Related papers: A scheme for solving hyperbolic problems with symb…
We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many…
We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of…
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
In this paper we study the construction of a discrete solution for a hyperbolic system of partial differentials of the strongly coupled type. In its construction, the discrete separation of matricial variable method was followed. Two…
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…
We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in divergence form involving measure on the right-hand side may be represented by solutions of some generalized…
The exact solutions of the Schrodinger equation with the hyperbolic Scarf potential reported in the literature so far rely upon Jacobi polynomials with imaginary arguments and parameters. We here show that upon a suitable factorization…
This paper deals with the analysis of the asymptotic limit toward the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory. After having chosen an appropriate…
In this paper we take an approach similar to that in [M] to establish a positive mass theorem for asymptotically hyperbolic spin manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…
In this paper we present an efficient computational and symbolic algorithms for solving a backward pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA,…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…
A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
This work introduces efficient symbolic algorithms for quantitative reactive synthesis. We consider resource-constrained robotic manipulators that need to interact with a human to achieve a complex task expressed in linear temporal logic.…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…