Subadditive functions and their (pseudo-)inversesdoi:10.1016/j.jmaa.2005.05.039Subadditive functionsSuperadditive functionsPseudo-inverseThe paper considers non-negative increasing functions on intervals with left endpoint closed at zero and investigates the duality between subadditivity and superadditivity via...
However, because so many functions have inverses—and mathematical consistency demands that a function composed with its inverse return the original input—we use a distinct test category to validate that functions and their inverses behave in consistent ways. The same caveats that...
今日知识点：Inverse functions and their graphs The inverse of f is the ‘opposite’ of f:thus the inverse of ‘multiply by 3’ is ‘divide by 3’ and the inverse of ‘square’ is ‘square root’.The inverse of f is written as f –1: note that this does not mean ‘1 over f ’...
how they are combined and transformed, and ways they can be classified. We review the trigonometric functions, and we discuss misrepresentations that can occur when using calculators and computers to obtain a function's graph.
Using expository text and examples available in 10 college textbooks we identify two conceptions of angles, trigonometric functions, and inverse trigonometric functions that rely on either a static or a dynamic definition of angle. Although the textbooks favor a conception of trigonometric functions that...
5 The functions f and g are defined with their respective domains by f(x)=√(2x-5) , forx≥2.5g(x)=(10)/x 10for real values o f x, x ≠ 0(a) State the range o f f.(2 marks)(b)(i) Find fg(x).(I mark)(ii) Solve the equation fg(x)=5.(2 marks)(c) The inver...
Matuszewska and W. Orlicz (1965, Studia Math. 26, 11–24). As a main result we describe, in terms of the class Kc, when two strictly increasing functions, as well as their inverse functions, are asymptoticaly equivalent in the strong sense. This result also gives a proper ...
作者: Hongyu Liu and Jun Zou 摘要: Some novel interlacing properties of the zeros for the Bessel and spherical Bessel functions are first presented and then applied to prove an interesting uniqueness result in inverse acoustic obstacle scattering. It is shown that in the resonance region, the ...
INTERPOLATION BY MEANS OF SPECIAL CLASSES OF ENTIRE FUNCTIONS AND RELATED EXPANSIONS IN SERIES OF EXPONENTIALS In this paper, we study the problems of interpolation by means of entire functions of exponential type which satisfy special restrictions on their growth, and the relationship of these proble...
In this paper, the fully complex NN design is extended to employ other complex activation functions of the hyperbolic, circular, and their inverse function family. They are shown to successfully restore the nonlinear amplitude and phase distortions of non-constant modulus modulated signals. 展开 ...