相关论文: Riccati equation-based generalization of Dawson's …

A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…

The Wright function arises in the theory of the fractional differential equations. It is a very general mathematical object having diverse connections with other special and elementary functions. The Wright function provides a unified…

We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…

Matrix differential Riccati equations are central in filtering and optimal control theory. The purpose of this article is to develop a perturbation theory for a class of stochastic matrix Riccati diffusions. Diffusions of this type arise,…

The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…

Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…

In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of…

In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…

Double field theory provides T-duality covariant generalized tensors that are natural extensions of the scalar and Ricci curvatures of Riemannian geometry. We search for a similar extension of the Riemann curvature tensor by developing a…

The classical concept of $Q$-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be…

The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…

While global convergence of the Douglas-Rachford iteration is often observed in applications, proving it is still limited to convex and a handful of other special cases. Lyapunov functions for difference inclusions provide not only global…

The Riccati equation method is used to establish an oscillatory and a non oscillatory criteria for nonhomogeneous linear systems of two first-order ordinary differential equations. It is shown that the obtained oscillatory criterion is a…

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent…

Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator. Compared to GTFs with…

This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.

We use a new approach with a matrix transformation to obtain a new global solvability criterion for matrix Riccati equations. The proven theorem completes an well known result in directions of extension of classes of coefficient of…

Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler…

Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows…

Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of…