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A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often this is an isosceles triangle of height 1 and base 2 in which case it is referred to as the triangular function. Triangular functions are useful in signal processing and communication systems ...
On a semi-log plot the spacing of the scale on the y -axis (or x -axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the y values (or x values) to their log, and plotting the data on linear scales. A log–log plot uses the logarithmic scale for both axes, and hence is not a semi-log plot.
In numerical analysis, Gauss–Hermite quadrature is a form of Gaussian quadrature for approximating the value of integrals of the following kind: {\displaystyle \int _ {-\infty }^ {+\infty }e^ {-x^ {2}}f (x)\,dx.} In this case. where n is the number of sample points used. The xi are the roots of the physicists' version of the Hermite ...
Euler (now Euler Mathematical Toolbox or EuMathT) is a free and open-source numerical software package. It contains a matrix language, a graphical notebook style interface, and a plot window. Euler is designed for higher level math such as calculus, optimization, and statistics. The software can handle real, complex and interval numbers ...
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]
Integral graph. In the mathematical field of graph theory, an integral graph is a graph whose adjacency matrix 's spectrum consists entirely of integers. In other words, a graph is an integral graph if all of the roots of the characteristic polynomial of its adjacency matrix are integers. [1]
Let M be a Banach manifold of class C r with r ≥ 2. As usual, TM denotes the tangent bundle of M with its natural projection π M : TM → M given by : (,). A vector field on M is a cross-section of the tangent bundle TM, i.e. an assignment to every point of the manifold M of a tangent vector to M at that point.
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s (t), is the real-valued function: where arg is the complex argument function.