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Digital systems 1 – Arduino output
Published in Charlie Cullen, Learn Audio Electronics with Arduino, 2020
In this listing, the variable names show that we are working with two points in 2D space relative to an origin (assumed to be x = 0). Although the names do not enforce the data (i.e. simply calling a variable myIntegerX does not make it an integer, only the type declaration counts) they do help to give descriptive meaning to operations – even simple mathematical calculations like the addition and subtraction examples in the listing above. You may also notice that the first letter of each word in these variable names is capitalized – this is called Camel Case. This makes descriptive variable names easier to read, alongside adding comments that relate to what the instruction is doing with the data. Another aspect of variables is the use of constants for values that do not change. C allows us to use the const keyword to declare read-only variables – once assigned they cannot be reassigned, only copied:
The Emergence of Chaos in Time
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
A linear equation is an expression of the type: y=a+b*x, where x and y are the independent and dependent variables, respectively. The equation (g) is an example. When we plot a linear equation, it looks like a straight line. An equation is nonlinear when the independent variable does not appear simply at the first power. Nonlinear equations contain power functions, product functions and/or transcendental functions. Examples of nonlinear equations are (a), (f), and (i). A differential equation is linear when the dependent variables and their derivatives appear only to the first power, and there are not products of dependent variables. Examples are the equations (c) and (d). In equation (d) there is a second derivative of the dependent variable, but it is to the first power. On the other hand, the equation (e) is nonlinear because the second derivative is elevated to the power of 2. Other examples of nonlinear differential equations are (b) and (h).
Q
Published in Carl W. Hall, Laws and Models, 2018
Keywords: doubled, response, temperature Source: Morris, C. G. 1992. See also METABOLISM; RESPIRATION; VAN'T HOFF; WILHELMY QUADRANTS, LAWS OF, FOR A SPHERICAL RIGHT TRIANGLE; OR RULE OF SPECIES For a spherical right triangle, this defines a relationship concerning the relative sizes of its sides and angles (species). For a spherical right triangle, let C be a right angle, and let a, b, c be the sides opposite vertices A, B, C. 1. Angle A and side a are the same species, and so are B and b. 2. If side c is less than 90, then a and b are of same species. 3. If side c is greater than 90, then a and b are of different species. Any angle and the side opposite it are in the same quadrant, and when two of the sides are in the same quadrant, the third is in the first quadrant, and when two are in different quadrants, the third side is in the second. The quadrants are first, 0 to 90; second, 90 to 180; third, 180 to 270; and fourth, 270 to 360 (Fig. Q.1). Keywords: algebra, angles, quadrant, sides, triangle Sources: James, R. C. and James, G. 1968; Karush, W. 1989. QUADRATIC EQUATION OR FORMULA An equation or formula giving the roots of a quadratic equation in which the highest power of x, a variable, is 2: ax2 + bx + c = 0, a 0 where a, b, and c = real numbers x = [{–b (b2 – 4ac)1/2}/2a] Keywords: equation, quadratic, roots Sources: James, R. C. and James, G. 1968; Mandel, S. 1972. QUADRATIC RECIPROCITY, LAW OF When p and q are distinct odd primes, then (p/q) (q/p) = (–1) [(p – 1)/2][(q – 1)/2] where p/q and g/p = Legendre symbols J. Gauss gave 6 proofs of the law of quadratic reciprocity, and more than 50 proofs have been devised by others. A number of assertions by P. Fermat can be shown to follow the above law.
Selected AI optimization techniques and applications in geotechnical engineering
Published in Cogent Engineering, 2023
Kennedy C. Onyelowe, Farid F. Mojtahedi, Ahmed M. Ebid, Amirhossein Rezaei, Kolawole J. Osinubi, Adrian O. Eberemu, Bunyamin Salahudeen, Emmanuel W. Gadzama, Danial Rezazadeh, Hashem Jahangir, Paul Yohanna, Michael E. Onyia, Fazal E. Jalal, Mudassir Iqbal, Chidozie Ikpa, Ifeyinwa I. Obianyo, Zia Ur Rehman
Analysis of variance (ANOVA) is tool used for statistical analysis which separates an observed aggregate variability found inside a data set into random and systematic factors. The random factors do not influence a given data set statistically, while the systematic factors do. Thus, analysts in diverse field of study make use of the ANOVA test for the determination of the effect that independent variables have on the dependent variable in a statistical regression study. The variables that are measured are called the dependent variables whereas; the variables that are controlled/manipulated are called independent variables or factors. ANOVA is an extension of the t—and z-tests and it is also called the Fisher analysis of variance. It is used to investigate if significance difference exists between the mean of two or more groups. The assumptions used in ANOVA are that the fundamental distributions are normally distributed and that the variances of the distributions being compared are analogous (Smith, 2018). The formula for ANOVA is given as:
A comparative analysis of linear functions in Korean and American standards-based secondary textbooks
Published in International Journal of Mathematical Education in Science and Technology, 2018
In UCSMP Algebra, after linear functions are covered, four lessons (Compound Interest, Exponential Growth, Exponential Decay, and Modelling Exponential Growth and Decay) are placed ahead of the lesson ‘The Language of Functions’. On page 426, UCSMP Algebra introduces function with the following definition: A function is a relationship between two variables in which the value of the first variable is associated with, or determines, a unique value of the second variable. (Brown et al. [48], p.426) Right below this definition, UCSMP Algebra includes the following paragraph. In this course, you have seen many situations that involve two variables. In an investment situation, the length of time that money has been invested determines the value of the investment. In temperatures, the Fahrenheit temperature determines the Celsius temperature or vice versa. In a sequence of dot patterns, the term number determines the number of dots. When the value of a first variable determines the value of a second variable, we call the relationship between the variables a function. (Brown et al. [48], p.426)As we mentioned, rate of change is the first lesson about a linear function and with the definition and the above paragraph, UCSMP Algebra places the focus on the relationship between two quantities. Additionally, as we already found, UCSMP Algebra includes many problems that are situated in real–life contexts. Thus, it appears that UCSMP Algebra takes a functional approach to teaching linear functions. Its approach is similar to another American standards-based textbook series [15].