Related papers: On modular forms arising from a differential equat…
We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…
Variants of the q-hypergeometric equation were introduced in our previous paper with Hatano. In this paper, we consider degenerations of the variant of the q-hypergeometric equation, which is a q-analogue of confluence of singularities in…
We study various properties of quasimodular forms by using their connections with Jacobi-like forms and pseudodifferential operators. Such connections are made by identifying quasimodular forms for a discrete subgroup $\G$ of $SL(2, \bR)$…
We give an explicit presentation of the module of differentials of order $n$ of a finitely generated algebra via a higher-order Jacobian matrix. We use the presentation to study some aspects of this module in the case of hypersurfaces. More…
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
We discuss an integrable partial differential equation arising from the hyperdeterminant.
Derived geometry provides powerful tools to handle non-transverse intersections and singular moduli problems arising in geometry and theoretical physics. While derived algebraic geometry has been extensively developed, classical field…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…
We investigate the integral representations of solutions to the variant of $q$-hypergeometric equation of degree 2 obtained through $q$-middle convolution by using transformation formulas for $q$-hypergeometric series. We show the…
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…
We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass…
This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…