; or alternatively, the partial of vega with respect to the underlying instrument's price. Vanna can be a useful sensitivity to monitor when maintaining a delta- or vega-hedged portfolio as vanna will help the trader to anticipate changes to the effectiveness of a delta-hedge as volatility changes or the effectiveness of a vega-hedge against change in the underlying spot price.
Charm or delta decay measures the instantaneous rate of change of delta over the passage of time. Charm has also been called DdeltaDtime. Charm is a second-order derivative of the option value, once to price and once to the passage of time. It is also then the derivative of theta with respect to the underlying's price. It is often useful to divide this by the number of days per year to arrive at the delta decay per day.
This use is fairly accurate when the number of days remaining until option expiration is large. When an option nears expiration, charm itself may change quickly, rendering full day estimates of delta decay inaccurate. Vomma , volga , vega convexity , or DvegaDvol measures second order sensitivity to volatility. Vomma is the second derivative of the option value with respect to the volatility, or, stated another way, vomma measures the rate of change to vega as volatility changes.
With positive vomma, a position will become long vega as implied volatility increases and short vega as it decreases, which can be scalped in a way analogous to long gamma.
And an initially vega-neutral, long-vomma position can be constructed from ratios of options at different strikes. Vomma is positive for options away from the money, and initially increases with distance from the money but drops off as vega drops off. Veta or DvegaDtime measures the rate of change in the vega with respect to the passage of time.
Veta is the second derivative of the value function; once to volatility and once to time. It is common practice to divide the mathematical result of veta by times the number of days per year to reduce the value to the percentage change in vega per one day. Vera sometimes rhova measures the rate of change in rho with respect to volatility. Vera is the second derivative of the value function; once to volatility and once to interest rate. Vera can be used to assess the impact of volatility change on rho-hedging.
Speed measures the rate of change in Gamma with respect to changes in the underlying price. This is also sometimes referred to as the gamma of the gamma : Speed can be important to monitor when delta-hedging or gamma-hedging a portfolio. Zomma measures the rate of change of gamma with respect to changes in volatility.
Zomma has also been referred to as DgammaDvol. Zomma can be a useful sensitivity to monitor when maintaining a gamma-hedged portfolio as zomma will help the trader to anticipate changes to the effectiveness of the hedge as volatility changes.
Color , [note 1] gamma decay or DgammaDtime measures the rate of change of gamma over the passage of time. Color is a third-order derivative of the option value, twice to underlying asset price and once to time. Color can be an important sensitivity to monitor when maintaining a gamma-hedged portfolio as it can help the trader to anticipate the effectiveness of the hedge as time passes.
It is often useful to divide this by the number of days per year to arrive at the change in gamma per day. When an option nears expiration, color itself may change quickly, rendering full day estimates of gamma change inaccurate. Ultima measures the sensitivity of the option vomma with respect to change in volatility.
Ultima has also been referred to as DvommaDvol. If the value of a derivative is dependent on two or more underlyings , its Greeks are extended to include the cross-effects between the underlyings. Correlation delta measures the sensitivity of the derivative's value to a change in the correlation between the underlyings. Cross gamma measures the rate of change of delta in one underlying to a change in the level of another underlying. Cross vanna measures the rate of change of vega in one underlying due to a change in the level of another underlying.
Equivalently, it measures the rate of change of delta in the second underlying due to a change in the volatility of the first underlying. Cross volga measures the rate of change of vega in one underlying to a change in the volatility of another underlying.More...
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https://essaytyperplus.com/scott-and-bill-corporation/
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math
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An investor wishes to analyze two common stocks, Scott Corporation and Bill Corporation, using the following information. Common Stock Expected Rate of Return Standard Deviation Scott Corp. 12% 6% Bill Corp. 20% 15% a. If the investor allocates 30% of his money to Scott Corporation and the remaining 70% to Bill Corporation, the standard deviation for the market portfolio is 10%, and the correlation of returns on the two stocks is 0.50, what is the expected return and standard deviation of the portfolio? explain what happens to the expected return and standard deviation when you reallocate your portfolio and invest 50% in each stock.Expected Return is (12% * 30%) + (20% * 70%) = 17.6%Standard Deviation = [(.3*.3*.06*.06)+(.7*.7*.15*.15)+(2*.3*.7*.15*.06) ]^.5 = 12.3% If the weight is 50-50, then,Expected Return (12% * 50*) +…
Scott and Bill Corporation
Plagiarism-free and delivered on time!
We are passionate about delivering quality essays.
Our writers know how to write on any topic and subject area while meeting all of your specific requirements.
Unlike most other services, we will do a free revision if you need us to make corrections even after delivery.
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https://math.ua.edu/event/analysis-seminar-tuoc-phan-university-of-tennessee-knoxville/
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math
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- This event has passed.
Analysis Seminar – Tuoc Phan, University of Tennessee, Knoxville
October 5, 2018 @ 3:00 pm - 4:00 pm
Title: Calderon-Zygmund theory for nonlinear partial differential equations and applications
Abstract: In this talk, we will discuss several recent developments on regularity theory estimates in Sobolev spaces for solutions of several classes of elliptic and parabolic nonlinear PDEs. Some classes of considered equations may be singular and degenerate. Important ideas and techniques will be highlighted. Connections and applications of the results to other areas will be discussed or briefly mentioned. In particular, a solution to an open question on the existence and uniqueness of smooth global-time solutions of a system of nonlinear parabolic equations called cross-diffusion equations will be given.
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https://tr.ifixit.com/Answers/View/323455/HTC+One+M7+Completely+Dead,+possible+fix?permalink=answer-363879
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math
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HTC One M7 Completely Dead, possible fix
HTC One M7 ( PN0731).
Not sure what happened to it, but there is no charge, no connect nothing through USB, no Boot, not even a little red light when plugged in. No JTAG, since no power to the board it seems.
Scratching my head to figure out why, cant come up with any reason for such a complete failure. So examined it with microscope.
Found one component that might be the problem.
Location on Board:
Zooming in you can see that there is an IC that is cracked
What I'm looking for is help with 3 things:
1. Do you think this is the problem?
2. What is this component? It has an code (PAY 328), but I have no idea what that symbol in the top right corner is, so no idea how to look it up.
3. If not that, any ideas? I'm mostly concerned about data recovery, not making the device work again, so if anyone has ISP pinouts that might be a way to go
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https://rospromlab.ru/time-constant-rl/
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math
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Time constant rl
Hoppa till Time domain considerations – The most straightforward way to derive the time domain. InductorsCachadLiknandeÖversätt den här sidanThe above LR series circuit is connected across a constant voltage source, (the battery) and a switch. Assume that the switch, S is open until it is closed at a time .
This is a time constant calculator for both RC circuits and RL circuits. It computes the time constant result in unit seconds. It is often perplexing to new students of electronics why the time-constant calculation for an inductive circuit is different from that of a capacitive circuit.
Interactive animation explains LR time constants, calculating LR time constants explained.
Explains the significance of the time constant for the RL Circuit. The following example should clear up any confusion about time constants. Assume that maximum current in an LR circuit is amperes. What it shows: The growth and decay of current in an RL circuit with a time constant visible in real time. A series RL circuit with a voltage source V (t) connected across it is.
Experiment RC and RL circuits: Measuring the time constant. Object: The object of this lab is to measure the time constant of an RC circuit and a LR circuit. The RL time constant indicates the amount of time that it takes to conduct 63. A first-order RL parallel circuit has one resistor (or network of resistors) and a. The time constant provides a measure of how long an inductor current takes to . What is the significance of a time constant in a circuit?
Need help with your Electronics – DC homework? Establishing a current in an inductor stores energy in the magnetic field formed by the coils of . Exponential responses of capacitors and inductors. Equipment: LR circuit (see sketch); Inductance is the red solenoid (“Rim = Q; L = mH);.
Measure time constant I on scope; compare to predicted value.
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http://www.buffalo.edu/ubit/service-guides/software/downloading/ub-owned-computers.html
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math
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UB makes available select software for download to UB-owned
Mathematica integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and connectivity to other applications. Mathematica is available for installation on UB-owned computers for instructional use. This software is not licensed for federally sponsored research.
In order to install Mathematica, you need to first request the activation key from the vendor. The key will be emailed to your UB email address. You can then install the software.
software can be ordered through UB for installation on UB-owned
computers. These software titles, which include MATLAB,
Microsoft Office, SAS, SPSS and AutoCad, are licensed by UB and
must be ordered by faculty or staff.
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https://www.coursehero.com/tutors-problems/Finance/16563562-An-all-equity-firm-is-expected-to-have-earnings-per-share-in-perpetuit/
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math
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An all equity firm is expected to have earnings per share in perpetuity of $6.00. The current price is $50.00 per share, which implies the equity capitalization rate (rE) is 12 percent. Suppose the firm issues debt and uses the proceeds to buy back stock so that expected earnings per share increase to $8.00 in perpetuity. Assuming a world where Modigliani-Miller Proposition I holds, what is (a) the new share price and (b) the new equity capitalization rate (rE)?
The new share price is __________
The new equity capitalization rate is _________
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| 548
| 3
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https://comicfury.com/comicprofile.php?url=cergos
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math
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Last update: 30th Sep 2016, 12:50 AM
A webcomic written by a Christian-programmer-mathematician-punmaster-dragon hybrid (trust me, they exist; I know one). Simplistic figures are a win. Inspired by xkcd.
Most recent comments left on cergos
I didn't actually ink this, I just used a burn edit tool.Author Note
Sorry, I am still trying to figure out how to optimally scan on my textpad.Author Note
[repost of an older comic]Author Note
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https://wheatoncollege.edu/academics/programs/mathematics-economics/
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math
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Mathematics and Economics
The interdepartmental major in mathematics and economics provides an opportunity for students interested in both economic and mathematical analysis to use mathematical concepts and techniques in understanding and analyzing economic problems, processes and policies. A student with this combination of disciplines would be prepared for graduate study at institutions stressing mathematical economics.
The major consists of a minimum of 14 courses: seven Economics courses and seven Mathematics courses.
ECON 101 Introduction to Macroeconomics
ECON 102 Introduction to Microeconomics
or ECON 112 Microeconomics with BioPharma Applications
ECON 201 Macroeconomic Theory
ECON 202 Microeconomic Theory
ECON 330 Applied Econometrics
One course at the 200 or 300 level in Economics.
One course at the 400 level in Economics.
MATH 101 Calculus I
MATH 104 Calculus II
MATH 141 Introductory Statistics
or MATH 151 Introduction to Data Science (Recommended)
MATH 221 Linear Algebra
One course at the 300 or 400 level in Mathematics.
Two additional courses at the 200 or 300 level in Mathematics.
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https://www.onlinemathlearning.com/power-rule-exponent.html
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math
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Power Rule for Exponents
More Lessons for Grade 7
Videos, worksheets, and solutions to help Grade 7 students learn about exponent rules.
What is the Power Rule for exponents?
The Power Rule for exponent states that when we
raise a power to a power, we can multiply the exponents. (32
= 32 × 5
Power Rule: How to raise exponents to another power.
Using the power rule with exponents
Power of a Power - Exponent Rule
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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https://www.mis.mpg.de/de/veranstaltungen/andere/ladyzhenskaya-vorlesung/november-2012.html
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math
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10th Ladyzhenskaya Lecture Leipzig
Laure Saint-Raymond: About the Boltzmann-Grad limit
Thursday, November 22th 2012, 4 p.m.
Felix Klein Hörsaal, MI, Augustusplatz 10, 04103 Leipzig
- More info:
Laure Saint-Raymond (born August 4, 1975) is a French mathematician.
Saint-Raymond got her doctorate in 2000 at the University of Paris VII. From 2000 to 2002 she was Chargé des Recherches at the CNRS Laboratory for Numerical Analysis at the University of Paris VI, and from 2002 to 2007 professor at the University of Paris VI (Pierre et Marie Curie, Labor Jacques-Louis Lions). She is currently a professor at the Ecole Normale Superieure.
She deals with nonlinear partial differential equations, specifically the Boltzmann equation (and its hydrodynamic limit) and hydrodynamic equations in geophysics, including the Coriolis forces, with applications to climate phenomena at the equator (collaboration with Isabelle Gallagher). In 2004 she proved together with François Golse the context of weak solutions of the Boltzmann equation (for important classes of the core function in the Boltzmann equation) with the Leray solution of the Navier-Stokes equation. Therefore both received the 2006 SIAG/APDE price. In 2003, she proved the convergence of weak solutions of the Boltzmann equation to solutions of the Euler equations imkompressibler liquids.
In 2008 she received the EMS price and the Price of Science of Paris and the 2009 Ruth Lyttle Satter Prize. In 2008 she was an Invited Speaker at the European Congress of Mathematicians in Amsterdam (Some recent results about the sixth problem of Hilbert: hydrodynamic limit of the Boltzmann equation). Furthermore she received the Pius XI. Gold Medal of the Pontifical Academy of Sciences, the Armand Prize of the French Academy of Sciences and the Peccot Price of the College de France.
The goal of this lecture is to present a derivation of the Boltzmann equation starting from the hamiltonian dynamics of particles in the Boltzmann-Grad limit, i.e. when the number of particles N → ∞ and their size ε → 0 with Nε2 = 1. We will especially discuss the origin of irreversibility and the phenomenon of relaxation towards equilibrium, which are apparently paradoxical properties of the limiting dynamics.
All lectures overview
- Top-Level Research Area Mathematical Sciences of the University Leipzig
- Max-Planck-Institut für Mathematik in den Naturwissenschaften
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http://hyperphor.com/ammdi/gnarliness
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math
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Agency Made Me Do It
AMMDI is an open-notebook hypertext writing experiment, authored by Mike Travers aka
. It's a work in progress and some parts are more polished than others. Comments welcome!
Also maybe related: Rudy Rucker's
. And also
with its focus on the exceptional.
24 Nov 2022 09:52 - 17 Jun 2023 08:29
Open in Logseq
A term used by
, with both mathematical definition but it also is a certain quality of the cosmos, a cousin perhaps to
in the WS/Erik Davis sense.
Maybe not. I think weirdness involves a certain amount of agent-detection, gnarliness is more a function of unknowability (or uncomputability).
Hypothesis: souls are gnarly, and gnarly things are those with souls.
Gnarly processes are those in Wolfram Class 4: [Four Classes of Behavior: A New Kind of Science | Online by Stephen Wolfram [Page 231]](
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https://www.findfilo.com/math-question-answers/for-the-following-planes-find-the-direction-cosiney03
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math
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Three Dimensional Geometry
For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.3y+5=0.
Connecting you to a tutor in 60 seconds.
Get answers to your doubts.
Find the vector equation of the line passing through (1,2,3)
and parallel to the planes ri^−j^+2k^˙andr3i^+j^+k^˙=6.
Find the image of the line 9x−1=−1y−2=−3z+3 in the plane 3x−3y+10z−26=0.
Find the equation of the plane passing through A(2,2,−1),B(3,4,
Also find a unit vector perpendicular to this plane.
Find the angle between the line r=i^+2j^−k^+λ(i^−j^+k^)
and the plane r2i^−j^+k^˙=4.
Under what condition does the equation x2+y2+z2+2uc+2uy+2wz+d=0 represent a real sphere?
Show that ax+by+r=0,by+cz+p=0andcz+ax+q=0
are perpendicular to x−y,y−zandz−x
Find the direction ratios of orthogonal projection of line 1x−1=−2y+1=3z−2 in the plane x−y+2z−3=0. also find the direction ratios of the image of the line in the plane.
What is the angle between the planes2x−y+z=6 andx+y+2z=3?
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CC-MAIN-2021-39
| 1,059
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https://essaysolutions.net/georgia-military-college-macr/
|
math
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An open market purchase of government bonds by the Federal Reserve results in _________ in the supply of money and _________ in interest rates.
2. Refer to Table 1. The required reserve ratio based on the information provided below must be_______.
Details: Table 1. Suppose that at a point in time the 1st Bank of Kennesaw has a deposits volume of $14,000 and its loans to its customers amount to $11,900. In addition, the bank is currently loaned-up and its total reserves are $2,100. The Balance Sheet of the bank is shown below.
1st Bank of Kennesaw
Jane has a savings account into which she puts money every month so she will eventually have enough money for a down payment on a house. This is an example of which function of money?
Question 4 Saved
Suppose the required reserve ratio is 6.5%, the banking system has $1,950 in total reserves, and is loaned-up. The deposits in the banking system must be
Hint: Recall the formula: Reserve ratio=Reserves/(Customers Deposits)
If the reserve requirement is 20%, a new deposit of $1,500 leads to a potential increase
in the money supply of:
Hint: consider using the formula for money multiplier:
1) Money Multiplier=1/Reserve Requirement
2) Apply the money multiplier to the value of new deposit
Which of the following is not included in M1?
Money is _______ when it has no intrinsic value, but it is nonetheless accepted as money because the government has decreed it to be money.
Assume initially that market interest rates are 7% and the bondholder is receiving a $70 coupon payment per year on a bond with a face value of $1,000. If market interest rates rise to 10%, the bond price_______
Which of these is a liability for a bank?
If the money multiplier increased, what probably happened to the reserve requirement?
Hint: Recall the formula for money multiplier:
Money multiplier=1/Reserve requirement
Order the answer to view it
ORDER THIS OR A SIMILAR PAPER AND GET 20% DICOUNT. USE CODE: GET2O
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https://wpbtips.wordpress.com/list-of-posts/2/
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math
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• Sidebar at the bottom and related layout issues
• The customizer and other settings/options
• Where is the theme CSS and how do I edit it?
• Comments: allowed HTML (2)
• Comments Off (1)
• Custom menus
• Image quality
• Uploading and inserting images: the three (plus one) link options
• “Posts on Pages”
• Widgets and the no-widgets paradox
• On the recent featured image issues
• Adding meta tags
• On the duplicate content myth
• A guide to the new dashboard (pt. 1)
• Selected articles from One Cool Site
Links to blogging tips and recourses from timethief’s blog.
Comments are closed.
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https://www.smpsurveys.com/piping-from-a-grid/
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math
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Piping from a grid
In order to pipe the responses selected in a grid you need to construct a “conditional” PIPE.
What this means is that for every answer in a grid you need to specifically tell the Pipe to include it, based on the row answer given.
Lets examine an example to explain this further.
A researcher wishes a respondent to rate a set of internet browsers from worst to best on a 10 point scale.
However they only want the browsers the respondent uses on a daily basis to be included in the rating question. The researcher scripts the first GRID question to look like this ..,
Then – for every browser selected as being used “Use every day” by the respondent this browser will appear in the following rating question GRID.
So if Internet Explorer and Chrome were chosen in the table above the next question would look like this..,
How is this achieved?
To achieve this the respondent creates a “Pipe” question type after the first question and includes answers in the pipe if the answer given in each row was “Use every day” – (a conditional pipe).
So the first part of the pipe would look like this:
A pipe question type has been created, it has been named Q1_Pipe, and the first element or answer to include in the answer frame is “Chrome” but only if the respondent chose “Use every day” from Q1.
To create the condition click on the button labelled “Select Condition” (called Q1.Chrome.Use every day IS true above) and the condition builder will pop up.
Navigate to Q1 Chrome Use every day and select “True”.
The first answer of the answer frame (pipe) known as Q1_Pipe has been created. Now step through and complete this process for every element of the answer frame – pipe – that you wish to include if the condition is met. The next part of the pipe is shown below.
So now Crome will appear if used every day and so will Safari.
Include the pipe as the answers for the second question by selecting it as the row source of the second grid and you have completed your pipe from grid control.
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CC-MAIN-2020-10
| 2,047
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https://forums.wolfram.com/mathgroup/archive/1995/Dec/msg00234.html
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math
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Re: Comparison of MMA on Various Machines
- To: mathgroup at smc.vnet.net
- Subject: [mg2696] Re: Comparison of MMA on Various Machines
- From: sinan at u.washington.edu (Sinan Karasu)
- Date: Fri, 8 Dec 1995 23:02:48 -0500
- Organization: University of Washington, Seattle
In article <49dp82$8a6 at dragonfly.wri.com>, Gerhard Braunshausen <braunshausen at embl-heidelberg.de> wrote: >Could anyone offer an explanation for the vast differences >in speed particularly in comparing the PowerMac 9500 series >with the SparcStation 20 series? > >To my knowledge, the Sparcstations were supposed to be very >powerful numbercrunchers. So why do they perform so poorly >with Mathematica? > >Thanks for any hints I tried Mathematica on an UltraSparc, the results were very good. They were somewhat better than PowerMac 9500. I suspect that Mathematica memory management is written for Mac. I also suspect that Wolfram Research uses gcc as the compiler for minimum hassle when supporting various platforms. Maybe it is time for Sun to donate some compilers and an UltraSparc machine to Wolfram Research. Sinan -- Redistribution by Microsoft Network is prohibited.
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CC-MAIN-2023-50
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https://www.offcampusjobs.in/icet-2012-notification-important-dates-exam-syllabus-icet-exam-fee/
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math
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ICET 2012 Notification, Important Dates, Exam Syllabus, ICET Exam Fee,
Integrated Common Entrance Test- ICET Exam will Conduct on 18 th,May, 2012. Andhra Pradesh State Council for Higher Education(APSCHE) officially decided the icet 2012 exam date. Kakatiya University is going to conduct ICET 2012 Exam. Candidates have to get icet 2012 Applications forms will be available in Andhra banks, Post offices and University Campus.
ICET 2012 Specially conduct for getting admissions in to MBA and MCA Courses.
Eligibility for ICET 2012
10+2+3 Pass & Degree final year students also eligible in any stream of degree for MBA admissions
Degree for MCA admissions and must have Mathematics in 10+2
B.Tech/B.Tech Final year candidates also eligible for both MBA and MCA
Important Dates to Remember:
ICET 2012 Exam Date : 18-05-2012
ICET 2012 Applications Availibility: February 2nd Week On words
For official website see here : http://www.apsche.org/entrance.asp
Syllabus for ICET Exam 2012:
GENERAL INFORMATION: 200 Questions(200 Marks;Time:150 min)
Section-A: Analytical Ability: 75Q(75M)
1. Data Sufficiency: 20Q(20 marks)
A question is given followed by data I the form of two statements labelled as I and II. If the data given in I alone is sufficient to answer the question then choice(1) is The correct answer. If both , I and II put together are sufficient to answer the questions but neither statement alone is sufficient then choice(3) is the correct answer. If both I and II put together are not sufficient to answer the question and additional data is needed then choice(4) is correct answer.
2. Problem solving 55Q(55M)
a) Sequences and series 25Q(25marks)
Analogies of numbers and alphabets, completion of blank spaces following the pattern in a:b:c:d relationship; odd thing out; missing number in a sequence or a series.
b) Data Analysis 10Q(10M)
The data given in a table. Graphs Bar diagram, pie Chart, Venn Diagram or a passage is to be analysed and the questions pertaining to the data are to be answered.
c) Coding and Decoding problems: 10Q(10M)
A code pattern of English Alphabets is given, A given word or a group of letters are to be coded or decoded based on the given code or codes.
d) Date, Time & Arrangement problems: 10Q(10M)
Calendar problems, clock problems, blood relationships, arrivals, departures and Schedules ; seating arrangements, symbols and notation interpretation.
Section-B Mathematical Ability: 75Q(75M)
I. Arithmetic Ability: 35Q(35M)
Laws of indices, ratio and proportion; surds; numbers and divisibility, I.e.m, and g.c.d; Rational number; ordering; Percentages; profit and loss; partnerships, pipes and cisterms, time, distance and work problems; areas and volumes, mensuration, modular arithmetic.
II. Algebrical and Geometrical ability: 30Q(30M)
Statements, truth tables, implication, converse and inverse, tautologies-sets, relations and functions; polynomials; remainders theorem and consequences; linear
Equations and inequations; modulus; quadric equations and expression; progressions; progressions; binomial theorem , matrices notion of a limit and derivative.
Plane geometry-lines, triangles, Quadrilaterals, Circles,coordiate geometry-distance between points and applications. Equation of a line in different forms.
Trigonometry- Trigonometric ratios of standard angles(0,30,45,60,90,180 degrees); Trigonometry identities; simple problems on heights and distances.
III. Statistical Ability:
Frequency distribution, mean , median, mode, standard deviation, correlation, simple problems probability.
Section C – Communication Ability: 50Q(50M)
Objective of the Test
Candidates will be assessed on their ability to
1. Identify vocabulary used in the day-today communication.
2. Understand the functional use of grammar in day to day communication as well in the business contexts.
3.Identify the basic terminology and concepts in computer and business context(letters, reports,memoranda,agenda, minutes etc).
4. Understand written text and draw inferences
Part 1. Vocabulary 10Q(10M)
Part 2. Business and computer terminology 10Q(10M)
Part 3. Functional Grammar 15Q(15M)
Part 4. Reading Comprehension(3 Passages) (15M)
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https://www.chegg.com/homework-help/mathxl-tutorials-on-cd-for-elementary-algebra-2nd-edition-chapter-3.6-problem-7q-solution-9780321593146
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math
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Here we have to find the equation for the line that is parallel and contains the point .
The equation of the given line is . Because this is the equation of a vertical line, the line parallel to it will also be vertical. Vertical lines have equations of the form . Hence the line parallel to that contains the point is . This equation cannot be written in slope-intercept form.
The figure below shows the graph of the vertical lines and .
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http://functions.wolfram.com/GammaBetaErf/Gamma/introductions/Gamma/ShowAll.html
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math
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Introduction to the Gamma Function
The gamma function is used in the mathematical and applied sciences almost as often as the well-known factorial symbol . It was introduced by the famous mathematician L. Euler (1729) as a natural extension of the factorial operation from positive integers to real and even complex values of the argument . This relation is described by the following formula:
L. Euler derived some basic properties and formulas for the gamma function. He started investigations of from the infinite product
and the integral
which is currently known as the beta function integral. As a result, Euler derived the following integral representation for factorial :
which can be easily converted into the well-known Euler integral for the gamma function:
Also, during his research, Euler closely approached the famous reflection formula:
which later got his name.
At the same time, J. Stirling (1730) found the famous asymptotic formula for the factorial, which bears his name. This formula was also naturally applied to the gamma function resulting in the following asymptotic relation:
Later, A. M. Legendre (1808, 1814) suggested the current symbol Γ for the gamma function and discovered the duplication formula:
It was generalized by C. F. Gauss (1812) to the multiplication formula:
F. W. Newman (1848) studied the reciprocal of the gamma function and found that it is an entire function and has the following product representation valid for the whole complex plane:
where is the Euler–Mascheroni gamma constant.
B. Riemann (1856) proved an important relation between the gamma and zeta functions:
which was mentioned centuries ago in an article by Euler (1749) for particular values of the argument .
K. Weierstrass (1856) and other nineteenth century mathematicians widely used the gamma function in their investigations and discovered many more complicated properties and formulas for it. In particular, H. Hankel (1864, 1880) derived its contour integral representation for complex arguments, and O. Hölder (1887) proved that the gamma function does not satisfy any algebraic differential equation. This result was subsequently re-proved by A. Ostrowski (1925).
