We develop a data-sparse and accurate approximation of the normalised hyperbolic operator sine family generated by a strongly P-positive elliptic operator deened in 4, 7]. In the preceding papers 14]-18], a class of H-matrices has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. An H-matrix approximation to the operator exponent with ...

Selfdecomposable variables obtained from series of Laplace (double exponential) are objects this study. We prove that hyperbolic-sine and hyperbolic-cosine in the difference Urbanik classes L2 L3 while generalized logistic variable is at least class L1. Hence some ratios those corresponding selfdecomposable characteristic functions again selfdecomposable.

The purpose of this paper is to establish a topological characterization of all the hyperbolic maps in the Sine family {λ sin(z) ̨ ̨λ 6= 0} which have super-attracting cycles.

in this paper. (1) we determine the complex-valued solutions of the following variant of van vleck's functional equation $$int_{s}f(sigma(y)xt)dmu(t)-int_{s}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin s,$$ where $s$ is a semigroup, $sigma$ is an involutive morphism of $s$, and $mu$ is a complex measure that is linear combinations of dirac measures $(delta_{z_{i}})_{iin i}$, such that for all $iin i$,...

The aim of this paper is to introduce the hybrid form hyperbolic Horadam function and investigate some its properties such as generating function. Another define sine cosine functions their symmetrical forms. For newly defined functions, recursive relations, derivatives, Cassini De Moivre type identities are examined. In addition, quasi-sine three-dimensional spiral defined.

We have presented a new hyperbolic auxiliary function method for obtaining traveling wave solutions of nonlinear partial differential equations. Applying this, exact traveling wave solutions for the coupled Sine-Gordon equations are constructed.

The paper aims are to impersonate some robust sine-hyperbolic operations laws determine the group decision-making process under fractional orthotriple linear Diophantine fuzzy set (FOLDFS) situation. FOLDFS has a notable feature trade with dubious information broader membership representation space than Spherical set. Based on it, present is classified into three phases. first phase introduce n...

The fractional-stochastic Radhakrishnan-Kundu-Lakshmanan equation (FSRKLE) is considered here. To attain new hyperbolic, elliptic, rational, and trigonometric stochastic-fractional solutions, we use two various methods such as the sine-cosine Jacobi elliptic function methods. solutions acquired are important in understanding some interesting physical phenomena due to significance of designing p...

We find exact rolling tachyon solutions in DBI type noncommutative field theory with constant open string metric and noncommutative parameter on an unstable Dp-brane. Their functional shapes span all possible homogeneous rolling tachyon solutions, i.e., they are hyperbolic-cosine, hyperbolic-sine, and exponential under 1/ cosh runaway NC tachyon potential. Even if general DBI type NC electric f...

A numerical study is given on the spectral methods and the high order WENO finite difference scheme for the solution of linear and nonlinear hyperbolic partial differential equations with stationary and non-stationary singular sources. The singular source term is represented by the δ-function. For the approximation of the δ-function, the direct projection method is used that has been proposed i...