Related papers: Krein's strings whose spectral functions are of po…
We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the complement of that of the other. We…
It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and…
We investigate the following three consistency conditions for constructing string theories on orbifolds: i) the invariance of the energy-momentum tensors under twist operators, ii) the duality of amplitudes and iii) modular invariance of…
This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the…
Empirical analysis of many colored knot polynomials, made possible by recent computational advances in Chern-Simons theory, reveals their stability: for any given negative N and any given knot the set of coefficients of the polynomial in…
Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations on Kerr background satisfy Teukolsky Master Equation. The two non-trivial equations obtained after separating the variables are the polar angle…
We show that sequences of skew Schur polynomials obtained from stretched semi-standard Young tableaux satisfy a linear recurrence, which we give explicitly. Using this, we apply this to finding certain asymptotic behavior of these Schur…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
We give a functorial construction of k-invariants for ring spectra and use these to classify extensions in the Postnikov tower of a ring spectrum.
In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in…
We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently "nice" random walk measures) a connected, compactly…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
We study string propagation in an exact, four-dimensional dyonic black hole background. The general solutions describing string configurations are obtained by solving the string equations of motion and constraints. By using the covariant…
We consider stable representations of non-Dynkin quivers with respect to a central charge. On one condition the existence of a stable representation with self-extensions implies the existence of infinitely many stables without…
Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.
In the paper a theorem of Piccard's type is proved and, consequently, the continuity of $\mathcal{D}$-measurable polynomial functions of $n$-th order as well as $\mathcal{D}$-measurable $n$-convex functions is shown. The paper refers to the…
We prove the existence of a polynomial invariant that satisfies the HOMFLY skein relation for links in a lens space. In the process we also develop a skein theory of toroidal grid diagrams in a lens space.
A covariant formalism for physical perturbations propagating along a string in an arbitrary curved spacetime is developed. In the case of a stationary string in a static background the propagation of the perturbations is described by a…
Answers are offered to the Gould's question to find spectral sufficient conditions for a graph to have a chorded cycle via signless Laplacian spectral radius. The conditions are tight.
The class of self-conjugate-reciprocal irreducible monic (SCRIM) polynomials over finite fields are studied. Necessary and sufficient conditions for monic irreducible polynomials to be SCRIM are given. The number of SCRIM polynomials of a…