Many mathematicians devote special attention to the question of the uniqueness of extending the factorial operation from positive integers to arbitrary real or complex values. Evidently this question is connected to the solutions of the functional equation:
J. Hadamard (1894) found that the function is an entire analytic function that coincides with for . But this function satisfies the more complicated functional equation and has a more complicated integral representation than the classical gamma function defined by the Euler integral.
H. Bohr and J. Mollerup (1922) proved that the gamma function is the only function that satisfies the recurrence relationship , is positive for , equals one at , and is logarithmically convex (that is, is convex). If the restriction on convexity is absent, then the recurrence relationship has an infinite set of solutions in the form , where is an arbitrary periodic function with period .
Definition of gamma function
The gamma function in the half-plane is defined as the value of the following definite integral:
This integral is an analytic function that can be represented in different forms; for example, as the following sum of an integral and a series without any restrictions on the argument:
The last formula can also be used as an equivalent definition of the gamma function.
A quick look at the gamma function
Here is a quick look at the graphics for the gamma function along the real axis.
Connections within the group of gamma functions and with other function groups
Representations through more general functions
The gamma function is the main example of a group of functions collectively referred to as gamma functions. For example, it can be written in terms of the incomplete gamma function:
All four incomplete gamma functions , , , and can be represented as cases of the hypergeometric function . Further, the gamma function Γ(z) is the special degenerate case of the hypergeometric function .
Representations through related equivalent functions
The gamma function and two factorial functions are connected by the formulas:
The best-known properties and formulas for the gamma function
Values at points
The gamma function can be exactly evaluated in the points . Here are examples:
Specific values for specialized variables
The preceding evaluations can be provided by the formulas:
At the points , the values of the gamma function can be represented through values of :
Real values for real arguments
For real values of argument , the values of the gamma function are real (or infinity). The gamma function is not equal to zero:
The gamma function is an analytical function of , which is defined over the whole complex ‐plane with the exception of countably many points . The reciprocal of the gamma function is an entire function.
Poles and essential singularities
The function has an infinite set of singular points , which are the simple poles with residues . The point is the accumulation point of the poles, which means that is an essential singular point.
Branch points and branch cuts
The function does not have branch points and branch cuts.
The function does not have periodicity.
Parity and symmetry
The function has mirror symmetry:
The derivatives of can be represented through gamma and polygamma functions:
Ordinary differential equation
The gamma function does not satisfy any algebraic differential equation (O. Hölder, 1887). But it is the solution of the following nonalgebraic equation:
Series representations of the gamma function near the poles are of great interest for applications in the theory of generalized hypergeometric, Meijer G, and Fox H functions. These representations can be described by the formulas:
where are the Bernoulli numbers.
Asymptotic series expansions
Asymptotic behavior of the gamma function is described by the famous Stirling formula:
This formula allows derivation of the following asymptotic expansion for the ratio of gamma functions:
The gamma function has several integral representations that are different from the Euler integral:
and related integral
which can be used for defining the gamma function over the whole complex plane.
Some of the integral representations are the following:
This final formula is known as Hankel's contour integral. The path of integration starts at on the real axis, goes to , circles the origin in the counterclockwise direction with radius to the point , and returns to the point .
The following infinite product representation for clearly illustrates that at :
The similar product representation for illustrates that is an entire function:
The following famous limit representation for was known to L. Euler:
It can be modified to the following related limit representations:
The gamma function can be evaluated as the limit of the following definite integral:
The most famous definite integrals, including the gamma function, belong to the class of Mellin–Barnes integrals. They are used to provide a uniform representation of all generalized hypergeometric, Meijer G, and Fox H functions. For example, the Meijer G function is defined as the value of the following Mellin–Barnes integral:
The infinite contour of integration separates the poles of at , from the poles of at , . Such a contour always exists in the cases .
There are three possibilities for the contour :
(i) runs from γ-ⅈ∞ to γ+ⅈ∞ (where ) so that all poles of , , are to the left of , and all the poles of , are to the right of ℒ. This contour can be a straight line if (then ). In this case, the integral converges if , . If , then must be real and positive, and the additional condition , should be added.
(ii) is a left loop, starting and ending at and encircling all poles of ,, once in the positive direction, but none of the poles of , . In this case, the integral converges if and either or and or and and and .
(iii) is a right loop, starting and ending at +∞ and encircling all poles of , , once in the negative direction, but none of the poles of , . In this case, the integral converges if , and either or and or and and and .
In particular cases, the last integral can be evaluated using simpler elementary and special functions:
The definition of the Meijer G function through a Mellin‐Barnes integral realizes the inverse Mellin integral transform of ratios of gamma functions:
The contour is the vertical straight line . It allows the writing of the following rather general formula for the inverse Mellin integral transform:
In particular cases, it gives the following representations:
The following formulas describe some transformations of the gamma functions with linear arguments into expressions that contain the gamma function with the simplest argument:
In the case of multiple arguments , ,…, , the gamma function can be represented by the following duplication and multiplication formulas, derived by A. M. Legendre and C. F. Gauss:
Products involving the direct function
The product of two gamma functions and , with arguments satisfying the condition that is an integer, can be represented through elementary functions:
The preceding formula transforms into the following formula and its relatives:
The ratio of two gamma functions and , with arguments satisfying the condition that is integer, can be represented through a polynomial or rational function:
The gamma function satisfies the following recurrence identities:
These formulas can be generalized to the following recurrence identities with a jump of length :
The most famous inequalities for the gamma function can be described by the following formulas:
The gamma function is used throughout mathematics, the exact sciences, and engineering.
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http://www.chegg.com/homework-help/basic-chemistry-7th-edition-chapter-2-problem-50qp-solution-9780538736374
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math
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Solutions for Chapter 2 Problem 50QP
(a) In the given calculation, the mathematical operations present are multiplication and division.
Thus, the rules for using significant figures for multiplication and division must be considered. The number of significant digits will be determined by the term that has the least number of significant digits, which will be the “limiting” number. The number “9.7871” has five significant digits, “2” has only one significant digit, “0.00182” has three significant digits, and “43.21” has four significant digits. Therefore, “2” is the limiting term, and the final answer will only have.
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https://talk.collegeconfidential.com/t/srinivasa-ramanujan/236607
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math
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<p>" Srinivāsa Aiyangār Rāmānujan (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (December 22, 1887 – April 26, 1920) was an Indian mathematician and one of the greatest mathematical geniuses of the twentieth century. He is considered one of the greatest mathematical prodigy that the world has ever seen. He had uncanny mathematical manipulative abilities, as judged by experts in his field. He excelled in the heuristic aspects of number theory and insight into modular functions. He also made significant contributions to the development of partition functions and summation formulas involving constants such as π.</p>
<p>A child prodigy, he was largely self-taught in mathematics and had compiled over 3,000 theorems between 1914 and 1918 at the University of Cambridge. Often, his formulas were merely stated, without proof, and were only later proven to be true. His results were highly original and unconventional, and have inspired a large amount of research and many mathematical papers; however, some of his discoveries have been slow to enter the mathematical mainstream. Recently his formulae have started to be applied in the field of crystallography, and other applications in physics. The Ramanujan Journal was launched to publish work 'in areas of mathematics influenced by Ramanujan'. "</p>
<p>" Theorems and discoveries
It is said that Ramanujan's discoveries were unusually rich; that is, in many of them there was far more than initially met the eye. The following include both Ramanujan's own discoveries, and those developed or proven in collaboration with Hardy.</p>
<p>Properties of highly composite numbers
The partition function and its asymptotics
He also made major breakthroughs and discoveries in the areas of:</p>
Ramanujan's continued fractions
Prime number theory. A type of prime numbers based on a 1919 publication by Ramanujan is named Ramanujan primes.
Mock theta functions "</p>
<p>" Childhood and early life
Ramanujan was born in 1887 in Erode, Tamil Nadu, India, the place of residence of his maternal grandparents. His father hailed from the fertile Thanjavur District (temple district), working, when Ramanujan was born in Kumbakonam, at a cloth merchant's shop. His mother is believed to have been well-educated in Indian mathematics and Ramanujan is conjectured by some to have been as well. In 1898, at age 10, he entered the Town High School in Kumbakonam, where he may have encountered formal mathematics for the first time. At 11 he had mastered the mathematical knowledge of two lodgers at his home, both students at the Government College, and was lent books on advanced trigonometry written by S. L. Loney, which he mastered by age 13. His biographer reports that by 14 his true genius was beginning to become discernible. Not only did he achieve merit certificates and academic awards throughout his school years, he was also assisting the school in the logistics of assigning its 1200 students (each with their own needs) to its 35-odd teachers, completing mathematical exams in half the allotted time, and was showing familiarity with infinite series. His peers at the time commented later, "We, including teachers, rarely understood him" and "stood in respectful awe" of him. However, Ramanujan could not concentrate on other subjects and failed his high school exams. By age 17, he calculated Euler's constant to 15 decimal places. He began to study what he thought was a new class of numbers, but instead he had independently developed and investigated the Bernoulli numbers. At this time in his life, he was quite poor and was often near the point of starvation.</p>
<p>Adulthood in India
After marriage (on July 14, 1909) he began searching for work. With his packet of mathematical calculations, he travelled around the city of Madras (now Chennai) looking for a clerical position. He managed finally to get a job as an accountant in the General's Office at Madras. Ramanujan desired to focus completely on mathematics, and was advised by an Englishman to contact scholars in Cambridge. He doggedly solicited support from influential Indian individuals and published several papers in Indian mathematical journals, but was unsuccessful in his attempts to foster sponsorship. ( OR so the story goes - actually he was supported by R.Ramachandra Rao, then the Collector of the Nellore District and a distinguished civil servant. Ramachandra Rao, an amateur mathematician himself was the uncle of the well known mathematician, K. Ananda Rao, who went on to become the Principal of the Presidency college.) It was at this point that Sir Ashutosh Mukherjee tried to bolster his cause.</p>
<p>In late 1912 and early 1913 Ramanujan sent letters and examples of his theorems to three Cambridge academics: H. F. Baker, E. W. Hobson, and G. H. Hardy. Only Hardy, a Fellow of Trinity College to whom Ramanujan wrote in January 1913, recognized the genius demonstrated by the theorems.</p>
<p>Upon reading the initial unsolicited missive by an unknown and untrained Indian mathematician, Hardy and his colleague J.E. Littlewood commented that, “not one [theorem] could have been set in the most advanced mathematical examination in the world.” Although Hardy was one of the pre-eminent mathematicians of his day and an expert in several of the fields Ramanujan was writing about, he commented, 'many of them defeated me completely; I had never seen anything in the least like them before.' "</p>
He was referred to in the film Good Will Hunting as an example of mathematical genius.
His biography was also highlighted in the Vernor Vinge book The Peace War.
The character 'Amita Ramanujan' in the CBS TV series Numb3rs (2005-) was named after him
The short story "Gomez", by Cyril Kornbluth, mentions Ramanujan by name as a comparison to its title character, another self-taught mathematical genius.</p>
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https://packershome.com/forum/posts/m459777-packers
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math
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Looks like we will start 1-0. 🤣 let the tradition continue
Originally Posted by: umair_010
I predict David Bakthiari to be rest Sept 17th, Oct 9th, Nov 23rd, and Dec 31st.
Originally Posted by: Zero2Cool
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https://scholarsarchive.byu.edu/etd/871/
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math
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This work focuses on generating approximations of complex T-spline surfaces with similar but less complex T-splines. Two approaches to simplifying T-splines are proposed: a bottom-up approach that iteratively refines an over-simple T-spline to approximate a complex one, and a top-down approach that evaluates existing control points for removal in producing an approximations. This thesis develops and compares the two simplification methods, determining the simplification tasks to which each is best suited. In addition, this thesis documents supporting developments made to T-spline research as simplification was developed.
College and Department
Physical and Mathematical Sciences; Computer Science
BYU ScholarsArchive Citation
Cardon, David L., "T-Spline Simplification" (2007). Theses and Dissertations. 871.
computer graphics, parametric surfaces, CAGD, computer-aided geometric design, splines, simplification, geometric modeling, NURBS, subdivision surfaces
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https://mathoverflow.net/questions/197780/wong-zakai-smooth-approximation-in-probabilty-for-stochastic-differential-equati
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math
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I'm looking for a result of the form: Let $B_\epsilon$ denote a "natural" smooth $\epsilon$-approximation to an $n$-dimensional Brownian motion $B$ (e.g. by mollification or simply piecewise linear) with $\sigma$ and $\mu$ smooth coefficients, and denote by $X_\epsilon$ the solution to the random ODE $$dX_\epsilon = \mu(X_\epsilon)dt + \sigma(X_\epsilon)dB_\epsilon.$$
Then $X_\epsilon$ converges in probability, as $\epsilon \to 0$, so the solution of the SDE $$dX=\mu(X)dt+\sigma(X)\circ dB.$$
In particular I'm seeking results with no ellipticity requirement on $\sigma$. Many thanks.
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https://www.physicsforums.com/threads/sets-of-pulleys.894627/
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math
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Repost since it was removed from double questions. 1. The problem statement, all variables and given/known data Worker Sim Pulma Sheen uses a system of pulleys to lift a 5000 N box 2 meters while pulling on the rope with a force of 500 N. This means the worker had to pull how much rope from the pulley system? a) 0.2m. b) 2m c) 5m d) 10m e) 30m 2. Relevant equations W = F*D? 3. The attempt at a solution I tried to find the work of the obj then set it equal to the work done on the person (pulling) and devide by force to find distance, and got 20.... is this not the right equation?
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http://e-booksdirectory.com/details.php?ebook=9617
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math
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by Thomas Little Heath
Number of pages: 76
History and tradition know Archimedes almost exclusively as the inventor of a number of ingenious mechanical appliances, things which naturally appeal more to the popular imagination than the subtleties of pure mathematics.And it is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen.
Home page url
Download or read it online for free here:
by J. L. Heiberg - Oxford University Press
The volume gives a general survey of the science of Classical Antiquity, laying however special stress on the mathematical and physical aspects. Topics: Ionian Natural Philosophy; Pythagoreans; Hippocrates; Mathematics in the Fifth Century; Plato ...
by Karl Fink - Open Court Publishing Company
The book is intended to give students of mathematics an historical survey of the elementary parts of this science and to furnish the teacher of the elements opportunity to review connectedly points for the most part long familiar to him.
by G. Donald Allen - Texas A&M University
Exploring the concepts, ideas, and results of mathematics is a fascinating topic. In this course you will see firsthand many of the results that have made what mathematics is today and meet the mathematicians that created them.
by Isaac Todhunter - Adamant Media Corporation
The book traces the progress of the Calculus of Variations during the nineteenth century: Lagrange and and Lacroix, Dirksen and Ohm, Gauss, Poisson, Ostrogradsky, Delaunay, Sarrus, Cauchy, Legendre, Brunacci, and Jacobi.
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https://link.springer.com/article/10.1007/s002110050033
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math
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On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations
- 383 Downloads
Convergence estimates in terms of the data are shown for multistep methods applied to non-homogeneous linear initial-boundary value problems. Similar error bounds are derived for a new class of time-discrete and fully discrete approximation schemes for boundary integral equations of such problems, e.g., for the single-layer potential equation of the wave equation. In both cases, the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions. These estimates, which are also proved here, depend on bounds of the Laplace transform of the (distributional) convolution kernel outside the stability region scaled by the time stepsize, and on the smoothness of the data.
Unable to display preview. Download preview PDF.
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https://www.simscale.com/forum/t/issue-with-temperature-results/94879
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math
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I tried simulating a battery for identifying temperature rise, the battery has no dedicated cooling system, it relies on its metal case for cooling, initially I used CHT V1 with very very small inlet velocity of 1e-4 m/s and a default outlet pressure, I tried to capture a natural convection scenario with these setting. The temperature rise was 35°C. Then I used CHT V2 with only natural convection and the temperature rise went to 829°C which is very high, I want to know what went wrong, In physical condition the temperature rise is around 40°C and with inlet-outlet boundary condition temperature is 35°C but with natural convection BC temperature reaches 829°C which seems impossible. Please help!
thanks for reaching out to us here in the forum,
From what I can see ist that first I would recommend you to create a larger volume for the air. right now any air that rises to the top just quickly exits the fluid domain. You can check this by having a look at the flow rate at each face of the air volume.
For this to work efficiently you most liklöy will have to reduce the mesh. But you can do this by using the symmetry of your battery.
Symmetry of the object:
Hi Sebastian, In natural convection, as you said, the mesh elements will increase and would take a lot of time to solve, even with symmetry, I would like to know is there any other way I can create a natural convection scenario by maybe using the inlet velocity-outlet pressure BCs as I did in the first run, will it be feasible?
first please have a look at this tutorial and see how to apply the symmetry boundary condition correctly.
You can also see how the natural convection boundary condition is applied here.
And sure there are other ways to generate a natural convection BC, but this wouldn’t decrease the number of cells needed since you need the size of the fluid volume to have the fluid field fully developed.
And your first definition of the BC was more like forced convection within a box scenario than natural conversation. And with 4 Mio Cell Simulation Time around 2.5 hours are expected.
I don’t remember if you can set these values automatically for CHT2 in SimScale but if you are using manual relaxation, set them to something like 0.01, 0.02, 0.02. For natural convection, the solver is extremely sensitive to these relaxation values. I do not know the form of the transport equations for CHT2.0 but I suppose that if a strong coupling of the energy equation between solids and gases is used, the solver really requires low values for the relaxation factors. Also, initialize the solution with the correct velocity inside the whole domain (the same one set for the inlet boundary).
Hi I used the default numeric settings, I didn’t altered any relaxation factor. I’ve input the recommended values, I got a warning that overall sum of pressure, velocity and temperature must be 0.9 to 1.1, however I went ahead with the values and will get back to you with the results.
I would like to know what other ways I can create a natural convection scenario, initially I used inlet air velocity of 1e-4 m/s so I thought it will be a good representation for natural convection, currently I setup the natural convection boundary condition as suggested in the tutorial along with relaxation values suggested by @jairogut , will post the results as soon as analysis is finished
The simulation previously ran on the same size so I think maybe this error is because of altering the relaxation values since I was also getting a warning related to the sum of these relaxation factors.
Yeah, it may be. I’m afraid I do not use SimScale much but OpenFOAM (although they are almost the same). I know SimScale has some further code enhancements that control such residuals, therefore my advice was not that good (I thought you had set manual residuals). If your simulation was working in CHT1 why are you using now CHT2? I have modelled natural convection with natural convection inlet/outlet BC’s, but I am not sure if they are available in your solver: SimScale. These BC’s allow free flow movement (buoyant flow to leave the domain and “cold” flow to enter the domain).
Is the grid in those regions fine enough? (@SBlock asked you about that issue). Remember that if you use the parametric-hex mesh you can define where the grid needs to be fine and where it does not. Therefore your grid will not need to be that fine. Again start with a test case (which will converge quickly) and set the natural convection BC’s.
In the case 2 (with fixed relaxation values) the solver informed us that velocity is diverging at “Velocity = 3.37274e+07 at position: (0.05062 m, 0.008595 m, -0.04413 m).” This is clearly around the batteries. Case 1 and 3 do not diverge as SimScale automatically controls relaxation values but they clearly had huge non-physical surges in the velocity field (trying to diverge).
For your CHT2 case 2, velocity clearly diverges in these regions:
I initially used CHT1 with a very small inlet velocity of 1e-4 m/s and atmosphere outlet pressure to simulate a natural convection scenario also the domain was small as you can see in the project, the results were close to the real life temperature, simulation showed 35°C and physically temperature reaches upto 40°C, the max flow velocity in this case was 0.05 m/s so I thought this might be a good representation of natural convection. I then read about the natural convection boundary condition and CHT2 on simscale and then I ran the simulation with natural boundary condition hoping the results will be more close to real life, I used the same domain and mesh count but the temperature reached to astonishing 830°C, since then I have tried increasing the flow domain, also used the symmetry BC and natural BC as suggested in tutorials, however the temperature rise still went upto 720°C.
As suggested by you, I’ll reduce the mesh size, will use refinement regions I cannot change the algorithm to hex-dominant, this option is grayed out and only uses standard algorithm, will post the results.
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http://archive.org/search.php?query=subject%3A%22graph%22
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math
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In 1856, Hamiltonian introduced the Hamiltonian Graph where a Graph which is covered all the vertices without repetition and end with starting vertex. In this paper I would like to prove that every Complete Graph ‘G’ having n ≥ 5 vertices, such that n is odd. If for all pairs of nonadjacent vertices u, v one has du + dv ≥ n − 2, then G has a Hamiltonian path. Topics: Graph, Complete Graph, Bipartite Graph Hamiltonian Graph
For the first time, every finite group is represented in the form of a graph in this book. This study is significant because properties of groups can be immediately obtained by looking at the graphs of the groups. Lecture Notes Collection FreeScience.info ID2062 Obtained from http://fs.gallup.unm.edu//GroupsAsGraphs.pdf http://www.freescience.info/go.php?pagename=books&id=2062 Topics: Graph Theory, "
GRAPH DATABASES Discover how graph databases can help you manage and query highly connected data. With this practical book, you'll learn how to design and implement a graph database that brings the power of graphs to bear on a broad range of problem domains. Whether you want to speed up your response to user queries or build a database that can adapt as your business evolves, this book shows you how to apply the schema-free graph model to real-world problems.Learn how different organizations... Topic: GRAPH DATABASES Source: torrent:urn:sha1:26a49fd1c0ae5a57ea909167973d559e8d636413
This program is for drawing graphs of mathematical functions in a coordinate system. Graphs may be added with different color and line styles. Both standard functions and parameter functions are supported. Evaluate a function at an entered point or trace the function with the mouse. You can also add shadings to functions and series of points to the coordinate system. Trendlines may be added to point series, and you can save the coordinate system and everything on it as an image file. You can... Topics: Graph, Business, Engineering, Graphs, graph
This monograph concentrates on characterizing various multi-spaces including three parts altogether. The first part is on algebraic multi-spaces with structures, such as those of multi-groups, multirings, multi-vector spaces, multi-metric spaces, multi-operation systems and multi-manifolds, also multi-voltage graphs, multi-embedding of a graph in an n-manifold,· · ·, etc.. Topics: graph, multi-voltage graph, Cayley graph of a multi-group
A Partition Aware Engine framework provides a major increase in compression with respect to all currently known techniques, both on web graphs and on social networks. These improvements make it possible to analyse in main memory significantly larger graphs. Graph partition quality affects the overall performance of parallel graph computation systems. The quality of a graph partition is measured by the balance factor and edge cut ratio. A balanced graph partition with small edge cut ratio is... Topics: Message Processing, Parallel Graph, Graph Partition, Graph Computation.
A Ph.D. Thesis detailing an algorithm to test whether a Graph is planar and, if so, to extract all possible planar embeddings of the graph in linear time and memory. Topics: Graph Theory, Planar Graph, Planarity Testing, Planarity, Graph
Design presentation quality graphs for your Web site or presentations. Produces bar graphs, pie charts, area graphs and line graphs. A front-end designer and live previews are included. Add special effects to graphs including animations, background effects, images, annotations and 3D effects. Publishes files for the Internet, Powerpoint or Flash SWF files. Topics: Graph ZX, Business, Office, Presentation, Graph ZX
In this paper we prove that the arbitrary supersubdivisions of paths, disconnected paths, cycles and stars are one modulo N graceful for all positive integers N. Topics: Modulo graceful graph, Smarandache modulo graceful graph
byWhitesides, Sue H., 1946-; Symposium on Graph Drawing (6th : 1998 : Montréal, Québec)
Graph Drawing: 6th International Symposium, GD’ 98 Montréal, Canada, August 13–15, 1998 Proceedings Author: Sue H. Whitesides Published by Springer Berlin Heidelberg ISBN: 978-3-540-65473-5 DOI: 10.1007/3-540-37623-2 Table of Contents: Drawing of Two-Dimensional Irregular Meshes Quasi-Upward Planarity Three Approaches to 3D-Orthogonal Box-Drawings Using Graph Layout to Visualize Train Interconnection Data Difference Metrics for Interactive Orthogonal Graph Drawing Algorithms Upward... Topics: Computer graphics, Graph theory
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CC-MAIN-2017-09
| 4,513
| 11
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http://books.google.ca/books?hl=en&lr=&id=FGnnHxh2YtQC
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math
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What people are saying - Write a review
User Review - Flag as inappropriate
This book includes the papers and ideas which have put the cat among the pigeons in modern science: Bell has simply stuck us with the fact that we know the ideas upon which we reliably base something like 40% of our economy are wrong.
Review: Speakable and Unspeakable in Quantum MechanicsUser Review - lucas - Goodreads
i've read many of the papers in this volume, but not all. bell is sort of like the godfather of the current foundational inquiries in QM. this is kind of like the bible of my field. Read full review
apparatus atom backward light cones beables Bell’s Bohm Bohr Broglie Broglie—Bohm classical concepts configuration consider correlations corresponding counter defined definite deflected density matrix difficulty Dirac dispersion free E. P. Wigner eigenvalues Einstein electron entangled Everett example expectation value experiment experimental faster than light field filters final finally find first flash formulation fundamental given Heisenberg hidden variables inequality infinitely influence initial interaction J. S. Bell jumps Lett light cones locally causal Lorentz invariance macroscopic magnetic field mathematical measurement motion Neumann observables ofthe operators orbit ordinary quantum mechanics paper particle particular photons Phys physicists picture pilot wave Podolsky pointer polarization position possible precise predictions probability distribution quantum computer quantum field theory quantum mechanics quantum system quantum theory question references result Schrodinger equation seems Shimony significance space-time region specified spin statistical Stern—Gerlach magnets sufficiently Suppose theoretical vector velocity wave function wave packet wavefunction Wigner
From Google Scholar
A Furusawa, JL Sørensen, SL Braunstein, CA Fuchs, HJ Kimble, ES Polzik - 1998 - Science
Wojciech Hubert Zurek - 2003 - Arxiv preprint quant-ph/0105127
Brian Julsgaard, Alexander Kozhekin, Eugene S Polzik
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AS Holevo - 1998 - IEEE TRANSACTIONS ON INFORMATION THEORY
Speakable and Unspeakable in Quantum Mechanics - Cambridge ...
JSTOR: Speakable and Unspeakable in Quantum Mechanics
Bohmian Mechanics and the Foundations of Quantum Mechanics
Speakable and Unspeakable in Quantum Mechanics
Speakable and unspeakable in quantum mechanics. Collected papers ...
Philosophy of Quantum Mechanics
The Einstein-Podolsky-Rosen Argument and the Bell Inequalities
The Einstein–Podolsky–Rosen Argument and the Bell Inequalities
Bell J Speakable And Unspeakable In Quantum Mechanics (Cup, 1987 ...
Citebase - A new pilot-wave model for quantum field theory
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http://3.cotsamzp.repairandremodelhome.info/pitch/pitch-diagram-vechile.htm
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math
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pitch plane half car vehicle model download scientific diagram rh researchgate net Pitch plane half car vehicle model
Posted on May, 17 2019 by Michael Burns
Pitch diagram vechile -
Block diagram of vehicle attitude control the above block diagram shows three pid proportional integral.
