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# Modeling With Sinusoidal Functions Calculator

They are usually only set in response to actions made by you which amount to a request for services, such as setting your. Below (and here) is an interactive model of a color calculator. When full, Karen's lungs hold 2. Reference Section. vertical shifting of sinusoidal graphs common core algebra 2 homework answers 7 Vertical Shifts of Sinusoidal. Amazon's Choice for 4 function calculator. Chapter 4 Sinusoidal Steady-State Analysis. First of all you should understand what sine cosine and tan function actually means. Meanwhile GoPower manufactures a 600 W inverter with a modified sine wave output (closer to a square wave); this model only fetches $693. Sine Group Pty Ltd © 2020 - v0. That value can be used in a calculation to find the required side length by multiplying or dividing. These trigonometric functions are extremely important in science, engineering and mathematics, and some familiarity with them will be assumed in most ﬁrst year university mathematics courses. This means that the total wavelength is and the frequency is 1. Write a sine function that describes the boat's distance above the ocean floor as it relates to time. The Human Contrast Sensitivity Function There's one major stumbling block to measuring a transfer function for human vision: we cannot duplicate with humans the procedure employed with a lens. Students will gather data, create their own sinusoidal function, and then verify their results with a calculator. b) Find the depth of water at noon. Too often, districts are forced to choose between curricular excellence and a usable digital platform. Awaytoselect thewaveform frequency. The total power (peak of the csp graph) corresponds to 2. We will also be able to calculate the output voltages, phase shift and resistor currents at specified frequencies, and compare the data to Multisim simulations. For which places would the sine function be a more obvious model for the temperature data? The long-term average temperatures for Wellington were given above. Become a fan!. It allows to draw graphs of the function and its derivatives. See full list on philschatz. Modeling With Sinusoidal Functions Calculator It mixes together the behaviors of both exponentials and powers (proportions, like rational functions). To let the software define the Y-axis automatically, leave both input fields for the Y-axis empty. They will use the sine function in later activities. Calculator supports derivatives up to 10th order as well as complex functions. $frequency = \dfrac{1}{period}$ A mathematical model is a function that describes some phenomenon. The cosine function has a number of properties that result from it being periodic and even. 1 millimeter radius of curvature deviation from the real sine. To do so we utilize the orthogonality of sine and cosine functions: Z ˇ ˇ cos(nt) cos(mt)dt= Z. Sinusoidal frequency doublers is popular in telecommunication for example using instrument processing, or circuit analysis in analog processing [1-2]. In addition, key operations and symbols on If the calculator fails to operate normally, press the reset switch on the back to reinitialise the unit. Sinusoidal functions are useful for describing anything that has a wave shape with respect to position or time. Graphing Trig Functions - 8 - www. Module 6: Modeling with Sinusoidal Functions. The most sophisticated and comprehensive graphing calculator online. binomial distribution calculator - step by step calculation to estimate the probability of success or failure in a sequence of n independent trials or In probability & statistics for data analysis, binomial distribution is a discrete probability function widely used method to model the number of successes. Three examples are that (1) any trigonometric expression can be converted to an expression in terms of only sin and cos, (2) expressions involving exp(x) can be converted to their hyperbolic forms, and (3) a trigonometric function with an argument of the form. Modeling With Trigonometric Equations Precalculus Ii. Provide a lot of different examples on making models dimensionless with physically correct scales. The same behavior is also observed sometimes with other "inverse" functions, such as exp and ln, or arcsine and sine. This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule. C is for Cosine(COS on your calculator) T is for Tangent (TAN on your calculator) o is for opposite. 8 liters of air. Use he formulas in the course and the model I built as an example to create a complex Fourier calculator. Beyond simple math and grouping (like "(x+2)(x-4)"), there are some functions you can use as well. Make sure the calculator is in the correct trigonometric mode. This calculator graph requires that the MODE be set for Radians. Inverse function rule. Using SymPy as a calculator ¶. The Derivative Calculator lets you calculate derivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. • The scatter plot appears to resemble the shape of the function y = ln(x). Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse, while cos(θ) is the ratio of the adjacent side to the hypotenuse. Students converted the times that were in hours:minutes to decimal hours (16 + 56/60) – (6+57/60). synthesizable Verilog code for sine and cosin function with accurate output. Scientific Calculator Functions. Sometimes, we need to find minimal (maximal) value of the function at some interval [a, b]. Write a C program to create menu driven calculator that performs basic arithmetic operations (add, subtract, multiply and divide) using switch case and functions. Sinusoidal Functions. Plus, call upon the FX300MS's basic scientific, exponential, and trigonometric functions for. Describe how the system behaves over time. And to avoid any confusion, we’d. The relationship is such that if any two of the four variables are known, the other two can be calculated. Then later it will be easy to correlate them to actual real time system. Write the equation of the function f of x graphed below. From the distance graph the wavelength may be determined. I have a series of data points that are governed by a sinusoidal function. (Assume that 8 am corresponds to t = 0). were growing at 18. In particular we will look at mixing problems (modeling the amount of a substance dissolved in a liquid and liquid both enters and exits), population problems (modeling a population under a variety of situations in which the population can enter or exit) and falling objects (modeling the velocity of a. Using transfer functions the response of the system (8. lumenlearning. Graphing calculator “TICTOC” application. Home » Engineering Calculators » RMS Voltage Calculator RMS Voltage Calculator This RMS voltage calculator can be used to determine the root mean square (RMS) voltage values of the most frequently employed periodic waveforms; for example, sine wave, triangle wave, square wave, and others. mastermathmentor. 4 Inverse Circular (Trigonometric) Functions Average Daily High Temperatures in New York City H(t) = 24sin(0. Hence this sinusoidal PWM technique is modified so that the carrier signal is applied during the first and last 600 intervals per half cycle as shown in Figure 5. Just enter the trigonometric equation by selecting the correct sine or the cosine function and click on calculate to get the results. The function_name is a character string that will be used to call the function. Examinations are proctored. I want to generate a variable frequency sinusoidal signal. Your xMin and xMax should be the. Choose the queuing model you want to calculate. The amplitude of a sinusoidal function is the distance from the midline to the maximum value, or from the midline to the minimum value. Calculus: Integral with adjustable bounds. 3 Problem 15E. Notice that for year 2000 the average temperature is 80. Tool/Calculator to simplify or minify Boolean expressions (Boolean algebra) containing logical expressions with AND, OR, NOT, XOR. This simple linear regression calculator uses the least squares method to find the line of best fit for a set of paired data, allowing you to estimate the value of a dependent variable ( Y ) from a given independent variable ( X ). 2 to 5 Tuesday 10/22 Graphing Sine and Cosine functions cont’d. 4 Average Rate of Change of a Function. Modeling with Sinusoidal Functions. There are several such algorithms that only use the four basic operations (+, −, ×, /) to find the sine, cosine, or tangent of a given angle. Use the model to estimate the period of Neptune. By substituting the values of x for the points the function must pass through (x=0,1,3,4,6) it is easy to see that the expression above achieves the result, namely y=2,1,3,0,5 respectively. If we want to model cumulative rainfall over the course of a year, would a sinusoidal. Trig calculator finding sin, cos, tan, cot, sec, csc. Description Of : Applications Of Sinusoidal Functions Answers Apr 06, 2020 - By Danielle Steel ~ Last Version Applications Of Sinusoidal Functions Answers ~ the frequency of a sinusoidal function is the number of periods or cycles per unit time frequency dfrac1period a mathematical model is a function that describes some phenomenon for objects that. 26Ratio Calculator (zip) - Calculates a standard set of ratios based on input of financial data. Scientific calculators make easy work of evaluating factorials, with most featuring dedicated keys to handle the function. Approximate the time when the temperature reaches the freezing point 32°F. In this section we will use first order differential equations to model physical situations. You will either need a table that gives the values of Sine for various angles or a calculator that can determine the Sine of an angle. We are assuming that the circuit was turned on a very long time ago and it is behaving in a pattern. Our inverse function calculator uses derivative formula to solve derivative of trig functions. KTF-Split, 3 Mar. Today in precalculus, we looked at some data that follow a sinusoidal pattern and calculated a regression function to model it. Chapter 1 Test. plot() arguments. Why: Sinusoids are used to model waves and periodic behavior. That is you supply the original x and the two calculated predictors as if you had three independent variables for your regression, so your now-linear model is:. Therefore, when you talk about sine and cosine functions, you are taking in terms of “frequencies”. Lesson 6 - 6: Models of Sinusoidal Functions Many real-world problems involving periodic behavior can be modeled using sine and cosine functions. • Form: y = a + b ln(x) • The calculator takes the natural log of the x-coordinates and then preforms a linear regression. Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. Graphing Sine & Cosine Functions (II) Graphing Trig Functions (A) Graphing Sine & Cosine Functions (I) Tangent Period Action (1)! Inverse Trigonometric Functions. (Assume that 8 am corresponds to t = 0). First Derivative Calculator(Solver) with Steps. Damped sine waves are often used to model engineering situations where a harmonic oscillator is losing energy with each oscillation. Refer to both the unit circle and the graph of the sine curve. (Source: Wikipedia, try not to get hypnotized. it's really close to a sine. For example, variables that depend on the seasons may be modeled with trigonometric functions because the seasons repeat every year just like the sine function repeats every 2π. Then the waveform shape produced by our simple single loop generator is commonly referred to as a Sine Wave as it is said to be sinusoidal in its shape. Use he formulas in the course and the model I built as an example to create a complex Fourier calculator. com you can easily calculate model size or model scale. 35Hamlin (zip) - Financial function add-on's for Excel. When thinking of models for sinusoidal waves, examples such as tides of the ocean, daily temperatures for one year in your town, light and sound waves, and certain types of motion are used. 'Syms' allows for a shorthand approach for assigning. The graphs of the cosine and sine functions are developed in Section 2. The amplitude of a sinusoidal function is the distance from the midline to the maximum value, or from the midline to the minimum value. Since the amplitude of the function is 2 or 2, draw dashed lines parallel to the midline which are 2 units above and below the midline. Modeling Sinusoidal Graphs Write a sine and cosine function that would model each graph shown below. The sine function does not generate unique values for every argument. For example, let's say you have a 60" wing that has 5° of dihedral. Nevermind it would help if my calculator was in radians mode instead of degrees. Characteristics: • The scatter plot appears to resemble the shape of the function y = ln(x). These are functions of the form: y = a sin (b x + c), where a, b and c are constants. Perform a Sinusoidal Regression with Scatter Plot with our Free, Easy-To-Use, Online Statistical Software. e) Graph f together with the data on the same coordinate axes. The sinusoidal functions (sine and cosine) appear everywhere, and they play an important role in circuit analysis. Thus any x-coordinate that is negative or zero will cause an ERR DOMAIN on the calculator. Hence, the amplitude is A =1. radical function calculator ; square root indices ; algebra 2 textbook teachers addition ; 2/3 as decimal ; GRE NOTES ; Adding and subtracting worksheets ; write a program that dtermine that the enterd integer is a pallindrome or not ; sample factor problems ; radical equations and expressions solver ; graphing calculator- finding the slope. Curves that follow this shape are called 'sinusoidal' after the name of the sine function. Calculate U ' and use the chain rule to obtain. - “The angle-scale: 2^n. Use the compound interest calculator to gain a picture of how the interest on your savings or investments might grow over a period of months and years. From the graph of sinx over this interval, shown in Figure 6, we see there is only one angle which has a sine equal to 1, that is x = 90. When finding the equation for a trig function, try to identify if it is a sine or cosine graph. You really need to pay attention for the starting point of the S and the bow, it's the great…. Then later it will be easy to correlate them to actual real time system. 2 Graph transformations of the sine and cosine functions (involving changes in amplitude, period, midline, and phase) and explain the relationship between constants in the formula and transformed graph. Understand the graph of Graph variations of Understand the graph of Graph variations of In this section, we use graphs of sine and cosine functions to visualize theirUse vertical shifts of sine and cosine curves. It takes advantage of Walsh function unified approach, simple algorithm and its. Choose the queuing model you want to calculate. Precalculus: Sinusoidal Modeling. Follow the same steps that we had with the previous problem to view the exponential graph with the. Free trigonometric equation calculator - solve trigonometric equations step-by-step. Boolean Expression Calculator. Interpret the graph of a sinusoidal function that models a situation, and explain the reasoning. The buttons may be labeled differently depending on the If you got a calculator that didn't come with a manual, you can usually search for the model online and Trig Functions: When you're working with angles, keep in mind many calculators let you select whether. This calculator here performs the simple function of calculating Percentage Value of any figure you enter. •A general class of signals used for modeling the inter-action of signals in systems, are based on the trigono-metric functions sine and cosine •The general mathematical form of a single sinusoidal signal is (2. A horizontal line is drawn at 70 indicating the midpoint of the average high and low temperatures. The function of a link mechanism is to produce rotating, oscillating, or reciprocating motion from the rotation of a crank or vice versa (Ham et al. Calculator Pro is a step beyond the typical Q&A website because we have the free online calculators and tools that you need to get instant answers to your questions. The rate of increase of the function at x is equal to the value of the function at x. Sinusoidal functions graph wave forms. A graph is shown below using -80,000 < x < +80,000 counting by units of 20,000. YOUR Linear. A linear function is a function whose graph is a line. Here is an example: Your exercise: This is the graph of your function. Functions of the form ce x for constant c are the only functions that are equal to their derivative (by the Picard–Lindelöf theorem). We are assuming that the circuit was turned on a very long time ago and it is behaving in a pattern. The duty cycle of the output is changed such that the power transmitted is exactly that of a sine-wave. Phase shift of the function is. (Calculator in radians). We model cyclical behavior using the sine and cosine functions. Also you can compute a number of solutions in a system of linear equations (analyse the compatibility) using Rouché-Capelli theorem. pdf: File Size: 1125 kb: File Type: Download File. ?More complex combinations of the above, using the product, quotient, and chain rules. Graphing Trig Functions - 8 - www. Fluid Dynamics. # Compute soft cosine similarity print(softcossim(sent_1, sent_2, similarity_matrix)) #> 0. Share skill. How well does f model the given data? Compare your equation and graph with a partner. Regression modeling is the process of finding a function that approximates the relationship between the two variables in two data lists. For each graph, use the following window settings: Xmin = 0 Xmax = 2π Xscl = π/2 Ymin = −5 Ymax = 5 Yscl = 5. , ISBN-10: 1118583191, ISBN-13: 978-1-11858-319-7. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. The result, as seen above, is a smooth curve that varies from +1 to -1. 8 Phase shift; Sinusoidal Curve Fitting In these sections, we will study the following topics. Import/Export. Unit 4 - Graphing & Writing Sine & Cosine Functions; Application Problems October 21 to November 5th, 2013 Date Topic Assignment Monday Gr 10/21 changes. At t = 2 seconds she has exhaled completely and at t = 5 seconds she has inhaled completely. ) Dec 14 – Lesson – 6. Graphing calculator “TICTOC” application. Lesson 6-6 Modeling Real-World Data with Sinusoidal Functions 389 Graphing Calculator Tip For keystroke instruction on how to find sine regression statistics, see page A25. population on this island. How to type a function ? Description: for one-variable real functions: limits, integrals, roots This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games. 