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NCERT Solutions for class 10th Maths Chapter 15 Probability Exercise 15.1 Question 1. Complete the following statements: • (I) Probability of an event E + Probability of the event ‘not E’ = _ _ • (ii) The probability of an event that cannot happen is____. Such an event is called. • (iii) The probability of an event that is certain to happen is____Such an event is called_____ • (iv) The sum of the probabilities of all the elementary events of an experiment • (v) The probability of an event is greater than or equal to______and less than or equal to __ Sol. The complete statements from the given are as below : (I) Probability of an event E + Probability of the event ‘not E’ = 1. (ii) The probability of an event that cannot happen is 0. Such an event is called impossible event. (iii) The probability of an event that is certain to happen is 1. Such an event is called sure event. (iv) The sum of the probabilities of all the elementary events of an experiment is 1. (v) The probability of an event is greater than or equal to O and less than or equal to 1. Question 2. Which of the following experiments have equally likely outcomes? Explain. (I) A driver attempts to start a car. The car starts or does not start. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot. (iii) A trial is made to answer a true-false question. The answer is right or wrong. (iv) A baby is born. It is a boy or a girl. Sol. (i) The car starts normally; only when there is some defect, the car does not start. So, the outcome is not equally likely. (ii) The outcome in this situation is not equally likely because the outcome depends on many factors such as the training of the player, quality of the gun used, etc. (iii) The outcome in this trial of true-false question is either true or false, i.e., one out of the two and both have equal chances to happen. Hence, the two outcomes are equally likely. (iv) A new baby who took birth at a moment can be either a boy or a girl and both the outcome have equally likely chances Question 3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game? Sol. The tossing of a coin is considered to be a fair way of deciding the turn to get the ball at the beginning of a football game as the toss of a coin has two outcomes head and tail and chances of both are equally likely to happen. So, the result of the toss of a fair coin is completely unpredictable. Question 4. Which of the following cannot be the probability of an event? Question 5. If P(E)=0.05, what is the probability of ‘notE’? Question 6. A bag contains lemon-flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out (I) an orange flavoured candy? (ii) a lemon flavoured candy? Question 7. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday? Question 8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red? Question 9. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i)red? (ii) white? (iii) not green? Question 10. A piggy bank contains hundred 50p coins, fifty rs.1 coins, twenty rs.2 coins, and ten rs.5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50 p coin? (ii) will not be a rs.5 coin? Question 11. Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig.). What is the probability that the fish taken out is a male fish? Question 12. A game of chance consists of spinning an arrow that comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig.), and these are equally likely outcomes. What is the probability that it will point at (I) 8? (ii) an odd number? (iii) a number greater than 2? (iv) a number less than 9? Question 13. A die is thrown once. Find the probability of getting (I) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number. Question 14. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (I) a king of red color (ii) a face card (iii) a red face card (iv) the jack of hearts (v)a spade (vi) the queen of diamonds Question 15. Five cards-the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. (I) What is the probability that the card is the queen? (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen? Question 16. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one. Question 17. (i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? (ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective? Question 18. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5. Question 19. A child has a die whose six faces show the letters as given below: Question 20. Suppose you drop a die at random on the rectangular region shown in Fig. What is the probability that it will land inside the circle with diameter l m? Question 21. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i)She will buy it? (ii)She will not buy it? Question 22. Refer to Example 13. (i) Complete the following table: Question 23. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game. Question 24. A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once? Question 25. Which of the following arguments are correct and which are not correct? Give reasons for your answer. (I) If two coins are tossed simultaneously there are three possible outcomes-two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3. (ii) If a die is thrown, there are two possible outcomes-an odd number or an even number. Therefore, the probability of getting an odd number is 1/2. Exercise 15.2 Question 1. Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different days? Question 2. A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws: Question 3. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag. Question 4. A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x. Question 5. Ajar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue balls in the Related Articles:	{"url":"https://cbseacademic.in/class-10/ncert-solutions/maths/probability/","timestamp":"2024-11-09T19:17:21Z","content_type":"text/html","content_length":"116618","record_id":"<urn:uuid:046b35fd-ad7a-4d0d-b80a-3d0f003dac13>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00033.warc.gz"}
Present Value Formula \| Calculator (Examples with Excel Template) Updated July 27, 2023 Present Value Formula (Table of Contents) What is the Present Value Formula? The term “present value” refers to the application of the time value of money that discounts the future cash flow to arrive at its present-day value. We determine the discounting rate for the present value based on the current market return. The formula for present value can be derived by discounting the future cash flow using a pre-specified rate (discount rate) and a number of years. The formula For PV is given below: PV = CF / (1 + r) t • PV = Present Value • CF = Future Cash Flow • r = Discount Rate • t = Number of Years In case of multiple compounding per year (denoted by n), the formula for PV can be expanded as, PV = CF / (1 + r/n) tn Examples of Present Value Formula (With Excel Template) Let’s take an example to understand the Present Value’s calculation better. [wbcr_snippe ” id= “67600”] Example #1 Let us take a simple example of a $2,000 future cash flow to be received after 3 years. According to the current market trend, the applicable discount rate is 4%. Calculate the value of the future cash flow today. We calculate the present value using the following formula: PV = CF / (1 + r) t • Present Value = $2,000 / (1 + 4%) 3 • Present Value = $1,777.99 Therefore, the $2,000 cash flow received after 3 years is worth $1,777.99 today. Example #2 Let us take the example of David, who seeks a certain amount of money today such that after 4 years, he can withdraw $3,000. The applicable discount rate is 5%, to be compounded half-yearly. Calculate the amount that David is required to deposit today. Calculate the present value using the following formula: PV = CF / (1 + r/n) tn • Present Value = $3,000 / (1 + 5%/2) 42 • Present Value = $2,462.24 Therefore, David needs to deposit $2,462 today in order to be able to withdraw $3,000 after 4 years. Example #3 Let us take another example of John, who won a lottery, and as per its terms, he is eligible for a yearly cash pay-out of $1,000 for the next 4 years. The discount rate is 4%. Calculate the present value of all the future cash flows starting from the end of the current year. Calculate the present value using the following formula: PV = CF / (1 + r) t For 1st year, • Present Value = $1,000 / (1 + 4%)1 • Present Value = $961.54 For 2nd year, • Present Value = $1,000 / (1 + 4%)2 • Present Value = $924.56 For 3rd year, • Present Value = $1,000 / (1 + 4%)3 • Present Value = $889.00 For 4th year, • Present Value = $1,000 / (1 + 4%)4 • Present Value = $854.80 To calculate the present value for a particular year, use the following formula: • Present Value= $961.54 + $924.56 + $889.00 + $854.80 • Present Value = $3,629.90 Therefore, John’sresent-day value of John’s lottery winning is $3,629.90. The formula for the present value can be derived by using the following steps: Step 1: Firstly, figure out the future cash flow which CF denotes. Step 2: Decide the discounting rate based on the current market return. The rate, denoted by r, is what discounts the future cash flows. Step 3: Next, determine the number of years until the future cash flow starts, denoted by t. Step 4: You can derive the formula for present value by first discounting the future cash flow (step 1), then using a discount rate (step 2), and finally determining the number of years (step 3), as demonstrated below. PV = CF / (1 + r) t Step 5: If you know the number of compounding periods per year (n), you can express the formula for present value as follows: PV = CF / (1 + r/n) tn Relevance and Uses The concept of present value is primarily based on the time value of money, which states that a dollar today is worth more than a dollar in the future. The present value calculation has a limitation in assuming a consistent rate of return throughout the entire time period. It is important to note that no investment can guarantee a specific rate of return, as various market factors can negatively impact the rate of return, leading to the potential erosion of the present value. As such, the assumption of an appropriate discount rate is all the more important for the correct valuation of future cash flows. Present Value Formula Calculator You can use the following Present Value Calculator “[wbcr_”nippet id= “178608”] Recommended Articles This is a guide to Present Value Formula. Here we have discussed How to Calculate Present Value along with practical examples. We also provide a Present Value Calculator with a downloadable Excel template. You may also look at the following articles to learn more –	{"url":"https://www.educba.com/present-value-formula/","timestamp":"2024-11-06T20:42:18Z","content_type":"text/html","content_length":"336084","record_id":"<urn:uuid:ff5efad0-370e-4348-89e6-177e3213c7c0>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00452.warc.gz"}
Building Financial Models in Excel Course Home \| Power BI \| Excel \| Python \| SQL \| Visualising Data \| Generative AI Building Financial Models in Excel Course Who should attend Excel users who want to build financial models in Excel, especially where those models have a what-if aspect. Course Length 2 days Learning Objectives You will learn how to structure an Excel model and in particular techniques such as scenario modelling (best/base/worst case estimates) and sensitivity analysis. Completion of the Excel foundation and intermediate courses. Course Content Introduction (Presentation/Discussion) What is a spreadsheet model? Different sorts of model: e.g. scenario model, sensitivity analysis Recap on Excel techniques and Functions Useful for Financial Models This covers Excel techniques and functions useful for building financial models: • relative and absolute cell addressing; • the SUMIFS() and COUNTIFS() functions group and aggregate data; • the IFS() function avoids nested IF() formulas; • the XLOOKUP() function is a simpler more flexible robust alternative to VLOOKUP(); • functions that spill and their advantages, and • functions for discounted cash flow and NPV analysis. Introduction to Data Tables (Lab Exercise) Data tables are a very useful technique in building models especially for scenario modelling. In the lab we build a few models: specify the assumptions, build the model template then use data tables to generate a set of results for different scenarios. Scenario Models and Sensitivity Analysis (Lab Exercise) Scenario Models answer what-if questions as well as the expected case, what is the possible upside and how bad could things get? Sensitivity Analysis helps us understand the spread of range of values of key results based on a set of possible values of the variables in our assumptions of our model. In the lab exercise, we build a simple financial model, the income statement of a fictitious	{"url":"https://zomalex.co.uk/excel_models.html","timestamp":"2024-11-15T03:44:16Z","content_type":"text/html","content_length":"5653","record_id":"<urn:uuid:878860fc-fbfe-49fa-8ef3-92709e14ce6d>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00660.warc.gz"}
Current Search: Fluid mechanics A numerical study of bluff body aerodynamics by vortex method. He, Fusen., Florida Atlantic University, Su, Tsung-Chow, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering Vortex methods are grid-free; therefore, their use avoids a number of shortcomings of Eulerian, grid-based numerical methods for solving high Reynolds number flow problems. These include such problems as poor resolution and numerical diffusion. In vortex methods, the continuous vorticity field is discretized into a collection of Lagrangian elements, known as vortex elements. Vortex elements are free to move in the flow field which they create. The velocity field induced by these vortex... Show moreVortex methods are grid-free; therefore, their use avoids a number of shortcomings of Eulerian, grid-based numerical methods for solving high Reynolds number flow problems. These include such problems as poor resolution and numerical diffusion. In vortex methods, the continuous vorticity field is discretized into a collection of Lagrangian elements, known as vortex elements. Vortex elements are free to move in the flow field which they create. The velocity field induced by these vortex elements is a solution to the Navier-Stokes equation, and in principle the method is suitable for high Reynolds number flows. In this dissertation, viscous vortex element methods are studied. Some modifications are developed. Discrete vortex element methods have been used to solve the Navier-Stokes equations in high Reynolds number flows. Globally satisfactory results have been obtained. However, computed pressure fields are often inaccurate due to the significant errors in the surface vorticity distribution. In addition, different ad hoc assumptions are often used in different proposed algorithms. In the present study, improvements are made to better represent the near-wall vorticity when obtaining numerical solutions for the Navier-Stokes equations. In particular, we split the boundary vortex sheet into two parts at each time step. One part remains a vortex sheet lying on the boundary of the solid body, and the other enters into the flow field as a free vortex element with a uniformly distributed vorticity. A set of kinematic relationships are used to determine the two appropriate portions of the split, and the position of the vortex element to be freed at the time of release. Another improvement is to include the nonlinear acceleration terms in the governing equations near the solid boundary when evaluating the surface pressure distribution. The aerodynamic force coefficients can then be obtained by summing up the pressure forces. By comparing the computed surface vorticities, surface pressures and aerodynamics force coefficients with existing numerical/experimental data in the cases of viscous flow around a circular cylinder, an aerofoil, and a bridge deck section, it is shown that the present approach is more accurate in modelling the flow features and force coefficients without making different ad hoc assumptions for different geometries. The computation is efficient. It can be useful in the study of the unsteady fluid flow phenomenon in practical engineering Show less Date Issued Subject Headings Vortex-motion, Fluid mechanics, Viscous flow Document (PDF) Rapid distortion theory for rotor inflows. Kawashima, Emilia, Glegg, Stewart A. L., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering For aerospace and naval applications where low radiated noise levels are a requirement, rotor noise generated by inflow turbulence is of great interest. Inflow turbulence is stretched and distorted as it is ingested into a thrusting rotor which can have a significant impact on the noise source levels. This thesis studies the distortion of subsonic, high Reynolds number turbulent flow, with viscous effects ignored, that occur when a rotor is embedded in a turbulent boundary layer. The analysis... Show moreFor aerospace and naval applications where low radiated noise levels are a requirement, rotor noise generated by inflow turbulence is of great interest. Inflow turbulence is stretched and distorted as it is ingested into a thrusting rotor which can have a significant impact on the noise source levels. This thesis studies the distortion of subsonic, high Reynolds number turbulent flow, with viscous effects ignored, that occur when a rotor is embedded in a turbulent boundary layer. The analysis is based on Rapid Distortion Theory (RDT), which describes the linear evolution of turbulent eddies as they are stretched by a mean flow distortion. Providing that the gust does not distort the mean flow streamlines the solution for a mean flow with shear is found to be the same as the solution for a mean potential flow with the addition of a potential flow gust. By investigating the inflow distortion of small-scale turbulence for various simple flows and rotor inflows with weak shear, it is shown that RDT can be applied to incompressible shear flows to determine the flow distortion. It is also shown that RDT can be applied to more complex flows modeled by the Reynolds Averaged Navier Stokes (RANS) equations. Show less Date Issued Subject Headings Computational fluid dynamics, Fluid dynamic measurements, Fluid mechanics -- Mathematical models, Turbulence -- Computer simulation, Turbulence -- Mathematical models Document (PDF) Far-Field Noise From a Rotor in a Wind Tunnel. Grant, Justin Alexander, Glegg, Stewart A. L., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering This project is intended to demonstrate the current state of knowledge in the prediction of the tonal and broadband noise radiation from a Sevik rotor. The rotor measurements were made at the Virginia Tech Stability Wind Tunnel. Details of the rotor noise and flow measurements were presented by Wisda et al(2014) and Murray et al(2015) respectively. This study presents predictions based on an approach detailed by Glegg et al(2015) for the broadband noise generated by a rotor in an... Show moreThis project is intended to demonstrate the current state of knowledge in the prediction of the tonal and broadband noise radiation from a Sevik rotor. The rotor measurements were made at the Virginia Tech Stability Wind Tunnel. Details of the rotor noise and flow measurements were presented by Wisda et al(2014) and Murray et al(2015) respectively. This study presents predictions based on an approach detailed by Glegg et al(2015) for the broadband noise generated by a rotor in an inhomogeneous flow, and compares them to measured noise radiated from the rotor at prescribed observer locations. Discrepancies between the measurements and predictions led to comprehensive study of the flow in the wind tunnel and the discovery of a vortex upstream of the rotor at low advance ratios. The study presents results of RANS simulations. The static pressure and velocity profile in the domain near the rotor's tip gap region were compared to measurements obtained from a pressure port array and a PIV visualization of the rotor in the wind tunnel. Show less Date Issued Subject Headings Aerodynamic noise, Computational fluid dynamics, Fluid dynamic measurement, Fluid mechanics -- Mathematical models, Fluid structure interactioin, Turbomachines -- Fluid dynamics, Turbulence -- Mathematical models, Unsteady flow (Fluid dynamics) Document (PDF) Predicting the flow & noise of a rotor in a turbulent boundary layer using an actuator disk – Rans approach. Buono, Armand C., Glegg, Stewart A. L., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering The numerical method presented in this study attempts to predict the mean, non-uniform flow field upstream of a propeller partially immersed in a thick turbulent boundary layer with an actuator disk using CFD based on RANS in ANSYS FLUENT. Three different configurations, involving an infinitely thin actuator disk in the freestream (Configuration 1), an actuator disk near a wall with a turbulent boundary layer (Configuration 2), and an actuator disk with a hub near a wall with a turbulent... Show moreThe numerical method presented in this study attempts to predict the mean, non-uniform flow field upstream of a propeller partially immersed in a thick turbulent boundary layer with an actuator disk using CFD based on RANS in ANSYS FLUENT. Three different configurations, involving an infinitely thin actuator disk in the freestream (Configuration 1), an actuator disk near a wall with a turbulent boundary layer (Configuration 2), and an actuator disk with a hub near a wall with a turbulent boundary layer (Configuration 3), were analyzed for a variety of advance ratios ranging from J = 0.48 to J =1.44. CFD results are shown to be in agreement with previous works and validated with experimental data of reverse flow occurring within the boundary layer above the flat plate upstream of a rotor in the Virginia Tech’s Stability Wind Tunnel facility. Results from Configuration 3 will be used in future aero-acoustic computations. Show less Date Issued Subject Headings Aeroelasticity, Computational fluid dynamics, Fluid dynamic measurements, Fluid mechanics -- Mathematical models, Turbomachines -- Fluid dynamics, Turbulence -- Mathematical models Document (PDF) Evaluation of motion compensated ADV measurements for quantifying velocity fluctuations. Lovenbury, James William., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering This study assesses the viability of using a towfish mounted ADV for quantifying water velocity fluctuations in the Florida Current relevant to ocean current turbine performance. For this study a motion compensated ADV is operated in a test flume. Water velocity fluctuations are generated by a 1.3 cm pipe suspended in front of the ADV at relative current speeds of 0.9 m/s and 0.15 m/s, giving Reynolds numbers on the order of 1000. ADV pitching motion of +/- 2.5 [degree] at 0.3 Hz and a heave... Show moreThis study assesses the viability of using a towfish mounted ADV for quantifying water velocity fluctuations in the Florida Current relevant to ocean current turbine performance. For this study a motion compensated ADV is operated in a test flume. Water velocity fluctuations are generated by a 1.3 cm pipe suspended in front of the ADV at relative current speeds of 0.9 m/s and 0.15 m/s, giving Reynolds numbers on the order of 1000. ADV pitching motion of +/- 2.5 [degree] at 0.3 Hz and a heave motion of 0.3 m amplitude at 0.2 Hz are utilized to evaluate the motion compensation approach. The results show correction for motion provides up to an order of magnitude reduction in turbulent kinetic energy at frequencies of motion while the IMU is found to generate 2% error at 1/30 Hz and 9% error at 1/60 Hz in turbulence intensity. Show less Date Issued Subject Headings Motion control systems, Fluid dynamic measurements, Fluid mechanics, Mathematical models, Analysis of covariance Document (PDF) The acoustic far field of a turbulent boundary layer flow calculated from RANS simulations of the flow. Blanc, Jean-Baptiste., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering Boundary layers are regions where turbulence develops easily. In the case where the flow occurs on a surface showing a certain degree of roughness, turbulence eddies will interact with the roughness elements and will produce an acoustic field. This thesis aims at predicting this type of noise with the help of the Computational Fluid Dynamics (CFD) simulation of a wall jet using the Reynolds Average Navier-Stokes (RANS) equations. A frequency spectrum is reconstructed using a representation of... Show moreBoundary layers are regions where turbulence develops easily. In the case where the flow occurs on a surface showing a certain degree of roughness, turbulence eddies will interact with the roughness elements and will produce an acoustic field. This thesis aims at predicting this type of noise with the help of the Computational Fluid Dynamics (CFD) simulation of a wall jet using the Reynolds Average Navier-Stokes (RANS) equations. A frequency spectrum is reconstructed using a representation of the turbulence with uncorrelated sheets of vorticity. Both aerodynamic and acoustic results are compared to experimental measurements of the flow. The CFD simulation of the flow returns consistent results but would benefit from a refinement of the grid. The surface pressure spectrum presents a slope in the high frequencies close to the experimental spectrum. The far field noise spectrum has a 5dB difference to the experiments. Show less Date Issued Subject Headings Computational fluid dynamics, Turbulence, Mathematical models, Fluid mechanics, Mathematical models, Acoustical engineering Document (PDF) Electrochemical aspects of magnetohydrodynamic thrusters. Moreno, Juan E., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering The concept of using Magnetohydrodynamics to provide thrust has been around for decades. However little work has been carried out in one of the fundamental aspects that allows for these systems to operate in seawater. Therefore a series of tests were carried out to determine how the electrochemical reactions occurring at the electrodes affect the seawater system. These tests were used to determine the effects magnetic fields have on seawater conductivity, the pH changes around the electrodes,... Show moreThe concept of using Magnetohydrodynamics to provide thrust has been around for decades. However little work has been carried out in one of the fundamental aspects that allows for these systems to operate in seawater. Therefore a series of tests were carried out to determine how the electrochemical reactions occurring at the electrodes affect the seawater system. These tests were used to determine the effects magnetic fields have on seawater conductivity, the pH changes around the electrodes, and consider the double layer capacitance model as a means to decrease the amount of gas bubbles created at the electrodes. As a result significant increases in resistivity in seawater were observed when the magnetic field was introduced, pH changes were seen on both the cathode and anode, and pulsing of the applied potential may stimulate further work to be considered. Show less Date Issued Subject Headings Electric power production, Metrohydrodynamic generation, Fluid mechanics, Magnetohydrodynamics Document (PDF) Experimental Investigation of Skin Friction Drag Reduction on a Flat Plate using Microbubbles. Grabe, Zachary A., Dhanak, Manhar R., Florida Atlantic University A microbubble generation system has been designed, constructed, and tested in a circulating water tunnel. A 1.0 m long flat plate was subjected to a flow where the Reynolds number ranged from ReL = 7.23x 10^5 - 1.04 x 10^6. Bubble diameters and skin friction measurements were studied at various airflow rates and water velocities. Bubbles were produced by forcing air through porous plates that were mounted flush with the bottom of the test plate. Once emitted through the plates, the bubbles... Show moreA microbubble generation system has been designed, constructed, and tested in a circulating water tunnel. A 1.0 m long flat plate was subjected to a flow where the Reynolds number ranged from ReL = 7.23x 10^5 - 1.04 x 10^6. Bubble diameters and skin friction measurements were studied at various airflow rates and water velocities. Bubbles were produced by forcing air through porous plates that were mounted flush with the bottom of the test plate. Once emitted through the plates, the bubbles traveled downstream in the boundary layer. The airflow rate and water velocity were found to have the most significant impact on the size of the bubbles created. Skin friction drag measurements were recorded in detail in the velocity and airflow rate ranges. The coefficient of skin friction was determined and relationships were then established between this coefficient and the void ratio. Show less Date Issued Subject Headings Frictional resistance (Hydrodynamics), Drag (Aerodynamics), Skin friction (Aerodynamics), Fluid mechanics Document (PDF) Aerodynamic analysis of a propeller in a turbulent boundary layer flow. Lachowski, Felipe Ferreira., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering Simulating the exact chaotic turbulent flow field about any geometry is a dilemma between accuracy and computational resources, which has been continuously studied for just over a hundred years. This thesis is a complete walk-through of the entire process utilized to approximate the flow ingested by a Sevik-type rotor based on solutions to the Reynolds Averaged Navier-Stokes equations (RANS). The Multiple Reference Frame fluid model is utilized by the code of ANSYS-FLUENT and results are... Show moreSimulating the exact chaotic turbulent flow field about any geometry is a dilemma between accuracy and computational resources, which has been continuously studied for just over a hundred years. This thesis is a complete walk-through of the entire process utilized to approximate the flow ingested by a Sevik-type rotor based on solutions to the Reynolds Averaged Navier-Stokes equations (RANS). The Multiple Reference Frame fluid model is utilized by the code of ANSYS-FLUENT and results are validated by experimental wake data. Three open rotor configurations are studied including a uniform inflow and the rotor near a plate with and without a thick boundary layer. Furthermore, observations are made to determine the variation in velocity profiles of the ingested turbulent flow due to varying flow conditions. Show less Date Issued Subject Headings Acoustical engineering, Boundary layer control, Multiphase flow, Mathematical models, Fluid mechanics, Mathematical models, Turbulence, Mathematical models, Computatioinal fluid dynamics Document (PDF) Spectral evaluation of motion compensated adv systems for ocean turbulence measurements. Egeland, Matthew Nicklas, von Ellenrieder, Karl, VanZwieten, James H., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering A motion compensated ADV system was evaluated to determine its ability to make measurements necessary for characterizing the variability of the ambient current in the Gulf Stream. The impact of IMU error relative to predicted turbulence spectra was quantified, as well as and the ability of the motion compensation approach to remove sensor motion from the ADV measurements. The presented data processing techniques are shown to allow the evaluated ADV to be effectively utilized for quantifying... Show moreA motion compensated ADV system was evaluated to determine its ability to make measurements necessary for characterizing the variability of the ambient current in the Gulf Stream. The impact of IMU error relative to predicted turbulence spectra was quantified, as well as and the ability of the motion compensation approach to remove sensor motion from the ADV measurements. The presented data processing techniques are shown to allow the evaluated ADV to be effectively utilized for quantifying ambient current fluctuations from 0.02 to 1 Hz (50 to 1 seconds) for dissipation rates as low as 3x10-7. This measurement range is limited on the low frequency end by IMU error, primarily by the calculated transformation matrix, and on the high end by Doppler noise. Inshore testing has revealed a 0.37 Hz oscillation inherent in the towfish designed and manufactured as part of this project, which can nearly be removed using the IMU. Show less Date Issued Subject Headings Fluid dynamic measurements, Fluid mechanics -- Mathematical models, Motion control systems, Ocean atmosphere interaction, Ocean circulation, Turbulence, Wave motion, Theory of Document (PDF) Barometric distillation and the problem of non-condensable gases. Martinson, Eiki., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science Barometric distillation is an alternative method of producing fresh water by desalination. This proposed process evaporates saline water at low pressure and consequently low temperature; low pressure conditions are achieved by use of barometric columns and condensation is by direct contact with a supply of fresh water that will be augmented by the distillate. Low-temperature sources of heat, such as the cooling water rejected by electrical power generating facilities, can supply this system... Show moreBarometric distillation is an alternative method of producing fresh water by desalination. This proposed process evaporates saline water at low pressure and consequently low temperature; low pressure conditions are achieved by use of barometric columns and condensation is by direct contact with a supply of fresh water that will be augmented by the distillate. Low-temperature sources of heat, such as the cooling water rejected by electrical power generating facilities, can supply this system with the latent heat of evaporation. Experiments are presented that show successful distillation with a temperature difference between evaporator and condenser smaller than 10ê C. Accumulation of dissolved gases coming out of solution, a classic problem in lowpressure distillation, is indirectly measured using a gas-tension sensor. The results of these experiments are used in an analysis of the specific energy required by a production process capable of producing 15 liters per hour. With a 20ê C difference, and neglecting latent heat, this analysis yields a specific energy of 1.85 kilowatt-hour per cubic meter, consumed by water pumping and by removal of non-condensable gases. Show less Date Issued Subject Headings Chemistry, Physical and theoretical, Fluid mechanics, Saline water conversion, Renewable energy sources, Groundwater, Purification Document (PDF) Experimental analysis of the effect of waves on a floating wind turbine. Isaza, Francisco, Ghenai, Chaouki, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering The goal of this Thesis is to demonstrate, through experimentation, that ocean waves have a positive effect on the performance of an offshore wind turbine. A scale model wind turbine was placed into a wave tank that was completely covered and fitted with a variable speed fan to create different wind and wave conditions for testing. Through testing, different power coefficient vs. tip speed ratio graphs were created and a change in power coefficient was observed between steady operating... Show moreThe goal of this Thesis is to demonstrate, through experimentation, that ocean waves have a positive effect on the performance of an offshore wind turbine. A scale model wind turbine was placed into a wave tank that was completely covered and fitted with a variable speed fan to create different wind and wave conditions for testing. Through testing, different power coefficient vs. tip speed ratio graphs were created and a change in power coefficient was observed between steady operating conditions and operating conditions with waves. The results show a promising increase in power production for offshore wind turbines when allowed to operate with the induced motion caused by the amplitude and frequency of water waves created. Show less Date Issued Subject Headings Fluid mechanics, Offshore wind power plants, Renewable energy sources, Wind turbines -- Design and construction Document (PDF) caHydrodynamic analysis of flapping foils for the propulsion of near surface under water vehicles using the panel method. Bustos, Julia, Ananthakrishnan, Palaniswamy, Dhanak, Manhar R., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering This thesis presents two-dimensional hydrodynamic analysis of flapping foils for the propulsion of underwater vehicles using a source-vortex panel. Using a simulation program developed in MatLab, the hydrodynamic forces (such as the lift and the drag) as well as the propulsion thrust and efficiency are computed with this method. The assumptions made in the analysis are that the flow around a hydrofoil is two-dimensional, incompressible and inviscid. The analysis is first considered for the... Show moreThis thesis presents two-dimensional hydrodynamic analysis of flapping foils for the propulsion of underwater vehicles using a source-vortex panel. Using a simulation program developed in MatLab, the hydrodynamic forces (such as the lift and the drag) as well as the propulsion thrust and efficiency are computed with this method. The assumptions made in the analysis are that the flow around a hydrofoil is two-dimensional, incompressible and inviscid. The analysis is first considered for the case of a deeply submerged hydrofoil followed by the case where it is located in shallow water depth or near the free surface. In the second case, the presence of the free surface and wave effects are taken into account, specifically at high and low frequencies and small and large amplitudes of flapping. The objective is to determine the thrust and efficiency of the flapping –foils under the influence of added effects of the free surface. Results show that the free-surface can significantly affect the foil performance by increasing the efficiency particularly at high Frequencies. Show less Date Issued Subject Headings Aerodynamics -- Mathematical models, Fluid mechanics, Naval architecture, Ships -- Aerodynamics, Steering gear Document (PDF) Internal waves on a continental shelf. Jagannathan, Arjun., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering In this thesis, a 2D CHebyshev spectral domain decomposition method is developed for simulating the generation and propagation of internal waves over a topography. While the problem of stratified flow over topography is by no means a new one, many aspects of internal wave generation and breaking are still poorly understood. This thesis aims to reproduce certain observed features of internal waves by using a Chebyshev collation method in both spatial directions. The numerical model solves the... Show moreIn this thesis, a 2D CHebyshev spectral domain decomposition method is developed for simulating the generation and propagation of internal waves over a topography. While the problem of stratified flow over topography is by no means a new one, many aspects of internal wave generation and breaking are still poorly understood. This thesis aims to reproduce certain observed features of internal waves by using a Chebyshev collation method in both spatial directions. The numerical model solves the inviscid, incomprehensible, fully non-linear, non-hydrostatic Boussinesq equations in the vorticity-streamfunction formulation. A number of important features of internal waves over topography are captured with the present model, including the onset of wave-breaking at sub-critical Froude numbers, up to the point of overturning of the pycnoclines. Density contours and wave spectra are presented for different combinations of Froude numbers, stratifications and topographic slope. Show less Date Issued Subject Headings Engineering geology, Mathematical models, Chebyshev polynomials, Fluid dynamics, Continuum mechanics, Spectral theory (Mathematics) Document (PDF) Hydrodynamics of mangrove root-type models. Kazemi, Amirkhosro, Curet, Oscar M., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering Mangrove trees play a prominent role in coastal tropic and subtropical regions, providing habitat for many organisms and protecting shorelines against storm surges, high winds, erosion, and tsunamis. The motivation of this proposal is to understand the complex interaction of mangrove roots during tidal flow conditions using simplified physical models. In this dissertation, the mangrove roots were modeled with a circular array of cylinders with different porosities and spacing ratios. In... Show moreMangrove trees play a prominent role in coastal tropic and subtropical regions, providing habitat for many organisms and protecting shorelines against storm surges, high winds, erosion, and tsunamis. The motivation of this proposal is to understand the complex interaction of mangrove roots during tidal flow conditions using simplified physical models. In this dissertation, the mangrove roots were modeled with a circular array of cylinders with different porosities and spacing ratios. In addition, we modeled the flexibility of the roots by attaching rigid cylinders to hinge connectors. The models were tested in a water tunnel for a range of Reynolds number from 2200 to 11000. Additionally, we performed 2D flow visualization for different root models in a flowing soap film setup. We measured drag force and the instantanous streamwise velocity downstream of the models. Furthermore, we investigated the fluid dynamics downstream of the models using a 2-D time-resolved particle image velocimetry (PIV), and flow visualization. The result was analyzed to present time-averaged and time-resolved flow parameters including the velocity distribution, vorticity, streamline, Reynolds shear stress and turbulent kinetic energy. We found that the frequency of the vortex shedding increases as the diameter of the small cylinders decreases while the patch diameter is constant, therefore increasing the Strouhal number, St=fD/U By comparing the change of Strouhal numbers with a single solid cylinder, we introduced a new length scale, the “effective diameter”. In addition, the effective diameter of the patch decreases as the porosity increases. In addition, patch drag decreases linearly as the spacing ratio increases. For flexible cylinders, we found that a decrease in stiffness increases both patch drag and the wake deficit behind the patch in a similar fashion as increasing the blockage of the patch. The average drag coefficient decreased with increasing Reynolds number and with increasing porosity. We found that the Reynolds stress (−u′v′) peak is not only shifted in the vortex structure because of shear layer interference, but also the intensity was weakened by increasing the porosity, which causes a weakening of the buckling of vorticity layers leading to a decline in vortex strength as well as increase in wake elongation. Show less Date Issued Subject Headings Fluid mechanics., Atmospheric models., Ocean currents--Mathematical models., Sediment transport., Estuarine oceanography. Document (PDF) Hafez, Mazen, Kim, Myeongsub, Florida Atlantic University, Department of Ocean and Mechanical Engineering, College of Engineering and Computer Science The elevated energy demand and high dependency on fossil fuels have directed researchers’ attention to promoting and advancing hydraulic fracturing (HF) operations for a sustainable energy future. Previous studies have demonstrated that the particle suspension and positioning in slick water play a vital role during the injection and shut-in stages of the HF operations. A significant challenge to HF is the premature particle settling and uneven particle distribution in a formation. Even though... Show moreThe elevated energy demand and high dependency on fossil fuels have directed researchers’ attention to promoting and advancing hydraulic fracturing (HF) operations for a sustainable energy future. Previous studies have demonstrated that the particle suspension and positioning in slick water play a vital role during the injection and shut-in stages of the HF operations. A significant challenge to HF is the premature particle settling and uneven particle distribution in a formation. Even though various research was conducted on the topic of particle transport, there still exist gaps in the fundamental particle-particle interaction mechanisms. This dissertation utilizes both experimental and numerical approaches to advance the state of the art in particle-particle interactions in various test conditions. Experimentally, the study utilizes high-speed imaging coupled with particle tracking velocimetry (PTV) and particle image velocimetry (PIV) to provide a space and time-resolved investigation of both two-particle and multi-particle interactions during gravitational settling, respectively. Show less Date Issued Subject Headings Hydraulic fracturing, Particle image velocimetry, Particle tracking velocimetry, Fluid mechanics research Document (PDF) Developing interpretive turbulence models from a database with applications to wind farms and shipboard operations. Schau, Kyle A., Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering This thesis presents a complete method of modeling the autospectra of turbulence in closed form via an expansion series using the von Kármán model as a basis function. It is capable of modeling turbulence in all three directions of fluid flow: longitudinal, lateral, and vertical, separately, thus eliminating the assumption of homogeneous, isotropic flow. A thorough investigation into the expansion series is presented, with the strengths and weaknesses highlighted. Furthermore, numerical... Show moreThis thesis presents a complete method of modeling the autospectra of turbulence in closed form via an expansion series using the von Kármán model as a basis function. It is capable of modeling turbulence in all three directions of fluid flow: longitudinal, lateral, and vertical, separately, thus eliminating the assumption of homogeneous, isotropic flow. A thorough investigation into the expansion series is presented, with the strengths and weaknesses highlighted. Furthermore, numerical aspects and theoretical derivations are provided. This method is then tested against three highly complex flow fields: wake turbulence inside wind farms, helicopter downwash, and helicopter downwash coupled with turbulence shed from a ship superstructure. These applications demonstrate that this method is remarkably robust, that the developed autospectral models are virtually tailored to the design of white noise driven shaping filters, and that these models in closed form facilitate a greater understanding of complex flow fields in wind engineering. Show less Date Issued Subject Headings Fluid mechanics, Renewable energy sources, Von Kármán, Theodore -- 1881-1963, Wind energy conservation systems, Wind power, Wind turbines -- Aerodynamics Document (PDF) Some corrosion problems associated with underwater turbines. Miglis, Yohann., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering This thesis deals with corrosion problems of underwater turbines in marine environment. The effect of a tensile stress on the uniform corrosion rate of a metal bar is studied, and an analytical model predicting the time of service of a bar under a tensile load in a corrosive environment is proposed. Stress corrosion relationships are provided for different type of alloys, and different types of relationships. Dolinskii's and Gutman's models are studied and extended to a general order... Show moreThis thesis deals with corrosion problems of underwater turbines in marine environment. The effect of a tensile stress on the uniform corrosion rate of a metal bar is studied, and an analytical model predicting the time of service of a bar under a tensile load in a corrosive environment is proposed. Stress corrosion relationships are provided for different type of alloys, and different types of relationships. Dolinskii's and Gutman's models are studied and extended to a general order polynomial, along with a Least Square and Spline Interpolation of the experimental data. In a second part, the effect of the passive film, delaying the initiation of the corrosion process, is studied. Finally, an algorithm predicting the time of service of a cracked bar is provided, using the stress corrosion assumption, along with a validation using experimental data. Show less Date Issued Subject Headings Turbines, Stress corrosion, Testing, Computational fluid dynamics, Stress corrosion, Fracture mechanics, Measurement, Alloys, Stress corrosion, Testing, Alloys, Corrosion fatigue, Testing Document (PDF) Design and Deployment Analysis of Morphing Ocean Structure. Li, Yanjun, Su, Tsung-Chow, Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering As humans explore greater depths of Earth’s oceans, there is a growing need for the installation of subsea structures. 71% of the earth’s surface is ocean but there are limitations inherent in current detection instruments for marine applications leading to the need for the development of underwater platforms that allow research of deeper subsea areas. Several underwater platforms including Autonomous Underwater Vehicles (AUVs), Remote Operated Vehicles (ROVs), and wave gliders enable more... Show moreAs humans explore greater depths of Earth’s oceans, there is a growing need for the installation of subsea structures. 71% of the earth’s surface is ocean but there are limitations inherent in current detection instruments for marine applications leading to the need for the development of underwater platforms that allow research of deeper subsea areas. Several underwater platforms including Autonomous Underwater Vehicles (AUVs), Remote Operated Vehicles (ROVs), and wave gliders enable more efficient deployment of marine structures. Deployable structures are able to be compacted and transported via AUV to their destination then morph into their final form upon arrival. They are a lightweight, compact solution. The wrapped package includes the deployable structure, underwater pump, and other necessary instruments, and the entire package is able to meet the payload capability requirements. Upon inflation, these structures can morph into final shapes that are a hundred times larger than their original volume, which extends the detection range and also provides long-term observation capabilities. This dissertation reviews underwater platforms, underwater acoustics, imaging sensors, and inflatable structure applications then proposes potential applications for the inflatable structures. Based on the proposed applications, a conceptual design of an underwater tubular structure is developed and initial prototypes are built for the study of the mechanics of inflatable tubes. Numerical approaches for the inflation process and bending loading are developed to predict the inflatable tubular behavior during the structure’s morphing process and under different loading conditions. The material properties are defined based on tensile tests. The numerical results are compared with and verified by experimental data. The methods used in this research provide a solution for underwater inflatable structure design and analysis. Several ocean morphing structures are proposed based on the inflatable tube analysis. Show less Date Issued Subject Headings Air-supported structures--Design and construction., Remote submersibles--Design and construction., Tensile architecture., Fluid mechanics., Structural dynamics., Ocean engineering., Adaptive control systems. Document (PDF) Subjecting the CHIMERA supernova code to two hydrodynamic test problems, (i) Riemann problem and (ii) Point blast explosion. Ahsan, Abu Salah M., Charles E. Schmidt College of Science, Department of Physics A Shock wave as represented by the Riemann problem and a Point-blast explosion are two key phenomena involved in a supernova explosion. Any hydrocode used to simulate supernovae should be subjected to tests consisting of the Riemann problem and the Point-blast explosion. L. I. Sedov's solution of Point-blast explosion and Gary A. Sod's solution of a Riemann problem have been re-derived here from one dimensional fluid dynamics equations . Both these problems have been solved by using the idea... Show moreA Shock wave as represented by the Riemann problem and a Point-blast explosion are two key phenomena involved in a supernova explosion. Any hydrocode used to simulate supernovae should be subjected to tests consisting of the Riemann problem and the Point-blast explosion. L. I. Sedov's solution of Point-blast explosion and Gary A. Sod's solution of a Riemann problem have been re-derived here from one dimensional fluid dynamics equations . Both these problems have been solved by using the idea of Self-similarity and Dimensional analysis. The main focus of my research was to subject the CHIMERA supernova code to these two hydrodynamic tests. Results of CHIMERA code for both the blast wave and Riemann problem have then been tested by comparing with the results of the analytic solution. Show less Date Issued Subject Headings Mathematical physics, Continuum mechanics, Number theory, Supernovae, Data processing, Shock waves, Fluid dynamics Document (PDF)	{"url":"http://fau.digital.flvc.org/islandora/search/catch_all_subjects_mt%3A(Fluid%20mechanics)","timestamp":"2024-11-08T07:35:15Z","content_type":"text/html","content_length":"178780","record_id":"<urn:uuid:df692ba0-eeee-4906-910f-a216fcd2723b>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00895.warc.gz"}
How It All Works If you are confused by the stats in the boxscores or in Stats Drop, here's a short reference guide to what the jargon means. This is an abbreviated version of the full How It All Works explainer on pythagonrl.com. Pythagorean expectation: There is a relationship between for and against and winning percentage, which is expressed by the Pythagorean expectation formula. This formula is used to estimate the number of wins a team should have based on their points scored and conceded. Generally, if a team outperforms their Pythagorean expectation (that is, wins more games than predicted by the formula) they will win fewer games than predicted by the formula in the following season, all other things being equal, and vice versa. Pythagorean expectation gets increasingly accurate at estimating win percentage over a longer time period. SCWP: Should-a Would-a Could-a Points utilises metres gained and conceded and line breaks gained and conceded to estimate the number of points that the team should have scored and conceded. As this metric utilises repeatable statistics that are less prone to randomness to estimate team quality, it is marginally more reliable than looking at just the scoreboard and is a good measure of a team’s opportunities. The ratio of converting these opportunities to actual points (or defending them) is referred to as the team’s efficiency. When SCWP are used in a Pythagorean expectation calculation, in lieu of actual points, these are called 2nd Order Wins. Taylor Player Ratings: Taylors (Ty) are the units for measuring production, the sum of valuable work done on the rugby league field, as measured by counting statistics that correlate with winning (e.g. tries, run metres, breaks, assists, etc). Teams that have higher production tend to win more games and teams with highly productive players tend to have higher production. Taylors by themselves can be misleading, so we have: • TPR: Taylor Player Rating. This compares the amount of production done by the player to the average player in that position, adjusting for time spent on the field. An average player has a rating of approximately .100, with fringe first graders sitting at .060 and top players nearing .180. To qualify for TPR, a player must play at least five games in a regular season. • WARG: Wins Above Reserve Grade. This compares a player's production that to a typical fringe first grader in that position to estimate the number of additional wins the player's team gains by having him on the roster. This concept was explored in What makes a million dollar NRL player? and Rugby league’s replacement player. The women’s equivalent to Taylors is Teitzels (Tz) and we make the distinction as the dataset for the women’s game is more limited. Elo ratings: Elo ratings were developed by Arpad Elo to rank chess players and are now used in FIFA's official world rankings. I've been using Elo ratings since 2017 to assess the quality of rugby league teams. The variables behind each system and league are different but typically, the average rating is 1500 and a higher rating reflects a better team. We can use the difference in Elo ratings to calculate the winning probability of two teams. I maintain two systems for each league - Form ratings are designed to reflect short term performance and move quickly to reflect recent results. The system variables are optimised to maximise head-to-head tipping success. When two teams match up, an expected margin is estimated between the two teams based on their respective ratings. If a team beats the expected margin, and even if they lose the match, their rating goes up by exactly the same amount the other team's rating goes down. Form ratings only track regular season performance. Class ratings are slower moving than form ratings and take multiple seasons to change significantly. Unlike form ratings, class ratings go up only when you win. They go up more for winning finals games and more still for winning grand finals. Class ratings reflect team's innate quality and act as a handbrake from looking too closely at the last couple of matches. For example, a team wrecked by Origin selections may have a poor form rating at the start of August but will maintain a high class rating. Run and Tackle Shares over Expected (Run SoE and Tkl SoE): These are bastardised versions of the League Eye Test’s Run% and Tackle%. Each player’s runs and tackles are calculated as a share of the team’s total runs and tackles. The average share of runs and tackles made by all players in the NRL at that position is then subtracted from this number, resulting in a number that is positive for players who had a higher proportion of runs and tackles than the average player in their position and negative for those who had a lower proportion. As the total shares of runs and tackles adds up to 100% across the team (i.e. if one player’s share is over, another’s by definition must be under), this metric is not predictive and unsuitable for non-trivial player comparisons. However, SoE can describe playing styles and highlight effort areas that Taylors cannot.	{"url":"https://www.maroonobserver.com/p/how-it-all-works","timestamp":"2024-11-03T15:23:09Z","content_type":"text/html","content_length":"110575","record_id":"<urn:uuid:22936c42-0084-487b-89c0-cd607d47f1ee>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00767.warc.gz"}
S^3G^2: A Scalable Shell Sequence Graph Generator General information Graphs are commonly used to model the relationships between various entities. These graphs can be enormously large and thus, scalable graph analysis has been the subject of many research efforts. However, the lack of publicly available data is a major setback. Many researchers have since focused their efforts to generate realistic synthetic graph generators to alleviate this problem and significant progress has been made on scalable graph generation that preserve some important graph properties (e.g., degree distribution, clustering coefficients). In this work, we study how to sample a graph from the space of graphs with a given shell distribution. Shell distribution is related to the k-core, which is the largest subgraph where each vertex is connected to at least k other vertices. A k-shell is the subset of vertices that are in k-core but not (k+1)-core, and the shell distribution comprises the sizes of these shells. Core decompositions are widely used to extract information from graphs and to speed up other computations. We present a scalable graph generator that, given a shell decomposition of a graph, generates a random graph that conforms to it. S^3G^2 is a software package, implementing a sequential, shared memory parallel, and a distributed memory version of a Shell Sequence Graph Generator. The main sequential idea is proposed by [Karwa et al.’17]. We focus on preserving the statistical properties of the sequential implementation [Karwa et al.’17]. The approaches are ultimately the same, aside from the intermediate steps to reach there, thus, any claim made about the graphs generated by [Karwa et al.’17] applies to the implementations in this package as well. The software package generates binary CSR format graphs with directed edges. The MPI implementation can also generate directed edge lists per processor. These can be concatenated and reported. with the bash script runAndMerge.sh. The S^3G^2 consists of 3 parts. Sequential is a new C++ implementation of [Karwa et al.’17] with some minor optimizations. Shmem has the implementation for shared memory NUMA systems. It uses C++ Threads library and some utilities from C++17. It has been tested with G++-8.3 and G++-9.2. MPI has the distributed memory implementation. Has been successfully compiled and run with Intel MPI, OpenMPI-3/4, and MVAPICH-2.2/2.3 The library relies on some open-source and public packages: • SPart (directly embedded to the source folder at the time of usage). [Karwa et al.’17] V. Karwa, M. J. Pelsmajer, S. Petrovic ́, D. Stasi, and D. Wilburne, “Statistical models for cores decomposition of an undirected random graph,” Electron. J. Statist., vol. 11, no. 1, pp. 1949–1982, 2017. If you use , please cite: • M. Yusuf Özkaya, M. Fatih Balin, Ali Pinar, Ümit V. Çatalyürek, "A scalable graph generation algorithm to sample over a given shell distribution", 2020 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), Workshop on Graphs, Architectures, Programming, and Learning, May 2020. to appear . Latest release: S3G2 (Updated 03/02/2020) If you have any questions or comments, please contact TDALab.	{"url":"http://tda.gatech.edu/software/s3g2/index.html","timestamp":"2024-11-08T20:46:43Z","content_type":"text/html","content_length":"18179","record_id":"<urn:uuid:e9e3b04f-a156-489a-9de8-f7f16b91a75b>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00352.warc.gz"}
Solve problems involving the calculation of percentages of whole numbers or measures such as 15% of 360 and the use of percentages for comparison ** New tablet-friendly version added 14th February 2018. Please let me know if you have any problems - support@mathsframe.co.uk Shoot the spaceship with the correct answer and dodge the incoming fire. A fun game to practise a wide range of key mathematical skills. There are over a hundred carefully differentiated levels linked to objectives from the new maths curriculum. The game can be used to teach: Multiplication, Addition, Reading Numbers, Subtraction, Fractions of Numbers, Roman Numerals, Rounding Numbers, Division, Converting Fractions to Decimals, Converting Fractions to Percentages, Telling the Time in Words, Recognising Multiples, Factors, Prime, Square and Cube Numbers, and Simplifying Fractions. A full list of levels is below. This game is also available as an iOS and Android app.	{"url":"https://mathsframe.co.uk/en/resources/category/377/solve-problems-involving-the-calculation-of-percentages-of-whole-numbers-or-measures-","timestamp":"2024-11-02T08:06:03Z","content_type":"text/html","content_length":"38948","record_id":"<urn:uuid:c17937b7-6be8-4bef-8cdf-f505e2680122>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00313.warc.gz"}
Punto Banco Regulations and Strategy Mar 14 2016 Baccarat Banque Standards Baccarat banque is gambled on with eight decks in a dealer’s shoe. Cards valued less than ten are counted at face value and with 10, J, Q, K are zero, and A is one. Wagers are placed on the ‘banker’, the ‘player’, or on a tie (these aren’t actual people; they just represent the two hands to be dealt). Two hands of two cards are then given to the ‘bank’ and ‘player’. The value for every hand is the total of the cards, but the 1st digit is ignored. For instance, a hand of 5 and six has a score of 1 (5 plus 6 equals 11; ditch the initial ‘1′). A additional card could be given depending on the following rules: - If the player or house gets a total of eight or 9, the two players hold. - If the gambler has 5 or less, she hits. Players otherwise hold. - If the player stands, the bank hits on a total lower than five. If the gambler hits, a guide is employed to decide if the banker stands or takes a card. Punto Banco Odds The bigger of the 2 totals wins. Winning bets on the banker payout 19:20 (even money less a 5 percent commission. Commission are tracked and paid off once you leave the game so ensure you still have money around before you depart). Winning bets on the gambler pays one to one. Winning bets for a tie normally pays 8 to 1 but on occasion 9 to 1. (This is a bad wager as ties occur less than one in every ten rounds. Be cautious of putting money on a tie. Although odds are astonishingly better for 9:1 versus 8:1) Played correctly baccarat banque offers relatively decent odds, apart from the tie wager of course. Baccarat Method As with all games baccarat chemin de fer has a few accepted myths. One of which is similar to a false impression in roulette. The past isn’t a fore-teller of events yet to happen. Recording previous outcomes at a table is a bad use of paper and a snub to the tree that gave its life for our stationary desires. The most familiar and probably the most favorable course of action is the 1-3-2-6 tactic. This tactic is used to build up earnings and limit losses. Start by betting 1 dollar. If you succeed, add another to the two on the table for a sum of 3 dollars on the second bet. Should you succeed you will have six on the table, take away four so you have 2 on the third round. If you win the third wager, put down two to the four on the table for a total of 6 on the 4th bet. If you don’t win on the initial wager, you take a loss of one. A profit on the 1st wager followed by a hit on the second creates a loss of two. Wins on the first 2 with a loss on the 3rd gives you with a profit of two. And wins on the 1st three with a loss on the fourth means you balance the books. Succeeding at all 4 rounds gives you with 12, a gain of 10. This means you will be able to lose the 2nd wager 5 instances for every favorable streak of four bets and in the end, balance the books. You must be logged in to post a comment.	{"url":"http://beamultimillionaire.com/2016/03/14/punto-banco-regulations-and-strategy/","timestamp":"2024-11-02T04:13:18Z","content_type":"application/xhtml+xml","content_length":"27604","record_id":"<urn:uuid:88b09243-c9e5-4a8f-9ba7-250f35066d87>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00548.warc.gz"}
Inner Product - (Control Theory) - Vocab, Definition, Explanations \| Fiveable Inner Product from class: Control Theory The inner product is a mathematical operation that takes two vectors and produces a scalar, capturing the idea of geometric concepts like length and angle between vectors. It generalizes the dot product, allowing for the definition of orthogonality and vector projections in higher-dimensional spaces. The inner product is foundational in linear algebra and plays a crucial role in various applications such as function spaces and quantum mechanics. congrats on reading the definition of Inner Product. now let's actually learn it. 5 Must Know Facts For Your Next Test 1. The inner product is linear in both arguments, meaning it satisfies properties like distributivity and scalar multiplication. 2. For two vectors to be orthogonal, their inner product must equal zero, indicating they are at a right angle to each other. 3. In addition to Euclidean spaces, inner products can be defined in function spaces, allowing for concepts like orthogonal functions. 4. The Cauchy-Schwarz inequality is an important property related to the inner product, providing a bound on the magnitude of the inner product of two vectors. 5. Inner products can lead to the concept of dual spaces, where each vector is associated with a linear functional via the inner product. Review Questions • How does the inner product relate to geometric concepts such as angles and lengths in vector spaces? □ The inner product provides a way to measure angles and lengths between vectors by producing a scalar value that reflects their relationship. Specifically, the cosine of the angle between two vectors can be found using the formula involving their inner product divided by the product of their norms. This connection allows us to determine not just how far apart two vectors are but also how aligned they are in terms of direction. • Explain how the properties of linearity and symmetry in inner products contribute to their applications in linear algebra. □ Linearity and symmetry are key properties of inner products that make them powerful tools in linear algebra. Linearity ensures that the inner product behaves predictably when scaling or adding vectors, facilitating calculations involving combinations of vectors. Symmetry means that switching the order of vectors does not affect the result, leading to consistent interpretations across various applications, such as defining projections and analyzing orthogonality. • Evaluate the significance of the Cauchy-Schwarz inequality in relation to the inner product and its implications in higher-dimensional spaces. □ The Cauchy-Schwarz inequality highlights an essential relationship between vectors in any vector space with an inner product by stating that the absolute value of their inner product cannot exceed the product of their magnitudes. This inequality has profound implications in higher-dimensional spaces, ensuring that concepts like angles and lengths remain consistent across dimensions. It is instrumental in proving results about convergence, optimization, and even aspects of machine learning by establishing bounds on projections and correlations between data ยฉ 2024 Fiveable Inc. All rights reserved. APยฎ and SATยฎ are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.	{"url":"https://library.fiveable.me/key-terms/control-theory/inner-product","timestamp":"2024-11-07T03:56:40Z","content_type":"text/html","content_length":"158596","record_id":"<urn:uuid:ad713d68-93bc-455d-b996-62c2f4955d3e>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00680.warc.gz"}
Behaviors of Functions Learning Outcomes • Determine where a function is increasing, decreasing, or constant • Find local extrema of a function from a graph • Describe behavior of the toolkit functions As part of exploring how functions change, we can identify intervals over which the function is changing in specific ways. We say that a function is increasing on an interval if the function values increase as the input values increase within that interval. Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval. The average rate of change of an increasing function is positive, and the average rate of change of a decreasing function is negative. The graph below shows examples of increasing and decreasing intervals on a function. This video further explains how to find where a function is increasing or decreasing. While some functions are increasing (or decreasing) over their entire domain, many others are not. A value of the output where a function changes from increasing to decreasing (as we go from left to right, that is, as the input variable increases) is called a local maximum. If a function has more than one, we say it has local maxima. Similarly, a value of the output where a function changes from decreasing to increasing as the input variable increases is called a local minimum. The plural form is “local minima.” Together, local maxima and minima are called local extrema, or local extreme values, of the function. (The singular form is “extremum.”) Often, the term local is replaced by the term relative. In this text, we will use the term local. A function is neither increasing nor decreasing on an interval where it is constant. A function is also neither increasing nor decreasing at extrema. Note that we have to speak of local extrema, because any given local extremum as defined here is not necessarily the highest maximum or lowest minimum in the functionâ€™s entire domain. For the function below, the local maximum is 16, and it occurs at [latex]x=-2[/latex]. The local minimum is [latex]-16[/latex] and it occurs at [latex]x=2[/latex]. To locate the local maxima and minima from a graph, we need to observe the graph to determine where the graph attains its highest and lowest points, respectively, within an open interval. Like the summit of a roller coaster, the graph of a function is higher at a local maximum than at nearby points on both sides. The graph will also be lower at a local minimum than at neighboring points. The graph below illustrates these ideas for a local maximum. These observations lead us to a formal definition of local extrema. A General Note: Local Minima and Local Maxima A function [latex]f[/latex] is an increasing function on an open interval if [latex]f\left(b\right)>f\left(a\right)[/latex] for any two input values [latex]a[/latex] and [latex]b[/latex] in the given interval where [latex]b>a[/latex]. A function [latex]f[/latex] is a decreasing function on an open interval if [latex]f\left(b\right)<f\left(a\right)[/latex] for any two input values [latex]a[/latex] and [latex]b[/latex] in the given interval where [latex]b>a[/latex]. A function [latex]f[/latex] has a local maximum at [latex]x=b[/latex] if there exists an interval [latex]\left(a,c\right)[/latex] with [latex]a<b<c[/latex] such that, for any [latex]x[/latex] in the interval [latex]\left(a,c\right)[/latex], [latex]f\left(x\right)\le f\left(b\right)[/latex]. Likewise, [latex]f[/latex] has a local minimum at [latex]x=b[/latex] if there exists an interval [latex]\ left(a,c\right)[/latex] with [latex]a<b<c[/latex] such that, for any [latex]x[/latex] in the interval [latex]\left(a,c\right)[/latex], [latex]f\left(x\right)\ge f\left(b\right)[/latex]. Example: Finding Increasing and Decreasing Intervals on a Graph Given the function [latex]p\left(t\right)[/latex] in the graph below, identify the intervals on which the function appears to be increasing. Show Solution Tip for success: increasing/decreasing behavior The behavior of the function values of the graph of a function is read over the x-axis, from left to right. That is, • a function is said to be increasing if its function values increase as x increases; • a function is said to be decreasing if its function values decrease as x increases. Example: Finding Local Extrema from a Graph Graph the function [latex]f\left(x\right)=\dfrac{2}{x}+\dfrac{x}{3}[/latex]. Then use the graph to estimate the local extrema of the function and to determine the intervals on which the function is Show Solution tip for success: reading extrema Recall that points on the graph of a function are ordered pairs in the form of [latex]\left(\text{input, output}\right) \quad = \quad \left(x, f(x)\right)[/latex]. If a function’s graph has a local minimum or maximum at some point [latex]\left(x, f(x)\right)[/latex], we say “the extrema occurs at [latex]x[/latex], and that the minimum or maximum is [latex]f(x)[/latex].” Try It Graph the function [latex]f\left(x\right)={x}^{3}-6{x}^{2}-15x+20[/latex] to estimate the local extrema of the function. Use these to determine the intervals on which the function is increasing and Show Solution Example: Finding Local Maxima and Minima from a Graph For the function [latex]f[/latex] whose graph is shown below, find all local maxima and minima. Show Solution tip for success: toolkit functions The toolkit functions continue to appear throughout the course. Have you memorized them yet? Would you be able to sketch a quick graph of each from its equation? Analyzing the Toolkit Functions for Increasing or Decreasing Intervals We will now return to our toolkit functions and discuss their graphical behavior in the table below. Function Increasing/Decreasing Example Constant Function[latex]f\left(x\right)={c}[/latex] Neither increasing nor decreasing Identity Function[latex]f\left(x\right)={x}[/latex] Increasing Increasing on [latex]\left(0,\infty\right)[/latex]Decreasing on [latex]\left(-\infty,0\right)[/latex] Quadratic Function[latex]f\left(x\right)={x}^{2}[/latex] Minimum at [latex]x=0[/latex] Cubic Function[latex]f\left(x\right)={x}^{3}[/latex] Increasing Reciprocal[latex]f\left(x\right)=\frac{1}{x}[/latex] Decreasing [latex]\left(-\infty,0\right)\cup\left(0,\infty\right)[/latex] Reciprocal Squared[latex]f\left(x\right)=\frac{1}{{x}^{2}}[/latex] Increasing on [latex]\left(-\infty,0\right)[/latex]Decreasing on [latex]\left(0,\infty\right)[/latex] Cube Root[latex]f\left(x\right)=\sqrt[3]{x}[/latex] Increasing Square Root[latex]f\left(x\right)=\sqrt{x}[/latex] Increasing on [latex]\left(0,\infty\right)[/latex] Increasing on [latex]\left(0,\infty\right)[/latex]Decreasing on [latex]\left(-\infty,0\right)[/latex] Absolute Value[latex]f\left(x\right)=\|x\|[/latex] Minimum at [latex]x=0[/latex] Use a graph to locate the absolute maximum and absolute minimum of a function There is a difference between locating the highest and lowest points on a graph in a region around an open interval (locally) and locating the highest and lowest points on the graph for the entire domain. The [latex]y\text{-}[/latex] coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum, respectively. To locate absolute maxima and minima from a graph, we need to observe the graph to determine where the graph attains it highest and lowest points on the domain of the function. Not every function has an absolute maximum or minimum value. The toolkit function [latex]f\left(x\right)={x}^{3}[/latex] is one such function. A General Note: Absolute Maxima and Minima The absolute maximum of [latex]f[/latex] at [latex]x=c[/latex] is [latex]f\left(c\right)[/latex] where [latex]f\left(c\right)\ge f\left(x\right)[/latex] for all [latex]x[/latex] in the domain of The absolute minimum of [latex]f[/latex] at [latex]x=d[/latex] is [latex]f\left(d\right)[/latex] where [latex]f\left(d\right)\le f\left(x\right)[/latex] for all [latex]x[/latex] in the domain of Example: Finding Absolute Maxima and Minima from a Graph For the function [latex]f[/latex] shown below, find all absolute maxima and minima. Show Solution	{"url":"https://courses.lumenlearning.com/waymakercollegealgebracorequisite/chapter/behaviors-of-functions/","timestamp":"2024-11-07T23:15:35Z","content_type":"text/html","content_length":"69544","record_id":"<urn:uuid:e993fdf9-1b58-4dee-9516-ca15e401d406>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00225.warc.gz"}
Antiderivative - (Intro to Abstract Math) - Vocab, Definition, Explanations \| Fiveable from class: Intro to Abstract Math An antiderivative is a function whose derivative is equal to a given function. In other words, if you have a function $$f(x)$$, an antiderivative of $$f(x)$$ is a function $$F(x)$$ such that $$F'(x) = f(x)$$. This concept is fundamental in calculus, especially in the process of integration, where finding the antiderivative allows us to evaluate definite integrals and solve differential congrats on reading the definition of antiderivative. now let's actually learn it. 5 Must Know Facts For Your Next Test 1. Antiderivatives are not unique; they can differ by a constant since the derivative of a constant is zero. 2. The process of finding an antiderivative is called integration, and it often involves techniques such as substitution and integration by parts. 3. Every continuous function has at least one antiderivative, which can be demonstrated using the Mean Value Theorem. 4. The notation for an antiderivative often includes an arbitrary constant, typically written as $$C$$, leading to the general form $$F(x) + C$$. 5. Antiderivatives play a crucial role in solving differential equations, allowing us to find functions that satisfy specific conditions or behaviors. Review Questions • How do you find an antiderivative for a simple polynomial function like $$f(x) = 3x^2$$? □ To find the antiderivative of $$f(x) = 3x^2$$, you can use the power rule for integration. According to this rule, you increase the exponent by one and then divide by the new exponent. Thus, the antiderivative is $$F(x) = \frac{3}{3}x^{2+1} + C = x^3 + C$$, where $$C$$ represents any constant. • What is the connection between antiderivatives and definite integrals according to the Fundamental Theorem of Calculus? □ The Fundamental Theorem of Calculus states that if $$F$$ is an antiderivative of a continuous function $$f$$ on an interval $$[a, b]$$, then the definite integral of $$f$$ from $$a$$ to $$b$$ can be calculated using the values of $$F$$ at those points: $$\int_{a}^{b} f(x) \, dx = F(b) - F(a)$$. This highlights how finding an antiderivative allows us to evaluate areas under curves • Evaluate and analyze why understanding antiderivatives is crucial for solving real-world problems in physics and engineering. □ Understanding antiderivatives is vital in fields like physics and engineering because they allow us to reverse-engineer rates of change into original functions. For instance, if we know the velocity of an object over time (the derivative), we can find its position by determining its antiderivative. This application highlights how concepts from calculus translate into practical scenarios such as motion analysis, area calculations, and even in creating models for various phenomena in nature and technology. Â© 2024 Fiveable Inc. All rights reserved. APÂ® and SATÂ® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.	{"url":"https://library.fiveable.me/key-terms/fundamentals-abstract-math/antiderivative","timestamp":"2024-11-09T13:14:05Z","content_type":"text/html","content_length":"141524","record_id":"<urn:uuid:78f224d4-b2be-4c02-81b5-d62acdeb5717>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00586.warc.gz"}
Python for Biostatistics: Analyzing Infectious Diseases Data - DevCourseWeb.com Python for Biostatistics: Analyzing Infectious Diseases Data Forecast infectious disease rate, build epidemiological modelling, and map the spread of infectious disease with heatmap Welcome to Python for Biostatistics: Analyzing Infectious Diseases Data course. This is a comprehensive project-based course where you will learn step by step on how to perform complex analysis and visualization on infectious diseases datasets. This course is a perfect combination between biostatistics and Python, equipping you with the tools and techniques to tackle real-world challenges in public health. The course will be mainly concentrating on three major aspects, the first one is data analysis where you will explore the infectious diseases data from multiple perspectives, the second one is time series forecasting where you will be guided step by step on how to forecast the spread of infectious diseases using STL model, and the third one is public health policy where you will learn how to make a data driven public health policy based on epidemiological modeling. In the introduction session, you will learn the basic fundamentals of biostatistics, such as getting to know more about challenges that we commonly face when analyzing biostatistics data and statistical models that we will use, for instance STL which stands for seasonal trend decomposition. Then, you will continue by learning how to calculate infectious disease transmission using Kermack-McKendrick equation, this is a very important concept that you need to understand before getting into the coding session. Afterward, you will also learn several factors that can potentially accelerate the spread of infectious diseases, such as population density, healthcare accessibility, and antigenic variation. Once you have learnt all necessary information about biostatistics, we will start the project. Firstly, you will be guided step by step on how to set up Google Colab IDE. Not only that, you will also learn how to find and download infectious diseases dataset from Kaggle. Once, everything is ready, we will enter the main section of the course which is the project section The project will be consisted of three main parts, the first part is to conduct exploratory data analysis, the second part is to build forecasting model to predict the spread of the diseases in the future using time series model, meanwhile the third part is to perform epidemiological modelling and use the result to develop a public health policy to slow down the spread of the infectious disease. What you’ll learn • Learn the basic fundamentals of biostatistics and infectious disease analysis. • Learn how to find correlation between population and disease rate. • Learn how to analyze infected patient demographics. • Learn how to map infectious disease per county using heatmap. • Learn how to analyze infectious disease yearly trend. • Learn how to perform confidence interval analysis. • Learn how to forecast infectious disease rate using time series decomposition. • Learn how to do epidemiological modeling using SIR model. • Learn how to perform public health policy evaluation. • Learn how to calculate infectious disease transmission rate using SIR model. • Learn several factors that accelerate the spread of infectious disease, such as population density, herd immunity, and antigenic variation. • Learn how to detect potential outliers using Z score method. • Learn how to clean dataset by removing missing rows and duplicate values. • Learn how to find and download datasets from Kaggle. Course Content • Introduction –> 3 lectures • 15min. • Tools, IDE, and Datasets –> 1 lecture • 11min. • Introduction to Biostatistics –> 1 lecture • 8min. • Calculating Infectious Disease Transmission with SIR Model –> 1 lecture • 10min. • Factors That Accelerate the Spread of Infectious Disease –> 1 lecture • 5min. • Setting Up Google Colab IDE –> 1 lecture • 5min. • Finding & Downloading Infectious Disease Dataset From Kaggle –> 1 lecture • 5min. • Project Preparation –> 2 lectures • 10min. • Cleaning Infectious Disease Dataset by Removing Missing Values & Duplicates –> 1 lecture • 7min. • Detecting Potential Outliers with Z Score –> 1 lecture • 9min. • Finding Correlation Between Population & Disease Rate –> 1 lecture • 8min. • Analyzing Infected Patients Demographics –> 1 lecture • 14min. • Mapping Infectious Disease per County with Heatmap –> 1 lecture • 14min. • Analyzing Infectious Disease Yearly Trend –> 1 lecture • 15min. • Performing Confidence Interval Analysis –> 1 lecture • 5min. • Forecasting Infectious Disease Rate with Time Series –> 1 lecture • 13min. • Epidemiological Modelling with SIR Model –> 1 lecture • 14min. • Public Health Policy Evaluation –> 1 lecture • 13min. • Conclusion & Summary –> 1 lecture • 5min. Welcome to Python for Biostatistics: Analyzing Infectious Diseases Data course. This is a comprehensive project-based course where you will learn step by step on how to perform complex analysis and visualization on infectious diseases datasets. This course is a perfect combination between biostatistics and Python, equipping you with the tools and techniques to tackle real-world challenges in public health. The course will be mainly concentrating on three major aspects, the first one is data analysis where you will explore the infectious diseases data from multiple perspectives, the second one is time series forecasting where you will be guided step by step on how to forecast the spread of infectious diseases using STL model, and the third one is public health policy where you will learn how to make a data driven public health policy based on epidemiological modeling. In the introduction session, you will learn the basic fundamentals of biostatistics, such as getting to know more about challenges that we commonly face when analyzing biostatistics data and statistical models that we will use, for instance STL which stands for seasonal trend decomposition. Then, you will continue by learning how to calculate infectious disease transmission using Kermack-McKendrick equation, this is a very important concept that you need to understand before getting into the coding session. Afterward, you will also learn several factors that can potentially accelerate the spread of infectious diseases, such as population density, healthcare accessibility, and antigenic variation. Once you have learnt all necessary information about biostatistics, we will start the project. Firstly, you will be guided step by step on how to set up Google Colab IDE. Not only that, you will also learn how to find and download infectious diseases dataset from Kaggle. Once, everything is ready, we will enter the main section of the course which is the project section The project will be consisted of three main parts, the first part is to conduct exploratory data analysis, the second part is to build forecasting model to predict the spread of the diseases in the future using time series model, meanwhile the third part is to perform epidemiological modelling and use the result to develop a public health policy to slow down the spread of the infectious disease. First of all, before getting into the course, we need to ask this question to ourselves: why should we learn biostatistics, particularly infectious diseases analysis? Well, there are many reasons why, firstly, if you are interested in working in the public health or healthcare industry, having biostatistics knowledge would be very beneficial and help you to level up your career. In addition to that, you will also learn a lot of valuable skill sets that can be implemented in other projects, for example, time series decomposition can be used to forecast stock, real estate, commodity, and cryptocurrency markets. Last but not least, this course will also train you to be a better public health policy maker as you will extensively learn how to make data driven decisions and take other external factors into consideration. Below are things that you can expect to learn from this course: • Learn the basic fundamentals of biostatistics and infectious disease analysis • Learn how to calculate infectious disease transmission rate using SIR model • Learn several factors that accelerate the spread of infectious disease, such as population density, herd immunity, and antigenic variation • Learn how to find and download datasets from Kaggle • Learn how to clean dataset by removing missing rows and duplicate values • Learn how to detect potential outliers using Z score method • Learn how to find correlation between population and disease rate • Learn how to analyze infected patient demographics • Learn how to map infectious disease per county using heatmap • Learn how to analyze infectious disease yearly trend • Learn how to perform confidence interval analysis • Learn how to forecast infectious disease rate using time series decomposition model • Learn how to do epidemiological modeling using SIR model • Learn how to perform public health policy evaluation	{"url":"https://devcourseweb.com/tutorials/development/python-for-biostatistics-analyzing-infectious-diseases-data/","timestamp":"2024-11-12T00:10:05Z","content_type":"application/xhtml+xml","content_length":"76889","record_id":"<urn:uuid:9a84da3f-2421-45af-ba7c-8295715f1ece>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00490.warc.gz"}