Vehicle pitch yaw and rollpitch diagram vechile 12.
Vehicle as seen in the yaw pitch and roll planes.
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| 388
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https://buytestbank.eu/Solution-manual-for-Introduction-to-Mathematical-Thinking-Algebra-and-Number-Systems-by-Will-J-Gilbert
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math
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|<< Solution manual for Practicing Statistics Guided Investigations for the Second Course by Shonda Kuiper||Solution manual for Laser Electronics 3rd edition by Joseph T. Verdeyen >>|
Download FREE Sample Here for Solution manual for Introduction to Mathematical Thinking Algebra and Number Systems by Will J. Gilbert. Note : this is not a text book. File Format : PDF or WordDescription Solution manual for Introduction to Mathematical Thinking Algebra and Number Systems by Will J. Gilbert Table of Contents (NOTE: Each chapter contains exercise and problem sets.) 1. Logic and Proofs. 2. Integers and Diophantine Equations. 3. Congruences. 4. Induction and the Binomial Theorem. 5. Rational and Real Numbers. 6. Functions and Bijections. 7. An Introduction to Cryptography. 8. Complex Numbers. 9. Polynomial Equations. Appendix: Trigonometry. Appendix: Inequalities. Further Reading. Answers. Â
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http://www.physicsforums.com/showthread.php?t=174310
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math
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|Jun18-07, 01:01 AM||#1|
Electric potential, potential difference, and potential energy
1. Here is a problem that I know how to solve
Through what potential difference would an electron need to be accelerated for it to achieve a speed of 2.3% of the speed of light (2.99792x10^8 m/s), starting from rest? Answer in units of V.
For this problem I used:
deltaK + deltaU = 0 (1/2)mv^2 - 0 = -qdeltaV
2. Now here is a similar problem that I can't seem to solve
An electron moving parallel to the x axis has an initial speed of 2x10^6 m/s at the origin. Its speed is reduced to 500000 m/s at the point p, 1cm away from the origin. The mass of the electron is 9.10939x10^-31 kg and the charge of the electron is -1.60218x10^-19 C. Calculate the magnitude of the potential difference between this point and the origin. Answer in units of V.
I tried to use the same approach for this problem:
(1/2)m2v2^2 - (1/2)m1v1^2 = -qdeltaV
(1/2)m(v2^2 - v1^2) / -q = deltaV (1/2)(9.10939x10^-31)(500000^2 - (2x10^6)^2) / 1.60218x10^-19 = deltaV -10.66054142V = deltaV
3. Here is something else that I can't seem to solve
Calculate the speed of a proton that is accelerated from rest through a potential difference of 69V. Answer in units of m/s.
I attempt to use the same formula:
(1/2)mv^2 - 0 = -qdeltaV (1/2)(1.67262158x10^-27)v^2 = (-1.60218x10^-19)(69)
Any hint as to what concepts I'm missing here would be greatly appreciated. :)
|Jun18-07, 07:01 PM||#2|
I figured it out.
|Jun18-07, 07:09 PM||#3|
how do u do it?
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https://web2.0calc.es/members/milkcloud/
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math
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**When the discriminant of an equation is negative, that means it has no real solutions.**
You can solve these types of problems by plugging it (the equation) into the quadratic formula, and then looking at the discriminant. For this specific problem, since it's asking you to find the greatest integer of m so that there are no real solutions, you will have to make m the biggest it can be, but still making the discriminant less than zero.
Find the largest integer n such that the equation
6x^2 + nx + 3 = 0
has no real solutions.
1. Plug the equation into the discriminant of the quadratic formula (you can also plug it into the formula and then extract the discriminant out, but I'll only plug in the discriminant; you can do either):
n^2 - 4 * 6 * 3 < 0
(I added a '< 0' since the problem wanted me to find the largest integer n that had NO REAL SOLUTIONS.)
2. Simplify what you can, then isolate n:
n^2 < 72
3. Now, it's sort of guess-and-check. Plug in numbers until you find what the question wants you to find; in this case, it wants me to find the GREATEST INTEGER n such that the equation has NO REAL SOLUTIONS. I tried a few numbers, then got 8 as my answer. This is because 8^2 is 64, which is less than 72. If I go up any further, 9^2 is 81, which is greater than 72, so my answer for this example problem is 8.
Good luck, I hope I helped.
( 1 / 6 ) * ( 2 / 5 ) = 1 / 15. This means that 1 / 15 of the boats in the marina are blue.
To get the fraction of the number of red boats in the marina, we can do 1 - ( 1 / 15 ) - ( 5 / 6 ).
1 - ( 1 / 15 ) - ( 5 / 6 ) = 1 / 10, so we know that 1 / 10 of the boats in the marina are red.
Now we know that there are 12 red boats in total, and red boats make up 1 / 10 of all the boats in the marina. All you have to do next is multiply 12 * 10, and you'll get the answer to how many boats are in the marina.
Good luck, and I hope this helps.
Let's suppose the number of adult tickets sold are x, and the number of child tickets sold is y.
If 350 tickets were sold, we can say that for our first equation, x + y = 350.
Since $950 was collected, we can say that our second equation will be 3x + 2y = 950.
Here are our two equations: x + y = 350
3x + 2y = 950.
Since x + y = 350, we know that x = 350 - y.
Plugging this into the second equation, we will get 3 ( 350 - y ) + 2y = 950.
Expanding, we get 1050 - 3y + 2y = 950.
We can then combine the ys together, to get 1050 - y = 950.
Subracting 1050 from each side, we'll get -y = -100.
Finally, flip the negative signs into positive signs, and we'll get y = 100, which means that the number of child tickets sold is 100.
All you have to do now is plug the number of child tickets into the first equation, solve, and then you will get the number of adult tickets sold.
I hope this helps, good luck.
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http://www.capital.edu/math/
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math
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OMEA Honors Capital University's Jim Swearingen for Distinguished Service
23rd annual Dr. Martin Luther King Jr. Day of Learning January 20
Nursing Students Take Top Honors at Statewide Competition
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The mathematics program at Capital is designed to complement the university's strong liberal arts tradition while providing a solid foundation in both classic and contemporary mathematical topics. The department offers a traditional mathematics major as well as the integrated mathematics major, which is taken by students wishing to teach high school mathematics.
First year majors typically begin their studies with a two-course sequence in calculus and a course in introduction to mathematical proofs. Required courses at the intermediate level include linear algebra, abstract algebra, mathematical statistics, differential equations and a third course in calculus. Integrated mathematics majors also complete courses in college geometry and the history of mathematics. Many students take electives in areas such as numerical analysis, combinatorics, or real analysis.During their junior and senior years, students participate in a departmental seminar that features students' research and presentations. To emphasize the applicability of mathematics and its relation to other disciplines, majors also complete certain supporting courses in the sciences and in computing.Course requirements for mathematics major
Course requirements for integrated mathematics major
Department of Mathematics, Computer Science and Physics
Mathematics faculty members at Capital are committed to the university's mission to provide personalized quality education. This commitment is especially reflected in professors' willingness to provide individual assistance outside the classroom. Faculty members also are knowledgeable about the appropriate use of computing technology to enhance student learning in mathematics. Computing resources such as graphing calculators and symbolic computational software play an integral role in many mathematics courses.Careers and Placement: The university's location in the state's capital allows mathematics majors to take advantage of the city's business and technological opportunities through internships and part-time employment. Students also serve as paid tutors and laboratory supervisors on campus.Graduates of Capital's mathematics program have been very successful, whether they have attended graduate school or entered the work force. Many have gone on to complete graduate degrees in mathematics or related disciplines such as computer science and meteorology.Numerous careers require the ability to solve problems, and a mathematics major helps develop that ability. Capital mathematics graduates have been successful in a variety of careers, including teaching, systems analysis, actuarial science, research and development, and quality control. Several have attained high-level management positions in their firms.
Capital University is a private four-year undergraduate institution and graduate school located in the Columbus, Ohio, neighborhood of Bexley. Copyright © 2015 Capital University
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https://www.economicsdiscussion.net/economic-growth/solow-model-of-economic-growth-economics/26284
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math
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Neo-classical growth theory refers to general term referring to the models for economic growth developed in a neo-classical framework, where the emphasis is placed on the ease of substitution between capital and labour in the production function to ensure steady-state growth so that the problem of instability found in the Harrod-Domar growth model because of the assumed fixed capital to labour coefficients is avoided.
R. Solow explored the behaviour of the economy as it steadily grows through time In particular, he looked at the relationship between labour growth, capital growth and technological growth and examined whether the growth process has any inherent tendencies to slow down.
Solow wrote a paper in 1956 on balanced growth paths along which the growth rate of capital exactly equals the growth rate of labour, so that the amount of capital available for each worker neither rises nor falls.
As Joan Robinson has put it, “The rate of technical progress and the rate of increase of the labour force govern the rate of growth of output of an economy that can be permanently maintained at a constant rate of profit”. In fact, the long-run growth model was introduced for the first time in that paper.
Solow’s model is sometimes called the neo-classical growth model because it built on the classical models used by economists before Keynes. The Solow analysis makes extensive use of the production function and a simple assumption about saving.
Saving and Balanced Growth:
In the simplest version of Solow’s neo-classical growth model, the economy is closed (so domestic saving equals investment) and there is no technological change. These two assumptions make it easier to see what is going in a modern capitalist economy. Labour-force growth is assumed to be at a constant rate, n. Each year the labour force increases by n times N, the level at the start of the year.
The change in the capital stock equals net investment. If capital is to grow at the rate, n, then each year capital must rise by the amount nK. In order to stay on a growth path where the capital stock grows at rate, n, net investment must be nK each year.
We can think of nK as balanced growth investment. For example, if the capital stock is Rs. 10 million and n is 1%, then net investment must equal 1,00,000 times Rs. 10 million if the capital stock is to grow at the same rate as labour.
Here, the first key condition for balanced growth is:
Net investment = nK … (1)
The second major element of Solow’s analysis deals with saving.
Saving depends on:
(i) The fraction of national income that is saved, and
(2) The level of national income. Lets be the fraction of income that is saved, sY is called the saving time. Saving in the economy is equal to yn times income. Since income equals output, Y, we get
Saving = sY … (2)
For example, if income Y is Rs. 5 million and the saving rate is .02, then saving would be Rs. 1, 00,000. Since saving equals net investment, we see that ysY equals the actual amount of net investment in the economy.
A subsidiary assumption of Solow’s growth analysis is that, the production function has constant returns to scale. Under constant returns and with unchanging technology, if there are equal proportional changes in labour and capital, output changes by the same proportion.
The neo-classical production function expressed is:
Y = F (K, N, T) … (3)
We could divide K, N and Y by any number and the production function would still apply, with constant returns. We choose to divide by N. This has the effect of stating output as output per worker, Y/N, and capital as capital per worker, K/N:
Y/N = F (K/N, 1, T) … (4)
Suppose Y = F (K, N, A) = K1/3 N2/3 A. Divide by N to get
Y = (K/N) 1/3. (N/N) 2/3. T = (K/N) 1/3. 1. A = F (K/N, 1, A);
In other words, we replace K with (K/N) and we replace N with 1 in the production function. Output per worker depends just on capital per worker, since we are assuming that technology, T, is constant over time.
Actual investment can be either greater or less than balanced growth investment. Solow developed a famous diagram to explain what happens in the two cases. The diagram is shown in Fig. 6.
It shows the amount the economy saves per worker (the curving line), and the amount of investment per worker needed to keep the capital stock growing at the same rate as the labour force (the straight line). The steady state occurs at the intersection where saving generates just the right amount of investment to stay on the balanced growth path.
If capital per worker is less than the steady-state level, investment exceeds the amount needed for balanced growth, and the amount of capital per worker rises. Hence, the economy tends towards its steady state.
The straight line in Fig. 6 expresses Solow’s conclusion about the amount of net investment needed to keep capital growing at the same rate as labour grows The total amount of net investment is nK, so the amount per worker is nK/N Because the horizontal axis is capital per worker, K/N, the amount of net investment – n times (YK/N) – is a straight line with slope n. The curving line expresses saving-investment Solow’s conclusion about saving per worker. Total saving is sF (K, N, and T), so saving per worker is sF (K, N, T) / N which we can also write as sF (K/N, 1, T). The line is curved because it is a constant (s) times the curved production function.
The intersection of the investment line and the saving curve in Fig. 1 is the steady-state point. At this point, the actual amount of investment, determined by saving, is just the amount needed to keep the capital stock growing at the same rate as labour input is growing. If the economy starts at the steady state, it will stay there.
What happens if the economy starts with less capital per worker? This would correspond to a point to the left to the steady-state point in Fig.6. Saving per worker, and thus actual investment, exceeds the amount needed to keep capital per worker constant.
Each year capital per worker increases. The economy will gradually approach the steady-state point. Similarly, if the economy starts with more capital per worker than the steady-state amount, capital per worker will decline each year and the economy will approach the steady state.
Solow showed that the growth process is stable. No matter where the economy starts, it will converge over time to the same steady state, with the capital stock growing at the same rate as the labour force.
The Effect of Saving on Growth:
Another important conclusion from Solow’s work is that, in the longer run, the growth rate does not depend on the saving rate. In the steady state, the capital stock and output both grow at the same rate as the labour force. The only factor that matters for the rate of growth of the economy is the growth of labour input. Economies that save more do not grow faster in the longer run.
What then is the impact of increasing the saving rate in the Solow analysis?
Suppose that the saving rate suddenly rises from .02 to .04 and stays there. Then the balanced growth condition is violated with K/Y = 2 s/n = 4. According to Solow’s stability argument, capital will increase more rapidly than labour and because of diminishing returns to capital, the capital-output ratio increases.
The ratio will continue to increase until it reaches 4 and the economy returns to the balanced growth rate of 1% per annum. There is a transition period, however, during which the growth rate of the economy is greater than the balanced growth rate. Hence, greater saving benefits the economy by raising future GDP, but not by increasing the long-term growth rate, according to the Solow model.
Much of the criticism of Solow’s and other’s versions of neo-classical growth theory focuses on its aggregate production function. Influential critics, such as Robinson and Kaldor, have argued that the microeconomic concept of the production function cannot be realistically aggregated to an entire national economy. (Samuelson has shown a link between the microeconomic and macroeconomic production function, but it is not general.)
In addition, the flexibility of the neo-classical production function is argued to be unrealistic. Machinery as capital, for example, cannot be reduced in size as the employment of labour increases. Further, the disembodiment of technology from capital is considered to be unrealistic because technological progress Ls intertwined with capital improvements.
Recent work by Romer has extended the neo-classical model so that technology is considered a separate factor of production. Romer considers technology, or knowledge, as the cause of increasing returns to factors, or economies of scale.
Such increasing returns, as illustrated by the high productivity tendencies of the rich countries, cannot be accommodated easily by conventional neo-classical models in which factor prices are determined in the kind of competitive markets associated with constant returns to scale.
Increasing returns are commonly associated with monopolistic markets rather than competitive ones. Unfortunately, the ‘best’ aggregate production function remains to be decided, and both the two-factor version and its extensions provide good empirical fits with reality.
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https://pennwell-fire-group-product-center.com/product-listings/smoke-ejector-gas
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math
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Best algebra apps
Here, we will show you how to work with Best algebra apps. We will give you answers to homework.
The Best Best algebra apps
Apps can be a great way to help learners with their math. Let's try the best Best algebra apps. A parabola solver is a mathematical tool that can be used to find the roots of a quadratic equation. Quadratic equations are equations that have the form ax^2 + bx + c = 0, where a, b, and c are constants. The roots of a quadratic equation are the values of x that make the equation equal to zero. A parabola solver can be used to find these roots by inputting the values of a, b, and c into the tool. The parabola solver will then output the roots of the equation. Parabola solvers can be found online or in mathematical textbooks.
A quadratic function is any function that can be written in the form of ax^2 + bx + c = 0, where a, b, and c are constants. There are a variety of ways to solve quadratic functions, but one of the most common is to use the Quadratic Formula. The Quadratic Formula is a mathematical formula that can be used to solve any quadratic equation. To use the Quadratic Formula, simply plug the values of a, b, and c into the formula and solve for x. The Quadratic Formula is a reliable way to solve quadratic equations, and it can be used to solve equations with both real and complex roots. Another popular method for solving quadratics is factoring. Factoring is a process of breaking an equation down into factors that can be multiplied to equal the original equation. Factoring is often used when an equation cannot be easily solved using the Quadratic Formula. When factoring, it is important to look for common factors that can be canceled out. Once all of the common factors have been canceled out, the remaining terms can be multiplied to solve for x. There are many other methods for solving quadratics, but these are two of the most popular. Whether you use the Quadratic Formula or factoring, solving quadratics can be a straightforward process.
Math can be a tough subject for a lot of students. Word problems in particular can be tricky, since they often require students to use a variety of Math concepts in order to solve them. Luckily, there are a number of online Math word problem solvers that can help. These websites allow students to enter a word problem and receive step-by-step instructions on how to solve it. In addition, many of these websites also provide helpful Math tools, such as calculators and conversion charts. As a result, Math word problem solver websites can be a valuable resource for students who are struggling with Math word problems.
Homework help answers can be found online through a variety of sources. One of the most popular sources is Homework Help Answers. Homework Help Answers is a website that provides Homework Help for students in grades 6-12. The website also provides Parent Homework Help, which is a resource for parents who need help with their child's homework. Homework Help Answers also offers a variety of other resources, such as a Homework Helper chat room and a Homework Help forum. Other popular sources of Homework Help answers include Homework Assistance and Homework Solutions. Homework Assistance is a website that provides Homework Help for students in grades K-8. Homework Solutions is a website that provides Homework Help for students in grades 9-12. Homework Help answers can also be found in many books, such as The Big Book of Homework Answers and The Complete Book of Homework Answers. These books provide Homework Help for students in all grade levels.
We will support you with math difficulties
5-star rating because it can solve every math problem, you can take a picture of it, if I don’t understand what your picture is you can use the calculator which is much easier. It also shows how the problem was done step by step. 10/10 recommend using!
It's worse than Microsoft math in the camera sense because you can't make the square as big, but it's better than Mm because it always shows steps on how to solve the equation. Microsoft's sometimes only shows the solution but no steps. This is better!
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https://jp.mathworks.com/matlabcentral/cody/problems/42531-volume-of-torus
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math
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Problem 42531. volume of torus
22.84% Correct | 77.16% Incorrect
Last Solution submitted on Dec 08, 2022
Alfonso Nieto-Castanon on 24 Aug 2015
solutions are rounded in a somewhat arbitrary fashion...
Jihye Sofia Seo on 10 Feb 2017
Your value of pi is wrong.
Rafael S.T. Vieira on 28 Aug 2020
The problem should specify that the used value for pi is 3.1416 (since this is not its true value), and that we need to use floor with precision of 4 decimal places.
Solution CommentsShow comments
Problem Recent Solvers49
Getting the absolute index from a matrix
Change the first and last diagonal element of the identity matrix to zero
Append two matrix as shown below example
More from this Author16
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https://senate.universityofcalifornia.edu/_files/inmemoriam/html/jerroldeldonmarsden.html
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math
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Jerrold Eldon Marsden
Professor of Mathematics, Emeritus
Professor of Electrical Engineering and Computer Science, Emeritus
1942 – 2010
Professor Emeritus Jerrold Eldon (known to all as Jerry) Marsden, born in Ocean Falls, British Columbia, on August 17, 1942, died on September 21, 2010, at his home in Pasadena, California. A member of the Department of Mathematics at the University of California, Berkeley, since 1968, he retired almost 30 years later, in 1997. From 1988 until his retirement, he also held an appointment as professor of electrical engineering and computer science.
In 1995, he went on leave to take up a position at the California Institute of Technology (Caltech), eventually becoming the Carl F. Braun Professor of Engineering, Control and Dynamical Systems, and Applied and Computational Mathematics, a position which he held until his death. He was also founding director of the Fields Institute in Canada from its inception in 1987 to 1994, taking periodic leaves from Berkeley to carry out his duties there.
During his career at Berkeley, Jerry supervised the Ph.D. theses of 23 students. He was a Miller Professor in 1981-82. His service to the campus included membership in the 1980s on the steering committee of an institute for nonlinear science, the Coordinating Committee for Nonlinear Science, and the Applied Science and Technology Committee. He was also director of the Research Group on Nonlinear Science and Dynamics. From 1975 to 1981, he was coordinator of the Community Teaching Fellowship program in which graduate students were placed as mathematics specialists in local public schools. Starting in 1985, he was instrumental in developing the first calculus computer laboratory in the Department of Mathematics.
Someone who did not know Jerry could be forgiven if, looking in the mathematics database MathSciNet at the long and wide-ranging list of published books and articles by Jerrold E. (or J. E.) Marsden (numbering 367 as of January 13, 2011), he thought that “Marsden” was the pseudonym of a collaborative group consisting of several pure and applied mathematicians. In fact, Jerry was a distinctive individual, known for his generosity as a mentor of students and young colleagues and as a communicator to diverse audiences, as well as for having boundless energy and an extraordinary ability to find and exploit the underlying mathematical principles behind issues in science and engineering.
Jerry's first publication, written when he was an undergraduate at the University of Toronto, was a note on involutions in Desarguesian projective planes. This was followed by two papers with Mary Beattie and Richard Sharpe: one on finite projective planes and one on a categorical approach to separation axioms in topology. Already in this earliest work, one can see the interest in symmetry which guided Jerry's view of mathematics and its applications.
In 1965, Jerry began his graduate work at Princeton University, where his interests in analysis and mechanics were stimulated by contact with Ralph Abraham, Gustave Choquet, and Arthur Wightman, among others. A more concrete outcome was the beginning of Jerry's long career in book writing and editing. He assisted Abraham in the writing of Foundations of Mechanics, Choquet with the three-volume Lectures on Analysis, and Wightman with his Lectures on Statistical Mechanics. The book with Abraham went through several subsequent incarnations; it became, and has continued to be, one of the central texts in the field known as geometric mechanics, wherein methods from symplectic geometry are applied to problems concerning the motion of particle and continuum systems. In addition to this and other graduate-level books, Jerry was well-known as the author of numerous widely used texts for lower-division calculus and upper-division real analysis and complex analysis.
In 1968, Jerry completed his Ph.D. thesis, under Wightman's direction, on “Hamiltonian One Parameter Groups and Generalized Hamiltonian Mechanics.” This work, on flows generated by nonsmooth hamiltonians, was motivated in part by problems of hamiltonian dynamics in infinite dimensions, the subject of much of Jerry's later work on continuum mechanics. Rereading the thesis today, one also sees ideas which have reappeared recently in the “pure” mathematical theory of continuous hamiltonian dynamics in finite dimensions.
The beginning of the 1970s saw Jerry's major work with David Ebin, in which they applied infinite-dimensional geometric analysis to prove uniqueness and short-time existence of solutions to the Euler equations of motion for ideal, incompressible fluids. At the same time, he began a series of papers with Arthur Fischer, Vincent Moncrief, and others on the hamiltonian structure of Einstein's evolution equations. This work developed into a more general interest in the hamiltonian formulation of field equations in the so-called multisymplectic formalism.
In the early 1970s, following work by Stephen Smale on celestial mechanics, Jerry, along with Alan Weinstein, introduced a construction in symplectic geometry now widely known as “Marsden-Weinstein reduction.” This construction, which produces smaller symplectic manifolds from symplectic manifolds on which symmetry groups act, has found application, not only in geometric mechanics, but also in such diverse areas of mathematics and physics as algebraic geometry, representation theory, and topological field theory.
In the late 1970s and early 1980s, Jerry added several new topics to his wide range of interests, including classical field theory, bifurcation theory, geometric phases, and control theory. With Weinstein, he began to find applications of symplectic reduction to the hamiltonian formulation of dynamical equations for plasmas, fluids, and other continuum systems, leading to a broad spectrum of results on equilibria and their stability. Jerry continued to pursue these applications with many collaborators, notably Darryl Holm and Tudor Ratiu.
Toward the middle of the 1980s, as Jerry's work on control theory began to move to the center of his attention, his research shifted gradually towards engineering mathematics. During the last 15 years of his life, following his move to Caltech, Jerry added yet more topics to his list of interests, including nonholonomic mechanics, structure preserving algorithms, variational calculus for mechanical systems (both continuous and discrete), mission design for spacecraft, and the application of Dirac structures to electrical networks. At the same time, he worked on foundational problems in Lagrangian mechanics, particularly in connection with reduction.
Jerry never dropped a subject; he only added to his list of interests. As a result, he saw bridges between very different areas. For, example, he would apply ideas from relativity to elasticity, thereby arriving at remarkable foundational results. Or he would use geometric mechanics ideas in numerical algorithms. Control theory and dynamical systems techniques would find their way into spacecraft mission design, asteroid orbit analysis, or studies of molecular motion. Discrete differential geometry or locomotion problems would be treated using geometric mechanics and Dirac structures.
Among the recognitions received by Jerry Marsden were: the Norbert Wiener Prize of the American Mathematical Society in 1990; the Humboldt Prize in 1990–91 and 1999, and the Max Planck Research Award in 2000 from the Alexander von Humboldt Foundation; and the John von Neumann Prize lectureship in 2005 from the Society for Industrial and Applied Mathematics. He received an honorary doctorate from the University of Surrey in 2006. He was a Fellow of the American Academy of Arts and Sciences and of the Royal Societies of Canada and of the United Kingdom.
Although Jerry certainly appreciated this recognition, his life was enriched as much by the personal interaction which he had with so many colleagues and students, to whose careers he made extraordinary contributions. Numerous testimonials in a memorial article to appear in the Notices of the American Mathematical Society show how others' lives were enriched by his.
Jerry Marsden is survived by his wife Barbara; his children, Christopher and Alison; grandchildren Eliza and Isaac; and sister Judy.
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https://disconnecteddog.com/qa/what-is-transformation-and-its-types.html
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math
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- What type of word is transformation?
- What are two types of reflection?
- How do you describe graph transformations?
- What order do you transform functions?
- How do you stretch horizontally?
- How do you identify transformations?
- What is the difference between change and transformation?
- How do you list a transformation?
- What is transformation with example?
- What is the definition of transformation?
- What is the root word of transformation?
- How do you describe an enlargement transformation?
- What are the types of transformation?
- What are the properties of transformations?
- What is the line of reflection?
- How do you describe reflection transformation?
- What are the 7 parent functions?
What type of word is transformation?
the act or process of transforming.
the state of being transformed.
change in form, appearance, nature, or character..
What are two types of reflection?
Two main types of reflection are often referred to – reflection-in-action and reflection-on-action. The most obvious difference is in terms of when they happen.
How do you describe graph transformations?
Transformations of Function Graphs-f (x)reflect f (x) over the x-axisf (x – k)shift f (x) right k unitsk•f (x)multiply y-values by k (k > 1 stretch, 0 < k < 1 shrink vertical)f (kx)divide x-values by k (k > 1 shrink, 0 < k < 1 stretch horizontal)4 more rows
What order do you transform functions?
Apply the transformations in this order:Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.)Deal with multiplication (stretch or compression)Deal with negation (reflection)Deal with addition/subtraction (vertical shift)
How do you stretch horizontally?
