Related papers: The new notion of Bohl dichotomy for nonautonomous…
The Bohl-Perron result on exponential dichotomy for a linear difference equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$ states (under some natural conditions) that if all solutions of the non-homogeneous equation…
We introduce and study the dynamics of Chebyshev polynomials on $d>2$ real intervals. We define isoharmonic deformations as a natural generalization of the Chebyshev dynamics. This dynamics is associated with a novel class of constrained…
Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified…
A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…
While Deep Neural Networks (DNNs) achieve remarkable performance, their tendency to produce overconfident predictions. Evidential Deep Learning (EDL) mitigates this by formulating predictions as a Dirichlet distribution over class…
In this paper, we firstly give the definition of dipersionless bigraded Toda hierarchy (dBTH) and introduce some Sato theory on dBTH. Then we define Orlov-Schulman's $\M_L$, $\M_R$ operator and give the additional Block symmetry of dBTH.…
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive…
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state…
Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed ``odd viscosity'', becomes…
Algebraic dichotomy is a generalization of an exponential dichotomy (Lin, JDE2009). This paper gives a version of Hartman-Grobman linearization theorem assuming that linear system admits an algebraic dichotomy, which generalizes the…
This paper extends the model reduction method by the operator projection to the one-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order globally hyperbolic moment system is built on our careful study of…
We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath\'eodory and the weaker property of angle preservation - in…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…
We obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies with respect to a sequence of norms and nonuniformly hyperbolic…
We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…
The aim of this work is to extend the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) based on the point-coupling density functionals to odd-$A$ and odd-odd nuclei and examine its applicability by taking odd-$A$ Nd…
Entropic Dynamics (ED) is an inference-based framework that seeks to construct dynamical theories of physics without assuming the conventional formalism --- the Hamiltonians, Poisson brackets, Hilbert spaces, etc. --- typically associated…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
We introduce the notion of Bohr chaoticity, which is a topological invariant for topological dynamical systems, and which is opposite to the property required by Sarnak's conjecture. We prove the Bohr chaoticity for all systems which have a…