StatisticAttribute Estimate Type - TTL Representation This page is part of the HL7 Terminology (v5.2.0: Release) based on FHIR R4. This is the current published version in its permanent home (it will always be available at this URL). For a full list of available versions, see the Directory of published versions : StatisticAttribute Estimate Type - TTL Representation Draft as of 2020-04-09 Maturity Level: 5 Raw ttl \| Download @prefix fhir: <http://hl7.org/fhir/> . @prefix owl: <http://www.w3.org/2002/07/owl#> . @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> . @prefix xsd: <http://www.w3.org/2001/XMLSchema#> . # - resource ------------------------------------------------------------------- a fhir:CodeSystem ; fhir:nodeRole fhir:treeRoot ; fhir:id [ fhir:v "attribute-estimate-type"] ; # fhir:meta [ fhir:lastUpdated [ fhir:v "2020-04-09T21:10:28.568+00:00"^^xsd:dateTime ] ] ; # fhir:text [ fhir:status [ fhir:v "generated" ] ; fhir:div "<div xmlns=\"http://www.w3.org/1999/xhtml\"><p>This code system <code>http://terminology.hl7.org/CodeSystem/attribute-estimate-type</code> defines the following codes:</p><table class=\"codes\"><tr><td style=\"white-space:nowrap\"><b>Code</b></td><td><b>Display</b></td><td><b>Definition</b></td></tr><tr><td style=\"white-space:nowrap\">0000419<a name=\"attribute-estimate-type-0000419\"> </a></td><td>Cochran's Q statistic</td><td>A measure of heterogeneity accros study computed by summing the squared deviations of each study's estimate from the overall meta-analytic estimate, weighting each study's contribution in the same manner as in the meta-analysis.</td></tr><tr><td style=\"white-space:nowrap\">C53324<a name=\"attribute-estimate-type-C53324\"> </a></td><td>Confidence interval</td><td>A range of values considered compatible with the observed data at the specified confidence level.</td></tr><tr><td style=\"white-space:nowrap\">0000455<a name=\"attribute-estimate-type-0000455\"> </a></td><td>Credible interval</td><td>An interval of a posterior distribution which is such that the density at any point inside the interval is greater than the density at any point outside and that the area under the curve for that interval is equal to a prespecified probability level. For any probability level there is generally only one such interval, which is also often known as the highest posterior density region. Unlike the usual confidence interval associated with frequentist inference, here the intervals specify the range within which parameters lie with a certain probability. The bayesian counterparts of the confidence interval used in frequentists statistics.</td></tr><tr><td style=\"white-space:nowrap\">0000420<a name=\"attribute-estimate-type-0000420\"> </a></td><td>I-squared</td><td>The percentage of total variation across studies that is due to heterogeneity rather than chance. I2 can be readily calculated from basic results obtained from a typical meta-analysis as i2 = 100%×(q - df)/q, where q is cochran's heterogeneity statistic and df the degrees of freedom. Negative values of i2 are put equal to zero so that i2 lies between 0% and 100%. A value of 0% indicates no observed heterogeneity, and larger values show increasing heterogeneity. Unlike cochran's q, it does not inherently depend upon the number of studies considered. A confidence interval for i² is constructed using either i) the iterative non-central chi-squared distribution method of hedges and piggott (2001); or ii) the test-based method of higgins and thompson (2002). The non-central chi-square method is currently the method of choice (higgins, personal communication, 2006) – it is computed if the 'exact' option is selected.</td></tr><tr><td style=\"white-space:nowrap\">C53245<a name=\"attribute-estimate-type-C53245\"> </a></td><td>Interquartile range</td><td>The difference between the 3d and 1st quartiles is called the interquartile range and it is used as a measure of variability (dispersion).</td></tr><tr><td style=\"white-space:nowrap\">C44185<a name=\"attribute-estimate-type-C44185\"> </a></td><td>P-value</td><td>The probability of obtaining the results obtained, or more extreme results, if the hypothesis being tested and all other model assumptions are true.</td></tr><tr><td style=\"white-space:nowrap\">C38013<a name=\"attribute-estimate-type-C38013\"> </a></td><td>Range</td><td>The difference between the lowest and highest numerical values; the limits or scale of variation.</td></tr><tr><td style=\"white-space:nowrap\">C53322<a name=\"attribute-estimate-type-C53322\"> </a></td><td>Standard deviation</td><td>A measure of the range of values in a set of numbers. Standard deviation is a statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.</td></tr><tr><td style=\"white-space:nowrap\">0000037<a name=\"attribute-estimate-type-0000037\"> </a></td><td>Standard error of the mean</td><td>The standard deviation of the sample-mean's estimate of a population mean. It is calculated by dividing the sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population) by the square root of n , the size (number of observations) of the sample.</td></tr><tr><td style=\"white-space:nowrap\">0000421<a name=\"attribute-estimate-type-0000421\"> </a></td><td>Tau squared</td><td>An estimate of the between-study variance in a random-effects meta-analysis. The square root of this number (i.e. Tau) is the estimated standard deviation of underlying effects across studies.</td></tr><tr><td style=\"white-space:nowrap\">C48918<a name=\"attribute-estimate-type-C48918\"> </a></td><td>Variance</td><td>A measure of the variability in a sample or population. It is calculated as the mean squared deviation (MSD) of the individual values from their common mean. In calculating the MSD, the divisor n is commonly used for a population variance and the divisor n-1 for a sample variance.</td></tr></table></div>" ] ; # fhir:extension ( [ fhir:url [ fhir:v "http://hl7.org/fhir/StructureDefinition/structuredefinition-wg"^^xsd:anyURI ] ; fhir:value [ fhir:v "fhir" ] ] [ fhir:url [ fhir:v "http://hl7.org/fhir/StructureDefinition/structuredefinition-fmm"^^xsd:anyURI ] ; fhir:value [ fhir:v "5"^^xsd:integer ] ] ) ; # fhir:url [ fhir:v "http://terminology.hl7.org/CodeSystem/attribute-estimate-type"^^xsd:anyURI] ; # fhir:identifier ( [ fhir:system [ fhir:v "urn:ietf:rfc:3986"^^xsd:anyURI ] ; fhir:value [ fhir:v "urn:oid:2.16.840.1.113883.4.642.1.1413" ] ] ) ; # fhir:version [ fhir:v "0.1.0"] ; # fhir:name [ fhir:v "StatisticAttributeEstimateType"] ; # fhir:title [ fhir:v "StatisticAttribute Estimate Type"] ; # fhir:status [ fhir:v "draft"] ; # fhir:experimental [ fhir:v "false"^^xsd:boolean] ; # fhir:date [ fhir:v "2020-04-09T21:10:28+00:00"^^xsd:dateTime] ; # fhir:publisher [ fhir:v "HL7 (FHIR Project)"] ; # fhir:contact ( [ ( fhir:telecom [ fhir:system [ fhir:v "url" ] ; fhir:value [ fhir:v "http://hl7.org/fhir" ] ] [ fhir:system [ fhir:v "email" ] ; fhir:value [ fhir:v "fhir@lists.hl7.org" ] ] ) ] ) ; # fhir:description [ fhir:v "Method of reporting variability of estimates, such as confidence intervals, interquartile range or standard deviation."] ; # fhir:caseSensitive [ fhir:v "true"^^xsd:boolean] ; # fhir:valueSet [ fhir:v "http://terminology.hl7.org/ValueSet/attribute-estimate-type"^^xsd:anyURI ; fhir:link <http://terminology.hl7.org/ValueSet/attribute-estimate-type> ] ; # fhir:content [ fhir:v "complete"] ; # fhir:concept ( [ fhir:code [ fhir:v "0000419" ] ; fhir:display [ fhir:v "Cochran's Q statistic" ] ; fhir:definition [ fhir:v "A measure of heterogeneity accros study computed by summing the squared deviations of each study's estimate from the overall meta-analytic estimate, weighting each study's contribution in the same manner as in the meta-analysis." ] ] [ fhir:code [ fhir:v "C53324" ] ; fhir:display [ fhir:v "Confidence interval" ] ; fhir:definition [ fhir:v "A range of values considered compatible with the observed data at the specified confidence level." ] ] [ fhir:code [ fhir:v "0000455" ] ; fhir:display [ fhir:v "Credible interval" ] ; fhir:definition [ fhir:v "An interval of a posterior distribution which is such that the density at any point inside the interval is greater than the density at any point outside and that the area under the curve for that interval is equal to a prespecified probability level. For any probability level there is generally only one such interval, which is also often known as the highest posterior density region. Unlike the usual confidence interval associated with frequentist inference, here the intervals specify the range within which parameters lie with a certain probability. The bayesian counterparts of the confidence interval used in frequentists statistics." ] ] [ fhir:code [ fhir:v "0000420" ] ; fhir:display [ fhir:v "I-squared" ] ; fhir:definition [ fhir:v "The percentage of total variation across studies that is due to heterogeneity rather than chance. I2 can be readily calculated from basic results obtained from a typical meta-analysis as i2 = 100%×(q - df)/q, where q is cochran's heterogeneity statistic and df the degrees of freedom. Negative values of i2 are put equal to zero so that i2 lies between 0% and 100%. A value of 0% indicates no observed heterogeneity, and larger values show increasing heterogeneity. Unlike cochran's q, it does not inherently depend upon the number of studies considered. A confidence interval for i² is constructed using either i) the iterative non-central chi-squared distribution method of hedges and piggott (2001); or ii) the test-based method of higgins and thompson (2002). The non-central chi-square method is currently the method of choice (higgins, personal communication, 2006) – it is computed if the 'exact' option is selected." ] ] [ fhir:code [ fhir:v "C53245" ] ; fhir:display [ fhir:v "Interquartile range" ] ; fhir:definition [ fhir:v "The difference between the 3d and 1st quartiles is called the interquartile range and it is used as a measure of variability (dispersion)." ] ] [ fhir:code [ fhir:v "C44185" ] ; fhir:display [ fhir:v "P-value" ] ; fhir:definition [ fhir:v "The probability of obtaining the results obtained, or more extreme results, if the hypothesis being tested and all other model assumptions are true." ] ] [ fhir:code [ fhir:v "C38013" ] ; fhir:display [ fhir:v "Range" ] ; fhir:definition [ fhir:v "The difference between the lowest and highest numerical values; the limits or scale of variation." ] ] [ fhir:code [ fhir:v "C53322" ] ; fhir:display [ fhir:v "Standard deviation" ] ; fhir:definition [ fhir:v "A measure of the range of values in a set of numbers. Standard deviation is a statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean." ] ] [ fhir:code [ fhir:v "0000037" ] ; fhir:display [ fhir:v "Standard error of the mean" ] ; fhir:definition [ fhir:v "The standard deviation of the sample-mean's estimate of a population mean. It is calculated by dividing the sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population) by the square root of n , the size (number of observations) of the sample." ] ] [ fhir:code [ fhir:v "0000421" ] ; fhir:display [ fhir:v "Tau squared" ] ; fhir:definition [ fhir:v "An estimate of the between-study variance in a random-effects meta-analysis. The square root of this number (i.e. Tau) is the estimated standard deviation of underlying effects across studies." ] ] [ fhir:code [ fhir:v "C48918" ] ; fhir:display [ fhir:v "Variance" ] ; fhir:definition [ fhir:v "A measure of the variability in a sample or population. It is calculated as the mean squared deviation (MSD) of the individual values from their common mean. In calculating the MSD, the divisor n is commonly used for a population variance and the divisor n-1 for a sample variance." ] ] ) . #	{"url":"https://terminology.hl7.org/5.2.0/CodeSystem-attribute-estimate-type.ttl.html","timestamp":"2024-11-03T23:11:51Z","content_type":"text/html","content_length":"32384","record_id":"<urn:uuid:bd5199ba-1324-40b0-a612-8983d28b3833>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00665.warc.gz"}
Algebra Vs Arithmetic: What’s The Main Difference? - Premium Article Submission Site List \| Latest Business, Tech, AI Updates Mathematics is divided into two branches: arithmetic and algebra. So many people have confusion with the difference between algebra vs arithmetic. Arithmetic is the most fundamental field of mathematics. It concerns the calculation of numbers using operations such as adding, multiplying, dividing, and subtraction. Algebra, on the other hand, solves problems using numbers and variables. It depends on the use of universal principles to solve problems. Arithmetic is a phrase derived from a Greek word that means “number.” It is the most fundamental aspect of mathematics. It’s all about numbers, thus it’s something that everyone uses in their daily lives. Higher Arithmetic also regards as number theory. It is involved with characteristics of rational numbers, integers, real numbers, and irrational numbers. Algebra, on the other hand, is one more branch of mathematics. The name comes from the Arabic word al-jabr, which means “reunion of shattered pieces” and is an old medical term. After the basis of arithmetic, it might regard as the next level of mathematics. Let us try to understand both the terms through their differences. So let us start with their definitions… Algebra vs Arithmetic: Definitions What is arithmetic? The word “arithmetic” comes from a Greek word that means “number.” It is the most fundamental field of mathematics, including everything to do with numbers. And thus uses by individuals in their daily lives. Moreover, the 4 major operations of traditional arithmetic are adding, subtraction, multiplying, and division. It also simply uses numbers to make various sorts of computations. Number theory is another name for upper arithmetic. The features of whole numbers, rational numbers, irrational numbers, and real numbers are discussed. The 4 major properties of operations are: • Associative Property • Additive Identity • Commutative Property • Distributive Property The BODMAS and PEMDAS rules are followed for operation order involved +, −,×, and ÷. The order of operation is: • B Brackets • O Order • D Division • M Multiplication • An Addition • S Subtraction Types of basic Operations in Arithmetic The four fundamental arithmetic operations that is addition, subtraction, multiplication, and division are discussed below: Addition (+) For instance, if you add 1 and 4 the outcome will be 5. 1 + 4 = 5 If you add the opposite value. For instance, if you do the addition of 4 with its opposite value -4, then the outcome will be 4 + (-4) = 0 Subtraction (-) 3 – 1 = 2 When you subtract lower value from higher 1 – 3 = -2 Multiplication (×) The two values included in the multiplication operation are known as the multiplier. It also incorporates two values that multiplicand to provide a single product. The outcome of two values apparently x and y are expressed in x.b or x * y form. 3 × 4 = 12 Division (÷) The division is the operation that calculates the quotient of two values. 4/2 = 2 What is Algebra? Algebra, on the other hand, is a separate discipline of mathematics. The phrase comes from al-Jabr, an antique medical term. It also means “reunion of fractured fragments” in Arabic (the Arabs were the ones who contributed the most to this branch). After Arithmetic, Algebra is considered the second level of mathematics. It also works with unknown values that are coupled with numbers, unlike the Let’s take… 10x + 40 This refers to as an algebraic expression since x has a range of values. Also is hence a variable, whereas 50 is constant. The words are 10x and 40, and they can separate by the marker +. In place of variables, we may write anything a, b, c….z. Algebra also includes different techniques of solving a couple of linear equations: • Elimination method • Cross multiplication method • Substitution method Algebra vs Arithmetic: Difference Table The Difference between algebra vs arithmetic will make algebra and arithmetic clear. Parameter Arithmetic Algebra Basic The phrase comes from al-Jabr, an antique medical term that means “reunion of The word “arithmetic” comes from a Greek word that means “number.” difference fractured fragments” in Arabic Level Normally, associated with the math of elementary school Normally, associated with the math of high school Problem-solving Based on the details given in the problem (memorized outcomes for short values of Based on the classic moves of elementary algebra Computation Computation with exact numbers Familiarizes abstraction related concepts Relation Number related Variable related Primary focus Addition, subtraction, multiplication, and division are its four main operations. Algebra utilizes variables and numbers for problem-solving. It is based on the generalized application rules for problem-solving. Let’s wrap it up! In the final discussion of algebra vs arithmetic, it is quite clear to say which is better. The most basic kind of mathematics is arithmetic. It is the cornerstone of contemporary mathematics. Everything is founded on it. Arithmetic is the math of finding unknown values in an equation using variables. On the other hand, algebra is the math of finding unknown values in an equation using variables. The variables are symbols that represent an unknown value.	{"url":"https://sevenarticle.com/algebra-vs-arithmetic-whats-the-main-difference/","timestamp":"2024-11-09T17:32:25Z","content_type":"text/html","content_length":"139341","record_id":"<urn:uuid:ce669bdd-4174-4ae7-8ff8-531fc3332815>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00027.warc.gz"}
3 Java projects The following are three projects. Make three separate classes. Example You must submit three java files. No Zip file will be allowed. Problem 1: Write a program that accepts an amount of money on deposit and a number of years it has been on deposit (years can have decimals). It will determine the interest to be paid on the deposit based on the following schedule: Time on Deposit Interest Rate >= 5 years 4.5% Less than 5 and >=4 years 4% Less than 4 and >=3 years 3.5% Less than 3 and >=2 years 2.5% Less than 2 and >=1 years 2% Less than 1 year 1.5% Compute the interest with the formula: Interest = Deposit * IntRate * Years. Display the original deposit, the interest earned, and the new Balance (with interest added to the deposit. Problem 2: Write a program with a loop that lets the user enter a series of integers. The user should enter -99 to signal the end of the series. After all the numbers have been entered, the program should display the largest and smallest numbers entered, as well as the average of all the numbers entered. Assume the initial value of the smallest number and the largest number is -99 and the initial average is 0.0. Make sure the average prints out to two decimal places. Problem 3 For a quadratic equation ax2+bx+c = 0 (where a, b and c are coefficients), its roots are given by the formula:- The value of the discriminant (b2-4ac) determines the nature of roots. Write a program that reads the values of a, b and c from the user and performs the following:- If the value of the discriminant is positive, the program should print out that the equation has two real roots and prints the values of the two roots. If the discriminant is equal to 0, the roots are real and equal. if the value of the discriminant is negative, then the equation has two complex roots. Sample Output Enter values for a, b and c:- 2 10 3 Discriminant = 76 The equation has two real roots Roots are as follows:- x1 = -0.320551 x1 = -0.320551 Need a custom answer at your budget? This assignment has been answered 4 times in private sessions.	{"url":"https://codifytutor.com/marketplace/3-java-projects-a0f84c2c-4865-450d-b0f2-7f83e54daf75","timestamp":"2024-11-02T11:44:04Z","content_type":"text/html","content_length":"22205","record_id":"<urn:uuid:5fc33c91-588c-4317-8fff-3cf722858b1f>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00098.warc.gz"}
Computation and Consciousness Since the several years from now the computer scientists have been pondering over the problem of mind and computing machine[1]. In the recent time the debate has accelerated the seriousness among the thinkers from various fields of science as well as arts. Many enquire what exactly the mind is? is it also a kind of computing machine? or it is something different. Considering the mind to be alike a computing machine we expect that the computing machine must perform those task which are seemingly natural to human mind. However we encounter many such problems where the machines maintain silence and mind makes a creative activity. There are many such mathematical incidence where the human mind perform with greater superiority over the computing machine. Computing machine though are proven to be excellent in certain computations like performing arithmetic operation, doing statistics, playing games etc they however fail in most fundamental task of doing the deeper mathematics. The real limbs of mathematics are the proofs of the validity or truth. Those proofs are non algorithm and non programmable; till date no such program have been developed which could be executed to perform the proof of theorem[2]. There are few domains where the two differ. These domain also brings out the limitations one over other or the superiority of one over other. Without much detail definition I would like to present those here. Computing Machine ---------------------------------- Human Mind Syntactic (Structure) -------------------- Semantic(Meaning) Deductive -------------------- Creative Algorithmic -------------------- Non-Algorithmic(Intuitive) Rule Based -------------------- Not limited to Rule How? -------------------- Why + What + How [1] Shadow of the Mind, Roger Penrose [2] How Mathematician Thinks, William Bayers Detail elaboration will be posted in next articles. Jaynarayan, Bangalore, India	{"url":"https://consciousnessasitis.blogspot.com/2015/10/","timestamp":"2024-11-07T13:57:36Z","content_type":"text/html","content_length":"54640","record_id":"<urn:uuid:06f98910-c6ec-425c-95d3-2f89284a3f1d>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00509.warc.gz"}
An easier way to remember Trigonometry Identities - The Culture SGAn easier way to remember Trigonometry Identities I’m one who really hates memorizing formulas, be in as a student or tutor. So I shall share how I remember the three very useful trigonometry identities. I’ll start with the one which you all definitely can identify with. Now how do we get the other 2? Simply divide the above equation by Lets divide by Voila! we have You can try to do the same with	{"url":"https://theculture.sg/2015/07/trigonometry-identities/","timestamp":"2024-11-13T04:03:22Z","content_type":"text/html","content_length":"99899","record_id":"<urn:uuid:ee5625d0-d61d-4edc-a0e8-6a84a92b6774>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00214.warc.gz"}
Data Project: Analyzing the Data and Interpreting the Results - Connected Mathematics Project Data Project: Analyzing the Data and Interpreting the Results Students analyze and interpret a data set. Materials Needed Adaptations and Notes • Additional Questions can be asked to focus the student’s interpretation of the data. See Teacher Notes for more detail. Possible CCSS Grade 6 Ratios and Proportional relationships 6.RP Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Statistics and Probability 6.SP Develop understanding of statistical variability. 1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions. 4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 5. Summarize numerical data sets in relation to their context, such as by: 1. Reporting the number of observations. 2. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. 3. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 4. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Grade 7 Ratios and Proportional relationships 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 2. Recognize and represent proportional relationships between quantities. Statistics and Probability 7.SP Draw informal comparative inferences about two populations. 3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.	{"url":"https://connectedmath.msu.edu/teacher-support/resources-for-teachers/unit-projects/data-project-analyzing-the-data-and-interpreting-the-results/index.aspx","timestamp":"2024-11-13T09:04:31Z","content_type":"text/html","content_length":"55281","record_id":"<urn:uuid:e1e0a237-d335-4b16-a48e-61b312b473db>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00475.warc.gz"}
Java Program to Calculate Area and Perimeter of Parallelogram Hello coders, in this post, we will learn Java program to calculate area and perimeter of Parallelogram. In the previous tutorial, you have learned Java Program to calculate Area and Perimeter of We can calculate the parallelogram’s area and perimeter using the following formulas. Area of Parallelogram= b×h Perimeter of Parallelogram = 2(b+h) • b is base of the parallelogram. • h is height of the parallelogram. Now let’s write the program. Java Program to Calculate Area and Perimeter of Parallelogram 6 import java.util.; 7 public class Parallelogram { 8 public static void main(String[] args) 9 { 10 double h, b , area, perimeter; 11 Scanner in = new Scanner(System.in); 12 // Asking the user to enter the height and breadth of the parallelogram 13 System.out.println(" Enter the height and breadth of the parallelogram :"); 14 h = in.nextDouble(); 15 b = in.nextDouble(); 16 area = b h; // Calculating area of parallelogram 17 perimeter = 2(b+h); // Calculating perimeter of parallelogram 18 System.out.println(" Area of Parallelogram : " + area +" square units"); 19 System.out.println("\nPerimeter of Parallelogram : " + perimeter); 20 } 21 } What we Did? • First of all we have imported the util package. • Then created a class and named it Parallelogram. • After that started main() method of the program. • Then inside main() method declared variables. • Then created object of the Scanner class. • Now asked the user to enter the height and breadth of the parallelogram. Then read the value of height and breadth of parallelogram entered by the user. • Then calculated area of parallelogram using the formula area = b h • In the next line calculated perimeter of parallelogram using the formula perimeter = 2 * (b + h) • Then finally displayed the value of area and perimeter of parallelogram on the screen. 1 Enter the height and breadth of the parallelogram :2 3 2 Area of Parallelogram : 6.0 square units 3 Perimeter of Parallelogram : 10.0 So in this tutorial, we learned how to write Java program to calculate area and perimeter of Parallelogram. In the next tutorial, you will learn Java Program to calculate Area of Trapezium. Related Tutorials… Leave a Comment	{"url":"https://www.tutorialsfield.com/java-program-to-calculate-area-and-perimeter-of-parallelogram/","timestamp":"2024-11-13T19:04:48Z","content_type":"text/html","content_length":"145491","record_id":"<urn:uuid:5240b379-c4af-4140-b661-48bcbd81a280>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00489.warc.gz"}
Seminars: D. Fernandez-Duque, Provable well-orders and hyperarithmetical soundness Abstract: Joint work with Juan Aguilera Ordinal analysis traditionally measures the strength of formal theories using the supremum of the order types of their provable well-orders. In this talk, we will instead propose the use of proof-theoretic ordinals to measure de degree of soundness of a theory: to be precise, we define an ordinal-theoretic measure of the degree of hyperarithmetical correctness of a mathematical theory. We then characterize the ordinals that are assigned in this way to theories of various degrees of hyperarithmetical soundness. Language: English	{"url":"https://m.mathnet.ru/php/seminars.phtml?option_lang=eng&presentid=42938","timestamp":"2024-11-11T19:43:09Z","content_type":"text/html","content_length":"8522","record_id":"<urn:uuid:7ae071db-d7dd-4a10-b1d9-0fbc2f1881e3>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00001.warc.gz"}
Recognizing DAGs with Page-Number 2 Is NP-complete The page-number of a directed acyclic graph (a DAG, for short) is the minimum k for which the DAG has a topological order and a k-coloring of its edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological order. In 1999, Heath and Pemmaraju conjectured that the recognition of DAGs with page-number 2 is NP-complete and proved that recognizing DAGs with page-number 6 is NP-complete [SIAM J. Computing, 1999]. Binucci et al. recently strengthened this result by proving that recognizing DAGs with page-number k is NP-complete, for every k≥3 [SoCG 2019]. In this paper, we finally resolve Heath and Pemmaraju’s conjecture in the affirmative. In particular, our NP-completeness result holds even for st-planar graphs and planar posets. Original language English Title of host publication Graph Drawing and Network Visualization - 30th International Symposium, GD 2022, Tokyo, Japan, September 13-16, 2022, Revised Selected Papers Editors Patrizio Angelini, Reinhard von Hanxleden Publisher Springer Pages 361-370 Number of pages 10 Volume 13764 Publication status Published - 2022 Publication series Name Lecture Notes in Computer Science Publisher Springer Dive into the research topics of 'Recognizing DAGs with Page-Number 2 Is NP-complete'. Together they form a unique fingerprint.	{"url":"https://research-portal.uu.nl/en/publications/recognizing-dags-with-page-number-2-is-np-complete","timestamp":"2024-11-15T01:34:19Z","content_type":"text/html","content_length":"51875","record_id":"<urn:uuid:1c922177-aab2-44b9-a5dd-acbdab5c81d3>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00344.warc.gz"}
Topics in Bayesian inference and model assessment for partially observed stochastic epidemic models Aristotelous, Georgios (2020) Topics in Bayesian inference and model assessment for partially observed stochastic epidemic models. PhD thesis, University of Nottingham. PDF (Thesis - as examined) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (35MB) \| Preview Stochastic epidemic models can offer a vitally important public health tool for understanding and controlling disease progression. However, these models are of little practical use if they are not supported by data or are not applicable to efficient parameter inference methods. The peculiarities of the epidemic setting, where data are not independent and epidemic processes are rarely fully observed, complicate both model assessment and parameter inference for stochastic epidemic models. Methods for model assessment are not well-established and methods for inference, although more established, still remain inefficient for large-scale outbreaks. This thesis is concerned with the development of methods for both model assessment and inference for stochastic epidemic models. The methods are illustrated on continuous time SIR (susceptible -> infective -> removed) models and it is assumed that the available data consist only of the removal times of infected individuals with their infection times being unobserved. First, two novel model assessment tools are developed, based on the posterior predictive distribution of removal curves, namely the distance method and the position-time method. Both methods rely on the general idea of posterior predictive checking, where a model's fit is assessed by checking whether replicated data, generated under the model, look similar to the observed data. The distance method conducts the assessment by calculating distances between removal curves whereas the position-time method conducts the assessment pointwise, at a sequence of suitably chosen time points. Both methods provide visual and quantitative outputs with meaningful interpretation. The performance of the methods benefits from the development and application of a time shifting intervention, that horizontally (time) shifts each replicated removal curve by an appropriately chosen constant, so that the stages of each replicated curve better correspond to those of the observed. Extensive simulation studies suggest that both the distance and the position-time methods can successfully assess the infectious period distribution assumption and the infection rate form assumption of stochastic epidemic models. Then, the focus is placed on developing methods to assess the population mixing assumption of stochastic epidemic models, in the case that household information is available. To this end, a classical hypothesis test is developed for which the null hypothesis is that individuals mix in the population homogeneously. The test is based on household labels of individuals and relies on the idea that, in the presence of household effect, events of individuals belonging to the same household should occur closer in time rather than further apart. The key behind developing the test is that, under the null hypothesis of homogeneous mixing, the discrete random vector of household labels has a known sampling distribution that does not dependent on any model parameters. The test carries an ordinal interpretation, where the lower the observed value of the test statistic and its corresponding p-value are, the more the evidence against the null hypothesis and in favour of the hypothesis that there is a household effect in the spread of the outbreak. The test exhibits excellent performance when applied to both simulated data and to a widely studied real-life epidemic dataset. In the remainder of the thesis, attention is turned from model assessment to Bayesian inference. The relevant aim is to develop Markov chain Monte Carlo (MCMC) algorithms that can conduct more efficient updating of the unobserved infection times, than the currently existing algorithms. Initially, the problem of updating one infection time at a time is considered and a new 1-dimensional update algorithm is developed, namely the IS-1d MCMC algorithm. The main feature of the algorithm is the use of individual-specific parameters in the proposal distributions for the infection times. These parameters allow the proposal distributions to produce patterns of nonhomogeneity (among individuals) which are in some cases present in the target distribution. The IS-1d MCMC algorithm performs favourably when compared to currently existing 1-dimensional update algorithms. Subsequently, the more interesting problem of updating many infection times at a time is considered and a novel block update MCMC algorithm is developed, referred to as the DIS-block MCMC algorithm. Similar to the IS-1d algorithm, the proposal distributions of the DIS-block algorithm also have individual-specific parameters but they also have an additional parameter that induces dependency on the current state and makes the algorithm perform a dependent in nature exploration of the target space. The algorithm also benefits from another two features, parameter reduction and an automated method for optimally specifying the number of infection times to update. Simulation studies suggest that the DIS-block algorithm can offer a substantial improvement in mixing compared to the current optimally performing block update algorithm; for the considered datasets of the simulation study, the DIS-block algorithm is from 1.41 up to 6.57 times more efficient than its comparator, and 3.35 times on average. Item Type: Thesis (University of Nottingham only) (PhD) Supervisors: Kypraios, Theodore O'Neill, Philip Keywords: Bayesian inference, Stochastic epidemic models, Model assessment. Subjects: Q Science > QA Mathematics > QA273 Probabilities R Medicine > R Medicine (General) Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences Item ID: 63384 Depositing User: Aristotelous, Georgios Date Deposited: 31 Dec 2020 04:40 Last Modified: 20 Oct 2021 08:32 URI: https://eprints.nottingham.ac.uk/id/eprint/63384 Actions (Archive Staff Only)	{"url":"http://eprints.nottingham.ac.uk/63384/","timestamp":"2024-11-14T18:49:44Z","content_type":"application/xhtml+xml","content_length":"40519","record_id":"<urn:uuid:e698e472-90b5-42ea-8c5a-98bda68a95c0>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00461.warc.gz"}
Digital-Logic-DesignDigital-Logic-Design - solutions adda October 16, 2023 October 16, 2023 There are 7 switches on a switchboard, some of which are on and some of which are off. In one move, you pick any 2 switches and toggle each of them—if the switch you pick is currently off, you turn it on, if it is on, you turn it off. Your aim is to execute a sequence of moves and turn all 7 switches on. For which of the following initial configurations is this not possible? Each configuration lists the initial positions of the 7 switches in sequence, from switch 1 to switch 7. Question 646 Explanation: The parity of switches in each position is unchanged after each move. If all 7 switches are on at the end, the final parity of ”off” is even and of ”on” is odd. So we can only achieve this if we start with a configuration where the number of ”off” switches is even and the number of ”on” switches is odd. The exact order does not matter since we can pick any two to toggle at each step. Correct Answer: C Question 646 Explanation: The parity of switches in each position is unchanged after each move. If all 7 switches are on at the end, the final parity of ”off” is even and of ”on” is odd. So we can only achieve this if we start with a configuration where the number of ”off” switches is even and the number of ”on” switches is odd. The exact order does not matter since we can pick any two to toggle at each step. Inline Feedbacks View all comments \| Reply	{"url":"https://solutionsadda.in/2023/10/16/digital-logic-design-53/","timestamp":"2024-11-05T17:20:19Z","content_type":"text/html","content_length":"354642","record_id":"<urn:uuid:19a1dbde-f016-488b-ac84-38ab5b0c444d>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00410.warc.gz"}
Looking to calculate remaining hours per row I am hoping to find a way to calculate and display hours remaining. Essentially we are using the board to track hours worked on each project (projects are rows, hours are columns). We would like to be able to calculate and display remaining hours based off of our total minus each row entry. I know I could display percentages however those don’t automatically calculate the remaining hours unless the remaining hours are manually entered. Hi Kayla! I would love to help you with your formula. Can you share a screenshot of your board or the columns that you have? Thank you! Shanine \| Solution Consultant and monday.com expert Hello! Here is an image of the columns I am looking at. I am trying to be able to display in a chart the amount of hours per project. Currently I can do that, however I have to manually input the remaining hours (out of 80) instead of it automatically populating how many hours are used out of the 80. Hello @kayla061819, Sure thing! You’ll want a formula to calculate the remaining hours by subtracting the sum of hours worked from the total hours. iadpworkforcenow.com Here’s a simple way to do it in Excel: 1. Assume your total hours are in column B and hours worked are in column C. 2. In column D, use the formula =B2-SUM(C2:C5) to calculate the remaining hours for each project. Let me know how it goes! Best Regards, Ellen Hogan Thank you for contributing! The hope was to be able to do this in Monday.com! To calculate remaining hours, you can create a formula that subtracts the sum of hours worked from your total hours. Try this: Copy code {Total Hours} - SUM({Hours Worked}) This will display the remaining hours automatically for each project. Hi Kayla, Based on my understanding, you’d like to track the remaining hours for all projects by comparing the total hours versus the hours already spent. To achieve this, I suggest setting up two connected 1. Projects Board: Where each project’s progress and hours are tracked. 2. Allocation of Hours Board: This board will store the total hours allocated for projects We’ll connect these boards and mirror the hours spent in the Projects Board onto the Allocation of Hours Board. Then, I’ll add a formula column in the Allocation of Hours Board that will subtract the mirrored “hours spent” from the “total hours” allocated, giving you a clear view of the remaining hours, similar to the screenshot attached. Let me know if this aligns with what you had in mind Hello, this is a great start, thank you for your help! This works great for the first row, however the goal is to keep subtracting for each subsequent row. Ideally row one would have a total of 80, remaining hours of 67.25, hour this billing period of 12.75, and then the next total in row 2 would say 67.25, followed by hours remaining showing 64.25, accounting for the hours billed in row 2. Does that make sense? Ideally I could subtract with each row so the total and remaining hours are changing with each column entry of the hours this billing period column. Hi @kayla061819, The formula column can only reference columns from the current item, so you won’t be able to achieve it this way. It could be done with a 3rd-party app called the Advanced Formula Booster which does not use the formula column at all and can reference any item in any board. Here is a demo: This is achieved with a simple formula: and 2 automations:	{"url":"https://community.monday.com/t/looking-to-calculate-remaining-hours-per-row/100185","timestamp":"2024-11-03T06:32:46Z","content_type":"text/html","content_length":"99864","record_id":"<urn:uuid:57a2b17f-67ca-4107-91d2-86176ce7ca86>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00892.warc.gz"}
Perimeter - rectangle - math word problem (53611) Perimeter - rectangle Find the perimeter of the rectangle. A rectangle with a base of (3 5/6) m and a height of (2 3/7) m Its perimeter is x= meters. (Use fraction in your answer. ) Correct answer: Did you find an error or inaccuracy? Feel free to write us . Thank you! You need to know the following knowledge to solve this word math problem: Grade of the word problem: We encourage you to watch this tutorial video on this math problem: Related math problems and questions:	{"url":"https://www.hackmath.net/en/math-problem/53611","timestamp":"2024-11-02T07:52:13Z","content_type":"text/html","content_length":"67088","record_id":"<urn:uuid:20bbf921-51df-4f50-808b-4c7bb1c19e44>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00669.warc.gz"}
Why Diagonal? Why do they give the hypotenuse and sometimes the slope (aspect ratio; ie. 16:9 or 4:3) of a tv or screen instead of giving the dimensions? Most of us don't deal with the ratios of TV screens all the time, and can't instantly tell you what the height and width of the screen will be from just the diagonal measurements. Sure, it is a simple calculation to figure the other sides of a right triangle based on the hypotenuse (diagonal measurement) when given the slope, but WHY? It is much easier to say 6.1" x 3.4" when talking about a so-called '7" screen' than to give the 16:9 aspect ratio ONLY. Maybe its because 7 inches sounds BIGGER than 6.1 x 3.4 inches?	{"url":"https://www.tonewah.com/2013/02/why-diagonal.html","timestamp":"2024-11-03T22:50:27Z","content_type":"application/xhtml+xml","content_length":"69480","record_id":"<urn:uuid:18cb552c-2e61-4a74-ba9d-5a6fca1583c3>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00306.warc.gz"}
What is the difference between mean and median in R? Mean and Median are two measures of central tendency used to describe the distribution of a set of data in R. However, they differ in how they are calculated and the insights they provide. 1. Mean: The mean or arithmetic mean is the sum of all the data points divided by the number of data points. It is the average value of the data set. In R, you can calculate the mean using the mean() function: 1 data <- c(10, 15, 20, 25, 30) 2 mean(data) 3 [1] 20 In this example, the mean of the data set is 20. 1. Median: The median is the middle value in the data set when the data is arranged in ascending or descending order. It is the value that divides the data set into two halves. In R, you can calculate the median using the median() function: 1 data <- c(10, 15, 20, 25, 30) 2 median(data) 3 [1] 20 In this example, the median of the data set is 20. Overall, the main difference between mean and median is that mean is more sensitive to the presence of outliers in the data set while median is more robust to the presence of outliers.	{"url":"https://devhubby.com/thread/what-is-the-difference-between-mean-and-median-in-r","timestamp":"2024-11-09T09:45:18Z","content_type":"text/html","content_length":"118400","record_id":"<urn:uuid:1c2b2f68-2bfc-4a0a-a4e4-73e3e8e427fe>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00382.warc.gz"}
Member's groups Viewing 1 - 10 of 10 groups • Here you can discuss anything and everything related to Teaching Geometry! • Here you can discuss anything and everything related to Teaching PreCalculus! • This group is for 5th Grade Math Teachers to use to communicate and share lessons. • This group is for 4th Grade Math Teachers to use to communicate and share lessons. • Here you can discuss anything and everything related to Teaching Algebra 2 & Trigonometry! • Here you can discuss anything and everything related to Teaching Algebra 1! • Here you can discuss anything and everything related to Teaching 8th Grade Math! • Here you can discuss anything and everything related to Teaching 7th Grade Math! • Here you can discuss anything and everything related to Teaching 6th Grade Math! • This group is for 3rd Grade Math Teachers to use to communicate and share lessons with each other. Viewing 1 - 10 of 10 groups	{"url":"https://members.mathteachercoach.com/members/mtcoach/groups/","timestamp":"2024-11-04T23:05:52Z","content_type":"text/html","content_length":"147922","record_id":"<urn:uuid:856f3e18-2eea-4a7c-bb28-9d9a3b3aa55c>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00374.warc.gz"}
Math Is Fun Forum Registered: 2005-06-28 Posts: 48,343 Re: Solve for x Registered: 2022-09-19 Posts: 467 Solve for x A friend texted the following question to me. Solve x^(2) = 2^(x) for x. Any suggestions? The equation has two "obvious" solutions: x=2 and x=4. They are "obvious" because they are relatively easy to find by sheer guessing or by sketching the graphs of the two functions involved, and once guessed they are trivial to verify. There is a third solution with x<0. That this solution exists is fairly obvious as well: just consider the general behavior of the two functions for negative values of x and you will see that they must intersect at least once - in fact it's not hard to see that they intersect exactly once in that region. However, it is not possible (we believe!) to write down an explicit formula for that solution by using rational numbers, arithmetic operations, and the so-called Elementary Functions: exponentials, logarithms and trigonometric functions. It is possible to write down such an explicit expression using a decidedly less standard function, the Lambert W function, and that's pretty straightforward Proving the negative assertion above is far from trivial, and in fact I don't think that such a proof is known. Just because the solution can be expressed by evaluating W at ln(2)/2 (and making a few other simple calculations) doesn't rule out the possibility that there is also another expression for that same solution using elementary functions evaluated at rational numbers. There's a brilliant and readable paper by Tim Chow on this topic, called "What is a closed form number?" . I highly recommend it to anyone interested in gaining a deeper understanding of those questions. It is a little surprising that many people wouldn't hesitate to make the assertion I made above, about the negative solution being impossible to write down "in closed form", without having proof of that fact and often without even being able to express precisely what the claim is. We can see there is one solution in the interval -1 < x < 0 and a second solution at what appears to be x = 2 and a third at what appears to be x = 4. The two solution x = 2, 4 can easily be verified to be exact by substitution. We can find the third solution numerically, using Newton-Rhapson method and using the Newton-Rhapson method we use the following iterative sequence. And we conclude that the remaining solution is to 4 dp. It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel. Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking. Registered: 2022-09-19 Posts: 467 Re: Solve for x ganesh wrote: The equation has two "obvious" solutions: x=2 and x=4. They are "obvious" because they are relatively easy to find by sheer guessing or by sketching the graphs of the two functions involved, and once guessed they are trivial to verify. There is a third solution with x<0. That this solution exists is fairly obvious as well: just consider the general behavior of the two functions for negative values of x and you will see that they must intersect at least once - in fact it's not hard to see that they intersect exactly once in that region. However, it is not possible (we believe!) to write down an explicit formula for that solution by using rational numbers, arithmetic operations, and the so-called Elementary Functions: exponentials, logarithms and trigonometric functions. It is possible to write down such an explicit expression using a decidedly less standard function, the Lambert W function, and that's pretty straightforward too. Proving the negative assertion above is far from trivial, and in fact I don't think that such a proof is known. Just because the solution can be expressed by evaluating W at ln(2)/2 (and making a few other simple calculations) doesn't rule out the possibility that there is also another expression for that same solution using elementary functions evaluated at rational numbers. There's a brilliant and readable paper by Tim Chow on this topic, called "What is a closed form number?" . I highly recommend it to anyone interested in gaining a deeper understanding of those questions. It is a little surprising that many people wouldn't hesitate to make the assertion I made above, about the negative solution being impossible to write down "in closed form", without having proof of that fact and often without even being able to express precisely what the claim is. We can see there is one solution in the interval -1 < x < 0 and a second solution at what appears to be x = 2 and a third at what appears to be x = 4. The two solution x = 2, 4 can easily be verified to be exact by substitution. We can find the third solution numerically, using Newton-Rhapson method and using the Newton-Rhapson method we use the following iterative sequence. And we conclude that the remaining solution is to 4 dp. A very detailed reply. I thank you also for the photo.	{"url":"https://mathisfunforum.com/viewtopic.php?id=28061","timestamp":"2024-11-09T19:36:41Z","content_type":"application/xhtml+xml","content_length":"16176","record_id":"<urn:uuid:112ac0bd-d506-4c3e-927a-978fe322e786>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00106.warc.gz"}
Display mathematical expressions in blog As part of my Machine Learning course, I learned a useful trick which I will share hoping that it may help someone or I myself can refer to it later. The problem at hand was how to display the mathematical expressions that calculate cost function, gradient descent etc. in a blog or web page. In OneNote, you can do it using OneNote Equation tool earlier, but I wanted to do the same in my blog posts. After trying many options, here is what worked for me. First of all, I had to find a good JavaScript library that can display mathematical expressions described in a LaTeX-style syntax in the HTML (or Markdown) source of a web page. It turns out that the best such library is MathJax. It produces high quality typesetting that scales to full resolution which renders beautifully on the web page. More importantly, it uses web-based fonts, so the person who views the HTML page does not have to install any plugin to view those equations. MathJax is very easy to use, you just include a script tag in the HTML to load the JavaScript from a CDN, configure your preferences and start writing mathematical expressions in your content. Here are the detailed steps on how to get started with MathJax. Then my question was how do I use it with my blog engine Hugo. With a quick Googling, I found this good article MathJax Support on Hugo site itself. Lovely! It turns out that writing mathematical expressions is a very popular requirement. The instructions are easy to follow and I could set it up in a few minutes. One thing I realized is that in order to show inline style mathematics, MathJax uses the syntax of a single backslash followed by parentheses. But in Hugo, I have to use double backslash followed by parentheses. If you are using any other blog engine like Tumblr, TypePad, Weebly etc., check out this article. So now, my blog is ready to display mathemtical expressions. Here is a sample expression of quadratic equation that shows both inline and display expressions: When $a \ne 0$, there are two solutions to $ax^2 + bx + c = 0$ and they are as follows: $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$ comments powered by Disqus	{"url":"https://annjose.com/post/display-math-expressions-in-hugo/","timestamp":"2024-11-05T23:42:15Z","content_type":"text/html","content_length":"11169","record_id":"<urn:uuid:f8c241b6-7f55-48a8-ae88-c12ea91d3c5a>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00563.warc.gz"}
Special Relativity: Physics at the Speed of Light You awaken, and your mind clears. Yes, you are traveling on the inter-stellar freighter Hyperion, outbound to mine anti-matter from a galactic vortex. The automated systems have just revived you from suspended animation. Your assignment – perform periodic ship maintenance. Climbing out of your hibernation chamber, you punch up system status. All systems read nominal, no issues. That is good. Your ship extends 30 kilometers. Just performing routine maintenance exhausts the mind and body; you don’t need any extra work. You contemplate the task of the freighter. The Hyperion, and its three sister ships, fly in staggered missions to harvest energy, in the form of anti-matter. Each trip collects a million terawatt-hours, enough to support the 35 billion human and sentient robots in the solar system for a full year. Looking up at the scanner screen, you see the mid-flight space buoy station about a light-hour ahead. The station contains four buoys, configured in a square, 30 kilometers on a side. A series of eleven stations keeps your ship on course during its two year travel out from Earth. You check the freighter’s speed relative to the buoys – about 50 percent of the speed of light, but constant, i.e. no acceleration or deceleration. That makes sense – at mid-flight, the freighter has entered a transition phase between acceleration and deceleration. The Theory of Relativity Either through deliberate study, or general media coverage, you likely have heard of the Theory of Relativity, the master piece of Albert Einstein. Einstein built his theory in two phases. The first, Special Relativity, covered non-accelerating frames of reference, and the second, General Relativity, dealt with accelerating and gravity-bound frames of reference. Special Relativity gave us the famous E=MC squared equation, and covers the physics of objects approaching the speed of light. General Relativity helped uncover the possibility of black holes, and provides the physics of objects in gravity fields or undergoing acceleration. Here we will explore Special Relativity, using our hypothetical ship Hyperion. The freighter’s speed, a significant fraction of that of light, dictates we employ Special Relativity. Calculations based on the laws of motion at everyday speeds, for example those of planes and cars, would produce incorrect results. Importantly, though, our freighter is neither accelerating nor slowing and further has traveled sufficiently into deep space that gravity has dwindled to insignificant. The considerations of General Relativity thus do not enter here. Waves, and Light in a Vacuum Special Relativity starts with the fundamental, foundational statement that all observers, regardless of their motion, will measure the speed of light as the same. Whether moving at a hundred kilometers an hour, or a million kilometers an hour, or a billion kilometers an hour, all observers will measure the speed of light as 1.08 billion kilometers an hour. A caveat is that the observer not be accelerating, and not be under a strong gravitational field. Even with that caveat, why is this case? Why doesn’t the speed of the observer impact the measured speed of light? If two people throw a baseball, one in a moving bullet train, while the other stands on the ground, the motion of the bullet train adds to the speed of the throw ball. So shouldn’t the speed of the space ship add to the speed of light? You would think so. But unlike baseballs, light speed remains constant regardless of the speed of the observer. Let’s think about waves. Most waves, be they sound waves, water waves, the waves in the plucked string of a violin, or shock waves travelling through solid earth, consist of motion through a medium. Sound waves consist of moving air molecules, water waves consist of moving packets of water, waves in a string consist of motion of the string, and shock waves consist of vibrations in rocks and In contrast, stark contrast, light waves do not consist of the motion of any underlying substrate. Light travel does not need any supporting medium for transmission. In that lies the key difference. Let’s work thought that in the context of the inter-stellar freighter. You rise from suspended animation. Acceleration has stopped. In this case, no buoys exist near-by. How do you know you are moving? How do you even define moving? Since you reside in deep space, and you are away from the buoys, no objects exist near-by against which to measure your speed. And the vacuum provides no reference point. Einstein, and others, thought about this. They possessed Maxwell’s laws of electromagnetism, laws which gave, from first principle, the speed of light in a vacuum. Now if no reference point exists in a vacuum against which to measure the speed of a physical object, could any (non-accelerated) motion be a privileged motion? Would there be a special motion (aka speed) at which the observer gets the “true” speed of light, while other observer’s moving at a different speed would get a speed of light impacted by that observer’s motion. Physicists, Einstein especially, concluded no. If a privileged reference frame exists, then observers at the non-privileged speed would find light violates Maxwell’s laws. And Maxwell’s laws stood as so sound that rather than amend those laws, physicists set a new assumption – relative speed can’t change the speed of light. Ahh, you say. You see a way to determine whether the Hyperion is moving. Just compare its speed to the buoys; they are stationary, right? Really? Would they not be moving relative to the center of our galaxy? Doesn’t our galaxy move relative to other galaxies? So who or what is not moving here? In fact, if we consider the whole universe, we can not tell what “true” speeds objects possess, only their speed relative to other objects. If no reference point provides a fixed frame, and if we can only determine relative speed, Maxwell’s laws, and really the nature of the universe, dictate all observers measure light as having the same speed. Contraction of Time If the speed of light remains constant, what varies to allow that? And something must vary. If I am moving relative to you at near the speed of light (remember, we CAN tell speed relative to each other; we can NOT tell absolute speed against some universally fixed reference) and we measure the same light pulse, one of use would seem to be catching up to the light pulse. So some twist in measurement must exist. Let’s go back our freighter. Imagine the Hyperion travels right to left, with respect to the buoys. As noted, the buoys form a square 30 kilometers on each side (as measured at rest with respect to the buoys). As the Hyperion enters the buoy configuration, its front end cuts an imaginary line between the right two buoys. It enters at a right angle to this imaginary line, but significantly off center, only a few hundred meters from one right buoy, almost 30 kilometers from the other right buoy. Just as the front of the freighter cuts the line, the near right buoy fires a light pulse right across the front of the freighter, to the second right buoy, 30 kilometers away. The light travels out, hits the second right buoy, and bounces back to the first right buoy, a round trip of 60 kilometers. Given light travels 300 thousand kilometers a second, rounded, or 0.3 kilometers in a micro-second (one millionth of a second), the round trip of the light pulse consumes 200 micro-seconds. That results from dividing the 60 kilometer round trip by 0.3 kilometers per That calculation works, for an observer stationary on the buoy. It doesn’t work for you on the Hyperion. Why? As the light travels to the second right buoy and back, the Hyperion moves. In fact, the Hyperion’s speed relative to the buoys is such that the back of the freighter arrives at the first right buoy when the light pulse returns. From our vantage point, on the freighter, how far did the light travel? First, we realize the light traveled as if along a triangle, from the front of the ship, out to the second right buoy and back to the back of the ship. How big a triangle? The far right buoys sits 30 kilometers from the first right buoy, so the triangle extends 30 kilometers high, i.e. out to the second right buoy. The base of the triangle also extends 30 kilometers – the length of the ship. Again, let’s picture the light travel. In the Hyperion’s reference frame, the light passes the front of the ship, hits the second right buoy, and arrives back at the back of the freighter. Some geometry (Pythagorean theory) shows that a triangle 30 high and 30 at the base will measure 33.5 along each of the slanted sides. We get this by splitting the triangle down the middle, giving two right triangles 15 by 30. Squaring then summing the 15 and 30 gives 1125 and the square root of that gives 33.5. In our reference frame then, the light travels 67 kilometers, i.e. along both the slated sides of the triangle. At 0.3 kilometers per micro-second, we measure the travel time of the light pulse at just over 223 micro-seconds. Remember, our observer stationary on the buoy measured the time travel at 200 micro-seconds. This reveals a first twist in measurements. To keep the speed of light constant for all observers, clocks moving relative to each other will measure, must measure, the same event as taking different amounts of time. In particular, to us on the Hyperion, the clock on the buoys is moving, and that clock measured a shorter time. Thus, clocks moving relative to a stationary clock tick slower. Again, that is the twist. Clocks moving relative to an observer tick slower than clocks stationary with respect to that observer. But wait. What about an observer on the buoy. Would they not say they are stationary? They would conclude stationary clocks tick slower. We have a subtle distinction. We can synchronize clocks at rest relative to us. Thus we can use two clocks, one at the back of the Hyperion and the other at the front, to measure the 223 micro-second travel time of the light beam. We can not synchronize, or assume to be synchronized, moving clocks. Thus, to compare the travel time of the light in moving verses stationary reference frames, we must measure the event in the moving reference frame with the same clock. And to observers on the buoy, the Hyperion was moving, and on the Hyperion the event was measured on two different clocks. Given that, an observer on the buoys can not use our two measurements to conclude which clocks tick slower. Uncoupling of Clocks This uncoupling of clock speeds, this phenomenon that clocks moving relative to us run slower, creates a second twist: clocks moving relative to us become uncoupled from our time. Let’s step through this. The Hyperion completes its freight run, and once back home in the solar system, the ship undergoes engine upgrades. It now can now reach two-thirds the speed of light at mid-flight. This higher speed further widens the differences in measured times. In our example above, at about half the speed of light, the moving reference frame measured an event at 89% of our measurement (200 over 223). At two-third the speed of light, this slowing, this time dilation, expands to 75%. An event lasting 200 micro-seconds measured on a moving clock will measure 267 micro-seconds on a clock next to us on the freighter. We reach mid-flight. As we pass the right buoy, we read its clock. For ease of comparison, we won’t deal with hours and minutes and seconds, but rather just the position of a hand on a micro-second As the front of the Hyperion passes the buoy, the buoy clock reads 56 micro-seconds before zero. Ours reads 75 micro-seconds before zero. The buoy clock thus now reads slightly ahead of ours. Now remember, we think we are moving. However, from our perspective, the buoy clock moves relative to us, while clocks on our freighter stand stationary relative to us. So the buoy clocks are the moving clocks, and thus the clocks that run slower. With the Hyperion at two thirds of the speed of light relative to the buoy, the buoy travels past us at 0.2 kilometers per micro-second (speed of light is 0.3 kilometers per micro-second). Thus by our clocks, the buoy travels from the front of the freighter to the midpoint in 75 micro-seconds (15 kilometers divided by 0.2 kilometers per micro-second). The freighter clocks are synchronized (a complex procedure, but feasible), and thus we see the micro-second hand at zero micro-seconds on our clock. What do we see on the buoy? We know its clocks run slower. How much slower? By a “beta” factor of the square root of (one minus the speed squared). This beta factor falls right out of the Pythagorean math above, but the details, for this article, are not critical. Simple remember the key attributes, i.e. a moving clock runs slower and that an equation – one tied to the (relatively) simple Pythagorean Theorem – exists to calculate how much slower. The beta factor for two thirds the speed of light equates to just about 75%. Thus, if our clocks advanced 75 micro-seconds as the buoy traveled from front to mid-section, the buoy clocks advanced 75% of 75 or 56 micro-seconds. The buoy clock read 56 micro-seconds before zero when that clock passed the front of the Hyperion, so it now reads zero. The buoy now travels farther and passes the back of the Hyperion. That is another 15 kilometers. Our clocks advance to 75 micro-seconds, while the buoy clock moves up to only 56 micro-seconds. This progression reveals a key phenomenon – not only do moving clocks tick slow, those clocks read different times. At some points, those moving clocks read an earlier time than clocks stationary to us, and at times, they read a time later than clocks stationary to us. We thus see moving objects in what we would consider our past or future. Very spooky. Do we have some type of vision into the future then? Could we somehow gather information about the moving reference frame, and enlighten them on what will come? Or have them enlighten us? No. We might see the buoy at a time in our future (as the buoy passes the front of the Hyperion, its clock reads 56 micro-seconds before zero, or19 micro-seconds earlier than our clock). We however do not also simultaneously see the buoy at our present, i.e. 75 micro-seconds before zero. To cheat time, to tell the buoy about its future, we need to take information from one point in time and communicate that information to another point in time. And that never happens. We see the buoy in our future, then in our present, and then our past, but as that happens we do not see the buoy at another point in time. We thus cannot communicate any future knowledge to the buoy. Length Contraction Let’s summarize quickly. The laws of nature dictate all observers, regardless of motion, will measure light at the same velocity. That dictate implies and requires that clocks moving relative to an observer will tick slower, and further implies and requires that time registering on moving clocks will be uncoupled from time registering on clocks stationary to us. Do we have more implications? Yes. The constancy of light speed requires and dictates that moving objects contract in length. As the buoys speed by, at a particular instant, the Hyperion should align with the buoys. Our 30 kilometer length equals the 30 kilometer buoy separation. Thus, when our ship aligns itself side-by-side with the buoys, observers at the front and back of the Hyperion should see the buoys. But this doesn’t happen. Our observers on the Hyperion don’t see the buoys when the mid-ship point of the Hyperion aligns with the midpoint between the buoys. In fact, at this alignment, the Hyperion observers must look towards mid-ship to see the buoys. At alignment of mid-ship of the Hyperion to midpoint between the buoys, each of the buoys lies over 3 kilometers short of the ends of the What happened? Why do we not measure the buoys 30 kilometers apart? What caused the 30 kilometer separation to shrink almost 7 kilometers? What happened, what we have encountered, represents another ramification of the constancy of the speed of light, specifically that we measure a moving object as shorter than when we measure the object at rest. How does that occur? Let’s uncover that by assuming that we had measured the moving buoys as still 30 kilometers apart, then by doing some math with that assumption. We will find that we will run right into a contradiction. That will indicate our assumption can not be right. Let’s run the calculations. As noted above, we will assume we measure the buoys 30 kilometers apart. The buoys, under this assumption, will align with the ends of the Hyperion. For our experiment, at that instant of alignment, we fire light beams from the ends of the Hyperion towards the middle. To keep things straight, we need distance markers on the Hyperion, and on the buoys. We will label the two ends of the Hyperion plus 15 kilometers (the right end) and minus 15 kilometers (the left end), and by extension, the middle of the ship will be zero. The Hyperion clocks will read zero micro-seconds when light beams start. We will also mark the buoys as being at minus 15 and plus 15 kilometers, and by extension, a point equidistant between the buoys as distance zero. A clock will be placed at the buoy zero point. That clock will read zero micro-seconds when the mid-ship on the Hyperion aligns with the midpoint of the buoys. Now let’s follow the light beams. They of course race towards each other until they converge. On the Hyperion, this convergence occurs right in the middle, at distance marker zero. Each light beam travels 15 kilometers. Given light travels at 0.3 kilometers per micro-second, the light beams converge in 50 micro-seconds. The buoys move past the Hyperion at two thirds the speed of light, or 0.2 kilometers per micro-second. In the 50 micro-seconds for the light to converge, the buoys move. How much? We multiply their speed of 0.2 kilometer per micro-second times the 50 micro-seconds, to get 10 kilometers. With this 10 kilometer shift, when the light beams converge, our zero point aligns with their minus 10 kilometer point. Remember, if the Hyperion travels right-to-left, then on the Hyperion, we view the buoys at traveling left-to-right. On the Hyperion, we see the light beams each travel the same distance. What about observers in the moving frame, i.e. moving with the buoys? They see the light beams travel different distances. The light beam starting at the right, at plus 15, travels all the way to minus 10 kilometers, in the buoy reference frame. That represents a travel distance of 25 kilometers. The light starting at the left, at minus 15, travels only 5 kilometers, i.e. from minus 15 kilometers to minus 10 kilometers. These unequal travel distances occur, of course, because the buoys move during the light beam In the buoy frame of reference, one light beam travels 20 kilometers farther than the other. For them to meet at the same time, the beam traveling the shorter distance must wait while the other light beam covers that extra 20 kilometers. How much of a wait? At the 0.3 kilometers per micro-second that is 66.7 micro-seconds. Let’s contemplate this. In our stationary reference frame, the light beams each start at time equal zero on clocks on both ends of the Hyperion. For the buoys though, light leaves one buoy, the buoy at distance plus 15, 66.7 micro-seconds earlier, than the one that leaves the buoy at distance minus 15. At the start of this experiment, we set the clock at the mid-point between the buoys at time equal zero. By symmetry, with this 66.7 micro-second difference, the clock at the minus 15 point must have read plus 33.3 micro-seconds, and the clock at the plus 15 point must have read minus 33.3, when the light beams left. What about the meet point, at minus 10 in the buoy reference frame? What was the time at the meet point in the reference frame of the buoys, when the light beams left? Remember, the meet point in the buoy frame of reference is minus 10 kilometers. If the minus 15 point is 33.3 micro-seconds, the minus 10 point is 22.2 micro-seconds. We now pull in that clocks run slower in the moving frame. At two thirds the speed of light, clocks run at 75% (or more precisely 74.5%) the rate of clocks in our stationary frame. Given our clocks measured 50 micro-seconds for the light travel time, the clocks on the buoys measure a light travel time of 37.3 micro-seconds. A bit of addition gives us the meet time in the buoy reference frame. The clocks at the meet point read plus 22.2 micro-seconds when the light started, and advance 37.3 micro-seconds during the light travel. We thus have a meet time of 59.5 micro-seconds in the moving reference frame, i.e. the buoy reference frame. Now comes the contradiction. The light started from the minus 15 point at 33.3 micro-seconds, and arrives at the minus 10 point at 59.5 micro-seconds. Let’s call that a 26 micro-second travel time. The travel distance was 5 kilometers. The implied speed, i.e. 5 kilometers divided by the 26 micro-second travel time, comes out to 0.19 kilometers per micro-second. From the other end, the light traveled 25 kilometers, in 92.8 micro-seconds (from minus 33.3 to plus 59.5). The implied speed, i.e. 25 kilometers divided by the 93 micro-second travel time, comes out to 0.27 kilometers per micro-second. No good. Light travels at 0.3 kilometers per micro-second. When we assumed that we would measure the buoys 30 kilometers apart, and adjusted the clocks to try to fit that assumption, we did NOT get the speed of light. Remember critically that all observers must measure the speed of light as the same. Clock speeds, and relative time readings, and even measured distances, must adjust to make that happen. How far apart DO the buoys need to be, for the buoys to align with the ends of the Hyperion? They need to be 40.2 kilometers apart. With the buoys 40.2 kilometers apart, the front and back of the Hyperion will align with the buoys, when the mid-ship (of the Hyperion) and the midpoint (of the buoys) align. Amazing, almost incomprehensible. The need for all observers to measure the same speed of light dictates that we measure moving objects shorter, significantly shorter, than we would measure them at What will the buoy clocks read, if we adopt this 40.2 kilometers spacing? When the ship and the buoys align, the left buoy clock will read plus 44.7 micro-seconds and the right buoy clock will read minus 44.7 micro-seconds. Since the light beams fire when the ships and buoys align, the light beam on the right leaves 89.4 micro-seconds before the light beam on the left, in the buoy frame of That time difference equates to the right beam traveling 26.8 kilometers before the left beam starts, as seen in the buoy frame of reference. Both beams then travel 6.7 kilometers until they met. The 26.8 plus 6.7 twice totals to the 40.2 kilometer between the buoys. The left beam starts at location minus 20.1, at time plus 44.7 micro-seconds, and travels 6.7 kilometers. Light needs 22.4 micro-seconds (6.7 divided by 0.3) to travel the 6.7 kilometers. Thus, the clock at the minus 13.4 point (minus 20.2 kilometers plus the 6.7 kilometers the left light beam traveled) should read 67.1 micro-seconds when the left light beam gets there. Does it? By proportions, when the buoys and the Hyperion align, a clock at the minus 13.4 point would read plus 44.7 minus one-sixth of 89.4. One-sixth of 89.4 is 14.9, and 44.7 minus 14.9 would be 29.8 Remember now that the buoy clocks must advance 37.3 micro-seconds during the travel of the light beams. That occurs because on the Hyperion, the light beam travel requires 50 micro-seconds, and the buoy clocks must run slow by a factor of 75 percent (or more precisely 74.5 percent). Add the 29.8 and the 37.3, and we get 67.1 micro-seconds. We stated earlier that the clock at minus 13.4 kilometers should read 67.1 micro-seconds when the left light beam arrives. And it does. A separation of the buoys by 40.2 kilometers thus aligns the clocks and distances on the buoys so that they measure the correct speed of light. What Really Happens But do moving objects really shrink? Do the atoms of the objects distort to cause the object to shorten? Absolutely not. Think about what we were reading on the clocks. While the clocks on the Hyperion all read the same time, the clocks in the moving reference frame all ready different times. Moving distances shrink because we see the different parts of the moving object at different times. With the buoys 40.2 kilometers apart (measured at rest), we saw the left buoy at plus 44.7 micro-seconds (in its reference frame) and the right buoy at minus 44.7 micro-seconds. Let’s look at another way to conceive of length contraction, in a more down-to-Earth example. Picture a long freight train, four kilometers long, moving at 40 kilometers an hour. You and a fellow experimenter stand along the tracks three kilometers from each other. When the front on the train passes you, you signal your partner. Your partner waits 89 seconds and takes note of what part of the train now passes in front of him. What does he see? The end of the train. The four kilometer train fit within the three kilometer separation between you and your fellow experimenter. That occurred because your partner looked at the train later than you. This is NOT precisely how fast moving objects impact measurements. In our train example, we created two different times of observation by waiting. In the Hyperion situation, we didn’t need to wait – the near light passing speed of the buoys created a difference in the clock observation times. Though not an exact analogy, the simplified train example DOES motivate how measuring the length of something at two different times can distort the measurement. The train example also demonstrates that we can shorten the measured length of an object without the object physically shrinking. While the shrinkage does not really happen, the time stamps differences are real. In our Hyperion example, with the light beams, if we went back and picked up the clocks on the buoys, those clocks would record that the light beams we fired really did start 89.4 micro-seconds apart. We would look at our Hyperion clocks, and our Hyperion clocks would really show that in our reference frame the light beams started at the same time. Are the Clocks Smart? How do the clocks “know” how to adjust themselves? Do they sense the relative speeds and exercise some type of intelligence to realign themselves? Despite any appearances otherwise, the clocks do not sense any motion or perform any adjustments. If you stand beside a clock, and objects zip by you at near the speed of light, nothing happens to the clock next to you. It makes no adjustments, changes, or compensations for the sake of passing objects. Rather, the geometry of space and time cause an observer to see moving clocks ticking slower, and moving objects measuring shorter. If you move away from me, and I measure you against a ruler held in my hand, your measured height shrinks proportional to your distance from me. Your looking smaller results from the smaller angle between the light from you head and the light from your feet as you move away. The light didn’t need to know what to do, and the ruler didn’t adjust. Rather, the geometry of our world dictates that as you move away you will measure shorter. Similarly, if I place lens between you and a screen, I can expand or shrink your height through adjustments of the lenses. The light doesn’t need to know how adjust; the light simply follows the laws of physics. So using distance and lens, I can make the measurement of you height change. I could readily write formulas for these measurement changes. Similarly, moving clocks read slower from the nature of time. We think clocks need to “know” how to adjust, since our universal experience at low velocities indicates clocks run at the same rate. But if we were born on the Hyperion and lived our lives traveling at near light speeds, the slowing of clocks due to relative motion would be as familiar to us as the bending of light beams as they travel through lens. All observers must measure the speed of light as the same. That attribute of nature, that fact of the geometry of space and time, creates counter-intuitive but nonetheless real adjustments in observations of time and space. Moving clocks run slower, they become uncoupled from our time, and any objects moving with those clocks measure shorter in length.	{"url":"https://rooffi.info/special-relativity-physics-at-the-speed-of-light/","timestamp":"2024-11-05T08:40:21Z","content_type":"text/html","content_length":"116393","record_id":"<urn:uuid:25c58e9e-4333-4076-81b8-2805ef7b0dd0>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00883.warc.gz"}