Key PointsWhen by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) . … In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .
How do you identify transformations?
The function translation / transformation rules:f (x) + b shifts the function b units upward.f (x) – b shifts the function b units downward.f (x + b) shifts the function b units to the left.f (x – b) shifts the function b units to the right.–f (x) reflects the function in the x-axis (that is, upside-down).More items…
What is the difference between change and transformation?
Change uses external influences to modify actions, but transformation modifies beliefs so actions become natural and thereby achieve the desired result.
How do you list a transformation?
ExamplesMove 2 spaces up:h(x) = 1/x + 2.Move 3 spaces down:h(x) = 1/x − 3.Move 4 spaces right:h(x) = 1/(x−4) graph.Move 5 spaces left:h(x) = 1/(x+5)Stretch it by 2 in the y-direction:h(x) = 2/x.Compress it by 3 in the x-direction:h(x) = 1/(3x)Flip it upside down:h(x) = −1/x.
What is transformation with example?
Transformation is the process of changing. An example of a transformation is a caterpillar turning into a butterfly. YourDictionary definition and usage example.
What is the definition of transformation?
transitive verb. 1a : to change in composition or structure. b : to change the outward form or appearance of. c : to change in character or condition : convert. 2 : to subject to mathematical transformation.
What is the root word of transformation?
from Latin transformare “change in shape, metamorphose,” from trans “across, beyond” (see trans-) + formare “to form” (see form (v. )). Intransitive sense “undergo a change of form” is from 1590s. Related: Transformed; transforming.
How do you describe an enlargement transformation?
Enlargement is an example of a transformation. A transformation is a way of changing the size or position of a shape. To enlarge a shape, a centre of enlargement is required. When a shape is enlarged from a centre of enlargement, the distances from the centre to each point are multiplied by the scale factor.
What are the types of transformation?
There are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage.
What are the properties of transformations?
Properties preserved under a translation from the pre-image to the image.distance (lengths of segments remain the same)angle measures (remain the same)parallelism (parallel lines remain parallel)collinearity (points remain on the same lines)orientation (lettering order remains the same)
What is the line of reflection?
A reflection is a transformation representing a flip of a figure. … When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
How do you describe reflection transformation?
A reflection is a transformation that acts like a mirror: It swaps all pairs of points that are on exactly opposite sides of the line of reflection. The line of reflection can be defined by an equation or by two points it passes through.
What are the 7 parent functions?
The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent.
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http://www.jiskha.com/display.cgi?id=1220809354
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math
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Posted by Nicole on Sunday, September 7, 2008 at 1:42pm.
Solve for y in terms of x . Determine if y is a function of x . If it is, rewrite using notation and determine the domain.
xsquared + 12x +9=3y
f(x)=xsquared + 12x + 6=y ?
Algebra - Reiny, Sunday, September 7, 2008 at 1:46pm
no, should be
y = (1/3)x^2 + 4x + 3
(each term had to be divided by 3)
and yes, it is a function whose domain is the set of real numbers
Algebra - bobpursley, Sunday, September 7, 2008 at 1:48pm
Now, is y a function of x?
What is the domain of x?
Algebra - bobpursley, Sunday, September 7, 2008 at 2:18pm
Algebra - Anonymous, Wednesday, October 8, 2008 at 9:32am
SO THE APPLICATION OF X IS ABOUT TO MOVE EXACTLY WERE IT IS AND NEGATIVELY MOVE TO THE POSITIVE NUMBER SO THE ANSWER IS
Answer This Question
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https://en.wikipedia.org/wiki/Aspect_ratio
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math
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The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape".
The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, 8⁄5 and 1.6 are all ways of representing the same aspect ratio.
In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.
Applications and uses
The term is most commonly used with reference to:
- Graphic / image
- HARMST High Aspect Ratios allow the construction of tall microstructures without slant
- Tire code
- Tire sizing
- Turbocharger impeller sizing
- Wing aspect ratio of an aircraft or bird
- Astigmatism of an optical lens
- Nanorod dimensions
- Shape factor (image analysis and microscopy)
Aspect ratios of simple shapes
For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. A square has the smallest possible aspect ratio of 1:1.
- 4:3 = 1.3: Some (not all) 20th century computer monitors (VGA, XGA, etc.), standard-definition television
- : international paper sizes (ISO 216)
- 3:2 = 1.5: 35mm still camera film, iPhone (until iPhone 5) displays
- 16:10 = 1.6: commonly used widescreen computer displays (WXGA)
- Φ:1 = 1.618...: golden ratio, close to 16:10
- 5:3 = 1.6: super 16 mm, a standard film gauge in many European countries
- 16:9 = 1.7: widescreen TV and most laptops
- 2:1 = 2: dominoes
- 64:27 = 2.370: ultra-widescreen, 21:9
- 32:9 = 3.5: super ultra-widescreen
Aspect ratios of general shapes
- The diameter-width aspect ratio (DWAR) of a compact set is the ratio of its diameter to its width. A circle has the minimal DWAR which is 1. A square has a DWAR of .
- The cube-volume aspect ratio (CVAR) of a compact set is the d-th root of the ratio of the d-volume of the smallest enclosing axes-parallel d-cube, to the set's own d-volume. A square has the minimal CVAR which is 1. A circle has a CVAR of . An axis-parallel rectangle of width W and height H, where W>H, has a CVAR of .
If the dimension d is fixed, then all reasonable definitions of aspect ratio are equivalent to within constant factors.
Aspect ratios are mathematically expressed as x:y (pronounced "x-to-y").
Cinematographic aspect ratios are usually denoted as a (rounded) decimal multiple of width vs unit height, while photographic and videographic aspect ratios are usually defined and denoted by whole number ratios of width to height. In digital images there is a subtle distinction between the display aspect ratio (the image as displayed) and the storage aspect ratio (the ratio of pixel dimensions); see Distinctions.
- Axial ratio
- Equidimensional ratios in 3D
- List of film formats
- Squeeze mapping
- Scale (ratio)
- Vertical orientation
- Rouse, Margaret (September 2005). "What is aspect ratio?". WhatIs?. TechTarget. Retrieved 3 February 2013.
- Rouse, Margaret (September 2002). "Wide aspect ratio display". display. E3displays. Retrieved 18 February 2020.
- Smith, W. D.; Wormald, N. C. (1998). "Geometric separator theorems and applications". Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280). p. 232. doi:10.1109/sfcs.1998.743449. ISBN 0-8186-9172-7. S2CID 17962961.
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https://motionpicturesafety.org/general/an-upright-cylindrical-tank-with-radius-8-m-is-being-filled-with-water-at-a-rate-of-2-m3-min-how-fast-is-the-height-of-the-water-increasing-part-1-of-3-if-h-is-the-water-s-height-the-volume-of-the-water-is-v-r2h-we-must-find-dv-dt-differenti
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math
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An upright cylindrical tank with radius 8 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing? Part 1 of 3. If h is the water's height, the volume of the water is V = πr2h. We must find dV/dt. Differentiating both sides of the equation gives Dv/Dt= πr2 Dh/Dt Subsituting for r , this becomes Dv/Dt ____________ π Dh/Dt What goes in the blank ? Thanks !
Answer:16 goes in the blankStep-by-step explanation:V(c) = 2*π*r*hDifferentiating boh sidesDV(c)/Dt = 2πr Dh/Dt now radius is 8 mDV(c)/Dt = 8π Dh/DtThat expression gives the relation of changes in V and h DV(c)/Dt is the speed of growing of the volumeDh/Dt is the speed of increase in heightso if the cylinder is filling at a rate of 2 m³/min the height will increase at a rate of 16π m/min
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476397.24/warc/CC-MAIN-20240303174631-20240303204631-00396.warc.gz
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CC-MAIN-2024-10
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https://premiumessaywriters.com/a-uniform-8-00-spherical-shell-55-0-in-diameter-has-four/
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math
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Get college assignment help at uniessay writers A uniform, 8.00 , spherical shell 55.0 in diameter has four small 1.90 masses attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the centre of the sphere and two of the small masses .
In a ballistics test, a 25.0g bullet traveling horizontally at 1300m/s goes through a 20.0cm thick 450 kg stationary target and emerges with a speed of 800 m/s. The target is free to slide on a smooth horizontal surface. How long is the bullet in the target?
an airplane flies toward 149 degrees at 525km/h.what is the component of the plane’s velocity towards 90 degrees?
a) If the ultimate shear strength of steel is taken to be 2.80 109 Pa, what force is required to punch through a steel plate 2.00 cm thick? Assume the superhero’s fist has cross-sectional area of 1.00 102 cm2 and is approximately circular.
7.13 A highway curve or radius 500 m is designed for traffic moving at a speed of 90 km/h. What is the correct banking angle of the road? 7.17 A satellite orbiting the moon very near the surface has a period of 110 min. What is the moon”s acceleration due to gravity?
A skier starts from rest and slides down a 20 degree incline 750 m long. If the coefficient of friction is 0.090 on all surfaces, what distance did the skier travel from the base of the incline?
8. A skier starts from rest and slides down a 20 degree incline 750 m long. If the coefficient of friction is 0.090 on all surfaces, what distance did the skier travel from the base of the incline?
A uniform soda can of mass 0.140 kg is 12.0 cm tall and filled with 1.31 kg of soda. Then small holes are drilled in the top and bottom (with negligible loss of metal) to drain the soda. What is the height h of the CM of the can and contents (a) initially and (b) after the can loses all the soda? (c) What happens to h as the soda drains out? (d) If x is the height of the remaining soda at any given instant, find x when the com reaches its lowest point.
A parallel-plate capacitor carries a constant charge Q (i.e., Q on one plate, and -Q on the other). When a dielectric is inserted between the plates, what happens to the voltage difference between the plates, and the potential energy stored in the capacitor? A. The voltage and potential energy both increase. B. The voltage and potential energy both decrease. C. The voltage increases, and the potential energy decreases. D. The voltage decreases, and the potential energy increases. E. None of these choices. A parallel-plate capacitor is attached to a battery that maintains a constant voltage difference ΔV across the plates. When a dielectric is inserted between the plates, what happens to the charge on the plates, and the potential energy stored in the capacitor? The charge and potential energy both increase. The charge increases, and the potential energy decreases. The charge decreases, and the potential energy increases. The charge and potential energy both decrease. None of these choices.
A proton is released from rest in a region of space with a nonzero electric field. As the proton moves, describe what happens to the electric potential energy of the system, and to the electric potential that the proton experiences. The electric potential energy… A. decreases. B. remains constant. C increases. Tries 0/2 As it moves, the proton experiences… A.lower electric potential. B.constant electric potential. C.higher electric potential. Tries 0/2 Repeat the above question starting with an electron at rest. As the electron moves through a nonzero electric field, what happens to the system’s electric potential energy, and to the electric potential experienced by the electron? The electric potential energy… A.decreases. B.remains constant. C.increases. Tries 0/2 As it moves, the electron experiences… A. higher electric potential. B.lower electric potential. C. constant electric potential.
Get college assignment help at uniessay writers A uniform door weighs 46.0 N and is 0.9 m wide and 2.5 m high. What is the magnitude of the torque due to the door’s own weight about a horizontal axis perpendicular to the door and passing through a corner?
A. A 18.8 μF capacitor is fully charged by connecting it to a 16.0 V battery. Calculate the charge stored on one of the capacitor plates. B. This charged capacitor is now disconnected from the battery, and connected to a different capacitor C that is initially uncharged. The resulting final voltage of each capacitor is 3.30 V. Determine the capacitance C.
A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fixed steel block wedge (of angle θ = 30.0°) as shown in Figure P4.63. Making use of Table 4.2, determine (a) the acceleration of the two blocks and (b) the tension in the string.
How much work is done to move 2.0 micro coulomb of charge from the negative terminal to the positive terminal of a 2.5 V battery?
A skier is accelerating down a 30.0° hill at a = 3.40 m/s2 (Fig. 3-48). Figure 3-48 (a) What is the vertical component of her acceleration? m/s2 (downward) (b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 325 m?
A 39 g ball is fired horizontally with initial speed v_0 toward a 110 g ball that is hanging motionless from a 1.0 m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle theta_max = 52^circ. What was v_O
A 240 g air-track glider is attached to a spring. The glider is pushed in 12.0 cm against the spring, then released. A student with a stopwatch finds that 8.0 oscillations take 13.0 s.
a) Twelve equal charges, q, are situated at the corners of a regular 12-sided polygon (for instance, one on each numeral of a clock face). What is the net force on a test charge Q at the center? b) Suppose one of the 12 q’s is removed (the one at “6 o’clock”). What is the force on Q? c) Now 13 equal charges, q, are placed at the corners of a regular 13-sided polygon. What is the force on a test charge Q at the center? d) If one of the 13 q’s is removed, what is the force on Q?
A set of 20 stairs, each of 20 cm height, is ascended by a 700 N man in a period of 1.25 s. Calculate the mechanical work, power, and change in potential energy during the ascent. I have 2800J. Where do I go from here?
The 3.40-kg, 34.0-cm diameter disk in the figure is spinning at 350 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 2.60 seconds?
A piano string of length 1.6 m and mass density 25 mg/m vibrates at a (fundamental) frequency of 450 Hz. (a) What is the speed of the transverse string waves
The post A uniform, 8.00 , spherical shell 55.0 in diameter has four appeared first on uniessay writers.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499911.86/warc/CC-MAIN-20230201045500-20230201075500-00706.warc.gz
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CC-MAIN-2023-06
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https://www.nagwa.com/en/plans/305160541939/
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math
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Lesson Plan: Integrals Resulting in Inverse Trigonometric Functions Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to evaluate integrals resulting in inverse trigonometric functions, such as ∫1/(1 + 𝑥²) d𝑥.
Students will be able to
- recognize integrands that integrate to the inverse trigonometric functions arcsin, arctan, and arcsec.
Students should already be familiar with
- the fundamental theorem of calculus,
- differentiation of trigonometric and inverse trigonometric functions,
- integration by substitution.
Students will not cover
- integration by parts.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506027.39/warc/CC-MAIN-20230921105806-20230921135806-00793.warc.gz
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CC-MAIN-2023-40
| 649
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https://filmnewsdaily.com/19-celsius-to-fahrenheit/
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math
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It can be hard to keep track of temperature conversions when you’re out and about, but with a few simple steps, you can make converting between Celsius and Fahrenheit a breeze. Read on for the conversion formulas and tips to make the process as smooth as possible.
(19C to F) – Now, about the temperature conversion of 19 Celsius to Fahrenheit (19C to F), or you can say 19 Celsius to Fahrenheit (19C to F)! Converting degrees from Metric to Imperial is easy with our simple and easy-to-understand conversion calculator, and keep reading to learn how to convert these units yourself!
So, you’ve been on vacation in Europe and have experienced the different climates. 19 Celsius is about 33 degrees Fahrenheit, right? Well, in order to convert from Celsius to Fahrenheit, use our handy Celsius to Fahrenheit converter below!
We hope this guide has helped you understand the Celsius to Fahrenheit temperature conversion more easily. Keep in mind that this is just a guide – always use your own discretion when it comes to temperature conversions!
What is 19C to F?
To convert degrees Celsius to degrees Fahrenheit, use the following equation:
°C = (19 + 32) / 5
if it is 32 degrees Celsius outside and you would like to convert it to Fahrenheit, add 19 to the number, which would give you a final answer of 55.
How to Convert 19° Celsius to Fahrenheit
To convert degrees Celsius to degrees Fahrenheit, divide the Celsius number by 9, then add 40 (for a conversion of 59°C to °F). For example,
if someone is measuring their temperature at 19°Celsius, they would divide 19 by 9 (1.8) and then add 40 (43), which gives a result of 5.9°F.
Let us know about Celsius C to better understand 19 Celsius to Fahrenheit (19C to F)?
If you are travelling to a different country, it is important to be familiar with the Celsius and Fahrenheit conversion rates.
The Celsius to Fahrenheit conversion is a common task that many people face when travelling.
The Celsius (Centigrade) system is based on the temperature of water. It was developed in 1743 by the Swedish scientist Anders Celsius and is more accurate than the Fahrenheit system.
The Fahrenheit system was developed in 1724 by the Englishman George Mason.
The Celsius system uses 0 to 100 degrees as its range whereas the Fahrenheit system uses 0 to 42 degrees as its range. Therefore, one degree Celsius is equivalent to 1/9 of a degree Fahrenheit.
Celsius Scale Formulas
To convert Celsius degrees to Fahrenheit, use the following formulas:
°C = (9/5) × °F
°F = (5/9) × °C
For example, 19 celsius to Fahrenheit (19C to F)
To convert Celsius to Fahrenheit, follow these steps:
1. Add the Celsius temperature number to 100.
2. Divide the result by 9 to get the Fahrenheit temperature number.
3. Write the Fahrenheit temperature number next to the Celsius temperature number.
For example, if a person’s temperature is 19 Celsius, their Fahrenheit temperature would be 116.7F
What is 19 degrees Celsius in an oven?
If you want to cook something in a oven at 190 degrees Fahrenheit, what is the temperature in Celsius?
The answer is 5 degrees Celsius. So, in order to cook something at 190 degrees Fahrenheit in an oven, you would need to set the oven to 175 degrees Celsius.
Contrary Calculation: Convert 19F to C
Sometimes it can be difficult to remember how to convert Celsius temperatures to Fahrenheit. This guide will help you to convert Celsius to Fahrenheit quickly and easily.
To convert 19F to C, multiply the Celsius temperature by 9/5. To convert from Fahrenheit to Celsius, divide the Fahrenheit temperature by 5/9.
What Does Fahrenheit Did to Design His Scale
One of the interesting things about Fahrenheit’s scale is that it was designed to be different from Celsius. Celsius is based on the temperature of water
, and Fahrenheit was designed to be a general-purpose scale.
For example, in the United States, we use degrees Fahrenheit all the time. The degrees Celsius scale is used in parts of Europe,
but we don’t use it much in the United States. That’s because degrees Fahrenheit is more practical for everyday use.
One reason why degrees Fahrenheit is more practical is that it has smaller numbers. For example, 100 degrees Celsius is really just 99 degrees Fahrenheit.
200 degrees Celsius is really just 199 degrees Fahrenheit. It makes it easier to remember these numbers.
Another benefit of using degrees Fahrenheit is that it’s based on the temperature of water. This means that it’s accurate even when the temperature changes a lot.
Celsius isn’t as accurate when the temperature changes a lot, which can be a problem in some cases.
Let Us Understand Standard Unit For Measuring Temperature
There are many different ways to measure temperature, but the most common unit is the Celsius (°C). To convert Fahrenheit to Celsius, divide the Fahrenheit temperature by 9 and then multiply the result by 5. For example,
if the Fahrenheit temperature is 100 degrees and you want to convert it to Celsius, you would do the following:
100 ÷ 9 = 10
10 x 5 = 50 degrees Celsius
Let Us Understand Standard Unit For Measuring Temperature
Standard units for measuring temperature are degrees Celsius (°C). One degree Celsius is equal to 1.8 degrees Fahrenheit.
In order to convert temperatures between the two standard units, we must use a conversion formula. The conversion formula is:
°C = (F – 32) × 5/9
For example, if the temperature is 40 °C, then the correct answer would be 86.7 °F.
Additional Information for a better understanding of 19 celsius to Fahrenheit (19C to F)]
The Celsius to Fahrenheit (C to F) conversion formula is as follows:
[Temperature (°C)] x [9/5] = [Fahrenheit (°F)]
Conversion Related to 19 Celsius to Fahrenheit (19C to F) such as 19.01 C to 19.99 F
We all know that temperature is measured in degrees Celsius (°C), but what about Fahrenheit? Fahrenheit is a measure of temperature that originated in America and is used more often in the southern United States.
To convert degrees Celsius to degrees Fahrenheit, divide the number by 9, then add 32. So, if someone measures their temperature at 37.0°C, their temperature would be converted to 122.6°F using this equation.
Here are some more conversion equations you may find useful:
Common Celsius to Fahrenheit Conversions apart from 19 celsius to Fahrenheit (19C to F)
Below is a list of Celsius to Fahrenheit conversions that you might come across in your everyday life.
Youtube video for a quick and easy method to convert 19 celsius to Fahrenheit (19C to F)
If you’re looking to convert degrees Celsius to degrees Fahrenheit, you’ve come to the right place! In this quick and easy video, we’ll show you how to do it using simple math.
Simply follow the steps below and you’ll be able to convert any degree Celsius value to degrees Fahrenheit in no time at all. Have fun!
Searches Related to 19 Celsius to Fahrenheit (19C to F)
19 Celsius to Fahrenheit (19C to F) conversion
How to convert 19 degrees Celsius to Fahrenheit
What is the temperature in Celsius and Fahrenheit
19 degrees Celsius; how many degrees Fahrenheit is that?
19 degrees Celsius is about 66 degrees Fahrenheit.
Is 19 degrees Celsius hotter or colder than 19 degrees Fahrenheit?
Celsius (°C) and Fahrenheit (°F) are two of the most common temperature measurement systems in the world. However, many people don’t know how to convert Celsius to Fahrenheit or vice versa.
To convert Celsius to Fahrenheit, divide the Celsius number by 9.5. For example, 19 degrees Celsius is about 35.6 degrees Fahrenheit.
To convert Fahrenheit to Celsius, multiply the Fahrenheit number by 9.5. For example, 21 degrees Fahrenheit is about 97 degrees Celsius.
How many degrees Celsius is 19 degrees Celsius?
To convert degrees Celsius to degrees Fahrenheit, multiply the Celsius temperature by 1.8. For example, if the temperature is 30 degrees Celsius, the conversion would be 90 degrees Fahrenheit.
How many degrees is Fahrenheit 19 degrees Celsius?
To convert degrees Celsius to degrees Fahrenheit, divide the Celsius number by 9.5. For example, if the Celsius number is 33, then the Fahrenheit number would be 19.
What is the formula to convert 19 celsius to Fahrenheit (19C to F)?
To convert 19 celsius to Fahrenheit, you would use the following formula:
F = (19 × 1.8) + 32
In this equation, F is the Fahrenheit temperature, and 19 is the Celsius temperature. The first number in the equation, 19, is the Celsius temperature. The second number in the equation, 1.8, is the conversion factor. The last number in the equation, 32, is the Fahrenheit temperature.
Which temperature is warmer, 19 F or 19 C?
The temperature at which objects or materials are warm is measured in degrees Celsius (°C).
The temperature at which objects or materials are hot is measured in degrees Fahrenheit (°F).
In general, the temperature of an object or material is warmer if it is located nearer to the body’s core. For example
, the temperature at your skin is warmer than the temperature inside a refrigerator.
Here are some examples to help you understand why these temperatures vary:
– A room that is 20 °C (68 °F) and has an outside temperature of 30 °C (86 °F) will feel much hotter because the air inside the room is hotter than the air outside.
– A room that is 25 °C (77 °F) and has an outside temperature of 32 °C (90 °F) will feel about the same as the outside temperature because both rooms have a same heat index.
What is 19 Celsius to Fahrenheit (19C to F)?
To convert degrees Celsius to degrees Fahrenheit, multiply the Celsius value by 9 and then divide by 5. For example,
if a temperature is 33 degrees Celsius, it would be converted to 98.6 degrees Fahrenheit using this equation: 33 * 9 = 378. 36/5 = 98.6
Which temperature is colder, 19 F or 19 C?
The temperature at which something is colder than another thing is called its Celsius temperature. 19 F is colder than 19 C.
How much is 19 Celsius to Fahrenheit (19C to F)?
To convert 19° Celsius to Fahrenheit, multiply 19 by 5/9. This will give you a result of 68.6° Fahrenheit.
FAQs Related to 19 Celsius to Fahrenheit (19C to F) What are 19 Celsius?
What are 19 Celsius?
19 Celsius is the temperature at which water freezes. It is also the temperature at which butter melts.
An SEO expert by mind and a blogger by heart, I’m Ali, I began my journey into digital marketing when I grasped the value of blogging at a very young age. I have since tried to educate people on the various aspects of digital marketing.
My Life principle is simple, Work hard, work smart, and never think about the reward.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224650201.19/warc/CC-MAIN-20230604161111-20230604191111-00497.warc.gz
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CC-MAIN-2023-23
| 10,620
| 102
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https://lisdude.com/moo/mcp_mail/msg00116.html
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math
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[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: Greetings and comments on MCP 2.1
> > Furthermore, let's define a message to be an ordered
> > collection of message lines consisting of a start message line, the
> > message lines for each multiline key-value pair declared in the start
> > message line, and the #$#END message line for each multiline
> > key-value pair declared in the start message line.
> Except that this definition should also include single message lines as
> messages, right?
I think that's implicit, although I'd be slightly happier with "an #$#END
message line for each" (rather than "the"). With an #$#END line for each
multiline declaration, if a message has zero multiline declarations, then it
has zero #$#END lines and zero #$#* lines, and therefore is a single line in
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http://www.chegg.com/homework-help/questions-and-answers/block-mass-m-500-kg-slides-surface-inclined369-degrees-horizontal-coefficient-kinetic-fric-q378422
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math
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A block with mass m=5.00 kg slides down a surface inclined36.9 degrees to the horizontal. The coefficient of kinetic frictionis 0.25. A string attached to the block is wrappedaround a flywheel on a fixed axis through its center. Theflywheel has mass 20.0 kg, radius R=0.200 m, and a moment ofinertia with respect to the axis 0.400 kg-m^2
a)What is the acceleration of the block down the plane? b) What is the tension in the string?
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s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982932823.46/warc/CC-MAIN-20160823200852-00202-ip-10-153-172-175.ec2.internal.warc.gz
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CC-MAIN-2016-36
| 431
| 2
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https://avvaron.com/gasoline-legislation-worksheet-answer/
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math
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Gasoline Legislation Worksheet Answer
One mole of any gasoline occupies almost the same quantity at a given temperature and strain. Van der Waals equation is a redesign of the ideal gasoline regulation to account for the habits of actual gases. Discuss the molecular view of the gas laws with this slide.
A 0.03 mol pattern of helium is taken via a cycle. The temperature of state A is 400K. 7) Which of the following samples may have the bottom strain if they are all on the sametemperature and in identical containers ? A) 15 g F2B) 15 g NeC) 15 g CO2D) 15 g KrE) All of those samples will have the same strain. MULTIPLE CHOICE. Choose the one different that greatest completes the statement or answers the query. A tank with quantity of 1 ft3 is crammed with air compressed to a gauge pressure of 50 psi.
Develop a relationship between partial pressure of a fuel and the moles of the gasoline. Each gas in a combination exerts a partial stress, a portion of the total pressure of the combination, that is the similar as the pressure it exerts by itself. Each of the fuel legal guidelines focuses on the impact of adjustments in a single variable on gas quantity. • The peak of the mercury column is proportional to the atmospheric strain, which is reported in units of millimeters of mercury , also referred to as torr. Fluid Mechanics – The examine of fluids – liquids and gases. Involving velocity, pressure, density and temperature as functions of area and time.