4 Average Rate of Change of a Function. The high tides and low tides follow a periodic pattern that you can model with the sine function. For the inverse trigonometric functions, branch cuts are defined as in Abramowitz and Stegun, figure 4. In short, all this is a small glimpse of what makes this calculator, what must be remembered is that it is a complete calculator that has powerful functions, and that can explain some calculations. In particular we will look at mixing problems (modeling the amount of a substance Of course we need to know when it hits the ground before we can ask this. In fact, you can even grab any of our calculators and put them on your own blog or website – for free!. the value of sine is 0, while at 0 radians the value of cosine is 1, the maximum value. The usage of sine, cosine and tan came as a notation to represent the relationship betwee. Whenever you see an "oscilloscope," for example when you play music using certain programs on a computer, you're really seeing a whole bunch of sine waves added together. Exponential functions. VERY VERY VERYEXTENSIVE. The polynomials, exponential function e x, and the trigonometric functions sine and cosine, are examples of entire functions. Online calculator is capable to solve the ordinary differential equation with separated variables, homogeneous, exact, linear and Bernoulli equation, including intermediate steps in the solution. Activation Functions¶. Ex: Model Daily Temperatures Using a Trig Function This video explains how to model daily temperatures using a sinusoidal function given the daily low and high temperature. m function, which then fits the entire signal with the specified peak model. At minute 13:27 I wrote the inverse cosine of. Sine wave oscillators are used as references or test waveforms by many circuits. I understand wat the values mean and how to find a b and d but c i am not to sure how to find unless there is a already given graph. The input is a sinusoidal function whose frequency increases with time. In other words the MATLAB function, foo'', must be stored in the file, foo. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them. Throwing it into lm() function in R, it doesn't recognize sinusoidal data so it just produces a straight line. The sine and cosine functions are flexible tools for modeling a wide array of periodic phenomena. Overriding singulars and plurals when defining aliases. h is for hypotenuse. functions act like "black boxes" – you just key in your angle and you get its sine, cosine or tangent. This calculator graph requires that the MODE be set for Radians. The transfer function of the system is given by (with m=1, b=0. Trigonometric functions also prove to be useful in the study of general periodic functions. Online calculator finds minimum and/or maximum of the function including on the given interval. You can also complete the operation on Scientific calculators make easy work of evaluating factorials. It occurs often in both pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. There are several such algorithms that only use the four basic operations (+, −, ×, /) to find the sine, cosine, or tangent of a given angle. 35Hamlin (zip) - Financial function add-on's for Excel. The Linear Systems Calculator does not require installation of any kind, just a browser with javascript support. Five experimental cases were used to assess the accuracy of the simulation. Download Free Intro to periodic functions - sine. Understanding data, modeling with the data collected and using that data to predict future events. In short, all this is a small glimpse of what makes this calculator, what must be remembered is that it is a complete calculator that has powerful functions, and that can explain some calculations. binomial distribution calculator - step by step calculation to estimate the probability of success or failure in a sequence of n independent trials or In probability & statistics for data analysis, binomial distribution is a discrete probability function widely used method to model the number of successes. This frustrating behavior is called loss of significance and is one kind of "gotcha" that can make some problems very hard to solve on a calculator. Identify periodic and sinusoidal functions, including those that arise from real-world applications involving primary data. These can be either Sine functions, or Cosine Function. Look below to see them all. GraphCalc allows you to graph 2D and 3D functions and equations as well as find intersects and create table values. Theory and calculation of alternating current phenomena. Looking at the data, determine the period, amplitude, and the vertical and horizontal translations. 5 value which is at $$2 \pi$$. Verify your answer with graphing software or a graphing calculator. The model will need functions to compute the speed, v, and will need two integrators with the appropriate initial position and velocity. First Order Systems. This simple linear regression calculator uses the least squares method to find the line of best fit for a set of paired data, allowing you to estimate the value of a dependent variable ( Y ) from a given independent variable ( X ). The first pair is x,y. Graphing calculator “TICTOC” application. When graphing such equations, it may be. FOCUS ON MODELING: Fitting Lines to Data. Each function calculation has a step-by-step solution so that you can easily understand how this problem is solved. The inverse hyperbolic sine transformation is defined as: log(y i +(y i 2 +1) 1/2) Except for very small values of y, the inverse sine is approximately equal to log(2y i) or log(2)+log(y i), and so it can be interpreted in exactly the same way as a standard logarithmic dependent variable. Scientific Calculator. Periodic functions can model events that reoccur in set cycles, like the phases of the moon, the hands on a clock, and the seasons in a year. We have which gives. 667 or arccos(. The cosine function has a number of properties that result from it being periodic and even. Then, you apply the sin () function to the values from the first column, in a second column. This tutorial show the procedure to open a layer of a MOD13A2, a MODIS. Hence, the amplitude is A =1. Course topics will include ratios and proportions, functions and graphs, linear and quadratic functions and equations, trigonometric functions and equations, sinusoidal curve-fitting, exponential and logarithmic functions and equations, all with an emphasis on applications. This calculator is convenient to use and accessible from any device, and the results of calculations of integrals and solution steps can be easily copied to the. When graphing such equations, it may be. Equations for Sinusoidal. To do so we utilize the orthogonality of sine and cosine functions: Z ˇ ˇ cos(nt) cos(mt)dt= Z. Intermediate Statistics More statistical functions such as Paired-variable statistical calculation, Quartiles and List display functions for speedy and thorough learning. The general function Sinusoidal wave's is shown in the figure below, in which, three parameters can be altered to get modulation - they are amplitude, frequency and phase; so, the types of analog modulation are. 4Sinusoidal Functions. An answer key is provided for all activit. c) Use the graph of d(t) and analytical calculations to calculate the interval of time during which the depth d is below 1. Use the model to estimate the period of Neptune. Free trigonometric equation calculator - solve trigonometric equations step-by-step This website uses cookies to ensure you get the best experience. Like all functions, the sine function has an input and an output. The results of the servo following test with a step input for the adjusted model are represented in This enables us to consider any frequency response function as being made up of a number of. For any sinusoidal function, there is both a sine and cosine equation. The graphs of the cosine and sine functions are developed in Section 2. The Sine Rule. m function, which then fits the entire signal with the specified peak model. Sine Functions Geogebra. • What is the period of the cosine wave you generated? Possible answer: The period is also 2π. Plan your 60-minute lesson in Math or Trigonometric functions with helpful tips from Jacob Nazeck. Hence, the amplitude is A =1. Find functions of the form that model the lynx and hare populations graphed in Figure 1. We have which gives. They are mostly standard functions written as you might expect. Get smarter in Precalculus on Socratic. Example 1: Solving a Problem Using a Sinusoidal Model. Calculates biologically effective dose (BED) and equivalent dose (EQD2) for cancer radiotherapy. ?More complex combinations of the above, using the product, quotient, and chain rules. Given the graph of either a cosine or a sine function, the wave number $$b$$, also known as angular frequency, tells us: how many fully cycles the curve does every $$360^{\circ}$$ interval It is inversely proportional to the function's period $$T$$. There are several parameters you can adjust here: Period Number of Revs to Complete Height of Lowest Car Diameter of Wheel You can also manually enter y -coordinate of the purple point. mastermathmentor. Look below to see them all. Precalculus: Sinusoidal Modeling. How can you use sinusoidal functions to model the tides? 1.  