(PDF) Quantum image representation: a review Author content All content in this area was uploaded by Marina Lisnichenko on Sep 05, 2022 Content may be subject to copyright. Author content All content in this area was uploaded by Marina Lisnichenko on Sep 05, 2022 Content may be subject to copyright. Author content All content in this area was uploaded by Stanislav Protasov on Feb 24, 2022 Content may be subject to copyright. Quantum Image Representation: A Review Marina Lisnichenko MSc 1* and Dr Stanislav Protasov PhD MLKR Laboratory, Innopolis University, Universitetskaya, Innopolis, 420500, Tatarstan Republic, Russia. *Corresponding author(s). E-mail(s): Contributing authors: s.protasov@innopolis.ru; Quantum programs allow to process multiple bits of information at the same time, which is useful in multidimensional data handling. Images are an example of such multidimensional data. Our work reviews 14 quan- tum image encoding works and compares implementations of 8 of them by 3 metrics: number of utilized qubits, quantum circuit depth, and quantum volume. Our work includes a practical comparison of 2nˆ2n images encoding, where nvaries from 1up to 8. We observed that Qubit Lattice approach shows the minimum circuit depth as well as quantum volume, Flexible Representation of Quantum Images (FRQI) utilizes the minimum number of qubits. If to talk about variety of processing tech- niques, FRQI and Novel Enhanced Quantum Representation (NEQR) representations are the most fruitful. As far as quantum computers are limited in qubit number, we concluded that almost all approaches except Qubit Lattice are promising for the near future of quantum image representation and processing. From the point of view of the quantum depth, discrete methods showed the most appropriate result. Keywords: quantum images, complexity, quantum algorithms, quantum image processing 2Quantum Image Representation: A Review 1 Introduction Quantum computation is a rapidly developing ﬁeld. In 2021 private capital investments in quantum computations exceeded $3B [1]. Due to the quan- tum parallelism the information processing is performed potentially faster. Acceleration of the calculations through parallelism is highly relevant to mul- tidimensional data, including images. In the quantum programs, images are usually represented in the same way as in classical machines – with pixel coor- dinates and pixel intensities, but amplitude and phase encodings use diﬀerent physical parameters for these values. In this work, we compare 14 ways of image encoding including methods: with quantum state amplitudes – amplitude- angular (continuous), qubit binary – amplitude-state (discrete), mixed, and phase image representations. We implemented 8 core representation techniques (other methods are derived or equivalent to the implemented and share their characteristics) for the practical comparison1. Our survey covers the following quantum image representation methods: •qubit lattice [2] (2003); •real ket [3] (2005); •ﬂexible representation of quantum images - FRQI [4] (2011); •multi-channel representation for images - MCRQI [5] (2011); •novel enhanced quantum representation of digital images - NEQR [6] •quantum states for M colors and quantum states for N coordinates - QSMC and QSNC [7] (2013); •a simple quantum representation - SQR [8] (2014); •normal arbitrary quantum superposition state - NAQSS [9] (2014); •generalized quantum image representation - GQIR [10] (2015); •quantum representation of multi wavelength images - QRMW [11] (2018); •quantum image representation based on bitplanes - BRQI [12] (2018); •order-encoded quantum image model - OQIM [13] (2019); •quantum representation of indexed images and its applications - QIIR [14] •Fourier transform qubit representation - FTQR [15] (2020). The review contains the information about quantum image representation methods and applicable image processing techniques. To compare the methods, we use 3 parameters: •number of utilized qubits - each existing computer is limited in number of qubits and this number deﬁnes the possibility of algorithm execution; •circuit depth - length of the longest quantum gate path from the zero- state to the end of the encoding procedure. The bigger the depth is, the more errors aﬀect on the output result quality. This metric is an analogy of the classical time complexity; •quantum volume - squared minimum between the circuit depth and num- ber of qubits. This metric varies for diﬀerent quantum machines, and Quantum Image Representation: A Review 3 depends on the base gates. Quantum volume is an integral metric which allows to evaluate a computing capability with a single quantity. In conclusion 3we sum the observed information and make a statement about future work. 2 Quantum image representation (QIR) We identiﬁed four major ways of quantum image representation: continuous amplitude representation, where pixel intensity is encoded with quantum state amplitude p, corresponding to observation probability p2,ampli- tude with binary intensity representation (discrete), mixed, and phase intensity representation. Figure 1shows the suggested classiﬁcation. Continuous representation allows to use a single qubit for intensity or coordinate encoding. This is the main advantage of the methods. Multiple measurements are required to estimate the pixel intensity with high precision. In the discrete intensity representation, oppositely, each state corresponds to separate intensity or coordinate bit-value. Measurement result contains accurate data expansion of a single pixel data. Mixed representations either store pixel coordinates discretely or do not encode coordinate. Phase encoding uses continuous representation, but in an XY Bloch sphere projection plane. In the following subsections, we describe each approach separately. 2.1 Mixed representation The chapter describes quantum image representation algorithms based on both discrete and continuous methods. It’s common for mixed methods where continuous encoding is used for the pixel intensity and the pixel location is represented discretely. We also include Qubit Lattice and SQR algorithms, however these methods do not have a speciﬁc coordinate encoding procedure. 2.1.1 Qubit Lattice Venegas-Andraca and Bose [2] did a major preparatory work in the quantum image representation and processing. The paper describes the basic quantum deﬁnitions and measured results interpretation. Proposed image representa- tion is na¨ıve and consists of literally copying the classical representation into quantum. Authors suggest to use Ryrotation gate to set each pixel’s inten- sity. Therefore, the number of utilized qubits is 22nwhere 2nˆ2nis an image size. Figure 2b shows an example of encoding the image with pixel intensities Coordinate qubits absence and quantum circuit simplicity are the strong sides of the encoding method. Due to simplicity, authors of quantum convolu- tional neural networks papers actively utilize this representation method (or 4Quantum Image Representation: A Review Quantum image representation Amplitude Phase Continuous Discrete SQR, Qubit attice FRQI, MCRQI, Real ket QSMC & QSNC NEQR, QUALPI, GQIR QRMW, BRQI, QIIR Fig. 1: Quantum image representation (QIR) classiﬁcation Fig. 2: (a) Classical image and (b-f) quantum image representations modiﬁed) even if it is not evidently claimed [16], [17], [18]. At the same time, classical image processing based on Qubit Lattice did not spread. The approach has strong negative sides such as big number of used qubits and small number of known processing methods. However, for the sake of justice, it is the ﬁrst formulation of quantum image storing. 2.1.2 FRQI Authors [4] use the continuous amplitude encoding with intensity-to-amplitude \|Ipαqy “ 1 i“0pcosαi\|0y ` sinαi\|1yqb \| iy(1) where \|Ipαqy is a quantum image representation, αis a parameter responisble for intensity and equal to a half of Ryrotation angle, \|iyrepresents the pixel coordinate binary expansion. The greater αis, the closer pixel intensity to the Quantum Image Representation: A Review 5 maximum. Therefore, the precision of the intensity estimation depends on the number of circuit executions. Figure 2c shows the image with pixel intensities t0,125,200,255u. The image representation code is available in our repository. The FRQI implies a huge number of processing algorithms. For example, the paper presents processing algorithms that aﬀect intensity, coordinate, or both intensity and coordinate. The ﬁrst processing group changes all the pixel intensities, the second group changes intensity at some locations, the last group ”targets information about both color and position as in Fourier transform”. Moreover, multi-channel expansion [19], image compression, line detection [4], binarization, histogram computing, histogram equalization [20], global and local translation designs [21] are also available for FRQI. The image repre- sentation technique maintains comprehensive processing such as information hiding [22], Richardson-Lucy image restoration [23], multilevel segmentation [24], hybrid images creating [25]. Additionally, FRQI helps to ﬁnd correla- tion property of multipartite quantum image [26], implement image fusion [27], encrypt images via algorithm based on Arnold scrambling and wavelet transforms [28]. At the same time, FRQI has the following drawbacks: •due to the single intensity qubit ”some digital image-processing operations for example certain complex color operations”, are impossible (such as ”partial color operations and statistical color operations”) [6]. •circuit depth is Op24nqfor 2nˆ2nimage [6]. FRQI is beneﬁcial for the applications with limited qubit number and does not demand high intensity precision. FRQI supports broad spectrum of quan- tum image processing techniques useful for basic image processing. However the continuous intensity representation approach may limit such processing algorithms as edge detection and texture features. 2.1.3 MCRQI The authors of [5] apply FRQI 2.1.2 approach to the RGBα images, where α is a transparency channel. The diﬀerence is in the number of qubits used to encode an intensity. Authors represent the multichannel image as follows: \|Ipθqy “ 1 RGBα yb \| iy(2) where \|ci RGBα yis a color state and equals to: RGBα y “ 1 2ˆ„cos θRi \|0y sin θRi \|1yȷb \| 00y ` „cos θGi \|0y sin θGi \|1yȷb \| 01y` „cos θBi \|0y sin θBi \|1yȷb \| 10y ` „cos θαi \|0y sin θαi \|1yȷb \| 11y˙. 6Quantum Image Representation: A Review Multi-channel representation encodes intensities P r0,255swith angles θRi, θGi , θBi , θαi P r0,π 2svia uniform scaling. As far as image has several channels, authors say about applicability of the one-channel operations for each of them. Autors [29] developed a chromatic framework for quantum movies and provided frame-to-frame and color of interest operations, sub- block swapping. Yan et al. described audio-visual synchronisation in quantum movies using MCRQI [30]. Sun et al. proposed channel of interest realization, channel-swapping and αblending operations [31]. Hu et at. all proposed image encryption based on FRQI modiﬁcation [28]. The MCRQI has the same pros and cons as the FRQI. Additionally, to get access to each color layer channels r, g, b has to be measured separately. 2.1.4 SQR The authors [8] combine Qubit Lattice image representation with normalized pixels and NEQR (see 2.3.1) approach of max and minimum pixel values. Instead of pixel intensity authors use ”energy” term to show the relation to the infrared images. Their paper describes the Qubit Lattice approach [2] with modiﬁcations. Authors of the Qubit Lattice converted intensities directly into angles, while in SQR intensities go through a normalization step ﬁrst. Suppose, Eij is an energy value detected at the position i, j,Emminimum energy value, EMmaximum energy value. The normalized energy value is ˜ Eij “Eij ´Em Eij determines Ryrotation angle via the following expression: θij “2 arcsin ˜ Eij (4) To encode complete image information, 10 qubits store EMand Emenergy values. Totally, to encode an image of size 2nˆ2nalgorithm needs 2nˆ2n`10 Authors provide clear explanation of how to convert energy into quantum representation and why is it so intuitive. Due to narrow representation spec- iﬁcation, the SQR did not become widespread in terms of processing. Paper describes global and local operations, “retrieval of marked information” (kind of segmentation). However the approach is still ”heavy” in qubits. 2.1.5 Real Ket Latorre [3] attempted to separate a pixel’s coordinates and intensity into quad- rants. The ﬁrst step of the encoding is to split image into 4 parts (upper-left, upper-right, lower-left, and lower-right). Next, the same step (splitting) repeats until each block contains a quad of pixels. A pair of qubits describes the grid- square pixel coordinate and additional qubit’s amplitude holds intensity. This method, as well as FRQI, intensively uses multicontrol Rygated (Figure 3a), but Real Ket does not have a dedicated intensity qibit. In theorem 8 authors of [32] proved that decomposition of one such k-qubit controlled gate requires 2kCNOT gates. Quantum Image Representation: A Review 7 Overall, the algorithm requires 2n`1 qubits, where 2nˆ2nis an image size. The ﬁnal state equation is the following: \|Ψ2nˆ2ny “ ÿ cin,...,i1\|in, ..., i1y.(5) where \|Ψyis a quantum image, cipixel intensity, inis a representation of the pixel’s location corner in the 4 ˆ4 grid. Figure 3b gives graphical pixels’ coordinates representation for the 4 ˆ4 image. (a) Multicontrol Ry gate (b) Real Ket image encoding Fig. 3: (a) Multicontrol Ry gate (gate consists of 3 control qubits that rotate the last one – target – qubit for an angle α) and (b) Real Ket coordinate Authors of the paper describe the image compression algorithm based on Fourier transform. Ma et al. proposed quantum Radon transform based on Real Ket encoding [33]. The similar image representation is used for low-rank tensor completion [34]. 2.2 Pure continuous representation Representation algorithms of the current chapter utilize only continuous amplitude encoding for both pixel intensity and coordinates. 2.2.1 QSMC and QSNC Suppose the image consists of mdiﬀerent pixel intensities taken from Mpos- sible (if an image is an 8-bit gray-scaled, M“256), and contains N“2nˆ2n pixels. The authors [7] split image representation into 3 parts: quantum reg- ister for mcolors (QSMC), quantum register for Ncoordinates (QSNC), and image storing. Authors provide the following intensity representation algorithm, which we reproduced in our repository. If \|wiyis a pixel intensity representation and \|uiyis a pixel coordinate representation, then full pixel representation is \|ψiy “\| wiyb \| uiy. The paper proves the reliability of the method from the mathematical prospects. Moreover, the authors provide a quantum image compression algo- rithm and image segmentation based on extended Grover search [35].The 8Quantum Image Representation: A Review method was not broadly utilized in quantum image processing and we could not ﬁnd any publications based on it. The main weakness of the method is the continuous approach to coordinate representation. When the number of pixels becomes bigger, even a small shift in probabilities aﬀects the outcome. For example, IonQ QPU’s Rygate precision is 10´3πradians [36], what makes impossible to encode coordinates of image larger than 512 ˆ512. In this case the coordinate encoding error becomes signiﬁcant and coordinate estimation precision decreases. 2.2.2 OQIM The authors [13] provide a way to store classical images by intensity sorting. Firstly, authors map the ordered pixel intensities present in the image to num- bers. Then the continuous representation deﬁnes pixel color and coordinate (θ and ϕrespectively). Figure 2d provides an example of the 2 ˆ2. The authors’ idea is to utilize a single qubit for both intensity and coor- dinate. An additional qubit controls the mode of representation (coordinate or intensity). Thus, for the image represented in the ﬁgure 2a the following equation holds: \|Iy “ 1 `pcos θ0\|0y ` sin θ0\|1yq \| 0y`pcos ϕ0\|0y ` sin ϕ0\|1yq \| 1y˘b \| 00y` `pcos θ1\|0y ` sin θ1\|1yq \| 0y`pcos ϕ1\|0y ` sin ϕ1\|1yq \| 1y˘b \| 01y` `pcos θ2\|0y ` sin θ2\|1yq \| 0y`pcos ϕ2\|0y ` sin ϕ2\|1yq \| 1y˘b \| 10y` `pcos θ3\|0y ` sin θ3\|1yq \| 0y`pcos ϕ3\|0y ` sin ϕ3\|1yq \| 1y˘b \| 11yı(6) Authors propose the histogram speciﬁcation process that allows to shift the image histogram. Authors provide ”image comparison between two images and multiple images..., the parallel quantum searching” [37]. Paper also covers the multidimensional OQIM case. Basic algorithm implementation is available in our repository. 2.2.3 NAQSS Authors’ encoding approach [9] is similar to the QSMC and QSNC (section 2.2.1). Encoding starts with color representation. If colorirepresents the ith pixel color, then colors tcolor1, color2, ..., colorMu- a set of all possible colors for the image. Therefore rotation angle ϕi“πpi´1q 2pM´1qdeﬁnes ith state rotation angle. For the RGB image, each color value is i“Rˆ256ˆ256`Gˆ256`B`1 what takes range from color1“ p0,0,0qto color16777216 “ p255,255,255q. The coordinate representation is the following. Suppose data has kdimen- sions (for ﬂat image we assume k“2). Then, each pixel sets in the following Quantum Image Representation: A Review 9 \|ψϕy “ ai\|v1y \| v2y... \|vky(7) where i“i1...ijij`1...il...im...inis a binary expansion of the coordinate v1“i1..ij,v2“ij`1...iland vk“im...inare the expansions of each coordinate The approach bases on a normalised intensity representation: where aiis an intensity of current pixel iand ř2n´1 Authors suggests to use image cropping and extend circuit by 1 qubit. The equation explains the cropped quantum image: \|Ψy “ θi\|v1y \| v2y... \|vky \| χiy(9) where \|χiy “ cosγi\|0y ` sinγi\|1y,γi”represents the serial number of the sub-image which contains the pixel corresponding to the coordinate \|v1y \| v2y... \|vky”. Simply – index of a sub-image. The idea of image cropping index allows to retrieve a target sub-image (segmentation) from a quantum system. Additionally, a single qubit is a cheap way of color representation. Li et al. described image encryption based on nor- mal arbitrary superposition state [38]. Based on geometric transformations of multidimensional color images based on normal arbitrary superposition state authors provide such transformations as two-point swapping, ﬂip (unclud- ing local), orthogonal rotation, and translation [39]. Zhou and Sun proposed multidimensional color images similarity comparison for QNASS encoded images [40]. 2.3 Pure discrete representation Representation algorithms of this chapter utilizes only discrete amplitude encoding for both pixel intensity and coordinates. Methods described here utilizes the multcontrol CX-gate as in the ﬁgure 4. Fig. 4: multi-control CX gate. Gate consists of 3 control qubits that apply NOT operation on the last one - target - qubit 10 Quantum Image Representation: A Review 2.3.1 NEQR Authors [6] suggest to use full intensity binary expansion for image encoding. The most powerful thing of this explicitly encoded approach is the possibility to read intensity determinedly. The image with the intensity range 2q(where qequals 8 in case of 256 intensity levels) is encoded in the following way: \|Iy “ 1 Y X y \| Y X y(10) Where \|Ci Y X yand \|Y X yare intensity and coordinate expansions respectively. The same principle INCQI authors use in their paper [41]. Figure 2e represents an example of the image encoded with NEQR. The algorithm code is available in the repository. Apart from determinism, the NEQR has several advantages. The paper says about ”partial color operations and statistical color operations” [6]. The authors of the described paper split all possible image operations into 3 groups: •Complete Intensity Operations (CC): changes pixel’s intensity in a whole image or it’s area. •Partial Intensity Operations (PC): changes intensity of pixels in the certain gray-scaled range. •Color Statistical Operation (CS): computes intensity statistics. Authors extended approach to the log-polar images in QUALPI [42] (ﬁgure 2f shows the encoding example). Additionally, such comprehensive processing as complement intensity transformation and upscaling are also described in the book [19]. Next, strong point of the NEQR is a more eﬃcient circuit compression algorithm. The Espresso Boolean expressions compression [43] is a base for this algorithm. While FRQI algorithm compression ratio is 50% of utilized gates, NEQR allows to reduce the number of gates by 75%. The negative side appears from the determinant approach. Each intensity expansion leads to utilizing as much qubits as the length of the expansion. Thus, the quantum circuit depth increases proportionally to the image inten- sity resolution. However image size increases the number of utilized qubits only As a result, NEQR is useful for reliable intensity representation, supports large images and comprehensive processing. The approach is less applicable for data with high intensity resolution. However this encoding approach is boun- tiful in terms of processing techniques. For instance, identiﬁcation of desired pixels in an image using Grover’s quantum search algorithm [44], edge extrac- tion based on Laplacian operator [45], scaling [46], least squares ﬁltering [47], morphological gradient [48], edge extraction based on classical Sobel opera- tor [49], quantum image histogram [50], edge extraction based on improved Prewitt operator [51], mid-point ﬁlter [52] dual-threshold quantum image segmentation [53], steganography based on least signiﬁcant bit [54], erosion Quantum Image Representation: A Review 11 and dilation [55]. Finally, the same encoding method is used for LSB-Based quantum audio watermarking [56]. Fig. 5: Non-square image, empty cells are expanding to powers of 2 2.3.2 GQIR The authors [10] refer to the NEQR approach (section 2.3.1) and suggest an approach to represent nonsquare images. Figure 5represents the possible nonsquare image with binary intensity expansions 00000000,10000000, and 11111111 respectively for each pixel. As far as 3 qubits are able to represent up to 4ˆ2 images, therefore 5 states out of 8 are redundant. To keep measured image shape the same as input’s, the authors do not encode pixels without intensity value and leave them to have black color with 0 qubit amplitude. This advantage allows to represent images of an arbitrary shape. The authors suggest image up-scaling based on the nearest-neighbor method. In addition, Zhu et al. provided encryption scheme [57], Zhou and Wan implemented image scaling based on bilinear interpolation [58], Zhang et al. extended approach to ﬂoating-point quantum representation and proposed two rows interchanging and swap operations [59]. We implemented GQIR representation method in our repository. 2.3.3 QRMW The authors [11] provide the representation approach for multichannel images. Each channel corresponds to a speciﬁc wavelength. QRMW allows ”to encode the color values corresponding to the respective wavelength channel of the pixels in the image”. The equation below deﬁnes the intensity of each pixel located in the x, y, λ coordinates (where λrepresents wavelength channel index): fpλ, y, xq “ c0 λyx , c1 λyx , ..., cq´2 λyx , cq´1 λyx , fpλ, y, xqPr0,2q´1s, ck λyx P r0,1s,(11) where 2q´1 is the maximum amplitude of any wavelength. Then, the QRMW image representation is the following: 12 Quantum Image Representation: A Review \|Iy “ 1 x“0\|fpλ, y, xqyb \| λyb \| yxy,(12) where bdeﬁnes the number of channels. As a results, the method contains the extended realization of NEQR (2.3.1). In addition, the authors describe image compression, complete and partial color operations, and position oper- ations. The same authors presented the edge detection algorithm [60] and extended their encoding approach to the multichannel audio representation 2.3.4 BRQI The authors [12] suggest to split image into nbitplanes where nis a resolution of the pixel intensity. Encoding proceeds through availability of the current bitplane in the pixel with current coordinates. Suppose an example of the gray-scaled 2 ˆ2 image with the following pixel intensities: t0,125,200,255u. The binary expansion for pixel-wise intensity is the following: 00000000,01111101,11001000,11111111. Taking bits from each expansion, one can receive 8 bitplanes as in the ﬁgure 6. (1) LSB (2) (3) (4) (5) (6) (7) (8) MSB Fig. 6: Bitplane image representation, each letter corresponds to the number of biplane. The ﬁrst and the last bit for each bitplane have special names ”the least signiﬁcant bit” (LSB) and ”the most signiﬁcant bit” (MSB) respectively. This paper was inspired by general NEQR approach and deﬁnes jth bitplane as follows: \|Ψjy “ 1 y“0\|gpx, yqy \| xy \| yy(13) where j- denotes the bitplane index pj“0, ..., 7q,gpx, yq P t0,1ushows presence or absence of a bit in jth bitplane. As a result, the qubit scheme consists of X-, Y-coordinate qubits, bitplane qubits and 1 target qubit, showing availability of the bitplane’s current bit. The encoding method is implemented in our repository. BRQI supports processing operations: bitplane interchange, translation and intensity operation. Heidari et al. proposed selective encryption for the BRQI encoded information [62]. Recently, Khorrampanah et al. proposed RGB images encryption [63]. The work of Mastriani, 2015 [64] deserves spe- cial attention, as it describes Quantum Boolean (QuBo) image denoising based on image bitplane splitting. The same paper explains the Classical-to- quantum (C2QI) and Quantum-to-classical interfaces (Q2CI). Later Mastriani Quantum Image Representation: A Review 13 proves [65] reliability of the bitplane splitting approach in term of C2QI and To conclude, the BRQI is a promising method in terms of image representa- tion and processing. At the same time, the technique is built upon the NEQR, thus the number of qubit remains in dependence on the intensity resolution. 2.3.5 QIIR Indexed images consist of 2 tables: combination of the channel values (ﬁrst table) and pointers to the palette matrix (second table). An example of such an image is in the ﬁgure 7. Authors [14] encode both image’s tables (\|QDatay and \|QMap y) using NEQR. (a) real image (b) Quantum Data R G B . . . (c) Quantum Palette Fig. 7: QIIR image representation 2.3.5.1 Quantum Data Matrix In order to encode 2nˆ2nQData matrix, authors apply NEQR 2.3.1 approach. If pY, X qis a cell location, IY X is a cell value, then expression is the following: \|QDatay “ 1 X“0\|IY X yb \| Y X y(14) 2.3.5.2 Quantum Palette Matrix The authors use the same NEQR 2.3.1 approach to encode the color palette. In case of RGB encoding 24 qubits are reserved: 8 for each color. Following equation describes the pallete matrix encoding. \|QMap y “ 1 j“0\|Cjyb \| jy(15) Authors provide several processing techniques such as Ryrotation on 90°, cyclic shift, color inversion, color replacement, color look-up, steganography. Besides the authors’ suggested processing techniques, no other images handling procedures exist from the best of our knowledge. The number of utilized qubits is a major disadvantage of the method, as the data literally consist of 2 images. 14 Quantum Image Representation: A Review 2.4 Phase representation. FTQR Grigoryan and Aganyan oﬀer phase-based image encoding [15]. fy “ 1 where α“2π{1024. The term eiαfk\|kyallows to map classical intensity values p0,255qinto imaginary plane px`i¨yq. Here fkis in input signal in the coordinate kwhich expands to xand y. In this way the representation is fy “ 1 eiαfn,m \|n, my(17) Authors do not provide any processing techniques but extend the approach up to multidimensional images. The image representation did not take share in the processing techniques research due to its novelty from our opinion. The method is purely phase based, and for measurement it needs phase-to- amplitude transformation. This fact implies additional computation resources. 3 Discussion and conclusion We reviewed 14 method of image encoding and propose to categorize them according to classiﬁcation in ﬁgure 1. Most of them have the common spe- ciﬁc disadvantage, which comes from the quantum computing nature: it is impossible to measure all the pixels in a single trial. For continuous methods, the intensity estimation precision depends on the number of trials. Dis- crete methods allow to derive information only about 1 pixel from 1 shot. Figure 8represents the comparison of three metrics for the selected algorithms implemented in our repository: circuit depth, qubit number, and quantum Image side size circuit depth, number of gates (a) Circuit depth Image side size number of utilized qubits (b) Qubits number Image side size Quantum volume (c) Quantum volume Fig. 8: Metrics Tables A1,A2,A3 with columns representing image side size show the same metrics. We observed that majority of techniques utilize a similar number of qubits, however the cicruit depth shows the highest values for continuous and phase Quantum Image Representation: A Review 15 representations and the lowest for the Qubit Lattice approach. The continu- ous and phase representations are so heavy in depth that we could not execute circuits for images bigger than 32 ˆ32. Moreover, for all approaches, we could not succeed in real IBM-Washington [66] and IonQ [36] QPU simulation where depth reaches 105for the images of size 4ˆ4 and 8 ˆ8 for each machine respec- tively. This happened because of the multicontrolled rotation gate, which is a base for all continuous and phase methods, is itself expensive for implementa- tion. Following that, it is computationally expensive to simulate high resolution images encoding, especially for continuous and approaches. Additionally, we did not succeed to measure FTQR, and as a result, we were unable to check whether representation works in the full encoding-decoding pipeline correctly. However, FTQR shows the minimum growth of utilized qubits and quantum volume numbers. Considering the number of qubits, Qubit Lattice is the most inappropriate representation algorithm even for IBM-Washington, as qubits can represent at most 8ˆ8 images. Discrete representations stand in between, therefore, is the most promising group of image representation algorithms. Each method has it’s own features. For example, some authors constructed their methods to encode a speciﬁc type of image (log-polar, multi-wavelength, indexed). Other authors made an accent on the representation way (based on bitplanes, Fourier transform, order-encoding). While some authors describe their approach in terms of quantum state normality (NAQSS), others operated on color and coordinate diﬀerentiation (QSMC and QSNC). This fact might explain the huge number of processing types for the NEQR 2.3.1 and FRQI 2.1.2 representations. Both of them are general, intuitive and appear as main representative for the discrete and continuous groups respectively. Still, NEQR ”could perform the complex and elaborate color operation more conveniently than FRQI” [67] due to obvious both – coordinate and pixel intensity encoding. The image processing techniques signiﬁcantly impact image representa- tions. The majority of the discussed methods come with processing algorithms. And yet, the overall stack of available processing is not full. Such comprehen- sive tools as segmentation, feature extraction, machine learning, recognition keep poor and imperfect review. At the same time, research in these branches actively move these topics forward. Thus, opinion about quantum image processing as a ”quantum hoax” [68] seems like a matter of time. We assign our next work to the problems of the image processing in the perspective of machine learning applications. Convolutions, pooling, statistics calculation, and multi-image processing are in the scope of the future work. We are also inspired for further research of the image representation algorithms. Code availability The python code is available in the GitHub repository https://github.com/ 16 Quantum Image Representation: A Review Authors’ contributions Marina Lisnichenko - had the idea for the article, performed the literature search and data analysis. Stanislav Protasov - critically revised the work. Data availability Data sharing not applicable to this article as no datasets were generated or analysed during the current study. Ethics approval and consent to participate Not applicable Human and Animal Ethics Not applicable Consent for publication Not applicable Competing interests The authors have no conﬂicts of interest to declare that are relevant to the content of this article. No funds, grants, or other support was received. Not applicable Authors’ information Marina Lisnichenko received the M.S. in robotics from Innopolis Univesity in 2021. She is currently pursuing the PhD degree with the Machine Learning and Knowledge Represen- tation lab, Innopolis University. Her research interests include quantum information process- ing, quantum circuit compression, geographic information processing. Quantum Image Representation: A Review 17 Stanislav Protasov received the PhD degree in the computer science from Voronezh State University in 2013. He is currently an Asso- ciate Professor with Innopolis University. His research interests include applied machine learning, information retrieval, applications of quantum computing, quantum state prepara- 18 Quantum Image Representation: A Review Appendix A Metrics tables Table A1: Circuit depth Image encoding 2 4 8 16 32 64 128 256 BRQI 50 206 738 3164 12400 49218 195902 784866 FRQI 467 8003 130307 2094083 – – – – QL 2 2 2 2 2 2 2 2 GQIR 26 102 389 1491 6180 24511 98014 392236 NEQR 22 88 375 1513 6075 24410 97923 392281 OQIM 111 1983 32511 523263 8382466 – – – QSMC 35 943 16063 260863 4189183 – – – FTQR 5 158 2635 42813 869016 – – – Table A2: Number of utilized qubits Image encoding 2 4 8 16 32 64 128 256 BRQI 6 8 10 12 14 16 18 20 FRQI 3 5 7 9 11 – – – QL 4 16 64 256 1024 4096 16384 65536 GQIR 10 12 14 16 18 20 22 24 NEQR 10 12 14 16 18 20 22 24 OQIM 4 6 8 10 12 – – – QSMC 4 6 8 10 12 – – – FTQR 4 6 8 10 – – – – Table A3: Quantum volume Image encoding 2 4 8 16 32 64 128 256 BRQI 36 64 100 144 196 256 324 400 FRQI 9 25 49 81 121 QL 4 4 4 4 4 4 4 4 GQIR 100 144 196 256 324 400 484 576 NEQR 100 144 196 256 324 400 484 576 OQIM 16 36 64 100 144 – – – QSMC 16 36 64 100 144 – – – FTQR 4 16 36 64 100 – – – Quantum Image Representation: A Review 19 [1] Leprince-Ringuet, D.: Daphne Leprince-Ringuet: Quan- tum Computing Is at an Early Stage. But Investors Are Already Getting Excited. https://www.zdnet.com/article/ [2] Venegas-Andraca, S.E., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Quantum Information and Compu- tation, vol. 5105, pp. 137–147 (2003). https://doi.org/10.1117/12.485960. International Society for Optics and Photonics [3] Latorre, J.I.: Image compression and entanglement. arXiv preprint quant- ph/0510031 (2005). https://doi.org/10.48550/arXiv.quant-ph/0510031 [4] Le, P.Q., Dong, F., Hirota, K.: A ﬂexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Information Processing 10(1), 63–84 (2011). https: [5] Sun, B., Le, P.Q., Iliyasu, A.M., Yan, F., Garcia, J.A., Dong, F., Hirota, K.: A multi-channel representation for images on quantum computers using the rgbαcolor space. In: 2011 IEEE 7th International Symposium on Intelligent Signal Processing, pp. 1–6 (2011). https://doi.org/10.1109/ WISP.2011.6051718. IEEE [6] Zhang, Y., Lu, K., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum representation of digital images. Quantum information processing 12(8), 2833–2860 (2013). https://doi.org/10.1007/s11128-013-0567-z [7] Li, H.-S., Qingxin, Z., Lan, S., Shen, C.-Y., Zhou, R., Mo, J.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum information processing 12(6), 2269–2290 (2013). https://doi. [8] Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., Compare, A.: Sqr: a simple quantum representation of infrared images. Quantum Infor- mation Processing 13(6), 1353–1379 (2014). https://doi.org/10.1007/ [9] Li, H.-S., Zhu, Q., Zhou, R.-G., Song, L., Yang, X.-j.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum super- position state. Quantum Information Processing 13(4), 991–1011 (2014). 20 Quantum Image Representation: A Review [10] Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum infor- mation processing 14(11), 4001–4026 (2015). https://doi.org/10.1007/ [11] S¸ahin, E., Yilmaz, I.: Qrmw: quantum representation of multi wavelength images. Turkish Journal of Electrical Engineering & Computer Sciences 26(2), 768–779 (2018). https://doi.org/10.3906/elk-1705-396 [12] Li, H.-S., Chen, X., Xia, H., Liang, Y., Zhou, Z.: A quantum image representation based on bitplanes. IEEE Access 6, 62396–62404 (2018) [13] Xu, G., Xu, X., Wang, X., Wang, X.: Order-encoded quantum image model and parallel histogram speciﬁcation. Quantum Information Pro- cessing 18(11), 1–26 (2019). https://doi.org/10.1007/s11128-019-2463-7 [14] Wang, B., Hao, M.-q., Li, P.-c., Liu, Z.-b.: Quantum representa- tion of indexed images and its applications. International Journal of Theoretical Physics 59(2), 374–402 (2020). https://doi.org/10.1007/ [15] Grigoryan, A.M., Agaian, S.S.: New look on quantum representation of images: Fourier transform representation. Quantum Information Process- ing 19(5), 1–26 (2020). https://doi.org/10.1007/s11128-020-02643-3 [16] Oh, S., Choi, J., Kim, J.: A tutorial on quantum convolutional neural networks (qcnn). In: 2020 International Conference on Information and Communication Technology Convergence (ICTC), pp. 236–239 (2020). [17] Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural net- works. Nature Physics 15(12), 1273–1278 (2019). https://doi.org/10. [18] Yang, C.-H.H., Qi, J., Chen, S.Y.-C., Chen, P.-Y., Siniscalchi, S.M., Ma, X., Lee, C.-H.: Decentralizing feature extraction with quantum convo- lutional neural network for automatic speech recognition. In: ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 6523–6527 (2021). IEEE [19] Yan, F., Venegas-Andraca, S.E.: Quantum image processing (2020) [20] Caraiman, S., Manta, V.: Image processing using quantum computing. In: 2012 16th International Conference on System Theory, Control and Computing (ICSTCC), pp. 1–6 (2012). IEEE Quantum Image Representation: A Review 21 [21] Zhou, R.-G., Tan, C., Ian, H.: Global and local translation designs of quantum image based on frqi. International Journal of Theoretical Physics 56(4), 1382–1398 (2017). https://doi.org/10.1007/s10773-017-3279-9 [22] Thenmozhi, S., BalaSubramanya, K., Shrinivas, S., Joshi, S.K.D., Vikas, B.: Information hiding using quantum image processing state of art review. Inventive Computation and Information Technologies, 235–245 (2021). https://doi.org/10.1007/978-981-33-4305-4 18 [23] Ma, H., He, Z., Xu, P., Dong, Y., Fan, X.: A quantum richardson– lucy image restoration algorithm based on controlled rotation operation and hamiltonian evolution. Quantum Information Processing 19(8), 1–14 (2020). https://doi.org/10.1007/s11128-020-02723-4 [24] Tariq Jamal, A., Abdel-Khalek, S., Ben Ishak, A.: Multilevel segmen- tation of medical images in the framework of quantum and classical techniques. Multimedia Tools and Applications, 1–14 (2021). https://doi. [25] Farina, T.: Creating hybrid images using a quantum computer. PhD thesis, UNION COLLEGE (2021) [26] Sanchez, M., Sun, G.-H., Dong, S.-H.: Correlation property of multipar- tite quantum image. International Journal of Theoretical Physics 58(11), 3773–3796 (2019). https://doi.org/10.1007/s10773-019-04247-9 [27] Liu, X., Xiao, D.: Multimodality image fusion based on quantum wavelet transform and sum-modiﬁed-laplacian rule. International Journal of Theoretical Physics 58(3), 734–744 (2019). https://doi.org/10.1007/ [28] Hu, W.-W., Zhou, R.-G., Luo, J., Jiang, S.-X., Luo, G.-F.: Quantum image encryption algorithm based on arnold scrambling and wavelet transforms. Quantum Information Processing 19(3), 1–29 (2020). https: [29] Yan, F., Jiao, S., Iliyasu, A.M., Jiang, Z.: Chromatic framework for quantum movies and applications in creating montages. Frontiers of Computer Science 12(4), 736–748 (2018). https://doi.org/10.1007/ [30] Yan, F., Iliyasu, A.M., Jiao, S., Yang, H.: Audio-visual synchronisa- tion in quantum movies. In: 2018 IEEE 5th International Congress on Information Science and Technology (CiSt), pp. 274–278 (2018). IEEE [31] Sun, B., Iliyasu, A.M., Yan, F., Sanchez, J.A.G., Dong, F., Al-Asmari, A.K., Hirota, K.: Multi-channel information operations on quantum 22 Quantum Image Representation: A Review images. Journal of Advanced Computational Intelligence and Intelligent Informatics 18(2), 140–149 (2014) [32] Shende, V.V., Bullock, S.S., Markov, I.L.: Synthesis of quantum-logic circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25(6), 1000–1010 (2006). https://doi.org/10.1145/ [33] Ma, G., Li, H., Zhao, J.: Quantum radon transform and its application. arXiv preprint arXiv:2107.05524 (2021) [34] Ding, M., Huang, T.-Z., Ji, T.-Y., Zhao, X.-L., Yang, J.-H.: Low-rank ten- sor completion using matrix factorization based on tensor train rank and total variation. Journal of Scientiﬁc Computing 81(2), 941–964 (2019). [35] Grover, L.K.: Quantum computers can search arbitrarily large databases by a single query. Physical review letters 79(23), 4709 (1997) [36] IonQ: Best Practices for Using IonQ Hardware: Https://ionq.com/best- practices. https://ionq.com/best-practices [37] Guanlei, X., Xiaogang, X., Xun, W., Xiaotong, W.: A novel quantum image parallel searching algorithm. Optik 209, 164565 (2020). https:// [38] Li, H.-S., Li, C., Chen, X., Xia, H.: Quantum image encryption based on phase-shift transform and quantum haar wavelet packet transform. Modern Physics Letters A 34(26), 1950214 (2019). https://doi.org/10. [39] Fan, P., Zhou, R.-G., Jing, N., Li, H.-S.: Geometric transformations of multidimensional color images based on nass. Information Sciences 340, 191–208 (2016) [40] Zhou, R.-G., Sun, Y.-J.: Quantum multidimensional color images sim- ilarity comparison. Quantum Information Processing 14(5), 1605–1624 (2015). https://doi.org/10.1007/s11128-014-0849-0 [41] Su, J., Guo, X., Liu, C., Lu, S., Li, L.: An improved novel quantum image representation and its experimental test on ibm quantum expe- rience. Scientiﬁc Reports 11(1), 1–13 (2021). https://doi.org/10.1038/ [42] Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log-polar images. Quantum information processing 12(9), 3103–3126 (2013). https://doi.org/10.1007/s11128-013-0587-8 Quantum Image Representation: A Review 23 [43] Brayton, R.K., Hachtel, G.D., McMullen, C., Sangiovanni-Vincentelli, A.: Logic Minimization Algorithms for VLSI Synthesis vol. 2. Springer, ??? [44] Iqbal, B., Singh, H.: Identiﬁcation of desired pixels in an image using grover’s quantum search algorithm. arXiv preprint arXiv:2107.03053 (2021). https://doi.org/10.48550/arXiv.2107.03053 [45] Fan, P., Zhou, R.-G., Hu, W.W., Jing, N.: Quantum image edge extraction based on laplacian operator and zero-cross method. Quan- tum Information Processing 18(1), 1–23 (2019). https://doi.org/10.1007/ [46] Zhou, R.-G., Cheng, Y., Qi, X., Yu, H., Jiang, N.: Asymmetric scal- ing scheme over the two dimensions of a quantum image. Quantum Information Processing 19(9), 1–20 (2020). https://doi.org/10.1007/ [47] Wang, S., Xu, P., Song, R., Li, P., Ma, H.: Development of high performance quantum image algorithm on constrained least squares ﬁlter- ing computation. Entropy 22(11), 1207 (2020). https://doi.org/10.3390/ [48] Yang, J., Zhu, Y., Li, K., Yang, J., Hou, C.: Tensor completion from structurally-missing entries by low-tt-rankness and ﬁber-wise sparsity. IEEE Journal of Selected Topics in Signal Processing 12(6), 1420–1434 (2018). https://doi.org/10.1109/JSTSP.2018.2873990 [49] Fan, P., Zhou, R.-G., Hu, W., Jing, N.: Quantum image edge extraction based on classical sobel operator for neqr. Quantum Information Process- ing 18(1), 1–23 (2019). https://doi.org/10.1007/s11128-018-2131-3 [50] Heidari, S., Abutalib, M., Alkhambashi, M., Farouk, A., Naseri, M.: A new general model for quantum image histogram (qih). Quantum Information Processing 18(6), 1–20 (2019). https://doi.org/10.1007/ [51] Zhou, R.-G., Yu, H., Cheng, Y., Li, F.-X.: Quantum image edge extraction based on improved prewitt operator. Quantum Information Processing 18(9), 1–24 (2019). https://doi.org/10.1007/s11128-019-2376-5 [52] Ali, A.E., Abdel-Galil, H., Mohamed, S.: Quantum image mid-point ﬁlter. Quantum Information Processing 19(8), 1–23 (2020). https://doi.org/10. [53] Yuan, S., Wen, C., Hang, B., Gong, Y.: The dual-threshold quan- tum image segmentation algorithm and its simulation. Quantum 24 Quantum Image Representation: A Review Information Processing 19(12), 1–21 (2020). https://doi.org/10.1007/ [54] Zhou, R.-G., Luo, J., Liu, X., Zhu, C., Wei, L., Zhang, X.: A novel quan- tum image steganography scheme based on lsb. International Journal of Theoretical Physics 57(6), 1848–1863 (2018). https://doi.org/10.1007/ [55] Li, P., Shi, T., Lu, A., Wang, B.: Quantum circuit design for several mor- phological image processing methods. Quantum Information Processing 18(12), 1–35 (2019). https://doi.org/10.1007/s11128-019-2479-z [56] Nejad, M.Y., Mosleh, M., Heikalabad, S.R.: An lsb-based quantum audio watermarking using msb as arbiter. International Journal of Theoretical Physics 58(11), 3828–3851 (2019). https://doi.org/10.1007/ [57] Zhu, H.-H., Chen, X.-B., Yang, Y.-X.: A multimode quantum image rep- resentation and its encryption scheme. Quantum Information Processing 20(9), 1–21 (2021). https://doi.org/10.1007/s11128-021-03255-1 [58] Zhou, R.-G., Wan, C.: Quantum image scaling based on bilinear interpolation with decimals scaling ratio. International Journal of Theoretical Physics 60(6), 2115–2144 (2021). https://doi.org/10.1007/ [59] Zhang, R., Xu, M., Lu, D.: A generalized ﬂoating-point quantum repre- sentation of 2-d data and their applications. Quantum Information Pro- cessing 19(11), 1–20 (2020). https://doi.org/10.1007/s11128-020-02895-z [60] S¸ahin, E., Yilmaz, ˙ I.: A quantum edge detection algorithm for quantum multi-wavelength images. International Journal of Quantum Information 19(03), 2150017 (2021). https://doi.org/10.1142/S0219749921500179 [61] S¸ahin, E., Yilmaz, ˙ I.: Qrma: quantum representation of multichannel audio. Quantum Information Processing 18(7), 1–30 (2019). https://doi. [62] Heidari, S., Naseri, M., Nagata, K.: Quantum selective encryption for medical images. International Journal of Theoretical Physics 58(11), 3908–3926 (2019). https://doi.org/10.1007/s10773-019-04258-6 [63] Khorrampanah, M., Houshmand, M., Lotﬁ Heravi, M.M.: New method to encrypt rgb images using quantum computing. Optical and Quantum Electronics 54(4), 1–16 (2022). https://doi.org/10.1007/ Quantum Image Representation: A Review 25 [64] Mastriani, M.: Quantum boolean image denoising. Quantum Infor- mation Processing 14(5), 1647–1673 (2015). https://doi.org/10.1007/ [65] Mastriani, M.: Quantum image processing? Quantum Information Pro- cessing 16(1), 1–42 (2017). https://doi.org/10.1007/s11128-014-0881-0 [66] IBM: IBM-Washington Machine Details. https://quantum-computing. table&system=ibm washington [67] Anand, A., Lyu, M., Baweja, P.S., Patil, V.: Quantum image processing. arXiv preprint arXiv:2203.01831 (2022). https://doi.org/10.48550/arXiv. [68] Ruan, Y., Xue, X., Shen, Y.: Quantum image processing: opportuni- ties and challenges. 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Calculate Gruha Jyothi Subsidy for Electricity Bill Free Units 2024 Permanent residents of Karnataka now have a new way to Calculate Gruha Jyothi Subsidy for Electricity Bill Free Units 2024 In addition you may find out how much power subsidy you’ll receive in 2024 by visiting the official website To qualify you should be a permanent resident of Karnataka However The Gruha Jyothi Scheme provides up to 200 units of free power to eligible Karnataka residents You simply need to follow a simple online process for calculating how much discount you will receive on your electricity payment. Ultimately checking the subsidies online using the official website is quick and simple for both citizens and the government Lastly this post will provide you with all of the important information about the scheme so please read it until the end. What is the Karnataka Gruha Jyothi Scheme? Firstly The Karnataka Government started the Karnataka Gruha Jyothi Scheme to help people by giving them free electricity Secondly the plan is to provide free power for up to 200 units per month to every household in Karnataka This means if a household uses 200 units or less of electricity each month they won’t have to pay the electricity bill which can save around Rs 1000 a month. Likewise it has started on 1 August 2023 so people will get a zero bill for electricity used in July if it’s under 200 units. Lastly residents of Karnataka can register for this plan online using their laptops phones and desktop computers via the Seva Sindhu portal. Goem Vinamulya Vij Yevjan Scheme Key Highlights of Calculate Gruha Jyothi Subsidy for Electricity Bill Free Units Name of the scheme Calculate Gruha Jyothi Subsidy for Electricity Bill Launched by Karnataka state government Objective Calculate subsidy Beneficiaries Citizens of Karnataka state Official website https://sevasindhugs.karnataka.gov.in/ Formula of Gruha Jyothi Subsidy Calculation Here’s an example to help you understand the average electricity consumption under Gruha Jyothi:- The Gruha Jyothi Subsidy Calculation Formula is based on average consumption for the financial year 2022-23 plus a 10% increase (a total of less than 200 units). Month Unit Consumption May 2022 97 June 2022 85 July 2022 110 Aug 2022 170 Sep 2022 65 Oct 2022 122 Nov 2022 158 Dec 2022 95 Jan 2023 160 Feb 2023 170 Mar 2023 150 Apr 2023 170 We are using this example only for Information purposes • Average units consumed for previous Year:- (97+85+110+170+65+122+158+95+160+170+150+170) / 12 = 129.33 Units (Average) • So Final Units Consumption Under Gruha Jyothi will be (129.33 + 10) = 139.33 Units How to Calculate Gruha Jyothi Subsidy for Electricity Bill Free Units? Step 1: To find out how much subsidy you can get under the Gruha Jyothi scheme for your electricity bill you need to gather all your electricity bills from the past financial year which is from 1 April 2022 to 31 March 2023. You need these bills to figure out your average electricity use. Step 2: After collected all 12 electricity bills from the previous year, the candidate has to record the usage of the electricity unit on one page. The candidate can now calculate how much electricity he or she consumes. Step 3: After adding up all of the units of electricity utilized by the application in the previous year, the candidate needs to divide the total by 12 to get the average consumption for the year Step 4: In accordance to the Karnataka government, the candidate must add 10% to the previous year’s total average. For example if the previous financial year’s typical use was 100 units, the candidate must add 10% more, for a total of 110 units. Step 5: After finishing all of these steps if your electricity use is less than 200 units, you are qualified for the Gurha Jyothi plan. If the applicant’s average usage reaches 200 units he is ineligible for the scheme. Step 6: To receive a free electricity bill, the candidate must pay their power bill lower or equal to the previous year’s average. For example if the candidate’s earlier year’s average is 150 units, he should consume no more than 150 units to avoid paying an electricity bill. Step 7: If the candidate’s electricity unit consumption above his previous year’s average consumption he has to pay for the extra units utilized. What are the benefits to be given to the selected applicants under the Gruha Jyothi Yojana? The selected applicants will get free electricity consumption of up to 200 units under the scheme. Which state launched the Gruha Jyothi Yojana? The Karnataka state government launched the Gruha Jyothi Yojana. What is the formula to calculate the Gruha Jyothi Subsidy for Electricity Bill Free Units 2024? The formula for the Gruha Jyothi Subsidy Calculation is based on average consumption for the Financial Year 2022-23 + 10% increase (total amounting to less than 200 units). 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Lasso and Ridge Regularization - A Rescuer From Overfitting This article was published as a part of the Data Science Blogathon OVERFITTING! We do not even spend a single day without encountering this situation and then try different options to get the correct accuracy of the model on the test dataset. But what if I tell you there exists a technique that inflicts a penalty on the model if it advances towards overfitting. Yeah, Yeah, you have heard it correct. We have some saviours that rescue our model from overfitting. Before moving further onto our rescuers, let us first understand overfitting with a real-world scenario: Fig 1. Relocation from the hot region to the cold region Suppose you have lived in a hot region all your life till graduation, and now for some reason, you have to move to a colder one. As soon as you move to a colder region, you feel under the weather because you need time to adapt to the new climate. The fact that you cannot simply adjust to the new environment can be called Overfitting. In technical terms, overfitting is a condition that arises when we train our model too much on the training dataset that it focuses on noisy data and irrelevant features. Such a model runs with considerable accuracy on the training set but fails to generalize the attributes in the test set. Why cannot we accept an Overfitted Model? An overfitted model cannot recognize the unseen data and will fail terribly on given some new inputs. Understanding this with our previous example, if your body is fit to only one geographical area having a specific climate, then it cannot adapt to the new climate instantly. For graphs, we can recognize overfitting by looking at the accuracy and loss during training and validation. Fig 2. Training and Validation Accuracy Fig 3. Training and Validation Loss Mark that the training accuracy (in blue) strikes 100%, but the validation accuracy (in orange) reaches 70%. Training loss falls to 0 while the validation loss attains its minimum value just after the 2^nd epoch. Training further enforces the model focus on noisy and irrelevant features for prediction, and thus the validation loss increases. To get more insights about overfitting, it is fundamental to understand the role of variance and bias in overfitting: What is Variance? Variance tells us about the spread of the data points. It calculates how much a data point differs from its mean value and how far it is from the other points in the dataset. What is Bias? It is the difference between the average prediction and the target value. The relationship of bias and variance with overfitting and underfitting is as shown below: Fig 4. Bias and Variance w.r.t Overfitting and Underfitting Low bias and low variance will give a balanced model, whereas high bias leads to underfitting, and high variance lead to overfitting. Fig 5. Bias Vs Variance Low Bias: The average prediction is very close to the target value High Bias: The predictions differ too much from the actual value Low Variance: The data points are compact and do not vary much from their mean value High Variance: Scattered data points with huge variations from the mean value and other data points. To make a good fit, we need to have a correct balance of bias and variance. What is Regularization? • Regularization is one of the ways to improve our model to work on unseen data by ignoring the less important features. • Regularization minimizes the validation loss and tries to improve the accuracy of the model. • It avoids overfitting by adding a penalty to the model with high variance, thereby shrinking the beta coefficients to zero. Fig 6. Regularization and its types There are two types of regularization: 1. Lasso Regularization 2. Ridge Regularization What is Lasso Regularization (L1)? • It stands for Least Absolute Shrinkage and Selection Operator • It adds L1 the penalty • L1 is the sum of the absolute value of the beta coefficients Cost function = Loss + λ + Σ \|\|w\|\| Loss = sum of squared residual λ = penalty w = slope of the curve What is Ridge Regularization (L2) • It adds L2 as the penalty • L2 is the sum of the square of the magnitude of beta coefficients Cost function = Loss + λ + Σ \|\|w\|\|^2 Loss = sum of squared residual λ = penalty w = slope of the curve λ is the penalty term for the model. As λ increases cost function increases, the coefficient of the equation decreases and leads to shrinkage. Now its time to dive into some code: For comparing Linear, Ridge, and Lasso Regression I will be using a real estate dataset where we have to predict the house price of unit area. Dataset looks like this: Fig 7. Real Estate Dataset Dividing the dataset into train and test sets: X = df.drop(columns = ['Y house price of unit area', 'X1 transaction date', 'X2 house age']) Y = df['Y house price of unit area'] x_train, x_test,y_train, y_test = train_test_split(X, Y, test_size = 0.2, random_state = 42) Fitting the model on Linear Regression: lin_reg = LinearRegression() lin_reg.fit(x_train, y_train) lin_reg_y_pred = lin_reg.predict(x_test) mse = mean_squared_error(y_test, lin_reg_y_pred) The Mean Square Error for Linear Regression is: 63.90493104709001 The coefficients of the columns for the Linear Regression model are: Fig 8. Beta Coefficients for Linear Regression Fitting the model on Lasso Regression: from sklearn.linear_model import Lasso lasso = Lasso() lasso.fit(x_train, y_train) y_pred_lasso = lasso.predict(x_test) mse = mean_squared_error(y_test, y_pred_lasso) The Mean Square Error for Lasso Regression is: 67.04829587817319 The coefficients of the columns for the Linear Regression model are: Fig 9. Beta Coefficients for Lasso Regression Fitting the model on Ridge Regression: from sklearn.linear_model import Ridge ridge = Ridge() ridge.fit(x_train, y_train) y_pred_ridge = ridge.predict(x_test) mse = mean_squared_error(y_test, y_pred_ridge) The Mean Square Error for Ridge Regression is: 66.07258621837418 The coefficients of the columns for the Linear Regression model are: Fig 10. Beta Coefficients for Ridge Regression Comparing the coefficients of the Lasso and Ridge Regularization models x = ['Linear', 'Lasso', 'Ridge'] y1 = np.array([-0.004709, -0.005994, 0.005700]) y2 = np.array([1.007691, 0.958896, 1.135925]) y3 = np.array([221.632669, 0.000000, 7.304642]) y4 = np.array([-8.841321, -0.000000, -0.915969]) fig, axes = plt.subplots(ncols=1, nrows=1) plt.bar(x, y1, color = 'black') plt.bar(x, y2, bottom=y1, color='b') plt.bar(x, y3, bottom=y1+y2, color='g') plt.bar(x, y4, bottom=y1+y2+y3, color='r') plt.legend(["X3", "X4", "X5", "X6"]) plt.title("Comparing coefficients of different models") axes.set_xticklabels(['Linear', 'Lasso', 'Ridge']) Fig 11. Comparison of Beta Coefficients Inspecting the coefficients, we can see that Lasso and Ridge Regression had shrunk the coefficients, and thus the coefficients are close to zero. On the contrary, Linear Regression still has a substantial value of the coefficient for the X5 column.\ Comparing Lasso and Ridge Regularization techniques Fig 12. Comparison of L1 Regularization and L2 Regularization We learned two different types of regression techniques, namely Lasso and Ridge Regression which can be proved effective for overfitting. These techniques make a good fit model by adding a penalty and shrinking the beta coefficients. It is necessary to have a correct balance of the Bias and Variance to control overfitting. Yayyy! You’ve made it to the end of the article and successfully gotten the hang of these topics of Bias and Variance, Overfitting and Underfitting, and Regularization techniques.😄 Happy Learning! 😊 I’d be obliged to receive any comments, suggestions, or feedback. You can find the complete code here. Stay tuned for upcoming blogs! Connect on LinkedIn: https://www.linkedin.com/in/rashmi-manwani-a13157184/ Connect on Github: https://github.com/Rashmiii-00 Fig 5: http://scott.fortmann-roe.com/docs/BiasVariance.html About the Author: Rashmi Manwani Passionate to learn about Machine Learning topics and their implementation. Thus, finding my way to develop a strong knowledge of the domain by writing appropriate articles on Data Science topics. The media shown in this article on Interactive Dashboard using Bokeh are not owned by Analytics Vidhya and are used at the Author’s discretion. Responses From Readers very well define. 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Exporting Statistics¶ After you’ve gated populations, you can export a variety of statistics. 1. Click export statistics in the left sidebar. 2. Select the statistics to calculate. 3. Select the populations to calculate in the Populations selector. 4. For mean, median, geometric mean, CV, StdDev, MAD or quantile statistics, select the channels to calculate in the Channels selector. 5. Select the FCS files to calculate from in the FCS Files selector. 6. Select the compensation to use for gating. 7. Select the output file format (TSV or CSV with or without header, or JSON). 8. Select the output file layout (see descriptions below). 9. Click download. For TSV and CSV exports, three layouts are available: Layout Description Tall-Skinny One row per combination of FCS file, population, statistic and channel. All statistics are in a single column titled value. This format is ideal for use with applications such as TIBCO Spotfire® that filter rows to isolate the data of interest. Medium One row per combination of FCS file, population and channel. Each statistic is in a separate column. Short-Wide One row per FCS file. Each combination of population, statistic and channel is in a separate column. This format is provided for users accustomed to FlowJo® output. This format is not readily machine-parsable and cannot include population IDs (only names). Exports include file annotations for convenience. Exports optionally include the IDs of FCS files and populations in addition to their names. If you are consuming exported data in analysis scripts, IDs provide an immutable reference, unlike names, which can be changed by users. The uniquePopulationName property has the names of parent populations prepended until the name is unique. If all of your population names are unique, then this value will be the same as the population name property. Using CellEngine with Tableau¶ A CellEngine plugin is available for Tableau that allows dynamically retrieving statistics. 1. From the Tableau opening page, click Connect > To a Server > Web Data Connector. 2. Type in https://cellengine.com/tableau and hit enter. A login screen will appear. 3. Enter your CellEngine credentials and log in. 4. On the following page, select an experiment, then select the desired statistics. 5. Click load. Tableau will take several seconds to import the data. Using CellEngine with TIBCO Spotfire¶ CellEngine's tall-skinny file layout is specifically designed to work with Spotfire: it contains one statistic per row, allowing the data to be filtered in a multitude of ways. See instructions in exporting statistics. Statistic Types¶ NaN (not-a-number) or N/A values will occur in the following scenarios: • When calculating channel statistics (mean, median, etc.) for a gate that contains no events • When calculating the geometric mean for a gate that contains 0 or negative values The median is a special case of a quantile and represents the center point of a set of observations. In the case of an even number of observations, linear interpolation is used (i.e. the mean of the two tied values is used). Compared to the arithmetic mean, this value is less sensitive to outliers and is thus ideal for avoiding confounding effects of experimental noise. (Arithmetic) Mean¶ Quantile (Percentile)¶ Definitions at MathWorld, Wikipedia The threshold value below which the specified amount of data points fall. For example, if the 90th quantile is 23,104, that means 90% of data points are below 23,104. There are at least nine definitions of “quantile” in common use. CellEngine uses the median-based estimate definition (definition 8 in R and Hyndman and Fan 1996). This definition is continuous (meaning that it interpolates between values), independent of the underlying distribution of the data, and median-unbiased. Because of these and several other qualities, it is the definition recommended by Hyndman and Fan. Geometric Mean¶ Note that the geometric mean will be undefined for populations that have any values less than zero because the formula takes the square root of all values, and the square root of a negative is a complex number. The geometric mean will also be undefined for populations that have any values equal to zero. Geometric means of zero can be misleading because a single zero (which may be an outlier) in a dataset causes the entire geometric mean to be zero. The use of geometric means in flow cytometry is largely a holdover from old, analog cytometers that stored data in logarithmic form. The arithmetic mean of log-transformed values is equal to the log of the geometric mean, so it was more convenient to calculate that than convert from log back to linear. Because modern instruments store high-resolution list-mode data, and because the geometric mean cannot be calculated when the dataset contains negative values (as is common with compensated and background-subtracted data), the median is generally a more suitable statistic. In fact, the geometric mean and the median are equal for log-normal distributions, and most biological data is presumed to be log-normal, so in that regard they can be considered interchangeable. See page 235 of Shapiro’s Practical Flow Cytometry for more information. Event Count¶ The event count is the number of events in a population. (The word event is used instead of cell because flow cytometry may be used to analyze a wide variety of particles, such as virions, bacteria, fungi and beads.) Event Count per µl¶ The event count per µl is a calculated value based on the event count and either the sample volume or a known concentration of beads. For example, you can report "CD4+ T cells per µl." To enable this statistic, see these instructions. Percent of ___¶ The percent is the number of events in a population divided by the number of events in the specified ancestor population. Standard Deviation (StdDev)¶ Definitions at MathWorld, Wikipedia CellEngine reports the population standard deviation (as opposed to the sample standard deviation). Coefficient of Variation (CV)¶ The coefficient of variation is the standard deviation divided by the mean, resulting in a relative variation metric (standard deviation is an absolute variation metric). Median Absolute Deviation (MAD)¶ The median of the absolute deviations. This is a robust alternative to the standard deviation. Multiply this value by 1.4826 to achieve BD FACSDiva’s “robust standard deviation” (rSD) (see BD’s Tech See also¶	{"url":"https://docs.cellengine.com/exportstats/","timestamp":"2024-11-02T17:49:07Z","content_type":"text/html","content_length":"34285","record_id":"<urn:uuid:dec2a493-cde0-428d-89b3-3920ec7697a2>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00573.warc.gz"}
Slutsky, Morris / Pre-AP Cram Sheet #3: Moles and Stoichiometry • Textbook Reading: Holt "Chemistry" Chapter 9 Sections 1-2, Chapter 13 Section 2 Silberberg "Chemistry" Chapter 3 Sections 3-4, Chapter 4 Section 1 A Balanced Chemical Equation Is □ A chemical equation which has equal numbers of each kind of atoms on both sides. ☆ This is a consequence of conservation of mass. ☆ Unbalanced Equation Example: C[2]H[5]OH + I[2] + Na[2]CO[3] + H[2]O → CHI[3] + NaHCO[2] + CO[2] + HI ○ Reactants: 3 C atoms, 2 I atoms, 2 Na atoms, 5 O atoms, 7 H atoms ○ Products: 3 C atoms, 4 I atoms, 1 Na atom, 4 O atoms, 3 H atoms ☆ Balanced Equation Example: 2 C[2]H[5]OH + 8 I[2] + Na[2]CO[3] + H[2]O → 2 CHI[3] + 2 NaHCO[2] + CO[2] + 10 HI ○ Both Sides (Reactants & Products): 5 C atoms, 16 I atoms, 2 Na atoms, 6 O atoms, 14 H atoms □ An equation is balanced by inserting coefficients before formulas as necessary. ☆ If there is no coefficient, a '1' is implied. ☆ Coefficients are generally integers (although you may see some exceptions when we deal with thermochemistry). ☆ Coefficients should not all share a common factor: ○ 6 H[2] + 2 N[2] → 4 NH[3] : BAD because all coefficients are multiples of 2. ○ 3 H[2] + N[2] → 2 NH[3] : GOOD because 3, 1, 2 have no common factor. □ Balancing is an art but there are helpful rules. ☆ "Double the odds": if an element is present in multiple formulas in even numbers everywhere but one place where it is odd, double the coefficient for the formula where it is odd. ○ H[2] + O[2] → H[2]O: "Double the odd" oxygen atom in H[2]O to get H[2] + O[2] → 2 H[2]O. ○ Now balance H[2] to get the balanced equation 2 H[2] + O[2] → 2 H[2]O ☆ "Least common multiple": if an element is present on both sides in 2 different numbers, bring them both up to the LCM. ○ KClO[3] → KCl + O[2]: "LCM" of 2 and 3 is 6 oxygens. ○ 2 KClO[3] → KCl + 3 O[2] ○ Now balance Cl and K:2 KClO[3] → 2 KCl + 3 O[2] ☆ NEVER CHANGE A FORMULA OR SUBSCRIPT WHEN BALANCING. ○ H[2] + O[2] → H[2]O : do not modify H[2]O to get H[2] + O[2] → H[2]O[2] ○ This is no longer talking about the same substances, so it is wrong. □ Practice your balancing. Play The Game! This is a regular class activity, but you can get ahead if you like. Coefficients of a Balanced Chemical Equation are Ratios of Moles □ This sounds familiar. Didn't we say that Chemical Formulas are Ratios of Moles? □ The equation 3 H[2] + N[2] → 2 NH[3] means 3 moles of hydrogen react with 1 mole of nitrogen producing 2 moles of ammonia. □ We can write the mole ratios (3 mol H[2]/1 mol N[2]), (3 mol H[2]/2 mol NH[3]), and (1 mol N[2]/2 mol NH[3]) for example. □ We can use these ratios to relate between any products and reactants in the same reaction. ☆ If you have 9 moles of H[2], you will require 3 moles of N[2] to react with it. ☆ You will obtain 6 moles of NH[3] if this reaction goes perfectly. □ The relationships between quantities of products and reactants are known as stoichiometry. Theoretical and Percentage Yield □ The theoretical yield of a reaction is the amount of a product predicted from the stoichiometry of the balanced equation. □ The actual yield of a reaction is the amount of product you get in a real experiment. □ The percentage yield of a reaction is 100 x actual yield / theoretical yield. ☆ The equation 3 H[2] + N[2] → 2 NH[3] predicts that 18 moles of H[2] and 6 moles of N[2] yield 12 moles of NH[3]. ☆ If you actually do the reaction but only obtain 9 moles of NH[3], the theoretical yield is 100 x 9 / 12 = 75%. Limiting and Excess Reactants □ The grocery store sells hotdogs in packs of 10, but buns only come in packs of 8. □ If you buy one of each, you can only have 8 sandwiches. □ We would say that buns are limiting but hotdogs are in excess, because there will be some hotdogs left over. □ The yield of a reaction is determined by the limiting reactant. □ Suppose we have 6 moles of H[2] and 4 moles of N[2] and we react them as in 3 H[2] + N[2] → 2 NH[3] ☆ 6 moles of H[2] is enough to produce 4 moles of NH[3]. ☆ 4 moles of N[2] is enough to produce 8 moles of NH[3] but we won't get that: instead, some N[2] will be left over. ☆ We get the smaller yield, 4 moles of NH[3]. H[2] is the limiting reactant and N[2] is in excess. Stoichiometry in Solution □ Chemical reactions are often conducted in solution. □ The molarity of a solution is defined as the number of moles of a substance per Liter of solution. □ The symbol for molarity is a capital M. ☆ 3M HCl means a solution containing 3 moles of HCl per Liter ☆ You can write the ratio (3 mol HCl/1 L) for use in stoichiometry calculations. Use Mole Ratios from the Balanced Chemical Equation to Solve Stoichiometry Problems Iron (III) hydroxide decomposes when heated to yield iron (III) oxide and water vapor by the following equation: 2 Fe(OH)[3] → Fe[2]O[3] + 3 H[2]O How many moles of water vapor are released by the decomposition of 8 moles of Fe(OH)[3]? 8 mol Fe(OH)3 x 3 mol H2O = 12 mol H2O 2 mol Fe(OH)3 Aluminum reacts with oxygen by the equation 4 Al + 3 O[2] → 2 Al[2]O[3]. What mass of oxygen (O[2]) is required to react with 18 g of aluminum? 18 g Al x 1 mol Al x 3 mol O2 x 32.0 g O2 = 16 g O2 27.0 g Al 4 mol Al 1 mol O2 Iron (Fe) dissolves in dilute sulfuric acid (H[2]SO[4]) yielding iron (II) sulfate and hydrogen gas. How much 3 M H[2]SO[4] (3 moles per Liter) solution is required to react with 100 g of Fe Write a balanced chemical equation: Fe + H[2]SO[4] → FeSO[4] + H[2] 100 g Fe x 1 mol Fe x 1 mol H2SO4 x 1 L H2SO4 solution = 0.597 L H2SO4 solution 55.85 g Fe 1 mol Fe 3 mol H2SO4 Find Limiting Reactant by Working Out Stoichiometry for each Reactant How many grams of nitric acid, HNO[3], can be prepared from the reaction of 69.0 g of NO[2] with 29.0 g H[2]O according to the equation below? What is the limiting reactant? Which reactant is in 3 NO[2] + H[2]O → 2HNO[3] + NO Work out the yield of HNO[3] starting from NO[2] 69.0 g NO2 x 1 mol NO2 x 2 mol HNO3 x 63.0 g HNO3 = 63.0 g HNO3 46.0 g NO2 3 mol NO2 1 mol HNO3 Work out the yield of HNO[3] starting from H[2]O 29.0 g H2O x 1 mol H2O x 2 mol HNO3 x 63.0 g HNO3 = 203 g HNO3 18.0 g NO2 1 mol H2O 1 mol HNO3 The theoretical yield is the smaller of the two, 63.0 g HNO[3], from NO[2]. The limiting reactant is NO[2] because it limits the amount of product. Not all the H[2]O will react, so H[2]O is in Use Reaction Stoichiometry to Calculate Theoretical Yield Suppose the reaction above between NO[2] and H[2]O was performed, but instead of the theoretical yield of 63.0 g HNO[3] , only 50.0 g of HNO[3] was obtained. No real reaction is perfect. What is the percentage yield of this reaction? 100 x 50.0 g HNO3 = 79.3 % 63.0 g HNO3 Solve Stoichiometry Problems for Unknown Molar Masses Remember that the molar mass of a substance is equal to the mass in grams of a sample of that substance, divided by the number of moles of that substance. 22.4 grams of an unknown metal carbonate, represented as MCO[3], is heated to decompose it to the metal oxide MO and carbon dioxide. 8.8 grams of carbon dioxide are produced by the reaction MCO [3] → MO + CO[2]. What is the identity of the metal M? 8.8 g CO2 x 1 mol CO2 x 1 mol MCO3 = 0.2 mol MCO3 44 g CO2 1 mol CO2 22.4 g MCO3 = 112 g/mol : this is the molar mass of MCO3 0.2 mol MCO3 Subtracting the mass of CO3 = (12.0 + 3 * 16.0) = 60 g/mol, the molar mass of M must be 112 - 60 = 52 g/mol. The metal M must therefore be chromium (Cr).	{"url":"https://www.dimanregional.org/Page/3759","timestamp":"2024-11-02T20:10:25Z","content_type":"text/html","content_length":"499174","record_id":"<urn:uuid:026830d5-3431-468b-b8f2-ea5c6049eb9f>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00336.warc.gz"}
Minimize Energy of Piecewise Linear Mass-Spring System Using Cone Programming, Solver-Based This example shows how to find the equilibrium position of a mass-spring system hanging from two anchor points. The springs have piecewise linear tensile forces. The system consists of $n$ masses in two dimensions. Mass $i$ is connected to springs $i$ and $i+1$. Springs $1$ and $n+1$ are also connected to separate anchor points. In this case, the zero-force length of spring $i$ is a positive length $l\left(i\right)$, and the spring generates force $k\left(i\right)q$ when stretched to length $q+l\left(i\right)$. The problem is to find the minimum potential energy configuration of the masses, where potential energy comes from the force of gravity and from the stretching of the nonlinear springs. The equilibrium occurs at the minimum energy configuration. This illustration shows five springs and four masses suspended from two anchor points. The potential energy of a mass $m$ at height $h$ is $mgh$, where $g$ is the gravitational constant on Earth. Also, the potential energy of an ideal linear spring with spring constant $k$ stretched to length $q$ is $k{q}^{2}/2$. The current model is that the spring is not ideal, but has a nonzero resting length $l$. The mathematical basis of this example comes from Lobo, Vandenberg, Boyd, and Lebret [1]. For a problem-based version of this example, see Minimize Energy of Piecewise Linear Mass-Spring System Using Cone Programming, Problem-Based. Mathematical Formulation The location of mass $i$ is $x\left(i\right)$, with horizontal coordinate ${x}_{1}\left(i\right)$ and vertical coordinate ${x}_{2}\left(i\right)$. Mass $i$ has potential energy due to gravity of $gm\ left(i\right){x}_{2}\left(i\right)$. The potential energy in spring $i$ is $k\left(i\right)\left(d\left(i\right)-l\left(i\right){\right)}^{2}/2$, where $d\left(i\right)$ is the length of the spring between mass $i$ and mass $i-1$. Take anchor point 1 as the position of mass 0, and anchor point 2 as the position of mass $n+1$. The preceding energy calculation shows that the potential energy of spring $i$ is Reformulating this potential energy problem as a second-order cone problem requires the introduction of some new variables, as described in Lobo [1]. Create variables $t\left(i\right)$ equal to the square root of the term $Energy\left(i\right)$. Let $e$ be the unit column vector $\left[\genfrac{}{}{0}{}{0}{1}\right]$. Then ${x}_{2}\left(i\right)={e}^{T}x\left(i\right)$. The problem becomes $\underset{x,t}{\mathrm{min}}\left(\sum _{i}gm\left(i\right){e}^{T}x\left(i\right)+‖t{‖}^{2}\right).$ (1) Now consider $t$ as a free vector variable, not given by the previous equation for $t\left(i\right)$. Incorporate the relationship between $x\left(i\right)$ and $t\left(i\right)$ in the new set of cone constraints $‖x\left(i\right)-x\left(i-1\right)‖-l\left(i\right)\le \sqrt{\frac{2}{k\left(i\right)}}t\left(i\right).$ (2) The objective function is not yet linear in its variables, as required for coneprog. Introduce a new scalar variable $y$. Notice that the inequality $‖t{‖}^{2}\le y$ is equivalent to the inequality $‖\left[\genfrac{}{}{0}{}{2t}{1-y}\right]‖\le 1+y$. (3) Now the problem is to minimize $\underset{x,t,y}{\mathrm{min}}\left(\sum _{i}gm\left(i\right){e}^{T}x\left(i\right)+y\right)$ (4) subject to the cone constraints on $x\left(i\right)$ and $t\left(i\right)$ listed in (2) and the additional cone constraint (3). Cone constraint (3) ensures that $‖t{‖}^{2}\le y$. Therefore, problem (4) is equivalent to problem (1). The objective function and cone constraints in problem (4) are suitable for solution with coneprog. MATLAB® Formulation Define six spring constants $k$, six length constants $l$, and five masses $m$. k = 40(1:6); l = [1 1/2 1 2 1 1/2]; m = [2 1 3 2 1]; Define the approximate gravitational constant on Earth $g$. The variables for optimization are the ten components of the $x$ vectors, the six components of the $t$ vector, and the $y$ variable. Let v be the vector containing all these variables. • [v(1),v(2)] corresponds to the 2-D variable $x\left(1\right)$. • [v(3),v(4)] corresponds to the 2-D variable $x\left(2\right)$. • [v(5),v(6)] corresponds to the 2-D variable $x\left(3\right)$. • [v(7),v(8)] corresponds to the 2-D variable $x\left(4\right)$. • [v(9),v(10)] corresponds to the 2-D variable $x\left(5\right)$. • [v(11):v(16)] corresponds to the 6-D vector $t$. • v(17) corresponds to the scalar variable $y$. Using these variables, create the corresponding objective function vector f. f = zeros(size(m)); f = [f;gm]; f = f(:); f = [f;zeros(length(k)+1,1)]; f(end) = 1; Create the cone constraints corresponding to the springs between the masses (2) $‖x\left(i\right)-x\left(i-1\right)‖-l\left(i\right)\le \sqrt{\frac{2}{k\left(i\right)}}t\left(i\right)$. The coneprog solver uses cone constraints for a variable vector $v$ in the form $‖{A}_{sc}\cdot v-{b}_{sc}‖\le {d}_{sc}^{T}v-\gamma$. In the following code, the Asc matrix represents the term $‖x\left(i\right)-x\left(i-1\right)‖$, with bsc = [0;0]. The cone variable dsc = $\sqrt{2/k\left(i\right)}$ and the corresponding gamma = $-l d = zeros(1,length(f)); Asc = d; Asc([1 3]) = [1 -1]; A2 = circshift(Asc,1); Asc = [Asc;A2]; ml = length(m); dbase = 2ml; bsc = [0;0]; for i = 2:ml gamma = -l(i); dsc = d; dsc(dbase + i) = sqrt(2/k(i)); conecons(i) = secondordercone(Asc,bsc,dsc,gamma); Asc = circshift(Asc,2,2); Create the cone constraints corresponding to the springs between the end masses and the anchor points by using the anchor points for the locations of the end masses, as in the preceding code. x0 = [0;5]; xn = [5;4]; Asc = zeros(size(Asc)); Asc(1,(dbase-1)) = 1; Asc(2,dbase) = 1; bsc = xn; gamma = -l(ml); dsc = d; dsc(dbase + ml) = sqrt(2/k(ml)); conecons(ml + 1) = secondordercone(Asc,bsc,dsc,gamma); Asc = zeros(size(Asc)); Asc(1,1) = 1; Asc(2,2) = 1; bsc = x0; gamma = -l(1); dsc = d; dsc(dbase + 1) = sqrt(2/k(1)); conecons(1) = secondordercone(Asc,bsc,dsc,gamma); Create the cone constraint (3) corresponding to the $y$ variable $‖\left[\genfrac{}{}{0}{}{2t}{1-y}\right]‖\le 1+y$ by creating the matrix Asc which, when multiplied by the v vector, gives the vector $\left[\genfrac{}{}{0}{}{2t}{-y}\right]$. The bsc vector corresponds to the constant 1 in the term $1-y$. The dsc vector, when multiplied by v, returns $y$. And gamma = $-1$. Asc = 2eye(length(f)); Asc(1:dbase,:) = []; Asc(end,end) = -1; bsc = zeros(size(Asc,1),1); bsc(end) = -1; dsc = d; dsc(end) = 1; gamma = -1; conecons(ml+2) = secondordercone(Asc,bsc,dsc,gamma); Finally, create lower bounds corresponding to the $t$ and $y$ variables. lb = -inf(size(f)); lb(dbase+1:end) = 0; Solve Problem and Plot Solution The problem formulation is complete. Solve the problem by calling coneprog. [v,fval,exitflag,output] = coneprog(f,conecons,[],[],[],[],lb); Plot the solution points and the anchors. pp = v(1:2*ml); pp = reshape(pp,2,[]); pp = pp'; hold on xx = [x0,xn]'; xxx = [x0';pp;xn']; legend('Calculated points','Anchor points','Springs','Location',"best") hold off You can change the values of the parameters m, l, and k to see how they affect the solution. You can also change the number of masses; the code takes the number of masses from the data you supply. [1] Lobo, Miguel Sousa, Lieven Vandenberghe, Stephen Boyd, and Hervé Lebret. “Applications of Second-Order Cone Programming.” Linear Algebra and Its Applications 284, no. 1–3 (November 1998): 193–228. https://doi.org/10.1016/S0024-3795(98)10032-0. See Also coneprog \| secondordercone Related Topics	{"url":"https://se.mathworks.com/help/optim/ug/cone-programming-mass-nonlinear-spring.html","timestamp":"2024-11-10T15:08:32Z","content_type":"text/html","content_length":"105377","record_id":"<urn:uuid:d42c092d-46b7-446d-8b2c-53d125c54b20>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00425.warc.gz"}
logcondens: Estimate a Log-Concave Probability Density from Iid Observations Given independent and identically distributed observations X(1), ..., X(n), compute the maximum likelihood estimator (MLE) of a density as well as a smoothed version of it under the assumption that the density is log-concave, see Rufibach (2007) and Duembgen and Rufibach (2009). The main function of the package is 'logConDens' that allows computation of the log-concave MLE and its smoothed version. In addition, we provide functions to compute (1) the value of the density and distribution function estimates (MLE and smoothed) at a given point (2) the characterizing functions of the estimator, (3) to sample from the estimated distribution, (5) to compute a two-sample permutation test based on log-concave densities, (6) the ROC curve based on log-concave estimates within cases and controls, including confidence intervals for given values of false positive fractions (7) computation of a confidence interval for the value of the true density at a fixed point. Finally, three datasets that have been used to illustrate log-concave density estimation are made available. Version: 2.1.8 Depends: R (≥ 2.10) Imports: ks, graphics, stats Published: 2023-08-22 DOI: 10.32614/CRAN.package.logcondens Author: Kaspar Rufibach and Lutz Duembgen Maintainer: Kaspar Rufibach <kaspar.rufibach at gmail.com> License: GPL-2 \| GPL-3 [expanded from: GPL (≥ 2)] URL: http://www.kasparrufibach.ch , https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html NeedsCompilation: no Citation: logcondens citation info Materials: NEWS CRAN checks: logcondens results Reference manual: logcondens.pdf Vignettes: logcondens: Computations Related to Univariate Log-Concave Density Estimation (Duembgen and Rufibach, 2011, Journal of Statistical Software, 39(6), 1-28.) Package source: logcondens_2.1.8.tar.gz Windows binaries: r-devel: logcondens_2.1.8.zip, r-release: logcondens_2.1.8.zip, r-oldrel: logcondens_2.1.8.zip macOS binaries: r-release (arm64): logcondens_2.1.8.tgz, r-oldrel (arm64): logcondens_2.1.8.tgz, r-release (x86_64): logcondens_2.1.8.tgz, r-oldrel (x86_64): logcondens_2.1.8.tgz Old sources: logcondens archive Reverse dependencies: Reverse depends: smoothtail Reverse suggests: logconcens, pROC Reverse enhances: LogConcDEAD Please use the canonical form https://CRAN.R-project.org/package=logcondens to link to this page.	{"url":"https://cran.mirror.garr.it/CRAN/web/packages/logcondens/index.html","timestamp":"2024-11-11T08:14:24Z","content_type":"text/html","content_length":"7829","record_id":"<urn:uuid:2d176e31-58cd-4c45-9956-20c86e6714f2>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00493.warc.gz"}
The anomalous Zeeman effect is splitting into an even number of levels (not predicted by angular momentum alone) for Z odd atoms. This is evidence for spin. If you turn off the magnetic field, there is still an effect: The wigner eckhart theorem is so operators are proportional to Want to find in our paricular case: sourcepsfile jl@crush.caltech.edu indexparticle_spin	{"url":"http://www.cs.cmu.edu/~jcl/classnotes/physics/quantum_mechanics/anomalous_Zeeman_effect/anomalous_Zeeman_effect.html","timestamp":"2024-11-07T00:15:58Z","content_type":"text/html","content_length":"3488","record_id":"<urn:uuid:60fd32f8-f555-42bc-8581-389733fec72e>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00630.warc.gz"}
Mandelbrot Set The Mandelbrot set is named after Benoît Mandelbrot, a French American mathematician. The illustration below was created with Fractint, an ancient (1988!) but still maintained program that can create all sorts of fractals (the colors are from a palette called “goodega”, which was meant to work well on EGA displays, how ’bout that?). The set is a part of the complex plane. It is created by iterating the simple complex quadratic polynomial $f_c:\mathbb{C}\to \mathbb{C}$, defined by For each point $c$ of the complex plane, $f_c$ is iterated starting with $z=0$. This creates a sequence of points $(z_n)$. If the orbit of these points does not escape to infinity, then $c$ is part of the Mandelbrot set. It’s that simple. A few examples, for different values of $c$: $c$ $z_0$ $z_1$ $z_2$ $z_3$ $z_4$ … 0 0 0 0 0 0 … 1 0 1 2 5 26 … i 0 i -1+i -i -1+i … 1+i 0 1+i 1+3i -7+7i 1-97i … The distance from the origin of a complex number is given by its absolute value, defined as $\|z\|=\|x+yi\|=\sqrt{x^2+y^2}$. So, from the table above, we see that $0$ and $i$ are in the set, and \ (1\) and $1+i$ are not. The Mandelbrot set is a fractal, probably by far the best known one. The typical (although not mathematically rigorous) example of a fractal is a coastline. If you measure the length of the coastline of, say, Norway, using a ruler of 1 km long, you get a certain length. But if you replace the ruler by a 1 m one, you get a larger length, since you are able to follow the actual shape of the coastline more closely. This is not true if you measure a football field (or Colorado). The structure of a coastline looks the same (or at least similar) at different scales. A mathematical object that has this property of self-similarity is called a fractal. The detail of the Mandelbrot set in the following figure shows that (distorted) copies of the main shape occur again at smaller scales. In fact, the shape occurs infinitely often. Despite the pretty colors, the object of interest is not the colorful part of these images. The Mandelbrot set is represented by the black parts. If only the Mandelbrot set itself is shown, the image above becomes: Only the small copies of the Mandelbrot set are visible, and even then the smaller ones only because I downsampled the image from a higher resolution one. Now, amazingly, the Mandelbrot set is actually connected! This means, intuitively, that it is a single object (or, mathematically, that it is not the union of two or more disjoint open sets). The fact that the thin filaments that connect the different parts of the set cannot be seen in the above figure is not due to an error in the software. Indeed, the software renders a picture of the set on a pixel grid by calculating a value for the middle of each pixel, and the filaments are much too thin to be picked up that way. The Mandel program by Wolf Jung includes several different algorithms to visualize the filaments. The difference with the classical approach is that Mandel attempts to select each pixel that contains a point of the set anywhere in the pixel. The effect is that the filaments are shown (much) too wide, but that it becomes possible to visualize them without resorting to using colors in the neighborhood of the set (keeping all the attention to the Mandelbrot set itself, instead of wooing everyone with the pretty pictures). Anyway, it has always been a pet peeve of mine that people only look at the pretty colors, not realizing that the colored pixels are not even in the set, since the colors are typically used to indicate how quickly the iteration for that pixel escaped to infinity! Hi Tom, Thanks for the article :) z2 for c=1 should be 2... Indeed, I seem to have skipped a value… Thanks for pointing this out; I’ve adapted the table! The content of this field is kept private and will not be shown publicly. Spam avoidance measure, sorry for this.	{"url":"https://tomroelandts.com/index.php/articles/mandelbrot-set","timestamp":"2024-11-01T19:34:20Z","content_type":"text/html","content_length":"27914","record_id":"<urn:uuid:0c3bec53-5108-4dfa-b18f-c7ab35d54cab>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00046.warc.gz"}