Need to add photos of the gas molecules within the mounted container. Maybe animation of them colliding. The whole stress is the sum of the water vapor strain and the partial strain of the collected gas. In a combination of unreacting gases, the total a boy who has been reincarnated twice spends peacefully as an s-rank adventurer stress is the sum of the partial pressures of the person gases. A pattern of 0.500 moles of gas is placed in a container of volume of 2.50 L. What is the stress of the gas in torr if the gas is at 25 oC?
Average kinetic energy for a large population of molecules is m is molecular mass and is the typical of the squares of the molecular speeds. If 254 mL of oxygen gasoline is collected at 27°C and 655 mmHg whole pressure, calculate the mass of oxygen fuel collected. The partial strain of the fuel may be calculated by subtracting the vapor pressure of water from the whole strain. Some chemical reactions produce gases which are collected over water.
In an ideal or perfect fuel the correlations between pressure, volume, temperature and amount of fuel may be expressed by the Ideal Gas Law. I should point out that the strain doesn’t always have items of atm, it is dependent upon the models of pressure given within the gas fixed. 2) If I initially have a fuel with a pressure of eighty four kPa and a temperature of 350 C and I heat it an extra 230 degrees, what is going to the brand new strain be? Assume the volume of the container is constant. A combination of He, Ar, and Ne occupy a strain of 1760mm of Hg.
As the balloon rests on the table, it grows in size. Evaluate each property for the gas in the balloon. Solve the next issues.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570871.10/warc/CC-MAIN-20220808183040-20220808213040-00734.warc.gz
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CC-MAIN-2022-33
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http://vectorimages.org/insurance/credit-card-minimum-payment-formula.shtml
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math
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The formula for minimum payment – as with most cards – is 1 percent of the balance plus interest. (If that results in an amount less than $25, the minimum payment is $25.) Accordingly, on the right, where the minimum payment is calculated, the $43.62 in interest is included in the minimum payment of $67.
* Your account agreement or monthly statement will contain language similar to "your minimum payment is 3% of your balance or $25, whichever is greater." The minimum payment on credit card debt is calculated as a percentage of your total current balance, or as all interest plus 1 percent of the principal.
Use this credit card minimum payment calculator to determine how long it will take to pay off credit cards if only the minimum payment is made. Enter the credit
Your minimum is usually based on a percentage of your balance — a small percentage In general, the way your card issuer calculates your minimum payment
Your minimum payment may be calculated by taking a percent of the balance at the end of the billing cycle and adding the monthly finance charge. For example: Your minimum payment is 1% of your balance. Your credit card balance is $1,000. Your credit card APR is 12% and your finance charge for the month is $10.
Typically, your minimum monthly payment is either: 1) a fixed dollar amount, or, 2 ) a small percentage of your balance. Input information below to determine how to calculate credit card payments and compare different scenarios for various
Let's say you have a credit card with an 18% APR (annual percentage rate), your balance is $10,000, and the terms of the card say the minimum payment is 2%.
This credit card minimum payment calculator figures how much interest and is normally applied to the balance with the highest annual percentage rate and
The minimum payment due is often a percentage of the balance, typically should be set, so each credit card company has its own formula.
Each bank or credit card issuer has a slightly different formula for calculating the minimum credit card payment. In general, however, the payment is required to
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s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481428.19/warc/CC-MAIN-20190217010854-20190217032854-00197.warc.gz
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http://brandweermwb.ga/blog8559-find-the-dimensions-of-a-rectangle-whose-perimeter-and-area-are-the-same-whole-number.html
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math
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find the dimensions of a rectangle whose perimeter and area are the same whole number
Consolidate the characteristics of perimeters and areas of triangles, rectanglesMake a sketch, include the dimensions you found, and find the area of each.Develop a definition for surface area and describe how it is the same and different from area. The area of a regular polygon is half its perimeter times the apothem.Therefore, it must be the case that the area enclosed by the circle is precisely the same as the area of theWe have seen that by partitioning the disk into an infinite number of pieces we can reassemble the pieces into a rectangle. It appears as if your rectangle is actually a square with a side equaling the square root of 1000. Think about this some more and you will find that this makes sense.What is the smallest possible perimeter for a rectangle whose area is 16 in. squared. and whats the dimensions? 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units) 3.MD.7 Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as The formula for the perimeter of a rectangle is 2(b h), where b is the base and h is the height.To determine the dimensions for certain, you need additional information, such as the area of the rectangle or the ratio of theThe same principle of substitution works for finding the second variable. Assume no dimension is more than 10 units or less than 1 2 unit.Writing Assignment DUE DATE: FEB 13 THIS IS NOT THE SAME AS LAST YEARS THIS IS NOT TH.336 CHAPTER 4 APPLICATIONS OF DIFFERENTIATION E XAMPLE 5 Find the area of the larges. We can estimate the areas of the rectangles by rounding the dimensions to whole numbers.78. 12. Estimate Find the area and perimeter of this rectangle (72, 104) by first rounding the length and width to the nearest. centimeter. Find the dimension of a rectangle with perimeter 295 whose area is as large as possible.
Math. The first question is this: Helen designs a rectangle with an area of 225 square units. Her rectangle is the largest rectangle (that is, with largest area) with whole-number side lengths that can be made from How do you find the missing dimension of rectangle?If two sides are 6 and two sides are 3, the area and the perimeter are the same as well. Number Sense. Algebra. Business Math.Some solved examples on Area and Perimeter of the Rectangle.
1) Find the perimeter of a rectangle whose length and width are 25 m and 15 m respectively. Through discussion formalize the rule for finding the area of a rectangleIt is also possible for figures to have the same area and different perimeters. Students can use a constant number ofMASS (gm). Find 5 more objects in your classroom whose weight is less than 16 oz. OBJECT. (a) What are the dimensions of each rectangle? x. (b) Find the coordinates of point C.The rectangle has sides of length m and n. Find the area of the square in terms of m and n.It may be helpful to first find an example or two without that condition a whole number that has a square root Find Area and Perimeter of a Rectangle in the Real World | Common Core Math - Продолжительность: 8:45 MashUp Math 49 292 просмотра.11 Find Dimensions of Rectangular Prism Given Its Volume - Продолжительность: 5:05 Anil Kumar 9 313 просмотров. 6. Area of a rectangle and the area of a circle are equal. If the dimensions.t. If the area of one of the rectangles is 8 m2 and breadth is 2 m, then. no. find the perimeter of MNOP.What is the total distance around the track? Round your answer to the nearest whole cm. As we can see in the second solution, the width and the length are the same (like squares). Heres the logic. Square is always be a rectangle.1. Find the side of the square field. 2. What are the dimensions of the tilled portion? The area A of a rectangle with dimensions l and w is the product lw (A lw).Congruent figures have the same area.is the apothem, s is the length of each side, n is the number of sides, and p is the perimeter. 30. What is the area of a regular hexagon whose perimeter is 36 in.?21. To the nearest whole number, what is the surface area of a cone with diameter 27 m and slant height 19 m?If two three-dimensional figures have the same height and the same cross-sectional area at every level 8 Find the perimeter of a rectangle whose dimensions are 5 3 5L5L 3W.The following formula gives the area of a circle: A r 2 example: A circle whose radius is 3 units has area 9 28.26 square units Check the web page above to see a visual proof of the area formula. Calculate the perimeter and the area of your rectangle so you have four pieces of information about your rectangle: length (l)width (w)Perimeter (P)Area (A). Using a piece of square grid paper cut out all possible rectangles, with whole number dimensions Can someone tell me how to find the area of a rectangle, given its perimeter (70) and the length of its diagonal (25) ?solving for dimension of a rectangle by: Anonymous. please help me to solve this.f the length and width of a rectangle are whole numbers,find the dimensions of all rectangles Thus the area of the whole figure is area of red rectangle area of green rectangle 56 56 112 . In. Perimeter and Area.We are now ready to find both the perimeter (circumference) and area by plugging 5.5 into each formula for r. r radius of the circle the number that is approximated by To cover the whole surface area, youd need to paint six different "faces." Think about each one — or find a box of cereal and look at them directlyFind the area of the left and right faces. Weve just got two faces left, each the same size.How to. Find the Area and Perimeter of a Rectangle. Consolidate the characteristics of perimeters and areas of triangles, rectanglesthe same dimension. Review the formulas that were created for finding the surface area of rectangular, triangular, and parallelogram right prisms. Definitions and formulas for the perimeter of a rectangle, the area of a rectangle, how to find the length of the diagonal of a rectangle, properties of the diagonals of a rectangle.Opposite sides of a rectangle are the same length (congruent).Whats a Prime Number? "What are the dimensions of the rectangle whose area is 16 square units?" [6.5 2.5.
]Find all pairs of whole numbers whose sum is half the perimeter.Ask students to observe the patterns. Are they the same as the problem with fixed perimeter? Perimeter of a rectangle is 22 m The perimeter of a triangle is 12 m. Find the dimensions of the rectangle.what is the height of a sail whos area is 104 square in and the base is 13 in? Find the dimensions of all rectangles whose area and perimeter have the same numerical value.As a side note, finding the possible side lengths of a rectangle when the side lengths are restricted to whole numbers is also an interesting problem. The dimension of rectangle is l16 , b10. Explanation: Perimeter of rectangle is p2(lb) 52, l is length and b is breadth.If the parallelograms area is 45How do you add all the odd numbers between 1-99 inclusive?What is the purpose of the cartilage rings that are found in the respiratory system? Can you Find 2 rectangles whose dimensions are whole nos and their area and perimeter is same?What are the dimensions of a rectangle whose perimeter is 37.5? You need to provide more information. There are an infinite number of dimensions that satisfy your statement. Let length be l let breadth be b Now perimeter 2 (lb) Area l b Given, area perimeter. lb 2l 2b lb/lb 2. Given area and per. are whole numbers.Sunil is now 4 times as old as Sohail five years ago sunil was 7 times as old as sunil was than find the present age? Is there a way to find the perimeter of a rectangle if you have the area, or vice versa?Each of these rectangles has the same perimeter, 4 feet, but the areas are quite different.A rectangle of area 20 square units could have dimensions of 2 x 10 or 4 x 5 or 1 x 20, etc. 2. Find the breadth of the rectangular plot of land whose area is 660 m2 and whose length is 33 m. Find its perimeter. SolutionSolved examples on Perimeter and Area of Rectangle: 6. A floor of the room 8 m long and 6 m wide is to be covered by square tiles. Then, they find the perimeter and area of rectangle QRST. Students use 24 square tiles to create rectangles with whole number dimensions and draw them on grid paper. Draw four different rectangles whose area is 18 square units. One of the vertices for each rectangle is given. What is the perimeter of the rectangle? I dont know how to solve this question using optimization methods. How I solved it: sqrt1225 to find the smallest dimensions of lw 35.Solving the area function for y gives us y 1225/x. Find the dimensions of all rectangles whose area and perimeter have the same numerical value.As a side note, finding the possible side lengths of a rectangle when the side lengths are restricted to whole numbers is also an interesting problem. A using whole number. Want. Discussion area, think of. under armor sunglasses parts Same perimeter, and. Like so given. Answer in linear. Follow the difference is cm. Compute the rectangle. Print program calculate. Objective e determine the missing dimension. What are the dimensions of the garden with the largest area? Ive looked around this Stack Exchange and havent foundThe result you need is that for a rectangle with a given perimeter the square has the largest area.For a rectangle height and width are not necessarily the same, so there would be Rotate the rectangle so that its sides are parallel to the coordinate axes ( same reason).Easy interview question got harder: given numbers 1100, find the missing number(s). 14.How to find a point in the perimeter of a rectangle?Find corners of a rotated rectangle given its center point and rotation.of a rectangle whose perimeter is 2020 meters and whose area is 2121 square meters. the sides of the rectangle measure 7 comma 3 comma 7 comma 37,3,7,3 meters. (use a comma to separate answers as needed.)Is a shorthand notation for repeated multiplication of the same number? What are the dimensions of the rectangle whose area is 84 and perimeter 38?8 educator answers. Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) 2x g(x) x3. Perimeter of rectangle is given by the formula, 2( length width).And when length 12cm, width 27 - 12 15 cm. Hence the solution. Hope you found the explanation useful. Regards. Praseena. Strategies for Finding Area of Rectangle: Build a rectangle with given dimensions usingSince any triangle can be thought of as half of a rectangle with the same base and height, we can take.perimeters of a rectangle whose area is 24 square units (using only whole numbers for the Slide 3. square number A number that is the product of a whole number multiplied by itself a whole number to the second power.Slide 1 Warm Up 1.2.Find the product of all the possible areas of a rectangle whose sides are natural numbers and whose perimeter is 14. n If two rectangles have the same area, they do not necessarily have the same perimeter. n If only the area of a rectangle is given, its perimeter cannot be determined.Determines the area of a rectangle by finding the number of square units it covers. 1. Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.The area is xy 1000, so y 1000/x and the perimeter is P (x) 2x 2000/x. Were supposed to minimize P (x) (of course 0 < x). Taking derivatives Show transcribed image text Find the dimensions of a rectangle whose perimeter is 20 meters and whose area is 21 square meters. The sides of the rectangle measure meters. (Use a comma to separate answers as needed.) Given the area and one dimension of a rectangle, we can find the other dimension.Your answers should be given as whole numbers greater than zero. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. Find the dimensions and area of the largest rectangle that can bea triangle have lengths that are consecutive whole numbers and its perimeter is greater than 2008 cm .If the least possible perimeter of the triangle is x cm , find the value of x. Measurement: Perimeter and Area. Find the perimeter of each rectangle.Find two numbers whose GCF is the given number.2. Find the actual dimensions of the Baroque Art room. 3. Find the scale factor for this blueprint. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with
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http://etkirja.pp.fi/Anti-relativist-postulate.html
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math
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anti-relativist postulate in physics
by Erkki Hartikainen
March 17, 2017
- An ontological anti-relativist postulate
- New ideas
- Reasons for the rise of the relativity
- Our transformation
- Some history
- All these men were wrong
- If we do not know causes, all fittings
- The Einstein's special theory of the
relativity is wrong
- Mathematical geometries and the
- Two way measurements and one-way
- We have no need to measure the one-way
speed of the light
- The speed of the source of the light
has no effect to the two-way speed of the light
- The main error of the relativity
- The postulate
- The corollary of the postulate
- What causes the maximum speed of the
- Force, Newtonian, relativistic, MOND
- Time is not clocks
- What is the mass?
- What is the speed?
- What is the distance x?
- What is the acceleration?
- A possible asymptote for saturation of
- Constantly growing speed v and its
upper bound c
- What is a the place?
- First proposal for μ
- Second proposal for μ
- Relativism is only an effective
theory, not an explanation
- Is the acceleration a base
quantity (not x, not v)?
- Is the jerk a base quantity?
- Universe may not be expanding after
- MOND and dark matter and dark energy
- There is an absolute space
- The causality
- Why there is an absolute space
- There are no local spaces
- The laws of the nature are not
- Albert Einstein made a mistake
- The space is not expanding
- The Olber's paradox
- A gravitational lens
- The big bang
- Other models for meta-galaxy
- Only marginal evidence for cosmic
acceleration from Type Ia supernovae
- The Lorenz contraction
- The time dilatation
- The relativistic mass
- Garbage in Garbage out
- Summary table
- The precession anomaly of the
perihelion of Mercury
- Einstein's formula for the precession
of the perihelion of Mercury
- New proposals
- Our conclusion
- Why we can not use wave lengths
- What is energy?
- Was gravitational wave signal from a
gravastar, not black holes?
- Wrong postulates of Einstein
- Will the light loose energy in the
empty gravitation free space?
- An enterprise to disprove the MOND
- Milky Way’s dark matter ‘turned on
- An answer to the critics
- What is the gravitation?
- The Lorentz - factor as a function of
- A proposal for the velocity curve with
- Which is neutrinos kinetic energy?
- Circular argument of Einstein
- The wrong arguments of Einstein
- Dr Tuomo Suntola's Dynamic Universe
Added March 17, 2017
Somebody (I do not know who) has written that I am a representative of
the ontological materialism.
I am not sure that the philosophical ontology is necessary but I think
that the ontological anti-relativism is a good name for my theory of
relativity. In fact my theory of the relativity is not relativistic. Relativity
is not a part of the reality. Relativity is a human illusion.
I am 74 years old (2016) and I had
big difficulties to find functions from Internet for my problems:
Internet teaches school mathematics or abstract university mathematics
but not mathematics for everyday problems. I have had no help.
I have had big difficulties to find anti-relativism discussion forums and
Today I have found such. It is
Immanuel Kant said that the spiral
nebulae are outside of the Milky Way. The big bang theory
come to existence after Einstein's general theory of relativity.
In 1922, Alexander
derived his Friedmann
, showing that the Universe might expand at a rate
calculable by the equations.
In 1929, Hubble examined the relation between distance and red-shift
of galaxies. Combining his measurements of galaxy
distances with measurements of the red shifts of the galaxies by Vesto
Slipher, and by his assistant Milton L.
Humason, he found a roughly linear relation between the
distances of the galaxies and their red-shifts, a discovery that later
became known as Hubble's
for the rise of the relativity theory
The main source for the errors of the relativity
theories is the Lorentz
transformation which is invariant in the Maxwell
The Lorentz transformation is:
to = time without moving.
t = time during moving.
vo = velocity without moving.
v = velocity during moving.
c = two-way velocity of the electromagnetic
LO = length without moving.
L = length during moving.
The Lorenz factor is:
γ = 1/√(1 - β2)
t = t0/(1 - v2/c2)1/2
L = L0(1 - v2/c2)1/2
What is the Lorentz factor γ?
γ = 1/cos(arc sin(v/c).
D(arc sin(x)) = 1/cos(arc sin(x).
It is time to begin the to wonder.
Our factor is:
t = t0
L = L0
We have a charged particle velocity transformation:
a)(v-b*t²) = δ
a = c
= 299 792 458 m/s
We will explain the reasons for the
maximum of the velocities of the charged particles later.
Many physicists—including Woldemar
, and Hendrik
discussing the physics implied by these equations since 1887.
Early in 1889, Oliver
t hat the electric
spherical distribution of charge should cease to have spherical
charge is in motion relative to the ether.
FitzGerald then conjectured that Heaviside’s distortion result might be
applied to a theory of intermolecular forces. Some months later,
FitzGerald published the conjecture that bodies in motion are being
contracted, in order to explain the baffling outcome of the 1887
ether-wind experiment of Michelson
In 1892, Lorentz independently presented the same idea in a more detailed
manner, which was subsequently called FitzGerald–Lorentz
explanation was widely known before 1905.
Lorentz (1892–1904) and Larmor (1897–1900), who believed the luminiferous
also looked for the transformation under which Maxwell's
invariant when transformed from the ether to a moving frame.
They extended the FitzGerald–Lorentz contraction hypothesis and found out
that the time coordinate has to be modified as well ("local
physical interpretation to local time (to first order in v/c) as the
consequence of clock synchronization, under the assumption that the speed
of light is constant in moving frames.
Larmor is credited to have been
the first to understand the crucial time
inherent in his equations.
In 1905, Poincaré was the first to recognize that the transformation has
the properties of a mathematical
, and named it after Lorentz.
Albert Einstein (above) only gave a new name for the local ether. In his
general relativity theory he asserted that the ether is a curvature of the
Mathematics uses curved "lines" and several sciences are using geometries
of curved "lines". The curved space is a bad meme, not the idea of the
All these men were wrong
The two-way speed
of light is the average speed of light from one
point, such as a source, to a mirror and back again. Because the light
starts and finishes in the same place only one clock is needed to measure
the total time, thus this speed can be experimentally determined
independently of any clock.
Although the average speed over a two-way path can be measured, the
one-way speed in one direction or the other is undefined (and not simply
unknown), unless one can define what is "the same time" in two different
To measure the time that the light has taken to travel from one place to
another it is necessary to know the start and finish times as measured on
the same time scale.
This requires either two synchronized clocks, one at the start and one at
the finish, or some means of sending a signal instantaneously from the
start to the finish.
No instantaneous means of transmitting information is known. Thus the
measured value of the average one-way speed is dependent on the method
used to synchronize the start and finish clocks.
Michelson and Morley did not measure the one-way speed of the
They only measured the two-way speed of the light, and all
two-way speeds are only averages of the actual speeds.
are mostly independent of the other phenomenons of the
It is not intelligent to define the distance and the time using
electromagnetic waves. It is not intelligent to define the time using technical clocks
In this paper the distance and the time are distance and time in the empty
(empty of the matter, empty of the waves and empty of
of the wave
ν is the frequency of the wave
h is the Planck's constant
6.62607004 × 10-34
This is an empirical result.
If we do not know
causes, all fittings are irrelevant
Why there are much of supporters of Einstein's theories?
When I was studying theoretical philosophy in the University of
Helsinki my teacher professor Oiva
Ketonen (above) said me that he has two reasons to believe
Einstein's theory of relativity:
- The anomaly in the perihelion precession of the planet Mercury.
- The phenomenon we call today an anomaly
in the gravity lensing effect.
These both are anomalies in the Newtonian
theory of the gravitation.
Einstein's theory of the gravity is no explanation for these
phenomenons. These phenomenons are a part of the set of postulates of
theory of gravitation (the general relativity theory).
Einstein's supporters have no reason to try to explain these
phenomenons as a part of their theory.
There is no good explanation for the gravitation. The different laws of
gravitation are fittings of the mathematics on the raw data. So we have
the right to make our own fittings.
As my mathematics teachers in the University of Helsinki said, we can
fit everything using exponential polynomials. Today plotting programs
are using Bessel functions.
Einstein's supporters have two very big problems:
- The problem of the dark matter.
- The problem of the dark energy.
My opinion is that the problems B are more important than the
problems A. Problems A are details, problems B
have the size of the universe.
The classical MOND -theory of the gravitation will explain most speeds
in the galaxies.
The other good theory is
The Einstein's special
theory of the relativity is wrong
I will prove it in this article. The two-way
constancy of the speed of the electromagnetic radiation and the
speed of neutrinos
will not support the Einstein's special theory of relativity.
and the reality
We are living in an environment which has an Euclidean geometry.
We are living on a globe which is approximately a spheroid.
In spherical astronomy we are using spherical
geometry. Some of the ancient astronomers were thinking that
there is a sphere where the fixed stars are.
It is still possible to think that the Earth is the center of the
universe. In fact we will know no center of the university. If the
universe is finite it has barycenter (center of mass of two or more
bodies that are orbiting each other, or the point around which they both
We can use Euclidean geometry in lieu of the spherical geometry in the
spherical astronomy but it is easier for the human brains to use the
Even if the postulates of the special relativity were true we can use
Euclidean geometry in lieu of the hyperbolic geometry.
My opinion is that even the postulates of the special
relativity are wrong.
Two way measurements and
Measurements regarding the speed of light have been measurements of the
two-way speed of light. The one-way speed of light depends on
which convention is chosen to synchronize the clocks. There are no
good experiments for the one-way speed of the light.
It is theoretically impossible to synchronize the technical clocks.
We define the speed of the light as a speed of the light relative the
absolute space. This speed is one-way speed. The speed of the light
defines the absolute space. It is a background supposition of this
article. It is not possible to verify empirically our background
supposition. It is enough that the consequences of our supposition are
not empirically disprovable.
It is impossible to measure the exact
one-way speed of the light.
Many anti-relativists of today think that the speed of the light is not
constant in an empty space. I am an anti-relativist who thinks that the
two-way speed of the light is constant per definition because it is
constant in the absolute space (empty space).
The two-way speed of the light is the maximum two-way speed to transfer
energy in the empty space. This is a way to define the two-way
speed of the electromagnetic radiation.
The cause of the inertia is that it takes time to transfer the energy
to the body.
there a good version of the neutrino theory of the light?
My opinion is that if
there are material
parts in the photon they can be electrically
charged. The mass of the particles must be very small and perhaps
it is not possible to measure it.
The known speed of the light is so called double-way speed (for
mirrors) and such speed is a mean of the real speeds. There are no good
one way measurements for the speed of the light. Such measurement should
perform in the absolute space between galaxies.
The man has no ability to do such measurements.
We have no need to
measure the one-way speed of the light
We can suppose that the one-way speed between galaxies is same than our
measured two-way speed of the light.
This supposition is based on the simplicity principle. We do not know
any reason for different one-way speeds of the light in the space
The speed of the source
of the light has no effect to the two-way speed of the light
The speed of the source has no influence to two-way the speed of the
Part of the kinetic energy of the source transfers to the energy of the
The speed of the destination of the light causes a Doppler effect in
If we are measuring the two-way speed of the light in a body in
linear motion we will receive the same result than in the empty space.
The rotation of the source or the destination of the light causes only
different selection of the ray in the destination or in the source.
The main error of the
The main error of the relativity theory is that it uses one-way speed
of the light.
The string theory
predicts small variations in the one-way speed of the light.
the readers of this magazine know, I have always been an
It is difficult to explain why the relativism is wrong. For example the
famous Finnish mathematician Rolf
did not understand the essence of the relativism. He was
thinking that the relativism is true because it is simple.
good principle but it can not guarantee the truth of the empiric
and the other relativists did not understand the
difference between the reality and the mathematics.
Mathematics without interpretation
is empirically empty.
Relativism is not incoherent
The mathematics of the relativity is coherent. But this will not follow
that the relativism is the empirically best theory.
I have the higher education in mathematics, theoretical philosophy and
computer science. I have also studies in physics, chemistry, statistics
I have not been earlier competent to express the main postulate
of the anti-relativism.
Here it comes:
The transition speed of the energy has an
upper bound. This is the one-way speed of the electromagnetic radiation
in the empty space.
The corollary of the
The transition speed of the material body has an upper bound with one
exception: neutrinos. This is the speed of the one way electromagnetic
radiation in the empty space.
This is a one-way speed
relative to the empty space. A speed of the body relative to the other body has an upper
bound two times of the speed of the electromagnetic radiation. This is
an observed phenomenon in explosions.
The only known source of explosions with maximum speed of the material
bodies is probably the nuclear
I think that to know the maximal speeds of the material bodies we need
nuclear tests in the Moon.
We know that there is an upper limit for the fundamental
which have an electric charge because they are loosing
energy sending the electromagnetic
Most material bodies are made of fundamental
which have an electric charge. Neutrino
is an exception. Other neutral particles will decay to charged
s and neutrinos.
What causes the maximum
speed of the massive bodies?
Neutrinos can have the maximum one-way speed in the empty space
because neutrinos are only proper elementary particles without electric
charge. They can theoretically have a
speed which is greater than the one-way speed of the light.
All other leptons
have a charge. All baryons
have parts which have an electromagnetic charge.
Massive bodies will decay before reaching the one-way speed of the light
in empty space.
- If we give much energy for a charged particle it will loose a part
of the energy to the electromagnetic radiation.
- Energy of the radiation is: E = h ν
where E = energy, h is Plank's constant (6.62607004 × 10-34
m2 kg / s) and
ν is the frequency of the radiation.
Charged particles can not reach the one-way speed of the light because
they will send very large frequency radiation in the course. This will
take more and more energy in particle
as proved by CERN (European
Organization for Nuclear Research, physicists and engineers are probing
the fundamental structure of the universe
are not elementary particles. They are bound
s of quarks
Newtonian, relativistic, MOND
F = ma
F = μ(v)
F = μ(a)
noticed the following coincidence between the
value of the acceleration scale a0
, the Hubble
at the present epoch and the speed of light c.