Change the window to appropriate settings: xmax: ymax: xmin: ymin: xscl: yscl:  Determine the equation of the sinusoidal regression function using C:SinReg. This button allows you to raise a number to a certain exponential value in a few keystrokes. This calculator will compute the cumulative distribution function (CDF) for the normal distribution (i. Includes basic handheld calculator functions for square, square root, percent, sign change, Pi and memory. The Cosine Graph a. This is basically the value of ½π in the fixed-point system. Glomerular filtration rate (GFR) is the best overall index of kidney function. But the sea is warming up faster in the summer and then cooling off slower in the fall. This is the opposite direction than you might expect, but it is consistent with the rules of. The motion equation for simple harmonic motion contains a complete description of the motion, and other parameters of the motion can be calculated from it. Write the equation of the function f of x graphed below. pdf file _____ Connections Additional and alternative explanation of sine graphs| Applications of trigonometric graphs at intmath. At what time (t) was point P first emerging from the water? Answer: a. It provided accurate computed forces for a wide range of tip speed ratios, and proved. Equations are given below the calculator. You can refer to the transformations section to examine the other transformations more closely. Try the free Mathway calculator and problem solver below to practice. Consider the harmonic motion of a periodic waveform shown in the figure. the tangent, secant, cosecant, and cotangent functions. I need to apply a periodic sinusoidal function to the wall such that the radius varies with time. I do not wish to fit an nth degree polynomial to this no matter how close it is to the sinusoidal function. encodes a sine wave. This calculator graph requires that the MODE be set for Radians. Adjusting the formula so we can use the calculator in degree mode is not difficult. What is the rule of this sinusoidal function? The rule of the sinusoidal function is _____. Law of Sine Introduction Solving Oblique Triangles (New) Oblique Triangles Law of Sines. This online calculator reduces given matrix to a reduced row echelon form (rref) or row canonical form and shows the process step by step. When modeling with sinusoidal functions it is sometimes more convenient to use sine versus cosine or visa versa. The waveform will repeat itself every 360° or expressed. We entered the months (January = 1, February = 2, etc. Each sine wave needs to have about 6 or 7 wavelengths. This means that point A is at 5 π / 3 − π, which is 2 π / 3 as you state. 14 is one model for the daylight in Brownsville. To operate a scientific calculator, locate the primary functions, like square root, sine, and tangent, since you'll be using these frequently. Graph the data and the curve on your graphing calculator. share to facebook share to twitter Questions. (Assume that 8 am corresponds to t = 0). this issue and many options were evaluated to open the HDF files and perform a geotransformation from Sinusoidal Coordinate System to The solution came from the powerful gdal library and some core Python functions. There are several such algorithms that only use the four basic operations (+, −, ×, /) to find the sine, cosine, or tangent of a given angle. This activity takes the Ferris wheel problem out of the abstract and has students explore a hands-on model of a sinusoidal scenario. Consider, first, the decaying sine wave. Sine is simply a function that operates on an argument. GCD Calculator. A simple wave function can be expressed as a trigonometric function of either sine or cosine. on your phone) will be able to calculate sine, cosine and tangent functions, and a few other trig. 667 or arccos(. The Lamp's Resistance during oscillation is 4V/((12V - 4V)/470) = 235 Ohms. The following is a graph of a sinusoidal function f : The coordinates of several points on the graph are given : , 0 , 4 7, - 2 , E 4 5 both of which follow a sinusoidal model. The SINH function in Excel returns the value of the hyperbolic sine of a given real number. Sinusoidal Model:$y=a \sin(bx+c)+d\$ Display output to 1 decimal place 2 decimal places 3 decimal places 4 decimal places 5 decimal places 6 decimal places 7 decimal places 8 decimal places 9 decimal places 10 decimal places Calculate. 5 Modelling data with sinusoidal functions. ) and length of daylight into the calculator’s lists and used SinReg to determine the sinusoidal function that best fits the data. a is for adjacent. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and three-dimensional volume of a solid. The Sine Rule. User can set the maximum output power of inverter, this can make the inverter work at cooler contition as user want and extend the lifespan of the inverter. It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition. While f(x) = sin(x) starts at the axis of the curve, f(x) = cos(x) starts at is maximum value. Learning Target: I can model real world data with sinusoidal functions. corresponding arc, and consequently the maximum variation of the sine bears to its average variation the same ratio as the av- 2erage variation of the arc to that of the sine, that is, 1 -^ -, and TT since the variations of a sine function are sinusoidal also, we have 2Mean value of sine wave -^ maximum value = —^ 1. The most sophisticated and comprehensive graphing calculator online. Note that this graph is the same as the graphs of y = sin (x±π) and y = cos(x+ $$\frac{π}{2}$$). Find amplitude, period, frequency, and graph (given an equation, draw the graph) Analyze the graph of a sinusoid (given a graph, write the equation) Solve application problems (will cover later) 4-4 Sinusoids Part 1 (Watch before Day #28 lesson) We start addressing for real the sine and cosine waves, a. Sinusoidal function can be defined as follows. This online calculator can help with RREF matrix problems. We use radians, so the calculator will have to be set to radian mode. The major differences are due to the two very important capabilities of LINGO: the ability to solve nonlinear models, and the availability of the set or. The sinusoidal function is periodic, meaning its graph contains a […]. (which might be due to the approximation i made in. Is there anyway to make MATLAB to fit my data to a sum of sine function with over 8 sinusoidal terms?. The greater the number of surgical outcomes that are fit to the RBF model, the greater the overall depth of accuracy. So, a sinusoidal function of y = 4 sin (x) will have an amplitude of 4. Trigonometric Functions- To define and demonstrate the six. Students will gather data, create their own sinusoidal function, and then verify their results with a calculator. Model this graph with a sinusoidal function. The period is, of course, the circumference of the wheel, and the wheel has a diameter of 24 inches. A horizontal line is drawn at 70 indicating the midpoint of the average high and low temperatures. (Evaluating Trig Functions ) If you've ever taken a ferris wheel ride then you know about periodic motion, you go up and down over and. The sine function does not generate unique values for every argument. Question 1 Solution The scaling along the y-axis is one unit for one large division and therefore the maximum value of y: y max = 1 and the minimum value of y: y min = - 7. Login to your Sine Dashboard. Result of drive involving both 1 Hz and 3 Hz accelerations. You can operate the calculator directly from your keyboard, as well as using the buttons with your mouse. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. 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Jorn-Harald Paulsen posts a little article describing how to create a sine function in Maya. Then later it will be easy to correlate them to actual real time system. Any given sinusoidal function equation can consist of any combination of these transformations. • However, the problem does not always state that a calculator is required, so use your own judgment. A SPECIAL CLASS OF FUNCTIONS 235 sinusoidal function will oscillate. For example, if the coefficient on "urban" is 0. 35 and on day 172 of the year. 56Mhz large sine wave signal for the function generators in my lab are not aimed to be able to drive this power level I have to use some differential buffer to measure certain parameter of my circuits. Solution:. The demo below performs the discrete Fourier transform on the function f(x). The function 'sym' will allow you to create a symbolic variable, with additional arguments specifying whether the object should be 'positive','real', and in the case of the second argument being a m x n array, will create m x n symbolic variables. On a sheet of graph paper, predict what the following graphs would look like. 3 Interpreting Sinusoidal Graphs (blank copy). By using this website, you agree to our Cookie Policy. 3 Know basic properties of the inverse trigonometric functions sin-1 x, cos-1 x, tan-1 x, including their domains and ranges. This means that the greater $$b$$ is: the smaller the period becomes. You can use trigonometry to graph the changes in high and low tides for a particular location. Online Geometry Calculators and Solvers. The sinusoidal functions (sine and cosine) appear everywhere, and they play an important role in circuit analysis. The sinusoidal wave might be a problemI've tryed this with no succes. 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It provided accurate computed forces for a wide range of tip speed ratios, and proved. four calculation methods with steps for each of them show help ↓↓ examples ↓↓. We are assuming that the circuit was turned on a very long time ago and it is behaving in a pattern. notebook 2 Using the graphing calculator:  Enter the data and create a scatter plot. 3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number. Additionally, familiarize yourself with the secondary functions above the primary keys, which can be accessed by pressing the “Shift” or “2ND” key. The calculators also typically support the Reverse Polish notation (RPN). Students converted the times that were in hours:minutes to decimal hours (16 + 56/60) – (6+57/60). Easy to use and 100% Free! We also have several other calculators. You can use the same method as the quadratic function above. 0 Time elapsed Time.