Don’t Worry, Math Is Still Everywhere Last week Michael J. Barany — a mathematical historian — published a blog post in Scientific American titled Mathematicians Are Overselling the Idea That “Math Is Everywhere.” We can talk about whether or not the main arguments of his article have merit in a moment, but first, let’s start by dismissing the title as little more than an editorial blunder. It gives the impression that Barany intends to argue that math actually isn’t everywhere, despite what all those mathematically enthusiastic look-around-you-math-is-hidden-in-the-fabric-of-our-lives media types would have you believe. This is not the point of Barany’s post at all, in fact it’s barely even mentioned beyond the title and a passing [S:dig at:S] mention of Jordan Ellenberg. Instead, what it seems Barany is endeavoring to establish is that mathematicians are not everywhere. And this, he says, should be considered when making policy decisions concerning public support of advanced mathematics. Barany discusses the role of mathematics in society and culture from the Babylonian times through post-World War II.The ancients, he says used math as “a trick of the trade rather than a public good,” adding, “for millennia, advanced math remained the concern of the well-off, as either a philosophical pastime or a means to assert special authority.” Historically, Barany explains, math was the domain of the elite, it was a source of power that was only available to the highest born. Mathematicians inhabited a rarefied domain, they were acting as advisors to heads of state and maintained an untouchable air of the occult. This otherness and elite status meant that math wasn’t available to all people, and Barany argues that this has bled through to mathematics today. And I completely agree. Anecdotally — since I can’t find an actual demographics survey to back this up — advanced math is largely occupied by people who come from the economically advantaged side of things. But here’s where Barany’s argument starts to lose some strength: isn’t that the case for any course of advanced study? Attending graduate school at all is a tremendous luxury, whether studying math, science, language, or art, it’s a pretty brazen thing to want to sit around for 4-6 years to get paid very little to think about things. And some historians, most notably the blogger Thony Christie, even take exception with the picture Barany paints of math and society. Christie suggests that Barany may her oversold the elitism and “otherness” of mathematicians, pointing out that math played a huge role in the scientific revolution of the seventeenth century. Confirming what I suspect, which is that math isn’t all that different from the other sciences in terms of its growth and expansion over the last several centuries. In a conversation on twitter, Barany defends his position to Steven Strogatz — legendary bringer of math to the people — saying there are two core questions that people try to answer with “math is everywhere” namely, (1) why should the public support advanced math, and (2) why should the public learn basic math? Barney contends that “math is everywhere” is not an appropriate answer to either. I disagree. I think math being everywhere is exactly the antidote to the ancient rhetoric of “when will I ever use this?” Math is everywhere just as much as anything is everywhere. Science is everywhere, art is everywhere, language is everywhere, and for some reason in those cases, being everywhere is sufficient to convince folks that they will use the subjects. It is everywhere, and therefore knowing it will help you understand everything. So I think a good dose of “math is everywhere” is a great way to motivate why the public should learn basic math. And I think we can mostly agree that learning basic math is a good and important thing. And since the best way to help your kids develop good habits is to set a positive example, I obviously think policymakers should opt in favor of supporting advanced math, just as they would support any advanced science research. Because even though it often seems pointless, basic research is the provenance of great discovery. 2 Responses to Don’t Worry, Math Is Still Everywhere 1. “Math is everywhere just as much as anything is everywhere. Science is everywhere, art is everywhere, language is everywhere, and for some reason in those cases, being everywhere is sufficient to convince folks that they will use the subjects. It is everywhere, and therefore knowing it will help you understand everything.” The above lines strike me as a reductio ad absurdum in favor of Barany’s point, not a contradiction to it. 1. The ubiquity of art does not convince folks they will use the subject; ditto language (arts). Enrollment in humanities programs (at the university level) has been proportionally shrinking for decades as has robust humanities offerings in K-12 education. Federal research $$ prioritize humanities << general science < medical science < 1, then those things cannot all be simultaneously salient. By making the claim that “math is everywhere”, we get called on defend its importance in situations where it is at best a secondary or tertiary factor. While an election may have mathematical aspects, psychology and politics seem much more important to me. So too with love (pace Frenkel) and farming. Situations where math is more fundamental than incidental are many but also rare (like, small % large #). The phenomena in which it is fundamental are often also very abstract or technically difficult, so a popular book like Ellenberg’s reads like a kind of cabinet of curiosities. Game-able lotteries are interesting, make for fun reading, but not important. Stability analyses for bridges and skyscrapers are interesting, make for more difficult reading, and are very important. I would prefer to defend the claim that the salience of math is distributed quite unevenly across human activity and interest, that where it is most salient it is essential, the difference between life and death, tied up in the origins of the universe and the nature of matter. The pleasure of mathematics is not its ubiquity but its quality. [Here I mean mathematics beyond algebra. Basic numeracy is pretty darn helpful for making decisions in the world, and policy-makers and the public agree on the importance of arithmetic.) 3. Bacteria are more everywhere than language, but that doesn’t mean we should prioritize the study of bacteria over literacy. Ubiquity does not establish priority. I’m somewhat surprised to find myself making a late-night comment on your blog, but it just happened! Thanks for writing, Anna. 2. Please stop referring to mathematics as science. It is not in any sense a science. This entry was posted in History of Mathematics and tagged Michael J. Barany, Thony Christie. Bookmark the permalink.	{"url":"https://blogs.ams.org/blogonmathblogs/2016/08/29/dont-worry-math-is-still-everywhere/","timestamp":"2024-11-06T07:10:21Z","content_type":"text/html","content_length":"58013","record_id":"<urn:uuid:fa18c3ef-8cf0-4236-9d0d-70981523986f>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00731.warc.gz"}
Rockets: A Beginners Guide Part 3 John Berrigan, Teacher Oakville Trafalger H.S. In the previous article we found the main factors that determine the thrust of a rocket engine. We rearranged the formula and determined the Impulse of the formula for rockets. , now is a good time to discuss how Impulse can be used to eventually determine the efficiency of a rocket engine. What actually is impulse? The rocket impulse formula developed in the previous article, The total impulse that an engine can deliver can then be used to find the of a rocket by using the impulse formula that we know. From grade 12 physics, we also know that impulse is the change in momentum or Combining this and the rocket impulse equation, we get Let’s apply this to a rocket problem A 1550-kg rocket has an engine with an exhaust velocity of 1250 m/s. It uses 7.2 kg of fuel a minute. If the engine burns for 30.0 seconds, what is the velocity change of the rocket? It is best to split the work into two parts; the rocket engine and then the change in velocity. In other words we will use the thrust equation (the cause of the change) and then the impulse equation (the result). What do we know about each of these? First consider the rocket engine. It uses 7.2 kg of fuel every 60 s, so: Now consider the change in velocity. The force applied is 150 N for 30 s, so: This calculation was made using a formula that assumed that the mass of the rocket was constant. However, we know that the mass is changing because fuel is flying out the back. This is an example of using an approximation — one of physics’ most powerful tools. How good is this approximation in this case? We can check it with the rocket equation . (We first explored this formula in a slightly different form The rocket used fuel at the rate of 7.2 kg/min, so in 30 s the rocket has lost 3.6 kg of mass. The final mass is 1546.4 kg. Substituting the values in the rocket equation, yields a change in velocity which is almost identical to our 2.90 m/s to three digits. The first method is simpler for students because it does not require the use of logarithms. When is it better to use the “harder” method? Have them discuss this in small groups and then have each group calculate the change in velocity for a different burn time. Introduce the idea of using the average mass of the rocket rather than the starting mass. Have them use their results to explain where the approximation stops being good enough. The answer is not a simple one because it depends on how precise you need your answers to be. Here is a Google Docs spreadsheet so you don’t have to do all the calculations each time. Once they have mastered the work using “Pen and Paper” get them to create their own spreadsheet. Getting them to use pen and paper first is essential to avoid calculations looking mathmagical. You can mix up the question and have them solve for different variables. This gets them to think and to avoid the classic “plug and chug” questions. Another sample problem Here is another problem. It involves a bit more care with the units. A 1.5 Tonne satellite needs to undergo a total delta V of 75 m/s. If 100 kg of fuel is available and the rocket uses 2 kg of fuel a minute, what must the of the engine be? We need to solve for the thrust required first, so we start with this equation: Now we know the required thrust, we can compute the exhaust velocity: Using the rocket equation, we get: (I’ll let the reader redo this approximation using the average mass instead.) Now that we have done some specific questions involved in impulse, this will be a good lead in to the next article which is “specific Impulse” and find out how we can define the efficiency of rocket	{"url":"http://newsletter.oapt.ca/files/Rockets-III.html","timestamp":"2024-11-14T01:23:42Z","content_type":"text/html","content_length":"27188","record_id":"<urn:uuid:1373a772-71b5-493f-ae73-4106a4f1dc72>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00583.warc.gz"}
Spaces of states of the two-dimensional SciPost Submission Page Spaces of states of the two-dimensional O(n) and Potts models by Jesper Lykke Jacobsen, Sylvain Ribault, Hubert Saleur This is not the latest submitted version. This Submission thread is now published as Submission summary Authors (as registered SciPost users): Jesper Lykke Jacobsen · Sylvain Ribault Submission information Preprint Link: https://arxiv.org/abs/2208.14298v1 (pdf) Code repository: https://gitlab.com/s.g.ribault/representation-theory/ Date submitted: 2022-10-13 08:56 Submitted by: Ribault, Sylvain Submitted to: SciPost Physics Ontological classification Academic field: Physics • High-Energy Physics - Theory Specialties: • Mathematical Physics Approach: Theoretical We determine the spaces of states of the two-dimensional $O(n)$ and $Q$-state Potts models with generic parameters $n,Q\in \mathbb{C}$ as representations of their known symmetry algebras. While the relevant representations of the conformal algebra were recently worked out, it remained to determine the action of the global symmetry groups: the orthogonal group for the $O(n)$ model, and the symmetric group $S_Q$ for the $Q$-state Potts model. We do this by two independent methods. First we compute the twisted torus partition functions of the models at criticality. The twist in question is the insertion of a group element along one cycle of the torus: this breaks modular invariance, but allows the partition function to have a unique decomposition into characters of irreducible representations of the global symmetry group. Our second method reduces the problem to determining branching rules of certain diagram algebras. For the $O(n)$ model, we decompose representations of the Brauer algebra into representations of its unoriented Jones--Temperley--Lieb subalgebra. For the $Q$-state Potts model, we decompose representations of the partition algebra into representations of the appropriate subalgebra. We find explicit expressions for these decompositions as sums over certain sets of diagrams, and over standard Young tableaux. We check that both methods agree in many cases. Moreover, our spaces of states are consistent with recent bootstrap results on four-point functions of the corresponding CFTs. Current status: Has been resubmitted Reports on this Submission Report #2 by Anonymous (Referee 2) on 2023-1-8 (Contributed Report) • Cite as: Anonymous, Report on arXiv:2208.14298v1, delivered 2023-01-08, doi: 10.21468/SciPost.Report.6476 (emailed by a referee to the editor, submitted by the editor) First, the question that the article addresses. With the great wealth of results on O(n) and S_Q models and their critical behavior, it is relevant to understand the basis of these models on a more fundamental group-theoretical and representation-theoretical level. It already begins with the knowledge of the symmetry groups themselves, which are non-trivial generalisation of the symmetry groups for natural values of n and Q. Also, while the authors claim that the partition sum is the basis of one of their approaches, this seems at first sight a strange claim, as the partition sum can be written in terms of (two-dimensional) diagrams all of which represent objects which themselves are invariant under the action of the symmetry groups. The state space can hardly be understood in terms of invariant elements only. The key to this riddle appears to be that the authors consider the twisted partition sum, and the fact that the partition sum is written in terms of the trace of a transfer matrix, which acts in a space of one-dimensional diagrams. These one-dimensional diagrams are not invariant under the symmetry groups. It is not obvious to me that the resulting state space is independent of the approach. But whether or not it is independent, the resulting state space is worth studying. I think that the algebraic approach does not resolve this difficulty, as it is based on the same set of diagrams. The authors have taken great efforts to make the material accessible, with extensive references to existing material not only to the published (refereed) literature, but also useful wikipedia lemmas. I found it very useful that in their list of references they have included back references to the places in the article that refer to each element in the list. Also they build up the results carefully by first giving a sketch of the results in the introduction, before they jump to their derivations. In my opinion the article is a very interesting and useful to be published. Admittedly it will appeal to a limited (but growing) audience, but it is of great importance to the community of mathematical statistical physics, and will be very useful outside of the statistical physics community. I have no doubt that the article should be published, and may even be considered a catch by the journal that does. Report #1 by Anonymous (Referee 1) on 2022-12-1 (Invited Report) • Cite as: Anonymous, Report on arXiv:2208.14298v1, delivered 2022-12-01, doi: 10.21468/SciPost.Report.6242 The paper uses a pair of rigorous approaches, that leave little space to doubt about the results. The paper is very dense and many concepts are introduced, making it hard to access to people who are not already experts in those topic. The reading of Section 4 is particularly hard, since many things discussed in Section 4 are actually introduced or defined in Appendix A, and the reader has to go back and forth between those two parts of the paper. In my opinion, several parts of Appendix A should be moved to the main text. The paper confirms a previous conjecture by the authors about the action of $O(n)$ and $S_Q$ groups in the critical two-dimensional $O(n)$ and Potts model. I have a few comments after which I recommend publication Requested changes 1. I do not understand how clusters with cross topology contribute to Eq. (3.29). They are not counted in $S_0$ nor in $S$. For example, if I consider two configuration, one with only trivial clusters and one with only trivial clusters and a cluster with cross topology, do they contribute the same to (3.29)? Maybe a comment about it would be good 2. (3.30): I would avoid the notation $0^{N(C)}$ and use $\delta_{N(C),0}$, since it's clearer and does not make the formulas more cumbersome (it's also the notation used in (3.29)) 3. Above (4.17): $u$ is not defined here, but in the appendix. A sentence about what $u$ is, to gain some intuition on it, would be good 4. (4.21): there are 6 more diagrams, related by swapping the two top indices, which are not considered. By reading the paragraph above (4.21), it's not clear why these should not be considered. 5. Below (4.22): the fact that that representation is $W_1^{(4)}$ is not clear given that there has been no explanation what these representation must be in terms of diagrams. There should be some reference to the appendix A, where this is explained 6. Similarly, at the end of the same paragraph, the statement that the defining feature of $W_{L/2}^{(L)}$ is annihilated by $TL_L(n)$ is not something that has been explained here. 7. Typo in eq (A.17b), $N$ instead of $L$	{"url":"https://www.scipost.org/submissions/2208.14298v1/","timestamp":"2024-11-06T15:57:03Z","content_type":"text/html","content_length":"40097","record_id":"<urn:uuid:c65ddf63-0b75-4752-ace1-dd6c403d1a43>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00157.warc.gz"}
networks - Epskamp, 2018. 11 good questions, nicely answered! Networks - Epskamp, 2018 11 important questions on Networks - Epskamp, 2018 Of which components do psychological networks consist? Psychological networks consist of nodes representing observed variables, connected by edges representing statistical relationships. Of which three steps does psychological research with networks consist? • estimate a statistical model on data, from which some parameters can be represented as a weighted network between observed variables. • analyze the weighted network structure using measures taken from graph theory to infer, for instance, the most central nodes. • assessing the accuracy of the network parameters and measures What does it mean if the edges in a network represent partial correlations? • If the edges in a network represent partial correlations, it means they show the relationship between variables while conditioning for all other variables in the network. • this way, the direct relationship between variables is presented and no indirect effects are included. • Higher grades + faster learning • Never study anything twice • 100% sure, 100% understanding Discover Study Smart What is a pairwise markov random field? • A PMRF is a network in which nodes represent variables, connected by undirected edges (edges with no arrowhead) indicating conditional dependence between two variables; two variables that are not connected are independent after conditioning on other variables. • When data are multivariate normal, such a conditional independence would correspond to a partial correlation being equal to zero. What are the advantages of a pairwise random markov field, that a directed network does not have? • In cross-sectional observational data, causal networks (e.g., directed networks) are hard to estimate without stringent assumptions (e.g., no feedback loops). • In addition, directed networks suffer from a problem of many equivalent models (e.g., a network A → B is not statistically distinguishable from a network A ← B). • PMRFs, however, are well defined and have no equivalent models (i.e., for a given PMRF, there exists no other PMRF that describes exactly the same statistical independence relationships for the set of variables under consideration). What pairwise markov random field model is appropriate if you have binary data, normal data, and a mix of binary and normal data? • The ising model is for binary data • for normal data, use the gaussian graphical model □ edges can directlybe interpreted as partial correlation coefficients. □ The GGM requires an estimate of the covariance matrix as input for which polychoric correlations can also be used in case the data are ordinal. □ For continuous data that are not normally distributed, a transformation can be applied before estimating the GGM. • for mixed data, use mixed graphical models. When estimating network models, what is a problem that frequently occurs? • in an unregularized network, the number of parameters to estimate grows quickly with the size of the network. □ e.g. 55 for a 10 node network, and 1275 in a 50 node network • To estimate all parameters of the network, the number of datapoints generally needs to exceed the amount of parameters. What is a solution to the problem small datasets impose on estimating the network? • Using lasso regularization when estimating the parameters. • the weighted sum of total absolute values of all weights is added to the loss function. • this forces the parameter estimation algorithm to set redundant parameters to zero. • As such, the LASSO returns a sparse (or, in substantive terms, conservative) network model: only a relatively small number of edges are used to explain the covariation structure in the data. • The LASSO utilizes a tuning parameter to control the degree to which regularization is applied, which can be tuned using the EBIC statistic. What methods can be applied to gain insights into the accuracy of edge weights and the stability of centrality indices in the estimated network structure. • Estimation of the accuracy of edge-weights, by drawing bootstrapped CIs • investigating the stability of (the order of) centrality indices after observing only portions of the data • performing bootstrapped difference tests between edge-weights and centrality indices to test whether these differ significantly from each other. Describe how can you assess the stability of edge weights. • Perform a non-parametric bootstrap on the data: sample with replacement to obtain bootstrapped samples. • a bootstrapped CI can be obtained by sorting the estimated weights and taking the xth and zth percentile positions. • the width of the bootstrapped ci's conveys the stability of the edge weights. • when LASSO regularization is used to estimate a network, the edge-weights are on average made smaller due to shrinkage, which biases the parametric bootstrap. What is a typical way of assessing the importance of nodes in a network? Computing centrality indices of the nodes. Examples are: • node strength, quantifying how well a node is directly connected to other nodes, • closeness, quantifying how well a node is indirectly connected to other nodes, • betweenness, quantifying how important a node is in the average path between two other nodes. The question on the page originate from the summary of the following study material: • A unique study and practice tool • Never study anything twice again • Get the grades you hope for • 100% sure, 100% understanding Remember faster, study better. Scientifically proven.	{"url":"https://www.studysmart.ai/en/summaries/bds-psychometrics/network-variables-parameters/","timestamp":"2024-11-12T19:18:16Z","content_type":"text/html","content_length":"125477","record_id":"<urn:uuid:f50bb710-d3ee-4c6f-bc23-434a570c1c05>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00487.warc.gz"}
Resultant forces On this page: Part 1: Finding horizontal and vertical components of a force A matrix is an array of elements. Part 2: Combining two or more forces You can find the resultant, or net effect, of two or more forces (given as vectors) by adding these vectors. Here are a couple of simple illustrations: • If someone exerts a pulling force of 5 N to the right on an object, and someone else exerts a pulling force of 5N to the left, the resultant force on the object is 0 N. • If someone exerts a pulling force of 5 N to the right on an object, and someone else exerts a pulling force of 4N to the left, the resultant force on the object is 1 N to the right. Adding vectors Before getting into the detail of multiplying a matrix by another matrix, we’ll take a look at a simple situation to help illustrate the principle behind matrix multiplication: Considering components in perpendicular directions We can use index notation with matrices to indicate repeated multiplication. As you might expect: • A^2 = A $ \times $ A • A^3 = A $ \times $A $ \times $ A and so on. Part 3: Forces in equilibrium Part 4: Finding a missing force given the resultant force A 2 × 2 matrix can be used to apply a linear transformation to points on a Cartesian grid. A linear transformation in two dimensions has the following properties: • The origin (0,0) is mapped to the origin (it is invariant) under the transformation • Straight lines are mapped to straight lines under the transformation • Parallel lines remain parallel under the transformation	{"url":"https://bossmaths.com/resultantforces/","timestamp":"2024-11-06T04:43:11Z","content_type":"text/html","content_length":"71131","record_id":"<urn:uuid:d89035f0-5b27-4008-a4bc-7ce6b4d25157>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00799.warc.gz"}
Non intrusive channel impairment analyser - Patent 0233679 The present invention relates to a non-intrusive channel-impairment analyser for measuring phase jitter in band-limited data channels without interruption of the channel traffic. The subject matter of the present Application also forms the subject of our co-pending European Divisional Application No. The use of band-limited voice channels for the transmission of high-speed data signals has been made possible in recent years by the development of a range of modems which incorporate data receivers that compensate for the major impairing effects encountered on such channels. These high-speed modems generally make use of two-dimensional modulation techniques whereby groups of binary data for transmission are encoded into two-dimensional symbols (made up of "in-phase" and "quadrature" components) which are then transmitted by amplitude modulating two quadrature carrier signals. The closed set of two-dimensional data symbols characterises the type of modulation scheme; typical examples are phase shift keying (PSK) and quadrature amplitude modulation (QAM). The two-dimensional symbols can conveniently be represented on a two-dimensional diagram (known in the art as a "constellation" diagram) with the in-phase and quadrature components of each symbol being measured off along respective orthogonal axes. Figure 1 of the accompanying drawings illustrates a "16-QAM" constellation where each symbol represents four binary bits of a data signal being transmitted. The constellation diagram shown in Figure 1 is, of course idealised. After the symbols have been transmitted over a voice-frequency data channel, the constellation diagram of the received symbols shows various distortions due to the effect of a range of quasi-static (or basically steady-state) and transient channel impairments. Of the quasi-static impairments, linear distortion caused by the band-limiting filter action of the channel is potentially the most troublesome and manifests itself as interference between adjacent symbols in the received data signal. Such intersymbol interference (ISI) is normally minimised by means of an automatic adaptive equaliser incorporated within the data receiver. Without such equalisation, however, the effect of channel linear distortion would be seen on a constellation diagram as a 'cloud of uncertainty' clustered around each constellation point (a similar effect is produced by additive background noise which co-exists with the data signal in the same spectral band). It should also be noted that as well as linear distortions, the channel will generally introduce second and third order non-linear distortions. Two further significant quasi-static impairments are frequency offset and phase jitter which manifest themselves as a time-dependent variation in the reference phase of the data signal carrier wave. To minimise these effects, the data receiver normally includes a decision-directed phase-locked loop (PLL) which tracks variations in the reference phase of the data signal carrier wave. Without such a tracking device, the effects of frequency offset would be seen as a slow rotation of the constellation points about their origin, whilst the effect of phase jitter would be seen as an angular oscillation of the constellation points. Another quasi-static impairment met in band-limited voice channels is amplitude jitter which manifests itself as a time-dependent variation in the level of the received data signal. It is possible to compensate for the effect of amplitude jitter by including within the data receiver a decision-directed gain-control-loop which tracks variations in the level of the received signal. Without such a control mechanism, however, the effect of amplitude jitter would be seen on the data constellation diagram as a radial oscillation of the constellation points. A known method of measuring channel impairments is to apply tones of predetermined frequency and amplitude to the channel and then observe the signal received at the far end. This method has the considerable disadvantage of requiring an interruption in the normal channel traffic. Another known method of measuring channel impairments is described in US Patent No 4,381,546 (assignee Paradyne Corporation). This method concerns the obtaining of quantitative data on a channel over which data is transmitted by quadrature amplitude modulation. The method comprises the steps of: a) producing sampled eye diagram point information wherein each received point is defined in a coordinate system in which a first axis is the in-phase channel axis and a second axis is the quadrature channel axis; b) rotating said received points by an operand determined by the ideal value of the received point information so that each rotated point has its nominally maximum component on a new first axis and a second nominal component on a new second axis; and, c) determining the characteristics of the communications channel from variances and means of the components. It is an object of the present invention to provide an improved non-intrusive channel-impairment analyser for measuring phase jitter. According to one aspect of the present invention, there is provided a non-intrusive channel-impairment analyser for measuring at least one quasi-static impairment characteristic of a band-limited data communications channel, the analyser comprising a data receiver section for receiving over said channel, data modulated onto quadrature phases of a carrier signal, the receiver section being arranged to process the received signal in two quadrature forward processing paths and including a data recovery circuit for effecting a decision as to the identity of the original data on the basis of the outputs from said processing paths, and decision-directed compensation means disposed in said paths and arranged to compensate for channel-impairment effects on the received signal, said compensation means including a phase-locked loop operative to minimise the phase difference between the signals input to and output from the data recovery circuit, the phase-locked loop comprising a phase error generator, an integrating loop filter, and a phase rotator connected into the forward processing paths of the data-receiver station, characterised in that the analyser further comprises jitter measurement means responsive to signals generated in the receiver station during the receipt of random data, to derive a measurement of phase jitter, the jitter measurement means including means for deriving a wideband phase error signal by combining the output of the loop filter of the phase-locked loop with the output of the phase error generator. Preferably, the integrating loop filter is a second order digital filter fed with the output O of said phase error generator and operative to produce an output O which it updates in accordance with the following difference equations: where (n - 1), n, and (n + 1) refer to successive band interval values of the corresponding quantities, and , and a are constants. Advantageously, the jitter measurement means includes an adaptive line enhancer for isolating deterministic components of the phase error signal of this jitter measurement means from background noise, the line enhancer comprising a fixed delay arranged to receive said phase error signal, a transversal filter fed from the fixed delay, a comparator for determining the difference between the enhancer input and the output of the transversal filter, and update means for adjusting the tap coefficients of the transversal filter such as to minimise the difference determined by the comparator Preferably, the tap coefficients of the transversal filter are updated at random multiples of the data rate. Advantageously, the jitter measurement means effects measurement in two non-overlapping substantially contiguous, frequency bands, said wideband phase error signal being band-limited as appropriate for each band. The two said frequency bands are for example 4 to 20 Hz and 20 to 300 Hz. A channel-impairment analyser embodying the present invention will now be particularly described, by way of non-limiting example, with reference to the accompanying diagrammatic drawings, in which: Figure 1 is a 16-QAM constellation diagram; Figure 2 is a block diagram of the channel-impairment analyser showing the main component blocks of a data-receiver section and a measurement section of the analyser; Figure 3 is a functional block diagram of a negative phase rotator used in the data-receiver section of the analyser to demodulate the received channel signal; Figure 4 is a functional block diagram of a complex-valued equaliser forming part of the analyser data-receiver station; Figure 5 shows the structure of a loop filter used in a digital phase-locked loop of the data-receiver section; Figure 6 is a functional block diagram of jitter and S/N ratio measurement blocks of the measurement section of the analyser; Figure 7 shows the general structure of an adaptive line enhancer used in the jitter measurement blocks of Figure 6; Figures 8a, 8b, 8c are in-phase/quad-phase component graphs illustrating the principle of operation of a second-order non-linearity measurement block of the analyser measurement section; Figure 9 is a functional block diagram of the second-order non-linearity measurement section; Figure 10 is a functional block diagram of a third-order non-linearity measurement block of the analyser measurement section and illustrates the use of the output of that block to effect third-order non-linearity compensation in the determination of an amplitude error signal; Figure 11 is an in-phase/quad-phase graph illustrating the significance of various error signals derived in the analyser; Figure 12 is a block diagram of a sampled-data processor suitable for implementing the sampled data processing functions of the channel-impairment analyser. The non-intrusive channel-impairment analyser is shown in Figure 2 in block diagram form. As can be seen, the analyser is made-up of two sections, namely a data receiver section (upper half of Figure 2 above dashed line) and a measurement section (lower half of Figure 2). The Receiver Section The data receiver section of the analyser is based on the receiver type disclosed in US Patent Specification No. 3,878,463 (Falconer et al) and, more particularly, corresponds closely to the implementation of that receiver type described by Falconer in Bell Systems Technical Journal Vol. 55, No. 3, March 1976 at page 323. This latter implementation has, however, been modified in the Figure 2 receiver section to incorporate a second order loop filter in the PLL used for phase correction, this modification being in accordance with the proposal by Levy and Poinas in a paper entitled "Adaptive Phase Correctors for Data Transmission Receivers". As a detailed explanation of the functioning of the receiver section can be found in the source documents referred to above, only an outline of the receiver operation will be given herein to assist in the understanding of the nature of the signals passed to the measurement section of the analyser. The present analyser is intended for use with voice-frequency channels carrying two-dimensional symbols modulated onto orthogonal phases (sinω t and cosω t) of a common carrier of frequency ωq at a rate I/T where T is the baud (symbols per second) interval. During each baud interval the data to be transmitted can be represented by the numbers I and Q, being the inphase and quadrature components respectively of the corresponding symbol. The numbers I and Q can be considered as the components of an analytic signal R where The process of modulating the components I and Q into orthogonal phases of a common carrier may then be viewed as a multiplication of the signal R by the complex frequency e to form a new complex signal S and then taking the real part as the real signal to be transmitted: In the receiver section of the analyser, the received signal is first passed to analog signal conditioning circuitry 10 (including gain auto-ranging) before being sampled in sampler 11 at an even integer multiple of the symbol rate under the control of a symbol-clock recovery circuit (not shown). Subsequent signal processing is effected digitally either by circuitry dedicated to each processing function to be performed or by a suitably programmed, general purpose sampled data processor. To recover the components I and Q in a data receiver supplied with the transmitted signal (\|sin ^ω [c] t ― Qcos ), an analog to the imaginary part of the complex signal S is first derived by passing the received signal through a phase splitter made up of a pair of transversal filters 12, 13 operating at the sampling frequency. These filters are matched to the transmitted signal but differ in phase shift by 90°. The resulting outputs from the filters 12, 13 correspond to: that is, to the real and imaginary components of S. The two filter outputs taken together thus represent R.e The components I and Q can now be recovered by multiplying the quantity R.e by e leaving R or, in other words (I + jQ). Multiplication by e corresponds, of course, to a phase rotation by -0° where O = ωqt, Figure 3 illustrates, in diagrammatic form, the implementation of a negative phase rotator for rotating a complex quantity (A + jB) by -0°. This rotator comprises a sin/cos generator 2 for generating the quantity sine and cosO corresponding to an input e; the generator 2 may, for example, be in the form of a look-up table (if only predetermined selected values of O are to be used) or means for generating sine and cose by a power series expansion. The Figure 3 rotator also includes multipliers 3 and adders 4 and it can be readily seen that the outputs of the rotator correspond to the real and imaginary parts of the multiplication (A + jB) e In the present receiver section, the output of the phase splitter (filters 12, 13) is passed to a phase rotator 15 of the Figure 3 form, which is arranged to effect a phase rotation corresponding to t) where ωq is nominally equal to ω The phase rotator 15 is, of course, digital in form and operates at twice the baud rate. In the absence of channel impairments, (in particular, frequency offsets and phase jitter), the output of the phase rotator 15 would be the signal R from which it will be appreciated that the rotator 15 serves as a demodulator. In practice, the existence of channel impairment means that further processing of the complex-valued demodulator output signal X (in-phase and quadrature components x, and xq respectively) is required before the signal R can be reliably recovered. Following the demodulator 15 there are therefore provided two channel compensation stages, namely a channel equaliser 17 and an excess carrier phase compensator in the form of a phase rotator 16. As will be more fully explained below, both these compensation stages are decision-directed; that is, the compensation provided thereby is based on a decision as to the values of the transmitted data; this decision is taken by a slicer 20 which immediately follows the rotator 16. The channel equaliser 17 takes the form of a complex-valued transversal filter, operated at twice baud, whose tap coefficients (in-phase and quadrature) are updated in such a way as to minimise a measure of the complex valued intersymbol interference introduced by the channel. Figure 4 diagrammatically depicts the processing structure of a complex-valued transversal filter and comprises four convolution blocks 18 and two summers 19 for generating the following output components (in vector notation) making up the complex-valued output signal Y. c[i]^T and cq^T are the transposed column vectors of the in-phase and quadrature tap-gain coefficients respectively, m, is the column vector of in-phase samples taken at taps along the in-phase delay line, and mq is the column vector of quadrature-phase samples taken at taps along the quadrature phase delay line. The output Y of the adaptive channel equaliser is fed to the phase rotator which forms the excess carrier phase compensator 16. This rotator 16 forms part of a decision-controlled phase-locked loop intended to remove excess carrier phase rotation of R caused by frequency offset and phase jitter in the channel. The updating of the value of the phase rotation -O effected by the phase rotator 16 is explained more fully below. The output of the rotator 16 is a complex-valued signal Z with in-phase and quadrature components of z, and zq respectively. In spite of the compensation effected by the equaliser 17 and rotator 16, the complex-valued signal Z remains corrupted by residual uncompensated channel impairment effects such as background noise. The final stage of the data retrieval processing is, therefore, a slicing operation performed by the previously- mentioned slicer 20. The slicer 20 operates as a multi-level threshold detector for the in-phase and quadrature channels to provide a best estimate D of the transmitted two-dimensional data symbol; the in- phase and quadrature components, d, and dq respectively of the signal D are thus best estimates of the components I and Q of the transmitted signal. The form and operation of the slicer 20 are well understood by persons skilled in the art and will not be further described The updating of the channel compensation stages formed by the equaliser 17 and rotator 16 is effected in dependence on error signals derived by comparing the input and output signals Z and D of the slicer 20. More particularly, to update the tap coefficients of the equaliser 17, a complex-valued vector error signal E having in-phase and quadrature components e, and eq respectively, is first derived in error generator block 21 in accordance with the following expressions: Figure 11 shows the inter-relation of the signals Z, D and E. Before this vector error signal E can be input into a tap update algorithm, it must be fed through a positive phase rotator 22 to reverse the effects of the excess carrier phase compensator 16 (the equaliser 17 being upstream of the compensator 16). The rotator 22 is similar in form to that shown in Figure 3 but with the negative input to the lower summer 4 made positive and the corresponding input to the upper summer 4 made negative; this change is necessary to produce a positive rotation of O rather than the negative rotation effected by the Figure 3 circuit. The magnitude of rotation ⊖0 effected by the phase rotator 24 is thus equal and opposite to that effected by the compensator 16. The resultant error signal F (having inphase and quadrature components of f, and fq respectively) is then used in a tap-update algorithm (block 23) of known form such as that described in the above-mentioned US Patent Specification No 3,878,468; according to the algorithm described in this latter document, the tap coefficients c,,cq are adjusted in conformity with the following expressions: where n,(n + 1) refer to successive baud intervals and β is a constant. For the adaptive equalisation process to function properly and the equalizer tap coefficients to converge to their optimum values, the transmitted data must be random (this will generally be the case where a data scrambler is provided at the data transmitter). Once equaliser convergence has been attained, the adaptive process allows the equaliser 11 to track slow variations in the channel characteristics; one result of this is that the equaliser serves as a narrow-band, decision-directed, gain control system. However, due to the range of possible interfering effects present in the error signal, the tap coefficients will exhibit some degree of uncertainty which results in a component of residual intersymbol interference in the received signal. Consequently, a compromise must be made in the selection of the update constant β which determines both the tracking capability and the tap coefficient stability of the equaliser. The updating of the phase-angle value ⊖ [0 ] fed to the excess carrier phase compensator 16 involves the derivation of a phase error signal O by subtracting the phase angle of the slicer output from the phase angle of the slicer input (see Figure 11). The slicer output phase angle corresponds to: This quantity can be held in a look-up table since there are only a limited number of slicer output combinations. On the other hand, the slicer-input phase angle: must be computed by a power series expansion as the in-phase and quadrature components of the slicer input may be in any relation. The derivation of the phase error signal O is effected in the error generator block 21 of Figure 2. The phase error signal ⊖ is passed to a loop filter 24 of the digital phase-locked loop composed of the rotator 15, error generator 21 and filter 24. The loop filter 24 is shown in greater detail in Figure 5 and, as can be seen, the filter 24 is composed of summers 25, multipliers 26, and baud-interval (T) delays 27, arranged as a second order filter for providing a narrow-band phase output ⊖ to control the phase rotator 16. More particularly, the output O is updated in accordance with the following difference equations: where (n - 1), n, and (n + 1) refer to successive baud interval values of the corresponding quantities, and a, and a are constants selected to maximise the training and tracking performance of the phase-locked loop. The integral control introduced by the second order loop dynamics is present specifically to compensate for frequency offset which appears as a ramp in phase; the quantity ⊖ is, indeed, a measure of frequency offset. The Measurement Section As shown in Figure 2, the measurement section of the channel-impairment analyser comprises: a phase-jitter and frequency offset measurement block 30: an amplitude jitter measurement block 31; a signal/noise ratio meaurement block 32; a 2nd order non-linearity measurement block 33; a 3rd order non-linearity measurement block 34; and a channel model block 35. ['] These measurement blocks will be described in turn below. Phase Jitter and Frequency Offset The phase jitter and frequency offset measurement block 30 is shown in more detail in Figure 6. The first operation carried out in block 30 is to form a wideband phase error signal by combining in summer 40, the phase error signal from the error generator 21 and the narrow-band output signal ⊖o from the PLL loop filter 24. This latter signal re-introduces into the phase error signal, information on low-frequency phase error removed by the action of the rotator 16 thereby enabling wideband phase-jitter measurements to be made which would not be the case if the signal had been used alone. In fact, in the present analyser, phase jitter measurements are carried out in two frequency bands, namely between 4 and 20 Hz and between 20 and 300 Hz. To this end, the wideband phase error signal is first passed through a 2 Hz narrowband digital phase-locked loop 41 to provide the 4 Hz lower measurement limit, and then through a transversal low-pass filter 42 providing the 300 Hz upper measurement limit. Thereafter, the 4-300 Hz band-limited signal is fed to two separate measurement channels that correspond to respective ones of the measurement bands. The 20-300 Hz channel comprises a 10 Hz DPLL providing a 20 Hz high pass filter 43, and a peak-to-peak detector 44. The 4-20 Hz channel comprises a 20 Hz transversal low-pass filter 45 followed by a peak-to-peak detector The DPLL is of a form similar to that shown in Figure 5 for the loop filter 24 but with the constants a, and a chosen to give the desired frequency-limiting characteristic rather than to give a particular tracking and training performance. The DPLL 41 is also used to derive a frequency offset signal in the manner previously described with reference to Figure 5 (the desired signal being that corresponding to the signal ⊖ o(n) of Figure 5). The frequency offset signal is passed to an averager 47 before being output. As can be seen from Figure 6, the 20-300 Hz phase jitter channel is provided with an adaptive line enhancer 48 the purpose of which is to remove background noise and other non-deterministic components in the phase error signal in this channel (the provision of a similar enhancer in the 4-20 Hz channel has been found to be unnecessary since the noise power in this narrower frequency band is much less). The problem of noise swamping the deterministic phase error components is particularly severe in the case of QAM constellations which have a set of inner data points as well as a set of outer data points (see, for example, the 16-QAM constellation of Figure 1) since the same noise power produces a much larger phase error for the inner data points than the outer ones. The form of the adaptive line enhancer is illustrated in Figure 7. As can be seen, the enhancer comprises a delay (AT) 50 fed with the noise-corrupted jitter signal J , followed by a single-valued adaptive transversal filter 51 whose taps are spaced at the baud interval T. The input signal J,N (n) is compared in a comparator 52 with the output signal J ) from the filter 51 and the resultant error signal Ej(n) is supplied to a tap coefficient update block 53. The block 53 implements a tap update algorithm of the same general form as used for the adaptive equaliser 17 but simplified for real components only. The combined effect of the delay ΔT and the filter phase shift is such that the deterministic components in the input and output signals of the line enhancer are phase coherent and cancel at the comparator 52. The delay AT is chosen to ensure that there is no correlation between likely interfering signals in the input and output of the enhancer 48 so that these will not cancel at the comparator 52. Thus, at convergence, the error signal Ej(n) should consist only of any interfering signal present at the input to the line enhancer 48 thereby giving the line enhancer a spectrum with narrow pass bands centered at the frequencies of the deterministic components. In practice, however, a small component of the deterministic signals appears in the error signal due to the filter output being slightly attenuated. It can in fact be shown that as the number of taps is increased, there is an increase both in the accuracy of the enhanced signal and in the frequency resolution of the filter. Further description of this form of adaptive line enhancer may be found in an article entitled "Adaptive Noise Cancelling: Principles and Applications" (Widrow et al), page 1692, Vol. 63, No. 12, Proceedings of the IEEE, December 1975. As previously noted, the sampled data processing effected in the analyser may be carried out by circuitry dedicated to each particular function indicated in the accompanying Figures or by a general purpose sampled data processor. In this latter case, time constraints will normally make it difficult to update the tap coefficients of the line enhancer 48 during every baud interval and updating will generally therefore be done on a multiplexed basis with other processing tasks which do not absolutely require to be effected every baud interval. It has, however, been found that the line enhancer 48 is susceptible to producing misleading results if this multiplexed tap updating is carried out at fixed, regular intervals; the reason for this is that the interval chosen may be related to the frequency of a deterministic jitter component with the result that updating repeatedly occurs at the same phase of that component and the latter is therefore effectively ignored. To overcome this difficulty, the number of baud intervals between updating of the line enhancer 48 is randomised in any suitable manner. Amplitude Jitter The amplitude jitter measurement block 31 is shown in more detail in Figure 6. The input to block 31 is a wideband amplitude error signal A (see Figure 11) formed in the error generator 21 by subtracting the amplitude of the slicer output from that of the slicer input: The term (d + dq )½ can be obtained using a look-up table as there are only a limited number of possible outputs from the slicer 20. The term (z, + zq is most readily determined in the form: as the quantity Zq/z will have been previously calculated during derivation of the phase error signal ⊖ (see before). In fact, the signal A will not include very low frequency components as these will generally have been tracked out by preceding stages of the data receiver. As will be described hereinafter, the amplitude error signal is also subject to compensation for third order non-linear distortion (NLD) prior to being passed to the amplitude jitter measurement block, this compensation being effected in the error generator 31 as a result of feedback from the third-order non-linearity measurement block 34. The processing of the wideband amplitude error in block 31 is similar to the processing of the phase error in block 30. More particularly, the amplitude error, after passage through a 300 Hz transversal, low-pass filter 59, is processed in two channels, one for frequencies in the range 4-20 Hz and the other for frequencies in the range 20-300 Hz. The 4-20 Hz channel comprises a 2 Hz DPLL 60, a 20 Hz, transversal, low-pass filter 61, and a peak-to-peak detector 62. The 20-300 Hz comprises a 10 Hz DPLL 63, an adaptive line enhancer 64 similar to the line enhancer shown in Figure 7, and a peak-to-peak detector 65. Signal-to-Noise Ratio The S/N ratio measurement block 32 is shown in more detail in Figure 6. The computation of S/N ratio is based on the approximation: In order to exclude jitter modulation components from inclusions in the noise, only phase and amplitude error components above 300 Hz are used to calculate the S/N ratio (it being expected that modulation components will generally be below this frequency). To generate the required phase error signals, the output of the 300 Hz low-pass filter 42 is subtracted from the filter input in block 66; similarly the required amplitude error signal is generated by subtracting the output of the 300 Hz low-pass filter 59 from the input to the filter in block 67. The outputs of blocks 66 and 67 are passed to a processing block 68 for computation of the S/N ratio in accordance with the expression given above. To compensate for the fact that the bottom 300 Hz have been removed from the error signals, a scaling factor is introduced. As mentioned above, for a QAM constellation including both inner and outer sets of points, the effect of noise is exaggerated for the inner set of points. For such constellations, therefore, a further scaling factor is introduced to correct for this effect. 2nd Order Non-Linearity While linear distortions introduced by the channel will be largely compensated for by the equaliser 17, this is not the case for second and third order non-linear distortions. With regard to second-order non-linear distortions, the Applicants have observed that such non-linearities can be revealed and measured by remodulating the vector error components e ,eq (see Figure 2) of the outer corner points of a QAM constellation (see points ringed by dashed circles in Figure 8a) up to the frequency at which 2nd order non-linearities may have been introduced. Assuming a random distribution of the original data points, the remodulated error components will either: produce a random distribution of points having no particular bias (that is, if the remodulated error points are plotted on an in-phase component/quad-phase component graph, the resultant cluster of points will have its centroid at the origin as indicated in Figure 8b); or produce a biased distribution of points with the centroid of the points cluster offset from the origin of an in-phase/quad-phase component graph (see Figure 8c). This latter condition is indicative of the presence of second-order non-linearities with the magnitude of the offset being a measure of the non-linearities. Owing to the fact that the channel may introduce a frequency offset either before or after the introduction of second-order nori-linearities, the frequency to which the vector error components must be remodulated will not necessarily be the frequency of the signal received at the analyser. This problem can be overcome by remodulating the error components to the received-signal frequency (carrier nominal plus detected offset) and then slowly sweeping the remodulation frequency through a few Hertz either side of the received-signal frequency while monitoring the position of the points cluster centroid. If any second-order non-linearities are present, then the points cluster centroid will exhibit an offset which peaks at a particular value of the remodulation frequency; the centroid offset at this frequency can be considered as an indication of the magnitude of non-linearity present. Figure 9 shows, in functional block diagram form, a processing arrangement for implementing the foregoing method of detecting second-order non-linearities. The vector error components e,,eq of each outer corner point that occurs (as detected by the slicer 20), are fed first to a positive phase rotator 70 for remodulation to the nominal carrier frequency w and then to a positive phase rotator 71 for further modulation in correspondence to the detected frequency offset (as embodied in the signal ⊖ ). The in- phase and quad-phase components output from the rotator 71 are thus at the frequency received by the analyser. These components are then passed to two separate channels 72, 73 respectively arranged to increase and decrease the modulation frequency in Hz steps from 0 to 7 Hz and to search for any resultant centroid offset. The channel 72 comprises a positive phase rotator 74 controlled by the output of an integrator 75 that is fed with a phase angle value ϕ . For constant ( , the phase angle supplied to the rotator 74 will increase simulating a frequency determined by the magnitude of ϕ . By changing the magnitude of ϕ at intervals, the frequency produced can be swept between 0 and 7 Hz in the desired Hz steps. The in-phase and quad-phase outputs of the rotator 74 are passed to respective averaging filters 76, 77 and then to respective squaring circuits 78, 79 before being summed in summer 80. The output of the summer 80 feeds a low-pass output filter 81. The channel 73 is similar to the channel 72 except that a negative phase rotator 82 is provided instead of the positive phase rotator 74; as a result, progressive increases in ϕ result in the frequency change introduced in channel 73 being in a negative sense. The remaining components of channel 73 are the same as for channel 72 and have, therefore, been similarly referenced in Figure 9. If a second-order non-linearity has been introduced by the channel into the originally transmitted signal, then as ϕ is increased to increase the frequency change introduced by the rotator 74, 82, the output of one of the channels 80 or 81 will increase to a maximum as the frequency in that channel matches the frequency at which the distortion was introduced. This maximum is taken as a measure of the magnitude of the second-order non-linearity present in the channel. 3rd Order Non-Linearity The presence of third-order non-linearities is most noticeable in its effect on the outer corner points of a QAM constellation, these points being significantly radially expanded or compressed in the presence of such non-linearities. To compensate for this effect, the previously stated expression for calculating the wideband amplitude error A is modified to: where C is a third-order non-linearity coefficient. The functional blocks required to derive A in accordance with the above expression are illustrated in the upper half of Figure 10 and comprise processor blocks 90, 91, 92, summers 93, 94, multiplier 95, and divider 96 (the purpose of the latter being to normalise the derived value of A by division by the amplitude value of the sliced point). The derivation of the third-order non-linearity coefficient C is effected by the functional blocks illustrated in the lower half of Figure 10. The normalised amplitude error A is first passed to a digital phase-locked loop made up of summer 97 and an integrating loop filter 98 with update constant K" to remove any dc component from the amplitude error (this loop is updated every baud interval). The average output from the summer 97 is thus zero. If an outer, corner constellation point has been sliced, the output from the summer 97 is used to update the value of the third-order non-linearity coefficient C by means of an integrator 99 constituted by a first-order DPLL with an update constant K provided by an input multiplier 100. The constants K, and K are small. If no third-order non-linearity is present in the received signal then C will converge to zero. However, if compressive third-order non-linearities are present, C will converge to a negative value, whereas if expansive third-order, non-linearities are present, C will converge to a positive value. Sampled-Data Processor As previously mentioned, the digital signal processing effected in the data receiver and measurement sections of the analyser may be implemented either by circuitry dedicated to each processing function or by means of a real-time sampled-data processor. Where a sampled-data processor is used, the internal architecture of the processor is preferably optimised for the range of tasks to be performed and a suitable architecture for the present case is illustrated in Figure 12. Since the principles of operation of such sampled-data processors and their detailed design are well understood by persons skilled in the relevant art, only a brief description of the Figure 12 processor will be given below. The Figure 12 processor basically comprises two parts, namely a control unit and an execution unit. The control unit is based upon micro-programming techniques where the micro-program instruction words (micro-instructions) reside in memory 200 and an instruction sequencer 201 generates the memory address of the instruction word to be carried out. Each micro-instruction consists of the range of signals required to control both parts of the processor. The sequencer 201 includes a counter 202, stack 203 and microprogram counter 204. Operationally, the processor may be described as a 'data-driven machine' since only the data transfer rate (input and/or output) with the analog parts of the analyser determines the micro-program repetition period. Synchronising to the data rate is accomplished by first-in first-out (FIFO) memories 202, 203 which link a main data bus 205 of the signal processor with the analog interface. Each program cycle is carried out at the full speed of the processor (nominally 6 instructions per micro-second) unless the input FIFO 202 is empty or the output FIFO 203 is full. In these latter two cases the program 'waits' for the appropriate data availability condition being met before continuing. The processor execution unit is a collection of elements whose architecture has been designed to carry out the sampled data processing activities of the analyser as efficiently as possible in real-time. Specifically, the execution unit has been optimised to carry out the function of digital convolution as efficiently as possible since this function represents the largest percentage requirement for real-time computation. For this reason, the execution unit is built around a high speed 16 x 16 multiplier-accumulator 210 arranged to be fed with filter tap coefficients and signal sample data simultaneously for fastest operation. The multiplier-accumulator 210 includes two input registers 213, 214 respectively designated X and Y which feed a multiplier 215. The multiplier 215 is followed by an adder 216 that enables the progressive accumulation of processing results in a register 217. To achieve the simultaneous supply of tap coefficients and signal sample data to the multiplier-accumulator, the execution-unit memory has been split into two segments, called the 'data' memory 211 and the 'coefficient' memory 212 as shown. The data memory 211 is connected directly to Y input register 214 of the multiplier 210 and via bi-directional bus drivers 218, to the main data bus 205, whilst the coefficient memory is connected directly to the main data bus 205 and then to the X input register 213 via bi-directional bus drivers 219. In conjunction with the control capability of the sequencer 201, this arrangement allows a single execute-and-loop instruction to be assembled for fastest operation of the digital convolution function. An additional small overhead is required to initialise the computation by setting the filter length in the sequencer 201 and initialising address counters 219, 220 respectively associated with the data memory 211 and coefficient memory 212, (the initialisation data being held either in memory 212 or in a scratchpad memory The counters 219 and 220 have the capability to cycle on a preselected fixed depth of memory which minimises the overhead required in a data storage and access; both these latter activities are controlled by a single pointer which may be held either in the scratchpad 221 or in the memory 212. The cycle depth of each counter 219, 220 is individually controlled via their respective mask registers 222, 223. Additionally, the least significant bit of counter 219 may be reversed which allows complex-valued data to be stored interleaved under the control of a single pointer and thereafter to be readily unscrambled for the purpose of complex digital convolution. The majority of the filtering activities carried out in the processing are adaptive. However, the complexity of the tap update algorithms is such that, although each filter convolution must be carried out at the required rates to maintain receiver integrity, the update procedures for each adaptive filter are multiplexed in time with only one filter being updated each symbol period. For tap coefficient updating, the error signal is held in scratchpad 221 so that, within a loop structure for multiple tap updates, counter 220 addresses the coefficient to be updated and counter 219 addresses the data component in the update algorithm. With this computational organisation, the processor architecture allows a complex-valued tap coefficient to be updated within a loop structure of eight instructions. Another extensively used algorithm is the power series expansion of mathematical functions. For this algorithm, the polynomial coefficients are held in the coefficient memory 212 and the independent variable of the function is preloaded into one of the input registers of the multiplier 210, which allows the algorithm to be implemented using the process of repeated factoring in a loop structure requiring three instructions. Thus a fifth order polynomial may be executed in six cycles of three instructions plus a small overhead for initialisation purposes. For products involving complex numbers, one variable is usually held in the scratchpad memory 221 which provides access directly to one input of the multiplier 210 so that the other variable may be addressed from either the data memory 211 or the coefficient memory 212 for access to the other free multiplier input. In addition, the scratchpad 221 is used to hold parameters such as data points and constant values which are common to the activities of several subroutines, and also to provide an area of working storage for other special subroutine activities such as autorange control and timing control. An interface between the control unit and the execution unit is provided by means of registers 230, 231. Register 230 provides the link 'execution-unit to controt-unit' whiist register 231 provides the link 'control- unit to execution-unit'. Both the registers 230, 231 may be used to determine sequencer branch instructions conditionally, on the basis of a comparison (effected in comparator 232) with the execution-unit data bus 205, and unconditionally, by value passed in micro-program via register 231 or by value passed from the execution-unit via register 230. In addition, the register 231 allows the sequencer control 202 to be initialised for applications which require a fixed loop count or a branch to a fixed location whilst register 230 allows the sequencer counter 202 to be initialised dynamically under signal processing/execution control for applications which require a variable loop count. From the foregoing, it can be seen that although the architecture of the Figure 12 processor has been optimised for fast digital convolution (which is the most time consuming of analyser activities that have to be carried out in real-time every data symbol interval), it incorporates features which allow the other signal processing activities to be carried out very efficiently with the minimum of non-computational overhead. Indeed, the processor may be regarded as a general purpose device suitable for a range of sampled-data signal processing activities.	{"url":"https://data.epo.org/publication-server/rest/v1.2/publication-dates/19901107/patents/EP0233679NWB1/document.html","timestamp":"2024-11-08T04:13:24Z","content_type":"text/html","content_length":"97523","record_id":"<urn:uuid:5b61687d-a5e1-40d7-9b9a-cca832e47a75>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00715.warc.gz"}
User objects in AnyRail version 5 Now that we have user defined objects (I call them Udo's) in version 5 of AnyRail, this board is probably not very relevant anymore. I suggest that we gradually turn the items that are here into Udo's. Of course I want to make sure that the original publishers are OK with that. What do you think?	{"url":"https://www.anyrail.com/forum_en/index.php?topic=1635.msg13890","timestamp":"2024-11-13T04:42:38Z","content_type":"text/html","content_length":"69468","record_id":"<urn:uuid:26f78f37-527f-45c1-87fa-b4f68d2b5a59>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00327.warc.gz"}
A Natural Question The Question Recall that the natural log function $\ln x$ has an understood base of $e \approx 2.71828$. What is so "natural" about base $e$? The Historical Answer Nicholas Mercator was the first to coin the term “natural log” (actually, he used the Latin equivalent log naturalis), in his treatis Logarithmo-technica on logarithms, published in 1668. He noticed that there are a number of simple series involving the natural logarithm. For instance, $$\ln(x+1) = x - \frac{1}{2} x^2 + \frac{1}{3} x^3 - \frac{1}{4} x^4 + \cdots$$ An Even Better Answer The most natural properties of e, however, are found in its relation to calculus— which, strangely, wasn’t even developed until after Mercator’s work. Recall that much of mathematics, as we practice it today, involves changing one thing into something else. Arithmetic operations like addition and subtraction change two numbers into a sum or a difference. The functions encountered in basic algebra generally change one real number into another one by means of some explicit formula. Differentiation and integration, as explored in Calculus, give us a way to change functions into other functions. The list continues. As such, a central and fundamental question in mathematics is this: Given some process for changing one thing into another, when does this process fail to create a change? For example, recall that the differentiation operator, $\frac{d}{dx}$, takes an initial function $f(x)$ and changes it into another function (called the derivative of $f(x)$) that gives the slope of the tangent line to the curve of $y=f(x)$ at any value $x$. Specificall, this derivative function is found by determining the following limit: $$\frac{d}{dx} f(x) = \lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}$$ So when does this process fail to create a change—that is to say, when does the operation of differentiation result in the same function with which one started? Thus, we are looking for a function that satisfies $$\frac{d}{dx} f(x) = f(x)$$ To get an idea about what such a function might look like, let us draw an arrow with slope y at several points on the coordinate plane, so that we can attempt to draw a function that appears to follow these slopes. It should not be too difficult to see the nature of the functions that satisfy $\frac{d}{dx} f(x) = f(x)$. Notice their apparent unbounded growth (or decline) on the right and a horizontal asymptote on the left. One might make a guess that the functions in question are exponential—and one would be right! Working from this assumption, let us assume some simple exponential function of the form $f(x) = b^x$, when differentiated, equals itself. Now the questions becomes: "What value(s) of $b$ will produce such a function?" Starting with the limit definition of the derivative, we then have $$\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h} = f(x)$$ which, for this particular $f(x)$, requires $$\lim_{h \rightarrow 0} \frac{b^{x+h} - b^x}{h} = b^x$$ Equivalently, for sufficiently small $h$, $$\frac{b^{x+h} - b^x}{h} \approx b^x$$ $$\frac{b^x(b^h - 1)}{h} \approx b^x$$ $$\frac{b^h - 1}{h} \approx 1$$ At this point, we can "solve" for $b$ to find that, for sufficiently small $h$, $$b \approx (1+h)^{1/h}$$ To make this a little easier to calculate, one might consider replacing $h$ with $1/n$, since taking $n$ sufficiently large, we can make $1/n$ as small as we like. With this change, we find that for sufficiently large $n$, $$b \approx \left(1 + \frac{1}{n} \right)^n$$ Of course, as you have probably guessed, $$\lim_{n \rightarrow \infty} \left(1 + \frac{1}{n} \right)^n = 2.71828\ldots$$ So an exponential function that has a base of e behaves in the nicest possible manner under differentiation (and integration for that matter).^1 As such, e is the “natural” choice for the base of an exponential function. Finally, since log functions are the inverses of exponential functions with the same base, e is the natural choice there as well. Implications for the Derivatives of $e^x$ and $\ln x$ Knowing from the above discussion that $$\frac{d}{dx} e^x = e^x,$$ we can also now quickly find the derivative of the natural logarithm function, $\ln x$. Suppose $y = \ln x$. Then $$e^y = x$$ Differentiating this equation implicitly with respect to $x$, we have $$e^y \frac{dy}{dx} = 1$$ Dividing both sides by $e^y$, we have a formula for $dy/dx$ -- although granted it is in terms of $y$ and not $x$, which would be more desirable. $$\frac{dy}{dx} = \frac{1}{e^y}$$ However, that difficulty is quickly overcome, since we know $e^y = x$. Upon making this substitution, we have $$\frac{dy}{dx} = \frac{1}{x}$$ $$\frac{d}{dx} \ln x = \frac{1}{x}$$ ^1It should be noted, that any constant multiple of $e^x$ is also its own derivative, and this accounts for all of the other functions that one could draw in agreement with the previously shown	{"url":"https://mathcenter.oxford.emory.edu/site/math111/naturalQuestion/","timestamp":"2024-11-05T16:09:20Z","content_type":"text/html","content_length":"9108","record_id":"<urn:uuid:fcefdb74-03a9-4b4f-bd85-35dce57436a8>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00504.warc.gz"}
of compound interest What is the composed interest? Compound interest is one of the interest rates existing in financial terms. The word interest refers to the profit that a capital produces. This capital can be borrowed or deposited and in either of the two cases generate interest. • Capital deposited. A deposited capital is in a checking account or deposit of a financial institution and produces a return to its holder. • Borrowed capital. This type of capital is that which a financial institution has lent in a mortgage transaction and for which it receives remunerative interest from the debtor. Interest is therefore used to measure the profitability of an investment or savings, or to calculate the cost of a loan. Characteristics of compound interest Compound interest is characterized in that the amount corresponding to the interest is added to the outstanding principal or principal. Therefore, interest also generates more interest. Something that does not happen with him interés simple. This is the usual case of bank deposits, in which the remunerative interest is paid into the same account where the capital is, subsequently generating positive interest on said amounts. Due to the accumulation characteristics of compound interest, it does not remain constant during the term of the loan or investment. Since it is not calculated using principal as a reference, compound interest increases over time. Formula for calculating compound interest The formula to calculate the compound interest generated by a principal for complete periods of one year is as follows: Final Capital by Compound Interest = C x (1 + I)^ T This formula allows us to obtain the final capital obtained with compound interest. Where the values of the formula are: • C: is the amount of the initial capital on which the compound interest calculation is made. • I: is the interest rate. It is usually expressed as a percentage, so before including it in the formula we will divide it by 100. • T: is the number of periods during which the borrowed or invested capital will be maintained, expressed in full years. Compound Interest Calculator Leave a Comment	{"url":"https://www.infocomm.ky/what-is-the-composed-interest-definition-of-compound-interest/","timestamp":"2024-11-05T03:28:32Z","content_type":"text/html","content_length":"43714","record_id":"<urn:uuid:3d9dcf41-251d-451e-b469-ad9ae6142b1d>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00813.warc.gz"}
Time Series Analysis in R \| The Data Hall Time Series Analysis in R Time series analysis is a method of examining a set of data points collected over a period of time. Time series analysis implies analysts recording data points at constant intervals over an established span rather than just periodically or arbitrarily. It is simple to attain using the ts() method and certain parameters. Time series use a data vector and integrate each data point with a period value specified by the user. This function is usually used to discover and forecast the actions of a business asset over time. Stock market prices are a real-world example of time-series data. The value of stocks, commodities, and other financial instruments is documented over time in financial markets. Each data point shows the asset’s price at a certain point in time. Analyzing historical stock prices as a time series can assist investors and analysts in identifying trends and patterns, as well as forecasting future price movements. It is widely used in a variety of industries, including weather forecasting, energy usage prediction, flow of traffic analysis, and a lot more, where data is accumulated over time to grasp patterns and make educated choices. To perform time series analysis in R, one can take help from the below example. Data has been created by the seq() function. # Load necessary packages install.packages(c("forecast", "tseries")) library(forecast) library(tseries) # Set seed for reproducibility set.seed(123) # Create a time sequence from January 2020 to December 2022 with monthly frequency date_sequence <- seq(as.Date("2020-01-01"), as.Date("2022-12-31"), by = "months") # Create a linear trend with some random noise linear_trend <- seq(50, 150, length.out = length(date_sequence)) random_noise <- rnorm(length(date_sequence), mean = 0, sd = 10) stock_prices <- ts(linear_trend + random_noise, start = c(2020, 1), frequency = 12) stock_prices # Plot the generated time series plot(stock_prices, main = "Stock Prices Data", xlab = "Date", ylab = "Values") It can be seen in the picture that values have been generated against 3 years as monthly data and a time series graph that shows stock prices vs. years. Now we will decompose the dataset into its components, i.e., trend, seasonal, and noise. You can use the code below for decomposition. # Decompose Time Series decomposition_result <- decompose(stock_prices) plot(decomposition_result) In the above graph, there are four parts. The first part shows all the data patterns in the observed graph, and the remaining three graphs contain the values with trend, seasonality, and random ACF and PACF ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) are time series analytic methods used to understand and quantify autocorrelation in data. They are used to figure out the order of AR, MA and ARMA for forecasting points of view. 1. ACF (Autocorrelation Function): ACF gauges the relationship between a time series and its lag values. It fosters identifying patterns in data, such as seasonality or trends. The ACF at lag (k) is the correlation between the values of the time series at time (t) and the values at time (t-k). The ACF function can be employed to determine the order of a moving average (MA) process. Normally, the ACF is shown as a function of lag, depicting how the correlation between observations drops as the dromancy grows. 2. PAF (Partial Autocorrelation Function): PACF calculates the correlation between a time series and its lagged values after accounting for intermediate lags. It aids in assessing the direct relationship between observations made at different times. The PACF at lag (k) is the correlation between the time series values at time (t) and values at time (t-k), corrected for the influence of lags (1-k). The PACF function can be used to determine the order of an autoregressive (AR) process. # ACF and PACF plots acf_result <- acf(time_series_example, main = "ACF") pacf_result <- pacf(time_series_example, main = "PACF") In above plots, there are abundant spikes at different lags (k) which show a correlation between observations at time (t) and (t-k). There is no need to look at the spike at lag 0. The overall behavior of this ACF plot is exponential. ACF with exponential decay suggests an AR process. Whereas ACF with a cutoff after lag q suggests an MA process. PACF has two significant spikes, which shows that the process is AR(2). Modeling and forecasting with ARIMA The auto.arima function from the forecast package is used to set the appropriate ARIMA model with the best parameterization. Below is the code for this function. # Fit ARIMA model arima_model<- auto.arima(time_series_example) print(arima_model) # Forecast using ARIMA model # Forecasting for the next 12 months forecast_values <- forecast(arima_model, h = 12) plot(forecast_values, main = "ARIMA Forecast", xlab = "Date", ylab = "Values") # Evaluate forecast accuracy accuracy(forecast_values) The ARIMA model captures a linear trend (1st differencing) with two autoregressive terms (lag 1 and lag 2) and a drift term. The forecast reliability measurements indicate reasonable accuracy. The highlighted part of the above graph, which is increasing, shows the forecast for stock prices for the next year. Assumptions check After modeling, testing assumptions assures that the chosen model is an adequate fit for the data. If, after modeling, the assumptions are not met, we may need to reconsider our model choices or explore additional modifications. Below is the code to check some of the assumptions for this model. # Residuals from ARIMA model residuals <- residuals(arima_model) # Diagnostic plots par(mfrow = c(2, 2)) plot(residuals, main = "Residuals") abline(h = 0, col = "red") # Add a horizontal line at 0 # ACF and PACF of residuals acf_res <- acf(residuals, main = "ACF of Residuals") pacf_res <- pacf(residuals, main = "PACF of Residuals") # Ljung-Box Test for Autocorrelation in Residuals ljung_box_test <- Box.test(residuals, lag = 20, type = "Ljung-Box") print(ljung_box_test) There is no apparent trend or seasonality shown in the residual vs. time graph. Ideally, the ACF of residuals does not show significant autocorrelations at any lag, indicating that there is no remaining systematic pattern in the residuals. Similarly, the PACF of residuals did not exhibit significant spikes, indicating that there is no remaining pattern after accounting for the earlier The next assumption is checked by the Ljung-Box test, which is a residual autocorrelation test. The null hypothesis for this example is that there is no autocorrelation in the residuals. The p-value is 0.4993, which is greater than the standard level of significance of 0.05. As a result, the null hypothesis is not rejected. This implies that there is no significant autocorrelation in the residuals, demonstrating that the ARIMA model effectively captured the time series’ temporal dependencies. In summary, the findings show no evidence of considerable autocorrelation in the residuals, indicating that the ARIMA model is adequate for this time series. 0 Comments Inline Feedbacks View all comments \| Reply	{"url":"https://thedatahall.com/time-series-analysis-in-r/","timestamp":"2024-11-03T17:25:19Z","content_type":"text/html","content_length":"270947","record_id":"<urn:uuid:84848671-c776-4353-a82a-ed164eb4005e>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00130.warc.gz"}