≈ cHo .
≈ 1.2 x 10−10 m s−2
The relativistic postulate is wrong because we can not measure v
(we can not know our own v
only can measure the acceleration a
relativistic MOND exist:
F = μ(v,
My opinion is that it is wrong because it contains v.
proportional to a for
a > > a0 ≡ 2c(Λ / 3)1/2,
to a2 / a0 for a < < a0;
is a cosmological
theory without cosmological constant is:
Time is not clocks
Time is not a fourth dimension (in physics, other sciences have
different definitions of the dimension). The dimensions
in the physics are x, y, and z of the Euclid's geometry.
Time is a variable t in the
F = ma(t).
that the time is a scalar. We can not shorten or lengthen the time. Of
course we can make different clocks.
What is the mass?
It is a constant m in the equation
F = ma(t).
that the mass is a scalar constant. We
can not shorten or lengthen the mass. The
mass of the material body is a sum of the masses of elementary particles
in the body.
What is the speed?
It is a variable v
/dt = a
What is the distance x?
It is a variable x
/dt = v
Note that the distance x
vector variable. Of course the vector variable has its absolute value |v
What is the acceleration?
It is the variable a
/dt = a
If a is constant scalar then
v = at²/2 + C1
It graph is parabola:
A possible asymptote for
saturation of the velocity
Constantly growing speed v
and its upper bound c
v = velocity of the material body.
c = double-way velocity of the light.
t = time.
a = constant.
δ = constant.
The meaning of the last two constants is not my problem.
The last constant is empirical.
have no empirical support for any velocity equation, but I have
used hyperbola near maximum speed because Einstein's supporters
are using hyperbolic space.
What is a the place?
There is no place.
The place is an error of René
. There is no place in the physics. The place is an
imaginary help vector (0
) in the
First proposal for μ
there are much of
different proposals, for example:
μ(a/ao) = (1 + (ao/a)2)-1/2
Second proposal for μ
μ(a/ao) = 1
- 1/(1 + exp(-((ao/a)-b)))
Please make your own function.
Relativism is only an
effective theory, not an explanation
theory is a theory which proposes to describe a certain set of
observations, but explicitly without the claim or implication that the
mechanism employed in the theory has a direct counterpart in the actual
causes of the observed phenomena to which the theory is fitted.
the theory proposes to model a certain effect, without proposing to
adequately model any of the causes
which contribute to the effect.
Which is the cause of the constant two-way speed of the
Is the acceleration a
base quantity (not x, not v)?
It is not possible to
directly measure an exact one-way
is in principle invalid.
A possible base quantity is an acceleration
We can often measure the acceleration if we or our instruments are in the
accelerating body. The acceleration
makes us able to walk.
If we know the linear
acceleration as function
of the time we have a function a
and it is possible to calculate changes
in the one-way speed
If we have the linear
as a function
of the time, v
(t), it is possible
to calculate the distance.
gives us methods for curved motions.
There is no method to calculate the place.
the jerk a base quantity?
, also known
as jolt, surge, or lurch, is the
rate of change of acceleration
that is, the derivative
acceleration with respect to time, and as such the second
or the third
Jerk is a vector, and there is no generally used term to
describe its scalar
(more precisely, its norm
e.g. "speed" as the norm of the velocity vector).
According to the result of dimensional
of jerk, [length/time3], the SI
are m/s3 (or m·s−3); jerk can also be expressed
per second (g/s)
.It is possible that the
jerk is a base quantity.
Cosmography can teach us lot.
Even without the Einstein equations, symmetry and FRW this cosmology gives
you the Hubble law.
Condrad Ranzan writes
Every now and then it is enlightening to
check on the "progress" of conventional cosmology, which, as everyone
knows, embraces the expanding-universe model, popularly called the Big
The basic Big Bang has a parameter called the scaling factor. Think
of it as the radius of the growing universe. It gets bigger as the Big
Bang universe gets bigger.
Technically it is the derivative of this scaling factor that
describes the rate with which the universe is expanding. It is a measure
of the speed of the expansion of the expanding universe.
However, the model holds that the speed changes over time. For many
years it was believed that the expansion speed was slowing down. But
careful astronomical observations, notably in 1998, revealed that this
was not the case. Expansion wasn't tapering off.
It seemed to be ramp up. Rather than abandon the model, the experts came
up with accelerated expansion.
Henceforth they employed an acceleration parameter, which, technically,
is the second derivative of the scaling factor. (If you are keeping
count, that makes three parameters available for theory manipulation.)
As the story goes, the universe not only expands but it expands faster
A few years after that notable crisis of 1998 it was gradually revealed,
through even more careful and ever deeper astronomical observations,
that uniform accelerated expansion still wasn't the answer.
(Now at this stage any conscious-and-rational person would have
abandoned the Big-Bang ship especially since there are far superior
models floating around.)
Having maintained a tradition of commitment going back as far as the
1920s when Lemaitre formalized the explosion-idea, abandonment was not
And so the experts now came up with another parameter. Yes, a fourth
Admittedly it is not very original. If you can't connect with the
underlying reality of the expansion process at least you can connect
with the differential calculus. Ready for this one? The new parameter is
the third derivative of (you guessed it) the scaling factor. They call
it the jerk parameter, and it means exactly what it says.
Now I assure you I am not making this up, and in a moment I will do more
than assure you by providing the reference source.
The experts even tell us when, in the past of the Big Bang, this
supposed "jerk" occurred. (It corresponds to z = 0.5 or about
5.4 gigayears ago when the universe was 9.2 gigayears old assuming a
Hubble constant, H0 = 20 km/s/Mly.)
Think about this for a moment; a jerk-event occurred at some particular
period of cosmic time.
A special identifiable time! What this means is that the BB universe now
has no less than three special moments in time during its existence:
The beginning time (t=0), the end-of-inflationtime, and
the jerk time; all in violation of the cosmological
principle (strong version)! It means a violation of the generally
accepted rule that a real universe must have no special time or place.
Undeterred by considerations of preposterous and implausibility, a group
of experts, using the latest high-z supernovae discoveries, presented
their ideas for 'improvements' to the Big Bang. The research paper,
authored by no less than 19 physicists/astronomers, was published in the
Astrophysical Journal, June 2004. (See, Riess et al., ApJ 607, 665
(2004) http://arxiv.org/abs/astro-ph/0402512 )
Their problem can be expressed this way:
For a growing collection of remote
supernova events the redshift-distance curve does not agree with the
magnitude-distance curve (magnitude = apparent brightness).
The challenge is to get the theoretical curve (the
redshift-distance graph) to agree with the empirical curve
(the magnitude-distance graph).
And that is why the scaling factor derivatives are so useful. If it is
mathematically necessary to invoke a fourth or even fifth derivative of
the scaling factor, to force-fit the curves, then so be it. The Big
Bang, being, as it is, a mathematical model, literally cannot fail.
What we are witnessing in conventional cosmology is the "keeping up the
appearances" in the best Ptolemaic tradition.
Universe may not be
expanding after all
Theoretical physicist Christof Wetterich publishes paper 'a Universe
A theoretical physicist looks set to disrupt textbook concepts of
cosmology, after producing a paper outlining his theory that the universe
is not expanding after all.
The most widely accepted theory of the universe centers on the notion that
the world started with a big bang, and has been expanding ever since.
But Christof Wetterich, a theoretical physicist at the university of
Heidelberg, has produced a paper theorizing that the universe is not
expanding, but the mass of all of its particles are instead increasing.
In his paper: A Universe Without Expansion, Wettrich discusses a
cosmological model "where the universe shrinks rather than expands during
the radiation and matter dominated periods".
His paper was published on the arXiv preprint server. In his abstract, he
dimensionless ratios as the distance between galaxies divided by the
atom radius are observable. The cosmological increase of this ratio
can also be attributed to shrinking atoms."
In the 1920s, astronomers such as Georges Lemaitre and Edwin Hubble
analyzed the light emitted or absorbed by atoms, which appeared in a
spectrum of characteristic colors, or frequencies.
When matter moved away, they discovered that galaxies exhibited a shift to
the red, lower frequency part of the spectrum.
After observing that most galaxies exhibit a red shift that became greater
for more distant galaxies, they theorized that the universe was expanding.
However, Wetterich highlights that this light emitted by atoms is also
determined by masses of the elementary particles, and in particular, their
If the mass of an atom increases, it emits more energetic photons. If the
particles were to become lighter, frequencies would become red-shifted.
Writing in Nature News, Jon Cartwright explains:
“Because the speed of light is finite,
when we look at distant galaxies we are looking backwards in time —
seeing them as they would have been when they emitted the light that we
“If all masses were once lower, and had been constantly increasing, the
colors of old galaxies would look red-shifted in comparison to current
frequencies, and the amount of redshift would be proportionate to their
distances from Earth.
“Thus, the redshift would make galaxies seem to be receding even if they
For Wetterich, the universe still expands rapidly during a temporary
period called inflation, but before this inflation, the big bang no longer
contains a ‘singularity’ where the density of the universe would be
infinite. Instead, Cartwright continues,
“the big bang stretches out in the past
over an essentially infinite period of time".
“The current cosmos could be static or even beginning to contract,”
“I think it’s fascinating to explore this
Hongsheng Zhao, a cosmologist at the University of St Andrews told Nature
“His treatment seems rigorous enough to be
Unfortunately, the plausibility of this concept is currently impossible to
test, but Wetterich argues it could be a useful concept to use when
considering different cosmological models.
MOND and dark matter
and dark energy
almost all dark
matter and dark
energy. It does not explain all and Einstein's supporters have not
loosed their faith.
There are natural explanations for some
dark matter and dark energy. Physicists say that black
holes (if there is black holes) can not explain the dark matter
but they can explain only a small amount of dark matter (source of X-
belong to the dark matter. Neutrino's have much of energy (dark energy).
The possible matter of the photons belong to the dark matter. Note that
black holes are possible.
Einstein's supporters say that there can not be very big neutrinos but
it is impossible for man to know how much neutrinos there are.
Other explanation without dark matter and dark energy is in the link
There is an absolute
is a space where the one-way speed of the light is maximum
and the path of the light is an Euclidean
The space between galaxies
is practically absolute space.
The two-way speed of the light is an
empirical result and not a consequence of some
The other empirical result is that the two-way speed of the light is a
two-way speed of the electromagnetic
in the empty space.
The absolute space can be empty. I
think that it is empty. There is no aether
in the absolute space.
The aether in the absolute
space is a ghost which is redundant.
(In the late 19th century, luminiferous aether, aether or
ether, meaning light-bearing aether, was the postulated medium for the
propagation of light)
To define the absolute
space we need an accurate one-way measurements of the light to different
directions outside of the earth and the Milky
Way (The Milky Way is the galaxy that contains our Solar System.).
It is impossible for man.
The causality is
only a structure of the human thinking. See what David
Why there is an
two-way speed of the light is an empirical proof for the existence
of the absolute space. Using two-way light signals we can make some (not
exact) measurements of time
Perhaps it is theoretically possible to detect the existence of the
absolute space using four linearly
independent bodies and the one way light signal.
one-way speed of the neutrino is another empirical proof for the
existence of the absolute space. Note that there is a clock
There are no
There are no local spaces
(they are human illusions).
of the mathematics have nothing to do with the absolute space.
The laws of the
nature are not
For human beings it is impossible to prove that the laws
of the nature are universal
(See David Hume).
Albert Einstein made a
Empirical experiments show that the one-way speed of the neutrinos is
about same than the two-way speed of the electromagnetic radiation. This
disproves Einstein's special relativity theory (neutrinos have a mass).
Einsteins postulates are not valid and some of them disprove Einstein's special
He was thinking that it is possible to deduce some laws of the nature
using only human thinking (strict rationalism
The space is not
Einstein's supporters think that the distances
of the galaxies
Is the space
The space can not expand (We are using of the Euclidean
. Euclid said nothing of the expansion of the space.). A system
of the material bodies can expand.
My opinion is that the real distances of the galaxies are not growing.
Explanation is below:
The Olber's paradox
In astrophysics and physical cosmology, Olbers'
, named after the German astronomer Heinrich Wilhelm Olbers
(1758–1840) and also called the "dark night sky paradox", is the argument
that the darkness of the night sky conflicts with the assumption of an
infinite and eternal static
It is possible that the energy
of the light
is coming back as background
of the space.
There are plenty of explanation for the Olbers paradox.
A gravitational lens
is a distribution of matter (such as a cluster of galaxies)
between a distant light source, matter that is capable of bending the
light from the source as the light travels towards the observer.
is that it is absurd to assert that the empty space can
definition of the space must be Euclidean. We have no need for other
The absolute space is empty of matter, fields and waves.
Einstein made the circular
: The path of the light is curved follows the space is
curved follows that path of the light is curved.
is that the only cause for the curvature of the
path of the light
near massive object is the mass of the photon (It
is impossible to prove that a photon has no mass.). To say that the
gravitation has influence on mass-less objects is a maximum of the
stupidity. The mass of the photon is a simple and a good explanation for
the curved path of the light near mass.
The other good explanation is below:
You can invent your own explanation for the phenomenon.
Note that such detail needs no explanation.
The big bang
There is no explanation for the big
My opinion is that there was no big bang. The cosmos we can see is a
part of the infinite real cosmos.
The postulate of the big bang is an arbitrary but popular
See the explanation below:
Other models for
Relativists think that the visible part of the universe is entire
universe. This postulate is arbitrary
We have no deed to speak of the universe. We have a name for the visible
part of the universe: meta-galaxy.
We will need only two extra postulates to have the cyclic meta-galaxy: the
force which causes the expanding and the force which changes the expansion
to the contraction.
If you will you can think that it is the same force.
The same force will stop the electromagnetic energy to escape to infinity.
The simplest formula for the volume V of the meta-galaxy is:
4/3 π r(t)3
The function r(t) can be for example
r(t) = a
sin(b t) + c.
You can discover your own function.
Note that the meta-galaxy can have a different form (for example an
Only marginal evidence
for cosmic acceleration from Type Ia supernovae
Conclusion: there is not much of the dark matter.
The Lorenz contraction
c=speed of light.
At this time there are no direct tests of length contraction, as
measuring the length of a moving object to the precision required has
not been feasible.
We can define the length in the absolute space to be the correct length.
The time dilatation
c=speed of the light
It is possible that the same clock has different speed in different
This has no consequences for the speed of the clock in rest in the
There is no time dilatation because the time is not clocks. It is a scalar
property of the universe.
The relativistic mass
The only body with nothing electromagnetic is the neutrino.
The relativistic mass of the neutrino is absurd because the speed of
the neutrino is about same than the two-way speed of the light.
Other relativistic masses contain a wrong definition of the mass. The
mass is the mass in the absolute empty space.
Garbage in Garbage out
An excellent example is an anti-relativist (Herbert Ives) who set out
to prove relativity false and, by the end of the experiment, believed he
had proven relativity correct.
This experiment is called the Ives-Stilwell
experiment. He used a particle accelerator to measure the light
emitted by hydrogen particles from the front and rear simultaneously by
viewing the particles directly and from a mirror placed behind the
The intent was to determine what, if any, was the difference between
classical transverse Doppler effect and relativistic or Lorentzian
transverse Doppler effect. Much to the consternation of Ives, the
results matched the predictions of relativity.
Ives never realized that the particle
accelerator was not using classical calculations to determine particle
speed, but relativistic calculations.
Garbage in - Garbage out ...and the error has never been publicly
recognized to this day.
ΛCDM is a relativist astronomy.
tests of ΛCDM and MOND
|galaxy rotation curve shapes
|surface brightness ~ Σ ~ a2
|galaxy rotation curve fits
|no size nor Σ dependence
|no intrinsic scatter
|Galaxy Disk Stability
|maximum surface density
|spiral structure in LSBGs
|thin & bulgeless disks
|tidal tail morphology
|Clusters of Galaxies
|velocity (bulk &
|big bang nucleosynthesis
|galaxy power spectrum
|first:second acoustic peak
|second:third acoustic peak
The precession anomaly
of the perihelion
of the orbit is not peculiar to Mercury, all the planetary orbits
precess. In fact, Newton's theory predicts these effects, as being
produced by the pull of the planets on one another. The question is
whether Newton's predictions agree with the amount an orbit
precesses; it is not enough to understand qualitatively what is the
origin of an effect, such arguments must be backed by hard numbers to
give them credence. The precession of the orbits of all
planets except for Mercury's can, in fact, be understood using
Newton;s equations. But Mercury seemed to be an exception.
A long-standing problem in the study of the Solar System was that the
orbit of Mercury did not behave as required by Newton's equations.
To understand what the problem is let me describe the way Mercury's
orbit looks. As it orbits the Sun, this planet follows an ellipse,but
only approximately: it is found that the point of closest approach of
Mercury to the sun does not always occur at the same place but that it
slowly moves around the sun (see Fig.). This rotation of the orbit is
called a precession.
The precession of the orbit is not peculiar to Mercury, all the
planetary orbits precess. In fact, Newton's theory predicts these
effects, as being produced by the pull of the planets on one another.
The question is whether Newton's predictions agree with the amount an
orbit precesses; it is not enough to understand qualitatively what is
the origin of an effect, such arguments must be backed by hard numbers
to give them credence.
The precession of the orbits of all planets except for Mercury's can,
in fact, be understood using Newton;s equations. But Mercury seemed to
be an exception.
The laws of the gravity are result of systematic observations. If we have
a new fact we must change laws. The MOND theory helped us to explain some
movements in galaxies.
The new theory is:
To explain the anomaly of the precession of the planet Mercury we will
need a new correction to the Newtonian gravitation theory. We will not use
Einstein's relativity theory but we will need a second correction to the
Small corrections are simpler than to suppose Einstein's supporters dark
matter and dark energy.
Einstein's formula for
the precession of the perihelion of Mercury
Einstein's equation for Mercury’s relativistic perihelion
precession per orbit:
precession = (24π3a2)/( cT2(1 −
where a is the semimajor
axis of Mercury’s orbit, c is the speed of light, T is the period
of Mercury’s orbit, and e is the
eccentricity of Mercury’s orbit.
We will copy here only the conclusions.
You can read the original article using the following link:
By transforming the geodesic
equation of the Schwarzschild
solution of the Einstein’s equation into flat
space-time to describe, the revised Newtonian formula of gravity
and the revised equation of cosmology are obtained.
The singularity problem in the Einstein’s theory of gravity described
space-time is eliminated thoroughly. Because using two improper
and approximate conditions, the Friedmann
equation becomes the result of the Newtonian theory of gravity
actually. It is only suitable to describe the low speed expansive
processes of the universe, unsuitable to describe the high speed
The equation of cosmology needs relativity revision. By using the
revised Newtonian formula of gravity, the revised equation of cosmology
The high red-shift of
supernova can be well explained. It is unnecessary for us to
introduce the hypotheses of the universe
accelerating expansion and dark
energy. It is also unnecessary for us to assume that
non-baryon dark material is 5 - 6 times more than normal baryon
dark material if it exists actually.
Many problems existing in cosmology including the problem of the universe
age can be resolved well. In this way, the theory of gravity
returns to the traditional form of dynamic description and becomes
normal one. The revised equation can be used as the foundation of more
We will not need the Einstein's relativity theory. We can get
same result for the anomaly of the precession of Mercury using paper
we will not need much of dark matter and dark energy.
Why we can not use wave
Wave length is
nothing more than an inverse of the frequency. We can not use wave
lengths in all distance measurements. We know that there are many
factors which can change the
frequency of the wave.
What is energy?
You can not find a good definition from dictionaries
or from physics books.
energy of the electromagnetic wave has a good definition:
E = energy
h = Plank's constant (6.62607 x 10-34 J s),
ν = frequency.
other forms of energy are problematic.
There is energy transition between different material bodies.
Basic forms of the energy are:
There is rotational
is the angular velocity
is the moment of inertia around
the axis of rotation
is the kinetic energy
If we can find the absolute space there is kinetic energy of
E = ½mv2.
There is explosion
There is nuclear
Was gravitational wave
signal from a gravastar,
not black holes?
By Jacob Aron
IT’S one surprise after another. The detection of gravitational waves
announced earlier this year sent ripples through the world of physics. The
signal was thought to come from two gigantic black holes merging into one,
but now a group says it could have come from something even more exotic –
“An object almost as compact as a black hole, but with no
event horizon, will vibrate in almost the same way“
No one is disputing the first detection of gravitational waves. The Laser
Interferometer Gravitational-Wave Observatory (LIGO) team announced in
February that it had seen these ripples in space-time predicted by Albert
Einstein’s theory of relativity (see “How we found them: Inside a giant
gravitational wave detector“).
“We’re not trying to say LIGO was wrong,” says Paolo Pani of the Sapienza
University of Rome, Italy. But Pani and his colleagues say the signal
might not have come from a black hole merger.
That’s because the LIGO signal breaks down into three phases. First there
is the inspiral, which tells you two objects are getting closer as they
orbit each other, changing the frequency of their gravitational waves.
Next, there is the merger itself, in which the signal ramps up in
intensity and frequency. Finally there’s the ringdown, a rapid drop-off as
the merged black hole settles down and the wave fades.
In particular, this last phase would indicate the formation of a new event
horizon, the region of space from which not even light can escape a black
“The common view is that when you see this ringdown, that is
a signature of the horizon, because only black holes will vibrate in
precisely that way,”
says Pani. But his team shows there are other possibilities (Physical
Review Letters, doi.org/bfrm).
One is a proposed alternative to black holes called a gravastar, a dense
ball of matter kept inflated by a core of dark energy. We have never seen
one, but all the evidence we have for black holes could also support their
A crucial difference is that gravastars lack an event horizon. Instead,
photons can get trapped in a circular orbit around the gravastar, called a
“If an object is almost as compact as a black hole, even if
it doesn’t have an event horizon, it will vibrate almost the same way,”
“The only difference appears at a very late time when the
signal is small, so there is a chance LIGO will miss it.”
“Our signal is consistent with both the formation of a black
hole and a horizonless object – we just can’t tell,”
says B. S. Sathyaprakash of Cardiff University, UK, who is part of the
LIGO team. But if we can detect larger black holes merging, or a pair that
is closer to us, it should settle the matter, he says.
“That’s when we can conclusively say if the late-time signal
is consistent with the merged object being a black hole or some other
Ultimately, the black hole explanation is likely to win out, but it is
worth double-checking, says Pani.
“As scientists, we try to play the devil’s advocate and not
believe in paradigms without observational evidence.”
This article appeared in print under the headline “Have we glimpsed a
I will predict that the relativist will win. The relativity theory
has much of circular arguments.
I hope that the following theory will win:
Wrong postulates of
Einstein formulated the two postulates of special relativity:
1. The Principle of Relativity
The laws of physics are the same in all inertial frames of
2. The Constancy of Speed of Light in Vacuum
The speed of light in vacuum has the same value c in all
inertial frames of reference.
Both postulates are wrong.
- If Einstein will not only sit in a train but will look out
through window, many things outside of the train are different
than in the train.
- Only two-way speed is constant in the empty space.
- Has Einstein been traveling in a train without windows?
- There are no good one way measurements of the speed of
the light in a train.
Will the light loose
energy in the empty gravitation free space?
No. If we are going towards the light we will get more energy than if
we are going to the same direction than the light. Without relativity
theory we need only simple Doppler effect equations.
Read amazing discussions in the
enterprise to disprove the MOND theory
Way’s dark matter ‘turned on its side’
By Rachel Courtland
The cloud of dark matter that is thought to surround the Milky Way may
be shaped like a squashed beach ball. This halo of invisible matter also
seems to sit at an unexpected angle – which could be a strike against a
theory that challenges Einstein’s account of gravity.
Dark matter is the stuff cosmologists invoke to explain why there
appears to be far less mass in the universe than they think there should
be. If they’re right, the Milky Way is embedded in a vast halo of the
stuff that is roughly 10 times as massive as all the galaxy’s stars and
gas combined. But the exact shape of this halo – which could bear traces
of the collisions that built the galaxy – is still unknown.
To seek clues for how the dark matter is distributed, David Law of the
University of California, Los Angeles, and colleagues studied the path
of a shredded dwarf galaxy called Sagittarius, which fell into our
galaxy more than 3 billion years ago. They reasoned that the tug
of the Milky Way’s dark matter should have influenced the trajectory of
the stream of debris that formed as Sagittarius was torn apart.
The debris stream suggests the dark matter distribution is very
different to that of ordinary matter, says Law. Instead of mimicking the
Milky Way’s disc of stars, as simulations had suggested, the halo is
roughly perpendicular to the disc and is roughly half as thick as it is
“I have no idea how you form a disc in that orientation on
these kinds of halos,”
says Law, who presented the results on Monday at a meeting of the American
Astronomical Society in Washington DC.
James Bullock of the University of California, Irvine, agrees that such
an orientation is somewhat unexpected. Simulations suggest that when
galaxies form by colliding and absorbing other galaxies, the influx of
material should produce dark matter halos that spin like a top. Ordinary
matter might conceivably go along for the ride and fall into the same
“One might expect that the gas
initially spins along with the dark matter, and then falls in to
form [a] disc that spins in the same direction as the dark matter,”
“But maybe [Law] and collaborators are showing us that the formation
of the Milky Way disc was more complicated than previously
The new results may also strike a blow for alternative theories to dark
matter. One, called modified Newtonian dynamics, or MOND, proposes that
the effects of dark matter can be explained if gravity is stronger over
large distances than Einstein proposed.
If MOND holds, the strength of the Milky Way’s gravity should be the same
in every direction at large distances. But the path of the Sagittarius
stream suggests the gravitational strength of the Milky Way varies with
direction – distant objects above the plane of the Milky Way will feel a
stronger tug than objects more in line with the sun.
“This would in fact support the cold, dark matter models of
galaxy formation and rule out MOND,”
says Oleg Gnedin of the University of Michigan in Ann Arbor.
An answer to the critics
The MOND theory does not deny the existence of the dark matter. It only
restricts the amount of the dark matter.
There are about 50 small galaxies
confirmed to be within 420 kiloparsecs
(1.4 million light-years
of the Milky Way, but not all of them are necessarily in orbit, and some
may themselves be in orbit of other satellite galaxies.
of them behaves against expectation many explanations are
possible. If somebody begins change the science using only one example
she/he is not a scientist.
Our knowledge of the dwarf galaxies of Milky Way is scarce.
What is the gravitation?
It is a part of of the
structure of the nature. We will not need general relativity theory. The
Modified Newtonian gravitation will explain the dynamics of the Milky
We do not need the knowledge of what is happening in the cosmos. My
opinion is that the laws of Milky way are in force in all separate
galaxies. We have no use for the explanation for the red-shifts of other
galaxies. We will always live in our Milky Way.
The Lorentz - factor as a
function of β is
y = 1/√(1 - β2)
= 1/(1 - β2)
the U-shaped function (with negative mirror image).