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# Solving $z^2=\bar z$

How would I solve this complex number equation? $$z^2=\bar z$$

basically I already solved it and got: $$z=-\frac{1}{2}\pm \sqrt {\frac {3}{4}}$$ BUT, they say the equation has two more solutions: $0$ and $1$, but I dont understand why.

Thanks

• Since $1^2=1=\bar{1}$. Same for zero. Sep 9 '15 at 21:12
• Note that $z=0$ works. If $z\ne 0$, taking norms we find that $z$ has norm $1$. Multiply through by $z$. We get that (for $z\ne 0$) the roots are the roots of $z^3=1$. Sep 9 '15 at 21:14
• How did you get your solutions? That would almost surely help identify whatever you missed. Sep 9 '15 at 21:14

If $z^2=\bar z$ then taking magnitude gives $|z|^2=|z|$ so $|z|=0,1$. The case $|z|=0$ gives $z=0$.

If $|z|=1$, then the equation $z^2=\bar z=z^{-1}$ so $z^3=1$. This gives the remaining 3 solutions which are the third roots of unity.

Let $z = r e^{i \theta}$. Then we need $r^2 e^{i 2 \theta} = r e^{-i \theta}$.

We at least require that their magnitudes be the same, so $r = 0$ or $r = 1$.

The first case $r = 0$ gives us one answer: $z = 0$. In the next case, we require that $2 \theta \equiv -\theta \pmod {360^\circ}$, i.e. $3 \theta \equiv 0 \pmod{360^\circ}$. Thus, this gives us $\theta = 120k^\circ$, which gives us three unique answers $\theta = 0^\circ, \theta=120^\circ, \theta = 240^\circ$, which completes the solution set.

If $z^2=\bar{z}$ then $|z|^2=|z|$, so either $|z|=0$ that is $z=0$ or $|z|=1$ in which case $\bar{z}=1/z$ and in this case the proposed equation becomes $z^2=1/z$ or $z^3=1$, which yields $z=1$, $z=\dfrac12+i\dfrac{\sqrt3}{2}$ and $z=\dfrac12-i\dfrac{\sqrt3}{2}$.

$$z^2=\bar{z}$$ $$(\Re(z)+\Im(z)i)^2=\overline{\Re(z)+\Im(z)i}$$ $$\Re(z)^2-\Im(z)^2+2\Re(z)\Im(z)i=\Re(z)-\Im(z)i$$ Taking purely imaginary parts: $$2\Re(z)\Im(z)=-\Im(z)$$ $$2\Re(z)\Im(z)+\Im(z)=0$$ $$(2\Re(z)+1)\Im(z)=0$$ $\Re(z)=-\frac{1}{2}$, OR $\boxed{\Im(z)=0}$.

Taking real parts: $$\Re(z)^2-\Im(z)^2=\Re(z)$$ Then if $\Re(z)=-\frac{1}{2}$,

$\left(-\frac{1}{2}\right)^2-\Im(z)^2=-\frac{1}{2}\implies \Im(z)=\pm\frac{\sqrt{3}}{2}$

But if $\Im(z)=0$, then

$\Re(z)^2-0^2=\Re(z)\implies \Re(z)=\frac{1\pm 1}{2}$

So there are your four solutions, $\left\{-\frac{1}{2}-\frac{\sqrt{3}}{2}i,-\frac{1}{2}+\frac{\sqrt{3}}{2}i,0,1\right\}$.

The thing to remember is: Don't divide by zero!

Suppose $z^2=\bar z.$ By conjugation, we find that $\bar z^2=z.$ Subtracting the latter identity from the former yields $$z^2-\bar z^2=\bar z-z,$$ or equivalently, $$\left(z+\bar z\right)\left(z-\bar z\right)=-\left(z-\bar z\right).$$ Hence*, we have $z=\bar z$ or $z+\bar z=-1.$ In the first case, the original identity becomes $$z^2=z,$$ and in the second case, it becomes $$z^2=-1-z.$$ Can you take it from there?

*Do you see why?

First notice that the the solutions should lie on the unit circle. Then you can try solving it geometrically. For every $z$ on the unit circle $z^2$ is also on the unit circle and the angle between it and $Ox$ is two times the angle between $z$ and $Ox$. In the same manner $\overline z$ is the number symmetric to $z$ by the line $Ox$.