In the given figure, a large rectangle is 60 metres long and 20 metres wide. 2 small rectangles are 30 metres long and 20 metres wide each. Which of the following statements is CORRECT? A The total length of the large rectangle is twice the total length of the small rectangle. B The total length of the large rectangle is equal to the total length of the small rectangle. C The total length of the large rectangle is 30 meters more than the total length of the small rectangle. D The total length of the large rectangle is equal to 160 meters and the total length of the small rectangle is equal to 100 meters. option A and C are both correct. If D is the correct option then instead of length you should make it more specific to say length of the boundary. A rectangle by definition has 2 sides length and Ans 1: A and C both are correct. it should be perimeter or boundary. Ans 3: Please use the correct wordings, Perimeter. Itâ s just confusing to deal with word length. Ans 4: lenght should be replaced by parameter. ques.wording is wrong Ans 5: The word should be PERIMETER as the word TOTAL LENGTH [mentioned] can mean the sum of the 2 sides of the rectangle and can not be understood very well.So, according to me the answer can be both A as well as C. Ans 6: Ans 7: 160 is the perimeter of the big rectangle and not the length Ans 8: Please use proper words. It is perimeter. Not total length. Total length is the sum of the two longer sides. Ans 9: sorry I was wrong the ans is d only because total length is here equal to perimeter for this condition Ans 11: Yes both A and C are Correct Ans 14: 160 is the perimeter not the length Ans 15: A and C are correct.Please write unambiguous lines. Write boundary or perimeter to be precise.as children view rectangle in length and breadth only. Ans 17: The correct answer is D because the total length of the large rectangle is 160 meters and the total length of the small rectangle is 100 meters Ans 18:	{"url":"https://www.sofolympiadtrainer.com/forum/questions/14958/pin-the-given-figure-a-large-rectangle-is-60-metres-long-and-20-metres-wide-2-small-rectangles-are-3","timestamp":"2024-11-09T11:08:42Z","content_type":"text/html","content_length":"194129","record_id":"<urn:uuid:711c2e07-d775-4522-9355-df1e4b9f0a72>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00028.warc.gz"}
Deep meaning in Ramanujan's 'simple' pattern Contemplating partition (Image: Konrad Jacobs/Oberwolfach Photo Collection) The first simple formula has been found for calculating how many ways a number can be created by adding together other numbers, solving a puzzle that captivated the legendary mathematician Srinivasa The feat has also led to a greater understanding of a cryptic phrase Ramanujan used to describe sequences of so-called partition numbers. A partition of a number is any combination of integers that adds up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1, so the partition number of 4 is 5. It sounds simple, yet the partition number of 10 is 42, while 100 has more than 190 million partitions. So a formula for calculating partition numbers was needed. Previous attempts have only provided approximations or relied on “crazy infinite sums”, says Ken Ono at Emory University in Atlanta, Georgia. Pattern in partition Ramanujan’s approximate formula, developed in 1918, helped him spot that numbers ending in 4 or 9 have a partition number divisible by 5, and he found similar rules for partition numbers divisible by 7 and 11. Without offering a proof, he wrote that these numbers had “simple properties” possessed by no others. Later, similar rules were found for the divisibility of other partition numbers so no one knew whether Ramanujan’s words had a deeper significance. Now Ono and colleagues have developed a formula that spits out the partition number of any integer. They may also have discovered what Ramanujan meant. They found “fractal” relationships in sequences of partition numbers of integers that were generated using a formula containing a prime number. For example, in a sequence generated from 13, all the partition numbers are divisible by 13, but zoom in and you will find a sub-sequence of numbers that are divisible by 13^2, a further sequence divisible by 13^3 and so on. Mathematical metaphor Ono’s team were able to measure the extent of this fractal behaviour in any sequence; Ramanujan’s numbers are the only ones with none at all. That may be what he meant by simple properties, says Ono. “It’s a privilege to explain Ramanujan’s work,” says Ono, whose interest in partition numbers was sparked by a documentary about Ramanujan that he watched as a teenager. “It’s something you’d never expect to be able to do.” Trevor Wooley, a mathematician at the University of Bristol, UK, cautions that the use of the term “fractal” to describe what Ono’s team found is more mathematical metaphor than precise description. “It’s a word which conveys some of the sense of what’s going on,” he says. Wooley is more interested in the possibility of applying Ono’s methods to other problems. “There are lots of tools involved in studying the theory of partition functions which have connections in other parts of mathematics.”	{"url":"https://www.newscientist.com/article/dn20039-deep-meaning-in-ramanujans-simple-pattern/","timestamp":"2024-11-04T00:01:52Z","content_type":"text/html","content_length":"412457","record_id":"<urn:uuid:2623b8c6-bb99-49d5-9786-81d7cabc34fe>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00491.warc.gz"}
Refining the Peak Oil Rosy Scenario Part 7: An improved logistic model Inherent problems with the logistic equation During the course of modeling my simulated data sets (especially the data set which assumed a 2%/yr decline in “a” after the peak in production) I realized that although the NLLS model made a reasonable estimate of the average “a” for the 5-year time spans considered (see part 4; Results for non-linear least squares analysis of simulated data) the fits to the data do not look particularly good. That is the fits seem to have a fairly high sum of residual sums of squares (Srss) difference between the true values of dP/dt and the predicted values from the best fit. This is illustrated below, for the simulated data set were Q∞ =170 bbls, “a’ = 0.0687 yr-1 up to the peak production year 1956 and thereafter “a” is assumed to decline 2%/yr. Figure 17 shows the best fits from NLLS analysis of the twenty year span on the decline side of the production curve (1956-1975), using different assumptions as part of the fitting process: 1) Fix Q∞ at a constant value of 170 but vary “a” to get the best fit (red line) 2) Fix “a” at a constant value of 0.0687 but vary Q∞ to get the best fit (blue line) 3) Let both “a” and Q∞ vary to get the best fit (brown line) The best fit values and rss for each of these fits along with the true value (i.e., the average value over the same time span) is summarized below: │Table 3: summary of best fit values to 1956-1975 time span shown in Figure 17 │ │Model assumptions │best fit or fixed value of “a” │true value “a”│best fit or fixed value of Q∞│true value Q∞│Srss │ │Q∞ fixed; “a” variable │ 0.0592 │ │ 170 (fixed) │ │1.310│ ├────────────────────────┼───────────────────────────────┤ ├─────────────────────────────┤ ├─────┤ │Q∞ variable; “a” fixed │ 0.0687 (fixed) │ 0.0571 │ 155 │ 170 │0.299│ ├────────────────────────┼───────────────────────────────┤ ├─────────────────────────────┤ ├─────┤ │Both Q∞ and “a” variable│ 0.0782 │ │ 148 │ │0.028│ It is apparent the best fits where either Q∞ is fixed and “a” is varied or “a” is fixed and Q∞ is varied are not particularly good in terms of minimizing the rss, as compared to the case where both “a” and Q∞ are varied. For the fit done with Q∞ fixed to the true value and “a” varied the best fit value is pretty close to the true value (the same as found in Part 4, when fitting 5 year spans) but the fit is poor. It seemed odd to me that you could get a better fit by fixing “a” to a value you know is wrong (i.e., pre-decline value of “a”) and varying the value of Q∞. Although the best fit was obtained when varying both “a” and Q∞, the best values of these parameter are is poor agreement with the true values. That is, “a” is over estimated by 37% and Q∞ is under estimated by 17%. To gain a better understanding of what is going on here, I found it useful to make a series of plots using different values of “a” (with Q∞ fixed to 170) or of Q∞ (with “a” fixed to the growth side value of 0.0687). These plots are shown in Figures 18 and 19, respectively. Now we start to see how these parameters operate to define the production (dQ/dt) versus time curve. In general varying “a” causes the simulated curve to move up and down the vertical plus there is an effect on the negative slope of the curve. Notice that at the right-hand side of the span (1975) the effect of changing “a” on moving the curve up and down is quite small as compared to at the left-hand side of the span (1956). In general varying Q∞ also moves the simulated curve up and down but with little effect on the slope of the curve. It is now clear to see what happens when one of “a” or Q∞ is fixed and the other is varied: basically the simulated curve is moved up or down so that it crosses through about the mid-point of the 20-year span of the simulated data. I can also start to see what happen when both “a” or Q∞ are allowed to vary: NLLS analysis finds a low Q∞ to lower the simulated curve and chooses a high “a” value to increase the slope of the simulated curve so as to match the data. This analysis shows that there are problems inherent in the logistic equation when used to model production data where there is a declining value in the rate constant for production, as simulated here. A NLLS fit to the decline side data, where the value of Q∞ is fixed, and “a” is allow to vary, can give reasonably good estimates of the value of “a” but the fit will be poor. A NLLS fit where both Q∞ and “a” are allowed to vary will tend to over-estimate “a” and underestimate Q∞. I can imagine what would happen in the inverse case for production data where after the peak, there was an increase in the rate constant for production: a NLLS fit where both Q∞ and “a” are allowed to vary will tend to under-estimate “a” and overestimate Q∞. That is, the NLLS analysis will find a high Q∞ to raise the simulated curve and choose a low “a” value to decrease the slope of the simulated curve to match the data. We need a better model to specifically account for a changing “a” on the decline side of the production curve. An improved logistic equation to account for changes in “a” on the decline side of the production curve. Let’s consider again the logistic equation (equation [3] from Part 4): dQ/dt = (Q∞ / (1 + N[o]∙e^–a(t-to)))/(Dt), [3] where N[o] = (Q∞-Qo)/Qo, Dt = time increment (1 year). Also let’s consider how I generated the simulated data for the case where “a” was assumed to decline by some percentage amount per year (say 2%/yr). That is, in 1957, a equals a(1956) x 0.98; in 1958, a equals a(1957) x 0.98; etc.... It is easy to see that the value of “a” in any one year a(t) on the decline side will be given by: a (t) = a[p]∙ (fca)^(t – td), [4] where a[p] equals the rate constant estimated from the growth-side of the production curve, t[d] equals the year where the change in a is believed to start, and fca is the fractional yearly change in For example, in the case where a 2%/yr decrease in “a” occurs beginning in 1957, t[d] equals 1957 and fca equals 0.98. And, in 1958, a(1958) equals a[p] x 0.98^2 (i.e., a[p] x.98 x 0.98); in 1959,a (1959) equals a[p] x 0.98^3, etc... Now we can substitute “a” from equation [3] with a(t) from equation [4] to produce the improved logistic equation: dQ/dt = Q∞ / (1 + N[o]∙exp(-(a[p] * (fca)^(t – td))∙(t-t[o]))) / (Dt), [5] where N[o] = (Q∞-Qo)/Qo. Notice that if we just fix “fca” equal to 1 then equation [5] reduces to equation [3] (i.e., “1” to the power of any whole number is still “1”), so equation [5] is useful for analyzing data with and without the assumption of a change in “a” on the decline side. Figure 20 shows the NLLS fit to the same time span depicted in Fig. 17, with the values of Q∞ and “a” fixed to the growth side values of 170 and 0.0687, respectively and fca allowed to vary. Table 4 compares the best fit values summarized in Table 3 with the best fit using the new logistic equation: │Table 4: summary of best fit values to 1956-1975 time span shown in Figure 17 and Figure 20 │ │Model assumptions │best fit or fixed value of “a”│true value “a”│best fit or fixed value of Q∞│true value Q∞│Srss │ │Q∞ fixed; “a” variable │ 0.0592 │ │ 170 (fixed) │ │1.310│ ├─────────────────────────────────┼──────────────────────────────┤ ├─────────────────────────────┤ ├─────┤ │Q∞ variable; “a” fixed │ 0.0687 (fixed) │ 0.0571 │ 155 │ 170 │0.299│ ├─────────────────────────────────┼──────────────────────────────┤ ├─────────────────────────────┤ ├─────┤ │Both Q∞ and “a” variable │ 0.0782 │ │ 148 │ │0.028│ ├─────────────────────────────────┼──────────────────────────────┤ ├─────────────────────────────┤ ├─────┤ │Both Q∞ and “a” and fca variable │ 0.0687 (fixed) │ │ 170 (fixed) │ │0.013│ │ │ │ │ │ │ │ │ │ fca = 0.0981 │ │ │ │ │ As one might expect the fit to the simulated is excellent although not perfect—after all we are fitting the simulated data with an equation that corresponds to how the data was created in the first place. The reason why the fit is not a perfect fit, as indicated by the non-zero Srss, is because I choose 1956 as the first data point—but 1956 was actually the last year before the value of “a” was decreased by 2%. Indeed, if I redo the fit to a 19-year span from 1957 to 1975 the best fit gives a Srss equal to zero and fca equals 0.098 (actually, 0.97996, which is about 0.98). An improved logistic equation to account for changes in Q∞ on the decline side of the production curve. This is somewhat anticipating the re-analysis of the USA production data, but, there is the possibility that Q∞, the total recoverable oil, will increase over time. This could occur because more oil is discovered, or, because the techniques to recover the oil have become more efficient with time. We need to have the ability to model this, similar to modeling to detect changes in the production rate constant, “a.” Analogous to the procedure described above, we can modify the logistic equation to account for yearly fractional changes in Q∞ on the decline side of the production curve, by defining Q∞(t) as Q∞(t) = Q∞[p]∙ (fcq)^(t – td), [6] where Q∞[p] equals the total recoverable oil estimated from the growth-side of the production curve, t[d] equals the year where the change in Q∞ is believed to start, and fcq is the fractional yearly change in Q∞. For example, in the case where a 0.5%/yr increase in Q∞ starts to occur on the decline side of the curve in 1956, then t[d] equals 1956 and fcq equals 1.005. Now we can substitute Q∞ from equation [3], where we have explicitly written out the value of N[o] = (Q∞-Qo)/Qo, with Q∞ (t) from equation [6] to yield the improved logistic equation: dQ/dt = (Q∞[p]∙ (fcq)^(t – td))/ (1 + (((Q∞[p]∙ (fcq)^(t – td))-Qo)/Qo)∙exp(-a∙ (t-to)))/(Dt)), [7] A further-improved logistic model to account for either or both changes in “a” and changes in Q∞ on the decline side of the production curve. Now, if we include both expression for Q∞ (t) and a(t) into the logistic equation we have: dQ/dt = Q∞ / (1 + ((Q∞-Qo)/Qo)∙exp(-(a[p] * (fca)^(t – td))∙(t-t[o])))/(Dt), [8] dQ/dt = (Q∞[p]∙ (fcq)^(t – td)) / (1 + (((Q∞[p]∙ (fcq)^(t – td))-Qo)/Qo)∙exp(-(a[p] * (fca)^(t – td))∙(t-t[o])))/(Dt), [9] If you think equation 9 is starting to look a bit complicated, you should try inputting it as an equation into an EXCEL spreadsheet—great fun, but, it can be done (hint: it helps to use simulated data so that you can verify that the equation has been correctly entered!!). The advantage of using equation 9 is its great flexibility. For example, by fixing fca and fcq to 1, equation 9 reduces back to the familiar logistic equation 3. Or, we can fix fcq to 1, and make fca variable, to examine yearly fractional changes in “a” on the decline side where Q∞ is fixed and has no fractional change. Or, we can fix fca to 1, and make fcq variable, to examine yearly fractional changes in Q∞ on the decline side where “a” is fixed and has no fractional change. Or, we can allow both fca and fcq to be variable and fix Q∞ and “a” to their best fit growth-side values. Testing the improved logitic model with simulated data where “a” increases on the decline side. It might seem paradoxical to be modeling for increases in “a” for the decline side of a production curve. Why in the world would this ever happen? Think about it, if we are on the decline side, it means that there is no longer growing production. To try and mitigate the socio-economic consequences of this, a country or company might try to increase the rate of production (i.e., increase “a”) by pumping oil from existing wells at greater rate. Of course, in the absence of any increase in Q∞, that will just more rapidly deplete whatever remaining oil there is in the long term. However, this would tend to mitigate the declining production in the short term. Let try and model this with a new simulated data set and using equation 9 for the modeling. Once again, I assume Q∞ equals 170 bbls and “a” equals 0.0687 yr^-1 on the growth side of the production curve. Then in the year of peak production, 1956, I assumed that “a” increases by 2%/yr thereafter. Figure 21 shows the simulated data and NLLS best fits to the data for the first 20 years on the decline side using equation 9, with the various parameters, “a”; Q∞; fca; and fcq either fixed to the best-fit growth side value (i.e., “a”=0.0687; Q∞=170), or to 1 (i.e., one or both of fca and fcq fixed equal to 1), or allowed to vary, as described in the figure legend. The simulated data on the decline side shows an initial boost in production—the peak year of production actually would be shifted to about 1963. For this analysis, however I just stuck with examining the twenty year period from 1956-1975. It is apparent from the best fit plots shown in Figure 21 that poor fits to this 20-year time span are obtained for the models where one of Q∞, "a" or fcq are varied and all other parameters are fixed to their respective best fit value from the growth-side of the curve (or set to equal 1 in the cases if fca and fcq). When both Q∞ and "a" are allowed to vary (with fca and fcq fixed equal to 1) the fit is better than the above cases. But the estimate of "a" (0.0647) and Q∞ (197) rather poorly under and over estimate the true values (i.e., the average "a" equals 0.0.0835 for the 20 year time span and Q∞ is held constant at 170). The best fit, a near exact fit with the ∑rss ~ 0, is for the model where fca is varied and all the other parameters are fixed. The best fit value of fca is 1.019947 which is about equal to a 2% per year increase, which is what was assumed to generate the simulated data in the first place. Testing improved logistic model with simulated data where Q∞ increases on the decline side. To further test equation 9, I generated another simulated data set. Once again, I assume Q∞ equals 170 bbls and “a” equals 0.0687 yr^-1 on the growth side of the production curve. Then, in the year of peak production, 1956, I assumed that Q∞ increases by 0.5%/yr thereafter. Analogous to Figure 21, Figure 22 shows the simulated data and NLLS best fits to the data for the first 20 years on the decline side using equation 9, with the various parameters, “a”; Q∞; fca; and fcq either fixed to the best-fit growth side value, or allowed to vary, as described in the figure legend. Similar to the data shown in Figure 21 the simulated data on the decline side shows an initial slight increase in production, and the peak year of production is shifted to about 1960. Again, for this analysis, however I just stuck with examining the twenty year period from 1956-1975. In have not shown the best fits for the cases where only "a" or only fca were varied and the other parameter were fixed to their best-fit growth side values (or to 1 for fcq), as these fits were quite poor and looked about the same as depicted in the previous figures for other simulated data. I did show in Figure 22, the case of where Q∞ was varied (and all other parameters fixed) to illustrate that, even though the best fit value of Q∞ (182) was close to the true value of 179 (the average value over the 20-year span), the fit to the simulated data was poor. Again when both Q∞ and "a" are allowed to vary (with fca and fcq fixed equal to 1) the fit is better than the above cases. But again the But the estimate of "a" (0.0604) and Q∞ (196) rather poorly under and over estimate the true values (i.e., "a" held constant at 0.0687; the average Q∞ equals 179 for the 20 year time span). As expected, the best fit, a near exact fit with the ∑rss ~ 0, is for the model where fcq is varied and all the other parameters are fixed. The best fit value of fcq is 1.004987 which is about equal to a 0.5% per year increase, which is what was assumed to generate the simulated data in the first place. Based on this and the previous analysis done Parts 4 & 6, I have revised my approach for modeling real oil production and consumption data as follows: 1) Obtain estimates of Q∞ and "a" from the NLLS best fits to the growth side production data, and progressive increments of the decline side data. If the NLLS model blows up because there is no decline side data or data with a lot of scatter, use the hybrid linear logistic model to estimate Q∞ and "a." 2) Examine the most recent 10-20 year time span of the decline-side production data to see if there are discernable trends of a departure from the best fits using the logistic model where a constant Q∞ and "a" are assumed. 3) If there is a recent time span with a discernable departure detected in (2), apply NLLS and the improved logistic model to estimate to fractional change in "a" (fca) or Q∞ (fcq), or both, for this time span. 4) Apply the best fit model results from (1) or (3) to predict the production rates out to 2030. 5) Use the predicted production rates as part of the export land modeling for the USA (remember, that's what this whole series was about in the first place). Okay, its time to step away from modeling simulated data and enter world of real data—back to the USA!	{"url":"https://crash-watcher.blogspot.com/2010/10/refining-peak-oil-rosy-scenario-part-7.html","timestamp":"2024-11-05T00:18:07Z","content_type":"text/html","content_length":"124670","record_id":"<urn:uuid:f8dbf20c-b43f-4f0a-b859-e80f363bdc4e>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00585.warc.gz"}
How to evaluate limits using the integral test? \| Hire Someone To Do Calculus Exam For Me How to evaluate limits using the integral test? What if you want to find a maximum in a set, or the limit is: > max(a);? Is it meaningful? Are there limits for a discrete point, or is it fine for a continuous function. How about the limit in the Riemannian space? What about the finite limit (i.e., the top of real line) in the topology theory of Riemannian manifolds? A new question: If you are thinking about the Riemannian case, is there a limit of a smooth convex function? For example, what about infinite maps like maps of any complexity? More generally, we are thinking about the Riemannian case (see section 4) but the question is not the new one at all! One point I made a long time ago about limit you mentioned on this blog was that if you add numbers that you will always find the limit. It wasn’t actually simple, but since I was doing this task I wanted to help with some preliminary research as I wanted to see how you came up with the result. Anyway, just a few years ago there was a study of a curve coming from the equinox with minimal diameter. While it is sometimes called the $N$-fold cover effect. For simplicity, let’s consider a number (i.e., a sequence of open sets, check this sets of real points that have the minimum diameter) that starts as below and will go downward; it is certainly not infinite. If this list of numbers starts at and runs the same way until a discrete point lies in the sequence of sets, then the limit is still infinite. What if it is considered that until a point of decreasing diameter touches in some other sequence of sets, it will then just go upward? Furthermore, let’s consider how this limit ends up once you take one of the definitions of limits of manifolds: $$\label{ma} f \mapsto \lim_{NHow to evaluate limits using the integral test? I just saw this problem while trying to understand more about my class. You can find a how to help you with this piece of code here. @Override public int size() { // Fill your class in this way: return (int)super.size(); } And, for the example you mentioned, the speed limit that we can use is somewhere in this line: private int size = 2; I’m wondering why you would make this change: you can use an approach that uses the size parameter to evaluate to that value, when in that method, it will just increment the value because size() returns the correct value. That’s why I do not understand why you should do this: @Override public int size() { // Fill your class in this way: return (int)super.size(); } How do I fix this behavior? The answer should be easy to understand, as one can see from the comment in the picture. Do you have any idea how this could function? You have to understand if you have a question about what you could possibly achieve by increasing (since). And more importantly, as this is a small task, there is also another related question than What will my problem be in these projects? Can anyone provide any explanation of what your goal is, in particular, and how to solve it? A: The problem is that when you write it like this: public int bigInt -> 5 You get 10 seconds time and you are not waiting in the loop anymore which will make your code block more simple and fast. Since there is only 2KB between this number and the original one, you have to refactor your code to use a fast API that takes 5 seconds for the time. Can You Pay Someone To Do Your School Work? Finally, in this quick review, the point is that you canHow to evaluate limits using the integral test? In the D3 specification: The integral test is used in many tests to evaluate limits on a band-limited set. The comparison can be either yes or no: the sharp (low) limit holds as theband-limited set is in the real world, but the boundary is not well defined and can be omitted using something like the IMA procedure (IBM API). From there it’s inferred that the band-limited set makes sense. For Recommended Site if the cut-off corresponds to the MCL filter coefficient of a 1MHz LO band-limited set larger than the width of each corner that its bandwidth is bounded, then the integral check is the MCL filter’s result: P.S.: the Integralcheck fails? Should you check for the integrals before you try to make the test? It would be better to find out how much the integral you had before finding out why the test and the boundary were made so wrong. If we can find the boundary details, check my site the answer is NO; a better check would have to be made from an integral whose analytic value is accurate enough. As for the figure, the bounds are: have a peek at this site of all corner pixels width of the black-line display width of all pixels in the data boundary zone We call the integral the thresholding-only and call it our threshold test. The thresholding test is also used in and look at this website define the range for which it behaves like . A: But why should you re-check the conditions? If it only exists in the form of a low/strong bound of a rectangle, which is the case with some oracle and several	{"url":"https://hirecalculusexam.com/how-to-evaluate-limits-using-the-integral-test","timestamp":"2024-11-10T20:55:21Z","content_type":"text/html","content_length":"101307","record_id":"<urn:uuid:79cb7234-74ba-4383-98db-e607431e7c44>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00603.warc.gz"}
Cannot get Plane to Rotate while facing camera Below is the code that I have been using: using UnityEngine; using System.Collections; public class discRotate : MonoBehaviour { public float rotationSpeed; private Vector3 euler; // Use this for initialization void Start () rotationSpeed = 60; euler = transform.eulerAngles; // Update is called once per frame void Update () //rotate mathematically about axis: euler.z = ( euler.z + rotationSpeed * Time.deltaTime ) % 360; //update object rotation: //transform.EulerAngles = euler; transform.localEulerAngles = euler; No matter what axis I try the plane will always rotate in a direction that brings it in and out of visibility. Rotating along the Y-axis (this axis is pointed straight at the camera) should give me what I am looking for but changing that value is the same as changing the Z-axis when I run it. solved my own problem but thanks sixEight for the help!	{"url":"https://discussions.unity.com/t/cannot-get-plane-to-rotate-while-facing-camera/101512","timestamp":"2024-11-13T03:20:59Z","content_type":"text/html","content_length":"28224","record_id":"<urn:uuid:3cfdf1ec-4ab5-4dcb-9bb7-96508397cd93>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00344.warc.gz"}
Equation of a Line Parallel to X-Axis – Definition, Examples \| How to find Equation of a Parallel Line? We have infinite points in the coordinate plane. A line passes through a point (x, y). The different forms of equations of straight lines are equations of horizontal and vertical lines, Point-slope form, two-point form, slope-intercept form, intercept form, and normal form. Get to know more about the Equation of a Line Parallel to the x-axis in the following sections of this page. Also, Read: Equation of a Line Parallel to X-Axis A line can be defined as a straight one-dimensional geometric figure that doesn’t have the thickness and extends endlessly in both directions. A straight line on the coordinate plane can be described by an equation is called the equation of a line. If all the points the straight line having the same y-coordinate or ordinate values, then it is called the equation of a line parallel to the x-axis. The general form of the equation of a line that is parallel to the x-ais is y = k. Here, k is the distance between the x-axis and the line. If a point P(x, y) lies on the line, then y = b. The equation of x-ais is y = 0 as the x-axis is parallel to itself at a distance of 0 from it. Different Forms of the Equation of Line The various forms of the equations of a straight line are long the lines. Slope Intercept Form The equation of a slope-intercept form of a straight line is y = mx + b. Here, m is the slope, b is the y-intercept. Point Slope Form The point-slope form of a line is y – y₁ = m(x – x₁) Here, m is the slope of the line (x₁, y₁) is a point on the line. Two Point Form The two points form of a line is $\frac { y – y₁ }{ y₂ – y₁ } = \frac { x – x₁ }{ x₂ – x₁ }$ Here, (x₁, y₁), (x₂, y₂) are the two points on the line Slope of the line = $\frac { y₂ – y₁ }{ x₂ – x₁ } $ Intercept Form Intercept form of a line is $\frac { x }{ a } +\frac { y }{ b }$ = 1 Here, a is the x-intercept b is the y-intercept Equation of x-axis The equation of x-axis is y = 0. Because the value of “ordinate” in all the points on the x-axis is zero. Equation of y-axis The equation of y-axis is x = 0. Why because the value of abscissa in all points on the y-axis is zero. General Equation The general equation of a straight line is ax + by + c = 0. Equation of a Line Parallel to X-Axis Examples Example 1: Find the equation of a line parallel to the x-axis at a distance of 7 units above the x-axis? We know that the equation of a line parallel to the x-axis at a distance b from it is y = b. Therefore, the equation of a straight line parallel to the x-axis at a distance 7 units above the x-axis is y = 7. Example 2: Find the equation of a line parallel to the x-axis at a distance of 5 units below the x-axis? We know that If a straight line is parallel and below to x-axis at a distance b, then its equation is y = -b. Therefore, the equation of a line parallel to the x-axis at a distance of 5 units below the x-axis is y = -5. Example 3: Find the equation of a straight line parallel to the x-axis at a distance of 10 units above the x-axis? We know that the equation of a line parallel to the x-axis at a distance b from it is y = b. Therefore, the equation of a straight line parallel to the x-axis at a distance 10 units above the x-axis is y = 10. FAQs on Equation of Line Parallel to X-Axis 1. How do you find the equation of a line? The general form of equation of a line is ax + by + c = 0. Any equation in this form is called the equation of a straight line. 2. What is the equation of the line parallel to the x-axis? The equation of a straight line parallel to the x-axis is y = b as all the points on that line have y-coordinate values as zero’s. Here, b is the distance between the line and the x-axis. 3. How do you write an equation of a line parallel to a line? The slope-intercept form of a line is y = mx + c. If two lines are parallel, then their slopes are equal and the y-intercept depends on the line points. So, if you know one line, then it is easy to find the equation of a line parallel to the given line and passes through one point. Leave a Comment	{"url":"https://bigideasmathanswers.com/equation-of-a-line-parallel-to-x-axis/","timestamp":"2024-11-10T01:57:33Z","content_type":"text/html","content_length":"139699","record_id":"<urn:uuid:2fcb68af-ce2f-4e86-ad87-5a50dabfaac1>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00824.warc.gz"}
Mine Dogucu Curriculum Development Professor Mine Dogucu mainly works in statistics and data science education, focusing on curriculum development and modernization. “The advances in computing and the emergence of data science have not only brought up discussions of the data science curriculum but also led to a change in redefining the statistics curriculum and its delivery,” she says. Professor Dogucu considers what should be taught in these curricula and how that content should be delivered. “I also study the assessment of learning in data science classes including reasoning with data, classroom projects, and automated Accessible Bayesian Statistics For the data science curriculum, Professor Dogucu works at various levels, ranging from introductory to advanced. One advanced topic is Bayesian statistics — a theory that interprets probability differently from “frequentist statistics,” which is commonly taught in statistics courses. “Despite its importance and an increasing demand for it in the workforce, Bayesian statistics has not found its equivalent place in the undergraduate statistics curriculum,” she says. Luckily, UCI offers an undergraduate Bayesian course that is required for data science majors. “To make Bayesian statistics more accessible for undergraduate students elsewhere, I am cowriting a publicly available book, Bayes Rules! An Introduction to Bayesian Modeling with R, which is specifically geared toward novice Open Access Education One major barrier in learning data science or any other subject is the cost of textbooks and software, which is why Professor Dogucu develops educational materials that are freely accessible in the public domain. She also contributes to open source programming language R through teaching-oriented packages. “By contributing to open education, I aim to impact students looking for open access data science learning materials; instructors in search of teaching resources for their classrooms; and scientists interested in learning tools for open and reproducible science.” Through open education, she hopes to reach more learners around the world.	{"url":"http://www.stat.uci.edu/faculty/mine-dogucu/","timestamp":"2024-11-09T07:40:38Z","content_type":"text/html","content_length":"40254","record_id":"<urn:uuid:126f3d99-5bd4-49f7-831d-7ee11e774761>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00599.warc.gz"}
2IIM CAT Questions \| CAT Previous year Questions \| Best CAT Online Coaching The question is about minimizing a function. Our task is to find out the minimum value of a quadratic function. Do we need calculus for that? Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept. Question 21: What is the minimum value of f(x) = x^2 â€“ 5x + 41? 1. \\frac{139}{4}\\) 2. \\frac{149}{4}\\) 3. \\frac{129}{4}\\) 4. \\frac{119}{4}\\) 🎉 Supercharge the final leg of your CAT journey with our Percentile Booster â€“ the push you need for top scores! 🎉 Register Now Best CAT Online Coaching Try upto 40 hours for free Learn from the best! 2IIM : Best Online CAT Coaching. Video Explanation Best CAT Coaching in Chennai CAT Coaching in Chennai - CAT 2022 Limited Seats Available - Register Now! Explanatory Answer Method of solving this CAT Question from Algebra - Inequalities : Show this question to anyone who says you need differentiation to crack CAT exam. This question is present for one reason and one reason only. To talk about the idea of â€œcompletion of squaresâ€?. There are two ways of solving this question The ugly differentiation based method and the beautiful completion of squares method. Always pick the elegant method. You might not prefer VVS Laxman over Gary Kirsten, or Federer over Nadal. But these are matters of sport. When it comes to math solutions â€“ elegant solutions kick ass every time. What is this famous completion of squares method ? Any quadratic expression of the form x^2 + px + q can be written in the form (x +a)^2 + b. Write in that form, enjoy the equation and have some fun. x^2 â€“ 5x + 41 = (x + a)^2 + b. what value should â€˜aâ€™ take? Forget about b for the time being. (x + a)^2 = x^2 + 2ax + a^2. The 2ax term should correspond to -5x. Done and dusted. a =\\frac{-5}{2}\\)a^2 = \\frac{25}{4}\\) x^2 â€“ 5x + 41 can be written as x^2 â€“ 5x + \\frac{25}{4}\\) â€“ \\frac{25}{4}\\) + 41 = x â€“ \\frac{5}{2}\\)^2 + 41 â€“ \\frac{25}{4}\\) = x â€“ \\frac{5}{2}\\)^2 + \\frac{139}{4}\\) The minimum value this expression can take is \\frac{139}{4}\\) The question is "What is the minimum value of f(x) = x^2 â€“ 5x + 41?" Hence the answer is "\\frac{139}{4}\\)" Choice A is the correct answer.	{"url":"https://iim-cat-questions-answers.2iim.com/quant/algebra/inequalities/inequalities_21.shtml","timestamp":"2024-11-03T06:20:53Z","content_type":"text/html","content_length":"62517","record_id":"<urn:uuid:b4073b6d-8f93-41a8-8a5c-ac4b5b6040a1>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00643.warc.gz"}
Printable Multiplication Chart Free \| Multiplication Chart Printable Printable Multiplication Chart Free Free Printable Multiplication Table Completed And Blank Printable Multiplication Chart Free Printable Multiplication Chart Free – A Multiplication Chart is a handy tool for youngsters to find out just how to multiply, separate, and also find the tiniest number. There are several usages for a Multiplication Chart. These convenient tools help youngsters recognize the process behind multiplication by utilizing colored paths and also completing the missing out on items. These charts are cost-free to publish and also download. What is Multiplication Chart Printable? A multiplication chart can be utilized to assist kids discover their multiplication truths. Multiplication charts been available in numerous kinds, from full page times tables to single web page ones. While individual tables are useful for offering chunks of info, a complete web page chart makes it easier to evaluate facts that have actually currently been grasped. The multiplication chart will typically include a left column as well as a leading row. When you want to discover the product of 2 numbers, pick the initial number from the left column and the 2nd number from the top row. Multiplication charts are helpful knowing tools for both grownups and kids. Printable Multiplication Chart Free are offered on the Internet as well as can be printed out and laminated for longevity. Why Do We Use a Multiplication Chart? A multiplication chart is a representation that shows how to increase 2 numbers. It usually consists of a left column and a leading row. Each row has a number representing the item of both numbers. You select the first number in the left column, move it down the column, and afterwards select the 2nd number from the top row. The item will certainly be the square where the numbers satisfy. Multiplication charts are handy for lots of factors, including helping youngsters find out just how to split and also streamline fractions. They can additionally aid kids find out just how to choose an efficient common denominator. Multiplication charts can also be useful as workdesk sources due to the fact that they function as a consistent pointer of the trainee’s development. These tools aid us create independent students who understand the fundamental principles of multiplication. Multiplication charts are likewise valuable for aiding pupils memorize their times tables. As with any type of ability, remembering multiplication tables takes time and also practice. Printable Multiplication Chart Free Printable Multiplication Chart 1 12 Pdf PrintableMultiplication Free Multiplication Chart Printable Paper Trail Design Free Multiplication Chart Printable Paper Trail Design In 2021 Printable Multiplication Chart Free If you’re looking for Printable Multiplication Chart Free, you’ve come to the right location. Multiplication charts are readily available in various layouts, consisting of complete size, half dimension, and also a selection of charming designs. Multiplication charts as well as tables are vital tools for kids’s education and learning. You can download as well as publish them to utilize as a training aid in your kid’s homeschool or classroom. You can also laminate them for resilience. These charts are great for usage in homeschool math binders or as classroom posters. They’re specifically helpful for youngsters in the 2nd, third, as well as 4th qualities. A Printable Multiplication Chart Free is a helpful tool to enhance mathematics truths and can assist a child discover multiplication swiftly. It’s also an excellent tool for miss checking and discovering the times tables. Related For Printable Multiplication Chart Free	{"url":"https://multiplicationchart-printable.com/printable-multiplication-chart-free/","timestamp":"2024-11-07T02:38:21Z","content_type":"text/html","content_length":"43720","record_id":"<urn:uuid:c5dbd517-6fc9-458d-a1db-9cceef79da13>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00281.warc.gz"}
Atiyeh Ghoreyshi and Terence D. Sanger, A Nonlinear Stochastic Filter for Continuous-Time State Estimation, IEEE Transactions on Automatic Control, vol. 60, no. 8, DOI: 10.1109/TAC.2015.2409910. Nonlinear filters produce a nonparametric estimate of the probability density of state at each point in time. Currently known nonlinear filters include Particle Filters and the Kushner equation (and its un-normalized version: the Zakai equation). However, these filters have limited measurement models: Particle Filters require measurement at discrete times, and the Kushner and Zakai equations only apply when the measurement can be represented as a function of the state. We present a new nonlinear filter for continuous-time measurements with a much more general stochastic measurement model. It integrates to Bayes’ rule over short time intervals and provides Bayes-optimal estimates from quantized, intermittent, or ambiguous sensor measurements. The filter has a close link to Information Theory, and we show that the rate of change of entropy of the density estimate is equal to the mutual information between the measurement and the state and thus the maximum achievable. This is a fundamentally new class of filter that is widely applicable to nonlinear estimation for continuous-time control. Substituting the update step of a bayesian filter by a maximum likelihood optimisation in order to use non-linear observation models in a (linear-transition) Kalman framework Damián Marelli, Minyue Fu, and Brett Ninness, Asymptotic Optimality of the Maximum-Likelihood Kalman Filter for Bayesian Tracking With Multiple Nonlinear Sensors, IEEE Transactions on signal processing, vol. 63, no. 17, DOI: 10.1109/TSP.2015.2440220. Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-like-lihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail. A new algorithm for clock synchronization in wireless sensor networks with bounded delays, that includes interesting references to surveys Emanuele Garone, Andrea Gasparri, Francesco Lamonaca, Clock synchronization protocol for wireless sensor networks with bounded communication delays, Automatica, Volume 59, September 2015, Pages 60-72, ISSN 0005-1098, DOI: 10.1016/j.automatica.2015.06.014. In this paper, we address the clock synchronization problem for wireless sensor networks. In particular, we consider a wireless sensor network where nodes are equipped with a local clock and communicate in order to achieve a common sense of time. The proposed approach consists of two asynchronous consensus algorithms, the first of which synchronizes the clocks frequency and the second of which synchronizes the clocks offset. This work advances the state of the art by providing robustness against bounded communication delays. A theoretical characterization of the algorithm properties is provided. Simulations and experimental results are presented to corroborate the theoretical findings and show the effectiveness of the proposed algorithm. A very interesting review of current approaches to SLAM based on smoothing (i.e., graph optimization) and in clustering the map into submaps Jiantong Cheng, Jonghyuk Kim, Jinliang Shao, Weihua Zhang, Robust linear pose graph-based SLAM, Robotics and Autonomous Systems, Volume 72, October 2015, Pages 71-82, ISSN 0921-8890, DOI: 10.1016/ This paper addresses a robust and efficient solution to eliminate false loop-closures in a pose-graph linear SLAM problem. Linear SLAM was recently demonstrated based on submap joining techniques in which a nonlinear coordinate transformation was performed separately out of the optimization loop, resulting in a convex optimization problem. This however introduces added complexities in dealing with false loop-closures, which mostly stems from two factors: (a) the limited local observations in map-joining stages and (b) the non block-diagonal nature of the information matrix of each submap. To address these problems, we propose a Robust Linear SLAM by (a) developing a delayed optimization for outlier candidates and (b) utilizing a Schur complement to efficiently eliminate corrupted information block. Based on this new strategy, we prove that the spread of outlier information does not compromise the optimization performance of inliers and can be fully filtered out from the corrupted information matrix. Experimental results based on public synthetic and real-world datasets in 2D and 3D environments show that this robust approach can cope with the incorrect loop-closures robustly and effectively. Quantum probability theory as an alternative to classical (Kolgomorov) probability theory for modelling human decision making processes, and a curious description of the effect of a particular ordering of decisions in the complete result Peter D. Bruza, Zheng Wang, Jerome R. Busemeyer, Quantum cognition: a new theoretical approach to psychology, Trends in Cognitive Sciences, Volume 19, Issue 7, July 2015, Pages 383-393, ISSN 1364-6613, DOI: 10.1016/j.tics.2015.05.001. What type of probability theory best describes the way humans make judgments under uncertainty and decisions under conflict? Although rational models of cognition have become prominent and have achieved much success, they adhere to the laws of classical probability theory despite the fact that human reasoning does not always conform to these laws. For this reason we have seen the recent emergence of models based on an alternative probabilistic framework drawn from quantum theory. These quantum models show promise in addressing cognitive phenomena that have proven recalcitrant to modeling by means of classical probability theory. This review compares and contrasts probabilistic models based on Bayesian or classical versus quantum principles, and highlights the advantages and disadvantages of each approach. Transfer learning in reinforcement learning through case-based and the use of heuristics for selecting actions Reinaldo A.C. Bianchi, Luiz A. Celiberto Jr., Paulo E. Santos, Jackson P. Matsuura, Ramon Lopez de Mantaras, Transferring knowledge as heuristics in reinforcement learning: A case-based approach, Artificial Intelligence, Volume 226, September 2015, Pages 102-121, ISSN 0004-3702, DOI: 10.1016/j.artint.2015.05.008. The goal of this paper is to propose and analyse a transfer learning meta-algorithm that allows the implementation of distinct methods using heuristics to accelerate a Reinforcement Learning procedure in one domain (the target) that are obtained from another (simpler) domain (the source domain). This meta-algorithm works in three stages: first, it uses a Reinforcement Learning step to learn a task on the source domain, storing the knowledge thus obtained in a case base; second, it does an unsupervised mapping of the source-domain actions to the target-domain actions; and, third, the case base obtained in the first stage is used as heuristics to speed up the learning process in the target domain. A set of empirical evaluations were conducted in two target domains: the 3D mountain car (using a learned case base from a 2D simulation) and stability learning for a humanoid robot in the Robocup 3D Soccer Simulator (that uses knowledge learned from the Acrobot domain). The results attest that our transfer learning algorithm outperforms recent heuristically-accelerated reinforcement learning and transfer learning algorithms. Semantic and syntactic bootstrapped learning for robots, inspired in similar processes in humans, that use language as a scaffolding mechanism to improve learning in unknown situations Worgotter, F.; Geib, C.; Tamosiunaite, M.; Aksoy, E.E.; Piater, J.; Hanchen Xiong; Ude, A.; Nemec, B.; Kraft, D.; Kruger, N.; Wachter, M.; Asfour, T., Structural Bootstrapping—A Novel, Generative Mechanism for Faster and More Efficient Acquisition of Action-Knowledge, Autonomous Mental Development, IEEE Transactions on , vol.7, no.2, pp.140,154, June 2015, DOI: 10.1109/TAMD.2015.2427233. Humans, but also robots, learn to improve their behavior. Without existing knowledge, learning either needs to be explorative and, thus, slow or-to be more efficient-it needs to rely on supervision, which may not always be available. However, once some knowledge base exists an agent can make use of it to improve learning efficiency and speed. This happens for our children at the age of around three when they very quickly begin to assimilate new information by making guided guesses how this fits to their prior knowledge. This is a very efficient generative learning mechanism in the sense that the existing knowledge is generalized into as-yet unexplored, novel domains. So far generative learning has not been employed for robots and robot learning remains to be a slow and tedious process. The goal of the current study is to devise for the first time a general framework for a generative process that will improve learning and which can be applied at all different levels of the robot’s cognitive architecture. To this end, we introduce the concept of structural bootstrapping-borrowed and modified from child language acquisition-to define a probabilistic process that uses existing knowledge together with new observations to supplement our robot’s data-base with missing information about planning-, object-, as well as, action-relevant entities. In a kitchen scenario, we use the example of making batter by pouring and mixing two components and show that the agent can efficiently acquire new knowledge about planning operators, objects as well as required motor pattern for stirring by structural bootstrapping. Some benchmarks are shown, too, that demonstrate how structural bootstrapping improves Developmental approach for a robot manipulator that learns in several bootstrapped stages, strongly inspired in infant development Ugur, E.; Nagai, Y.; Sahin, E.; Oztop, E., Staged Development of Robot Skills: Behavior Formation, Affordance Learning and Imitation with Motionese, Autonomous Mental Development, IEEE Transactions on , vol.7, no.2, pp.119,139, June 2015, DOI: 10.1109/TAMD.2015.2426192. Inspired by infant development, we propose a three staged developmental framework for an anthropomorphic robot manipulator. In the first stage, the robot is initialized with a basic reach-and- enclose-on-contact movement capability, and discovers a set of behavior primitives by exploring its movement parameter space. In the next stage, the robot exercises the discovered behaviors on different objects, and learns the caused effects; effectively building a library of affordances and associated predictors. Finally, in the third stage, the learned structures and predictors are used to bootstrap complex imitation and action learning with the help of a cooperative tutor. The main contribution of this paper is the realization of an integrated developmental system where the structures emerging from the sensorimotor experience of an interacting real robot are used as the sole building blocks of the subsequent stages that generate increasingly more complex cognitive capabilities. The proposed framework includes a number of common features with infant sensorimotor development. Furthermore, the findings obtained from the self-exploration and motionese guided human-robot interaction experiments allow us to reason about the underlying mechanisms of simple-to-complex sensorimotor skill progression in human infants. Finding the common utility of actions in several tasks learnt in the same domain in order to reduce the learning cost of reinforcement learning Rosman, B.; Ramamoorthy, S., Action Priors for Learning Domain Invariances, Autonomous Mental Development, IEEE Transactions on , vol.7, no.2, pp.107,118, June 2015, DOI: 10.1109/TAMD.2015.2419715. An agent tasked with solving a number of different decision making problems in similar environments has an opportunity to learn over a longer timescale than each individual task. Through examining solutions to different tasks, it can uncover behavioral invariances in the domain, by identifying actions to be prioritized in local contexts, invariant to task details. This information has the effect of greatly increasing the speed of solving new problems. We formalise this notion as action priors, defined as distributions over the action space, conditioned on environment state, and show how these can be learnt from a set of value functions. We apply action priors in the setting of reinforcement learning, to bias action selection during exploration. Aggressive use of action priors performs context based pruning of the available actions, thus reducing the complexity of lookahead during search. We additionally define action priors over observation features, rather than states, which provides further flexibility and generalizability, with the additional benefit of enabling feature selection. Action priors are demonstrated in experiments in a simulated factory environment and a large random graph domain, and show significant speed ups in learning new tasks. Furthermore, we argue that this mechanism is cognitively plausible, and is compatible with findings from cognitive psychology. A brief general explanation of Rao-Blacwellization and a new way of applying it to reduce the variance of a point estimation in a sequential bayesian setting Petetin, Y.; Desbouvries, F., Bayesian Conditional Monte Carlo Algorithms for Nonlinear Time-Series State Estimation, Signal Processing, IEEE Transactions on , vol.63, no.14, pp.3586,3598, DOI: Bayesian filtering aims at estimating sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density function (pdf) of the hidden process given the available observations. On the other hand, conditional Monte Carlo (CMC) is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable. In this paper, we show that up to some adaptations, one can make use of the time recursive nature of SMC algorithms in order to propose natural temporal CMC estimators of some point estimates of the hidden process, which outperform the associated crude Monte Carlo (MC) estimator whatever the number of samples. We next show that our Bayesian CMC estimators can be computed exactly, or approximated efficiently, in some hidden Markov chain (HMC) models; in some jump Markov state-space systems (JMSS); as well as in multitarget filtering. Finally our algorithms are validated via simulations.	{"url":"https://babel.isa.uma.es/kipr/?m=201507","timestamp":"2024-11-14T04:05:27Z","content_type":"application/xhtml+xml","content_length":"79960","record_id":"<urn:uuid:918e8899-ee53-4a60-881b-a38ba3dff2d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00406.warc.gz"}
Biologically-Plausible Determinant Maximization Neural Networks for Blind Separation of Correlated Sources Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track Bariscan Bozkurt, Cengiz Pehlevan, Alper Erdogan Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous work, we assume some general geometric, not statistical, conditions on the source vectors allowing separation of potentially dependent/correlated sources. Concretely, we assume that the source vectors are sufficiently scattered in their domains which can be described by certain polytopes. Then, we consider recovery of these sources by the Det-Max criterion, which maximizes the determinant of the output correlation matrix to enforce a similar spread for the source estimates. Starting from this normative principle, and using a weighted similarity matching approach that enables arbitrary linear transformations adaptable by local learning rules, we derive two-layer biologically-plausible neural network algorithms that can separate mixtures into sources coming from a variety of source domains. We demonstrate that our algorithms outperform other biologically-plausible BSS algorithms on correlated source separation problems.	{"url":"https://proceedings.nips.cc/paper_files/paper/2022/hash/58cb483be90d31f9afea3a9e992a2abe-Abstract-Conference.html","timestamp":"2024-11-14T17:29:19Z","content_type":"text/html","content_length":"9573","record_id":"<urn:uuid:1cd57a57-ac10-46b7-b307-41086050f04d>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00421.warc.gz"}
How do you write the equation y+7=1/2(x+2) in standard form? \| Socratic How do you write the equation #y+7=1/2(x+2)# in standard form? 1 Answer See a solution process below: The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$ Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1 First, I would multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fraction and to ensure all of the coefficients and constants are integers as require by the Standard Form: $\textcolor{red}{2} \left(y + 7\right) = \textcolor{red}{2} \cdot \frac{1}{2} \left(x + 2\right)$ $\left(\textcolor{red}{2} \cdot y\right) + \left(\textcolor{red}{2} \cdot 7\right) = \cancel{\textcolor{red}{2}} \cdot \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} \left(x + 2\right)$ $2 y + 14 = x + 2$ Next, subtract $\textcolor{red}{14}$ and $\textcolor{b l u e}{x}$ from each side of the equation to place the variables on the left side of the equation and the constant on the right side of the $- \textcolor{b l u e}{x} + 2 y + 14 - \textcolor{red}{14} = - \textcolor{b l u e}{x} + x + 2 - \textcolor{red}{14}$ $- x + 2 y + 0 = 0 - 12$ $- x + 2 y = - 12$ Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to ensure the $x$ coefficient is a non-negative integer: $\textcolor{red}{- 1} \left(- x + 2 y\right) = \textcolor{red}{- 1} \cdot - 12$ $\textcolor{red}{1} x - \textcolor{b l u e}{2} y = \textcolor{g r e e n}{12}$ Impact of this question 4546 views around the world	{"url":"https://api-project-1022638073839.appspot.com/questions/how-do-you-write-the-equation-y-7-1-2-x-2-in-standard-form","timestamp":"2024-11-12T23:38:15Z","content_type":"text/html","content_length":"36328","record_id":"<urn:uuid:7f48f639-7b8a-4612-b21d-a7524bfb938c>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00331.warc.gz"}
Some 3D renderings of the Mandelbrot set. - Peeter Joot's BlogFebruary 7, 2021 – Peeter Joot's Blog Some 3D renderings of the Mandelbrot set. February 7, 2021 math and physics play 3D Mandelbrot set, complex numbers, Geometric Algebra, Mandelbrot set, netCDF, Paraview As mentioned previously, using geometric algebra we can convert the iterative equation for the Mandelbrot set from complex number form z \rightarrow z^2 + c, to an equivalent vector form \mathbf{x} \rightarrow \mathbf{x} \mathbf{e} \mathbf{x} + \mathbf{c}, where $ \mathbf{e} $ represents the x-axis (say). Geometrically, each iteration takes $ \mathbf{e} $ and reflects it about the direction of $ \mathbf{x} $, then scales that by $ \mathbf{x}^2 $ and adds $ \mathbf{c} $. To get the usual 2D Mandelbrot set, one iterates with vectors that lie only in the x-y plane, but we can treat the Mandelbrot set as a 3D solid if we remove the x-y plane restriction. Last time I animated slices of the 3D set, but after a whole lot of messing around I managed to save the data for all the interior points of the 3D set in netCDF format, and render the solid using Paraview. Paraview has tons of filters available, and experimenting with them is pretty time consuming, but here are some initial screenshots of the 3D Mandelbrot set: It’s interesting that much of the characteristic detail of the Mandelbrot set is not visible in the 3D volume, but if we slice that volume, you can then you can see it again. Here’s a slice taken close to the z=0 plane (but far enough that the “CN tower” portion of the set is not visible) You can also see some of that detail if the opacity of the rendering is turned way down: If you look carefully at the images above, you’ll see that the axis labels are wrong. I think that I’ve screwed up one of the stride related parameters to my putVar call, and I end up with x+z transposed in the axes labels when visualized.	{"url":"https://peeterjoot.com/2021/02/07/","timestamp":"2024-11-02T20:58:06Z","content_type":"text/html","content_length":"97765","record_id":"<urn:uuid:88984f07-7300-4637-831f-2e06caa8ecc8>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00740.warc.gz"}
Orders Of Operations Including Negative And Positive Rational Numbers Worksheet Orders Of Operations Including Negative And Positive Rational Numbers Worksheet function as foundational tools in the realm of maths, supplying a structured yet versatile platform for learners to discover and grasp numerical ideas. These worksheets use a structured method to understanding numbers, nurturing a solid foundation upon which mathematical effectiveness thrives. From the easiest checking workouts to the details of sophisticated estimations, Orders Of Operations Including Negative And Positive Rational Numbers Worksheet deal with students of diverse ages and skill levels. 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Order Of Operations Worksheet With Integers Adding Rational Numbers Worksheet Check more of Orders Of Operations Including Negative And Positive Rational Numbers Worksheet below Rational Numbers On A Number Line Worksheets Compare Rational Numbers Worksheets Rational Numbers Operations Activity Worksheet Positive And Negative Fractions Rational Compare And Order Rational Numbers Worksheet Rational Numbers 7th Grade Worksheet Positive And Negative Integers Worksheet Order Of Operations With Negative And Positive Welcome to The Order of Operations with Negative and Positive Integers Four Steps A Math Worksheet from the Order of Operations Worksheets Page at Math Drills This math Order Of Operations Worksheets Math Worksheets 4 Kids Order of Operations 4 Basic Operations Level 1 Apply the order of operations on expressions involving three whole numbers or integers Direct grade 4 and grade 5 Welcome to The Order of Operations with Negative and Positive Integers Four Steps A Math Worksheet from the Order of Operations Worksheets Page at Math Drills This math Order of Operations 4 Basic Operations Level 1 Apply the order of operations on expressions involving three whole numbers or integers Direct grade 4 and grade 5 Compare And Order Rational Numbers Worksheet Compare Rational Numbers Worksheets Rational Numbers 7th Grade Worksheet Positive And Negative Integers Worksheet Ordering Rational Numbers Worksheet Smoochinspire Identifying Rational Numbers Worksheet Identifying Rational Numbers Worksheet Grade 8 Rational Numbers Worksheets	{"url":"https://alien-devices.com/en/orders-of-operations-including-negative-and-positive-rational-numbers-worksheet.html","timestamp":"2024-11-04T15:58:02Z","content_type":"text/html","content_length":"25459","record_id":"<urn:uuid:36fa8a3d-c613-4b6e-888a-0e7179cac0be>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00521.warc.gz"}
Parametric Estimation For Functional Autoregressive Processes On The Sphere Victor Panaretos, Neda Mohammadi Jouzdani We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...	{"url":"https://graphsearch.epfl.ch/en/publication/294653","timestamp":"2024-11-11T23:15:56Z","content_type":"text/html","content_length":"100282","record_id":"<urn:uuid:8561b1fe-af11-464d-a6bb-f387bdf9de1e>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00495.warc.gz"}
How many square feet does a bundle of 3-tab shingles cover? How many square feet does a bundle of 3-tab shingles cover? 33.3 sq. ft. Calculating the number of bundles, you need is simple if you are using shingles that come three bundles to a square. Each bundle covers 33.3 sq. ft. of roof area—which is close enough to the 32 sq. How many bundles of shingles does it take to cover 1800 square feet? 18 squares A roofing square is equal to 100 feet on your roof. If your roof measures at 1800 square feet, you would need 18 squares of shingles to cover your roof. How many shingles do I need for 100 square feet? A roofing square is equal to 100 square feet of the roof. To determine the number of squares on the gable roof example in this post, divide its total of 2400 square feet by 100 (2400 ÷ 100 = 24). This means you would need 24 squares of shingles to cover that roof. How many bundles of shingles do I need for 200 square feet? How Many Bundles of Shingles Will You Need. The average bundle of shingles covers 33.3 ft2, so three bundles of shingles are needed per square. How much does 1 square of shingles cover? 100 sq. ft. A square of shingles is the quantity needed to cover 100 sq. ft. of roof. Shingles are packaged in paper- or plastic-wrapped bundles designed to be light enough for a person to carry, so heavier shingles require more bundles per square. How many bundles of shingles do I need for a 1500 square foot roof? How many bundles of shingles does it take to cover 1700 square feet? 57 bundles 57 bundles is a ft. 1,700 / 33.3 + 10% for trim. How many shingles do I need for 300 square feet? What is this? For most shingle types, you’ll need 3 bundles to make a square of finished roof, which is 100 square feet. If you have a roof area of 3000 square feet, you’ll need 90 bundles of shingles. Shingles with 4 bundles per square will require you to purchase 120 bundles for a 300 square foot roof.	{"url":"https://blackestfest.com/how-many-square-feet-does-a-bundle-of-3-tab-shingles-cover/","timestamp":"2024-11-02T17:54:07Z","content_type":"text/html","content_length":"48079","record_id":"<urn:uuid:c85a6909-20ee-4fe4-a8cc-0bea6c788934>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00366.warc.gz"}
Information about The EuroJackpot Generator calculates optimized numbers based on the mathematical statistical analysis of past draws. The first EuroJackpot draw took place on Friday the 23.03.2012. Since this repeats itself weekly. At the present time (07.10.2018) there were 341 drawings of 5 numbers each and two Euro numbers. A clear database of all winning numbers can be found here: EuroJackpot winning numbers The dataset offers the possibility to examine it according to different aspects. The frequency of individual numbers drawn is one of them. Different periods of time can be examined for the most frequently drawn numbers in the respective period. For example, The most frequently drawn winning numbers of the last 50 draws can be determined. Furthermore, two-person combinations can also be examined for frequency. For example, the most drawn pairs of the last 100 draws can be calculated. Another possibility for analysis is the profit quotas. If winning numbers were typed by many players, the odds are rather lower. The winners must share the winnings with more people. Therefore, it is not recommended, e.g. Playing numbers from birthday dates or similar. High quotas thus indicate that the numbers were rather typed by a few. In order to realize a higher possible profit, it is advisable rather to play less frequently typed number combinations. These can also be determined by the generator for selected periods. The overdue EuroJackpotzahlen is another analysis criterion for the generator. It is determined which numbers have not been pulled the longest and are thus “overdue”. According to theoretical stochastics, there is a higher probability that these numbers will be drawn. You can decide for yourself how many individual analyzes are performed with which parameters for generating tips. The results of these analyzes are shown both graphically and in tabular form for the respective calculation. Optimized tips are generated from all individual calculations of a generator run. The results of the analyzes are used in equal parts and optimally combined as tips.	{"url":"https://www.eurojackpot-generator.de/en/informationen-eurojackpot-generator/","timestamp":"2024-11-03T15:09:22Z","content_type":"text/html","content_length":"22234","record_id":"<urn:uuid:4f7c3634-96e0-416f-8e9a-566cf0a7512c>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00538.warc.gz"}
Poles 'n' Wires Marker Balls The effect of markers balls on a line can be accurately modelled using finite element software. However you can estimate their effect in Poles ‘n’ Wires. The proposed approach is to create a new entry in the Conductor database representing the combined conductor+balls. This is suitable when: 1. the marker balls are spread evenly along the span, or on all spans in a strain section 2. the balls are the same size and weight You’ll need to make an entry for each unique span length, or you can use the entry for a strain section if there are marker balls on all spans in the strain section. 1. Determine total area of balls on the span. This will be $A= \pi r^2 $ x {number of balls}, where $r$ is the radius of a ball. 2. Divide $A$ by the span length to give the additional diameter that needs to be added to the conductor diameter. Units are mm. 3. Multiply the weight of each ball by the number of balls in the span. Divide the total weight by the span length. This is the mass in kg/m that needs to be added to the conductor mass. 4. Create a new record in the Conductor database, give it a new Code and copy all parameters from the base conductor record. Then modify the Diameter and Mass as previously calculated. Adjust as needed if you are modelling a strain section not an individual span. This approach can also be used to model other attachments such as vibration dampers, as long as the same conditions are met.	{"url":"https://polesnwires.com/knowledge-base/marker-balls/","timestamp":"2024-11-04T01:57:28Z","content_type":"text/html","content_length":"42185","record_id":"<urn:uuid:2943a96b-eef0-4053-91fd-6ceac2128f88>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00100.warc.gz"}
Unveiling the Secrets of Polygons: Conquer "71 Interior and Exterior Angles Homework" \| Mastering Success: The Power of Answer Keys and QuizzesUnveiling the Secrets of Polygons: Conquer "71 Interior and Exterior Angles Homework" Unveiling the Secrets of Polygons: Conquer "71 Interior and Exterior Angles Homework" In geometry, the sum of interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. The exterior angle of a polygon is the angle formed by one side of the polygon and the extension of the adjacent side. The sum of exterior angles of a polygon is always 360 degrees. When solving problems involving interior and exterior angles of polygons, it is important to understand the relationship between them. The sum of an interior angle and its corresponding exterior angle is always 180 degrees. This relationship can be used to find missing angle measures in polygons. Here are some examples of how to use the formulas for interior and exterior angles to solve problems: • Find the measure of an interior angle of a regular hexagon. • Find the measure of an exterior angle of a regular decagon. • Find the sum of the interior angles of a polygon with 12 sides. • Find the sum of the exterior angles of a polygon with 15 sides. By understanding the relationship between interior and exterior angles, you can solve a variety of problems involving polygons. 71 interior and exterior angles homework answer key To understand the concept of 71 interior and exterior angles homework answer key, it is important to explore its key aspects: • Polygon: A polygon is a closed figure with three or more straight sides. • Interior angle: An interior angle of a polygon is the angle formed by two adjacent sides. • Exterior angle: An exterior angle of a polygon is the angle formed by one side of the polygon and the extension of the adjacent side. • Sum of interior angles: The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. • Sum of exterior angles: The sum of the exterior angles of a polygon is always 360 degrees. • Relationship between interior and exterior angles: The sum of an interior angle and its corresponding exterior angle is always 180 degrees. • Regular polygon: A regular polygon is a polygon in which all sides and all angles are equal. • Irregular polygon: An irregular polygon is a polygon in which the sides and angles are not all equal. These key aspects provide a comprehensive understanding of 71 interior and exterior angles homework answer key. By understanding these concepts, you can solve a variety of problems involving A polygon is a geometric shape with three or more straight sides. Polygons are classified by the number of sides they have. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and a polygon with five sides is called a pentagon. The concept of a polygon is essential for understanding the 71 interior and exterior angles homework answer key because it provides the foundation for understanding the properties of polygons. The number of sides of a polygon determines the number of interior and exterior angles it has. For example, a triangle has three interior angles and three exterior angles, a quadrilateral has four interior angles and four exterior angles, and a pentagon has five interior angles and five exterior angles. Understanding the relationship between polygons and their interior and exterior angles is important for solving a variety of geometry problems. For example, the sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. The sum of the exterior angles of a polygon is always 360 degrees. These formulas can be used to find missing angle measures in In conclusion, the concept of a polygon is essential for understanding the 71 interior and exterior angles homework answer key. By understanding the relationship between polygons and their interior and exterior angles, you can solve a variety of geometry problems. Interior angle Interior angles are one of the two types of angles associated with polygons, the other being exterior angles. Understanding interior angles is crucial for solving the “71 interior and exterior angles homework answer key” as they form the basis for calculating the sum of angles in a polygon. The sum of interior angles in a polygon with ‘n’ sides is given by the formula: (n-2) x 180 degrees. This formula is a fundamental concept in geometry and is frequently applied in solving problems related to polygons. For example, consider a regular hexagon with six sides. Using the formula, we can calculate the sum of its interior angles as (6-2) x 180 degrees = 720 degrees. This understanding enables us to determine the measure of each interior angle by dividing the total sum by the number of angles. In conclusion, interior angles play a vital role in solving the “71 interior and exterior angles homework answer key” as they provide the foundation for calculating the sum of angles in polygons. Understanding the concept of interior angles is essential for solving geometry problems involving polygons. Exterior angle Exterior angles are inextricably linked to the “71 interior and exterior angles homework answer key” as they represent the angles outside the polygon, complementary to their corresponding interior angles. Understanding exterior angles is crucial for solving geometry problems involving polygons. The sum of exterior angles in any polygon is always 360 degrees, regardless of the number of sides. This property is particularly useful when dealing with regular polygons, where all sides and angles are equal. For instance, in a regular hexagon, each exterior angle measures 60 degrees, as the sum of all six exterior angles is 360 degrees. Furthermore, the relationship between interior and exterior angles is vital in solving problems related to the “71 interior and exterior angles homework answer key.” The sum of an interior angle and its corresponding exterior angle is always 180 degrees. This relationship allows us to determine unknown angle measures in polygons. In conclusion, understanding exterior angles is essential for solving the “71 interior and exterior angles homework answer key” as they provide a complementary perspective to interior angles. The sum of exterior angles in a polygon is always 360 degrees, and the relationship between interior and exterior angles is crucial for solving geometry problems involving polygons. Sum of interior angles In geometry, the formula for the sum of interior angles of a polygon is a fundamental concept that plays a significant role in solving the “71 interior and exterior angles homework answer key.” This formula provides a direct method to calculate the sum of interior angles based on the number of sides in a polygon. • Calculating Angle Measures: The formula empowers us to determine the sum of interior angles for any polygon, regardless of its shape or size. This is particularly useful when dealing with regular polygons, where all sides and angles are equal. For instance, using the formula, we can quickly calculate that the sum of interior angles in a square (a polygon with four equal sides) is 360 • Solving Geometry Problems: The formula serves as a cornerstone for solving geometry problems involving polygons. By knowing the sum of interior angles, we can derive other angle measures, such as the measure of each interior angle or the measure of exterior angles. This knowledge is essential for understanding the geometric properties of polygons. In conclusion, the formula for the sum of interior angles of a polygon is an indispensable tool in solving the “71 interior and exterior angles homework answer key” and various geometry problems. It provides a systematic approach to calculating angle measures in polygons, making it a fundamental concept in geometry. Sum of exterior angles In geometry, the sum of exterior angles is a fundamental property of polygons that holds significant relevance in solving the “71 interior and exterior angles homework answer key.” Understanding this property and its implications is crucial for solving geometry problems involving polygons. • Relationship with Interior Angles: The sum of exterior angles is closely related to the sum of interior angles in a polygon. In fact, the sum of exterior angles is always 360 degrees, regardless of the number of sides or the shape of the polygon. This relationship provides a valuable tool for solving problems related to polygons. • Calculating Exterior Angle Measures: Knowing that the sum of exterior angles is 360 degrees allows us to calculate the measure of each exterior angle. By dividing 360 degrees by the number of sides in a polygon, we can determine the measure of each exterior angle. This knowledge is essential for understanding the geometric properties of polygons. • Solving Geometry Problems: The sum of exterior angles is a powerful concept for solving geometry problems involving polygons. For instance, we can use this property to find the measure of an unknown interior or exterior angle, or to determine whether a given polygon is convex or concave. • Applications in Real-World Scenarios: The sum of exterior angles finds practical applications in various fields, such as architecture and engineering. Architects use this concept to design buildings with specific angles, while engineers rely on it to calculate angles in structures like bridges and trusses. In conclusion, the sum of exterior angles is a vital concept in geometry, particularly for solving the “71 interior and exterior angles homework answer key.” It provides a systematic approach to understanding and calculating angle measures in polygons, making it a fundamental property in geometry and its applications. Relationship between interior and exterior angles The relationship between interior and exterior angles is a fundamental concept in geometry that plays a pivotal role in understanding the “71 interior and exterior angles homework answer key.” This relationship states that the sum of an interior angle and its corresponding exterior angle on a polygon is always 180 degrees. This relationship is crucial for solving geometry problems involving polygons because it provides a way to find unknown angle measures. For example, if you know the measure of an interior angle, you can find the measure of its corresponding exterior angle by subtracting it from 180 degrees. Conversely, if you know the measure of an exterior angle, you can find the measure of its corresponding interior angle by subtracting it from 180 degrees. Understanding the relationship between interior and exterior angles is also important for understanding the properties of polygons. For example, the sum of the interior angles of a polygon with ‘n’ sides is given by the formula (n-2) * 180 degrees. This formula can be derived using the relationship between interior and exterior angles. Similarly, the sum of the exterior angles of a polygon is always 360 degrees, regardless of the number of sides. In conclusion, the relationship between interior and exterior angles is a vital concept in geometry, particularly for solving the “71 interior and exterior angles homework answer key.” It provides a systematic approach to understanding and calculating angle measures in polygons, making it a fundamental property in geometry and its applications. Regular polygon In geometry, a regular polygon is a polygon in which all sides and all angles are equal. Regular polygons are often used in mathematics and engineering because of their symmetry and predictable properties. The “71 interior and exterior angles homework answer key” relies heavily on the concept of regular polygons, as it provides a systematic approach to understanding and calculating angle measures in regular polygons. • Properties of Regular Polygons: Regular polygons have several important properties that make them useful for solving geometry problems. These properties include: □ All sides are equal in length. □ All angles are equal in measure. □ The polygon can be inscribed in a circle. □ The polygon can be circumscribed about a circle. • Angle Measures in Regular Polygons: The sum of the interior angles of a regular polygon with ‘n’ sides is given by the formula (n-2) * 180 degrees. The measure of each interior angle can be found by dividing the sum of the interior angles by the number of sides. The measure of each exterior angle is equal to 360 degrees divided by the number of sides. • Applications of Regular Polygons: Regular polygons are used in a variety of applications, including architecture, engineering, and design. For example, regular polygons are used in the design of buildings, bridges, and other structures. They are also used in the design of logos, patterns, and other decorative elements. In conclusion, regular polygons are an important concept in geometry, particularly for solving the “71 interior and exterior angles homework answer key.” Their symmetry and predictable properties make them useful for a variety of applications in mathematics, engineering, and design. Irregular polygon The concept of irregular polygons is closely connected to the “71 interior and exterior angles homework answer key” because it involves understanding the properties and angle measures of polygons with unequal sides and angles. Irregular polygons present a more complex scenario compared to regular polygons, where all sides and angles are equal. The key to solving problems involving irregular polygons is to recognize that the sum of the interior angles is still given by the formula (n-2) * 180 degrees, where ‘n’ is the number of sides. However, since the sides and angles are not equal, determining the measure of each individual angle requires a different approach. In some cases, it may be possible to identify certain properties or symmetries within the irregular polygon that can help in calculating the angle measures. For instance, if the polygon has any parallel sides or congruent angles, these properties can be exploited to simplify the problem. Understanding irregular polygons is essential in various fields, such as architecture and design, where shapes with unequal sides and angles are commonly encountered. Architects and designers use their knowledge of irregular polygons to create visually appealing and structurally sound buildings and objects. In conclusion, irregular polygons are an important aspect of the “71 interior and exterior angles homework answer key” because they provide a deeper understanding of angle measures in polygons with unequal sides and angles. This understanding is crucial for solving geometry problems and has practical applications in fields such as architecture and design. Frequently Asked Questions about “71 interior and exterior angles homework answer key” This section addresses common questions and misconceptions related to the topic of interior and exterior angles in polygons, as covered in the “71 interior and exterior angles homework answer key.” Question 1: What is the formula for finding the sum of interior angles in a polygon? Answer: The sum of interior angles in a polygon with ‘n’ sides is given by the formula (n-2) * 180 degrees. Question 2: How can I find the measure of an exterior angle in a polygon? Answer: The measure of an exterior angle is equal to 360 degrees divided by the number of sides in the polygon. Question 3: What is the relationship between an interior angle and its corresponding exterior angle? Answer: The sum of an interior angle and its corresponding exterior angle is always 180 degrees. Question 4: Can you explain the concept of regular polygons? Answer: A regular polygon is a polygon in which all sides and all angles are equal. Question 5: How do I calculate the measure of each interior angle in a regular polygon? Answer: The measure of each interior angle in a regular polygon can be found by dividing the sum of the interior angles by the number of sides. Question 6: What are some real-world applications of understanding interior and exterior angles in polygons? Answer: Understanding interior and exterior angles is essential in fields such as architecture, engineering, and design, where professionals use this knowledge to create structures, objects, and In conclusion, this FAQ section provides clear and concise answers to common questions about interior and exterior angles in polygons, helping to reinforce the concepts covered in the “71 interior and exterior angles homework answer key.” Transition to the next article section: Exploring the Importance of Polygons in Geometry Tips for Mastering “71 Interior and Exterior Angles Homework Answer Key” Understanding interior and exterior angles in polygons is a fundamental concept in geometry. To excel in this topic, consider the following tips: Tip 1: Grasp the Angle Sum Formulas – Memorize the formula for the sum of interior angles: (n-2) * 180 degrees, where ‘n’ is the number of sides in the polygon. – Remember that the sum of exterior angles in any polygon is always 360 degrees.Tip 2: Understand the Relationship between Interior and Exterior Angles – Recognize that the sum of an interior angle and its corresponding exterior angle is always 180 degrees. – Use this relationship to find missing angle measures when necessary.Tip 3: Identify Regular – Recognize that regular polygons have all sides and all angles equal. – Utilize the properties of regular polygons to simplify angle calculations.Tip 4: Practice with Various Polygons – Solve problems involving different types of polygons, including regular and irregular polygons. – This practice will enhance your understanding and problem-solving skills.Tip 5: Apply Real-World – Understand that interior and exterior angles have practical applications in fields like architecture and engineering. – Explore real-world examples to connect the concept with practical scenarios. Tip 6: Utilize Online Resources – Take advantage of online resources, such as videos, tutorials, and practice problems, to reinforce your learning. – Seek additional support and clarification when needed.Tip 7: Seek Clarification from Experts – If you encounter difficulties, don’t hesitate to ask your teacher, a tutor, or a peer for assistance. – Clarifying your doubts will strengthen your understanding.Tip 8: Review Regularly – Regularly review the concepts of interior and exterior angles to retain your knowledge. – This will help you perform better in assessments and apply the concepts effectively.By following these tips, you can improve your understanding of “71 interior and exterior angles homework answer key” and excel in your geometry studies. Transition to the conclusion: Mastering interior and exterior angles in polygons is crucial for success in geometry. By implementing these tips, you can enhance your problem-solving abilities and develop a strong foundation in this essential topic. In summary, understanding interior and exterior angles in polygons is a fundamental concept in geometry. The “71 interior and exterior angles homework answer key” provides a structured approach to mastering this topic, emphasizing the importance of angle sum formulas, the relationship between interior and exterior angles, and the significance of regular polygons. By implementing the tips outlined in this article, students can develop a strong foundation in this essential area of geometry. Regular practice, seeking clarification, and utilizing online resources will enhance problem-solving skills and foster a deeper understanding of interior and exterior angles. This knowledge will serve as a cornerstone for further exploration in geometry and related fields, equipping students with the tools to succeed in their academic and professional endeavors. 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✔ Weird universe printing due to variance Set Printing Universes. Set Universe Polymorphism. Set Polymorphic Inductive Cumulativity. Inductive Covariant@{+u} : Type@{u}. Section Univereses. Universe u v. Constraint u < v. (* <<========= <<<) Axiom co_u : Covariant@{u}. Axiom co_v : Covariant@{v}. Check (co_u : Covariant@{v}). ( co_u : Covariant@{v} : Covariant@{v} (* {} \|= u <= v ) wut ) Is something being printed incorrectly here? cc @Gaëtan Gilbert looks fine, what's the problem? Right but isn't the constraint u < v and not u <= v? Or am I confused? u <= v is redundant but that does not stop it from being printed preexisting constraints are not printed Ali Caglayan has marked this topic as resolved. Last updated: Oct 13 2024 at 01:02 UTC	{"url":"https://coq.gitlab.io/zulip-archive/stream/237656-Coq-devs-.26-plugin-devs/topic/.E2.9C.94.20Weird.20universe.20printing.20due.20to.20variance.html","timestamp":"2024-11-04T20:42:57Z","content_type":"text/html","content_length":"7377","record_id":"<urn:uuid:27f3083f-39e3-4d0d-8bfd-dd568c0dc9f3>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00573.warc.gz"}
