Related papers: Generalized Donaldson's functionals and related no…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…
This work aims to initiate a discussion on finding solutions to non-homoge\-neous differential equations in terms of generalized functions. For simplicity, we conduct the analysis within the specific context of the stationary Klein-Gordon…
We discuss a system of third order PDEs for strictly convex smooth functions on domains of Euclidean space. We argue that it may be understood as a closure of sorts of the first order prolongation of a family of second order PDEs. We…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
We provide an angular parametrization of the special unitary group $\textrm{SU}(2^{n})$ generalizing Euler angles for $\textrm{SU}(2)$ by successively applying the KAK decomposition. We then determine constraint equations for the parametric…
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for the Macdonald functions.
In this paper, we study a Hamiltonian structure of the Vlasov-Poisson system, first mentioned by Fr\"ohlich, Knowles, and Schwarz. To begin with, we give a formal guideline to derive a Hamiltonian on a subspace of complex-valued $L^2$…
The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a…
A gauge-invariant form of the nonlinear Hodge equations is studied.
We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…
In this paper we consider families of mutually commuting endomorphisms of the generalized tangent bundle. We identify natural tensorial constraints extending the notion of a generalized K\"ahler structure to endomorphisms that are not…
We consider the generalized eigenvalue problem for the classical Euler differential equation and demonstrate its intimate connection with Meijer's $G$-functions. In the course of deriving the solution of the generalized Euler eigenvalue…
We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong K\"ahler with torsion…
Let $L$ be a holomorphic line bundle over a compact K\"ahler manifold $X$. Motivated by mirror symmetry, we study the deformed Hermitian-Yang-Mills equation on $L$, which is the line bundle analogue of the special Lagrangian equation in the…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
In this paper, we characterize meromorphic solutions $f(z_1,z_2),g(z_1,z_2)$ to the generalized Fermat Diophantine functional equations $h(z_1,z_2)f^m+k(z_1,z_2)g^n=1$ in $\mathbf{C}^2$ for integers $m,n\geq2$ and nonzero meromorphic…
We investigate the relative logarithmic connections on a holomorphic vector bundle over a complex analytic family. We give a sufficient condition for the existence of a relative logarithmic connection on a holomorphic vector bundle singular…
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on…
We define and study a certain category of vector bundles on a p-adic curve to which we can associate in a functorial way finite dimensional p-adic representations of the geometric fundamental group. Among other things we investigate two…