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# Microeconomics

All new and solved questions in Microeconomics category

##### In the process of implementing a project, you have sub- contracted JAB Enterprise to supply supplements worth 1480 cartons of two varieties X and Y. Suppose the joint cost function for the two varieties of supplements is given by C = 250X2 + 120Y2. The quantity of X and Y are not specified; therefore, the firm may decide to supply any combination. The firm wishes to minimize the cost of producing the supplement but meet your demand. Using Lagrangian multiplier technique find the amounts of X a
In the process of implementing a project, you have sub- contracted JAB Enterprise to supply supplements worth 1480 cartons of two varieties X and Y. Suppose the joint cost function for the two varieties of supplements is given by C = 250X2 + 120Y2. The quantity of X and Y are not specified; therefo...
##### Suppose that the supply schedule of Maine lobsters is as follows: Price of lobster (per pound) 252015105Quantity of lobster supplied (pounds)800700600500400 Suppose that Maine lobsters can be sold only in the United States. The U.S. demand schedule for Maine lobsters is as follows: Price of lobster (per pound) 252015105Quantity of lobster supplied (pounds)2004006008001000 a. Draw the demandthe equilibrium price and quantity of lobsters?curve and the supply curve for Maine
Suppose that the supply schedule of Maine lobsters is as follows: Price of lobster (per pound) 25 20 15 10 5 Quantity of lobster supplied (pounds) 800 700 600 500 400 Suppose that Maine lobsters can be sold only in the United States. The U.S. demand schedule for Maine lobst...
##### United Healthcare insures 200,000 people in Metropolis. These people average 2.5 physician visits per year. After analyzing claims data, United has determined that some of these visits were unnecessary. They want to raise their copayment by 10% in Metropolis to discourage physician visits. They estimate that the elasticity of demand for physician visits in Metropolis is -0.3. How much will visits to United physicians decline in Metropolis? What will happen to United’s copayment revenue (as a per
United Healthcare insures 200,000 people in Metropolis. These people average 2.5 physician visits per year. After analyzing claims data, United has determined that some of these visits were unnecessary. They want to raise their copayment by 10% in Metropolis to discourage physician visits. They esti...
##### By using graph (4 different graphs), show the effect of the event below (ceteris paribus) onthe motorcycle market: (20 points)a. Increasing the value added tax that paid by the buyerb. Decreasing the price of car significantlyc. Technological advance reduces the cost of producing motorcycled. Increasing the price of metal, as the one input of producing motorcycle
By using graph (4 different graphs), show the effect of the event below (ceteris paribus) on the motorcycle market: (20 points) a. Increasing the value added tax that paid by the buyer b. Decreasing the price of car significantly c. Technological advance reduces the cost of producing motorcycle ...
##### Explain what is hierarchy of events in 170 words
Explain what is hierarchy of events in 170 words...
##### Now suppose the secretary of labor proposes an increase in the minimum wage. What effect wouldthis increase have on employment? Does the change in employment depend on the elasticity ofdemand, the elasticity of supply, both elasticities, or neither?
Now suppose the secretary of labor proposes an increase in the minimum wage. What effect wouldthis increase have on employment? Does the change in employment depend on the elasticity ofdemand, the elasticity of supply, both elasticities, or neither?...
##### The government decides that tax evaders should receive heavier punishments and increases the punishment that tax evaders face in a manner that brings no benefit to the IRS. The matrix of the new game is given below.Find the equilibrium of the new game.
The government decides that tax evaders should receive heavier punishments and increases the punishment that tax evaders face in a manner that brings no benefit to the IRS. The matrix of the new game is given below. Find the equilibrium of the new game....
##### . Laws that limit interstate sale of wine over the Internet were relaxed significantly as a result of a Supreme Court decision in 2005. How would you expect this to affect the scale of production in the wine industry?
. Laws that limit interstate sale of wine over the Internet were relaxed significantly as a result of a Supreme Court decision in 2005. How would you expect this to affect the scale of production in the wine industry?...
##### If you pay 5,000va year fin tuition and gave up 2p, 000 a year of income to attend college then the yearly opportunity cost is
If you pay 5,000va year fin tuition and gave up 2p, 000 a year of income to attend college then the yearly opportunity cost is...
##### If you pay 5,000va year fin tuition and gave up 2p, 000 a year of income to attend college then the yearly opportunity cost is
If you pay 5,000va year fin tuition and gave up 2p, 000 a year of income to attend college then the yearly opportunity cost is...
...
##### Calculate TC, VC, FC, AC, AVC, and MC. Plot the AC and MC curves.b. Assume that the price of labor doubles. Calculate the new AC and MC. Plot andcompare with the previous AC and MC curves.c. Assume that total factor productivity doubles (the level of output doubles for eachinput combination). Calculate the new AC and MC. Plot and compare with theprevious AC and MC curves.d. Which two major factors affect a firm’s cost curves?
Calculate TC, VC, FC, AC, AVC, and MC. Plot the AC and MC curves. b. Assume that the price of labor doubles. Calculate the new AC and MC. Plot and compare with the previous AC and MC curves. c. Assume that total factor productivity doubles (the level of output doubles for each input combination)...
##### Consider the following table:Output(tons of wheat)Lan Inputs(acres)Labor Inputs Land Rent (Phpper acre)Labor Wage (Phpper worker)0 15 0 1200 5001 15 6 1200 5002 15 11 1200 5003 15 15 1200 5004 15 21 1200 5005 15 31 1200 5006 15 45 1200 5007 15 63 1200 500a. Calculate TC, VC, FC, AC, AVC, and MC. Plot the AC and MC curves.b. Assume that the price of labor doubles. Calculate the new AC and MC. Plot andcompare with the previous AC and MC curves.c. Assume that total factor productivity doubles (the
Consider the following table: Output (tons of wheat) Lan Inputs (acres) Labor Inputs Land Rent (Php per acre) Labor Wage (Php per worker) 0 15 0 1200 500 1 15 6 1200 500 2 15 11 1200 500 3 15 15 1200 500 4 15 21 1200 500 5 15 31 1200 500 6 15 45 1200 500 7 15 63 1200 500 a. Calculat...
##### (i) In the wage equation in Example $14.4,$ explain why dummy variables for occupation might beimportant omitted variables for estimating the union wage premium.(ii) If every man in the sample stayed in the same occupation from 1981 through $1987,$ would youneed to include the occupation dummies in a fixed effects estimation? Explain.(iii) Using the data in WAGEPAN include eight of the occupation dummy variables in the equationand estimate the equation using fixed effects. Does the coefficient o
(i) In the wage equation in Example $14.4,$ explain why dummy variables for occupation might be important omitted variables for estimating the union wage premium. (ii) If every man in the sample stayed in the same occupation from 1981 through $1987,$ would you need to include the occupation dummi...
##### Use SMOKE for this exercise. (i) A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness, or productivity effects) is $\log ($ income $)=\beta_{0}+\beta_{1}$ cigs $+\beta_{2} e d u c+\beta_{3} a g e+\beta_{4} a g e^{2}+u_{1}$ where cigs is number of cigarettes smoked per day, on average. How do you interpret $\beta_{1} ?$ (ii) $\quad$ To reflect the fact that cigarette consumption might be jointly determined with income, a demand for cigaret
Use SMOKE for this exercise. (i) A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness, or productivity effects) is $\log ($ income $)=\beta_{0}+\beta_{1}$ cigs $+\beta_{2} e d u c+\beta_{3} a g e+\beta_{4} a g e^{2}+u_{1}$ where cigs is number...


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# Time-Stamped Claim Logic

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. We introduce the Time-Stamped Claim Logic including a sound and complete sequent calculus that allows one to reduce the size of the collected set of evidence and removes inconsistencies, i.e., the logic ensures that the result is consistent with respect to the trust relations considered. In order to show how Time-Stamped Claim Logic can be used in practice, we consider a concrete cyber-attribution case study.

## Authors

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• ### An Argumentation-Based Framework to Address the Attribution Problem in Cyber-Warfare

Attributing a cyber-operation through the use of multiple pieces of tech...
04/27/2014 ∙ by Paulo Shakarian, et al. ∙ 0

• ### Time-Aware Evidence Ranking for Fact-Checking

Truth can vary over time. Therefore, fact-checking decisions on claim ve...
09/10/2020 ∙ by Liesbeth Allein, et al. ∙ 4

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## 1 Introduction

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, most notably the ability to reason about the attribution of cyber-attacks.

When reasoning about a cyber-attack, a digital forensics analyst typically collects a huge amount of pieces of evidence from different sources. Some of the pieces of evidence may be contradictory and the analyst might consider some sources to be more trustworthy than others. Inferring conclusions from such evidence thus requires particular care and time. A similar problem is faced by historians when they are trying to date particular historic events.

The Time-Stamped Claim Logic that we introduce in this paper provides the forensics analyst with a sound and complete means to reduce the size of the collected set of evidence and remove inconsistencies, i.e., the logic ensures that the result is consistent with respect to the trust relations that the analyst considers to hold. More specifically, the Time-Stamped Claim Logic is a monotonic propositional logic whose language contains assertions of different kinds: labeled assertions to expressing statements of agents about time-stamped claims and relational assertions indexed by propositional symbols that are used to relate agents. In particular, a trust relation with respect to each propositional subject is defined between agents.

We formalize a Gentzen calculus for our logic, which allows one to infer a time-stamped claim whenever (i) there is an agent that states the claim and (ii) each agent that is more trustworthy with respect to the subject does not state the opposite claim. We define a modal and many-valued semantics for our logic, and prove that the calculus is sound and complete with respect to this semantics. In order to show how Time-Stamped Claim Logic can be used in practice, we consider, as a proof of concept, a concrete cyber-attribution case study, inspired by the Ukraine Power Grid Attack that occurred in December 2015.