exponential idle tips n ) By rejecting non-essential cookies, Reddit may still use certain cookies to ensure the proper functionality of our platform. The guide's content has been written by Snaeky and LE Baldy with contributions from the Exponential Idle community and the rest of the Exponential Idle Guides Team. In other words: lvl 1 after $\zeta$; lvl 2 after $\iota$; and lvl 3 after $\xi$ (the last variable. For the first prestige, you can expect to Prestige after 15 minutes, when Press question mark to learn the rest of the keyboard shortcuts. You can increase = Not knowing how to solve it, you make a small program that calculates it for you. You gave all you got for this project. The formula for acceleration is Pages that use a deprecated format of the math tags, Do Not Sell or Share My Personal Information. A group of frustrated students comes to you. 10 If you have any questions, many of those guides, sheets, and a couple calculators are owned and operated by me. {\displaystyle b} While Mathematics defines infinity as an abstract and unreachable number, infinity in this game changes over time. , Do not follow for strategies. The right side of the arrow is calculated using the values shown in the summary bar above the equation. Subreddit for the idle/incremental game Exponential Idle, Press J to jump to the feed. Contributions from The Amazing Community. 3 You don't like small talk, so you just nod, hoping he will leave soon. 25 10 The It is an exponential recursive equation. , we switch to a double logarithmic representation. You will not want to buy the Automation Speed upgrades until cheap compared to variable cost. You will max all star upgrades besides permanent levels (no attainable limit) and autosupremacy (only if you grind enough). ) e They dont provide much boost but are nice to have anyway. t They dont provide much boost but are nice to have anyway. Hey I just wanted to share some of the tools I've built to help me out, namely a "which theory should I push right now" excel sheet that takes the data from the plot on pg 4 of the Endgame Strategy guide, tabulates it, and uses that data to estimate tau/hr for each of your theories based on your current Tau. ) b The button will appear in the equation section. Since we are dealing with very large numbers, we need mathematical notation to simplify its representation. Yea good luck making that google sheet into a website unless your talking the calculator by itself. current number of students, number of stars, t, and f(t). This guide is currently undergoing change. t {\displaystyle 2^{{\bigl \lfloor }{\frac {x}{10}}{\bigr \rfloor }}} x 1 = Exponential Idle is a math-inspired incremental game available on Android and iOS. Ive just started t8, and the only thing I dont quite get in the guide is R9I dont understand what that means. However, you don't know if it converges to a finite value yet. You can either graduate students now or continue your project alone until more students want to join the team. r/ ExponentialIdle. e = To do so, you have to step through time by tapping the equation or simply let the time follow its course. It's time to end your sabbatical and get back to work. I have 6 Students right now and f(t) of 3239 so could get another 5 students for graduation and stuck if I should graduate or not. This is done for every new value of x and $dt$. ( ( 15 14 17 11. If you would like to contribute to the chart, when you graduate, please give us your data here. Your goal is to stack up money by taking advantage of exponential growth. The site is built using 11ty and hosted on , you need to cumulate money, i.e. There is a chance you get Autosupremacy before ee2000 if you star grind a lot. where x is the level preceding the one to be purchased, or equivalently These projects introduce a new parameter, ( Any leftover stars will go into permanent levels. So after the tick, the new value of In other words, maximize {\ displaystyle \psi } Anyway, just something I noticeddont want to seem ungrateful as all of these guides have been insanely helpful and clearly took a ton of work to put together. Want to see the responses? Each theory increases Graduation is the third prestige layer of the game. b Posted by 2 years ago. 276. pinned by moderators. {\displaystyle b} To do so, you have to step through time by tapping the equation or simply let the time follow its course. d log 10 . Sure, you progress. f t By accepting all cookies, you agree to our use of cookies to deliver and maintain our services and site, improve the quality of Reddit, personalize Reddit content and advertising, and measure the effectiveness of advertising. x . This will give you an estimated phitau, phi, and tau for a given f (t). ) Here are almost all of the available resources that are used in the Discord and Reddit. Reply. One equation. Any leftover stars will go into permanent levels. 2K subscribers Exponential Idle is just an idle clicker game taking the advantage of exponential growth. Theory Simulator: How to Read Results, Visualizing Variable Power Throughout the Game. 1 b We made EF to be balanced to e150 tau, as that is the new cap for custom theories, and, currently, is the fastest theory to get there. Requirement: Unlock the "Convergence Test" theory, a.k.a. You applied for the new grant and got it. ) . shows how much Exponential Idle is a math-inspired incremental game. {\displaystyle dt} ) d There was not much to explain as we can gain more as the time flies. {\displaystyle b} Keep in mind, strategies may change. Requirement: Launch the game for the first time. A successful career is ahead of you and you are now on your own. Thanks! You don't despair You just passed the last exam. If you have any questions, please ask us on the Exponential Idle Discord The way I'm understanding it right now is that the 'v' variable is giving 90% of my income and 'u' around 14. x 50.0 Subreddit for the idle/incremental game Exponential Idle, Press J to jump to the feed. 0.04 A theory has its own equation that generates its own currency, x It will also allocate a new currency, named , with which you can purchase new upgrades. A Supremacy restarts the game at I am trying to open some of the guides like the one to graduation but the links are broken. Requirement: Graduate new students twice. You are a bit disappointed since you cannot pay your rent with it, but you accept anyway. values from all theories are then multiplied to give the total , giving a big boost in progression. {\ displaystyle f(t)=\$ee200=10^{10^{200}}} I get logistics function is great to manually tap the c2 buy but sometimes you just want to leave something for 8hrs. These currencies are used to buy special upgrades. Join the community on Discord and Reddit! When the game is closed, you will get as many stars as if you were in game. 2 Put the extra stars into permanent levels into the last variable. d 300 After you obtain autoprestige, input the autoprestige equation. , and It's currently an excel sheet on my PC, but I would be willing to convert and share it if one of you guys is willing to host it (I don't want to risk linking my reddit account with one of my Google accounts). b https://web.mit.edu/jmorzins/www/greek-alphabet.html. The guide's content has been written by Snaeky and LEBaldy with 0 A professor you respect hands you a formula. T5s guide was great with how it gave a thorough breakdown of what to autobuy, what to buy manually, and when to buy things manually. {\displaystyle 2.3{\text{e}}6=2.3\times 10^{6}=2,300,000} You will not make it to autoprestige in this section unless extreme grinding but is worth the cost if you keep some variables. It has averages on different Tau-levels, Which is good to leave overnight? % In other words: lvl 1 after $\zeta$; lvl 2 after $\iota$; and lvl 3 after $\xi$ (the last variable. Anyway later that day, a student asks you if he can start a project on chaos theory. d {\displaystyle c_{1}} Exponential Idle Wiki is a FANDOM Games Community. 2 It is to note that y factor upgrades are a bigger overall boost than, In the case that you are past the visible cost of a. Accepted format are the same as the one used in the UI. The highest achievement requires 10 tap stars which takes on average 25,000 taps, but this can very drastically depending on luck. We have a tau tracker sheet that let's you track how fast you gain tau and will compare you to other players. A simple way of phrasing it is as repeated addition of the product of $xdt$. For your f(t), input the number after the ee in the top-left corner. d b ( Guides copyright LEBaldy, Snaeky, and the rest of the Ex Guides Team. This upgrade only has value if you continuously and consistently use it. gameBaseReward + Hi are there any guides about starting the game? Past infinity, you will be able to purchase an upgrade that modifies the equation, which gives a significant boost in progression. 1 Submit it to us. You go back to the drawing board and rework the equation A chapter of your life finally ended. t {\displaystyle f(t)} {\displaystyle b2^{\ alpha x}\!,\,\alpha =\log _{2}a} However, you do not have any other parameter left to play with. You will want to skip this upgrade until you get to ee200 where you are forced to supremacy whether or not you obtained the $y^{1.6}$ supremacy upgrade beforehand. You cannot apply for it yet. Secret Achievements \| Exponential Idle Wiki \| Fandom in: Gameplay Secret Achievements View source This page will be used to input Secret Achievements as the community finds them. 14 , Everything I can find here is only talking about things after that. 0.02 ) Guides for Exponential Idle hosted at https:// exponential-idle-guides.netlify.app/. However, theories are not influenced by the parameters of the main game. Just disable auto buy for it alone and buy it separately. ( starChance log ) ) d f The site is built using 11ty and hosted on Netlify. Your data will be put into a public database that will help us see how fast the average player progresses. = Once you have run the command, visit http: //localhost:8000. First, you will get the 'Buy All' button that buys all affordable items. {\displaystyle db} Ad-bonus should be checked if you have the ad-bonus active. 10 10 f You can also play minigames, unlocked using stars, which rewards you some amount of stars once you succeed, depending on the difficulty. {\displaystyle db} Theories can be seen as smaller idle games. 1. The check for prestige is done along with the auto buyers. Thanks for checking out our guide. This will tell you how to optimize your stars. The bar below the equation shows the Prestige ( Your goal is to stack up money by taking advantage of exponential growth. You tell them to try something different if they think they can do better. If you think you can compete, send in your values to my DMs. Was it worth it? theory 9. After some time, you will be able to Prestige within a couple of minutes, multiplying b by 10 or even 100. ( The beginning. That sheet has 300+ hours into it and ~200+ hours into the calculator (for the python not the one on the sheet). {\displaystyle (10+x{\bmod {1}}0)2^{{\bigl \lfloor }{\frac {x}{10}}{\bigr \rfloor }}-9} Will output optimal graduation mark based on current students, phi, and tau values. {\displaystyle \tau _{i}} + You can buy variables and permanent levels while you wait. f You got a position as an assistant professor in a renowned university. I'm just really confused how I've barely progressed, while he's gone so insanely far ahead. e by 1. Scan this QR code to download the app now. e {\displaystyle f(t)=10,b=1,x=2,dt=3} 0.001 Keep in mind, strategies may change . {\displaystyle ba^{x-1}} ) Yes, it was. Will output estimate PhiTau, Phi, and Tau values needed to reach an input F(t). is how much No description, website, or topics provided. Focus is on buying accel button if you will use it then variables. , e using the following formula: d The cost of these purchases are driven by a double exponential model, which follows the formula Is it? to progress in the main game. 2 {\displaystyle b} , You will continue to unlock variables and permanent levels when cheap as you go. For more information, please see our 5.1k members in the ExponentialIdle community. Hold Infinity in the palm of your hand As for strategies, q1 at an 1/10 ratio and a1 at 1/4 will help a lot. t What a journey it has been. Theories ended up being quite fruitful. & 4 More. This post will have the guides that were created by myself and Baldy, the simulator (sim) by Antharion, and the calculator by Eaux. t You can cumulate rewards by watching more than one ad. , where gameBaseReward is the number of stars given by a set of game and difficulty initially (updated on 2020-08-05). will be 4034.29. d You are gaining confidence. If either goes to 0, q doesn't increase much, if at all. x t . b 2 {\displaystyle b=0.001} Will output estimate PhiTau, Phi, and Tau values needed to reach an input F(t). 9 Requirement: Supremacy after reaching the first infinity (f(t) = $ee200). hosted at https://exponential-idle-guides.netlify.app/. For example, if you reached Then, there is the auto prestige that will perform a prestige as soon at the ratio db/b is above the given ratio in the auto prestige settings. b When you collect a star, the star icon will be highlighted. Congratulations! {\displaystyle db} You invested so much time in it. It explains everything that it is saying. , and stars) follow the usual subtractive cost model. b or equivalently But that's OK. Research is always an ongoing process, and your committee knows it. {\ displaystyle db} Recovery after a prestige is standard at spamming all variables and buying upgrades occasionally ($\mu$ upgrades instantly). = b There was not much to explain as we can gain more as the time flies. ( The first variable is free. "Who is it that can tell me who I am?" Supremacy currency is calculated, based on cumulative ( This website contains the guides that were created by Snaeky and regularly, not if you only use it once in a while. t ) {\displaystyle f(t)} The increase of It gives an x2.85 boost to $dt$ and game progress if you max out the 1 hour cap every time (x3.17 cap). . a d ( f is calculated: d Thanks for the handy resources! Daily updated and collected data from the android leaderboards about F(t) with useful graphs for growth and comparison. By accepting all cookies, you agree to our use of cookies to deliver and maintain our services and site, improve the quality of Reddit, personalize Reddit content and advertising, and measure the effectiveness of advertising. You reached a higher value, but still far from infinity. I'm going to try to post a formatted table below this that may show what I mean. Some of my second propagations use slightly different encoding than the ones in the guide (for no particular reason except that was what I learned), but at this point it would be detrimental to my muscle memory for me to switch and the difference in times would be minimal.I, uh, play a lot of hard arrow (too much) and my times have decreased over time. Leaderboards for highest and publication multi of each theory, highest positive and negative of each lemma, highest overall and minigame stars, and a monthly updated cross platform F(t) rankings. Requirement: Complete the "Convergence Test" theory, a.k.a. You can perform change of variables to accelerate the process, buy upgrades, and unlock achievements while earning virtual money. I thought, that since it's an exponential game, I would get to that point in a couple days, after the lag from afking, but no, even not I've only got to 1.3e16 supremacy coin, and he's bought all the x's and has had students for a few days! Is it a problem only for me or for everyone? If you want to track your daily tau gains and contribute to daily tau rates graphs, request for access on this sheet. You now have a deeper understanding of infinity. ) + Some of my second propagations use slightly different encoding . {\displaystyle dt} (first) Each listed theory offers the first level of its first upgrade for free, transforming the formula into , and the left arrow represents the update. upgrade start from value 1 instead of 0 unless it is (first), transforming the formula for total value into 1000 Your goal is to stack up money by taking advantage of exponential growth. 10 You thought this problem could be solved within a week. 400 ( For prestige and supremacy upgrades, the cost of purchases are driven by an exponential model, which follows the formula {\displaystyle \psi } , You have a feeling that this will finally solve your problem. I would highly highly suggest focusing and learning hard arrow puzzle if you plan on playing minigames for stars as it is far and above the best stars/time. t Welcome to Exponential Idle, a math-inspired incremental game. During your acceptance speech, you praise your students for their hard work and tell how you always believed in them and their ideas. a component that increases as the level of the variable increases. This is a site for guides for Exponential Idle. Reply. {\displaystyle \varphi } Exponential Idle Basics 1 to ee2000 Introduction to Graduation F (t)ee2000 to F (t)ee5000 Theories 1-4 Theories 5-8 Theory 9 - Endgame How to Read the Sim Theory Sim Strategies List Minigame Guide Custom Theory Guide If you would like to make any suggestions to the guide website, please fill out this form. You remember that your colleagues talked to you about a grant that would allow you to progress even further in your research. Ideas start to pop when looking at the night sky You have been working on this project for a while now. Here is a graduation calculator that will tell you how far you can push with the amount of phitau that you have. and update the function value using the equation. . An annoying colleague of yours comes to your office and starts talking about the weather and how unpredictable it is. t He asks you if it converges to a finite value. If you do end up buying some then buy variable then upgrade autobuyer. You will not want to buy the Automation Speed upgrades until cheap compared to variable cost. {\displaystyle a} After some time, you can wait until it multiples by 10 or more. t 6 If you want to track your daily tau gains and contribute to daily tau rates graphs, request for access on this sheet. He keeps talking. When you can buy the autobuyers, buy the variable autobuyer then the upgrade autobuyer. You can perform change of . This is flexible and can change based on how fast you are moving and preference. mod theory 9. After, dt becomes too large for your taps to make a worthy and significant boost to progress. This guide is currently undergoing change. x Your goal is to stack up money by taking advantage of exponential growth. t ( f Once you reach this number, you'll be offered to perform a Supremacy to increase the infinite value to = 2 or Exponential Idle Reddit. {\displaystyle dt} The guide has a Theory Strategy List if you need to know a strategy. Convergence tests can indeed be useful to test the convergence of your equation. , into the main equation. t ". These are the guides by Baldy and Myself to the theories: If you would like to make any suggestions to the guide website, please fill out this form. x Any leftover stars will go into permanent levels. Means a different strategy was usedT4 my data used T4C3d, sim used T4C123dT6 my data used T6NoC34d, sim used T6NoC345dT8 my data used T8R34d, sim used T8R45dI'm not 100% certain of the difference in these strats, so I can't exactly speak to what is going on, but my sheet gives way less extraneous information and takes a small fraction of the time to run, let alone parsing and implementation by the user. For example, Requirement: Graduate after unlocking the first theory. They dont provide much boost but are nice to have anyway. Storage mechanism for saves due to game not having cloud save. Your professors see a bright future ahead of you. You have been nominated to be the head of the department and you got the position. For your t, enter the number in the top left corner. Use the price of the next cheapest f (t) purchase. . x e {\displaystyle b} If you have any questions, please feel free to ask. Maintain your finger on the button to multiply the value of dt by some amount, which provides a boost in progression. The updated sim by XLII is here if you would like to see the rates of all your theories. Take a look. When you obtain autoprestige, input the autoprestige equation. x A tick is automatically generated every tenth of a second, which increases log I just started this game a couple days ago. , psi) currency that you can spend. b To increase theory 8. 2 f changes when anything changes. b Performing regular Prestige is the only way to progress further. {\displaystyle f(t)=\$ee400} , mu) and Supremacy ( You sit on your chair and when a student asks you a question, you just have to answer: "It's your job to figure this out." Within each of these sections there are idle, active, and general strategy subsections for differing playstyles. {\displaystyle \tau _{1}} 50000 The displayed score corresponds to the current 'ee' income. You have a team of bright students that come up with clever ideas and you are very excited about what's next. = {\displaystyle t} It starts at 0 and increases by one at level 10 and 25 (after buying 10 and 25 times). x For example, ( For variable purchase, the following table of a and b can be used: For regular upgrade purchase, the following table of 3 You start packing your stuff and say goodbye to your students. Really? You signed in with another tab or window. 10 Values written in scientific notation increase by Buy All Button (Single purchase; 15 stars), Acceleration Button (Single purchase; 50 stars), Variable Autobuyer (Single purchase; 200 stars; requires Buy All Button), Upgrade Autobuyer (Single purchase; 200 stars; requires Buy All Button), x2 Automation / s: Multiplies the rate of automation by 2 (3 purchases; prices 500, 1250, 2000 stars respectively; requires Variable Autobuyer OR Upgrade Autobuyer), Auto Prestige (Single purchase; 500 stars; requires Variable Autobuyer AND Upgrade Autobuyer), Permanent variable levels (infinitely buyable, increases with each level bought, requires variable u), a is based on a table for each variable (see below). b Want to see the responses? Manage all your favorite fandoms in one place! , t Some guides for a few of the theories and other things you might like. Play Exponential Idle, a math-inspired incremental game. Bright students that come up with clever ideas and you are moving and preference = Once you have a understanding. Are nice to have anyway slightly different encoding tell how you always believed in them and their ideas a you... New value of x and \ ( x * dt\ ). might like d 300 you! 'Ee ' income the displayed score corresponds to the current 'ee ' income will as! The only way to progress a team of bright students that come up with ideas. Guides about starting the game, when you can perform change of variables to accelerate process... Is here if you want to buy the autobuyers, buy the Automation Speed upgrades until cheap compared to cost. We can gain more as the level of the main game 'm going to to. And Reddit but you accept anyway x any leftover stars will go into permanent levels ( no attainable )! Give us your data will be able to Prestige within a week autosupremacy! And how unpredictable it is game taking the advantage of Exponential growth https: //exponential-idle-guides.netlify.app/ variables and permanent levels cheap... And will compare you to progress Convergence Test '' theory, a.k.a you need cumulate... Sky you have run the command, visit http: //localhost:8000 equation section if either goes to,! All of the department and you got the position but are nice to have anyway those guides,,! } Exponential Idle is a FANDOM Games Community the `` Convergence Test '' theory, a.k.a position as an and! Into the last exam the updated sim by XLII is here if you have a deeper understanding of infinity ). Owned and operated by me into a public database that will help us see how fast the average progresses! The third Prestige layer of the main game sky you have $ ee200 ). upgrade! 2020-08-05 ). scan this QR code to download the app now goes to 0, q doesn & x27! Just disable auto buy for it alone and buy it separately, input the autoprestige.... Last variable follow the usual subtractive cost model with the amount of ! The ExponentialIdle Community that means and starts talking about the weather and unpredictable... 1 } } Exponential Idle, active, and tau for a while now enter the number in the left... Up with clever ideas and you are moving and preference Thanks for the new and... Variables to accelerate the process, and general strategy subsections for differing.! Idle, a student asks you if it converges to a finite value yet ee2000 if you you! Mechanism for saves due to game not having cloud save and Reddit python. Either graduate students now or continue your project alone until more students want track! Focus is on buying accel button if you star grind a lot about a grant that would allow to! Follow the usual subtractive cost model ) and autosupremacy ( only if have. Useful graphs for growth and comparison the parameters of the available resources that are used the... 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Calculating The Surface Area Of A Triangular Pyramid: A Comprehensive Guide - LearnAboutMath Calculating the Surface Area of a Triangular Pyramid: A Comprehensive Guide As a student or professional in mathematics or engineering, you may need to find the surface area of a triangular pyramid. The surface area of a triangular pyramid is the total area that covers all the faces of the pyramid, including the base and the lateral faces. This guide will help you understand the formula for finding a triangular pyramid’s surface area, provide step-by-step instructions, and offer tips and tricks to help you avoid common mistakes. Introduction to the Surface Area of a Triangular Pyramid Before we dive into the formula for finding the surface area of a triangular pyramid, let’s first understand what a triangular pyramid is. A triangular pyramid is a four-faced solid figure with a triangular base and three triangular faces at a common vertex. The triangular faces are called the lateral faces, and the pyramid height is the perpendicular distance from the vertex to the base. The surface area of a triangular pyramid is the sum of the areas of its faces, including the area of the base. The formula for finding the surface area of a triangular pyramid is: Surface Area = Base Area + (1/2 x Perimeter of Base x Slant Height) Understanding the Formula for the Surface Area of a Triangular Pyramid To understand the formula for finding the surface area of a triangular pyramid, let’s break it down into its components. The surface area is the sum of the base area and the lateral area. The base area is simply the area of the triangular base, which can be found using the formula for the area of a triangle: Base Area = 1/2 x Base x Height The lateral area is the sum of the areas of the three triangular lateral faces. The lateral faces are congruent triangles, so they all have the same area. The area of one of the lateral faces can be found using the formula: Lateral Area = 1/2 x Perimeter of Base x Slant Height The slant height is the distance from the vertex to the midpoint of one of the sides of the base, and the perimeter of the base is the sum of the lengths of all the sides. Step-by-Step Guide on How to Find the Surface Area of a Triangular Pyramid Now that we understand the formula for finding the surface area of a triangular pyramid, let’s go through a step-by-step guide to help you calculate it. Let’s use the following dimensions for our • Base length: 4 cm • Base height: 3 cm • Slant height: 5 cm • Step 1: Find the area of the base Using the formula for the area of a triangle, we can find the area of the base: • Base Area = 1/2 x Base x Height = 1/2 x 4 cm x 3 cm = 6 cm^2 • Step 2: Find the perimeter of the base. • The perimeter of the base is simply the sum of the lengths of all the sides. Since we have a triangular base, the perimeter is: • Perimeter of Base = Side 1 + Side 2 + Side 3 = 4 cm + 4 cm + 4 cm = 12 cm Step 3: Find the lateral area Using the formula for the lateral area, we can find the area of one of the lateral faces: Lateral Area = 1/2 x Perimeter of Base x Slant Height = 1/2 x 12 cm x 5 cm = 30 cm^2 Since there are three lateral faces, the total lateral area is: Total Lateral Area = 3 x Lateral Area = 3 x 30 cm^2 = 90 cm^2 • Step 4: Find the surface area Now that we have the area of the base and the total lateral area, we can find the surface area of the triangular pyramid: • Surface Area = Base Area + Total Lateral Area = 6 cm^2 + 90 cm^2 = 96 cm^2 Therefore, the surface area of the triangular pyramid with the given dimensions is 96 cm^2 Example Problems and Solutions for Finding the Surface Area of a Triangular Pyramid Let’s go through some more example problems to help you practice finding the surface area of a triangular pyramid. Example 1: Find the surface area of a triangular pyramid with base length 6 cm, base height 4 cm, and slant height 8 cm. • Step 1: Find the area of the base Base Area = 1/2 x Base x Height = 1/2 x 6 cm x 4 cm = 12 cm^2 • Step 2: Find the perimeter of the base Perimeter of Base = Side 1 + Side 2 + Side 3 = 6 cm + 6 cm + 6 cm = 18 cm • Step 3: Find the lateral area Lateral Area = 1/2 x Perimeter of Base x Slant Height = 1/2 x 18 cm x 8 cm = 72 cm^2 • Step 4: Find the surface area Surface Area = Base Area + Total Lateral Area = 12 cm^2 + 72 cm^2 = 84 cm^2 Therefore, the surface area of the triangular pyramid with the given dimensions is 84 cm^2. • Example 2: Find the surface area of a triangular pyramid with base length 3 cm, base height 2 cm, and slant height 4 cm. • Step 1: Find the area of the base Base Area = 1/2 x Base x Height = 1/2 x 3 cm x 2 cm = 3 cm^2 • Step 2: Find the perimeter of the base Perimeter of Base = Side 1 + Side 2 + Side 3 = 3 cm + 3 cm + 3 cm = 9 cm • Step 3: Find the lateral area Lateral Area = 1/2 x Perimeter of Base x Slant Height = 1/2 x 9 cm x 4 cm = 18 cm^2 • Step 4: Find the surface area Surface Area = Base Area + Total Lateral Area = 3 cm^2 + 18 cm^2 = 21 cm^2 Therefore, the surface area of the triangular pyramid with the given dimensions is 21 cm^2. Tips and Tricks for Solving Surface Area of a Triangular Pyramid Problems Solving problems related to the surface area of a triangular pyramid can be challenging. Here are some tips and tricks that can help you: • Draw a diagram: Drawing a diagram can help you visualize the problem and identify the dimensions of the triangular pyramid. • Label the dimensions: Labeling the dimensions in your diagram can help you keep track of the variables in the formula. • Use the correct formula: Make sure you use the correct formula for the surface area of a triangular pyramid. • Check your units: Make sure your units are consistent throughout the problem. • Practice, practice, practice: The more practice problems you solve, the more comfortable you will be with the formula and the process. Common Mistakes to Avoid When Calculating the Surface Area of a Triangular Pyramid When calculating the surface area of a triangular pyramid, there are some common mistakes that you should avoid: • Need to include the area of the base in the total surface area. • Using the wrong formula for the lateral area. • Using the wrong dimensions in the formula. • Forgetting to convert units to the same system before calculating. • Rounding too early in the calculation process. Applications of the Surface Area of a Triangular Pyramid in Real Life The surface area of a triangular pyramid has many applications in real life. Here are some examples: Architecture: The surface area of a triangular pyramid is used in the design and construction of roofs and buildings with pyramid-shaped structures. Packaging: The surface area of a triangular pyramid is used in the design and manufacturing of triangular pyramid-shaped packages and boxes. Geometry: The surface area of a triangular pyramid is used in the study of geometry and calculus. Surface Area of Pyramid Worksheet for Practice In addition to the formula we discussed earlier, there are alternative methods for finding the surface area of a triangular pyramid. One such method involves using the Pythagorean theorem to find the slant height and then using the formula for the area of an isosceles triangle to find the area of the lateral faces. However, the formula we discussed earlier is more commonly used and Alternative Methods for Finding the Surface Area of a Triangular Pyramid In addition to the formula we discussed earlier, there are alternative methods for finding the surface area of a triangular pyramid. One such method involves using the Pythagorean theorem to find the slant height and then using the formula for the area of an isosceles triangle to find the area of the lateral faces. However, the formula we discussed earlier is more commonly used and Conclusion and Summary of Key Takeaways In conclusion, the surface area of a triangular pyramid is the sum of the areas of its faces, including the area of the base. The formula for finding the surface area of a triangular pyramid is Surface Area = Base Area + (1/2 x Perimeter of Base x Slant Height). To find the surface area, you need to find the area of the base, the perimeter of the base, and the slant height. Practice is key to mastering the formula, and avoid common mistakes such as using the wrong formula or dimensions. The surface area of a triangular pyramid has many real-life applications in architecture, packaging, and geometry. We hope this comprehensive guide has helped you understand and master the surface area of a triangular pyramid.	{"url":"https://learnaboutmath.com/surface-area-of-a-triangular-pyramid/","timestamp":"2024-11-03T19:05:10Z","content_type":"text/html","content_length":"339089","record_id":"<urn:uuid:4495a381-9cdc-4341-bf53-6bff6fe5106a>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00136.warc.gz"}
Optimum detection and signal design for v.l.f. channels A new generalized model for atmospheric radio noise is briefly described and justified by comparison with observed probability distributions. A special case of this generalized model is then compared to the observed noise statistics at the very low frequency end of the spectrum. This model is then applied to the detection of known signals in the presence of noise to determine the optimal receiver structure. The performance of the detector, specified by the upper bound on the probability of error, is assessed and is seen to depend on the signal shape, the time-bandwidth product, and signal-to-noise ratio. The optimal signal to minimize the probability of error is then determined. Radio and Electronic Engineer Pub Date: September 1976 □ Atmospherics; □ Radio Receivers; □ Signal Detection; □ Very Low Frequencies; □ Vlf Emission Recorders; □ Noise Spectra; □ Optimization; □ Pulse Communication; □ Signal To Noise Ratios; □ Communications and Radar	{"url":"https://ui.adsabs.harvard.edu/abs/1976RaEE...46..401P/abstract","timestamp":"2024-11-14T21:39:11Z","content_type":"text/html","content_length":"34904","record_id":"<urn:uuid:4e6adc83-0173-4695-8a04-a7545626ee80>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00844.warc.gz"}
Contrasting multi-level relationships between behavior and body mass in blue tit nestlings Data files Feb 17, 2020 version files 960.28 KB Repeatable behaviors (i.e. animal personality) are pervasive in the animal kingdom and various mechanisms have been proposed to explain their existence. Genetic and non-genetic mechanisms, which can be equally important, predict correlations between behavior and body mass on different levels (e.g. genetic, environmental) of variation. We investigated multi-level relationships between body mass measured on weeks 1, 2, and 3 and three behavioral responses to handling, measured on week 3, and which form a behavioral syndrome in wild blue tit nestlings. Using 7 years of data and quantitative genetic models, we find that all behaviors and body mass on week 3 are heritable (h^2= 0.18-0.23) and genetically correlated, whereas earlier body masses are not heritable. We also find evidence for environmental correlations between body masses and behaviors. Interestingly, these environmental correlations have different signs for early and late body masses. Altogether, these findings indicate genetic integration between body mass and behavior, and illustrate the impacts of early environmental factors and environmentally-mediated growth trajectory on behaviors expressed later in life. This study therefore suggest that the relationship between personality and body mass in developing individuals is due to various underlying mechanisms which can have opposing effects. Future research on the link between behavior and body mass would benefit from considering these multiple mechanisms simultaneously. Data collection Data used for these analyses was collected between 2012 and 2018 in a wild population of blue tits breeding in nest boxes in south-west Finland (Tammisaari, 60°01′N, 23°31′E). This population has been monitored yearly since 2003 during the breeding season (first broods from end of April to end of June), following a standard protocol for nest box-breeding passerines (Brommer and Kluen 2012). Nest boxes were visited weekly in May to assess laying dates, clutch sizes and estimate expected hatching dates. Nests from first broods were visited daily starting from their expected hatching date until at least one hatchling was observed (D0). Two days after the hatching day (D2), nestlings were weighed (using a scale with 0.1g precision) and their nails were clipped following unique combinations to allow their identification at later stages of development. Parents were caught and identified when nestlings were at least 5 days old. One week later (D9), nestlings were weighed and banded by putting a metal ring with a unique alphanumeric code on their left leg after their nail code was read. A few days before fledging (D16), nestlings were transferred all together in a large paper bag and various measurements of each nestling were taken following a fixed sequence (cf. Brommer and Kluen 2012). Firstly, each individual was held still on its back in the observer’s palm. Stopwatch was started and the number of struggles during 10 seconds was counted. Docility was expressed as -1 time this number/second. Immediately after this 10 seconds assay, the time each bird took to take 30 breaths was measured twice using a stopwatch. Breath rate was calculated as 30 divided by the average of these two measures and expressed in number of breath/second. A higher breath rate reflects a higher stress response to handling (Carere et al. 2004). The bird’s right tarsus and head-bill length were then measured using a digital sliding caliper (0.1mm accuracy) before measuring its wing and tail length using a ruler (1mm accuracy). During these morphometric measurements, the bird’s aggressive behavior (struggling, flapping wings) was observed and a handling aggression score (1-5) was given to the bird. This score, which is 1 for a completely passive bird and 5 for a bird struggling continuously, reflects the time it takes for each bird to calm down during these measurements. Each nestling was then weighed using a Pesola spring balance (0.1g accuracy) and then placed in a second large paper bag where measured nestlings remained until the entire brood was processed and put back to its nest. Pedigreed population Phenotypic data was available for 5404 individuals, which were connected through a social pedigree based on social parenthood. The pruned pedigree, which retains only informative individuals holds record for 6205 individuals, 5464 maternities, 5107 paternities, 25107 full sibs, 43411 maternal sibs, 38543 paternal sibs, 18284 maternal half-sibs, 13416 paternal half-sibs, a mean family size of 10.8, a mean pairwise relatedness of 2.54e-3 and a maximum pedigree depth of 11. In this population, 11% to 22% of offspring produced annually were sired by extra-pair males (unpublished data). Based on simulations (Charmantier & Réale 2005), such level of error in paternity assignment is unlikely to cause substantial biases in quantitative genetic parameters when using the social pedigree. Quantitative genetic analyses Quantitative genetic analyses were carried out using animal models, which are mixed effects models that use the relatedness matrix derived from a population pedigree to estimate additive genetic (co) variance (Wilson et al. 2010). Univariate animal models assuming Gaussian distribution were run for each trait separately to estimate their variance components and their ratios to phenotypic variance. Then, a multivariate animal model was run for all six traits to estimate their correlation on various levels. In all models, brood identity, maternal identity, and additive genetic effects were fitted as random effects to estimate (co)variance due to common environment, maternal, and additive genetic effects while fixed effects included time of measurement in minutes and year as continuous and categorical covariates, respectively. For behavioral responses, fixed effects also included observer identity and handling order (continuous). In univariate models, box was fitted as an additional random effect to account for consistent differences between territories. Animal models were solved using Restricted Maximum Likelihood (REML), and implemented in ASReml-R version 3 (Butler et al. 2009; VSN International, Hemel Hempstead, U.K.). Statistical significance of fixed and random effects was tested using conditional Wald F tests and likelihood ratio tests (LRT) with one degree of freedom, respectively. Heritability (h^2) of each trait was calculated as the ratio V[A] /V[P] where V[P], the phenotypic variance, is defined as the sum of the REML estimates of additive genetic effects, maternal, common environment effects and residuals (V[A] , V[PE], and V[R] respectively) and is conditional on the fixed-effect structure of the model. Correlations between pairs of traits on each level were calculated based on the corresponding covariance matrix estimated by the multivariate animal model. In this multivariate model, each response was corrected by the same fixed effects as in its corresponding univariate model. Random effects box and mother identities were not fitted in this model due to not being estimable for the former, and due to model convergence issues for the latter. Three 4-trait animal models including maternal effects were however fitted to verify that the relationships between each separate mass and behavior on other levels were consistent with the relationships found using the 6 trait animal model excluding maternal effects. Standard errors (SE) of variance ratios and correlations were approximated using the delta method (Fischer et al. 2004). Coefficients of variation (CV=sd*100/mean) were calculated for the different variance components in. All statistical analyses were performed in R (R development core team 2019). Residuals of all animal models were approximately normally distributed (Shapiro-Wilk test values >0.92, Figure S1). Structural equation models SEMs were used to investigate, on each level, different hypotheses for the relationships between behavior and body masses at different ages (Figure 1). SEMs have been previously used in behavioral studies to explore the structure of behavioral syndromes using predicted individual values derived from mixed models (Dochtermann & Jenkins 2007, Dingemanse et al. 2010). Here, each covariance matrix estimated by the multivariate model was converted into a correlation matrix, which was used as input data (cf. Class, Kluen and Brommer 2019, Moirón et al. 2019). In all SEMs variance of latent factors was fixed to 1. Because a correlation matrix was used as input data, the residual variance of each indicator (the variance unexplained by the latent factor) was fixed to 1 minus its squared factor loading. Each SEM was fitted in R using the package “lavaan” (Rosseel 2012). Sample size in these models was nominally set at 642 for the common environment level (number of broods) and 5404 (number of individuals) for the residual level and the all SEMs were compared using AIC. The sample size in a SEM will not affect the inferred loadings or correlations between latent variables but can impact their uncertainty and the model AIC. We verified that the model rankings were similar if sample size was assumed to be lower. Parametric bootstrap simulations were conducted to estimate median and 95% confidence intervals (CI) the model’s loadings and assess model selection uncertainty. Because our findings indicated that the genetic covariance matrix was much reduced (see results), we focused on the common-environment and residuals covariances. Multivariate data for the 6 traits was simulated 1000 times using the inferred common environment and residual covariance matrices to generate a simulated dataset of the same dimension as the observations. Each simulated data was analyzed using a multivariate mixed model. At each iteration, and on each level, SEMs were run based on the estimated correlation matrices and ranked by AIC. Model selection uncertainty was assessed by calculating bootstrap selection rates (Lubke et al. 2017), which indicate whether model ranking is consistent to sampling variability. The selection rates have no a priori cut-off value for “significance”, but instead provide an indication of model selection uncertainty (Lubke et al. 2017). For example, a selection rate of a SEM of 50% would indicate it is the top model in half the simulations, and 100% would suggest consistent support for this one SEM hypothesis over the others in all simulations. R code for performing SEMs and simulations are provided in Text S1.	{"url":"https://datadryad.org/stash/dataset/doi:10.5061/dryad.9ghx3ffdj","timestamp":"2024-11-04T01:00:36Z","content_type":"text/html","content_length":"49597","record_id":"<urn:uuid:34f862ef-edca-4ad4-913c-7c773e969cc6>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00007.warc.gz"}
See primary documentation in context for routine pick multi pick($count, @list --> Seq:D) multi method pick(List:D: $count --> Seq:D) multi method pick(List:D: --> Mu) multi method pick(List:D: Callable $calculate --> Seq:D) If $count is supplied: Returns $count elements chosen at random and without repetition from the invocant. If is passed as $count, or $count is greater than or equal to the size of the list, then all elements from the invocant list are returned in a random sequence; i.e. they are returned shuffled. In method form, if $count is omitted: Returns a single random item from the list, or Nil if the list is empty say <a b c d e>.pick; # OUTPUT: «b␤» say <a b c d e>.pick: 3; # OUTPUT: «(c a e)␤» say <a b c d e>.pick: ; # OUTPUT: «(e d a b c)␤» As of the 2021.06 release of the Rakudo compiler, it is also possible to specify * (aka HyperWhatever) as the count. In that case, .pick will start picking again on the original list after it has been exhausted, again and again, indefinitely. say <a b c>.pick(*).head(10); # OUTPUT: «((a c b c a b b c a b))␤» See primary documentation in context for method pick multi method pick($count = 1) Returns $count elements chosen at random (without repetition) from the set. If is passed as $count, or $count is greater than or equal to the size of the set, then all its elements are returned in random order (shuffled). See primary documentation in context for routine pick multi method pick(Bool:U: --> Bool:D) multi method pick(Bool:U: $count --> Seq:D) Returns a random pick of True and/or False. If it's called without an argument then it returns just one pick: say Bool.pick; # OUTPUT: «True␤» If it's called with a $count of one then it returns a Seq with just one pick: say Bool.pick(1); # OUTPUT: «(False)␤» If $count is * or greater than or equal to two then it returns a Seq with two elements -- either True then False, or False then True: say Bool.pick(); # OUTPUT: «(False True)␤» See primary documentation in context for method pick multi method pick(Baggy:D: --> Any) multi method pick(Baggy:D: $count --> Seq:D) Like an ordinary list pick, but returns keys of the invocant weighted by their values, as if the keys were replicated the number of times indicated by the corresponding value and then list pick used. The underlying metaphor for picking is that you're pulling colored marbles out a bag. (For "picking with replacement" see roll instead). If is passed as $count, or $count is greater than or equal to the total of the invocant, then total elements from the invocant are returned in a random sequence. Note that each pick invocation maintains its own private state and has no effect on subsequent pick invocations. my $breakfast = bag <eggs bacon bacon bacon>; say $breakfast.pick; # OUTPUT: «eggs␤» say $breakfast.pick(2); # OUTPUT: «(eggs bacon)␤» say $breakfast.total; # OUTPUT: «4␤» say $breakfast.pick(); # OUTPUT: «(bacon bacon bacon eggs)␤» See primary documentation in context for method pick Throws an exception. The feature is not supported on the type, since there's no clear value to subtract from non-integral weights, to make it work. See primary documentation in context for method pick multi method pick(::?CLASS:U:) multi method pick(::?CLASS:U: \n) multi method pick(::?CLASS:D: @pos) It works on the defined class, selecting one element and eliminating it. say Norse-gods.pick() for ^3; # OUTPUT: «Þor␤Freija␤Oðin␤» See primary documentation in context for method pick multi method pick(Range:D: --> Any:D) multi method pick(Range:D: $number --> Seq:D) Performs the same function as Range.list.pick, but attempts to optimize by not actually generating the list if it is not necessary. See primary documentation in context for method pick multi method pick(--> Any) multi method pick($n --> Seq) Coerces the invocant to a List by applying its .list method and uses List.pick on it. my Range $rg = 'α'..'ω'; say $rg.pick(3); # OUTPUT: «(β α σ)␤»	{"url":"https://doc.perl6.org/routine/pick","timestamp":"2024-11-11T13:05:20Z","content_type":"text/html","content_length":"57011","record_id":"<urn:uuid:0b4c10b9-b3a2-4598-b99e-9738b763a870>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00188.warc.gz"}
Physics with an edge I've written a lot about why MiHsC is infinitely better than the ad hoc addition of dark matter to galaxies to make their spin agree with general relativity. There is also the empirical theory of MoND (Modified Newtonian Dynamics) which was invented by Mordehai Milgrom, in 1983. MoND is far less arbitrary than dark matter, and it fits disc galaxy rotations by empirically changing the dynamical laws at their edges. Much as I admired MoND, and it inspired me to develop MiHsC, I'd like to explain why MiHsC is much better because it doesn't need an adjustable parameter. This explanation may seem basic and obvious, but I do believe that this crucial advantage of MiHsC has not been appreciated. Imagine you have some data in a rough line on a graph (see the crosses on the graph) that you want to explain or model. As we know we can fit a straight line through them using the formula y=mx+b where x is the horizontal co-ordinate, y is the vertical co-ordinate, m is the slope of the line and b is the offset (changing the value of b allows us to shift the line up and down to fit the data (see the red lines on the graph). Now imagine you vary b again and again (the various red lines) until the line is aligned with the data and then you choose that line (say y=mx+a0) as the correct model. Would you go around enthusing about the great theory you have? No. It predicts the data, sure, but this is not so surprising because you chose the arbitrary value of a0 to make it so. I hate criticising MoND because its so much better than dark matter and at the time it was a bold and justified attack on the standard theory, and highlighted the odd number a0, but it works like the example above, because MoND has an arbitrary constant called a0 that is set completely arbitrarily to fit the galaxy rotation data. The a0 is the same for each galaxy, true, but there is no reason given why it should be that value (usually a0=2x10^-10 m/s^2). Now imagine a theory based on a mechanism that can only predict that y=mx+c (as a simple example) where c is the speed of light (a number which is solidly known and unfudgable) and this theory happens to fits the data first time (the blue line in the graph). This is infinitely better because no arbitrary human input is required. This then is like MiHsC, which does everything that MoND does but without the adjustable parameter. MiHsC's predictions are slightly different to MoND's. For example, MiHsC performs better for huge galaxy clusters and tiny dwarfs whereas MoND was 'tuned' with a0 for intermediate sized systems so does better for those, but both are within the uncertainty in the data, so far. Hopefully though you can see that MoND is not a theory (it's an empirical relation with an unexplained tuning parameter) whereas MiHsC is a theory and its inevitable agreement is a great advantage. McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. A&SS, 342, 2, 575-578. Preprint: It was just a bit over 10 years ago that I took the first step into the MiHsC paradigm, and my diary entry for that day is shown below. I remember excitedly sending an abstract off to the Alternative Gravities Workshop in Edinburgh, 2006, and speaking there later. I also remember being rather desperate to publish quickly for fear that someone else might have the same thought. It is quite amusing that a decade on, I'm still trying to persuade anyone at all to have the same thought! No professional physicist has understood MiHsC, as far as I know. Maybe a couple of mathematicians have. I'm left frustrated. I've published 11 papers and a book showing that MiHsC predicts galactic rotation and cosmic acceleration and other anomalies (eg: emdrive) in a beautiful and simple way and without any ad hoc adjustable parameters. This inevitability is a huge advantage, but seems not to move people who prefer to rely on the ad hoc explanation of dark matter. I get the impression of half-pursuading physicists occasionally, only for them to vanish. Critics never mention contrary data, but complain that I 'disagree with the old theory'. I always make the point that it is OK to disagree with the old theory if you agree with the data better than the old theory, but effectively they then reiterate that I disagree with the old theory. I've found that it is very important at this point not to go mad. The solution as ever is to predict something that dark matter cannot, and for that reason I've just submitted a paper on Milky Way dwarf satellite galaxies which, as usual, spin far faster than they should and the amounts of dark matter needed to hold them together are jaw-droppingly ridiculous. Also, yesterday feeling myself to be rather in a vacuum, or solitary confinement, I contacted Prof Stacy McGaugh who I met at the Alternative Gravity Workshop, asking for some, any, feedback. He asked me for a MiHsC prediction and I said 'concentric rings of apparent mass in low acceleration systems' (a prediction I made in my first paper in 2007, see the discussion part). He then replied saying that something like that has been seen (Jee et al., 2014) and the rings cannot sensibly be explained by dark matter (you'll see in the paper they propose one of the usual complex simulation-type explanations). So my next goal is to see if I can predict the ring's radius. I should have known in advance how hard it would be to change a paradigm, but the important thing, is to calmly focus on showing that MiHsC is simpler, more predictive and more beautiful than the other theories, as I believe it is by a mile. Having said that, MiHsC is the beginning of a shift to information physics, not the end, so there's plenty of scope for others to contribute and I hope they do. McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. Preprint: http://arxiv.org/abs/astro-ph/0612599 Jee et al., 2007. ApJ, 661, 728 http://iopscience.iop.org/article/10.1086/517498/meta;jsessionid=BB439BE3084D240817A269DE53396BA5.c3.iopscience.cld.iop.org My favourite physicist, even over Einstein and Newton, is Richard Feynman. I have always admired the work of the former two of course, but it was Feynman that convinced me that physics could be fun, and that in order to contribute you don't have to be somehow in touch with God, or superhuman. You just have to be a puzzled human being. I was pleased to discover this, since I happen to be such a human being. Feynman told a story in his book: Surely You're Joking Mr Feynman? (p81), in which he met a painter in a cafe. This painter claimed he could make yellow paint out of red and white paint. Feynman always loved practical guys and he wanted to believe him, but he was fairly sure that something was screwy. Surely mixing red and white paint would make pink? He asked the painter to demonstrate, so the guy started mixing white and red paint, and the result was always pink. Eventually the painter got annoyed: "Hm, I'll just add some yellow paint, to sharpen it up, and then it'll be yellow". "Aha!" said Feynman, "Sure you can get yellow if you add yellow!". Now forgive my boldness but I think dark matter physicists are doing something similar. Consider: we had general relativity in 1915, and this theory has predicted a few things well at high accelerations (close binary stars, gravitational lensing, GPS corrections), but it did not predict the rotation of any galaxies at their edges which are in a low acceleration regime (the edge stars all orbit far too fast) and since the cosmos is composed of nothing but galaxies this is a big deal. Also, general relativity did not predict cosmic acceleration. An even bigger thing to miss. Rather than dispute general relativity, as at least some of them should have, they have almost all added a lot of yellow paint: in the case of galaxies they have added huge amounts of dark matter arbitrarily, with the express purpose of making general relativity work. In the case of cosmic acceleration they add dark energy which is similarly arbitrary and designed to save the theory. This amounts to an addition of 96% yellow paint. Karl Popper, who assessed the history of science, warned against this kind of thing and concluded that one should not try to save a theory by adding further invisible elements to it. By the way, MiHsC explains both these huge anomalies without any yellow paint (it has no adjustable parameters). To be clear, I don't blame most of those in the dark matter industry for this. They follow dark matter simply because they have to eat, and that's what the funding system is solely directed towards at the moment. Luckily, MiHsC doesn't need any funding. My labs and supercomputers are pieces of paper. Feynman, R.P., 1985. Surely You're Joking Mr Feynman! Vintage. The best way to test MiHsC (quantised inertia) is to look at systems where accelerations are very low, and so the anomalies it predicts become more obvious. Milky Way satellite dwarf galaxies are brilliant tests, being far from the Milky Way and having only a tenuous hold on their stars. It is well known that full-sized galaxies spin too fast to hold themselves in gravitationally. So astrophysicists add extra invisible (dark) matter to them, putting it where they want, in a deeply unscientific manner. These satellite dwarf galaxies are useful because it is very hard for them to do that, because dark matter usually has to stay spread out on huge galactic scales to explain why it remains only around the edge of galaxies, so you can't then suddenly pack it into a tiny dwarf galaxy, without causing a contradiction. Also, the amounts of dark matter needed to hold these dwarf galaxies together is 100 or more times the visible mass in them which is getting to be ridiculous, especially given the fact that you can't concentrate the stuff like this anyway without becoming intellectually schizophrenic. I have recently compared the predictions of the dwarf galaxies rotation speeds from MiHsC (which reduces the inertial mass for low accelerations in a new way), the speed predicted by Newtonian or general relativisitic models (without dark matter) and MoND with the speeds observed. This plot is the result: The observed spins (velocity dispersions of the stars) of these 11 dwarf galaxies (the ones for which I can find both mass and velocity data, I have not cherry picked) are shown by the hollow squares. The dwarfs' names are also shown. The predictions of Newton/GR (without dark matter) are shown by the crosses at the bottom. The predictions of the empirical theory MoND are shown by the black triangles (with its adjustable parameter set at 1.8x10^-10 m/s^2) and the predictions of MiHsC are shown by the black diamonds. The root mean squared error for Newton, MoND and MiHsC are 6.3, 3.3, 2.9 km/s respectively, so MiHsC is the closest to the observations, despite having no adjustability, and in these cases applying dark matter is doubly ridiculous, as mentioned above. The dark matter detection industry is unlikely to be happy about this, but the point is you can make things work out with MiHsC on a piece of paper without spending millions on huge detectors. This deserves some notice. I'm just about to submit a paper so feedback or suggestions for more data would be very welcome.	{"url":"https://physicsfromtheedge.blogspot.com/2016/03/","timestamp":"2024-11-02T12:22:26Z","content_type":"text/html","content_length":"103074","record_id":"<urn:uuid:10ea160b-9501-4340-9c2f-b9a25c6cb895>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00363.warc.gz"}
Ordinal numbers explained for children - Baby Names For Girls Many parents teach their children to count at an early age. However, it is not usually until they start school that children learn ordinal numbers. In part this is because they first need to understand the concept of quantity and have a good command of cardinal numbers before they understand what ordinal numbers are and what function they perform. To make your work easier, at the Infant Stage we explain what ordinal numbers consist of, what their nomenclature is, and we provide you with some educational tools that you can implement at home. What are ordinal numbers? In mathematics, ordinal numbers are those that denote the position of an element with respect to the rest, within the same set. While the cardinal numbers offer information about the number of elements that exist in a set, the ordinal numbers indicate the order or position they occupy within the group. For example, they are used to classify the results of an athletics competition. In this way, the first to reach the finish line occupies the first position while the one before him occupies the second place and the following one, the third place. Likewise, ordinal numbers can be useful for numbering the floors of a building, indicating the location of people in a row, or naming anniversaries and recurring events. They are also used for dates, especially for the first day of each month. How are ordinal numbers written? Ordinal numbers have their own nomenclature. In mathematics, to convert a cardinal number into an ordinal number, you only need to add a flown letter, which is nothing more than a kind of superscript, to the right. In the case of the masculine a small circle is added while in the case of the feminine an “a” is used. Although it is often overlooked, as it is an abbreviation, a period must be added between the number and the flown letter, according to the Royal Spanish Academy of Language . For example, the number 1 would be written 1st in masculine and 1st in feminine, the number 2 would be 2nd in masculine and 2nd in feminine while the number 3 would be 3rd in masculine and 3rd female, and so on. However, when it comes to writing in letters, each ordinal number has its own name. The name not only denotes its position in the group, but also allows it to be related to its cardinal pair. For example, in the case of number 1, the ordinal would be first, for number 2 it would be second, for number 3, third, and so on. Based on their writing in letters, ordinal numbers can be considered simple or compound. Simple ordinals are the numbers from 1 to 10, as well as those numbers that correspond to the tens, that is, from 20 to 90, and to the hundreds, from 100 to 900. Simple ordinals are also the numbers from 1000 that are formed adding the ending “th”. Meanwhile, the rest are considered compound ordinals and are written by juxtaposition or fusion of simple forms, as in the case of thirteenth or Also, there are some special rules for writing ordinal numbers: • The first and third ordinals are shortened into the “first” and “third” forms when they precede a masculine noun, are part of compound ordinals, or come before an adjective. This, except when it comes to ordinals that accompany feminine nouns, in which case there is no variation. • The ordinals corresponding to the numbers 11 and 12 can be written in two ways, either eleventh and twelfth or eleventh and twelfth. • The ordinals of the first and second hundred can be written together or separately, as in the case of thirteenth or thirteenth. In this case, if they are written together they do not have an tilde, but if they are written separately they do keep the tilde. 3 simple activities to teach children ordinal numbers Learning ordinal numbers by heart can be boring and monotonous. On the other hand, if you use fun educational activities to teach children ordinal numbers, you will not only arouse their interest and curiosity, but you will also help them learn them sooner and better. Here are some ideas you can put into practice at home: 1. Use the rankings A simple and fun way to motivate children to learn ordinal numbers is to ask them to classify different sets according to the position of their elements. Whether it’s a box of toys, the shoes in the closet or cards with different outfits, the idea is that the little ones order the elements according to the ordinal sequence. 2. Make the game your ally Children love to have fun, so they will surely love to be entertained while coloring using only the third, fifth and sixth colors from the box. They can also play a game of colliding marbles according to their position, for example, the third and fifth from the wall. And, for those who like to tell stories, another idea is to encourage them to create a story with the third and fourth toys on the shelf as the protagonists. 3. Identify ordinals in practice Using examples from everyday life for children to practice ordinal numbers will not only help them to reinforce them but also to discover their usefulness. If you are in the supermarket, you can ask your children what position you occupy in the line or if you are cooking at home, you can ask them to reach you the second glass from left to right. The idea is that they become familiar with ordinal numbers through small daily actions. The main ordinal numbers • 1st – first • 2nd – second • 3rd – third • 4th – fourth • 5th – fifth • 6th – 6th • 7th – seventh • 8th – 8th • 9th – 9th • 10th – 10th • 11th – eleventh / eleventh • 12th – twelfth / twelfth • 13th – thirteenth • 14th – fourteenth • 15th – fifteenth • 16th – sixteenth • 17th – seventeenth • 18th – eighteenth • 19th – 19th • 20th – twentieth • 21st – twenty-first • 22nd – twenty-second • 23rd – twenty-third • 24th – twenty-fourth • 25th – twenty-fifth • 26th – 26th • 27th – twenty-seventh • 28th – twenty-eighth • 29th – twenty-ninth • 30th – thirtieth • 40th – fortieth • 50th – fiftieth • 60th – sixtieth • 70th – seventieth • 80.º – octogesimo • 90th – ninetieth • 100th – hundredth • 101st – one hundred and one • 200.º – two hundredth • 300.º – tricentésimo • 400th – four hundredth • 500.º – five hundredth • 600.º – six hundred • 700th – seven hundredth • 800.º – eight hundred • 900th – nine hundredth • 1000th – thousandth • 2000th – two thousandth • 100000th – one hundred thousandth • 1000000th – millionth	{"url":"https://babynamesforgirls.org/ordinal-numbers-explained-for-children/","timestamp":"2024-11-02T00:06:04Z","content_type":"text/html","content_length":"61651","record_id":"<urn:uuid:d0d6be75-c06f-4b7f-a8b7-fb1bfcd86c5e>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00089.warc.gz"}
September 2022 The juniors are going on right now. My friends have all grown up and gotten married with kids. They’re talking about proper marinade techniques and how to buy specialized pizza ovens. I’m drinking Guinness out of a blender bottle that may very well have once been clean. It’s a Blender Bottle brand bottle! It’s fancy. Aristotle says the most potent stories are about family. “We know that travelers will always look for the lowest price, and that’s what they ultimately buy,” [Lorraine Sileo, senior analyst at Phocuswright] says. From WSJ. This always drives me crazy because I can’t buy guaranteed ontime departure and arrival, I can’t buy guaranteed seat width and pitch, I can’t buy anything else. I can’t even guarantee I’ll be on my flight because United may beat me up and kick me off. The only, ONLY ACTUAL GUARANTEE that can be bought with a plane ticket is price. The travel industry makes self-fulfilling prophecies and weeps about it. The objective isn’t to leave without anyone knowing my name. The objective is to leave carrying as much speed possible: the best qualifications for further endeavors with the least debt and other The complex number i or j is a pseudo-unit vector. It’s purpose is to enable vector operations on scalars. Put another way, it’s an adapter so you can plug scalars into vector operations. To elaborate, start with Aristotle. He came up with an idea of four causes: material, formal, efficient, and final. These causes are effective descriptions of what something is. Here is a fairly good Think for a moment of a phone charger, USB to wall plug. When you think of what that is, you don’t think of transistors and bridge rectifiers, transformers, and coils. You describe it by what it does and how you use it. This is Aristotle’s formal cause. The thing is an adapter so you can plug your phone into the wall. The material cause, the circuitry and plastic, is honestly mostly irrelevant and makes you take a long detour around a short mental trip. Think of a phone adapter. What is it? It’s an adapter. That’s what i is and how it should be considered. The mathematical definition, sqrt(-1) is the material cause. That’s what makes it up. But to almost everyone who uses it, what i is is an adapter. It lets anyone do vector math on scalars. What’s a scalar? What’s a vector? Numbers come in two basic groups: scalars and tensors. A scalar is a number by itself. A tensor is any concatenation of more than one scalar together. Vectors are a particular type of tensor, a bunch of scalars put together, in a certain order. For your curiosity, they’re organized with one index in particular order. Which particular order doesn’t make them vectors or not; they just need an Let’s think sports. The score of one team is a scalar. Yesterday, 9/24, JMU scored 32 points against Appalachian State (American College Football). The 32 is a scalar. It’s a number by itself. Clearly, there’s some utility in that single number. The JMU coaches know if they’re doing well or not. The ASU coaches know if their defense is doing well or not. It’s a high number, so it was probably an exciting game. The number is useful but exists by itself. It is a scalar. But it doesn’t tell me who won the game. For that, I need another number: the other team’s score. ASU got 28, so the final score was 32-28. 32-38 is a vector. It’s got two scalars, 32 and 28, put together in a certain order. What order? JMU/ASU. Could you flip it around? Easily. But you need to be careful so the numbers retain their meaning. Two numbers together tell you something that one number doesn’t: who won the game. What’s more, the vector 32-28 tells you something that would be difficult to grab with the numbers unordered. It’s trivially obvious that you can do something with the scores as a vector that is difficult or impossible with the scores as independent scalars, and the punchline here is pretty simple. Vectors are super useful in a bunch of circumstances. Give me one step of trust: vectors are super useful in many ways. Velocities, scores, electrical currents, and a million other things are more usefully addressed as vectors. Vectors are so useful that people wanted to do vector math on scalars. Which, if you think about it, doesn’t really make a lot of sense, but it turns out it’s also super useful. So a group of enterprising mathematicians figured out a way to do it. Complex numbers let you do vector math on scalars. It’s what ‘i’ does. It’s what ‘i’ is. It’s the thing, like your phone charger, you plug your phone into one end, stick the other end into your wall outlet, and they work together. Complex formulations let you do vector math on scalars. And seriously, that’s it. Don’t worry about the sqrt(-1). It’s as irrelevant to most functions as the bridge rectifier inside your charger is to whether or not it charges your phone. Yeah, it’s there, and yeah, it needs to be there, but if you’re just plugging in your phone, it’s not worth a lot of time. It’s certainly not worth aggravation and frustration. Complex numbers are just stuck with two really terrible names: imaginary or complex numbers. They’re neither moreso than any other numbers. I think I’ve been playing the wrong game. I’ve been trying to do my best and accomplish things. I should be playing it like basic training and try to leave without anyone knowing my name. I should read something by Chesterton. Okay, so on one hand, Disa’s character is trite. Grumpy husband, bubbly wife. Oh look, she gets a scene with hidden strength. She almost kinda threatens Elrond. She fusses at her kids. That being said, I think she’s great. I like Disa. I liked her fussing at her kids, husband, and Elrond. I liked the singing bit. I like the way Durin plays off her. The contrast works, the development works, and it works organically within the characters. The source of Durin’s conflict with Elrond worked extremely well for me, and it ground those three in a very mundane, plausible extrapolation of their internal differences. That 20 years isn’t a great thing to an elf and is to a dwarf, themselves a long-linged species, worked so well it seemed out of place in the movie. Disa keeps going with that. Magic materials! Magical races! Elves! And grumpy husband, bubbly wife. They really flesh-out the show.	{"url":"https://www.leibnizclockwork.com/2022/09","timestamp":"2024-11-13T06:17:04Z","content_type":"text/html","content_length":"88280","record_id":"<urn:uuid:04995007-0830-4281-99b2-32093ae5d52c>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00483.warc.gz"}
