相关论文: On modular forms arising from a differential equat…
The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are…
In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
We explicitly describe the Jacquet-Langlands correspondence at the level of modular forms. This gives a simpler and more flexible solution to Eichler's basis problem for general level than earlier work of Hijikata-Pizer-Shemanske for…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…
We show that nontrivial solutions to higher and fractional order equations with certain nonlinearity are radially symmetric and nonincreasing on geodesic balls in the hyperbolic space $\mathbb{H}^n$ as well as on the entire space…
Second-order automorphic forms are similar to the usual automorphic forms but have a weaker automorphy condition. We answer a question of Zagier and find the dimensions of spaces of holomorphic, even weight, second-order forms. We also…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
We describe algorithms based on invariant theory to solve problems on the geometry of curves, mainly those of genus 2, 3 and 4. New theoretical results building on the first author's PhD thesis are also included.
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…
We investigate the meromorphic quasi-modular forms and their $L$-functions. We study the space of meromorphic quasi-modular forms. Then we define their $L$-functions by using the technique of regularized integral. Moreover, we give an…
We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…
We survey on-shell and off-shell higher derivative supergravities in dimensions $1\le D\le 11$. Various approaches to their construction, including the Noether procedure, (harmonic) superspace, superform method, superconformal tensor…
Singularities of plane into plane mappings described by parabolic two-component systems of quasi-liner partial differential equations of the first order are studied. Impediments arising in the application of the original Whitney's approach…