Related papers: Generalizations of R0 and SSM properties; Extended…
For an in invertible quasihomogeneous singularity $w$ we prove an all-genus mirror theorem establishing an isomorphism between two cohomological field theories. On the $B$-side it is the Saito-Givental theory given by a certain choice of a…
In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the…
This paper is concerned with the existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation on real line. By introducing some new variables, the equation is transformed into two different semi-linear systems.…
We devise a method that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. Canonical matrices of (i) bilinear or sesquilinear forms, (ii) pairs of symmetric,…
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…
We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras…
We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schr\"odinger equation is written through the first derivative of a double-confluent Heun function. One of…
In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…
Matrix inequalities play a pivotal role in mathematics, generalizing scalar inequalities and providing insights into linear operator structures. However, the widely used L\"owner ordering, which relies on real-valued eigenvalues, is limited…
We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-su-persymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather…
We study a connection problem between the fundamental systems of solutions at singular points $0$ and $1$ for the generalized hypergeometric equation which is satisfied by the generalized hypergeometric series ${}_nF_{n-1}$. In general, the…
A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
The notion of {\it generalised structure groups} and {\it generalised holonomy groups} has been introduced in supergravity, in order to discuss the spinor rotations generated by commutators of supercovariant derivatives when non-vanishing…
We introduce a minimal supersymmetric extension of a higgsless model for electroweak symmetry breaking in a warped extra dimension. In contrast to the non supersymmetric version, our model naturally contains a candidate for cold dark…
We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…
This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring $A=k[x_1, \dots ,x_n]$.…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem (HCCP). Employing the $T$-algebraic characterization of homogeneous cones, we generalize the $P, P_0, R_0$ properties for a nonlinear…