We proceed as follows. In Section 2, we define the language of Time-Stamped Claim Logic. In Section 3, we formalize a Gentzen calculus for the logic together with a running example. In Section 4, we introduce the semantics, and we then prove the soundness and the completeness of the calculus in Section 5 and Section 6, respectively. In Section 7, we apply Time-Stamped Claim Logic to a realistic case study taken from the cyber-security area. We discuss the most relevant related work in Section 8 and provide some concluding remarks and ideas for future work in Section 9.

## 2 The Language of Time-Stamped Claim Logic

In this section, we introduce the language of the Time-Stamped Claim Logic.

###### Definition 2.1

Let be a non-empty set of propositional symbols and assume fixed non-empty pairwise disjoint sets and of variables, which represent agents names and time points, respectively. The set of time-stamped propositional claims is defined as

 KP={−(t⋅p), t⋅p∣t∈XT and p∈P}

###### Definition 2.2

The language of assertions is defined as follows:

• ;

• whenever ;

• whenever and ;

• whenever and ;

• whenever and ;

• whenever and ;

• whenever and .

Let us briefly discuss the intuitive meaning of these assertions:

• establishes that and are equivalent time points.

• establishes that agent is more trustworthy with respect to than agent .

• establishes that is the most trustworthy agent with respect to statements about .

• establishes that states .

• establishes that there are no agents more trustworthy with respect to than that state . That is, each agent more trustworthy with respect to than does not claim . Similarly, for .

• establishes that states conditional to statements .

Given the relation of with respect to the other statements we will refer to as a derived evidence. We will instead refer to the previous two assertions and simply as evidence.

Let us now illustrate how our logic is used by means of a running example.

###### Example 2.3

Let us suppose that we want to model a crime situation C that possibly occurred at time in which there is a potential culprit J and some sources , and providing statements on the case. Let us further suppose that for the source a person is a culprit provided that person was at the scene of the crime, is capable of committing the crime and has a motive. This can be expressed by the assertion

 a1::(t⋅inplaceJC,t⋅capableJC,t⋅motiveJC/t⋅culpritJC)

over . Moreover, we can write the assertion

 ∀x.x⊴motiveJ% Ca3

to express that is a source recognized to be the most trustworthy with respect to knowing the motive of the potential culprit . Furthermore, the assumptions

• is less trustworthy than with respect to knowing the motive of to have committed the crime ,

• claims that does not have a motive to have committed the crime at time ,

• claims that has a motive to have committed the crime at time

can be expressed in the Time-Stamped Claim Logic by means of the assertions

• ,

• and

• ,

respectively. Hence, if does not have an opinion about whether or not has a motive to have committed the crime at time , then

• and should hold,

• should hold and should not hold, and

• both and should not hold.

Before we introduce the calculus of our logic, which will allow us to draw conclusions from assertions like the ones in Example 2.3, let us define some useful notation. In the following, we will write

 varA:℘LP→℘XA

to denote the map that assigns to each set of assertions the set of elements of that occur in it; mutatis mutandis for and . We may confuse a singleton set with its unique element. Given , and , we write to denote the subset of including all the assertions using only symbols in and variables in and .

## 3 The Calculus of Time-Stamped Claim Logic

Let us begin by recalling what is a sequent and an inference rule. Let be a non-empty set of propositional symbols. A sequent over is a pair and is denoted by

 Γ→Δ,

where and are finite multisets of formulas in . An inference rule over is of the form

 Γ1→Δ1⋯Γn→ΔnΓ→ΔF

where is a set of fresh variables with at most a variable in .

For convenience, below, we will sometimes write

 −−(t⋅p)

to mean and vice-versa, in order to avoid the replication of rules NS, NK, SCR, SCL, SKR, and SKL.

###### Definition 3.1

The calculus over is composed by the following inference rules:

• Axiom (Ax):

 β,Γ→Δ,β

where is of the form , or

• Cut (Cut):

 β,Γ→ΔΓ→Δ,βΓ→Δ

where is of the form , or

• Reflexivity of (ER):

 Γ→Δ,t≅t
• Symmetry of (ES):

 t1≅t2,Γ→Δ,t2≅t1
• Transitivity of (ET):

 t1≅t2,t2≅t3,Γ→Δ,t1≅t3
• Congruence of (EC):

 t1≅t2,[a:ϕ]t1t2,Γ→Δ,a:ϕ

where is a formula obtained from by replacing by

• Agent preference transitivity (AT):

 a1⊴pa2,a2⊴pa3,Γ→Δ,a1⊴pa3
• Agent preference reflexivity (AR):

 Γ→Δ,a⊴pa
• Agent preference congruence (AC):

 a1⊴pa2,a2⊴pa1,[a:ϕ]a1a2,Γ→Δ,a:ϕ

where is a formula obtained from by replacing by

• Agent preference maximum on the right (AMR):

 Γ→Δ,b⊴paΓ→Δ,∀x.x⊴pab
• Agent preference maximum on the left (AML):

 a′⊴pa,∀x.x⊴pa,Γ→Δ∀x.x⊴pa,Γ→Δ
• Negative statement (NS):

 a:−ϕ,Γ→Δ,a:ϕa:−ϕ,Γ→Δ
• Negative knowledge (NK):

 −ϕ,Γ→Δ,ϕ−ϕ,Γ→Δ
• Statement propagation over time (SP):

 Γ→Δ,t1≅t2,a:−(t1⋅p),a:t2⋅pΓ→Δ,t1≅t2,a:−(t1⋅p)
• Knowledge propagation time (KP):

 Γ→Δ,t1≅t2,−(t1⋅p),t2⋅pΓ→Δ,t1≅t2,−(t1⋅p)
• Statement confirmation on the right (SCR):

 b:−ϕ,a⊴varP(ϕ)b,Γ→ΔΓ→Δ,a:⊡ϕb
• Statement confirmation on the left (SCL):

 a:⊡ϕ,Γ→Δ,a⊴varP(ϕ)a′a:⊡ϕ,Γ→Δ,a′:−ϕa:⊡ϕ,Γ→Δ
• Extracting knowledge from statement on the right (SKR):

 b:−ϕ,b:⊡−ϕ,Γ→ΔΓ→Δ,ϕ,a:ϕΓ→Δ,ϕ,a:⊡ϕΓ→Δ,ϕb
• Extracting knowledge on the left (KL):

 b:ϕ,b:⊡ϕ,Γ→Δϕ,Γ→Δb
• Extracting knowledge from statement on the left (SKL):

 ϕ,Γ→Δ,a:−ϕϕ,Γ→Δ,a:⊡−ϕϕ,Γ→Δ
• Conditional reasoning on the right (CR1):

 ϕ1,…,ϕn,Γ→Δ,a:ϕΓ→Δ,a::(ϕ1,…,ϕn/ϕ)
• Conditional reasoning on the left (CR2):

 Γ→Δ,ϕ1⋯Γ→Δ,ϕna:ϕ,Γ→Δa::(ϕ1,…,ϕn/ϕ),Γ→Δ

Most of the rules are self-explanatory, so let us briefly explain only some of them.

The rule states that the claims of an agent are not contradictory, in the sense that an agent cannot claim and . Observe that we do not have the right counterpart of NS that introduces in the right hand side. This is because the logic is not bivalent since there is a third truth-value . Therefore, is not a classical negation.

The rule states that in order to conclude that an agent does not state a certain claim at a particular time it is enough to show that he states the opposite claim at a different time.

The rule states that it is possible to conclude when there is no agent more trustworthy than that claims .

On the other hand, rule states that in order to conclude , it is enough to show that there is an agent stating that is not contradicted by a more trustworthy agent and that each agent stating the opposite claim is contradicted by a more trustworthy agent.