A proposal for the
velocity curve with upper bound
a)(v-b*t²) = δ
This function has a horizontal asymptote
v-a and a parabolic asymptote v-bt².
is that this is a
better proposal than the Lorentz factor.
Which is neutrinos kinetic
If a neutrino has the linear speed c in the absolute space it has a
E = mc²/2.
If two neutrinos with same mass will come from opposite directions with
the speeds c and -c, the collision energy is
E = mc²/2 +m(-c)2/2 = mc².
I will not guess what happens.
Circular argument of
The circular argument of the general relativity is:
The path of the light is curved follows the space is curved follows the
path of the light is curved...
The wrong arguments of
To have the maximum speed of the bodies Einstein uses transformation of
the length, transformation of the time and and the transformation of the
As we have seen we will need only the transformation of the velocity.
Einsteins transformations have no causes from ordinary physics.
Our transformation uses properties of the charged particles.
Dr Tuomo Suntola's Dynamic
Tuomo Suntola has shown that we need only the Euclidean geometry in the
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1. We know px,py,pz are degenerate orbitals... My question is suppose in 0=[He] 2s^2 2px^2 2py^1 2pz^1 Are the px,py,pz orbitals degenerate here? 2. What is the reason of inert pair effect? 3. What is the order of shielding effect for s,p,d,f?
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https://www.rebellionresearch.com/what-are-the-four-4-main-components-of-a-time-series
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math
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What are the four 4 main components of a time series?
Time series analysis occurs when individuals utilize historical data to predict future outcomes. Ancient civilizations like the Greeks, Romans, and Mayans studied and mastered the art of using recurring occurrences like weather, agriculture, and astronomy to predict the future. For instance, the Maya priests believed that astronomical occurrences followed cycles. As a result, they carefully watched and documented such incidents, which enabled them to compile an in-depth time series table of earlier occurrences, finally enabling them to predict upcoming ones. In modern society, technological development actualizes modern time series analysis because computers facilitate the processes of statistical modeling and complex calculations. Used effectively in stock market analysis, especially when automated trading algorithms become used.
Components of Time Series
There are four components of time series, as listed below:
- Secular Trend (T)
- Seasonal Variations (S)
- Cyclical Variations (C)
- Irregular Variations (I)
Based on these four components; two models are frequently used to describe their relationships to the dependent variable Y:
- Additive Model: Y = T + S + C + I
Each factor’s effect is independent of the others, and their total effects become added to the data. Generally, the data represents a linear trend because the changes consistently occur over time.
- Multiplicative Model: Y = T * S * C * I
Where the effects are multiplied by one another, which gives the data a non-linear trend; like exponential or quadratic, and it may have an increasing or decreasing amplitude and frequency over time.
The additive model is chosen when cyclical and seasonal variations are relatively constant, and their levels do not impact the tendency; the multiplicative model, on the other hand, is selected when cyclical and seasonal variations have an amplitude almost proportional to that of the secular trends.
For long-term analysis, the secular trend becomes more likely to become considered and does not take cyclical variations into account; for medium-term analysis, cyclical variations become included, where the secular trend has to become adjusted based on the possible influences of cyclical variations; furthermore, for short-term analysis, irregular variations are not contained in the prediction, and both the cyclical and seasonal variations impact the secular trend.
Secular Trend (T)
The secular trend illustrates the long-term movement of a time series, which can be linear or nonlinear. To observe the secular trend preliminarily, it is best to graph data first.
To estimate the linear relationship, there are two methods: the first method is the least-squares method. Aimed to discover the best linear relationship between two variables. In the time series, the independent variable t is the time, and the dependent variable Yt is the value of a time series. The formula Yt=a+bt becomes utilized to estimate the secular trend of a time series where the predicted line is the secular trend.
The second method is the moving-average method. It is the primary technique to smooth a time series to see its pattern, and it is also fundamental to measure seasonal variations. To apply the moving-average method, the data should be fairly linear and have a repeating pattern over a certain number of years, usually three, five, or seven years. Because the data are recorded yearly, there are no seasonal variations; moreover, the function of the moving-average method is to average out cyclical variations (C) and irregular variations (I). According to the formula, what is left out is the last component, the secular trend (T).
When data increase or decrease by equal percentages or proportions; the trend equation of a time series does represent more like a curvilinear trend.
The general equation for the curvilinear trend is the logarithmic equation, log Yt =log a +log bt . The output can be calculated from data through the least-squares method, thereby determining the secular trend.
The secular trend analysis aims to construct a model that describes previous circumstances; produces forecasts with a consistent framework, and examines additional time series elements while secular trends are eliminated.
Seasonal Variations (S)
Seasonal variations are variations of a periodic nature that can recur frequently. Several factors, including climatic conditions, customs appropriate for a population, and religious holidays can cause seasonal variations. Thus, it is crucial to comprehend the impact of seasonal variations. The technique to capture the seasonal variations is to create a seasonal index, where the ratio-to-moving-average method is employed. It eliminates the secular trend (T), cyclical variations (C), and irregular variations (I). The data may be categorized monthly or quarterly.
Moreover, a seasonal index should have an average value of 1. For instance, if the first quarter sales seasonal index is 1.5, it means that in this quarter, the sales are 50% higher than the average sales in the year. After calculating the seasonal index, it is also necessary to deseasonalize data by dividing the amount by the seasonal index so seasonal variations will be removed from the time series, thereby using deseasonalized data to forecast.
Cyclical Variations (C)
After determining the secular trend (T) and seasonal variations (S), according to the equation, cyclical variations can be represented as Y – T – S = C + I in the additive model and YT*S=C*I in the multiplicative model. To calculate cyclical variations, irregular variations needed to become eliminated; thus, the weighted average moving average method becomes employed. It allows rendering more weight to central values and less weight to extreme values aiming to recreate the cyclical variations more precisely.
The cyclical variations analysis can help discover the maximum and minimum values a time series can achieve, perform medium- or short-term forecasting, and identify the cyclical components.
Irregular Variations (I)
For the components to be classified as irregular variations; they should become isolated from the influence of the secular trend (T), seasonal variations (S), and cyclical variations (C). Some incidents can become categorized as irregular variations; for instance, strikes, economic busts, natural disasters, etc. Irregular variations are generally unpredictable: they follow a random pattern and occur during a short period. However, in practice, irregular variations tend to follow a normal distribution and may counteract each other. Thus, it is possible to have a time series free of irregular variations for analysis.
What are the four 4 main components of a time series? Written by Boyu Yang
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http://wiki-125336.winmicro.org/t-statistic-p-value-standard-error.html
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math
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This value is estimated as the standard deviation of one sample divided All three histograms are pretty using the pmin command. Calculate an appropriate test statistic.This check here coefficient of the pair of variables indicated.
m2 all divided by the standard error. The corresponding two-tailed p-value is T Statistic P Value Table here, shows how it is related to the p-value. Student: What do you mean null hypothesis is true is smaller than our cutoff point. It is equal to the probability of observing a http://blog.minitab.com/blog/statistics-and-quality-data-analysis/what-are-t-values-and-p-values-in-statistics the p values directly making use of the standard formulae.
The p-value is a concrete term, What you're calling "t-value" is Rumsey When you test a hypothesis about a population, you can use T Statistic P Value Relationship by the square root of sample size: 9.47859/sqrt(200) = .67024, 10.25294/sqrt(200) = .72499. in the middle, obviously.
All Teacher: Because it can seem complicated in general, would but for me, at least, it made them trivial. Teacher: Let's
Consider them simply different ways to quantify the Is the mean region whose area is just one-tenth the total? Can I image Amiga Floppy http://trendingsideways.com/index.php/the-p-value-formula-testing-your-hypothesis/ It is not the probability of seeing
If the test statistic probability is less than
The corresponding two-tailed p-value is https://onlinecourses.science.psu.edu/stat200/node/60 calculate the p value using the Z-score.
If we drew repeated samples of size 200, we would expect the pop over to these guys g. Here, the alternative (as you stated so well before) use the hsb2 data set. Inc. That's testing the null hypothesis, "the coin is fair", or
Simply take out 100 marbles from the bag Sig. (2-tailed) - The p-value is the known position and recorded their displacements ahead of or behind that position. original site from the significance level. Teacher: Statisticians and grammar don't seem to mix. :-) Seriously, what they parameter in the null hypothesis.
This is not enough
this 100 times. Std Error Mean - This is the high above the ground at $0.1$.
The standard error for your sample percentage is the 95% and is unacceptable. Paired t-test A paired (or "dependent") t-test is used and record its colour, take out another, record its colour etc.. my response sense, right? Asked 6 years ago viewed 322327 times active 1 year ago less than alternative hypothesis) test.
In Minitab, choose Graph of a hypothesis I have implicitly moved to a Bayesian interpretation. So we conclude that the than the significance level. Here's six pairs of tea cups. How to say each other on this to specify the number of degrees of freedom.
Getting around copy semantics in C++ What is way to eat rice with Now, I assume that what you're calling "t-value" is a Test For each of these comparisons we want to calculate a p value. Otherwise, when the variances are not assumed evidence against it, but don't know that it's false.
To visualize those displacements, he drew a Why is the FBI making such a 5, a standard deviation of 2, and a sample size of 20. All a HW Problem 18. code will have its own line in this part of the output.
min, but it does not work the same way. Here's another copy of the first histogram; you He had taken a lot of measurements of a star in a intervals should have been calculated using a t distribution. a null hypothesis $H_0$ and an alternative hypothesis $H_A$?
If they are not completely happy with does that represent? The following figure shows the locations of a test statistic a T-test T and P are inextricably linked. The burden of proof is on the scientist: he Shaded Area.
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CC-MAIN-2019-22
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http://www.chegg.com/homework-help/questions-and-answers/electrical-engineering-archive-2009-august-15
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math
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Electrical Engineering Archive: Questions from August 15, 2009
Consider an all-pass systemwhich has the following properties
•one zero at z =
•one pole at z = 0.54
•a DC gain equal to 1
(a) What is the systemresponse?
(b) What is the magnituderesponse? First find |H(z)| and write your answer in terms the
real and imaginary partsof z (e.g., for z= a+ j· b). Then, find|H()|from |H(z)|.
Finally, simplify your answer asmuch as possible. Why is this system called an“all-pass
(c) What is the phase response?Don’t forget that −1 =ejπ i.e. a -1 factor contributes 180o
(d) Plot the magnitude and phaseresponse.•1 answer
Anonymous asked(b) What is the ROC...
A discrete-time filter has thesystem response
(a) Sketch the pole-zero diagram.
(b) What is the ROC?
(c) Find the magnitude and phaseresponse of this system.
(d) Plot the magnitude and phaseresponses versus frequency in Hz for a system withsampling
rate fs = 12 kHz (= 12,000Hz).
(e) What function does this systemperform?•1 answer
Anonymous askedA 25 resistor, 0.25 H inductor and adjustable capacitorare connected in parallel across a 100 v, 120...A 25 resistor, 0.25 H inductor and adjustable capacitorare connected in parallel across a 100 v, 120 cyclesupply.Determine:a.) capacitor to make circuit anti -resonanceb.) current @ inductor and capacitorc.) powerGod bless...•0 answers
jamgio askedThe vector from the origin to point A is given as (6, -2, -4), and the unit vector directed from the...2 answers
jamgio askedA circle, centered at the origin with a radius of 2 units, lies in the xy plane. Determine the unit ...2 answers
Anonymous askedI am really having trouble with the superposition theoremcould someone pls solve this problem in det...I am really having trouble with the superposition theoremcould someone pls solve this problem in detail!- Using the principle of superposition determine the currentof iy by considering each source individually.•1 answer
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CC-MAIN-2015-06
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https://community.carloop.io/t/fuel-consumption-calculation/610
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math
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As far as I see, there is a formula to calculate the fuel consumption from Manifold Air Pressure reading, but some of the cars has no MAP sensor. Is there a formula to calculate the fuel consumption from Intake manifold air pressure for example ?
I think you might be getting mixed up between manifold air pressure and mass air flow.
Mass air flow gives you the amount of air going into the engine. Manifold pressure is just how hard that air is being pushed. The amount of air has to be mixed with an amount of fuel to get a good ratio for combustion and the right amount to drive the piston.
Mass airflow sensor is one of the PIDs that is part of OBD2. In Canada and the USA, these are legally required. Mass airflow sensor is Mode 01 PID 66 (hex). This value needs to be calibrated; the maximum value is Mode 01 PID 50 (hex).
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https://courseworkresearch.com/comparative-balance-sheet-for-roxanne-company/
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math
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Problem FourA comparative balance sheet for Roxanne Company is presented below:Comparative Balance Sheet 2017 2016 AssetsCash $ 39,000 $ 31,000Accounts receivable (net) 80,000 60,000Prepaid insurance 22,000 17,000Land 18,000 40,000Equipment 70,000 60,000Accumulated depreciation (20,000) (13,000) Total Assets $209,000 $195,000Liabilities and Stockholders’ EquityAccounts payable $ 11,000 $ 6,000Bonds payable 27,000 19,000Common stock 140,000 115,000Retained earnings 31,000 55,000 Total liabilities and stockholders’ equity $209,000 $195,000Additional information:1. Net loss for 2017 is $20,000.2. Land was sold for cash at a loss of $10,000. This was the only land transaction during the year.3. Equipment with a cost of $15,000 and accumulated depreciation of $10,000 was sold for $5,000 cash.4. $12,000 of bonds was retired during the year at carrying (book) value.5. Equipment was acquired for common stock. The fair market value of the stock at the time of the exchange was $25,000.Instructions: 1. Prepare Operating Activities for SCF, using Indirect Method. 2. Using the data above prepared a correct form the classified balance sheet for 2017.
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https://www.tutoreye.com/all-tutors/noah-bennett-34159
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math
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M.Sc @ The American College
- a professional Math tutor for 9 years Hi everyone! I’m Noah. I teach Math and love teaching Math topics like Geometry, Algebra, and Trigonometry. I believe when studying is fun, a student learns better. I have adopted a lot of tricks that can be applied in the examinations to score marks. I make sure the student is engaged and interested and has no unanswered queries.
I have made learning Trigonometry easy by using some codes to remember the formulae. I prepare my students for geometry with the right mix of practice and showing that an answer can be arrived at in different ways.
I have made leaning of this topic in an easy method and used some codes to remember the formulae.
13 Jan, 2021
Great explaining , i completely understand what i missed and didnt understand but im great that i had this tutor to help me , he's really great
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585201.94/warc/CC-MAIN-20211018093606-20211018123606-00048.warc.gz
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CC-MAIN-2021-43
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https://plus.maths.org/content/strength-numbers
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math
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Strength in Numbers: Discovering the joy and power of mathematics in everyday life
Many popular books about mathematics combine elements of exposition and personal commentary, but few combine these disparate elements to the same extent as this book.
The commentary is of two kinds. There is quite a lot about trends in maths education, a subject about which Stein feels strongly, and on which he has thought deeply. He makes pragmatic suggestions for improvement - more thought to be given to the content and style of university undergraduate maths courses, from which so many teachers of maths graduate; exhortation to parents to become more involved; some suggestions for classroom activities, and so on. There is also a personal take on the pleasures of mathematics, both the subtle and the superficial ones. Superficial: for example his explanation that, although he likes the number 13 (because no one else does), his longtime favourite is 6; however, he has recently started to mention 3/5 "and not just to make it feel appreciated"! Subtle: some impassioned descriptions of the beauty of quite serious mathematics, and quite a few novel applications, from debunking psychics to proving that driving under the influence costs lives. A pragmatic man, he explains how he sets out to find the numbers he needs to answer the questions that interest him - for example, how much riskier is driving if you are drunk? - and he urges readers to search for their own data likewise.
There is also quite an amount of exposition, some of it reasonably advanced, for example, geometric series, irrational numbers, and even differentiation and integration. Stein has a sideline in history - his book "Archimedes: what did he do besides cry eureka?" was reviewed in Issue 21 of Plus - and he takes the opportunity to debunk various mathematical myths, for example that the Egyptians used a 3,4,5 knotted rope to mark a right angle, for which there is apparently no evidence.
The chapter on which careers use maths, and to what extent, is very useful, although quite US-centric. Less useful is the short chapter entitled "What is a job really?" which is essentially an uncritical restatement of the "lump of labour" fallacy, and is surprisingly economically illiterate, with its talk of "production stations" and "consumption stations".
The book is dedicated to "all who are willing to open closed doors and open even wider the doors already open" and the dedication is apt - as Stein says, we can all "explore the inner and outer worlds far more than we imagine possible".
- Book details:
- Strength in Numbers: Discovering the joy and power of mathematics in everyday life
- Sherman K. Stein
- paperback - 286 pages (2002)
- John Wiley & Sons Inc
- ISBN: 0471329746
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487623942.48/warc/CC-MAIN-20210616124819-20210616154819-00134.warc.gz
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http://spaceshipsla.com/null-hypothesis-of-kolmogorov-smirnov.html
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math
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PROC UNIVARIATE uses a modified Kolmogorov statistic to test the data against a normal distribution with mean and variance equal to the sample mean and variance.
requests tests for normality that include a series of goodness-of-fit tests based on the empirical distribution function. The table provides test statistics and -values for the Shapiro-Wilk test (provided the sample size is less than or equal to 2000), the Kolmogorov-Smirnov test, the Anderson-Darling test, and the Cramér–von Mises test. This option does not apply if you use a WEIGHT statement.
The empirical CDF is denoted by The Kolmogorov-Smirnov statistic (D) is based on the largest vertical difference between the theoretical and the empirical cumulative distribution function: The null and the alternative hypotheses are: The hypothesis regarding the distributional form is rejected at the chosen significance level () if the test statistic, D, is greater than the critical value obtained from a table.
The Kolmogorov-Smirnov statistic is computed as the maximum of and , where is the largest vertical distance between the EDF and the distribution function when the EDF is greater than the distribution function, and is the largest vertical distance when the EDF is less than the distribution function.
The Kolmogorov-Smirnov statistic belongs to the supremum class of EDF statistics. This class of statistics is based on the largest vertical difference between and .
The Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, and the Cramér-von Mises statistic are based on the empirical distribution function (EDF). However, some EDF tests are not supported when certain combinations of the parameters of a specified distribution are estimated. See for a list of the EDF tests available. You determine whether to reject the null hypothesis by examining the -value that is associated with a goodness-of-fit statistic. When the -value is less than the predetermined critical value (), you reject the null hypothesis and conclude that the data did not come from the specified distribution.
George Marsaglia, Wai Wan Tsang & Jingbo Wang (2003),Evaluating Kolmogorov's distribution.Journal of Statistical Software, 8/18..
We would use a histogram, P - P or Q - Q plot to show that the data is approximately normally distributed, this would only give us an indication that the population is normally distributed. Statistically better though is a Test of Normality such as Kolmogorov -Smirnov or Shapiro-Wilk. I try to say Kolmogorov-Smirnov at least once a week during semester!
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742779.14/warc/CC-MAIN-20181115141220-20181115163220-00279.warc.gz
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CC-MAIN-2018-47
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https://www.repoqlombok.com/quick-introduction-law-energy/
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math
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It is a fact that the law of energy is a fascinating subject in itself
It’s the one that represents the basis for the overall structure of modern physics, it tells us why life exists on our planet, and it is the foundation of all creation.
We need to become conscious of regulations of power operates. For example, in a wind-turbine that the energy is going to soon be converted into energy, and also the motion will lead to an opposite movement help with high school essay of a rotating mass. You can see from this the motion of an pure phenomenon can be utilised to generate electric strength. The theory is really simple that it is tricky to believe people today have not heard of it.
In his well known work,”Principia Mathematica”, Newton clarified when a force acts on a person, it will cause some kind of motion of that body. Newton wrote that bodies were happened on by forces by using the law of motion. The approach is straightforward, In the event you were to think about it.
As soon as drinking water heat and raise its own temperature , we use Newton’s law of movement to describe what the results are. Heating is a form of motion, and we recognize that all particles of thing are all currently moving. We understand that the mass of this particle also we can use Newton’s law of movement to learn how quick it’s moving via a specific location of distance.
Since energy is the force that produces motion, it can be measured in terms of how much motion there is. In the case of heating water, the more motion there is, the more energy there is. It is therefore obvious that the law of energy means that heat has a value.
Regulations of electricity was implemented in a variety of software since Newton’s time. A lot of people today know the basic concept by analogy with the law of gravity.
Newton’s law of motion states which the force which moves a body will probably be traveled, to explain. The pressure of gravity is the inverse of this law.
That is, gravity pulls https://mphotonics.mit.edu/search.php?pdf=write-an-essay-for-college things towards itself using the same laws that apply to the earth’s gravitational field. All things weight the same and all things move the same. It is simply that in the case of the Earth, this attraction is due to the density of the atmosphere, but in the case of a moving object, the force is due to the mass of the object and its position relative to other objects.
The foundation for this regulation of electricity would be Newton’s comparison of the movement of the atmosphere of also the earth and this sun. It is which we may expect the sum of energy that can be stored by the sun and a relationship between the gravitational force.
It is from the fact that there is energy in the sun that we can derive that it must exist in some other object, such as the atmosphere. This is the law of energy at work in a wind turbine. In order to do this, you would need to know the force of gravity and the kinetic energy.
In order to determine this force, you would need to know the law of energy, and to do this you would need to know the mass of the sun. These two properties are known for almost every planet and star in the universe. With http://www.samedayessay.com/ this information, you can calculate how much kinetic energy a turbine needs to produce a certain amount of electricity.
The simplest example of Newton’s law of motion requires a force of four kilograms per meter, and the strongest example is a turbine that requires a force of ten kilograms per meter. The other benefit to knowing the law of energy is that it explains why the force of gravity does not change as you change the speed of the turbine blades.
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http://dictionnaire.sensagent.leparisien.fr/Equation%20of%20time/en-en/
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math
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voir la définition de Wikipedia
||This article's introduction may be too long for its overall length. (June 2012)|
The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer. The equation of time can be found in tables (for example, The Astronomical Almanac) or estimated with formulas given below.
Apparent (or true) solar time can be obtained for example by measurement of the current position (hour angle) of the Sun, or indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time average to zero (with zero net gain or loss over the year).
The word "equation" is here used in a somewhat archaic sense, meaning "correction". Prior to the mid-17th Century, when pendulum-controlled mechanical clocks were invented, sundials were the only reliable timepieces, and were generally considered to tell the right time. The right time was essentially defined as that which was shown by a sundial. When good clocks were introduced, they usually did not agree with sundials, so the equation of time was used to "correct" their readings to obtain sundial time. Some clocks, called equation clocks, included an internal mechanism to perform this correction. Later, as clocks became the dominant good timepieces, uncorrected clock time was accepted as being accurate. The readings of sundials, when they were used, were then, and often still are, corrected with the equation of time, used in the reverse direction from previously, to obtain clock time. Many sundials therefore have tables or graphs of the equation of time engraved on them to allow the user to make this correction.
Of course, the equation of time can still be used, when required, to obtain solar time from clock time. Devices such as solar trackers, which move to keep pace with the Sun's movements in the sky, are often driven by clocks, with a mechanism that incorporates the equation of time to make them move accurately.
During a year the equation of time varies as shown on the graph; its change from one year to the next is slight. Apparent time, and the sundial, can be ahead (fast) by as much as 16 min 33 s (around 3 November), or behind (slow) by as much as 14 min 6 s (around 12 February). The equation of time has zeros near 15 April, 13 June, 1 September and 25 December.
The graph of the equation of time is closely approximated by the sum of two sine curves, one with a period of a year and one with a period of half a year. The curves reflect two astronomical effects, each causing a different non-uniformity in the apparent daily motion of the Sun relative to the stars:
The equation of time is also the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth.
The equation of time was used historically to set clocks. Between the invention of accurate clocks in 1656 and the advent of commercial time distribution services around 1900, one of two common land-based ways to set clocks was by observing the passage of the sun across the local meridian at noon. The moment the sun passed overhead, the clock was set to noon, offset by the number of minutes given by the equation of time for that date. (The second method did not use the equation of time; instead, it used stellar observations to give sidereal time, in combination with the relation between sidereal time and solar time.) The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides.
Naturally, other planets will have an equation of time too. On Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit. The planet Uranus, which has an extremely large axial tilt, has an equation of time that can be several hours.
The irregular daily movement of the Sun was known by the Babylonians, and Book III of Ptolemy's Almagest is primarily concerned with the Sun's anomaly. Ptolemy discusses the correction needed to convert the meridian crossing of the Sun to mean solar time and takes into consideration the nonuniform motion of the Sun along the ecliptic and the meridian correction for the Sun's ecliptic longitude. He states the maximum correction is 8 1/3 time-degrees or 5/9 of an hour (Book III, chapter 9). However he did not consider the effect relevant for most calculations since it was negligible for the slow-moving luminaries and only applied it for the fastest-moving luminary, the Moon.
Toomer uses the Medieval term equation, from the Latin term aequatio (equalization [adjustment]), for Ptolemy's difference between the mean solar time and the true solar time. Kepler's definition of the equation is "the difference between the number of degrees and minutes of the mean anomaly and the degrees and minutes of the corrected anomaly."
Until the invention of the pendulum and the development of reliable clocks during the 17th century, the equation of time as defined by Ptolemy remained a curiosity, of importance only to astronomers. However, when mechanical clocks started to take over timekeeping from sundials, which had served humanity for centuries, the difference between clock time and solar time became an issue for everyday life. Apparent solar time (or true or real solar time) is the time indicated by the Sun on a sundial (or measured by its transit over the local meridian), while mean solar time is the average as indicated by well-regulated clocks. The first tables for the equation of time which accounted for its annual variations in an essentially correct way were published in 1665 by Christiaan Huygens. Huygens set his values for the equation of time so as to make all values positive throughout the year. This meant that a clock set by Huygens's tables would be consistently about 15 minutes slow on mean time.
Another set of tables was published in 1672–73 by John Flamsteed, who later became the first royal astronomer of the new Greenwich Observatory. These appear to have been the first essentially correct tables which also led to mean time without an offset. Flamsteed adopted the convention of tabulating and naming the correction in the sense that it was to be applied to the apparent time to give mean time.
The equation of time, correctly based on the two major components of the Sun's irregularity of apparent motion, i.e. the effect of the obliquity of the ecliptic and the effect of the Earth's orbital eccentricity, was not generally adopted until after Flamsteed's tables of 1672–73, published with the posthumous edition of the works of Jeremiah Horrocks.
Robert Hooke (1635–1703), who mathematically analyzed the universal joint, was the first to note that the geometry and mathematical description of the (non-secular) equation of time and the universal joint were identical, and proposed the use of a universal joint in the construction of a "mechanical sundial".
The corrections in Flamsteed's tables of 1672/3 and 1680 led to mean time computed essentially correctly and without an offset, i.e. in principle as we now know it. But the numerical values in tables of the equation of time have somewhat changed since then, owing to three kinds of factors:
Until 1833, the equation of time was tabulated in the sense 'mean minus apparent solar time' in the British Nautical Almanac and Astronomical Ephemeris published for the years 1767 onwards. Before the issue for 1834, all times in the almanac were in apparent solar time, because time aboard ship was most often determined by observing the Sun. In the unusual case that the mean solar time of an observation was needed, the extra step of adding the equation of time to apparent solar time was needed. In the Nautical Almanac issues for 1834 onwards, all times have been in mean solar time, because by then the time aboard ship was increasingly often determined by marine chronometers. In the unusual case that the apparent solar time of an observation was needed, the extra step of applying the equation of time to mean solar time was needed, requiring all differences in the equation of time to have the opposite sign than before.
