arXiv subjects
Publications and source records attributed to Nikolaj M. Glazunov.
This paper presents a brief overview of ravine functions using the example of the Minkowski-Cohn moduli surface from the point of view of optimization on it. Elements of representation and solution of the minimization problem at a point are presented.
A brief overview of results concerning the connection between the Hilbert-Polya conjecture and the Riemann hypothesis about the Riemann zeta function, some new results on p-adic quantum computing, quantum entanglement based on lattice spin models and algebraic entanglement models is given. Quantum computing uses both photons and electrons, so their known properties are (very briefly) presented.
We review novel results and investigate actions and transformations of groups and semigroups on (quantum) spaces, present dynamical systems and zeta functions arising from these spaces, actions and transformations, discuss their stochastic properties.
The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra framework for Calabi-Yau supermanifolds and stacks in open and closed string theory. In the framework we investigate supersymmetries and integrability.
We survey and investigate some computational aspects of the Fourier-Mukai transform.
By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
We present some methods and results in the application of algebraic geometry and computer algebra to the study of algebraic vector bundles, foliations and zeta functions. A connection of the methods and results with noncommutative geometry will be consider.
This paper describes some validated numerics aspects of Riemann zeta function, Dirichlet L-functions, Dedekind zeta functions and Hasse-Weil L-functions.
In this paper I consider the applications of several kinds of approximations of real functions to the problem of verified computation (reliable computing) of the range of implicitly defined real function $x_{n+1} = G(x_{1}, ..., x_{n}),$ where dependency $F(x_{1}, ..., x_{n+1}) = 0$ is defined on some compact domain by a sufficiently smooth real function $F(x_{1}, ..., x_{n+1}) >.$ Constructive version of Kolmogorov-Arnold and implicit function theorems, results about floating-point approximation, floating-point approximations which give lower-bound and upper-bound estimates of some real functions, and approximate algebraic computation are used for the purpose. The rigorous theory can be build on the base of analysis on manifolds over floating points domains. In the text we demonstrate our approach on examples from investigation of Minkowski's conjecture on critical determinant of the region $\mid x \mid^p + \mid y \mid^p \leq 1, p > 1.$.