Results 291 to 300 of about 277,915 (332)
Some of the next articles are maybe not open access.
Complex Hyperbolic function charts
Electrical Engineering, 1935Discussion of a paper by L. F. Woodruff published in the May 1935 issue, pages 550–4. A. E. Kennelly (Harvard University, Cambridge, Mass.): The charts offered in the paper will be serviceable to transmission engineers and to all those who are interested in alternating current lines having at operating frequency an angle not exceeding 0.4 in size.
openaire +2 more sources
On hyperbolically convex functions
Journal of Geometric Analysis, 2000Let $$\mathbb{D}$$ be the unit disk of the complex plane. A conformai map of $$\mathbb{D}$$ into itself is called hyperbolically convex if the non-Euclidean segment ...
Diego Mejía, Ch. Pommerenke
openaire +2 more sources
Advances in Applied Clifford Algebras, 2008
The hyperbolic version of the standard Clifford analysis will be considered. In this modification the power function x m becomes a solution. In more details, the Dirac operator \(Df = \sum^n_{i=0} e_i \frac{\partial f} {\partial x_i}\) with e 0 = 1, defined with respect to the Clifford algebra Cl n , is replaced by the operator \(M_kf(x) = Df (x ...
Sirkka-Liisa Eriksson, Heinz Leutwiler
openaire +2 more sources
The hyperbolic version of the standard Clifford analysis will be considered. In this modification the power function x m becomes a solution. In more details, the Dirac operator \(Df = \sum^n_{i=0} e_i \frac{\partial f} {\partial x_i}\) with e 0 = 1, defined with respect to the Clifford algebra Cl n , is replaced by the operator \(M_kf(x) = Df (x ...
Sirkka-Liisa Eriksson, Heinz Leutwiler
openaire +2 more sources
The hyperbolic–hypergeometric functions
Journal of Mathematical Physics, 2001In this work we present a new function to represent the approximate solution of a system of three charged particles. This function is based on an extension to two variables of the confluent hypergeometric function 1F1 of Kummer and can be obtained using a method similar to that used by Appell and Kampé de Fériet.
Gustavo Gasaneo +3 more
openaire +2 more sources
Elliptic and Hyperbolic Functions
2016In this chapter, we go on into the methods for obtaining the analytical solutions of the SD oscillator. A series of irrational elliptic functions and hyperbolic functions is proposed for the unperturbed oscillator to provide the analytical solutions for both the smooth and discontinuous cases with periodic solutions and the homoclinic ones which could ...
Qingjie Cao, Alain Léger
openaire +2 more sources
1968
Publisher Summary This chapter discusses hyperbola functions. Sum and difference of ex, e- x occur as natural combinations, so it is convenient to have an abbreviated notation to express these relations. Functions thus defined are found to possess properties closely paralleling those of the trigonometrical functions.
openaire +2 more sources
Publisher Summary This chapter discusses hyperbola functions. Sum and difference of ex, e- x occur as natural combinations, so it is convenient to have an abbreviated notation to express these relations. Functions thus defined are found to possess properties closely paralleling those of the trigonometrical functions.
openaire +2 more sources
Generalized Hyperbolic Functions
The American Mathematical Monthly, 1982(1982). Generalized Hyperbolic Functions. The American Mathematical Monthly: Vol. 89, No. 9, pp. 688-691.
openaire +2 more sources
Functions inverse to weakly hyperbolic and hyperbolic pencils
Mathematical Notes, 2017Necessary and sufficient conditions under which a matrix-valued function of a complex argument is inverse to a weakly hyperbolic or a hyperbolic pencil are established. For hyperbolic pencils, a constructive description of the inverse functions in terms of their partial fraction expansion with matrix coefficients is presented.
O. G. Konyukhova, A. I. Barsukov
openaire +2 more sources
Trigonometric and Inverse Trigonometric Functions. Hyperbolic and Inverse Hyperbolic Functions
1994If theoretical problems are under consideration, angles are not measured in degrees, but in radians (circular measure): The magnitude of an angle α is given by the length l of the arc, intercepted by the arms of the angle α on the unit circle with centre at the vertex of the angle (Fig. 2.1).
openaire +2 more sources
Hyperbolic Lagrangian functions
Applied Mathematics and Mechanics, 1998Hyperbolic complex numbers correspond with Minkowski geometry. The hyperbolic Lagrangian equation and the Hamilton-Jacobi equation will be derived from the invariants of four-dimensional space-time intervals and hyperbolic Lorentz transformations.
openaire +2 more sources