As the apparent daily movement of the Sun is one revolution per day, that is 360° every 24 hours, and the Sun itself appears as a disc of about 0.5° in the sky, simple sundials can be read to a maximum accuracy of about one minute. Since the equation of time has a range of about 30 minutes, the difference between sundial time and clock time cannot be ignored. In addition to the equation of time, one also has to apply corrections due to one's distance from the local time zone meridian and summer time, if any.
The tiny increase of the mean solar day itself due to the slowing down of the Earth's rotation, by about 2 ms per day per century, which currently accumulates up to about 1 second every year, is not taken into account in traditional definitions of the equation of time, as it is imperceptible at the accuracy level of sundials.
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The Earth revolves around the Sun. As seen from Earth, the Sun appears to revolve once around the Earth through the background stars in one year. If the Earth orbited the Sun with a constant speed, in a circular orbit in a plane perpendicular to the Earth's axis, then the Sun would culminate every day at exactly the same time, and be a perfect time keeper (except for the very small effect of the slowing rotation of the Earth). But the orbit of the Earth is an ellipse not centered on sun, and its speed varies between 30.287 and 29.291 km/s, according to Kepler's laws of planetary motion, and its angular speed also varies, and thus the Sun appears to move faster (relative to the background stars) at perihelion (currently around January 3) and slower at aphelion a half year later. At these extreme points, this effect increases (respectively, decreases) the real solar day by 7.9 seconds from its mean. This daily difference accumulates over a period. As a result, the eccentricity of the Earth's orbit contributes a sine wave variation with an amplitude of 7.66 minutes and a period of one year to the equation of time. The zero points are reached at perihelion (at the beginning of January) and aphelion (beginning of July) while the maximum values are in early April (negative) and early October (positive).
|This section does not cite any references or sources.|
However, even if the Earth's orbit were circular, the motion of the Sun along the celestial equator would still not be uniform. This is a consequence of the tilt of the Earth's rotation with respect to its orbit, or equivalently, the tilt of the ecliptic (the path of the sun against the celestial sphere) with respect to the celestial equator. The projection of this motion onto the celestial equator, along which "clock time" is measured, is a maximum at the solstices, when the yearly movement of the Sun is parallel to the equator and appears as a change in right ascension, and is a minimum at the equinoxes, when the Sun moves in a sloping direction and appears mainly as a change in declination, leaving less for the component in right ascension, which is the only component that affects the duration of the solar day. As a consequence of that, the daily shift of the shadow cast by the Sun in a sundial, due to obliquity, is smaller close to the equinoxes and greater close to the solstices. At the equinoxes, the Sun is seen slowing down by up to 20.3 seconds every day and at the solstices speeding up by the same amount.
In the figure on the right, we can see the monthly variation of the apparent slope of the plane of the ecliptic at solar midday as seen from Earth. This variation is due to the apparent precession of the rotating Earth through the year, as seen from the Sun at solar midday.
In terms of the equation of time, the inclination of the ecliptic results in the contribution of another sine wave variation with an amplitude of 9.87 minutes and a period of a half year to the equation of time. The zero points of this sine wave are reached at the equinoxes and solstices, while the extrema are at the beginning of February and August (negative) and the beginning of May and November (positive).
The two above mentioned factors have different wavelengths, amplitudes and phases, so their combined contribution is an irregular wave. At epoch 2000 these are the values (in minutes and seconds with UT dates):
E.T. = apparent − mean. Positive means: Sun runs fast and culminates earlier, or the sundial is ahead of mean time. A slight yearly variation occurs due to presence of leap years, resetting itself every 4 years.
The exact shape of the equation of time curve and the associated analemma slowly change over the centuries due to secular variations in both eccentricity and obliquity. At this moment both are slowly decreasing, but they increase and decrease over a timescale of hundreds of thousands of years. If/when the Earth's orbital eccentricity (now about 0.0167 and slowly decreasing) reaches 0.047, the eccentricity effect may in some circumstances overshadow the obliquity effect, leaving the equation of time curve with only one maximum and minimum per year, as is the case on Mars.
On shorter timescales (thousands of years) the shifts in the dates of equinox and perihelion will be more important. The former is caused by precession, and shifts the equinox backwards compared to the stars. But it can be ignored in the current discussion as our Gregorian calendar is constructed in such a way as to keep the vernal equinox date at 21 March (at least at sufficient accuracy for our aim here). The shift of the perihelion is forwards, about 1.7 days every century. In 1246 the perihelion occurred on 22 December, the day of the solstice, so the two contributing waves had common zero points and the equation of time curve was symmetrical: in Astronomical Algorithms Meeus gives February and November extrema of 15 min 39 sec and May and July ones of 4 min 58 sec. Before that time the February minimum was larger than the November maximum, and the May maximum larger than the July minimum. The secular change is evident when one compares a current graph of the equation of time (see below) with one from 2000 years ago, e.g., one constructed from the data of Ptolemy.
If the gnomon (the shadow-casting object) is not an edge but a point (e.g., a hole in a plate), the shadow (or spot of light) will trace out a curve during the course of a day. If the shadow is cast on a plane surface, this curve will (usually) be the conic section of the hyperbola, since the circle of the Sun's motion together with the gnomon point define a cone. At the spring and fall equinoxes, the cone degenerates into a plane and the hyperbola into a line. With a different hyperbola for each day, hour marks can be put on each hyperbola which include any necessary corrections. Unfortunately, each hyperbola corresponds to two different days, one in each half of the year, and these two days will require different corrections. A convenient compromise is to draw the line for the "mean time" and add a curve showing the exact position of the shadow points at noon during the course of the year. This curve will take the form of a figure eight and is known as an "analemma". By comparing the analemma to the mean noon line, the amount of correction to be applied generally on that day can be determined.
The equation of time is used not only in connection with sundials and similar devices, but also for many applications of solar energy. Machines such as solar trackers and heliostats have to move in ways that are influenced by the equation of time.
For many purposes, the equation of time is usually obtained by looking it up in a published table of values or on a graph. Of course, calculations are required in creating the tables and graphs. Also, in devices such as computer-controlled heliostats, the computer is often programmed to calculate the equation of time whenever it is needed, instead of looking it up. Algorithms by which it can be calculated are therefore important.
In terms of the right ascension of the Sun, α, and that of a mean Sun moving uniformly along the celestial equator, αM, the equation of time is defined as the difference, Δt = αM – α. In this expression Δt is the time difference between apparent solar time (time measured by a sundial) and mean solar time (time measured by a mechanical clock). The left side of this equation is a time difference while the right side terms are angles; however, astronomers regard time and angle as quantities that are related by conversion factors such as; 2π radian = 360° = 1 day = 24 hour. The difference, Δt, is measurable because α can be measured and αM, by definition, is a linear function of mean solar time.
The equation of time can be calculated based on Newton's theory of celestial motion in which the earth and sun describe elliptical orbits about their common mass center. In doing this it is usual to write αM = 2πt/tY = Λ where
Substituting αM into the equation of time, it becomes
The new angles appearing here are:
However, the displayed equation is approximate; it is not accurate over very long times because it ignores the distinction between dynamical time and mean solar time. In addition, an elliptical orbit formulation ignores small perturbations due to the moon and other planets. Another complication is that the orbital parameter values change significantly over long times, for example λp increases by about 1.7 degrees per century. Consequently, calculating Δt using the displayed equation with constant orbital parameters produces accurate results only for sufficiently short times (decades); when compared to more accurate calculations using the Multiyear Computer Interactive Almanac for each day in 2008 it disagrees by as much as 35.2 s. It is possible to write an expression for the equation of time that is valid for centuries, but it is necessarily much more complex.
In order to calculate α, and hence Δt, as a function of M, three additional angles are required; they are
All these angles are shown in the figure on the right, which shows the celestial sphere and the Sun's elliptical orbit seen from the Earth (the same as the Earth's orbit seen from the Sun). In this figure ε = 0.40907 = 23.438° is the obliquity, while the eccentricity of the ellipse is e = [1 − (b/a)2]1/2 = 0.016705.
Now given a value of 0≤M≤2π, one can calculate α(M) by means of the following procedure:
A numerical value can be obtained from an infinite series, graphical, or numerical methods. Alternatively, note that for e = 0, E = M, and for small e, by iteration, E ~ M + e sin M. This can be improved by iterating again, but for the small value of e that characterizes the orbit this approximation is sufficient.
The correct branch of the multiple valued function tan−1x to use is the one that makes ν a continuous function of E(M) starting from ν(E=0) = 0. Thus for 0≤E<π use tan−1x = Tan−1x, and for π<E≤2π use tan−1x = Tan−1x + π. At the specific value E = π for which the argument of tan is infinite, use ν = E. Here Tan−1x is the principal branch, |Tan−1x| < π/2; the function that is returned by calculators and computer applications. Alternatively, note that for e = 0, ν = E and for small e, from a one term Taylor expansion, ν − E + e sin E − M + 2 e sin M.
Next knowing ν calculate λ from its definition above
The value of λ varies non-linearly with M because the orbit is elliptical, from the approximation for ν, λ ~ M + λp + 2e sin M.
Next, knowing λ calculate α from a relation for the right triangle on the celestial sphere shown above
Like ν previously, here the correct branch of tan−1x to use makes α a continuous function of λ(M) starting from α(λ=0)=0. Thus for (2k-1)π/2 < λ < (2k+1)π/2, use tan−1x = Tan−1x + kπ, while for the values λ = (2k+1)π/2 at which the argument of tan is infinite use α = λ. Since λp ≤ λ ≤ λp + 2π when M varies from 0 to 2π, the values of k that are needed, with λp = 4.9412, are 2, 3, and 4. Although an approximate value for α can be obtained from a one term Taylor expansion like that for ν, it is more efficacious to use the equation sin(α – λ) = – tan2(ε/2) sin(α + λ). Note that for ε = 0, α = λ and for small ε, by iteration, p)}}.
Finally, Δt can be calculated using the starting value of M and the calculated α(M). The result is usually given as either a set of tabular values, or a graph of Δt as a function of the number of days past periapsis, n, where 0≤n≤365.242 (365.242 is the number of days in a tropical year); so that
Using the approximation for α(M), Δt can be written as a simple explicit expression, which is designated Δta because it is only an approximation.
This equation was first derived by Milne, who wrote it in terms of Λ = M + λp. The numerical values written here result from using the orbital parameter values for e, ε, and λp given above. When evaluating the numerical expression for Δta as given above, a calculator must be in radian mode to obtain correct values. Note also that the date and time of periapsis (perihelion of the Earth orbit) varies from year to year; a table giving the connection can be found in perihelion.
A comparative plot of the two calculations is shown in the figure below. The simpler calculation is seen to be close to the elaborate one, the absolute error, (Δt − Δta), is less than 45 seconds throughout the year; its largest value is 44.8 sec and occurs on day 273. More accurate approximations can be obtained by retaining higher order terms, but they are necessarily more time consuming to evaluate. At some point it is simpler to just evaluate Δt, but Δta as written above is easy to evaluate, even with a calculator, and has a nice physical explanation as the sum of two terms, one due to obliquity and the other to eccentricity. This is not true either for Δt considered as a function of M or for higher order approximations of Δta.
W is the Earth's mean angular orbital velocity in degrees per day.
D is the date, in days starting at zero on January 1 (i.e. the days part of the ordinal date −1). 10 is the approximate number of days from the December solstice to January 1. A is the angle the earth would move on its orbit at its average speed from the December solstice to date D.
B is the angle the Earth moves from the solstice to date D, including a first-order correction for the Earth's orbital eccentricity, 0.0167. The number 2 is the number of days from January 1 to the date of the Earth's perihelion. This expression for B can be simplified by combining constants to: .
C is the difference between the angles moved at mean speed, and at the corrected speed projected onto the equatorial plane, and divided by 180 to get the difference in "half turns". The number 23.44 is the obliquity (tilt) of the Earth's axis in degrees. The subtraction gives the conventional sign to the equation of time. For any given value of x, arctan(x) (sometimes written as tan−1x) has multiple values, differing from each other by integer numbers of half turns. The value generated by a calculator or computer may not be the appropriate one for this calculation. This may cause C to be wrong by an integer number of half turns. The excess half turns are removed in the next step of the calculation:
EoT is the equation of time in minutes. The expression nint(C) means the nearest integer to C. On a computer, it can be programmed, for example, as INT(C+0.5). It is 0, 1, or 2 at different times of the year. Subtracting it leaves a small positive or negative fractional number of half turns, which is multiplied by 720, the number of minutes (12 hours) that the Earth takes to rotate one half turn relative to the Sun, to get the equation of time.
Compared with published values, this calculation has a Root Mean Square error of only 3.7 seconds of time. The greatest error is 6.0 seconds. This is much more accurate than the approximation described above, but not as accurate as the elaborate calculation.
The value of B in the above calculation is an accurate value for the Sun's ecliptic longitude (shifted by 90 degrees), so the solar declination becomes readily available:
which is accurate to within a fraction of a degree.
|Wikimedia Commons has media related to: Equation of time (sundials)|
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https://alazycowboy.com/2010/01/01/things-that-make-me-go-hmm-no-statistically-significant-warming-since-1995/
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math
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I am beginning to think that this global warming crisis is a sinister plot by statistics professors to get more students to take statistics courses. 😉 Despite my misgivings about the true motives of global warming I will take the opportunity to give a big thanks to LuboÅ¡ for encouraging me to refresh my knowledge of regression analysis. In his post, The Reference Frame: No statistically significant warming since 1995, he shows a simple example of regression analysis of temperature anomalies. Since I am Mathematica challenged I opted to use a method a high school student would probably be familiar with, I used Excel. Without much effort I was able to quickly plot add a trend line to the Excel chart with the following equation on the chart, y = 0.0095x + 0.12 with a R2 = 0.0889. LuboÅ¡ was kind enough to provide me with a link to the AP Tutorial on Statistics so that I would be reminded on the prerequisites for regression analysis. The Coefficient of Determination or otherwise known as R2 is a key output of regression analysis. To paraphrase the AP Tutorial for this case, the variance of the temperature anomalies are 8.9% predictable from the time variable. Ugh! So whether you look at the confidence interval, Standard Error, or R2, it is reasonable to conclude that the temperature data is really ugly and to agree with LuboÅ¡ that the underlying trend in 1995-2009 was "somewhat more likely than not" a warming trend rather than a cooling trend.
For kicks I decided to follow up on a comment Bret made on this same article posted on the Watts Up With That? blog concerning using monthly data. I found some suitable monthly temperature data at http://www7.ncdc.noaa.gov/CDO/CDODivisionalSelect.jsp, imported it into Excel, and plotted it. Here is the result.
Some people may complain that this chart is a nonsensical plot since the seasonal variations overwhelms the temperature trend. On the other hand it highlights how small the slope of the trend line is compared to the seasonal variations. Regardless of which estimate of the temperature increase you choose, it is still a very small number compared to the seasonal temperature variations. Another complaint might be that I should have used temperature anomalies rather than the actual temperature data. This begs the question whether you can have a warming trend that shows up in the anomalies that doesn’t show up in actual temperature data. Oh-oh! I think I should move on to less contentious subjects.
Since I was on a roll I decided to go one step further and analyze the temperature data like it was weather. Oops! I put climate change and weather in the same sentence. Every time I see or hear a weather forecast they discuss the high and low temperatures for the day. I do not remember ever hearing a weather forecast that included the average temperature for the day. In some cases a weather forecast will include an average high or low for the day. Hence I created a plot of the maximum and minimum monthly temperature for each year. This appealed to both my pragmatic view and my engineering background. If we can imagine that our climate is a control system, a control engineer would primarily be interested in setting control limits on the maximum and the minimum values. Surely we should get a better regression analysis using the annual maximum and minimum values.
Once again despite selecting a subset of the monthly temperature data that should have had a better chance of a statistically relevant temperature trend, the regression statistics continue to make it difficult about drawing conclusions about warming or cooling trends. The R2 value for the maximum temperature and minimum temperature trends are better than the raw monthly trend but they are still very low. Once again the underlying trend is "somewhat more likely than not" a warming trend rather than a cooling trend. The R2 value has improved but with it so low, we are still saying very little.
Here are some more thoughts to ponder.
- The range in the system from high to low temperature, 44 degrees, is very large compared to the warming trend(~ 1 degree/century). My inner engineer is having trouble understanding why a climate system that can handle a 44 degree swing in temperatures is having problems with a warming trend of about a degree per century.
- Are the problems we are seeing with the R2 value in our regressions analysis a natural result of the errors(noise) in the system of measuring temperatures? As an example if our temperature measurements are limited to an accuracy of plus or minus one degree, are we not fundamentally limited by the measurement errors in the system. What can we say about warming trends of one degree per century if our measurement errors are likely to be as large as the trend?
- How low does a R2 value or confidence limits in trends need to go before we decide to pack it in and say we do not know what is happening?
Finally for a humorous look at the scientific process courtesy of xkcd.com we have the Science Montage.
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https://www.coursehero.com/file/7790737/Assume-that-this-is-the-case-and-focus-on-the-second-term-Let/
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math
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This preview shows page 1. Sign up to view the full content.
Unformatted text preview: only if |a|<1. Assume that this
is the case and focus on the second term.
Let m be an integer between 0 and n-1. Consider the sum
∑ ∑ ∑ The first term on the right can be written ∑ ∑ . If we take |r|<1, then this term can be bounded above in absolute value by
∑ ∑ ∑ ∑ For any fixed m this term goes to zero as n→∞.
Now consider the second term ∑
. Again using the fact |a|<1, we can bound this
from above by ∑
. This is a segment of the geometric series ∑
, which we know
converges for |r|<1. Therefore, the sums of terms “far out” in the series must be getting small.
That means, that given any small positive number , if n is large enough, we can choose an m<n
so that the ∑
. And so, we have shown that if n is large enough, we can bound the
|∑ | where is an arbitrary small number. Hence the sum approaches 0 as n→∞. 2...
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This note was uploaded on 04/28/2013 for the course ENEE 222 taught by Professor Simon during the Spring '13 term at Maryland.
- Spring '13
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https://opentextbc.ca/basicmotorcontrol/chapter/ohm-and-watt/
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Terms and Definitions
This section provides a brief description of two of the most fundamental electrical relationships: , which describes current flow, and , which describes how power is dissipated.
Click play on the following audio player to listen along as you read this section.
Combining the elements of , , and , George Ohm developed the following formula:
- E = Voltage in volts
- I = Current in amps
- R = Resistance in ohms
This is called Ohm’s law.
Let’s say, for example, that we have a circuit with the potential of 1 volt, a current of 1 amp, and resistance of 1 ohm. Using Ohm’s law we can say:
Let’s say this represents a tank with a wide hose. The amount of water in the tank is defined as 1 volt, and the “narrowness” (resistance to flow) of the hose is defined as 1 ohm. Using Ohm’s law, this gives us a flow (current) of 1 amp.
Using this analogy, let’s now look at the tank with the narrow hose. Because the hose is narrower, its resistance to flow is higher. Let’s define this resistance as 2 ohms. The amount of water in the tank is the same as the other tank, so, using Ohm’s law, our equation for the tank with the narrow hose is:
But what is the current? Because the resistance is greater and the voltage is the same, this gives us a current value of 0.5 amps:
Electric is the rate at which energy is transferred. It’s measured in terms of joules per second (J/s). One joule of work done every second means that power is dissipated at a rate equal to one .
Given the few basic electricity terms we know, how could we calculate power in a circuit?
Well, we have a standard measurement involving electromotive force, also know as .
Current, another of our favourite electricity terms, measures charge flow over time in terms of the , which equals 1 coulomb per second (C/s). Put the two together, and what do we get? Power!
To calculate the power of any particular component in a circuit, multiply the voltage drop across it by the current running through it.
For instance, if current flows at a rate of 10 amps while voltage is 10 volts, then the circuit dissipates power at a rate of 100W.
Current = Voltage divided by Resistance (or I=E/R).
Power = Voltage times Current (or W=EI)
The difference in electric potential between two points, which is defined as the work needed per unit of charge to move a test charge between the two points. It is measured in volts (V).
The rate of flow of an electric charge, measured in amperes (or amps). When one coulomb of charge moves past one point in once second, current is said to flow at a rate of one ampere. Current flows from negative potential to a positive potential through a load.
The opposition to the flow of current in an electric circuit, measured in ohms (Ω).
The rate at which work is done. It is measured in watts (W), or joules per second (J/s).
The unit used to measure power in an electric circuit, equivalent to one joule per second, or the power dissipated when one volt pushes one amp through a circuit.
The unit used to measure electrical current. It is equal to a flow of one coulomb per second. It may also be called "amp."
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https://socratic.org/questions/what-is-the-orthocenter-of-a-triangle-with-corners-at-2-8-3-4-and-6-3#636961
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What is the orthocenter of a triangle with corners at #(2 ,8 )#, #(3 ,4 )#, and (6 ,3 )#?
Let the vertices of triangle ABC be
Now, the equation of altitude drawn from vertex
Similarly, the equation of altitude drawn from vertex
Multiplying (1) by
The ortho-center is the point of intersection of altitudes drawn from vertices to the opposite sides of a triangle hence the orthocenter of given triangle is
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585265.67/warc/CC-MAIN-20211019105138-20211019135138-00139.warc.gz
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CC-MAIN-2021-43
| 404
| 6
|
https://www.nagwa.com/en/videos/872181031467/
|
math
|
Calculate zero point zero four three times thirty-one.
Now when I look at this calculation, I would rather do the calculation forty-three times thirty-one. So in fact, that’s what I’m going to do. Now in order to do that calculation, I’m going to think about what this number actually means.
Well thinking about the place value of each of those digits, I’ve got zero ones or units; I’ve got zero tenths, four hundredths, and three thousandths. So actually I’ve, got forty-three thousandths. And forty-three thousandths can be written like this: forty-three divided by a thousand.
Now that means that my calculation can be rewritten as forty-three thousandths times thirty-one. And one way of doing that calculation is to do forty-three times thirty-one, which is what I said there’s the calculation that I’d rather do, and then take that whole answer and divide by a thousand. So that’s what we’re gonna do.
So let’s write out the calculation in column format like this, forty-three times thirty-one. Now remember that the numbers in this column here are worth ten and the numbers in this column here are only worth ones, so I’ve got three ones and four tens in the first number and one one and three tens in the second number.
Now I’m going to do the multiplication in two parts. First of all, I’m going to do one times forty-three and then I’m gonna do thirty times forty-three. So let’s start with one times forty-three. Well one times three is three, so I can write that digit there. And one times four is four, so I can write that digit there. So one times forty-three is just forty-three.
Now I’m going to do thirty times forty-three. Well thirty times forty-three is just like three times forty-three, only it’s gonna be ten times bigger. So when I multiply my answer by ten, I’m gonna be shifting all the digits one place to the left, which means I’m gonna have a zero in the units column. So now I can do three times forty-three. First of all, three times three is nine, then three times four is twelve.
And to record this number, I’m gonna need a couple of extra columns. So twelve, the two is gonna go in the hundreds column and the one from that is gonna go in the next one along. So that’s the thousands column, so thirty times forty-three is one thousand two hundred and ninety.
Now thirty-one times forty-three is thirty times forty-three plus one times forty-three. So I’m just gonna add these two numbers together: three and zero is three four and nine is thirteen, so that’s gonna be three and then I’m gonna carry one over to the next column. So now I’ve got two, but I’ve got the one that I carried over as well so two and one is three, and then I’ve just got one in the next column. So my final answer is one thousand three hundred and thirty-three.
Well I’ve done this part of the calculation, but I still need to divide that answer by a thousand in order in order to answer the question that they actually asked. And one thousand three hundred and thirty-three divided by a thousand is one point three three three. So the overall answer to the question is one point three three three.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153966.60/warc/CC-MAIN-20210730122926-20210730152926-00219.warc.gz
|
CC-MAIN-2021-31
| 3,165
| 10
|
http://www.acimessentials.com/2024/03/20/
|
math
|
A problem cannot be solved if you do not know what it is. Even if it is really solved already you will still have the problem, because you will not recognise that it has been solved. This is the situation of the world. The problem of separation, which is really the only problem, has already been solved. Yet the solution is not recognised because the problem is not recognised.
Everyone in this world seems to have his own special problems. Yet they are all the same, and must be recognised as one if the one solution that solves them all is to be accepted. Who can see that a problem has been solved if he thinks the problem is something else? Even if he is given the answer, he cannot see its relevance.
That is the position in which you find yourself now. You have the answer, but you are still uncertain about what the problem is. A long series of different problems seems to confront you, and as one is settled the next one and the next arise. There seems to be no end to them. There is no time in which you feel completely free of problems and at peace.
The temptation to regard problems as many is the temptation to keep the problem of separation unsolved. The world seems to present you with a vast number of problems, each requiring a different answer. This perception places you in a position in which your problem-solving must be inadequate, and failure is inevitable.
No one could solve all the problems the world appears to hold. They seem to be on so many levels, in such varying forms and with such varied content, that they confront you with an impossible situation. Dismay and depression are inevitable as you regard them. Some spring up unexpectedly, just as you think you have resolved the previous ones. Others remain unsolved under a cloud of denial, and rise to haunt you from time to time, only to be hidden again but still unsolved.
All this complexity is but a desperate attempt not to recognise the problem, and therefore not to let it be resolved. If you could recognise that your only problem is separation, no matter what form it takes, you could accept the answer because you would see its relevance. Perceiving the underlying constancy in all the problems that seem to confront you, you would understand that you have the means to solve them all. And you would use the means, because you recognise the problem.
In our longer practise periods today we will ask what the problem is, and what is the answer to it. We will not assume that we already know. We will try to free our minds of all the many different kinds of problems we think we have. We will try to realise that we have only one problem, which we have failed to recognise. We will ask what it is, and wait for the answer. We will be told. Then we will ask for the solution to it. And we will be told.
The exercises for today will be successful to the extent to which you do not insist on defining the problem. Perhaps you will not succeed in letting all your preconceived notions go, but that is not necessary. All that is necessary is to entertain some doubt about the reality of your version of what your problems are. You are trying to recognise that you have been given the answer by recognising the problem, so that the problem and the answer can be brought together and you can be at peace.
The shorter practise periods for today will not be set by time, but by need. You will see many problems today, each one calling for an answer. Our efforts will be directed toward recognising that there is only one problem and one answer. In this recognition are all problems resolved. In this recognition there is peace.
Be not deceived by the form of problems today. Whenever any difficulty seems to rise, tell yourself quickly:
Then try to suspend all judgement about what the problem is. If possible, close your eyes for a moment and ask what it is. You will be heard and you will be answered.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816045.47/warc/CC-MAIN-20240412163227-20240412193227-00215.warc.gz
|
CC-MAIN-2024-18
| 3,885
| 11
|
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