We say that a sequent is a theorem, written

 ⊢Γ→Δ,

if there is a finite sequence of sequents

 Γ1→Δ1⋯Γn→Δn

such that:

• is ,

• for each ,

• either is the conclusion of a rule without premises,

• or is the conclusion of a rule where each premise is a sequent in the sequence with .

In this case, the sequence is said to be a derivation for and is said to be derivable.

The notion of derivable can be brought to the realm of formulas. For , we say that is derivable from , denoted by

 Ψ⊢α,

whenever there is a finite set such that .

For the sake of readability, in the derivations that we give below we underline the principal formula(s) of the rule/axiom that is applied.

###### Example 3.2

Let us return to the crime situation described in Example 2.3. Let be the set composed by the following propositional symbols: , , , , , , , and Let be the set containing the assertions

and let be the singleton set with the assertion . The derivation in Figure 1 establishes that is derivable. The subderivation of is in Figure 2.

We will show the use of Time-Stamped Claim Logic with a more complex case study in Section 7.

## 4 The Semantics of Time-Stamped Claim Logic

In this section, we define the semantics of the Time-Stamped Claim Logic. In the following sections, we will then prove the soundness and completeness of the sequent calculus with respect to this semantics. We start by introducing the notion of interpretation structure, which has a modal and many-valued flavour.

###### Definition 4.1

An interpretation structure over a non-empty set of propositional symbols is a tuple

 (DA,DT,≅I,{⊴Ip}p∈P,V)

such that

• and are non-empty sets,

• is a reflexive, symmetric and transitive relation over ,

• is a transitive and reflexive binary relation over for each ,

• such that for every , and ,

• if , then for every such that ,

• whenever ,

• whenever and .

In an interpretation structure, means that agent claims that occurred at time , means that agent claims that does not occur at time and means that agent does not have an opinion about the occurrence of at time .

An assignment over is a pair such that and are maps. Moreover, we say that assignments and are equivalent up to , written

 ρ≡Abρ′,

whenever and for every .

Given an interpretation structure over and an assignment over , satisfaction of an assertion by and , denoted by

 Iρ⊩α,

is defined as follows

• whenever ,

• whenever ,

• whenever for every ,

• whenever

• whenever, for each assignment and such that , if then ,

• whenever

• for each assignment and with , if then ,

• there are assignment and with , and ,

• whenever if for then .

Note that in the definition of satisfaction the truth-value does not play an explicit role. However, it allows the following to be possible:

 Iρ⊮a:ϕandIρ⊮a:−ϕ.

To simplify the presentation, given a set , we will write

 Iρ⊩Γ

whenever for each .

###### Definition 4.2

Given and , we say that entails , denoted by

 Ψ⊨α,

whenever for every interpretation structure and assignment over we have

 Iρ⊩α if Iρ⊩Ψ.

## 5 Soundness

In this section, we prove that the theorems derived using the calculus of the Time-Stamped Claim Logic introduced in Section 3 are valid according to the semantics introduced in Section 4. We start by providing some relevant semantic notions related to sequents.

###### Definition 5.1

We say that an interpretation structure and an assignment satisfy a sequent , denoted by

 Iρ⊩Γ→Δ,

whenever for some if . We say that a sequent is valid, denoted by

 ⊨Γ→Δ,

whenever it is satisfied by every interpretation structure and assignment . We say that and satisfy a rule with a fresh variable ,

 Γ1→Δ1⋯Γn→ΔnΓ→Δb,

whenever if


text:
# Trying to make Gasoline from scratch, need help figuring it out.

by black phantom
Tags: gasoline
 Sci Advisor HW Helper PF Gold P: 3,724 Trying to make Gasoline from scratch, need help figuring it out. If you can find a natural oil from either plant or animal that is fairly rich in C8-C12 fatty acids it is fairly straightforward. First, hydrolyze the oil into the free fatty acid with aqueous sodium hydroxide and work up the soap solution with acid and extract withhexane (or gasoline). treat the free fatty acid with either quicklime or slaked lime and heat until the free fatty acid salt decarboxylates. Distill the remainder to obtain an alkylate fuel. should be able to pull it off for about $20K in equipment and permits (50K-75K if you need to hire an engineer to figure out the details for you... education pays!) and you might be able to make gasoline for about$25/ gallon. Easy peasy.


text:
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

There are nice examples in geometry. For example, the Euclidean plane can be characterized on the one hand by Hilbert's axioms, on the other hand by axioms for complete ordered field $+$ vector space $+$ inner product.
Another example is that of a Pappian plane, characterized on the one hand by the three projective plane axioms $+$ Pappus theorem, on the other hand by the field axioms (from which the plane may be constructed via homogeneous coordinates).


text:
9 views

Write L-attributed SDD's analogous to that of Example $5.19$ for the following productions, each of which represents a familiar flow-of-control construct, as in the programming language C. You may need to generate a three  address statement to jump to a particular label $L$, in which case you should generate goto $L$.

1. $S\rightarrow f (C) S_{1}\:else\:S_{2}$
2. $S\rightarrow do\:S_{1}\: while\:(C)$
3. $S\rightarrow '\{'L'\}';\:L\rightarrow LS\mid \epsilon$

Note that any statement in the list can have a jump from its middle to the next statement, so it is not sufficient simply to generate code for each statement in order.

| 9 views


text:
How to get a wheel pump to deposit water near the top of the wheel?

Suppose I have a wheel, about 6 feet in diameter, with empty soup cans affixed around it, powered by a big windmill. This drawing only has four spokes, but there will be more:

                      ___
___| <-- tin can
...   \       |       /
.... <--bamboo chute| <--spoke
...               \     |     /
<--water is sent that way    /
\   |   /
\  |  /
__                   \ | /                  |  |
|  |-------------------( )-------------------|__|
|  |                  / | \
/  |  \
/   |   \
/    |    \
/     |     \
~~~~~~~~~~~~~~~~~~~~~~~~|~~~~~~~~~~~~~~~~~~~~~~~~~ <-- water
|__
|___ <--water is picked up here

The water needs to be dispensed into a chute, or aqueduct, made from bamboo, cut in half. The water is sent down the chute to another higher pool of water.

The first problem I'm running into with this design is that there isn't any way to position the chute in a way that catches the water pouring out of the cans. If I position the chute under the can, it falls within the radius of rotation, and blocks the turning.

How can I get the water from the cans to spill out into the chute, at ideally the highest point possible?

• you could have your cans on pivots and a stop at the top that causes them to tip... – Solar Mike Jun 24 '20 at 8:02
• Then you can have two cans, mounted outside the wheel frame so they pour into chutes that then join. – Solar Mike Jun 24 '20 at 8:04
• For a windmill drive, a simple chain pump would probably match the torque and rpm of the mill and the pump better. See 3.6.7 here – Phil Sweet Jun 26 '20 at 1:45


text:
OMBROSI Sheldy Javier
artículos
Título:
On the $A_{\infty }$ conditions for general bases
Autor/es:
JAVIER DUOANDIKOEXTEA; F.J. MARTÍN-REYES; SHELDY OMBROSI
Revista:
MATHEMATISCHE ZEITSCHRIFT
Editorial:
SPRINGER
Referencias:
Lugar: Berlin; Año: 2015 vol. 282 p. 955 - 955
ISSN:
0025-5874
Resumen:
We discuss several characterizations of the A∞ class of weights in the setting ofgeneral bases. Although they are equivalent for the usual Muckenhoupt weights, we showthat they can give rise to different classes of weights for other bases. We also obtain newcharacterizations for the usual A∞ weights.