The development version of Mathematica contains extensive support for piecewise functions throughout the system. An arbitrary piecewise function (with a finite number of pieces) can be represented using the new
Supports arbitrary objective and constraint functions, including those defined in terms of special functions (for example, Bessel, hypergeometric), derivatives and integrals, andpiecewise functionsetc. 支持任意类型的目标函数和约束条件,包括内置的特殊函数(例如贝赛耳和超几何分布 ) 、 导数和积分、分段函数等...
One important consequence of the theorem is that path integrals of holomorphic functions on simply connected domains can be computed in a manner familiar from the fundamental theorem of calculus: let U be a simply connected open subset of C, let f : U C be a holomorphic function, and let ...
Trying to create a plot using heaviside function after being given a piecewise function. The code, I managed to get 2 different results, so I am not sure which is correct. The piecewise function is the following: x^2 - 1; if 0 <= x < 2 f(x) = 2x - 3; if 2 <= x < 5 si...
In fact, I wanted to optimize an objective function with complex integrals using BONMIN's toolbox, but the complexity of the objective function led to an error. 国静 2023년 8월 28일 Thanks for your suggestion. 댓글을 달려면 로그인...
function with a set D of unbounded breakpoints. For each closed subinterval Ii = [x b i−1 , x b i ], let the quantityI i f(x)dx .d o c in .c o m exist in the sense of improper integrals. There exists a func- tion g, called an integral of f on [a, b], which is...
Although polynomials have several attractive features, polynomial interpolation of a given function often has the drawback of producing approximations that may be wildly oscillatory. To overcome this difficulty we divide the interval of interest into small subintervals and in each subinterval consider polyn...
In Section 3, we introduce two types of partition of unity shape functions: two-piece piecewise polynomial PU function and the convolution PU function with flat-top. We prove the characterization of the two-piece piecewise polynomial basic PU functions, and also prove the relation between these ...
In order to prove Theorem 1.1, we shall get the lower bound of the number of isolated zeros of the first order Melnikov function M(h) of system (2.3). Note that by Theorem 2.1 M(h) can be taken as a linear combination of its generating functions. Then we use the following lemma. ...
One important consequence of the theorem is that path integrals of holomorphic functions on simply connected domains can be computed in a manner familiar from the fundamental theorem of real calculus: let U be a simply connected open subset of C, let f : U → C be a holomorphic function, ...