Related papers: The Method of Geodesic Expansions and its Applicat…
The computational complexity of simulating seismic waves demands continual exploration of more efficient numerical methods. While Finite Volume methods are widely acclaimed for tackling general nonlinear hyperbolic (wave) problems, their…
The classification of (proper) compactifications of topological groups with respect to the possibility of extensions of algebraic operations is presented. Ellis' method of construction compactifications of topological groups allows one to…
The question under consideration is Gevrey summability of power expansions of solutions to the third and fifth Painlev\'{e} equations near infinity. Methods of French and Japaneese schools are used to analyse these properties of formal…
Several applications in optimization, image, and signal processing deal with data that belong to the Stiefel manifold St(n,p), that is, the set of n-by-p matrices with orthonormal columns. Some applications, like the Riemannian center of…
We prove an extension of the Index Theorem for Morse-Sturm systems of the form $-V''+RV=0$, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint.…
In this paper we describe the topological behavior of the geodesic flow for a class of closed 3-manifolds realized as quotients of nonstrictly convex Hilbert geometries, constructed and described explicitly by Benoist. These manifolds are…
This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping…
The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their…
We study properties of typical closed geodesics on expander surfaces of high genus, i.e. closed hyperbolic surfaces with a uniform spectral gap of the Laplacian. Under an additional systole lower bound assumption, we show almost every…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
In the symplectic category there is a `connect sum' operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a…
Starting from the equation obeyed by the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the Appell generalized hypergeometric functions of two variables of the fist kind. Several cases…
We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure $\mu(\om)$ of (not necessarily compact) basic semi-algebraic sets$\om\subset\R^n$. We obtain two monotone (non increasing and non…
It is shown in this paper that, almost all current prevalent iterative \mbox{methods} for solving linear system of equations can be classified as what we called extended Krylov subspace methods. In this paper a new type of iterative methods…
It is proved that the Maslov index naturally arises in the framework of PDEs geometry. The characterization of PDE solutions by means of Maslov index is given. With this respect, Maslov index for Lagrangian submanifolds is given on the…
A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for…
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an…
The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…
In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…
Ratner's theorem implies topological rigidity of immersed totally geodesic subspaces of noncompact type in finite-volume locally symmetric spaces. In higher rank and infinite volume, however, counter-examples to this rigidity have remained…