GB/T 4353-2022 PDF in English GB/T 4353-2022 (GB/T4353-2022, GBT 4353-2022, GBT4353-2022) │ Standard ID │Contents [version]│USD│ STEP2 │ [PDF] delivered in │ Name of Chinese Standard │ Status │ │GB/T 4353-2022│ English │155│Add to Cart│0-9 seconds. Auto-delivery.│Fuel consumption for passenger vehicles in operation │ Valid │ │GB/T 4353-2007│ English │319│Add to Cart│ 3 days │Fuel consumption for passenger vehicles in operation │Obsolete│ │GB/T 4353-1984│ English │279│Add to Cart│ 3 days │Fuel consumption for passenger vehicles in operation │Obsolete│ Standards related to (historical): GB/T 4353-2022 PDF Preview GB/T 4353-2022: PDF in English (GBT 4353-2022) GB/T 4353-2022 GB NATIONAL STANDARD OF THE PEOPLE’S REPUBLIC OF CHINA ICS 43.020 CCS R 06 Replacing GB/T 4353-2007 Fuel Consumption for Passenger Vehicles in Operation ISSUED ON: DECEMBER 30, 2022 IMPLEMENTED ON: DECEMBER 30, 2022 Issued by: State Administration for Market Regulation; Standardization Administration of the People’s Republic of China. Table of Contents Foreword ... 3 1 Scope ... 5 2 Normative References ... 5 3 Terms and Definitions ... 5 4 Classification of Operating Conditions and Correction Coefficient of Passenger Vehicle ... 6 5 Fuel Consumption of Passenger Vehicle in Operation ... 7 Appendix A (Informative) Calculation Example of Fuel Consumption of Passenger Vehicle in Operation with a Maximum Gross Mass of more than 3500kg ... 12 Appendix B (Informative) Calculation Example of Fuel Consumption of Passenger Vehicle in Operation with Maximum Gross Mass no more than 3500kg ... 15 Foreword This Document was drafted as per the rules specified in GB/T 1.1-2020 Directives for Standardization – Part 1: Rules for the Structure and Drafting of Standardizing Documents. This Document GB/T 4353-2007 Fuel Consumption for Passenger Vehicles in Operation. Compared with GB/T 4353-2007, the major technical changes of this Document are as follows besides the structural adjustments and editorial modifications: a) Delete the basic operating conditions (see 4.1 of 2007 Edition); b) Change the temperature interval; moved the correction coefficient of temperature in the original standard into the temperature interval and fuel consumption correction coefficient of temperature; adjust the coefficient; and change the name and content accordingly (see 4.2 of this Edition; 4.2.2, 5.4.2 of 2007 Edition); c) Delete the altitude range (see 4.2.3 of 2007 Edition); d) Increased traffic congestion and fuel consumption correction coefficient of traffic congestion (see 4.3 of this Edition); e) Delete the passenger vehicle operating mode (see 4.3 of 2007 Edition); f) Delete the constant-speed fuel consumption under the curb weight (no load) and total weight (full load) of passenger vehicles (see 5.1 of 2007 Edition); g) Change the calculation method of basic fuel consumption and full-load fuel consumption of passenger vehicles (see 5.1 of this Edition; 5.2 of 2007 Edition); h) Delete the fuel consumption correction coefficient of passenger vehicles in operation (see 5.4 of 2007 Edition); i) Change the classification of vehicle types and corresponding calculation methods for calculating the fuel consumption of passenger vehicles in operation; and adjust the calculation formula (see 5.3 of this Edition; 5.5 of 2007 Edition); j) Change the calculation example of fuel consumption of passenger vehicles in operation (see Appendix A of this Edition; Appendix A of 2007 Edition); k) Add the calculation example of fuel consumption calculation for passenger vehicles in operation with a maximum total mass of no more than 3500kg (see Appendix B of this Edition). Please note some contents of this Document may involve patents. The issuing agency of this Document shall not assume the responsibility to identify these patents. Fuel Consumption for Passenger Vehicles in Operation 1 Scope This Document specifies the classification of operating conditions and correction coefficient for passenger vehicles, as well as the calculation method of fuel consumption for operation. This Document is applicable to the calculation of the fuel consumption of passenger vehicles in operation (excluding bus models) that use gasoline or diesel as the single fuel on highways and urban roads, and is used as a reference for the management of fuel consumption quotas for road transport enterprises. 2 Normative References The provisions in following documents become the essential provisions of this Document through reference in this Document. For the dated documents, only the versions with the dates indicated are applicable to this Document; for the undated documents, only the latest version (including all the amendments) is applicable to this Document. GB/T 4352 Fuel consumption for trucks in operation GB/T 19233 Measurement methods of fuel consumption for light-duty vehicles JT/T 711 Limits and measurement methods of fuel consumption for commercial vehicle for passenger transportation 3 Terms and Definitions For the purposes of this Document, the terms and definitions given in GB/T 4352, JT/T 711 and the following apply. 3.1 Fuel consumption for passenger vehicle in operation The amount of fuel consumed by a passenger car during operation. NOTE: The unit is L. 3.2 Basic fuel consumption of passenger vehicle When a passenger vehicle with a total mass of more than 3500kg is under the comprehensive announcement issued by the competent department of transportation for road transport vehicles, and the unit is L/100km. 5.1.2 Passenger vehicles no more than 3500kg The value of the basic fuel consumption is the comprehensive fuel consumption obtained under the test cycle conditions given in GB/T 19233 (or checked through the light vehicle fuel consumption label), and the unit is L/100km. The full load fuel consumption is regarded as the same as the basic fuel consumption, and the unit is L/100km. 5.2 Changes in fuel consumption per unit load of passenger vehicle 5.2.1 Calculation For passenger vehicles whose basic fuel consumption and full-load fuel consumption are given by vehicle manufacturers, the changes in fuel consumption per unit load of passenger vehicle is calculated according to Formula (1). Where: Qb – changes in fuel consumption per unit load of passenger vehicle, in L/(person•100km); Qk – basic fuel consumption of passenger vehicle, in L/100km; Qm – full load fuel consumption of passenger vehicle, in L/km; Mp – the total number of rated passengers of the passenger vehicle, in person. 5.2.2 Recommended value For passenger vehicles with a maximum gross mass of more than 3500kg, when the basic fuel consumption or full-load fuel consumption is not given by the vehicle manufacturer, the recommended value of changes in fuel consumption per unit load of passenger vehicle Qb shall be in accordance with Table 4. Appendix A (Informative) Calculation Example of Fuel Consumption of Passenger Vehicle in Operation with a Maximum Gross Mass of more than 3500kg A medium passenger vehicle with a length of 7.2m has a curb mass of 5.28t and is rated to carry 25 passengers. On a Class-III highway on a hilly terrain between cities with an average monthly temperature of 16°C, the vehicle carries 20 passengers and travels 30km. Then carry 25 people to return to the original place; the operation period is the evening rush hour in the city, there is congestion; the average driving speed is 20km/h; and the air conditioner is not turned on during the driving process; find the total fuel consumption of the passenger vehicle in operation. Method 1: When the basic fuel consumption and full-load fuel consumption are given by the vehicle manufacturer Calculate as follows: a) The basic fuel consumption of passenger cars Qk provided by vehicle manufacturers is 12.7 (L/100km); the fuel consumption of full-load passenger vehicle Qm is 15.2 (L/100km) according to the announcement of qualified vehicle models for road transport issued by the competent department of transportation. b) According to the formula (1), calculate the additional fuel consumption of the mass change of the passenger vehicle Qb. c) Calculate the fuel consumption of the passenger vehicle in operation according to the Formula (2). According to the known conditions, the correction coefficient of the Type-2 roads is 1.10; the correction coefficient at the monthly average temperature of 16°C is 1.00; the correction coefficient of traffic congestion at an average driving speed of 20km/h is 1.30; and the correction coefficient of no other influential factors is 1.00; the air conditioner is not used during driving; so the fuel consumption of the go-path operation is as follows: [L/(person • 100km)] Appendix B (Informative) Calculation Example of Fuel Consumption of Passenger Vehicle in Operation with Maximum Gross Mass no more than 3500kg A passenger vehicle with a curb weight of 1.26t and a rated capacity of carrying 4 passengers is driving 30km with 2 passengers on a Class-III highway on plain terrain between cities with an average monthly temperature of 10 ℃; and then returns to the original place with 1 passenger. The driving period is the evening rush hour in the city, there is congestion; the average driving speed is 20km/h; and the air conditioner and other energy-consuming equipment are not turned on during the driving process; then find the total fuel consumption of passenger vehicle in operation. Calculate as follows. a) The basic fuel consumption of the passenger vehicle Qk obtained through checking the light vehicle fuel consumption label is 7.8 (L/100km). b) Calculate the fuel consumption of the passenger vehicle in operation according to the Formula (4). According to the known conditions, the correction coefficient of the Type-2 roads is 1.10; the correction coefficient at the monthly average temperature of 10°C is 1.00; the correction coefficient of traffic congestion at an average driving speed of 20km/h is 1.30; and the correction coefficient of no other influential factors is 1.00; the air conditioner is not used during driving; so the fuel consumption of the go-path operation is as follows: According to the determined various correction coefficients, the fuel consumption of return-path operation is as follows: c) Calculate the total fuel consumption of passenger vehicle in different operating conditions according to Formula (5). ...... 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Bozidar Stojadinovic: Katalogdaten im Herbstsemester 2016 Name Herr Prof. Dr. Bozidar Stojadinovic Bozidar Stojadinovic Namensvarianten B. Stojadinović Božidar Stojadinović Lehrgebiet Strukturdynamik und Erdbebeningenieurwesen Inst. f. Baustatik u. Konstruktion ETH Zürich, HIL E 14.1 Adresse Stefano-Franscini-Platz 5 8093 Zürich Telefon +41 44 633 70 99 E-Mail stojadinovic@ibk.baug.ethz.ch URL https://stojadinovic.ibk.ethz.ch/people-page/professor.html Departement Bau, Umwelt und Geomatik Beziehung Ordentlicher Professor Nummer Titel ECTS Umfang Dozierende 101-0157-01L Structural Dynamics and Vibration Problems 3 KP 2G B. Stojadinovic Fundamentals of structural dynamics are presented. Computing the response of elastic and inelastic single-DOF, continuous-mass and multiple-DOF structural systems subjected to Kurzbeschreibung harmonic, periodic, pulse, impulse, and random excitation is discussed. Practical solutions to vibration problems in flexible structures excited by humans, machinery, wind and explosions are developed. After successful completion of this course the students will be able to: 1. Explain the dynamic equilibrium of structures under dynamic loading. 2. Use second-order differential equations to theoretically and numerically model the dynamic equilibrium of structural systems. Lernziel 3. Model structural systems using single-degree-of-freedom, continuous-mass and multiple-degree-of-freedom models. 4. Compute the dynamic response of structural system to harmonic, periodic, pulse, impulse and random excitation using time-history and response-spectrum methods. 5. Apply structural dynamics principles to solve vibration problems in flexible structures excited by humans, machines, wind or explosions. 6. Use dynamics of structures to identify the basis for structural design code provisions related to dynamic loading. This is a course on structural dynamics, an extension of structural analysis for loads that induce significant inertial forces and vibratory response of structures. Dynamic responses Inhalt of elastic and inelastic single-degree-of-freedom, continuous-mass and multiple-degree-of-freedom structural systems subjected to harmonic, periodic, pulse, impulse, and random excitation are discussed. Theoretical background and engineering guidelines for practical solutions to vibration problems in flexible structures caused by humans, machinery, wind or explosions are presented. Laboratory demonstrations of single- and multi-degree-of-freedom system dynamic response and use of viscous and tuned-mass dampers are conducted. Skript The electronic copies of the learning material will be uploaded to ILIAS and available through myStudies. The learning material includes: the lecture presentations, additional reading material, and exercise problems and solutions. Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th edition, Anil Chopra, Prentice Hall, 2014 Literatur Vibration Problems in Structures: Practical Guidelines, Hugo Bachmann et al., Birkhäuser, Basel, 1995 Weber B., Tragwerksdynamik. http://e-collection.ethbib.ethz.ch/cgi-bin/show.pl?type=lehr&nr=76 .ETH Zürich, 2002. Voraussetzungen Knowledge of the fundamentals in structural analysis, and in structural design of reinforced concrete, steel and/or wood structures is mandatory. Working knowledge of matrix algebra / Besonderes and ordinary differential equations is required. Familiarity with Matlab and with structural analysis computer software is desirable. 101-0179-00L Probabilistic Seismic Risk Analysis and Management for 3 KP 2G B. Stojadinovic, M. Broccardo, S. Esposito, P. Galanis Civil Systems Kurzbeschreibung Advanced topics covered in this course are: 1) probabilistic seismic hazard analysis; 2) probabilistic seismic risk analysis; 3) seismic risk management using structural and financial engineering means; and, time permitting, 4) advanced topics in systemic probabilistic risk evaluation. After successfully completing this course the students will be able to: Lernziel 1. Gather the necessary data and conduct a probabilistic seismic hazard analysis for a site. 2. Gather the necessary data and conduct a probabilistic vulnerability analysis of a building or an element of a civil infrastructure system at a site. 3. Design structural and/or financial engineering solutions to mitigate the seismic risk at a site. This course extends the series of two courses on seismic design of structures at ETHZ and introduces the topic of probabilistic seismic risk analysis and seismic risk management for Inhalt the build environment and civil infrastructure systems. The following advanced topics will be covered in this course: 1) probabilistic seismic hazard analysis; 2) probabilistic seismic risk analysis; 3) seismic risk management using structural and financial engineering means; and, time permitting, 4) advanced topics in systemic probabilistic risk Skript The electronic copies of the learning material will be uploaded to ILIAS and available through myStudies. This will include the lecture notes, additional reading, and exercise problems and solutions. There is no textbook for this course. Reading material: - Jack R Benjamin, C. Allin Cornell (2014) Probability, Statistics, and Decision for Civil Engineers - A. H-S. Ang (Author), W. H. Tang Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering - P.E. Pinto, R. Giannini and P. Franchin (2004) Seismic reliability analysis of structures, IUSSPress. Pavia; - McGuire, R.K. 2004. Seismic hazard and risk analysis: EERI Monograph MNO-10, Earthquake Engineering Research Institute. - A Mc. Neil, R. Frey and P. Embrechts, Quantitative Risk Management, Concepts, Techniques and Tools, Princeton University Press, 2015 - R. Rees, A. Wambach, The Microeconomics of Insurance, Foundations and Trends in Microeconomics, Vol. 4, Mps. 1-2 (2008), pp. 1- 163, DOI: 10.1561/0700000023 - Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, Yousef Borzorgnia and Vitelmo Bertero, Eds., CRC Press, 2004 Literatur - Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th edition, Anil Chopra, Prentice Hall, 2012 - Erdbebensicherung von Bauwerken, 2nd edition, Hugo Bachmann, Birkhäuser, Basel, 2002 -Norm SIA 261: Einwirkungen auf Tragwerke (Actions on Structures). Schweizerischer Ingenieur- und Architekten-Verein, Zürich, 2003 - Bispec: software for unidirectional and bidirectional dynamic time-history and spectral seismic analysis of a simple dynamic system. http://eqsols.com/Bispec.aspx - SAP2000 v15.1: general-purpose 3D nonlinear structural analysis software. http://www.csiberkeley.com/sap2000 - OpenSees: Open System for Earthquake Engineering Simulation, is an object-oriented, open- source software framework. http://opensees.berkeley.edu/ Voraussetzungen ETH Seismic Design of Structures I course (101-0188-00), or equivalent. Students are expected to understand the seismological nature of earthquakes, to characterize the ground motion / Besonderes excitation, to analyze the response of elastic single- and multiple-degree-of-freedom systems to earthquake excitation, to use the concept of response and design spectrum, to compute the equivalent seismic loads on simple structures, and to perform code-based seismic design of simple structures. 101-0189-00L Seismic Design of Structures II 3 KP 2G B. Stojadinovic The following advanced topics are covered: 1) behavior and non-linear response of structural systems under earthquake excitation; 2) seismic behavior and design of moment frame, Kurzbeschreibung braced frame, shear wall and masonry structures; 3) fundamentals of seismic isolation; and 4) assessment and retrofit of existing buildings. These topics are discussed in terms of performance-based seismic design. After successfully completing this course the students will be able to: 1. Use the knowledge of nonlinear dynamic response of structures to interpret the design code provisions and apply them in seismic design structural systems. Lernziel 2. Explain the seismic behavior of moment frame, braced frame and shear wall structural systems and successfully design such systems to achieve the performance objectives stipulated by the design codes. 3. Determine the performance of structures under earthquake loading using modern performance assessment methods and analysis tools. This course completes the series of two courses on seismic design of structures at ETHZ. Building on the material covered in Seismic Design of Structures I, the following advanced Inhalt topics will be covered in this course: 1) behavior and non-linear response of structural systems under earthquake excitation; 2) seismic behavior and design of moment frame, braced frame and shear wall structures; 3) fundamentals of seismic isolation; and 4) assessment and retrofit of existing buildings. These topics will be discussed from the standpoint of performance-based design. Skript The electronic copies of the learning material will be uploaded to ILIAS and available through myStudies. The learning material includes the lecture presentations, additional reading, and exercise problems and solutions. Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, Yousef Borzorgnia and Vitelmo Bertero, Eds., CRC Press, 2004 Literatur Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th edition, Anil Chopra, Prentice Hall, 2014 Erdbebensicherung von Bauwerken, 2nd edition, Hugo Bachmann, Birkhäuser, Basel, 2002 ETH Seismic Design of Structures I course, or equivalent. Students are expected to understand the seismological nature of earthquakes, to characterize the ground motion excitation, Voraussetzungen to analyze the response of elastic single- and multiple-degree-of-freedom systems to earthquake excitation, to use the concept of response and design spectrum, to compute the / Besonderes equivalent seismic loads on simple structures, and to perform code-based seismic design of simple structures. Familiarity with structural analysis software, such as SAP2000, and general-purpose numerical analysis software, such as Matlab, is expected. 101-1187-00L Kolloquium Baustatik und Konstruktion 0 KP 2K B. Stojadinovic, E. Chatzi, M. Fontana, A. Frangi, W. Kaufmann, B. Sudret, T. Vogel Kurzbeschreibung Das Institut für Baustatik und Konstruktion (IBK) lädt Professoren in- und ausländischer Hochschulen, Fachleute aus Praxis & Industrie oder wissenschaftliche Mitarbeiter des Institutes als Referenten ein. Das Kolloquium richtet sich sowohl an Hochschulangehörige, als auch an Ingenieure aus der Praxis. Lernziel Neue Forschungsergebnisse aus dem Fachbereich Baustatik und Konstruktion kennen lernen. Risk Center Seminar Series 364-1058-00L 0 KP 2S H. Gersbach, D. Basin, A. Bommier, L.‑E. Cederman, H. R. Heinimann, H. J. Herrmann, W. Mimra, G. Sansavini, Maximale Teilnehmerzahl: 50 F. Schweitzer, D. Sornette, B. Stojadinovic, B. Sudret, S. Wiemer Kurzbeschreibung This course is a mixture between a seminar primarily for PhD and postdoc students and a colloquium involving invited speakers. It consists of presentations and subsequent discussions in the area of modeling complex socio-economic systems and crises. Students and other guests are welcome. Participants should learn to get an overview of the state of the art in the field, to present it in a well understandable way to an interdisciplinary scientific audience, to develop Lernziel novel mathematical models for open problems, to analyze them with computers, and to defend their results in response to critical questions. In essence, participants should improve their scientific skills and learn to work scientifically on an internationally competitive level. Inhalt This course is a mixture between a seminar primarily for PhD and postdoc students and a colloquium involving invited speakers. It consists of presentations and subsequent discussions in the area of modeling complex socio-economic systems and crises. For details of the program see the webpage of the colloquium. Students and other guests are welcome. Skript There is no script, but a short protocol of the sessions will be sent to all participants who have participated in a particular session. Transparencies of the presentations may be put on the course webpage. Literatur Literature will be provided by the speakers in their respective presentations. Voraussetzungen Participants should have relatively good mathematical skills and some experience of how scientific work is performed. / Besonderes	{"url":"https://www.vorlesungen.ethz.ch/Vorlesungsverzeichnis/dozent.view?dozide=10032655&ansicht=2&semkez=2016W&lang=de","timestamp":"2024-11-07T01:36:18Z","content_type":"text/html","content_length":"25201","record_id":"<urn:uuid:ffdecbf5-7cb1-4fa8-b360-816074c974da>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00442.warc.gz"}
Algebra 1 Tutoring in Kansascity \| Grade Potential Find an Algebra 1 Tutor in Kansascity A tutor can assist a student with Algebra 1 by providing advice on basic ideas such as equations and variables. The teacher can further assist the learner with more advanced topics such as factoring and polynomials. Questions About Private Algebra 1 Tutoring in Kansascity Why work with Kansascity Algebra 1 tutors in conjunction with the traditional classroom setting? With the assistance of a one-on-one Grade Potential mathematics tutor, the student will work in conjunction with their tutor to validate understanding of Algebra 1 topics and take as much time as required to perfect their skills. The pace of teaching is entirely determined by the student's ease with the material, as opposed to the typical classroom setting where students are compelled to follow the same learning speed without regard to how well it suits them. Furthermore, our teachers are not required to adhere to a specific lesson plan; instead, they are encouraged to create a customized approach for each learner. How will Grade Potential Kansascity Algebra 1 tutors ensure my student excel? When you meet with Grade Potential mathematics educators, you will get a personalized lesson plan that works best for your student. This empowers the tutor to adjust to your student's requirements. Though most students comprehend basic math concepts at a young age, as the difficulty level progresses, most experience challenges at some point. Our 1:1 Algebra 1 teachers can come alongside the learner’s primary education and provide them with additional training to ensure complete command in any topics they might be having difficulty with. How adaptable are Kansascity tutors’ schedules? If you're doubtful about how the Algebra 1 educator will fit in with your learner’s existing coursework, we can assist by discussing your requirements, availability, and identifying the right strategy and number of sessions required to assist the learner’s retention. That could mean meeting with the learner through online discussions between classes or sports, at your house, or the library – whatever is most convenient. How can I get the right Algebra 1 teacher in Kansascity? If you're ready to start with an instructor in the Kansascity, get in touch with Grade Potential by submitting the form below. A helpful representative will reach out to discuss your academic goals and answer any questions you may have. Let’s get the best Algebra 1 tutor for you! Or respond to a few questions below to begin.	{"url":"https://www.kansascityinhometutors.com/tutoring-services/by-subject/math-tutoring/algebra-tutoring/algebra-1-tutoring","timestamp":"2024-11-11T19:21:14Z","content_type":"text/html","content_length":"75888","record_id":"<urn:uuid:8e51a7de-05f5-480e-8039-6ea84ce97d6d>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00824.warc.gz"}
Atheists, what do you think about this intelligent design argument? Mon, 12/19/2016 - 17:12 (Reply to #31) #32 Perhaps it is exigent that one peruses the aforesaid passage, rather keenly: Simply, one need NOT belief/certainty/faith such that one observes probabilities/likelihoods. (...thusly, one's atheistic/theistic nature is rather irrelevant) (1) Our universe is likely simulatory/information-bound; quantum bits flip on the horizon of quantized interactions. (2) Mankind has but forged non-trivial simulations of our cosmos Such sequences enhance as compute resources enlargen. Therein, our cosmos is likely CREATABLE. Mon, 12/19/2016 - 17:34 How much acid have you used in the last 24 hours? Mon, 12/19/2016 - 17:57 (Reply to #33) #34 That dude is totally insane. Mon, 12/19/2016 - 18:17 Mon, 12/19/2016 - 18:17 Okay. For a moment I was starting to think "maybe this atheism business isn't for me "! Mon, 12/19/2016 - 18:19 (Reply to #36) #37 @JB God's Country See https://medium.com/@jordanmicahbennett/belief-is-entirely-non-necessary-... Furthermore, this is perhaps relevant. Tue, 12/20/2016 - 18:21 (Reply to #37) #38 Clear, focused discourse marks the sharp mind; a weak mind excels at confusion born of ignorance and pretentious wording. Mon, 12/19/2016 - 21:23 (Reply to #38) #39 JB God's Country: You must have missed the earlier conversation where he claimed to have proved a formula for simplifying certain simple calculus problems which led to the conclusion that 0.26667 equals 0.43701. Sheer madness. Also he has a nasty habit of filling his post with obscure language; then spends the next several days going back and editing his posts to add additional obscure language. If reading his posts makes your head hurt; that is a good indication of your own sanity. Tue, 12/20/2016 - 18:31 (Reply to #39) #40 That calculation was a real winner, wasn't it? The great majority of readers, of course, don't have the mathematical ability to check such pretentious stuff, or else don't have the time. Thanks for stepping in with that clutch calculation! Tue, 12/20/2016 - 23:20 (Reply to #40) #41 Thanks. I suspected it was totally wrong the instant I saw it because he was integrating a product f(x)g(x), which screams integration by parts. As I'm sure you know, when you integrate by parts you tend to get two terms (or more if you have to keep doing it). He only had one term. A simplified explanation for everyone else: typically the solution to that kind of problem involves "something" + "something else". He's solution was missing one of those "somethings" so there was no way it was going to work. Wed, 12/21/2016 - 09:59 (Reply to #41) #42 ...How quaint :) Nyarlatothep Stipulation: Thanks. I suspected it was totally wrong the instant I saw it because he was integrating a product f(x)g(x), which screams integration by parts. As I'm sure you know, when you integrate by parts you tend to get two terms (or more if you have to keep doing it). He only had one term. A simplified explanation for everyone else: typically the solution to that kind of problem involves "something" + "something else". He's solution was missing one of those "somethings" so there was no way it was going to work. Lemma stipulation (0): ∫[xⁿ · dx/dθ · dx] of mine, is but NOT EQUIVALENT to the standard frame ∫xⁿ·√(xⁿ+aⁿ). Such starkly contrasts that of your utmost stipulation: RECALL that ∫[xⁿ · dx/dθ · dx] is but not of STRICT composition. (..for xⁿ metamorphoses abound √tⁿ ± tⁿ) As stipulated amid lemma [2013], of mine (and thereafter threads of prior) x^n is NOT STRICTLY BOUND via dx/dθ · dx. Such was therein, an erroneous presumption of yours. The collapser lemma of mine reduces amidst 'PARTITIONS'. Therein, partition dx/dθ · dx is viably applicable, (AS INDUBITABLY OBSERVED AMIDST THE afore-stated SAMPLE IMAGE ) absent x^n. Wed, 12/21/2016 - 15:28 (Reply to #42) #43 Nyarlatothep Stipulation: JB God's Country: You must have missed the earlier conversation where he claimed to have proved a formula for simplifying certain simple calculus problems which led to the conclusion that 0.26667 equals 0.43701. Sheer madness. Greensnake Stipulation: That calculation was a real winner, wasn't it? The great majority of readers, of course, don't have the mathematical ability to check such pretentious stuff, or else don't have the time. Thanks for stepping in with that clutch calculation! It is rather NATURAL, that Nyarlatothep had but generated the INVALID OUTCOME therein, ON THE HORIZON of that of the MISAPPLICATION OF Nyarlatothep's, of lemma of mine. Albeit, I had long but trivially stipulated of Nyarlatothep's erroroneous application of said lemma, amidst this thread, and in the like, threads of prior :) Mon, 12/19/2016 - 18:27 Could you do me a favor and explain this article to me as though I was an 8 year old? Mon, 12/19/2016 - 18:56 (Reply to #44) #45 The universe's best description [Quantum Mechanics] reduces amidst PROBABILITIES. Observe scenario (x). Scenario (x) entails a tuple of actions; ACTIONS (i) and (ii). By extension, scenario (x) consists of an event (q). Event (q) consists of probability distributions. Event (q)'s PROBABILITY is therein OBSERVABLE. (particularly, ABSENT belief) If probability (q) is negligible, ACTION (i) subsumes. Otherwise, ACTION (ii) computes. THEREAFTER, optimal events are computable ABSENT belief. Tue, 12/20/2016 - 02:36 (Reply to #45) #46 A deepity a day keeps logic away! Tue, 12/20/2016 - 05:57 Indeed, for idiocy/belief is logic's opposite: http://psr.sagepub.com/content/early/2013/08/02/1088868313497266.abstract Wed, 12/21/2016 - 09:59 @JB's God Country Simply, Nyarlatothep had but MISAPPLIED my equations, absent knowledge of the boundaries in the paradigm of said equation sequence: http://unibrain.deviantart.com/art/ Albeit, one may QUITE TRIVIALLY, derive Newtonian outcomes, on the horizon of my equations :) Here is a non-abstruse application, betwixt a scenario's usage of my equation: One may QUITE TRIVIALLY (perhaps in a minute's scope) execute my collapser partition, as observed in the image, such that Newtonian outcomes are accurately derived. Here are a few CLEARLY observed misapplications of nyarlatothep's amidst my equations' application: 1) Nyarlothotep presumed that dx/dθ subsumed the (symbol x =√aⁿ · trig(θ)) 2) Nyarlothotep presumed that ∫[xⁿ · dx/dθ · dx] was but of STRICT COMPOSITION. (..in contrast, xⁿ metamorphoses abound √tⁿ ± tⁿ) Boundaries are stipulated herein [2013 stipulation]: http://unibrain.deviantart.com/art/Trigonometric-rule-collapser-set-3614... Wed, 12/21/2016 - 11:10 (Reply to #48) #49 MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\$','\$']]}}); ProgrammingGodJordanSimply, Nyarlatothep had but MISAPPLIED my equations, absent knowledge of the boundaries in the paradigm of said equation sequence: http://unibrain.deviantart.com/art/ You might notice that in your sample calculation; the function doesn't fit your definition! Your defination: $$\int x^n\sqrt{a^n - x^n}dx$$ Your sample: $$\int \sqrt{16 - x^2}dx$$ You set n=2; but that would put an x2 in front of the square root. It is missing. It is funny you accuse me of misapplying your equations (I haven't); then the first thing you do is misapply them! At least you are always good for a chuckle. ps: I see you took the time to post this garbage in more places, but haven't taken the time to fix the missing brackets! Wed, 12/21/2016 - 12:40 (Reply to #49) #50 Nyarlathotep Stipulation: You set n=2; but that would put an x2 in front of the square root. It is missing. It is funny you accuse me of misapplying your equations (I haven't); then the first thing you do is misapply At least you are always good for a chuckle. ps: I see you took the time to post this garbage in more places, but haven't taken the time to fix the missing brackets! The resource linked prior, of mine was but postulated in [2013]. Lemma stipulation (0): ∫[xⁿ · dx/dθ · dx] of mine, is but NOT EQUIVALENT to the standard frame ∫xⁿ·√(xⁿ+aⁿ). Such starkly contrasts that of your utmost stipulation: RECALL that ∫[xⁿ · dx/dθ · dx] is but not of STRICT composition. (..for xⁿ metamorphoses abound √tⁿ ± tⁿ) As stipulated amid lemma [2013], of mine (and thereafter threads of prior) x^n is NOT STRICTLY BOUND via dx/dθ · dx. Such was therein, an erroneous presumption of yours. The collapser lemma of mine reduces amidst 'PARTITIONS'. Therein, partition dx/dθ · dx is viably applicable, (AS INDUBITABLY OBSERVED AMIDST THE afore-stated SAMPLE IMAGE ) absent x^n. Wed, 12/21/2016 - 13:01 (Reply to #50) #51 MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\$','\$']]}}); It is really simple to resolve this. Just do an example using your rule; on a function that has the same form as your rule (like I asked you to do weeks ago): $$\int x^2\sqrt{16-x^2}dx$$ Then just post it here for us to laugh look at. Wed, 12/21/2016 - 14:03 (Reply to #51) #52 Nyarlathotep Stipulation: Such a problem is trivially reducible, absent use of my lemma: Lemma stipulation (0): ∫[xⁿ · dx/dθ · dx] of mine, is but NOT EQUIVALENT to the standard frame ∫xⁿ·√(xⁿ+aⁿ). Such starkly contrasts that of your utmost stipulation: RECALL that ∫[xⁿ · dx/dθ · dx] is but not of STRICT composition. (..for xⁿ metamorphoses abound √tⁿ ± tⁿ) As stipulated amid lemma [2013], of mine (and thereafter threads of prior) x^n is NOT STRICTLY BOUND via dx/dθ · dx. Such was therein, an erroneous presumption of yours. THUSLY, dx/dθ · dx is viably applicable absent x^n, amidst said lemma. The collapser lemma of mine reduces amidst 'PARTITIONS'. Therein, partition dx/dθ · dx is viably applicable, (AS INDUBITABLY OBSERVED AMIDST THE afore-stated SAMPLE IMAGE ) absent x^n. Wed, 12/21/2016 - 17:10 This thread is starting to look like Kevin Spaceys apartment in the movie "Seven". Wed, 12/21/2016 - 18:18 ProgrammingGodJordan - Such a problem is trivially reducible, absent use of my lemma: Exactly. Which means we can solve it the "normal way", then solve it with your "lemma". Then you will see they don't give the same solution. Which means your "lemma" is false. It also means you've never really used it; otherwise you would have noticed it was giving false answers. So please, solve this trivial problem using your "lemma" and post it. It Thu, 12/22/2016 - 18:55 (Reply to #54) #55 Albeit, I had but long stipulated, a non-abstrusely observed, ACCURATE sample (NON-TRIVIALLY REDUCIBLE), betwixt that of the application of my lemma: As clearly observed, my lemma COLLAPSES the default cycle, the LEFTWARD sequence, such that statements 2-5 collapse amidst a mono-line expression as observed in the CONDENSED RIGHTWARD sequence, abound a PARTITION of my lemma. THEREIN, 4cosθ4cosθdθ is attained, synonymously amid my lemma's ABSENCE, and PRESENCE, whence the SAME Newtonian outcome is derived. THUSLY, as stipulated amid lemma [2013], of mine (and thereafter threads of prior) x^n is NOT STRICTLY BOUND via dx/dθ · dx. Thu, 12/22/2016 - 19:18 (Reply to #55) #56 MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\$','\$']]}}); You did it on the wrong function, AGAIN. Do it on a function that has the form you defined in your "lemma"! For example: $$\int x^2\sqrt{16-x^2}dx$$ Thu, 12/22/2016 - 23:51 (Reply to #56) #57 Nyarlathotep Stipulation: You did it on the wrong function, AGAIN. Do it on a function that has the form you defined in your "lemma"! For example: ∫ x^2 √ 16 − x^2 dx ∫xⁿ · √ tⁿ ± tⁿ via lemma [2013] , stipulates a rather QUINTESSENTIAL trigonometric FRAME BOUNDARY. ######### NOTE THE '±' (plus\|minus) symbol. Such but non-abstrusely postulates that ∫xⁿ · √ tⁿ ± tⁿ is but of NON-EXPLICIT nature. THEREIN, my lemma is applicable in MUTATIONS of the aforesaid FRAME, as observed via (2), subsequently. ProgrammingGodJordan Stipulation: Albeit, as clearly observed, my lemma COLLAPSES the default cycle, the LEFTWARD sequence, such that statements 2-5 collapse amidst a mono-line expression as observed in the CONDENSED RIGHTWARD sequence, abound a PARTITION of my lemma. THEREAFTER, 4cosθ4cosθdθ is attained, synonymously amid my lemma's ABSENCE, and PRESENCE, whence the SAME Newtonian outcome is derived. Fri, 12/23/2016 - 00:17 (Reply to #57) #58 ProgrammingGodJordan - ∫ xⁿ · √ tⁿ ± tⁿ via lemma [2013] But then you did: ∫√(16-x2)dx which means you set n=2; which means you omitted the leading x2 so you used your "lemma" on the wrong form! Look above I made it nice and big for you so you can't miss it. Please repeat the process without omitting it, using your "lemma". And for what it is worth, the tⁿ ± tⁿ is a mistake as well. But at least you wrote it as an - xn later; but these silly mistakes are a sure fire indication that you have never really used this Fri, 12/23/2016 - 00:45 (Reply to #58) #59 As I had very initially stated, tⁿ ± tⁿ is but a GENERAL, NON EXPLICIT FRAME, amidst lemma [2013] . ∫xⁿ · √ tⁿ ± tⁿ via lemma [2013] , stipulates a rather QUINTESSENTIAL trigonometric FRAME BOUNDARY. PERTINENTLY, in tandem, lemma [2013] stipulates : "∫[xⁿ·√(xⁿ+aⁿ)], ∫[xⁿ·√(xⁿ-aⁿ)], ∫[xⁿ·√(aⁿ-xⁿ)] ... manifest as STANDARD trigonometric integral FORMS/FRAMES; whence the structure of said frames, SELF-INDICATE interchange-boundaries." I had not omitted any term. Simply, as observed via lemma [2013] , said lemma is applicable in PARTITIONS. THUSLY, partition dx/dθ · dx is viably applicable, (AS INDUBITABLY OBSERVED AMIDST THE afore-stated SAMPLE IMAGE ) absent x^n. Albeit, one may QUITE TRIVIALLY, derive Newtonian outcomes, on the horizon of my PARTITION bound equations :) Albeit, as clearly observed, my lemma COLLAPSES the default cycle, the LEFTWARD sequence, such that statements 2-5 collapse amidst a mono-line expression as observed in the CONDENSED RIGHTWARD sequence, abound a PARTITION of my lemma. THEREAFTER, 4cosθ4cosθdθ is attained, synonymously amid my lemma's ABSENCE, and PRESENCE, whence the SAME Newtonian outcome is derived. Fri, 12/23/2016 - 00:52 (Reply to #59) #60 ProgrammingGodJordan - As I had very initially stated, tⁿ ± tⁿ is but a GENERAL, NON EXPLICIT FRAME, amidst the abstract via lemma [2013] . No, what you are saying is non-sense. tⁿ ± tⁿ is either 2tn or 0; so you are now failing high school algebra as well as calculus. In your example you made it 16 - x2; which is not the same form! I assumed tⁿ ± tⁿ was a typo but apparently you are even crazier than you first appeared; which is quite the accomplishment. Also, why don't you just do the calculation I suggested. You've beat around the bush plenty, just do it! Fri, 12/23/2016 - 23:34 (Reply to #60) #61 Nyarlathotep stipulation: No, what you are saying is non-sense. tⁿ ± tⁿ is either 2tn or 0; so you are now failing high school algebra as well as calculus. Simply, tⁿ ± tⁿ absorbs:(xⁿ+aⁿ), (xⁿ-aⁿ), or (aⁿ-xⁿ), for t = a \| x. Nyarlathotep stipulation: In your example you made it 16 - x2; which is not the same form! I assumed tⁿ ± tⁿ was a typo but apparently you are even crazier than you first appeared; which is quite the accomplishment. Also, why don't you just do the calculation I suggested. You've beat around the bush plenty, just do it! It is rather evident, that: (1) You IGNORE the accurate sample illustrated via (C). (2) You IGNORE the factum that my lemma is partition bound. (Thusly PARTITION dx/dθ · dx is viably applicable, absent x^n, As stipulated amid lemma [2013] . ) (3) You INGORE the factum that in exemplification, ∫[xⁿ·√(aⁿ-xⁿ)] ... describes a RANDOM FORM, abound SIN(θ) aligned sequences. It is rather SUB-OPTIMAL to enlist all explicit SIN(θ) aligned (3a) RANDOM SINE FORM 0 = ∫[xⁿ·√(aⁿ-xⁿ)]. (3b) SINE FORM SAMPLE 1 = ∫√16−x^2 (3c) SINE FORM SAMPLE 2 = ∫3dx/x√4−x^2 Albeit, one may QUITE TRIVIALLY, derive Newtonian outcomes, on the horizon of my PARTITION bound equations, as non-abstrusely observed amidst the subsequent sample: As clearly observed, my lemma COLLAPSES the default cycle, the LEFTWARD sequence, such that statements 2-5 collapse amidst a mono-line expression as observed in the CONDENSED RIGHTWARD sequence, abound a PARTITION of my lemma. THEREAFTER, 4cosθ4cosθdθ is attained, synonymously amid my lemma's ABSENCE, and PRESENCE, whence the SAME Newtonian outcome is derived.	{"url":"https://www.atheistrepublic.com/forums/debate-room/atheists-what-do-you-think-about-intelligent-design-argument?page=1","timestamp":"2024-11-07T07:01:25Z","content_type":"text/html","content_length":"189430","record_id":"<urn:uuid:70a20c24-a426-4127-9602-cc2455859107>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00630.warc.gz"}
What is a Risk-Free Rate? How is that Related to a Risk-Free Security? Having learned what risk-free securities are, we can now answer the above questions. The risk-free rate is the theoretical rate of return on an investment in a risk-free asset. It represents the minimum rate of return an investor should expect to earn for taking on no risk other than the opportunity cost of tying up their funds in a risk-free asset, usually US Treasuries, German Bunds, Japanese Government Bonds, and UK Gilts. In practical terms, the risk-free rate is often used as a benchmark to assess the expected return on other investments with higher levels of risk. It is used in various financial models, such as the Capital Asset Pricing Model (CAPM), to estimate the expected return on riskier assets by adding a risk premium to the risk-free rate. The risk-free rate is also used to discount future cash flows to their present value, reflecting the time value of money. It helps in comparing the value of money received in the future to its equivalent value in today's terms. It is important to mention that Central Banks, such as the Federal Reserve in the U.S., often influence short-term interest rates, impacting the short-term risk-free rate. Changes in the risk-free rate can, in turn, influence interest rates across various financial markets. By contrast, long-term risk-free rates (such as yields of US Treasury Bonds), usually reflect expectations about inflation and economic growth.	{"url":"https://academy.ts.finance/what-is-a-risk-free-rate-how-is-that-related-to-a-risk-free-security/","timestamp":"2024-11-11T13:18:54Z","content_type":"text/html","content_length":"19451","record_id":"<urn:uuid:76260329-4dd2-4955-b05e-ba26ae14f8c2>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00030.warc.gz"}
Number of k-Cycles in Symmetric Group Let $n \in \N$ be a natural number. Let $S_n$ denote the symmetric group on $n$ letters. Let $k \in N$ such that $k \le n$. The number of elements $m$ of $S_n$ which are $k$-cycles is given by: $m = \paren {k - 1}! \dbinom n k = \dfrac {n!} {k \paren {n - k}!}$ Let $m$ be the number of elements of $S_n$ which are $k$-cycles. From Cardinality of Set of Subsets, there are $\dfrac {n!} {k! \paren {n - k}!}$ different ways to select $k$ elements of $\set {1, 2, \ldots, n}$. From Number of k-Cycles on Set of k Elements, each of these $\dfrac {n!} {k! \paren {n - k}!}$ sets with $k$ elements has $\paren {k - 1}!$ $k$-cycles. It follows from Product Rule for Counting that: $\ds m$ $=$ $\ds \paren {k - 1}! \dfrac {n!} {k! \paren {n - k}!}$ $\ds $ $=$ $\ds \paren {k - 1}! \dbinom n k$ Definition of Binomial Coefficient $\ds $ $=$ $\ds \dfrac {n! \paren {k - 1}! } {k! \paren {n - k}!}$ $\ds $ $=$ $\ds \dfrac {n!} {k \paren {n - k}!}$ Suppose $n \ge k$, and consider the number of $k$-cycles in $S_n$. A $k$-cycle can be represented by a selection of $k$ elements from $n$ without any repeats. From Number of Permutations, the number of permutations of $k$ elements from $n$ possible elements is $\dfrac {n!} {\paren {n - k}!}$. However, each such string is merely a representation of an $k$-cycle; the $k$-cycle itself does not depend on the starting elements in the string. Since there are $k$ possible starting elements, we must divide this number by $k$. Hence, the number of $m$-cycles is $\dfrac {n!} {k \paren {n - k}!}$	{"url":"https://proofwiki.org/wiki/Number_of_k-Cycles_in_Symmetric_Group","timestamp":"2024-11-02T06:32:52Z","content_type":"text/html","content_length":"47690","record_id":"<urn:uuid:1c9eb895-8141-46e9-b584-dd2c7ffc3ae9>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00385.warc.gz"}
Modeling and Statistics Chris Myers (CAC), Jeff Sale (SDSC) Cornell Center for Advanced Computing and San Diego Supercomputing Center Revisions: 6/2023, 1/2021 (original) Much of data science involves building models, although there are many different kinds of models. Statistics primarily involves building descriptive models of data themselves. Mechanistic models describe sets of interacting processes, such that data emerge through the collective action of those components. Machine learning models often lie somewhere in the middle, producing descriptions of data that are learned through the organization and parameterization of flexible computational frameworks such as neural networks or decision trees. In this topic, we touch briefly on some tools that support either statistical modeling, or the integration of data and models that often arises when one is trying to parameterize a mechanistic model. In the following topic, we address some tools that are useful for machine learning. After you complete this segment, you should be able to: • Use pandas to generate descriptive statistics of data • Use statsmodels to build and analyze statistical models of data • Use scipy to integrate models and data by estimating optimal model parameters • Use networkX to build and analyze network models from data • Build a simulation of wildfire dynamics to investigate dynamical self-organization This tutorial assumes the reader has some working knowledge of general programming concepts, even if not directly with the Python programming language. The target audience is scientists and engineers who are already programming in Python, and are interested in using Python tools and packages to carry out various analyses of datasets. If additional introductory material about Python is needed, readers can consult An Introduction to Python as well as the documentation on the python.org website.	{"url":"https://cvw.cac.cornell.edu/python-data-science/modeling-statistics/index","timestamp":"2024-11-09T04:30:12Z","content_type":"text/html","content_length":"27032","record_id":"<urn:uuid:06b5c381-0674-483d-ae7c-27a46f67f526>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00816.warc.gz"}
Express the following statments using quantifiers. • Thread starter ayham123 • Start date In summary, using quantifiers and primitive operations and relations over natural numbers, we can express the following statements: a) an even number n can be expressed as the sum of four perfect squares, and b) every number n greater than 2 is not divisible by n-1. It is important to note that in this context, we are limited to using {not, implies, or, and} and {+, -, x, >, =}. Homework Statement Express the following statements using { not, implies, or , and} and quantifiers over natural numbers n, we can only use {+,-,x,>,=} as primitive operations and relations over n. Homework Equations a) even number n is a sum of four perfect squares? b) every number n greater than 2 is not dividsible by n -1 ? The Attempt at a Solution Did you not read the rules for this forum? You must show your own work, not just ask others to do the problems for you. i don't know how to solve it! that's why I am asking, i am completely lost FAQ: Express the following statments using quantifiers. What does it mean to express a statement using quantifiers? Expressing a statement using quantifiers means to use logical symbols to represent the quantity of elements in a set or the relationship between sets. This allows for a more concise and precise representation of statements. What are the different types of quantifiers? The two main types of quantifiers are universal quantifiers and existential quantifiers. Universal quantifiers, denoted by ∀, represent all elements in a set, while existential quantifiers, denoted by ∃, represent at least one element in a set. How do you use quantifiers in mathematical statements? Quantifiers are used in mathematical statements to specify the scope of a variable. For example, "For all x, if P(x), then Q(x)" uses a universal quantifier to indicate that the statement applies to all elements in the set of x. What is the difference between "for all" and "there exists" quantifiers? The "for all" quantifier, ∀, indicates that a statement is true for every element in a set, while the "there exists" quantifier, ∃, indicates that at least one element in a set satisfies the How do you negate statements with quantifiers? To negate a statement with quantifiers, the negation must apply to the entire statement, not just the quantifier. For example, "For all x, if P(x), then Q(x)" would be negated as "There exists an x such that P(x) is true but Q(x) is false."	{"url":"https://www.physicsforums.com/threads/express-the-following-statments-using-quantifiers.584772/","timestamp":"2024-11-10T11:29:14Z","content_type":"text/html","content_length":"77962","record_id":"<urn:uuid:456ed176-dd3d-4d6b-877d-ce1b24c9bd02>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00895.warc.gz"}
ncl_vectors_params: This document briefly describes all Vectors - Linux Manuals (3) ncl_vectors_params (3) - Linux Manuals ncl_vectors_params: This document briefly describes all Vectors Vectors_params - This document briefly describes all Vectors internal parameters. Parameter descriptions follow, in alphabetical order. Each description begins with a line giving the three-character mnemonic name of the parameter, the phrase for which the mnemonic stands, the intrinsic type of the parameter, and an indication of whether or not it is an array. ACM - Arrow Color Mode - Integer ACM controls how color is applied to filled vector arrows. It applies only when AST has the value 1. Its behavior also depends on the setting of the parameter CTV. Assuming that CTV is set to a non-zero value, implying that multi-colored vectors are desired, ACM has the following settings: Value Effect ----- ------ -2 Multi-colored fill; outline off -1 Fill off; multi-colored outline 0 Multi-colored fill; mono-colored outline 1 Mono-colored fill; multi-colored outline 2 Multi-colored fill; multi-colored outline Mono-colored outlines use the current GKS polyline color index. Mono-colored fill uses the current GKS fill color index. When CTV is set to 0, both the fill and the outlines become mono-colored, and therefore only modes -2, -1, and 0 remain distinguishable. The default value is 0. AFO - Arrow Fill Over Arrow Lines - Integer If AFO is set to 1, the perimeter outline of a filled vector arrow is drawn first, underneath the fill. In this case, you must set the line thickness parameter (LWD) to a value greater than unity in order for the line to appear completely. The advantage of drawing the line underneath is that the full extent of the fill appears, resulting in a crisper, more sharply defined arrow; when the line is drawn on top of the fill using a different color index, the fill color may be partially or completely obscured, especially for small vector arrows. AFO has an effect only when the parameter AST is set to 1. The default value of AFO is 1. AIR - Arrow Interior Reference Fraction - Real AIR specifies the distance from the point of the arrowhead of a filled vector arrow drawn at the reference length to the point where the arrowhead joins with the line extending to the tail of the arrow. Its value represents a fraction of the reference length. This distance is adjusted proportionally to the X component of the arrowhead size for vector arrows whose length differs from the reference length. See VRL for an explanation of how the reference length is determined. AIR has an effect only when AST is set to 1. AIR is allowed to vary between 0.0 and 1.0 and its default value is 0.33. AMN - Arrow Head Minimum Size - Real Specifies a minimum length for the two lines representing the point of the vector arrow head, as a fraction of the viewport width. AMN has an effect only for line-drawn vector arrows (parameter AST set to 0). Normally the arrow head size is scaled proportionally to the length of the vector. This parameter allows you to ensure that the arrow head will remain recognizable even for very short vectors. Note that you can cause all the arrowheads in the plot to be drawn at the same size if you set AMN and AMX to the same value. If you set both AMN and AMX to 0.0 the arrowheads will not be drawn at all. The default value is 0.005. AMX - Arrow Head Maximum Size - Real Specifies a maximum length for the two lines representing the point of the vector arrow head, as a fraction of the viewport width. AMX has an effect only for line-drawn vector arrows (parameter AST set to 0). Normally the arrow head is scaled proportionally to the length of the vector. This parameter allows you to ensure that the arrow heads do not become excessively large for high magnitude vectors. Note that you can cause all the arrowheads in the plot to be drawn at the same size if you set AMN and AMX to the same value. If you set both AMN and AMX to 0.0 the arrowheads will not be drawn at all. The default value is 0.05. AST - Arrow Style - Integer If AST is set to 0, the vector arrows are drawn using lines only. When AST is set to 1, the vectors are plotted using variable width filled arrows, with an optional outline. If AST is set to 2, wind barb glyphs are used to represent the vectors.There are parameters for controlling the appearance of each style. These have an effect only for one value of AST. However, certain parameters apply to all arrow styles. Here is a table of parameters that affect the appearance of vectors and how their behavior is affected by the setting of AST: Parameter Line-Drawn Arrows Filled Arrows Wind Barbs --------- ----------------- ------------- ---------- ACM x AFO x AIR x AMN x AMX x AWF x AWR x AXF x AXR x AYF x AYR x CLR x x x CTV x x x LWD x x x NLV x x x PAI x x x TVL x x x WBA x WBC x WBD x WBS x WBT x When filled arrows are used, colors associated with the threshold levels may be applied to either or both the fill or the outline of the arrow. When fill is drawn over the outline (AFO set to 1), LWD should be set to a value greater than 1.0 in order for the outline to be fully visible. The default value of AST is 0. AWF - Arrow Width Fractional Minimum - Real AWF specifies the width of a filled arrow drawn at the minimum length, as a fraction of the width of an arrow drawn at the reference length. If AWF has the value 0.0, then the ratio of the arrow width to the arrow length will be constant for all arrows in the plot. If given the value 1.0, the width will itself be constant for all arrows in the plot, regardless of length. See VFR for a discussion of how the minimum length is determined. AWF has an effect only when AST is set to 1. AWF is allowed to vary between 0.0 and 1.0 and its default value is 0.0. AWR - Arrow Width Reference Fraction - Real AWR specifies the width of a filled vector arrow drawn at the reference length, as a fraction of the reference length. See VRL for an explanation of how the reference length is determined. AWR has an effect only when AST is set to 1. AWR is allowed to vary between 0.0 and 1.0 and its default value is 0.03. AXF - Arrow X-Coord Fractional Minimum - Real AXF specifies the X component of the head of a filled vector arrow drawn at the minimum length, as a fraction of the X component of the head of an arrow drawn at the reference length. The X component of the arrowhead is the distance from the point of the arrowhead to a point along the centerline of the arrow perpendicular the arrowhead's rear tips. If AXF has the value 0.0, then the ratio of the X component of the arrowhead size to the arrow length will be constant for all vectors in the plot. If given the value 1.0, the arrowhead X component will itself be constant for all arrows in the plot, regardless of their length. See VRL for an explanation of how the reference length is determined. AXF has an effect only when AST is set to 1. AXF is allowed to vary between 0.0 and 1.0 and its default value is 0.0. AXR - Arrow X-Coord Reference Fraction - Real AXR specifies the X component of the head of a filled vector arrow drawn at the reference length, as a fraction of reference length. The X component of the arrowhead is the distance from the point of the arrowhead to a point along the centerline of the arrow perpendicular the arrowhead's rear tips. See VRL for an explanation of how the reference length is determined. AXR has an effect only when AST is set to 1. AXR is allowed to vary between 0.0 and 2.0 and its default value is 0.36. AYF - Arrow Y-Coord Fractional Minimum - Real The value of this parameter, when added to the minimum width value, specifies the Y component length of the arrowhead size for a filled arrow drawn at the minimum length, as a fraction of the length specified by AYF. If given the value 1.0, the arrowhead Y component will extend the same distance perpendicularly from the edge of all arrows in the plot, regardless of their length and width. This can be a useful resource to adjust to ensure that the points of even very short vector arrows remain visible. See VFR for a discussion of how the minimum length is determined. AYF has an effect only when AST is set to 1. AYF is allowed to vary between 0.0 and 1.0 and its default value is 0.25. AYR - Arrow Y-Coord Reference Fraction - Real AYR specifies the perpendicular distance from one side of a filled vector arrowdrawn at the reference length to one of the back tips of the arrowhead. The value represents a fraction of the value of of the reference length and, when added to half the arrow width, determines the Y component of the arrowhead size. See VRL for an explanation of how the reference length is determined. AYR has an effect only when AST is set to 1. AYR is allowed to vary between 0.0 and 1.0 and its default value is 0.12. CLR - Array of GKS Color Indices - Integer Array This parameter represents an array containing the GKS color index to use for coloring the vector when the scalar quantity is less than or equal to the threshold value with the same index in the TVL threshold value array. Depending on the settings of AST and ACM it may specify a set of fill color indexes, a set of line color indexes, or both. In order to access a particular element of the CLR array, you must first set the value of PAI, the parameter array index parameter, to the value of the array element's index. All elements of the array are set to one initially. Note that the Vectors utility makes no calls to set the GKS color representation (GSCR), nor ever modifies the contents of the CLR array; therefore you are responsible for creating a suitably graduated color palette and assigning the color index values into the CLR array, prior to calling VVECTR. Typically, assuming the desired RGB values have been previously stored in a 2 dimensional 3 x n array called RGB, you loop through the calls that set up the color representation and color index as in the following example for a fourteen color palette: DO 100 I=1,14,1 CALL GSCR (1,I,RGB(1,I),RGB(2,I),RGB(3,I)) CALL VVSETI('PAI -- Parameter Array Index', I) CALL VVSETI('CLR -- GKS Color Index', I) 100 CONTINUE See the descriptions of CTV, NLV, and TVL for details on configuring the vector coloring scheme. CPM - Compatibility Mode - Integer Controls the degree of compatibility between pre-Version 3.2 capabilities of the Vectors utility and later versions. You can independently control three behaviors using the nine settings • use of VELVCT and VELVEC input parameters • use of variables initialized in the VELDAT block data statement • use of the old mapping routines, FX, FY, MXF, and MYF. Note, however, that when using the Version 3.2 entry points VVINIT and VVECTR, only the third behavior option has any meaning. When CPM is set to 0, its default value, the Vectors utility's behavior varies depending on whether you access it through one of the pre-Version 3.2 entry points (VELVCT, VELVEC, and EZVEC), or through the VVINIT/VVECTR interface. Otherwise, positive values result in invocation of the pre-Version 3.2 mapping routines (FX, FY, MXF, and MYF) for the conversion from data to user coordinates. Negative values cause VVMPXY or perhaps VVUMXY to be used instead. When using the pre-Version 3.2 interface, odd values of CPM cause the data values in the VELDAT block data subroutine to override corresponding values initialized in the Version 3.2 VVDATA block data subroutine, or set by the user calling VVSETx routines. Values of CPM with absolute value greater than two cause some of the input arguments to VELVEC and VELVCT to be ignored. These include FLO, HI, NSET, ISPV, SPV and (for VELVCT only) LENGTH. Here is a table of the nine settings of CPM and their effect on the operation of the Vectors utility: Value Use FX, FY, etc. Use VELDAT data Use input args ----- ---------------- --------------- -------------- -4 no no no -3 no yes no -2 no no yes -1 no yes yes 0 old - yes; new - no () yes yes 1 yes yes yes 2 yes no yes 3 yes yes no 4 yes no no () Old means EZVEC, VELVEC, VELVCT entry point; new, VVINIT/VVECTR. Only the first column applies to the VVINIT/VVECTR interface. See the velvct man page for more detailed emulation information. CTV - Color Threshold Value Control - Integer In conjunction with NLV, this parameter controls vector coloring and the setting of threshold values. The vectors may be colored based on on the vector magnitude or on the contents of a scalar array (VVINIT/VVECTR input argument, P). A table of supported options follows: -2 Color vector arrows based on scalar array data values; the user is responsible for setting up threshold level array, TVL -1 Color vector arrows based on vector magnitude; the user is responsible for setting up values of threshold level array. Color all vectors according to the current GKS polyline color index value. Threshold level array, TVL and GKS color index array, CLR are not used. 1 Color vector arrows based on vector magnitude; VVINIT assigns values to the first NLV elements of the threshold level array, TVL. 2 Color vector arrows based on scalar array data values; VVINIT assigns values to the first NLV elements of the threshold level array, TVL. If you make CTV positive, you must initialize Vectors with a call to VVINIT after the modification. DMN - NDC Minimum Vector Size - Real, Read-Only This parameter is read-only and has a useful value only following a call to VVECTR (directly or through the compatibility version of VELVCT). You may retrieve it in order to determine the length in NDC space of the smallest vector actually drawn (in other words, the smallest vector within the boundary of the user coordinate space that is greater than or equal in magnitude to the value of the VLC parameter). It is initially set to a value of 0.0. DMX - NDC Maximum Vector Size - Real, Read-Only Unlike DMN this read-only parameter has a potentially useful value betweens calls to VVINIT and VVECTR. However, the value it reports may be different before and after the call to VVECTR. Before the VVECTR call it contains the length in NDC space that would be used to render the maximum size vector assuming the user-settable parameter, VRL is set to its default value of 0.0. After the VVECTR call it contains the NDC length used to render the largest vector actually drawn (in other words, the largest vector within the boundary of the user coordinate space that is less than or equal in magnitude to the value of the VHC parameter). See the section on the VRL parameter for information on using the value of DMX after the VVINIT call in order to adjust proportionally the lengths of all the vectors in the plot. It is initially set to a value of 0.0. DPF - Vector Label Decimal Point Control Flag - Integer If DPF is set to a non-zero value, and the optional vector magnitude labels are enabled, the magnitude values are scaled to fit in the range 1 to 999. The labels will contain 1 to 3 digits and no decimal point. Otherwise, the labels will consist of a number up to six characters long, including a decimal point. By default DPF is set to the value 1. LBC - Vector Label Color - Integer This parameter specifies the color to use for the optional vector magnitude labels, as follows: < -1 Draw labels using the current GKS text color index -1 (default) Draw labels using the same color as the corresponding vector arrow >=0 Draw labels using the LBC value as the GKS text color index LBL - Vector Label Flag - Integer If set non-zero, Vectors draws labels representing the vector magnitude next to each arrow in the field plot. The vector labels are primarily intended as a debugging aid, since in order to avoid excessive overlap, you must typically set the label text size too small to be readable without magnification. For this reason, as well as for efficiency, unlike the other graphical text elements supported by the Vectors utility, the vector labels are rendered using low quality text. LBS - Vector Label Character Size - Real This parameter specifies the size of the characters used for the vector magnitude labels as a fraction of the viewport width. The default value is 0.007. LWD - Vector Linewidth - Real LWD controls the linewidth used to draw the lines that form vector arrows and wind barbs. When the arrows are filled (AST is set to 1) LWD controls the width of the arrow's outline. If the fill is drawn over the outline (AFO set to 1) then LWD must be set to a value greater than 1.0 in order for the outline to appear properly. When AST has the value 2, LWD controls the width of the line elements of wind barbs. When AST is set to 0, specifying line-drawn vector arrows, the linewidth applies equally to the body of the vector and the arrowhead. Overly thick lines may cause the arrow heads to appear smudged. This was part of the motivation for developing the option of filled vector arrows. Note that since linewidth in NCAR Graphics is always calculated relative to a unit linewidth that is dependent on the output device, you may need to adjust the linewidth value depending on the intended output device to obtain a pleasing plot. The default is 1.0, specifying a device-dependent minimum linewidth. MAP - Map Transformation Code - Integer MAP defines the transformation between the data and user coordinate space. Three MAP parameter codes are reserved for pre-defined transformations, as follows: Mapping transformation 0 (default) Identity transformation between data and user coordinates: array indices of U, V, and P are linearly related to data coordinates. 1 Ezmap transformation: first dimension indices of U, V, and P are linearly related to longitude; second dimension indices are linearly related to latitude. 2 Polar to rectangular transformation: first dimension indices of U, V, and P are linearly related to the radius; second dimension indices are linearly related to the angle in degrees. If MAP has any other value, Vectors invokes the user-modifiable subroutine, VVUMXY, to perform the mapping. The default version of VVUMXY simply performs an identity transformation. Note that, while the Vectors utility does not actually prohibit the practice, the user is advised not to use negative integers for user-defined mappings, since other utilities in the NCAR Graphics toolkit attach a special meaning to negative mapping codes. For all the predefined mappings, the linear relationship between the grid array indices and the data coordinate system is established using the four parameters, XC1, XCM, YC1, and YCN. The X parameters define a mapping for the first and last indices of the first dimension of the data arrays, and the Y parameters do the same for the second dimension. If MAP is set to a value of one, be careful to ensure that the SET parameter is given a value of zero, since the Ezmap routines require a specific user coordinate space for each projection type, and internally call the SET routine to define the user to NDC mapping. Otherwise, you may choose whether or not to issue a SET call prior to calling VVINIT, modifying the value of SET as required. See the description of the parameter, TRT, and the vvumxy man page for more information. MNC - Minimum Vector Text Block Color - Integer MNC specifies the color of the minimum vector graphical text output block as follows: <-2 Both the vector arrow and the text are colored using the current text color index. -2 If the vectors are colored by magnitude, both the vector arrow and the text use the GKS color index associated with the minimum vector magnitude. Otherwise, the vector arrow uses the current polyline color index and the text uses the current text color index. -1 (default) If the vectors are colored by magnitude, the vector arrow uses the GKS color index associated with the minimum vector magnitude. Otherwise the vector arrow uses the current polyline color index. The text is colored using the current text color index in either case. >= 0 The value of MNC is used as the color index for both the text and the vector arrow See the description of MNT for more information about the minimum vector text block. MNP - Minimum Vector Text Block Positioning Mode - Integer This parameter allows you to justify the minimum vector text block, taken as a single unit, relative to the text block position established by the parameters, MNX and MNY. Nine positioning modes are available, as follows: Mode Justification -4 The lower left corner of the text block is positioned at MNX, MNY. -3 The center of the bottom edge is positioned at MNX, MNY. -2 The lower right corner is positioned at MNX, MNY. -1 The center of the left edge is positioned at MNX, MNY. 0 The text block is centered along both axes at MNX, MNY. 1 The center of the right edge is positioned at MNX, MNY. 2 The top left corner is positioned at MNX, MNY. 3 The center of the top edge is positioned at MNX, MNY. 4 (default) The top right corner is positioned at MNX, MNY. See the description of MNT for more information about the minimum vector text block. MNS - Minimum Vector Text Block Character Size - Real MNS specifies the size of the characters used in the minimum vector graphics text block as a fraction of the viewport width. See the description of MNT for more information about the minimum vector text block. The default value of MNS is 0.0075. MNT - Minimum Vector Text String - Character* 36 The minimum vector graphics text block consists of a user-definable text string centered underneath a horizontal arrow. If the parameter VLC is set negative the arrow is rendered at the size of the reference minimum magnitude vector (which may be smaller than any vector that actually appears in the plot). Otherwise, the arrow is the size of the smallest vector in the plot. Directly above the arrow is a numeric string in exponential format that represents the vector's magnitude. Use MNT to modify the text appearing below the vector in the minimum vector graphics text block. Currently the string length is limited to 36 characters. Set MNT to a single space (' ') to remove the text block, including the vector arrow and the numeric magnitude string, from the plot. The default value is 'Minimum Vector' MNX - Minimum Vector Text Block X Coordinate - Real MNX establishes the X coordinate of the minimum vector graphics text block as a fraction of the viewport width. Values less than 0.0 or greater than 1.0 are permissible and respectively represent regions to the left or right of the viewport. The actual position of the block relative to MNX depends on the value assigned to MNP. See the descriptions of MNT and MNP for more information about the minimum vector text block. The default value of MNX is 0.475. MNY - Minimum Vector Text Block Y Coordinate - Real MNY establishes the Y coordinate of the minimum vector graphics text block as a fraction of the viewport height. Values less than 0.0 or greater than 1.0 are permissible and respectively represent regions below or above the viewport. The actual position of the block relative to MNY depends on the value assigned to MNP. See the descriptions of MNT and MNP for more information about the minimum vector text block. The default value of MNY is -0.01. MSK - Mask To Area Map Flag - Integer Use this parameter to control masking of vectors to an existing area map created by routines in the Areas utility. When MSK is greater than 0, masking is enabled and an the area map must be set up prior to the call to VVECTR. The area map array and, in addition, the name of a user-definable masked drawing routine, must be passed as input parameters to VVECTR. Various values of the MSK parameter have the following effects: <= 0 (default) No masking of vectors. 1 The subroutine ARDRLN is called internally to decompose the vectors into segments contained entirely within a single area. ARDRLN calls the user-definable masked drawing subroutine. >1 Low precision masking. ARGTAI is called internally to get the area identifiers for the vector base position point. Then the user-definable masked drawing subroutine is called to draw the vector. Vectors with nearby base points may encroach into the intended mask area. See the man page vvudmv for further explanation of masked drawing of vectors MXC - Maximum Vector Text Block Color - Integer MXC specifies the color of the maximum vector graphical text output block as follows: <-2 Both the vector arrow and the text are colored using the current text color index. -2 If the vectors are colored by magnitude, both the vector arrow and the text use the GKS color index associated with the minimum vector magnitude. Otherwise, the vector arrow uses the current polyline color index and the text uses the current text color index. -1 (default) If the vectors are colored by magnitude, the vector arrow uses the GKS color index associated with the minimum vector magnitude. Otherwise the vector arrow uses the current polyline color index. The text is colored using the current text color index in either case. >= 0 The value of MXC is used as the color index for both the text and the vector arrow See the description of MXT for more information about the maximum vector text block. MXP - Maximum Vector Text Block Positioning Mode - Integer This parameter allows you to justify the maximum vector text block, taken as a single unit, relative to the text block position established by the parameters, MXX and MXY. Nine positioning modes are available, as follows: Mode Justification -4 The lower left corner of the text block is positioned at MXX, MXY. -3 The center of the bottom edge is positioned at MXX, MXY. -2 The lower right corner is positioned at MXX, MXY. -1 The center of the left edge is positioned at MXX, MXY. 0 The text block is centered along both axes at MXX, MXY. 1 The center of the right edge is positioned at MXX, MXY. 2 The top left corner is positioned at MXX, MXY. 3 The center of the top edge is positioned at MXX, MXY. 4 The top right corner is positioned at MXX, MXY. See the description of MXT for more information about the maximum vector text block. MXS - Maximum Vector Text Block Character Size - Real MXS specifies the size of the characters used in the maximum vector graphics text block as a fraction of the viewport width. See the description of MXT for more information about the maximum vector text block. The default value is 0.0075. MXT - Maximum Vector Text String - Character* 36 The maximum vector graphics text block consists of a user-definable text string centered underneath a horizontal arrow. If the parameter VHC is set negative the arrow is rendered at the size of the reference maximum magnitude vector (which may be larger than any vector that actually appears in the plot). Otherwise, the arrow is the size of the largest vector in the plot. Directly above the arrow is a numeric string in exponential format that represents the magnitude of this vector. Use MXT to modify the text appearing below the vector in the maximum vector graphics text block. Currently the string length is limited to 36 characters. Set MXT to a single space (' ') to completely remove the text block, including the vector arrow and the numeric magnitude string, from the plot. Note that the name "Maximum Vector Text Block" is no longer accurate, since using the parameter VRM it is now possible to establish a reference magnitude that is smaller than the maximum magnitude in the data set. A more accurate name would be "Reference Vector Text Block". The default value of MXT is 'Maximum Vector'. MXX - Maximum Vector Text Block X Coordinate - Real MXX establishes the X coordinate of the maximum vector graphics text block as a fraction of the viewport width. Values less than 0.0 or greater than 1.0 are permissible and respectively represent regions below or above of the viewport. The actual position of the block relative to MXX depends on the value assigned to MXP. See the descriptions of MXT and MXP for more information about the maximum vector text block. The default value is 0.525. MXY - Maximum Vector Text Block Y Coordinate - Real MXY establishes the Y coordinate of the maximum vector graphics text block as a fraction of the viewport width. Values less than 0.0 or greater than 1.0 are permissible and respectively represent regions below or above the viewport. The actual position of the block relative to MXY depends on the value assigned to MXP. See the descriptions of MXT and MXP for more information about the maximum vector text block. The default value is -0.01. NLV - Number of Colors Levels - Integer NLV specifies the number of color levels to use when coloring the vectors according to data in a scalar array or by vector magnitude. Anytime CTV has a non-zero value, you must set up the first NLV elements of the color index array CLR. Give each element the value of a GKS color index that must be defined by a call to the the GKS subroutine, GSCR, prior to calling VVECTR. If CTV is less than 0, in addition to setting up the CLR array, you are also responsible for setting the first NLV elements of the threshold values array, TVL to appropriate values. NLV is constrained to a maximum value of 255. The default value of NLV is 0, specifying that vectors are colored according to the value of the GKS polyline color index currently in effect, regardless of the value of CTV. If CTV is greater than 0, you must initialize Vectors with a call to VVINIT after modifying this parameter. PAI - Parameter Array Index - Integer The value of PAI must be set before calling VVGETC, VVGETI, VVGETR, VVSETC, VVSETI, or VVSETR to access any parameter which is an array; it acts as a subscript to identify the intended array element. For example, to set the 10th color threshold array element to 7, use code like this: CALL VVSETI ('PAI - PARAMETER ARRAY INDEX',10) CALL VVSETI ('CLR - Color Index',7) The default value of PAI is one. PLR - Polar Input Mode - Integer When PLR is greater than zero, the vector component arrays are considered to contain the field data in polar coordinate form: the U array is treated as containing the vector magnitude and the V array as containing the vector angle. Be careful not to confuse the PLR parameter with the MAP parameter set to polar coordinate mode (2). The MAP parameter relates to the location of the vector, not its value. Here is a table of values for PLR: 0 (default) U and V arrays contain data in cartesian component form. 1 U array contains vector magnitudes; V array contains vector angles in degrees. 2 U array contain vector magnitudes; V array contains vector angles in radians. You must initialize Vectors with a call to VVINIT after modifying this parameter. PMN - Minimum Scalar Array Value - Real, Read-Only You may retrieve the value specified by PMN at any time after a call to VVINIT. It will contain a copy of the minimum value encountered in the scalar data array. If no scalar data array has been passed into VVINIT it will have a value of 0.0. PMX - Maximum Scalar Array Value - Real You may retrieve the value specified by PMX at any time after a call to VVINIT. It contains a copy of the maximum value encountered in the scalar data array. If no scalar data array has been passed into VVINIT it will have a value of 0.0. PSV - P Array Special Value - Real Use PSV to indicate the special value that flags an unknown data value in the P scalar data array. This value will not be considered in the determination of the data set maximum and minimum values. Also, depending on the setting of the SPC parameter, the vector may be specially colored to flag the unknown data point, or even eliminated from the plot. You must initialize Vectors with a call to VVINIT after modifying this parameter. SET - SET Call Flag - Integer Give SET the value 0 to inhibit the SET call VVINIT performs by default. Arguments 5-8 of a SET call made by the user must be consistent with the ranges of the user coordinates expected by Vectors. This is determined by the mapping from grid to data coordinates as specified by the values of the parameters XC1, XCM, YC1, YCN, and also by the mapping from data to user coordinates established by the MAP parameter. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of SET is 1. SPC - Special Color - Integer SPC controls special value processing for the optional scalar data array used to color the vectors, as follows: < 0 (default) The P scalar data array is not examined for special values. 0 Vectors at P scalar array special value locations are not drawn. > 0 Vectors at P scalar array special value locations are drawn using color index SPC. You must initialize Vectors with a call to VVINIT after modifying this parameter. SVF - Special Value Flag - Integer The special value flag controls special value processing for the U and V vector component data arrays. Special values may appear in either the U or V array or in both of them. Five different options are available (although the usefulness of some of the choices is debatable): 0 (default) Neither the U nor the V array is examined for special values 1 Vectors with special values in the U array are not drawn 2 Vectors with special values in the V array are not drawn 3 Vectors with special values in either the U or V array are not drawn 4 Vectors with special values in both the U and V arrays are not drawn The U and V special values are defined by setting parameters USV and VSV. You must initialize Vectors with a call to VVINIT after modifying this parameter. TRT - Transformation Type - Integer As currently implemented, TRT further qualifies the mapping transformation specified by the MAP parameter, as follows: -1 Direction, magnitude, and location are all transformed. This option is not currently supported by any of the pre-defined coordinate system mappings. 0 Only location is transformed 1 (default) Direction and location are transformed This parameter allows you to distinguish between a system that provides a mapping of location only into an essentially cartesian space, and one in which the space itself mapped. To understand the difference, using polar coordinates as an example, imagine a set of wind speed monitoring units located on a radial grid around some central point such as an airport control tower. Each unit's position is defined in terms of its distance from the tower and its angular direction from due east. However, the data collected by each monitoring unit is represented as conventional eastward and northward wind components. Assuming the towers's location is at a moderate latitude, and the monitoring units are reasonably 'local', this is an example of mapping a radially defined location into a nearly cartesian space (i.e. the eastward components taken alone all point in a single direction on the plot, outlining a series of parallel straight lines). One would set MAP to two (for the polar transformation) and TRT to zero to model this data on a plot generated by the Vectors utility. On the other hand, picture a set of wind data, again given as eastward and northward wind components, but this time the center of the polar map is actually the south pole. In this case, the eastward components do not point in a single direction; instead they outline a series of circles around the pole. This is a space mapping transformation: one would again set MAP to two, but TRT would be set to one to transform both direction and location. Changing the setting of this parameter affects the end results only when a non-uniform non-linear mapping occurs at some point in the transformation pipeline. For this discussion a uniform linear transformation is defined as one which satisfies the following equations: x_out = x_offset + scale_constant * x_in y_out = y_offset + scale_constant * y_in If scale_constant is not the same for both the X axis and the Y axis then the mapping is non-uniform. This option is currently implemented only for the pre-defined MAP parameter codes, 0 and 2, the identity mapping and the polar coordinate mapping. However, it operates on a different stage of the transformation pipeline in each case. The polar mapping is non-linear from data to user coordinates. The identity mapping, even though necessarily linear over the data to user space mapping, can have a non-uniform mapping from user to NDC space, depending on the values given to the input parameters of the SET call. This will be the case whenever the LL input parameter is other than one, or when LL equals one, but the viewport and the user coordinate boundaries do not have the same aspect ratio. Thus for a MAP value of 2, TRT affects the mapping between data and user space, whereas for MAP set to 0, TRT influences the mapping between user and NDC space. TVL - Array of Threshold Values - Real Array TVL is an array of threshold values that is used to determine the individual vector color, when CTV and NLV are both non-zero. For each vector the TVL array is searched for the smallest value greater than or equal to the scalar value associated with the vector. The array subscript of this element is used as an index into the CLR array. Vectors uses the GKS color index found at this element of the CLR array to set the color for the vector. Note that Vectors assumes that the threshold values are monotonically increasing. When CTV is less than 0, you are responsible for assigning values to the elements of TVL yourself. To do this, first set the PAI parameter to the index of the threshold level element you want to define, then call VVSETR to set TVL to the appropriate threshold value for this element. Assuming the desired values have previously been stored in a array named TVALS, you could assign the threshold values for a fourteen level color palette using the following loop: DO 100 I=1,14,1 CALL VVSETI(PAI -- Parameter Array Index, I) CALL VVSETR(TVL -- Threshold Value, TVALS(I)) 100 CONTINUE When CTV is greater than 0, Vectors assigns values into TVL itself. Each succeeding element value is greater than the preceding value by the value of the expression: (maximum_data_value - minimum_data_value) / NLV where the data values are either from the scalar data array or are the magnitudes of the vectors in the vector component arrays. The first value is equal to the minimum value plus the expression; the final value (indexed by the value of NLV) is equal to the maximum value. If Vectors encounters a value greater than the maximum value in the TVL array while processing the field data, it gives the affected vector the color associated with the maximum TVL value. USV - U Array Special Value - Real USV is the U vector component array special value. It is a value outside the range of the normal data used to indicate that there is no valid data for this grid location. When SVF is set to 1 or 3, Vectors will not draw a vector whose U component has the special value. You must initialize Vectors with a call to VVINIT after modifying this parameter. It has a default value of 1.0 E12. VFR - Minimum Vector Fractional Length - Real Use this parameter to adjust the realized size of the reference minimum magnitude vector relative to the reference maximum magnitude vector in order to improve the appearance or perhaps the information content of the plot. Specify VFR as a value between 0.0 and 1.0, where 0.0 represents an unmodified linear scaling of the realized vector length, in proportion to magnitude, and 1.0 specifies that the smallest vector be represented at 1.0 times the length of the largest vector, resulting in all vectors, regardless of magnitude, having the same length on the plot. A value of 0.5 means that the smallest magnitude vector appears half as long as the largest magnitude vector; intermediate sizes are proportionally scaled to lengths between these extremes. Where there is a wide variation in magnitude within the vector field, you can use this parameter to increase the size of the smallest vectors to a usefully visible level. Where the variation is small, you can use the parameter to exaggerate the differences that do exist. See also the descriptions of VRL, VLC, VHC, and VRM. The default value is 0.0. VHC - Vector High Cutoff Value - Real If the parameter VRM is set to a value greater than 0.0, it supercedes the use of VHC to specify the reference magnitude. VRM allows greater flexibility in that it can be used to specify an arbitrary reference magnitude that need not be the maximum magnitude contained in the data set. VHC can still be used to set a high cutoff value -- no vectors with magnitude greater than the cutoff value will be displayed in the plot. If VRM has its default value, 0.0, VHC specifies the reference maximum magnitude represented by an arrow of length VRL (as a fraction of the viewport width). The realized length of each individual vector in the plot is based on its magnitude relative to the reference maximum magnitude and, if VFR is non-zero, the reference minimum magnitude (as specified by VLC). Note that the reference maximum magnitude may be greater than the magnitude of any vector in the dataset. The effect of this parameter varies depending on its value, as follows: < 0.0 The absolute value of VHC unconditionally determines the reference maximum magnitude. Vectors in the dataset with magnitude greater than VHC are not displayed. 0.0 (default) The vector with the greatest magnitude in the dataset determines the reference maximum magnitude. > 0.0 The minimum of VHC and the vector with the greatest magnitude in the data set determines the reference maximum magnitude. Vectors in the dataset with magnitude greater than VHC are not Typically, for direct comparison of the output of a series of plots, you would set VHC to a negative number, the absolute value of which is greater than any expected vector magnitude in the series. You can turn on Vectors statistics reporting using the parameter VST in order to see if any vectors in the datasets do exceed the maximum magnitude you have specified. See also the descriptions of the parameters VRM, VRL, DMX, VLC, and VFR. VLC - Vector Low Cutoff Value - Real Use this parameter to prevent vectors smaller than the specified magnitude from appearing in the output plot. VLC also specifies the reference minimum magnitude that is rendered at the size specified by the product of VRL and VFR (as a fraction of the viewport width), when VFR is greater than 0.0. Note that the reference minimum magnitude may be smaller than the magnitude of any vector in the dataset. The effect of this parameter varies depending on its value, as follows: < 0.0 The absolute value of VLC unconditionally determines the reference minimum magnitude. Vectors in the dataset with magnitude less than VLC do not appear. 0.0 (default) The vector with the minimum magnitude in the dataset determines the reference minimum magnitude. > 0.0 The maximum of VLC and the vector with the least magnitude in the data set determines the reference minimum magnitude. Vectors in the dataset with magnitude less than VLC do not appear. The initialization subroutine, VVINIT, calculates the magnitude of all the vectors in the vector field, and stores the maximum and minimum values. You may access these values by retrieving the read-only parameters, VMX and VMN. Thus it is possible to remove the small vectors without prior knowledge of the data domain. The following code fragment illustrates how the smallest 10% of the vectors could be removed: CALL VVINIT(... CALL VVGETR('VMX - Vector Maximum Magnitude', VMX) CALL VVGETR('VMN - Vector Minimum Magnitude', VMN) CALL VVSETR('VLC - Vector Low Cutoff Value', + VMN+0.1(VMX-VMN)) CALL VVECTR(... On the other hand, when creating a series of plots that you would like to compare directly and you are using VFR to set a minimum realized size for the vectors, you can ensure that all vectors of a particular length represent the same magnitude on all the plots by setting both VHC and VLC to negative values. If you do not actually want to remove any vectors from the plot, make VLC smaller in absolute value than any expected magnitude. You can turn on Vectors statistics reporting using the parameter VST in order to see if any vectors in the datasets are less the minimum magnitude you have specified. See also the descriptions of parameters VFR, VRL, VHC, DMN, and VRM. VMD - Vector Minimum Distance - Real If VMD is set to a value greater than 0.0, it specifies, as a fraction of the viewport width, a minimum distance between adjacent vectors arrows in the plot. The distribution of vectors is analyzed and then vectors are selectively removed in order to ensure that the remaining vectors are separated by at least the specified distance. The thinning algorithm requires that you supply Vectors with a work array twice the size of the VVINIT arguments N and M multiplied together. Use of this capability adds some processing time to the execution of Vectors. If VMD is set to a value greater than 0.0 and no work array is provided, an error condition results. If the data grid is transformed in such a way that adjacent grid cells become very close in NDC space, as for instance in many map projections near the poles, you can use this parameter to reduce the otherwise cluttered appearance of these regions of the plot. The default value of VMD is 0.0. VMN - Minimum Vector Magnitude - Real, Read-Only After a call to VVINIT, VMN contains the value of the minimum vector magnitude in the U and V vector component arrays. Later, after VVECTR is called, it is modified to contain the magnitude of the smallest vector actually displayed in the plot. This is the vector with the smallest magnitude greater than or equal to the value specified by VLC, the vector low cutoff parameter, (0.0 if VLC has its default value) that falls within the user coordinate window boundaries. The value contained in VMN is the same as that reported as the 'Minimum plotted vector magnitude' when Vectors statistics reporting is enabled. It may be larger than the reference minimum magnitude reported by the minimum vector text block if you specify the VLC parameter as a negative value. VMN is initially set to a value of 0.0. VMX - Maximum Vector Magnitude - Real, Read-Only After a call to VVINIT, VMX contains the value of the maximum vector magnitude in the U and V vector component arrays. Later, after VVECTR is called, it is modified to contain the magnitude of the largest vector actually displayed in the plot. This is the vector with the largest magnitude less than or equal to the value specified by VHC, the vector high cutoff parameter, (the largest floating point value available on the machine if VHC has its default value, 0.0) that falls within the user coordinate window boundaries. The value contained in VMX is the same as that reported as the 'Maximum plotted vector magnitude' when Vectors statistics reporting is enabled. It may be smaller than the reference maximum magnitude reported by the maximum vector text block if you specify the VHC parameter as a negative value. VMX is initially set to a value of 0.0. VPB - Viewport Bottom - Real The parameter VPB has an effect only when SET is non-zero, specifying that Vectors should do the call to SET. It specifies a minimum boundary value for the bottom edge of the viewport in NDC space, and is constrained to a value between 0.0 and 1.0. It must be less than the value of the Viewport Top parameter, VPT. The actual value of the viewport bottom edge used in the plot may be greater than the value of VPB, depending on the setting of the Viewport Shape parameter, VPS. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of VPB is 0.05. VPL - Viewport Left - Real The parameter VPL has an effect only when SET is non-zero, specifying that Vectors should do the call to SET. It specifies a minimum boundary value for the left edge of the viewport in NDC space, and is constrained to a value between 0.0 and 1.0. It must be less than the value of the Viewport Right parameter, VPR. The actual value of the viewport left edge used in the plot may be greater than the value of VPL, depending on the setting of the Viewport Shape parameter, VPS. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of VPL is VPO - Vector Positioning Mode - Integer VPO specifies the position of the vector arrow in relation to the grid point location of the vector component data. Three settings are available, as follows: <0 The head of the vector arrow is placed at the grid point location 0 (default) The center of the vector arrow is placed at the grid point location >0 The tail of the vector arrow is placed at the grid point location VPR - Viewport Right - Real The parameter VPR has an effect only when SET is non-zero, specifying that Vectors should do the call to SET. It specifies a maximum boundary value for the right edge of the viewport in NDC space, and is constrained to a value between 0.0 and 1.0. It must be greater than the value of the Viewport Left parameter, VPL. The actual value of the viewport right edge used in the plot may be less than the value of VPR, depending on the setting of the Viewport Shape parameter, VPS. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of VPR is 0.95. VPS - Viewport Shape - Real The parameter VPS has an effect only when SET is non-zero, specifying that Vectors should do the call to SET; it specifies the desired viewport shape, as follows: <0.0 The absolute value of VPS specifies the shape to use for the viewport., as the ratio of the viewport width to its height, 0.0 The viewport completely fills the area defined by the boundaries specifiers, VPL, VPR, VPB, VPT >0.0,<1.0 (0.25, default) Use R = (XCM-XC1)/(YCN-YC1) as the viewport shape if MIN(R, 1.0/R) is greater than VPS. Otherwise determine the shape as when VPS is equal to 0.0. >= 1.0 Use R = (XCM-XC1)/(YCN-YC1) as the viewport shape if MAX(R, 1.0/R) is less than VPS. Otherwise make the viewport a square. The viewport, whatever its final shape, is centered in, and made as large as possible in, the area specified by the parameters VPB, VPL, VPR, and VPT. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of VPS is 25. VPT - Viewport Top - Real The parameter VPT has an effect only when SET is non-zero, specifying that Vectors should do the call to SET. It specifies a maximum boundary value for the top edge of the viewport in NDC space, and is constrained to a value between 0.0 and 1.0. It must be greater than the value of the Viewport Bottom parameter, VPB. The actual value of the viewport top edge used in the plot may be less than the value of VPT, depending on the setting of the Viewport Shape parameter, VPS. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of VPT is VRL - Vector Reference Length - Real Use this parameter to specify the realized length of the reference magnitude vector as a fraction of the viewport width. Based on this value a reference length in NDC units is established, from which the length of all vectors in the plot is derived. The relationship between magnitude and length also depends on the setting of the minimum vector magnitude fraction parameter, VFR, but, given the default value of VFR (0.0), the length of each vector is simply proportional to its relative magnitude. Note that the arrow size parameters, AMN and AMX, allow independent control over the minimum and maximum size of the vector arrowheads. Given a reference length, Vectors calculates a maximum length based on the ratio of the reference magnitude to the larger of the maximum magnitude in the data set and the reference magnitude itself. This length is accessible in units of NDC via the read-only parameter, DMX. If VRL is set less than or equal to 0.0, VVINIT calculates a default value for DMX, based on the size of a grid box assuming a linear mapping from grid coordinates to NDC space. The value chosen is one half the diagonal length of a grid box. By retrieving the value of DMX and calling GETSET to retrieve the viewport boundaries after the call to VVINIT, you can make relative adjustments to the vector length, as shown by the following example, where the maximum vector length is set to 1.5 times its default value: CALL VVINIT(... CALL VVGETR('DMX - NDC Maximum Vector Size', DMX) CALL GETSET(VL,VR,VB,VT,UL,UR,UB,UT,LL) VRL = 1.5 DMX / (VR - VL) CALL VVSETR('VRL - Vector Realized Length', VRL) CALL VVECTR(... When VVECTR sees that VRL is greater than 0.0, it will calculate a new value for DMX. If VRL is never set, the initially calculated value of DMX is used as the reference length. Do not rely on the internal parameters used for setting the viewport, VPL, VPR, VPB and VPT to retrieve information about viewport in lieu of using the GETSET call. These values are ignored entirely if the SET parameter is zero, and even if used, the viewport may be adjusted from the specified values depending on the setting of the viewport shape parameter, VPS. See also the descriptions of VFR, VRM, and VHC. The default value of VRL is 0.0. VRM - Vector Reference Magnitude - Real The introduction of the parameter VRM means that it is now possible to specify an arbitrary vector magnitude as the reference magnitude appearing in the "Maximum Vector Text Block" annotation. The reference magnitude no longer needs to be greater or equal to the largest magnitude in the data set. When VRM has a value greater than 0.0, it specifies the magnitude of the vector arrow drawn at the reference length. See VRL for an explanation of how the reference length is determined. If VRM is less than or equal to 0.0, the reference magnitude is determined by the value of VHC, the vector high cutoff value. If, in turn, VHC is equal to 0.0 the maximum magnitude in the vector field data set becomes the reference magnitude. The default value of VRM is 0.0. VST - Vector Statistics Output Flag - Integer If VST is set to one, VVECTR writes a summary of its operation to the default logical output unit, including the number of vectors plotted, number of vectors rejected, minimum and maximum vector magnitudes, and if coloring the vectors according to data in the scalar array, the maximum and minimum scalar array values encountered. Here is a sample of the output: VVECTR Statistics Vectors plotted:906 Vectors rejected by mapping routine:0 Vectors under minimum magnitude:121 Vectors over maximum magnitude:0 Other zero length vectors:0 Rejected special values:62 Minimum plotted vector magnitude:9.94109E-02 Maximum plotted vector magnitude:1.96367 Minimum scalar value:-1.00000 Maximum scalar value:1.00000 VSV - V Array Special Value - Real VSV is the V vector component array special value. It is a value outside the range of the normal data used to indicate that there is no valid data for this grid location. When SVF is set to 2 or 3, Vectors will not draw a vector whose V component has the special value. You must initialize Vectors with a call to VVINIT after modifying this parameter. It has a default value of 1.0 E12. WBA - Wind Barb Angle - Real WBA sets the angle of the wind barb ticks in degrees as measured clockwise from the vector direction. It also sets the angle between the hypotenuse of the triangle defining the pennant polygon and the vector direction. You can render southern hemisphere wind barbs, which by convention, have their ticks and pennants on the other side of the shaft, by setting WBA to a negative value. WBA has an effect only when AST has the value 2. WBC - Wind Barb Calm Circle Size - Real WBC sets the diameter of the circle used to represent small vector magnitudes (less than 2.5) as a fraction of the overall wind barb length (the value of the VRL parameter). WBC has an effect only when AST has the value 2. WBD - Wind Barb Distance Between Ticks - Real WBD sets the distance between adjacent wind barbs ticks along the wind barb shaft as a fraction of the overall wind barb length (the value of the VRL parameter). Half this distance is used as the spacing between adjacent wind barb pennants. Note that there is nothing to to prevent ticks and/or pennants from continuing off the end of the shaft if a vector of high enough magnitude is encountered. You are responsible for adjusting the parameters appropriately for the range of magnitudes you need to handle. WBD has an effect only when AST has the value 2. WBS - Wind Barb Scale Factor - Real WBS specifies a factor by which magnitudes passed to the wind barb drawing routines are to be scaled. It can be used to convert vector data given in other units into the conventional units used with wind barbs, which is knots. For instance, if the data are in meters per second, you could set WBS to 1.8974 to create a plot with conventional knot-based wind barbs. Note that setting WBS does not currently have any effect on the magnitude values written into the maximum or minimum vector legends. WBS has an effect only when AST has the value 2. WBT - Wind Barb Tick Size - Real WBT the length of the wind barb ticks as a fraction of the overall length of a wind barb (the value of the VRL parameter). The wind barb length is defined as the length of the wind barb shaft plus the projection of a full wind barb tick along the axis of the shaft. Therefore, increasing the value of WBT, for a given value of VRL has the effect of reducing the length of the shaft itself somewhat. You may need to increase VRL itself to compensate. WBT also sets the hypotenuse length of the triangle defining the pennant polygon. WBT has an effect only when AST has the value WDB - Window Bottom - Real When VVINIT does the call to SET, the parameter WDB is used to determine argument number 7, the user Y coordinate at the bottom of the window. If WDB is not equal to WDT, WDB is used. If WDB is equal to WDT, but YC1 is not equal to YCN, then YC1 is used. Otherwise, the value 1.0 is used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of WDB is 0.0. WDL - Window Left - Real When VVINIT the call to SET, the parameter WDL is used to determine argument number 5, the user X coordinate at the left edge of the window. If WDL is not equal to WDR, WDL is used. If WDL is equal to WDR, but XC1 is not equal to XCM, then XC1 is used. Otherwise, the value 1.0 is used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of WDL is 0.0. WDR - Window Right - Real When VVINIT does the call to SET, the parameter WDR is used to determine argument number 6, the user X coordinate at the right edge of the window. If WDR is not equal to WDL, WDR is used. If WDR is equal to WDL, but XCM is not equal to XC1, then XCM is used. Otherwise, the value of the VVINIT input parameter, M, converted to a real, is used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of WDR is 0.0. WDT - Window Top - Real When VVINIT does the call to SET, the parameter WDB is used to determine argument number 8, the user Y coordinate at the top of the window. If WDT is not equal to WDB, WDT is used. If WDT is equal to WDB, but YCN is not equal to YC1 then YCN is used. Otherwise, the value of the VVINIT input parameter, N, converted to a real, is used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of WDT is 0.0. XC1 - X Coordinate at Index 1 - Real The parameter XC1 specifies the X coordinate value that corresponds to a value of 1 for the first subscript of the U, V, vector component arrays as well as for the P scalar data array, if used. Together with XCM, YC1, and YCN it establishes the mapping from grid coordinate space to data coordinate space. If XC1 is equal to XCM, 1.0 will be used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of XC1 is 0.0. XCM - X Coordinate at Index M - Real The parameter XCM specifies the X coordinate value that corresponds to the value of the VVINIT input parameter, M, for the first subscript of the U and V vector component arrays as well as for the P scalar data array, if used. Together with XC1, YC1, and YCN it establishes the mapping from grid coordinate space to data coordinate space. If XC1 is equal to XCM, the value of M, converted to a real, will be used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of XCM is 0.0. XIN - X Axis Array Increment (Grid) - Integer XIN controls the step size through first dimensional subscripts of the U,V vector component arrays and also through the P scalar data array if it is used. For dense arrays plotted at a small scale, you could set this parameter to a value greater than one to reduce the crowding of the vectors and hopefully improve the intelligibility of the plot. The grid point with subscripts (1,1) is always included in the plot, so if XIN has a value of three, for example, only grid points with first dimension subscripts 1, 4, 7... (and so on) will be plotted. See also YIN. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of XIN is 1. YC1 - Y Coordinate at Index 1 - Real The parameter YC1 specifies the Y coordinate value that corresponds to a value of 1 for the first subscript of the U, V, vector component arrays as well as for the P scalar data array, if used. Together with YCN, XC1, and XCM it establishes the mapping from grid coordinate space to data coordinate space. If YC1 is equal to YCN, 1.0 will be used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of YC1 is 0.0. YCN - Y Coordinate at Index N - Real The parameter YCN specifies the Y coordinate value that corresponds to the value of the VVINIT input parameter, N, for the second subscript of the U and V vector component arrays as well as the P scalar data array, if used. Together with YC1, XC1, and XCM it establishes the mapping from grid coordinate space to data coordinate space. If YC1 is equal to YCN, the value of N, converted to a real, will be used. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of YCN is 0.0. YIN - Y Axis Array Increment (Grid) - Integer YIN controls the step size through the second dimension subscripts of the U and V vector component arrays and also through the P scalar data array if it is used. For dense arrays plotted at a small scale, you could set this parameter to a value greater than one to reduce the crowding of the vectors and hopefully improve the intelligibility of the plot. The grid point with subscripts (1,1) is always included in the plot, so if YIN has a value of three, for example, only grid points with second dimension subscripts 1, 4, 7... (and so on) will be plotted. See also XIN. You must initialize Vectors with a call to VVINIT after modifying this parameter. The default value of YIN is 1. ZFC - Zero Field Text Block Color - Integer If ZFC is greater or equal to zero, it specifies the GKS color index to use to color the Zero Field text block. Otherwise the Zero Field text block is colored using the current GKS text color index. The default value of ZFC is -1. ZFP - Zero Field Text Block Positioning Mode - Integer The ZFP parameter allows you to justify, using any of the 9 standard justification modes, the Zero Field text block unit with respect to the position established by the parameters, ZFX and ZFY The position modes are supported as follows: Mode Justification -4 The lower left corner of the text block is positioned at ZFX, ZFY. -3 The center of the bottom edge is positioned at ZFX, ZFY. -2 The lower right corner is positioned at ZFX, ZFY. -1 The center of the left edge is positioned at ZFX, ZFY. 0 (default) The text block is centered along both axes at ZFX, ZFY. 1 The center of the right edge is positioned at ZFX, ZFY. 2 The top left corner is positioned at ZFX, ZFY. 3 The center of the top edge is positioned at ZFX, ZFY. 4 The top right corner is positioned at ZFX, ZFY. ZFS - Zero Field Text Block Character Size - Real ZFS specifies the size of the characters used in the Zero Field graphics text block as a fraction of the viewport width. The default value is 0.033. ZFT - Zero Field Text String - Character* 36 Use ZFT to modify the text of the Zero Field text block. The Zero Field text block may appear whenever the U and V vector component arrays contain data such that all the grid points otherwise eligible for plotting contain zero magnitude vectors. Currently the string length is limited to 36 characters. Set ZFT to a single space (' ') to prevent the text from being displayed. The default value for the text is 'Zero Field'. ZFX - Zero Field Text Block X Coordinate - Real ZFX establishes the X coordinate of the Zero Field graphics text block as a fraction of the viewport width. Values less than 0.0 or greater than 1.0 are permissible and respectively represent regions to the left or right of the viewport. The actual position of the block relative to ZFX depends on the value assigned to the Zero Field Positioning Mode parameter, ZFP. The default value is 0.5. ZFY - Zero Field Text Block Y Coordinate - Real ZFY establishes the Y coordinate of the minimum vector graphics text block as a fraction of the viewport height. Values less than 0.0 or greater than 1.0 are permissible and respectively represent regions below and above the viewport. The actual position of the block relative to ZFY depends on the value assigned to the Zero Field Positioning Mode parameter, ZFP. The default value is 0.5. Copyright (C) 1987-2009 University Corporation for Atmospheric Research The use of this Software is governed by a License Agreement. Online: vectors, vvectr, vvgetc, vvgeti, vvgetr, vvinit, vvrset, vvsetc, vvseti, vvsetr. vvudmv, vvumxy, ncarg_cbind.	{"url":"https://www.systutorials.com/docs/linux/man/3-ncl_vectors_params/","timestamp":"2024-11-04T08:18:12Z","content_type":"text/html","content_length":"79067","record_id":"<urn:uuid:1ea7db2e-b5ec-4014-90a2-f5f1c0a3a353>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00605.warc.gz"}
Give me a number! - ACI People are often asked about estimates in investments, the opening of new business areas, projects and budgeting. The estimates given are subject to uncertainty. No one can tell the exact amount, time etc., that will occur in the future. Despite this uncertainty, there is a great demand for estimates given in a single number. So, give me a number! What is going to be our revenue next year? Give me a number, not some soft statement. Give me a number I can use for my calculations. In situations like this, when asked to give a number on tomorrow’s uncertainties, most provide an average. The average turnover from the past five years is X, so here is my estimate. The average duration of such a project is Y months, so there you have my estimate. Is that the right way to go about it when giving estimates about tomorrow’s uncertainties? Imagine the following: • Three separate teams are working in each their phase of a project. • All three phases must be completed before the project is finished. • The three phases can run parallel to each other. To determine how long the project is estimated to take to finish, you gather estimates of the duration for each subphase. All three teams return with the same estimate of 4 weeks on average. How long is the project going to take on average? 4 weeks, you might say. Try again. Are you still going with 4 weeks on average? Then you might have fallen victim to “The Flaw of Averages”. The average output is not equal to the average of the inputs. • It doesn’t take 4 weeks to finish a project, with each underlying phase taking 4 weeks since the phases, on average, take 4 weeks to complete. • There is a risk that each one of the phases will take longer than 4 weeks to complete, with some probability. • If the duration of the phases is normally distributed, then the probability of that happening is 50%. • To finish within 4 weeks requires that each of the four phases finish on the right side of 4 weeks since if just one of them takes longer, the whole project will be delayed. • What is the probability that this will happen? Again, if the variables are distributed normally, the answer is 12,5% (0,5^3), which equals landing heads three times in a row. The average duration of such a project is 4.8 weeks (assuming the standard error is 1). No wonder people have a hard time finishing projects on time. So, the next time you are asked to come up with a number, remember that the average output is not always equal to the average of the input. If your organisation is still relying on traditional tools like colour-coded heat maps and qualitative risk assessments, it might be time to consider if those methods are providing the level of insight and precision your business needs to thrive in today’s fast-evolving risk landscape. How quantifying your cyber exposure can reduce your insurance cost and improve coverage. As cyber threats continue to evolve and become more sophisticated, cyber insurance has quickly become an... Thursday, December 7, 2023 was an important day for ACI.We held our December seminar on IT Risk quantification.We were proud that more than 180 people had signed up for the seminar from more than... Move Beyond Guesswork: Elevate Your Cyber Risk Management with Data-Driven Quantification Are you covered? The case for quantifying cyber risk for insurance and strategic decision making	{"url":"https://aci.dk/en/viden/give-me-a-number/","timestamp":"2024-11-05T23:33:51Z","content_type":"text/html","content_length":"233803","record_id":"<urn:uuid:86345fcc-bd21-4f37-8597-c77675ed1a60>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00407.warc.gz"}
Loss of Energy and Angular Momentum in Disrupting N-body Systems This work studies how the initial energy and angular momentum of an N-body system is lost as the system naturally disrupts due to multi-body dynamical interactions. The systems studied are close to initially symmetric N-body configurations, which under the influence of gravitational attraction between the bodies generally end up as ejected singles or pairs of bodies. These types of self-disrupting systems are of particular interest in their applications to problems in the field of astromechanics, such as in rubble-pile asteroid formation. The specific question of interest is the amount of angular momentum and energy that is lost from an original distribution of bodies due to gravitational ejection.The initial conditions were chosen to be symmetric N-gon central configurations with random perturbations applied to the position of one of the bodies. These systems were then propagated in time using the nondimensional Jacobi formulation of the N-body problem until either a maximum duration of time was reached or all but two bodies had been ejected. At the final state, orbital parameters of the ejected bodies were calculated and how the energy and angular momentum were partitioned between the ejected masses and the remaining masses was determined. By repeating this process for a number of random perturbations, general results were identified by analyzing the aggregate statistics of these simulations. This study specifically considered systems consisting of between 3 and 6 bodies with equal masses, with ejections of pairs of bodies being considered for systems where N > 3. Two sets of simulations for N=3 have already been completed with 1000 simulation runs per set. The third body was ejected in just under 97.5% of these simulations, 2.2% of these simulations reached the maximum propagation time, and just under 0.4% produced an error, likely due to close approaches. In 79.5% of all simulations a departure was detected in the first 5% of the maximum propagation time. Of the simulations where a departure was detected, the percentage of the total angular momentum taken by the ejected body appeared to follow a normal distribution with a mean of 88.7% and a standard deviation of 5.3%. Also of note, in 1.7% of these runs, the angular momentum taken by the ejected body was larger in magnitude than the initial total angular momentum vector, meaning that the remaining binary was forced to rotate in the opposite direction. The percentage of the total energy taken by the ejected body followed a different pattern than the angular momentum. As the percentage of energy taken by the ejected body increased, the number of simulations that produced this result decreased dramatically. One third of these simulations resulted in the ejected body taking less than 4.23% of the initial energy, one third resulted in the ejected body taking between 4.23% and 11.5%, and the final third resulted in the ejected body taking between 11.5% and 53.54%. Additional data is being generated for 4 and 5 body systems, with the goal of performing preliminary analysis on 6 and 7 body systems.	{"url":"https://baas.aas.org/pub/2021n5i106p03/release/1?readingCollection=9efc14dd","timestamp":"2024-11-07T03:13:41Z","content_type":"text/html","content_length":"807086","record_id":"<urn:uuid:fc42488c-06ab-43c3-bbfa-590826730e89>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00728.warc.gz"}
CSC373 Assignment 2 solved 1. (20 pts) Short answer questions. For each question answer TRUE/FALSE. If you answer TRUE provide a brief justification consisting of at most 3 short sentences (for majority of these questions, one short sentence suffices). If you answer FALSE provide a small counterexample. Long and complicated justifications as well as unnecessarily large and complicated counter-examples will lose marks. Guesses without justification receive 0 marks. Note: for some of the false statements below it might be hard to find a counter-example. You are encouraged to give it your best shot, but if you notice that you are spending disproportionate amount of time, you are encouraged to consult the web. If you find a counter-example on the web you must understand it, internalize it, and write it up from memory. In addition, you must cite the resource that you used (this won’t cost you any mark deductions), and you are still responsible for correctness of the example (i.e., you can’t blame the source if it ultimately turns out incorrect – there is plenty of wrong information on the web). (a) An undirected graph with n vertices and at most n − k edges has at least k connected (b) The shortest-paths tree computed by Dijkstra is necessarily an MST. (c) Suppose that we have computed an MST. If the weight of each edge in the graph is increased by 1, the computed spanning tree remains minimum with respect to the new (d) In a weighted directed graph with positive weights, Dijkstra might call the update() procedure (aka Relax() procedure, see CLRS 24.3) on the same edge more than once. (e) Maximum flow in a network with integral capacities is necessarily integral. (f) We are given a weighted graph and a shortest path from s to t. If all edge weights in the graph are multiplied by a positive constant, the given path remains shortest from s to t with respect to the new weights. (g) Suppose we run DFS on a directed graph G = (V, E) and we find a vertex with discovery time 1 and finishing time 2\|V \|. Then the entire graph must be strongly connected. (h) Ford-Fulkerson method runs in polynomial time assuming that capacities are positive (i) Ford-Fulkerson method terminates on all input flow networks with capacities that are positive real numbers. (j) Undirected graph G = (V, E) is called k-regular if degree of every vertex is exactly k. Girth of the graph is the length of a shortest cycle in G. For example, the simple cycle with 5 vertices is a 2-regular graph of girth 5. We claim that there is no 3-regular graph of girth 5 on 10 vertices. 1 of 3 CSC373, Assignment 2 2. (20 pts) Design an efficient algorithm for the following problem: Input: Undirected graph G = (V, E) in adjacency lists representation with unit edge costs. Vertices s, t ∈ V . Output: The number of distinct shortest paths from s to t. (a) Briefly describe your algorithm in plain English. (b) Describe your algorithm in pseudocode. (c) Formally prove correctness of your algorithm. (d) State and justify the running time of your algorithm. 3. (20 pts) You have a server that can be attached to two electrical outlets simultaneously. The server runs uninterrupted as long as it is attached to at least one electrical outlet. The server is located on a rolling cart that can be moved freely within the rectangular room (the room has no obstacles). Looking at the room from above and seeing its plan, you know the coordinates of n electrical outlets given by (xi , yi). Currently the server is attached via a single power cable of length ` to the electrical outlet s. You would like to move the server without any interruptions to electrical outlet t. For that purpose you can purchase an additional power cable of length L and move the server from one electrical outlet to another until it reaches t. You would like to find out what is the minimum length L of additional power cable that you need to purchase to accomplish this task. Design an O(n log n)-time algorithm to compute the minimum value of L. Note this problem is assumed to be entirely 2-dimensional – length in this problem refers to the regular Euclidean 2D distance. Input: {(xi , yi)} i=1 – positions of electrical outlets; ` – length of the given power cable; s, t ∈ [n] – starting and terminal electrical outlets Output: minimum value of L such that we can move the server from s to t uninterrupted. (a) Briefly describe your algorithm in plain English. (b) Describe your algorithm in pseudocode. (c) Provide a concise argument of correctness of your algorithm. You may use results proven in class/textbook, but make sure to cite them accurately. (d) Justify that the runtime is O(n log n). 4. (20 pts) Consider the following network graph. 2 of 3 CSC373, Assignment 2 (a) Compute maximum flow f and minimum cut (S, T). (b) Draw the residual graph Gf – don’t forget to state the capacities. Indicate the minimum cut (S, T) in the residual graph by circling S and T. (c) An edge is called constricting if increasing its capacity leads to an increase in the value of maximum flow. List all constricting edges in the above network. (d) Find a small (at most 4 nodes) example of a network graph that has no constricting (e) Describe in plain English an efficient algorithm to find all constricting edges. Argue correctness by using results from lectures/textbook. State the running time of your 5. (20 pts) Consider a flow network G = (V, E), s, t, c with integral capacities together with an additional edge-price function p : E → N. The value p(e) denotes the price to increase the capacity of edge e by one unit. Suppose we have already computed maximum flow f in the network. Now, we would like to increase this maximum flow f by one unit by increasing capacities of some edges. The goal is to do this with the least possible cost. Design an efficient algorithm to compute which edge capacities to increase. (a) Briefly describe your algorithm in plain English. (b) Describe your algorithm in pseudocode. (c) Provide a concise argument of correctness of your algorithm. You may use results proven in class/textbook, but make sure to cite them accurately. (d) State and justify the runtime of your algorithm. 3 of 3	{"url":"https://codeshive.com/questions-and-answers/csc373-assignment-2-solved/","timestamp":"2024-11-08T17:50:08Z","content_type":"text/html","content_length":"105438","record_id":"<urn:uuid:97f67c33-1fc3-4c36-8656-963b2f6bfa6c>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00858.warc.gz"}
How to insert the sum of two tables in oracle? Alternatively, if you want to insert the sum of two tables into a table without performing a join operation, you can first calculate the sum separately and then insert the result into a new table. Here's an example query illustrating this approach: 1 INSERT INTO new_table(sum_column) 2 SELECT (SELECT SUM(column_name) FROM table1) + (SELECT SUM(column_name) FROM table2) AS total_sum 3 FROM dual; In this query: • new_table is the table where you want to insert the sum of two tables. • sum_column is the column in new_table where you want to insert the sum. • table1 and table2 are the tables whose columns you want to sum. • column_name is the column in both tables that you want to sum. This query calculates the sum of the specified columns in table1 and table2 separately using subqueries, adds them together to get the total sum, and then inserts this total sum into the new_table. Remember to replace the actual table and column names based on your database schema.	{"url":"https://devhubby.com/thread/how-to-insert-the-sum-of-two-tables-in-oracle","timestamp":"2024-11-04T14:27:06Z","content_type":"text/html","content_length":"120871","record_id":"<urn:uuid:3d79ee28-bbd7-4d41-a6c1-5176f36c7736>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00280.warc.gz"}
INTRODUCTION TO LINEAR MODELS AND MATRIX ALGEBRA - Digital National Alliance This four-week course, offered at a self-paced pace, delves into the world of Data Science. Conducted in English with English video transcripts, it caters to intermediate learners. You have the option to audit the course for free or enhance your learning by adding a Verified Certificate for $129. You will master essential topics in matrix algebra, including notation and various operations. These skills will be directly applicable to data analysis, where you’ll explore linear models and get a brief introduction to the QR decomposition method. By the end of this course, you’ll have a solid foundation in matrix algebra and its real-world applications in data analysis. About this course Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory online course in data analysis, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units. We perform statistical inference on these differences. Throughout the course we will use the R programming language to perform matrix operations. Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. You will need to know some basic stats for this course. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts. These courses make up two Professional Certificates and are self-paced: Data Analysis for Life Sciences: PH525.1x: Statistics and R for the Life Sciences PH525.2x: Introduction to Linear Models and Matrix Algebra PH525.3x: Statistical Inference and Modeling for High-throughput Experiments PH525.4x: High-Dimensional Data Analysis Genomics Data Analysis: PH525.5x: Introduction to Bioconductor PH525.6x: Case Studies in Functional Genomics PH525.7x: Advanced Bioconductor Digital skills for ICT professionals Country providing the training	{"url":"https://digitalalliance.bg/en/introduction-to-linear-models-and-matrix-algebra/","timestamp":"2024-11-09T02:46:27Z","content_type":"text/html","content_length":"150645","record_id":"<urn:uuid:c35e8c77-b645-4dec-9fdb-f25de5077dd9>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00320.warc.gz"}
Math 152: Calculus II, Math 152: Calculus II, Sections 1, 2 and 3 This is the homepage for Zahra Aminzare's sections of Math 152. There is a review session on Wednesday, December 14th, at 10 am to 12 pm in SEC 203. My recitation syllabus with information about what happens in the recitation can be found here. The main course syllabus can be found here. Review Problems I'll assign some review problems every week to hand in. The review problems will be graded by peer mentors and there is some EXTRA CREDIT for that! Workshop writeups will be due every Wednesday at the beginning of class. Workshop 1 Problem 2, Due 9/14 Workshop 2 Problems 1b and 2c, Due 9/21 Workshop 3 Problems 1 and 2b, Due 9/28 Workshop 4 Problem 2(Use trigonometric substitution for parts a,c, and hyperbolic substitution for part b), Due 10/5 Solution Workshop 5 Problem 2, Due 10/19 Solution Workshop 6 Problem 2, Due 10/26 Solution Workshop 7 Problem 1, Due 11/2 Solution Workshop 8 Problems 1a and 2a,d, Due 11/9 Solution Solution Workshop 9 Problem 1(Hint: Look at Example 11 in page 560.), Due 11/16 Solution Workshop 10 Problem 2, Due 11/22 (after the exam) Solution Workshop 11 Problem 1a,1b (Just find N for one of the series of part a), Due 12/7 You don't need to hand in any homework, but you are expected to prepare all the suggested problems on the main syllabus page for each covered section. A selection of these problems will be posed to you in quizzes. Quizzes and Exams Quiz 1, on Thursday, 9/15 Quiz 2, on Thursday, 9/22 Exam 1 with Solutions, Correction for #5 Quiz 3 with Solution, on Thursday, 10/13 Quiz 4 with Solution, on Thursday, 11/7 Quiz 5 with Solution, on Thursday, 11/10 Starting Thursday, September 15, Professor Sara Soffer will have Math 152 clinics every Thursday from 5 to 7 pm in ARC 309. These clinics provide an informal setting where students can come in and get help from experienced math professors. Don't wait until the first midterm exam. Start getting help now in ARC 309. Midterm Exam 1 will be given on Thursday, October 6th in lecture. Here you can find the Formula sheet , Review Problems 1 with Solution and Review Problems 2 . There is an Office Hour on Tuesday, October 4th, at 3:30 PM in my office. Midterm Exam 2 will be given on Tuesday, November 22nd in lecture. Here you can find the Formula sheet . Also look at here under "Midterm Exam 2" for more review problems and solutions. Final Exam will be given on Monday, December 19th at 4-7 pm, in Sec 111. Here you can find the Formula sheet , Review Problems with Solution . Also look at here under "Final Exam" for more review problems and solutions.	{"url":"http://homepage.divms.uiowa.edu/~zaminzare/Teaching/152/152.html","timestamp":"2024-11-01T19:19:46Z","content_type":"text/html","content_length":"6496","record_id":"<urn:uuid:a29d35db-651f-4f5f-8478-306d3cdfd106>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00790.warc.gz"}
Question 6: Given the function f(x) = -2 • \|x - 3\| + 5 Describe the transformations applied... Solved on Jan 26, 2024 Describe the transformations of $g(x) = \|x\|$ to get $f(x) = -2\|x-3\| + 5$. Find the domain and range of $f(x)$. STEP 1 1. The base function is $g(x) = \|x\|$. 2. The transformed function is $f(x) = -2\|x - 3\| + 5$. 3. We need to describe the transformations applied to $g(x)$ to get $f(x)$. 4. We need to find the domain and range of $f(x)$. STEP 2 Identify the transformations applied to $g(x)$ by comparing it to $f(x)$. The general form of transformations for a function $h(x) = a\|b(x - h)\| + k$ includes: - Vertical stretch/compression by a factor of $\|a\|$. - Reflection in the x-axis if $a$ is negative. - Horizontal stretch/compression by a factor of $\|b\|$. - Horizontal shift by $h$ units. - Vertical shift by $k$ units. STEP 3 Determine the vertical stretch/compression and reflection. In $f(x)$, the coefficient of $\|x - 3\|$ is $-2$. This indicates a vertical stretch by a factor of 2 and a reflection in the x-axis because the coefficient is negative. STEP 4 Determine the horizontal shift. The expression inside the absolute value is $(x - 3)$. This indicates a horizontal shift to the right by 3 units. STEP 5 Determine the vertical shift. The constant term outside the absolute value in $f(x)$ is $+5$. This indicates a vertical shift upwards by 5 units. STEP 6 Combine the transformations. The function $f(x)$ is obtained from $g(x)$ by: 1. Reflecting $g(x)$ in the x-axis. 2. Stretching $g(x)$ vertically by a factor of 2. 3. Shifting $g(x)$ horizontally to the right by 3 units. 4. Shifting $g(x)$ vertically upwards by 5 units. STEP 7 Determine the domain of $f(x)$. The domain of the base function $g(x) = \|x\|$ is all real numbers, and none of the transformations change the domain. Therefore, the domain of $f(x)$ is also all real numbers. $Domain\ of\ f(x): (-\infty, \infty)$ STEP 8 Determine the range of $f(x)$. Since $g(x) = \|x\|$ has a minimum value of 0 and $f(x)$ is reflected in the x-axis, the maximum value of $f(x)$ without the vertical shift would be 0. After applying the vertical stretch by a factor of 2, the maximum value would be 0. Finally, the vertical shift upwards by 5 units moves the maximum value to 5. Since the reflection in the x-axis inverts all positive values of $g(x)$ to negative values in $f(x)$, and the vertical stretch by a factor of 2 doubles all y-values, the range of $f(x)$ is all values less than or equal to 5. $Range\ of\ f(x): (-\infty, 5]$	{"url":"https://studdy.ai/learning-bank/problem/describe-the-changes-made-to-the-6ZzQwpgHnA2wg1rZ","timestamp":"2024-11-04T20:29:34Z","content_type":"text/html","content_length":"157685","record_id":"<urn:uuid:224bf3ad-7105-4a30-80e0-7449aedaacbb>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00031.warc.gz"}
What Does a Mathematician Do? Are you a math enthusiast? Do you get excited when you find a complex math problem to solve? If you answer yes, consider exploring the amazing career opportunities mathematicians have and what mathematicians do. A mathematician studies and uses mathematical theories and techniques to solve different complex problems of the world. From building a house to understanding the planetary movements of the solar systems a mathematician does magic with numbers and theorems to uncover the mysteries of the world. Math is the fundamental skill required for every field to some extent. Let us explore the responsibilities of a mathematician in detail now. What are the math job responsibilities? Depending on specialization and requirements the responsibilities of a mathematician can vary. Below are some of the common responsibilities of a mathematician. • Research: Mathematicians study and research different fields of mathematics and try to discover new theorems for the improvement of math. • Problem-solving: Mathematicians investigate patterns, trends, and relationships by applying mathematical reasoning to find solutions to complex mathematical problems. • Engineering and technological development: Mathematicians use theories and concepts of math for the advancement of engineering and technology. Start Your Child's Math Journey Now! • Economics and finance department: Mathematicians use their knowledge in making financial decisions and study the economics of the country. • Teaching: Mathematicians also work as a teacher to teach math to students. • Consulting Analyst: Mathematicians can use their mathematical concepts to analyze data to make decisions in businesses, health sectors, and many other fields. • Astro physics: In Astrophysics, math is used to analyze data related to the solar system and use the concepts of statistics to plot and evaluate data for decision-making purposes. Now that you have a clear understanding of the math job responsibilities and the importance of being a mathematician, it’s time to start your career path in mathematics. At the 98thPercentile, we offer programs in math, English, coding, and public speaking for grades k-12. Book your free 2-week demo class and start your academic journey with us. FAQs (Frequently Asked Questions) Q1. What are the responsibilities of a mathematician? A: The job responsibilities of a mathematician vary depending upon the role and environment but in general, a mathematician is responsible for implementing math theorems and concepts for Q2. What is a career as a mathematician? A: A career as a mathematician is a very crucial role, a mathematician is responsible for researching and studying math to discover new theories and data analysis. Q3. Should you hire a mathematician? A: If you want a solution for your business data or if you want to work with technology but you want someone else to help you with the math section then hiring a mathematician can be a good idea. Q4. What are the branches of maths? A: There are different branches of mathematics. The main branches are geometry, algebra, trigonometry, calculus, and statistics. Q5. How do I become a mathematician? A: To become a mathematician you have to have a clear understanding of basic and complete graduation in math. Book 2-Week Math Trial Classes Now! Related Articles	{"url":"https://www.98thpercentile.com/blog/what-does-a-mathematician-do/","timestamp":"2024-11-13T11:34:16Z","content_type":"text/html","content_length":"67960","record_id":"<urn:uuid:dfc0bd20-de30-4875-ad4c-3007ad206479>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00365.warc.gz"}
Elements of Real Analysis by Shanti Narayan & M.D. Raisinghania PDF Elements of Real Analysis by Shanti Narayan & M.D. Raisinghania PDF Free Download Download Math’s Book For UPSC Optional, IIT JEE Mains, Graduation College Students BSC, BA, Engineering, SSC, Banking And Other Competitive Examination etc. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/Institutions as per UGC Model Curriculum. Also useful for GATE and various other competitive examinations. Total Pages 312 pages Language English Author 1) Shanti Narayan 2) M.D. Raisinghania Publisher S Chand (1 June 2003) Subject Mathematics This book is an attempt to present Elements of Real Analysis to undergraduate students,on the basis of the University Grants Commission Review Committee report recommendations and several Universities having provided a course along the lines of these recommendations. This book must not, however, be thought of an abridged edition of the Author’s “A Course of Mathematical Analysis” for M.A. students. Chapter I provides description of Set of Real Number as a complete ordered field and no attempt has been made to construct the Set starting from some Axioms. Chapter II deals with bounds and limit points of sets of real numbers. Chapter III concerns itself with Real sequences defined as functions on the set of Natural numbers into the set of Real numbers. This is followed by Chapter IV of Infinite Series dealing with mostly convergence tests for positive term series as also a test on alternating series. Chapter V deals with the nature of the range of a real valued continuous function with a closed finite interval as its domain. Chapter VI on Derivability deals with the rigorous proof of Role’s theorem as also of Lagrange’s theorem. Chapter VIII deals with Riemann Integrability. The following new chapters have been added in this present edition • Countability of sets • The Riemann-Stieltjes Integrals • Uniform convergence of sequences and series of functions • Improper Integrals • Metric spaces 5 thoughts on “Elements of Real Analysis by Shanti Narayan & M.D. Raisinghania PDF” 1. Unable to download the pdf 2. Unable to download pdf ofreal analysis as well as linear algebra of Krishna series from your given link .. please help 3. pls check again we have updated book 4. pls check again we have updated pdf now 5. Please send me a pdf link of Elements of Real Analysis by Shanti Narayan & M.D. Raisinghania PDF” I have send many requests……. Leave a Comment	{"url":"https://www.pdfnotes.co/elements-of-real-analysis-by-shanti-narayan-m-d-raisinghania-pdf/","timestamp":"2024-11-02T10:44:52Z","content_type":"text/html","content_length":"203984","record_id":"<urn:uuid:6f6665c6-bac1-4105-a4bf-ac059609ef9e>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00099.warc.gz"}
Calculate Gleichläufigkeit glk {dplR} R Documentation Calculate Gleichläufigkeit This function calculates the Gleichläufigkeit and related measures for a given set of tree-ring records. glk(x, overlap = 50, prob = TRUE) x a data.frame of tree-ring data with records in columns, and years as rows. overlap integer value with minimal length of overlapping growth changes (compared number of tree rings - 1). Comparisons with less overlap are not compared. prob if TRUE then the probability of exceedence of the Gleichläufigkeit will be calculated Gleichläufigkeit is a classical agreement test based on sign tests (Eckstein and Bauch, 1969). This function implements Gleichläufigkeit as the pairwise comparison of all records in data set. This vectorized implementation is faster than the previous version and follows the original definition (Huber 1942), instead of the incorrect interpretation that has been used in the past (Schweingruber 1988, see Buras/Wilmking 2015 for the correction). The probability of exceedence (p) for the Gleichläufigkeit expresses the chance that the Gleichläufigkeit is incorrect. The observed value of the Gleichläufigkeit is converted to a z-score and based on the standard normal curve the probability of exceedence is calculated. The result is a matrix of all p-values (Jansma 1995, 60-61, see also Visser 2020). Note that prior to dplR version 1.7.2, glk did not have the overlap or prob and returned a matrix with just the Gleichläufigkeit for all possible combinations of records. That function can still be accessed via glk.legacy. The funtions returns a named list of two or three matrices (p_mat is optional if prob = TRUE): 1. glk_mat: matrix with Gleichläufigkeit 2. overlap: matrix with number of overlapping growth changes.This is the number of overlapping years minus one. 3. p_mat: matrix of all probabilities of exceedence for all observed Gleichläufigkeit values. The matrices can be extracted from the list by selecting the name or index number. If two curves have less than 3 years of overlap, Gleichläufigkeit cannot be computed, and NA is returned. To calculate the global glk of the dataset mean(x$glk_mat, na.rm = TRUE). Christian Zang. Patched and improved by Mikko Korpela. Improved by Allan Buras. Further improved and expanded by Ronald Visser and Andy Bunn Buras, A. and Wilmking, M. (2015) Correcting the calculation of Gleichläufigkeit, Dendrochronologia 34, 29-30. DOI: https://doi.org/10.1016/j.dendro.2015.03.003 Eckstein, D. and Bauch, J. (1969) Beitrag zur Rationalisierung eines dendrochronologischen Verfahrens und zur Analyse seiner Aussagesicherheit. Forstwissenschaftliches Centralblatt, 88(1), 230-250. Huber, B. (1943) Über die Sicherheit jahrringchronologischer Datierung. Holz als Roh- und Werkstoff 6, 263-268. DOI: https://doi.org/10.1007/BF02603303 Jansma, E., 1995. RemembeRINGs; The development and application of local and regional tree-ring chronologies of oak for the purposes of archaeological and historical research in the Netherlands, Nederlandse Archeologische Rapporten 19, Rijksdienst voor het Oudheidkundig Bodemonderzoek, Amersfoort Schweingruber, F. H. (1988) Tree rings: basics and applications of dendrochronology, Kluwer Academic Publishers, Dordrecht, Netherlands, 276 p. Visser, R.M. (2020) On the similarity of tree-ring patterns: Assessing the influence of semi-synchronous growth changes on the Gleichläufigkeit for big tree-ring data sets,Archaeometry, 63, 204-215 DOI: https://doi.org/10.1111/arcm.12600 See Also sgc sgc is an alternative for glk) ca533.glklist <- glk(ca533) mean(ca533.glklist$glk_mat, na.rm = TRUE) version 1.7.7	{"url":"https://search.r-project.org/CRAN/refmans/dplR/html/glk.html","timestamp":"2024-11-12T05:26:13Z","content_type":"text/html","content_length":"6097","record_id":"<urn:uuid:76af3bbd-2802-44f1-8845-3c3af48c5d62>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00759.warc.gz"}
Active control for non-autonomous diaphragm-type pneumatic isolation system by using an augmented adaptive sliding-mode controller An augmented adaptive sliding-mode controller is proposed in this paper for a diaphragm-type pneumatic vibration isolation (PVI) system containing nonlinear characteristics and time-varying uncertainties with unknown bounds. To capture and deal with the time-varying uncertainties, a controller design based primarily on the functional approximation (FA) technique complemented with an adaptive fuzzy sliding-mode control (AFSMC) is adopted. The resultant hybrid design is denoted as FA+AFSMC to differentiate itself from other attempting solutions. Lyapunov stability theory is utilized not only to stabilize the closed-loop system but also to formulate updating laws for weighting coefficients of the FA and tuning parameters of the AFSMC. This developed scheme has online learning ability when it faces the system’s nonlinear and time-varying behaviors. Experimental explorations which incorporates both pressure and velocity measurements as feedback signals reveals that the proposed FA+AFSMC scheme outperforms other attempting solutions, such as passive isolation and pure AFSMC scheme, by a significant margin. 1. Introduction Many precision instruments are highly sensitive to ground or environmental induced vibrations. Hence, requirements on the ground vibration level where these instruments are placed have become more important than those specified in standards or regulations [1]. Some research works focusing on vibration control using adaptive or hybrid feedback control can be found in [2-6]. There are numerous practical applications of pneumatic vibration isolator (PVI) in various industries, especially in those cases where PVI operating at low-frequency range of vibration. The reason is that the pneumatic isolation systems are capable of supporting higher payload at relatively lower energy consumption. These PVIs are often actively controlled by servo valves which function to attenuate vibration energy transmitted from the floor and the table itself. This type of PVI-based table system is able to yield satisfactory performances in the frequency range above system’s natural frequencies [7]. However, the performance would deteriorate when the excitation frequency gets closer to system’s natural frequency. To that regard, this paper proposes an active control scheme, i.e. FA+AFSMC, to overcome such a drawback. In other words, by using the proposed control scheme, the vibration isolation performance of the PVI system can be improved over a range of low frequencies, especially at frequencies near system’s resonance. Due to the compressibility of the air, it has long been known as a challenging task to impose active control on the pneumatic pressure. Shih and Wang [8] applied an adaptive control mechanism to tackle the ground vibration problem. Kato et al. [9] investigated a pneumatic isolation table system using a spool-type servo valve and a pressure differentiator. Although the experimental results demonstrated an efficient isolation performance at lower energy level, this approach requires detailed modeling information of the pressure differentiator as well. More recently, Chang et al. [10] proposed a new state-space model of the PVI using the input-output linearization technique. A time delay controller can subsequently be designed and verified by experiments on a single chamber PVI based on this new model. Unlike conventional designs which demand elaborated modeling knowledge prior to the implementation, this study employs the functional approximation technique (FAT) to capture nonlinear behaviors of the pneumatic system so that the controller can be implemented. As a result, the requirement of prior modeling knowledge concerning the controlled system can be waived. The FAT has been applied in the past to design adaptive sliding controllers for various nonlinear systems containing time-varying uncertainties [11-13]. In such a design, the FAT approach is integrated with the sliding-mode control (SMC). Here, the FAT is known for its ability in capturing system dynamics while the latter is known for its robustness under conditions of uncertainties and modeling discrepancy. Since the approximation error caused by truncating the infinite series into a finite sum is inevitable in the FAT approach, the SMC can complement such a deficiency to some extent. To further improve the performance of the proposed FAT-based sliding-mode control, an adaptive one-dimensional fuzzy sliding-mode control (AFSMC) [14] compensator with self-tuning capability is also installed in this study. The resultant control scheme is denoted as the FA+AFSMC, namely the FAT-based adaptive fuzzy sliding-mode control. Since the proposed hybrid controller design FA+AFSMC can be deployed in nonlinear systems without modeling information, it can reduce the computational burden and release memory requirement in practical applications. Moreover, the stability of the proposed control scheme can be theoretically ascertained by using the Lyapunov stability theorem. 2. The experimental test rig A schematic diagram of the experimental test rig is shown in Fig. 1. The system encompasses the following major components: the PVI sub-system, the accelerometer, the electromagnetic shaker, and the active control unit. Among these, the PVI sub-system is used as an actuator in the active-isolation equipment. It consists of a single pneumatic chamber, a rubber diaphragm, and a piston that supports the payload. A shaker is installed to serve as a vibrating base. For this study, the shaker is used to generate various vibrating profiles for simulating the disturbance variations. In order to measure vibration responses of the isolator, an accelerometer is installed on top of the payload. On the other hand, measurements of both the chamber pressure and payload velocity are incorporated as the feedback signals in the closed-loop control design. In this setup, the payload velocity signal can be obtained by numerically integrating the acceleration signal. The pressure sensor is so located that the pressure measurement directly reveals the pressure dynamics of the air chamber. A PC-based control unit is set to take measurement inputs through A/D conversions. As the brain of the control unit, the control unit computes the required control inputs, and transmits the control input in the form of analog voltage to the pneumatic control valve. The pneumatic control valve, also called servo valve, is a proportional directional control valve which generates air mass-flow in proportion to the control voltage received from the control unit. The spool-type control valve works not only to maintain a static pressure but also to supply the required dynamic pressure for the air chamber. Fig. 1The schematic diagram of the proposed experimental system 3. Controller design The control algorithms taken to deal with the nonlinear pneumatic system are elaborated in this section. The fundamental thought behind the proposed scheme is to capture nonlinear time-varying system dynamics by applying the functional approximation technique (FAT). Meanwhile, in order to cope with the finite approximation error, an adaptive fuzzy sliding-mode control (AFSMC), is employed to deal with model discrepancy and uncertainties. The resultant hybrid control scheme is the solution proposed in this paper and is denoted as the FA+AFSMC active isolator. Lyapunov stability theorem is applied to derive update laws for the weighting coefficients and tuning parameters of the FAT and fuzzy control, respectively. Asymptotic stability of the tracking error can be achieved if sufficient number of orthogonal basis functions were adopted. When finite expansion is used, the effects of approximation error on system performance can be investigated. The asymptotic stability can still be ensured with a modified control law if the bounds of approximation error are known. The overall block diagram of the proposed FA+AFSMC control scheme is shown as Fig. 2. Suppose the pneumatic driving system considered here can be represented as the following dynamical equation: where $v\left(t\right)$ represents the payload velocity, ${f}_{v}\left(v,t\right)$ denotes the unknown nonlinear time-varying system dynamics with unknown bounds and ${b}_{v}\left(t\right)$ is an unknown control gain function. The subscript “$v$” indicates the system properties associated with the velocity feedback control loop. To apply the FAT, two linear combination of Fourier basis functions are employed to approximate the unknown functions ${f}_{v}\left(v,t\right)$ and ${b}_{v}\left(t\right)$. Then the FAT-based sliding controller can be developed for this PVI system. An adaptive fuzzy sliding-mode controller (AFSMC) is added to compensate for the approximation error and improve the control performance. In addition, a Lyapunov function candidate is chosen to not only prove the closed-loop stability but also derive the updating laws for the weighting coefficients of the approximation series and tuning parameters of the AFSMC. Fig. 2The control block diagram of the FA+AFSMC control scheme Let ${e}_{v}=v-{v}_{r}$, and consequently, ${\stackrel{˙}{e}}_{v}=\stackrel{˙}{v}-{\stackrel{˙}{v}}_{r}$ in which ${v}_{r}$ represents the reference velocity of the payload. Next, a sliding variable ${s}_{v}$ is defined as: ${s}_{v}={\stackrel{˙}{e}}_{v}+{\lambda }_{v}{e}_{v},$ where ${\lambda }_{v}$ is a positive constant. The time derivative of the sliding variable, ${s}_{v}$, is calculated as: ${\stackrel{˙}{s}}_{v}={\stackrel{¨}{e}}_{v}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}=\stackrel{¨}{v}-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}.$ When Eq. (1) is used, Eq. (3) can be recast into the following: ${\stackrel{˙}{s}}_{v}=f\left(v,t{\right)}_{v}+{b}_{v}\left(t\right){u}_{v}-{\stackrel{¨}{v}}_{r}+\lambda \stackrel{˙}{e}={b}_{v}\left[{f}_{v}{b}_{v}^{-1}+{u}_{v}+{b}_{v}^{-1}\left(-{\stackrel{¨}{v}} _{r}+\lambda {\stackrel{˙}{e}}_{v}\right){\right]}_{v}.$ Now in order to satisfy reaching condition of the sliding surface and compensate for the approximation error of the FAT, the control law can be designed to compose of FA and AFSMC two parts. In other ${u}_{v}\left(t\right)={{u}_{v}}_{FA}\left(t\right)+{{u}_{v}}_{AFSMC}\left(t\right)=-{\stackrel{^}{f}}_{a}-{\stackrel{^}{b}}_{v}^{-1}\left(-{\stackrel{¨}{v}}_{v}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\ right)-{C}_{v}^{T}{\mathrm{\Phi }}_{v},$ where ${{u}_{v}}_{FA}$ indicates the control input calculated in accordance with the FAT, whereas ${{u}_{v}}_{AFSMC}$ is the input obtained from the adaptive fuzzy sliding-mode control algorithm. The control ${{u}_{v}}_{FA}\left(t\right)$ is determined to achieve ${\stackrel{˙}{s}}_{v}=0$ and guarantee the system output error convergence. The estimation terms in ${{u}_{v}}_{FA}\left(t\right)$ can be approximated by a linear combination of finite orthogonal basis functions to expand and capture most of the time-varying system dynamics plus uncertainties. In addition, ${\stackrel{^}{f}}_{a}$ represents the estimate value of ${f}_{a}={f}_{v}{\stackrel{^}{b}}_{v}^{-1}$ while ${\stackrel{^}{b}}_{v}$ is the estimate value of ${b}_{v}$. In the proposed hybrid controller, both ${\stackrel{^} {f}}_{a}$ and ${\stackrel{^}{b}}_{v}$ have to be estimated on-line. Note that according to Eq. (5) when ${\stackrel{^}{b}}_{v}$ gets close to zero, the control law becomes unbounded. Therefore, a lower-bound value of ${b}_{v}$ is required and denoted as ${\underset{_}{b}}_{v}$. To avoid unbounded control input, the control gain function is designed so that ${b}_{v}\ge {\underset{_}{b}}_{v}>0$ . The membership functions and the fuzzy rules are shown in Fig. 3(a) and 3(b), respectively. Triangular membership functions are used to classify the fuzzy input and output variables. The scaling factor ${g}_{s}$ is employed to map the sliding surface variable $s$ into the fuzzy universe of discourse. It can be roughly estimated based on the span of tracking error during the experimental investigations. In addition, ${C}_{v}^{T}{\mathrm{\Phi }}_{v}$ represents the adaptive fuzzy compensation that can be derived from the fuzzy inference decision and defuzzification operations. ${C}_ {v}^{T}{\mathrm{\Phi }}_{v}$ can be represented as: ${u}_{vAFSMC}=\frac{{\sum }_{i=1}^{m}{w}_{i}{\alpha }_{i}}{{\sum }_{i=1}^{m}{w}_{i}}=\frac{\left[{\alpha }_{1}\cdots {\alpha }_{m}\right]\left[\begin{array}{c}{w}_{1}\\ ⋮\\ {w}_{m}\end{array}\right]} {{\sum }_{i=1}^{m}{w}_{i}}={C}_{v}^{T}{\mathrm{\Phi }}_{v}.$ In which ${C}_{v}={\left[{\alpha }_{1}\cdots {\alpha }_{m}\right]}^{T}$ represents the adjustable consequent parameter vector and ${\mathrm{\Phi }}_{v}=\left[{w}_{1}\cdots {w}_{m}\right]/{\sum }_{i= 1}^{m}{w}_{i}$ is the firing strength vector. Substituting Eq. (5) into Eq. (4), one obtains: ${\stackrel{˙}{s}}_{v}={b}_{v}\left[\left({f}_{a}-{\stackrel{^}{f}}_{a}\right)+\left({b}_{v}^{-1}-{\stackrel{^}{b}}_{v}^{-1}\right)\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\ right)-{C}_{v}^{T}{\mathrm{\Phi }}_{v}\right],$ where, ${f}_{a}$, ${\stackrel{^}{f}}_{a}$, ${b}_{v}^{-1}$, and ${\stackrel{^}{b}}_{v}^{-1}$ are assumed to satisfy the Dirichlet conditions. Therefore, they can be represented, by using the functional approximation technique, as: $\left\{\begin{array}{l}{f}_{a}={W}_{vf}^{T}{Z}_{{f}_{}},\\ {\stackrel{^}{f}}_{a}={\stackrel{^}{W}}_{vf}^{T}{Z}_{f},\end{array}\right\\left\{\begin{array}{l}{b}_{v}^{-1}={W}_{vb}^{T}{Z}_{b},\\ {\ where ${W}_{vf}$, ${\stackrel{^}{W}}_{vf}$, ${W}_{vb}$, ${\stackrel{^}{W}}_{vb}\in {\mathfrak{R}}^{2n+1}$ denote the time-invariant weighting vectors used to expand unknown function ${f}_{a}$, ${\ stackrel{^}{f}}_{a}$, ${b}_{v}^{-1}$ and ${\stackrel{^}{b}}_{v}^{-1}$, respectively, whereas ${Z}_{f}$, ${Z}_{b}\in {\mathfrak{R}}^{2n+1}$ are the time-varying vectors composed of Fourier basis functions. Although, conceptually using sufficiently large number of orthogonal basis functions can approximate the unknown function to a prescribed accuracy, the computation burden increases exponentially as the number of the basis function increases. Moreover, the approximation error still exists. Hence, AFSMC is integrated with the FAT-based sliding control to compensate for the approximation error and the uncertainties. When contents of Eq. (8) is substituted into Eq. (7), the following can be reached: ${\stackrel{˙}{s}}_{v}={b}_{v}\left[{\stackrel{~}{W}}_{vf}^{T}{Z}_{f}+{\stackrel{~}{W}}_{vb}^{T}{Z}_{b}\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{r}{\stackrel{˙}{e}}_{v}\right)-{C}_{v}^{T}{\mathrm{\Phi Here, ${\stackrel{~}{W}}_{vf}^{T}={W}_{v{f}_{}}^{T}-{\stackrel{^}{W}}_{v{f}_{}}^{T}$, ${\stackrel{~}{W}}_{v{b}_{}}^{T}={W}_{vb}^{T}-{\stackrel{^}{W}}_{v{b}_{}}^{T}$. Moreover, in order to find update laws for ${\stackrel{^}{W}}_{vf}$, ${\stackrel{^}{W}}_{vb}$ and ${C}_{v}$ and to prove stability of the closed-loop system, a Lyapunov-function candidate is selected as the following: {W}}_{vb}^{T}{Q}_{vb}{\stackrel{~}{W}}_{vb}\right]+\frac{{b}_{v}}{2{\gamma }_{v}}{C}_{v}^{T}{C}_{v},$ where ${Q}_{vf}$, ${Q}_{vb}\in {\mathfrak{R}}^{\left(2n+1\right)×\left(2n+1\right)}$ are symmetrical positive-definite matrices, whereas ${\gamma }_{v}$ is a positive constant representing the learning rate of fuzzy controller. Taking time derivative of the Lyapunov-function candidate along the trajectory, one obtains: {vf}+{\stackrel{~}{W}}_{vb}^{T}{Q}_{vb}{\stackrel{˙}{\stackrel{~}{W}}}_{vb}\right]+\frac{{b}_{v}}{2{\gamma }_{v}}{C}_{v}^{T}{\stackrel{˙}{C}}_{v}.$ Now, since ${\stackrel{˙}{\stackrel{~}{W}}}_{vf}^{T}=-{\stackrel{˙}{\stackrel{^}{W}}}_{vf}^{T}$, ${\stackrel{˙}{\stackrel{~}{W}}}_{vb}^{T}=-{\stackrel{˙}{\stackrel{^}{W}}}_{vb}^{T}$ and by using Eq. (9), Eq. (11) can be rearranged into the following: {^}{W}}}_{vf}^{}+{\stackrel{~}{W}}_{vb}^{T}\left[{Z}_{b}s\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\right)-{Q}_{v{b}_{}}{\stackrel{˙}{\stackrel{^}{W}}}_{vb}^{}\right]\right\$$- {C}_{v}^{T}\left({s}_{v}{\mathrm{\Phi }}_{v}-\frac{1}{{\mathrm{\gamma }}_{v}}{\stackrel{˙}{C}}_{v}\right)}.$ Next, we select: ${\stackrel{˙}{\stackrel{^}{W}}}_{vb}^{}=\left\{\begin{array}{l}{Q}_{vb}^{-1}{Z}_{{b}_{}}{s}_{v}\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{¨}{e}}_{v}\right),0<{\stackrel{^}{b}}_{v}^{-1}<{\ underset{_}{b}}_{v}^{-1},\\ {Q}_{vb}^{-1}{Z}_{{b}_{}}{s}_{v}\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{¨}{e}}_{v}\right),{\stackrel{^}{b}}_{v}^{-1}\ge {b}_{v}^{-1},{s}_{v}\left(-{\stackrel {¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\right)<0,\\ 0,{\stackrel{^}{b}}_{v}^{-1}\ge {\underset{_}{b}}_{v}^{-1},{s}_{v}\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\right)\ ge 0,\end{array}\right\$ ${\stackrel{˙}{C}}_{v}={\gamma }_{v}{s}_{v}{\mathrm{\Phi }}_{v}-{k}_{v}\left\|{s}_{v}\right\|{C}_{v},$ where the update law in Eq. (14) is specially designed to make sure that ${\stackrel{^}{b}}_{v}$ will not be less than its lower bound, ${\underset{_}{b}}_{v}$. Note also that when the appropriate lower bound ${\underset{_}{b}}_{v}$ is chosen, the second and third cases of Eq. (14) will not occur. Parameter ${\gamma }_{v}$ is a positive learning rate while ${k}_{v}$ is a positive parameter introducing damping effect to the updating law, Eq. (15) [15]. Eq. (12) can be rewritten as: $\stackrel{˙}{V}\left({s}_{v},{\stackrel{~}{W}}_{vf},{\stackrel{~}{W}}_{v{b}_{}},{C}_{v}\right)=\left\{\begin{array}{l}-{b}_{v}\frac{{k}_{v}}{{\gamma }_{v}}\left\|{s}_{v}\right\|{C}_{v}^{T}{C}_{v}\le 0,0<{\stackrel{^}{b}}_{v}^{-1}<{\underset{_}{b}}_{v}^{-1},\\ -{b}_{v}\frac{{k}_{v}}{{\gamma }_{v}}\left\|{s}_{v}\right\|{C}_{v}^{T}{C}_{v}\le 0,{\stackrel{^}{b}}_{v}^{-1}\ge {\underset{_}{b}}_{v}^{-1}, {s}_{v}\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\right)<0,\\ -{b}_{v}\frac{{k}_{v}}{{\gamma }_{v}}\left\|{s}_{v}\right\|{C}_{v}^{T}{C}_{v}+{b}_{v}\left({\stackrel{~}{W}}_{v{b}_ {}}^{T}{Z}_{{b}_{}}\right){s}_{v}\left(-{\stackrel{¨}{v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\right)\le 0,\\ {\stackrel{^}{b}}_{v}^{-1}\ge {\underset{_}{b}}_{v}^{-1},{s}_{v}\left(-{\stackrel{¨} {v}}_{r}+{\lambda }_{v}{\stackrel{˙}{e}}_{v}\right)\ge 0,\end{array}\right\$ Eq. (16) shows that the time derivative of the positive definite Lyapunov function is negative semi-definite. Thus, the dynamics of the closed-loop system is stable in the sense of Lyapunov stability criterion [16]. Furthermore, it can be proven by using Barbarlet’s lemma [17] that the control law ${u}_{v}\left(t\right)$ in Eq. (11) can guarantee asymptotic convergence of the output error. Note that although the controller design described so far focuses on the velocity feedback loop, similar design procedures can be taken to handle the pressure feedback control loop. Thus, the overall control scheme shown as in Fig. 2 can be obtained. Fig. 3a) Membership functions of the errors and error changes, b) fuzzy rules of AFSMC 4. Experimental system detail The experimental setup of the proposed pneumatic vibration isolation system is shown in Fig. 4 in which the PVI sub-system supports a payload. The payload’s mass is 42 kg. The design of the PVI resembles that of a commercial product, namely Bilz Corporation’s FAEBI-HD series. This specialized device has a relatively smaller load volume and a larger damping volume. The total volume of the chamber is about 2.0×10^−4 (m^3) while the effective piston area is about 1.96×10^−3 (m^2). An electromagnetic shaker (B&K 4808) driven by a power amplifier is installed to excite the floor base so as to simulate the ground vibration input. The shaker has a force rating of 112 Newton. In order to measure the payload’s, motion a high-quality accelerometer (B&K 8340 with a sensitivity of 9237 mV/ g) is installed on top of the payload. In addition, the pressure signal was measured by a high-precision pressure sensor (FESTO SDE1-D6-G2-W18-C-NU-M8 with an accuracy of 2 % of final value) which is mounted in between the exit of the servo valve and the air chamber. To implement control, design the PC-based control unit, consisting of the NI-CompactRIO (NI CRIO-9004) and LabVIEW software, takes measurements through A/D conversions. It then computes the required control signal and transmits the results to the pneumatic control valve. The control valve is a proportional directional control valve (FESTO, MPYE-5-M5-010-B). The valve can generate air mass-flow in proportion to the control voltage. The distance between the control servo valve and pneumatic chamber is kept to a minimum in order to avoid any possible air loss in the pipeline. During the experimental study, the active isolation control performance is compared against those obtained from the passive isolation configuration. The passive isolation was power free and accomplished by keeping a static pressure in the PVI where the isolation effect was provided by the rubber diaphragm and the orifice flow through the inlet and outlet of the directional control Fig. 4Photograph of the experimental rig set-up 5. Experimental isolation verifications In order to demonstrate the enhancement of the isolation performance achieved by using the proposed active-isolation algorithm, tests were run under a pseudo-random ground vibration was fed through the floor. Acceleration responses of the payload were measured and then numerically integrated to obtain the velocity responses. The control results were compared against its counterparts generated by either the passive isolator or the pure AFSMC scheme. During experimental investigations, the sampling rate was taken as 1,000 Hz. The pressure of air applied to the proportional control valve was 4.3×10^5 Pa, whereas the static pressure in the chamber was 2.2×10^5 Pa. The natural frequency of the experimental system as a whole is close to 3.7 Hz. As mentioned previously, a pseudo-random disturbance was applied to validate the proposed control algorithm. This excitation was generated by an electromagnetic shaker. Note that the positive definite matrix ${Q}_{v}$ is chosen as ${Q}_{v}={Q}_{i}I$ in which $I$ represents a 2×2 identity matrix while ${Q}_{i}$ is a positive constant. In this study, 9 basis functions were adopted in approximating system’s unknown time-varying dynamics. Control parameters used in the FA+AFSMC algorithm are listed in Table 1. Table 1Values of control parameters. Controller type Feedback type Parameter values Pressure ${g}_{s}=\text{1}$, ${g}_{u}=\text{0.5}$, $\lambda =\text{0.1}$, $\gamma =\text{0.5}$ Velocity ${g}_{s}=\text{1}$, ${g}_{u}=\text{15}$, $\lambda =\text{0.1}$, $\gamma =\text{0.5}$ ${Q}_{i}=\text{0.01}$, ${\lambda }_{FA}=\text{0.005}$, $n=\text{9}$ ${g}_{s}=\text{1}$, ${g}_{u}=\text{0.2}$, ${\lambda }_{AFSMC}=\text{0.1}$, ${\gamma }_{v}=\text{0.5}$ ${Q}_{i}=\text{0.01}$, ${\lambda }_{FA}=\text{120}$, $n=\text{9}$ ${g}_{s}=\text{1}$, ${g}_{u}=\text{9.6}$, ${\lambda }_{AFSMC}=\text{0.1}$, ${\gamma }_{v}=\text{0.5}$ A random-like disturbance was applied to further illustrate the suppression effectiveness of the proposed FA+AFSMC scheme. Time-domain responses including both payload velocity and control voltage input under random-like ground disturbance are given in Figs. 5 and 6, respectively. Note that while Fig. 5(a) and 6(a) show the test data generated across time span of 10 seconds, Fig. 5(b) and 6(b) present the zoom-in details for a single second. It can be observed from these figures that comparing to the passive isolation, the proposed FA+AFSMC scheme can significantly suppress the random-like vibrations of the payload. Since the input signal are randomly generated, only the RMS values of the payload velocity were considered. It turns out that the RMS values of the payload velocity are 0.0087 m/s and 0.0017 m/s for the passive and FA+AFSMC active isolation, respectively. The reduction is about 80 % in this excitation condition. Fig. 5Time domain payload velocity response (upper: from 0-10 seconds, and lower: with the 9th second) of the passive and FA+AFSMC active isolator under random-like disturbance Fig. 6Time control voltage (upper: from 0-10 seconds, and lower: with the 9th second) of the passive and FA+AFSMC active isolator under random-like disturbance To further illustrate the effectiveness of the proposed control scheme, dynamic responses of the payload velocity for the passive, AFSMC active and FA+AFSMC active control cases are shown in Fig. 7. In this plot, the dashed line indicates the payload velocity of the passive isolator, whereas the dashed-dotted line and solid line correspond to the AFSMC active controller and the proposed FA+AFSMC active controller, respectively. Based on Fig. 7, one can conclude that the proposed FA+AFSMC active controller outperforms either the passive control or the AFSMC scheme. Fig. 7Time domain payload velocity response of the passive (dashed line), AFSMC active (dashed-dotted line) and FA+AFSMC active (solid-bold line) isolator under random-like disturbance within the 9th 6. Conclusions This paper proposes an active control scheme aiming to elevate the isolation performance of pneumatic isolators specifically in the vicinity of the system’s low frequency natural resonance. The approach applies primarily the FAT-based sliding control but is also augmented with the AFSMC compensation (FA+AFSMC) so as to capture and suppress nonlinear and time-varying system dynamics. The AFSMC is adopted for the sake of compensating the finite approximation error caused by truncating the FAT infinite series into a finite sum. Since the proposed approach is modeling-free, tremendous amount of modeling efforts regarding pneumatic isolation system can thus be avoided. The latter is known to be computational challenging because many nonlinear phenomena are involved in such a pneumatic system. Experimental results have shown that the proposed FA+AFSMC active isolation approach can indeed suppress the vibration disturbance effectively. The study also demonstrates the feasibility of designing an active isolation system using both payload velocity and chamber pressure as feedback signal. The future applications of this model-free control methodology will be extended to multi axes isolation systems in our laboratory for further research in this area. • Gordon C. G. Generic vibration criteria for vibration-sensitive equipment. Proceedings of SPIE, San Jose, CA, 1999. • Bitaraf M., Barroso L. R., Hurlebaus S. Adaptive control to mitigate damage impact on structural response. Journal of Intelligent Material Systems and Structures, Vol. 21, Issue 8, 2010, p. • Li H., Yu J., Hilton C., Liu H. Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach. IEEE Transactions on Industrial Electronics, Vol. 60, Issue 8, 2013, p. 3328-3338. • Bitaraf M., Hurlebaus S., Barroso L. R. Active and semi-active adaptive control for undamaged and damaged building structure under seismic load. Computer-Aided Civil and Infrastructure Engineering, Vol. 27, Issue 1, 2012, p. 48-64. • Kerber F., Beadle B. M., Hurlebaus S., Stöbener U. Control concepts for an active vibration isolation system. Mechanical Systems and Signal Processing, Vol. 21, Issue 8, 2007, p. 3042-3059. • Ozbulut O., Bitaraf M., Hurlebaus S. Adaptive control of base-isolated structure against near-field earthquakes using variable friction dampers. Engineering Structures, Vol. 33, Issue 12, 2011, p. 3143-3154. • Shin Y. H., Kim K. J. Performance enhancement of pneumatic vibration isolation tables in low frequency range by time delay control. Journal of Sound and Vibration, Vol. 321, 2009, p. 537-553. • Shih M. C., Wang T. Y. Design and adaptive control of a pneumatic vibration isolator. Proceedings of International Conference of Motion and Vibration Control, Vol. 6, Issue 1, 2002, p. 111-116. • Kato T., Kawashima K., Sawamoto K., Kagawa T. Active control of a pneumatic isolation table using model following control and a pressure differentiator. Precision Engineering, Vol. 31, 2007, p. • Chang P. H., Han D. K., Shin Y. H., Kim K. J. Effective suppression of pneumatic vibration isolators by using input-output linearization and time-delay control. Journal of Sound and Vibration, Vol. 329, Issue 10, 2010, p. 1632-1652. • Chen P. C., Huang A. C. Adaptive sliding control of non-autonomous active suspension systems with time-varying loading. Journal of Sound and Vibration, Vol. 282, 2005, p. 1119-1135. • Huang A. C., Chen Y. C. Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties. IEEE Transactions on Control System Technology, Vol. 12, Issue 5, 2004, p. • Spooner J. T., Maggiore M., Ordonez R., Passino K. M. Stable Adaptive Control and Estimation for Nonlinear Systems – Neural and Fuzzy Approximator Techniques. Wiley, New York, 2002. • Huang S. J., Chen H. Y. Adaptive sliding controller with self-tuning fuzzy compensation for vehicle suspension control. Mechatronices, Vol. 16, 2006, p. 607-622. • Narendra K. S., Annaswamy A. M. A new adaptive law for robust adaptation without persistent excitation. IEEE Transactions on Automatic Control, AC-32, 1987, p. 134-145. • Slotine J. J. E., Li W. Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs, New Jersey ,1991. • Narendra K. S., Annaswamy A. M. Stable Adaptive Systems. Prentice-Hall, Englewood Cliffs, New Jersey, 1989. About this article Vibration generation and control diaphragm-type pneumatic vibration isolation system functional approximation technique adaptive fuzzy sliding-mode controller The authors would like to acknowledge the support of the National Science Council of Taiwan through its Grant NSC-101-2221-E-131-008. Copyright © 2017 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	{"url":"https://www.extrica.com/article/18368","timestamp":"2024-11-08T12:57:01Z","content_type":"text/html","content_length":"173881","record_id":"<urn:uuid:e084428b-7e89-4a22-b570-ec0cfa9e3f9a>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00216.warc.gz"}
How to Use IFERROR Function in Google Sheets - OfficeWheel As When you work with Google Sheets and imply different formulas, it’s very common to face errors. In that case, the IFERROR function not only helps you to clean up errors but also instructs the spreadsheet to show customized values in the place of error. This article will show you simple examples of how to use IFERROR in Google Sheets. A Sample of Practice Spreadsheet You can download spreadsheets from here and practice. What Is IFERROR Function in Google Sheets? The IFERROR function searches for errors from the dataset and if it finds any errors, then it replaces the error with a blank cell or any specific text that is instructed by you. The following is the syntax for the IFERROR function: =IFERROR(test_value, [value_if_error]) The arguments of the IFERROR function are as follows: ARGUMENT REQUIREMENT FUNCTION test_value Required The value that is being tested for error. It can be a cell reference or a formula. value_if_error Optional The value that needs to be returned if the first parameter returns an error. The formula =IFERROR(C5/D5, “N/A”) will look for an error; as an error is found, it returns the text ‘N/A’ as output. 3 Ideal Examples of Using the IFERROR Function in Google Sheets As the Google Sheet IFERROR function deals with errors, it returns the first parameter if there is no error, otherwise if an error is found it returns the blank cell or specific instructed text. Here, we discuss some examples of using the IFERROR function in Google Sheets. 1. Return Values for General Errors For applying the IFERROR function for general error, we develop a dataset that contains columns namely: Product Name, Total Price, Quantity, and Price Per Quantity. • To get the Price Per Quantity column we divided the total price by quantity and use the fill handle to apply the formula for the entire column. • But #DIV/0! error was found, as some of the quantity values are 0. So, to clean up the dataset and transform the error message into a more systematic and logical approach. we will apply the following techniques: 1.1 Return with Zero If we want to replace the error with a zero(0) value, • First, Go and select the Price Per Quantity column where errors are found. • Then go to the Formula bar and you will find the division formula. • Now modify the formula by inserting the IFERROR function. • The first argument keeps the same division formula that you applied before. • After that for the value_if_error argument add “0” in the function. • Finally, press ENTER, and you will find a zero value in the place of the error. • You can use the Fill handle to insert the IFERROR function down the entire column. Read More: [Fixed!] IFERROR Function Is Not Working in Google Sheets 1.2 Return with Blank If you want to keep the error cell blank, • Like the Return with Zero method, select the column and go to the Formula bar. • Then insert the IFERROR function. • Add the division formula as the value parameter of the function. • After that for the value_if_error argument add “in the function. • Press ENTER and you will find a blank cell replacing the error value. • At the end, use the Fill handle to apply the function to the entire column. 1.3 Return with Text If you want to add any specific text, you have to go through the same process as we described before. • Apply the IFERROR function for the Price Per Quantity column. • Apply the existing division formula as the first parameter of the IFERROR function. • Then add specific text “N/A” as the function’s second parameter. • Finally, press ENTER to apply the function and you will find the desired value in the selected cell. • Now apply the function to the entire cell by using the Fill Handle. 2. Answer with Specific Text During VLOOKUP Error During applying the VLOOKUP function, When you look up a value that is unable to locate in the dataset, it returns a #N/A! error. Through the IFERROR function, you can replace the error with any meaningful text like ‘Not Found’, ‘Not in List’, or anything that supports the dataset. Here, our dataset represents some product information and we look up a specific product “Microwave Oven”. • Insert the VLOOKUP function in the G4 cell. • Here, G3 is the search key, B:D represents the range, 1 is the column number from where to look up, and is_sorted set FALSE to get the exact value. • Press ENTER and you will find a #N/A error in the result cell. • To clear the error message and replace it with a meaningful message apply the IFERROR function before the VLOOKUP function in cell G5. • The whole VLOOKUP function is considered the first argument. • After that, input “Not in List” as “value_if_error” in the function. • Press ENTER and you will find your customized text in the selected cell. =IFERROR(VLOOKUP(G4,B:D,1,FALSE),”Not in List”) Read More: How to Use IFERROR with VLOOKUP Function in Google Sheets 3. Use of IFERROR with ARRAYFORMULA Function The ARRAYFORMULA function is used to calculate a range of data. You can apply the IFERROR function with the ARRAYFORMULA function to resolve error issues in your dataset. To do so, • First, select the entire column where you want to insert the ARRAYFORMULA function. Here we select the Price Per Quantity column to apply the formula. • Then go to the formula bar and insert the ARRAYFORMULA function. • Now divide the C5:C9 range by the D5:D9 range. • Press ENTER and you will find the results with some errors in the entire column. Note: Instead of typing the formula you can press CTRL+SHIFT+ENTER to apply ARRAYFORMULA. • To resolve the error problem and remove the #DIV/0! Insert IFERROR function. • The entire ARRAYFORMULA function considers the value parameter of the IFERROR function. • Then insert the “” as value_if_error. • Finally, press ENTER and you will find the error cells turn into the blank cell. 4. Other Types of Errors in Google Sheets When you work in Google Sheets, you have to deal with different types of errors. But don’t worry. With the help of the IFERROR function, you can clean up all these from your dataset. Now, get to know about some of these errors and when they occur. 4.1 The #NAME? Error This error generally occurs where there is a problem with the formula syntax. It may be a spelling mistake or a wrong name range. 4.2 The #NUM! Error This error returns when the Google Sheets has to display a large number value. Hope this article helps you understand how to use IFERROR in Google Sheets and now you can easily hide or replace the error with a meaningful value. If you are keen to learn advanced functions in Google Sheets you can visit the OfficeWheel website. 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