Related papers: Functional Version for Furuta Parametric Relative …
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
Recently, M. Tsukamoto (New approach to weighted topological entropy and pressure, Ergod. Theory Dyn. Syst. 43 (2023) 1004-1034) used a new approach to define the weighted topological entropy and pressure. Inspired by his ideas, we…
This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…
This note contains a short proof of the functional equation for the zeta function.
Boundary value problem for a fractional power of an elliptic operator is considered. An integral representation by means of a standard solution problem for parabolic equations is used to solve such problems. Quadrature generalized…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
The weighted forms of generalized survival and failure entropies of order ($\alpha,\beta$) are proposed and some properties are obtained. We further propose the dynamic versions of weighted generalized survival and failures entropies and…
We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down…
Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a…
This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…
In a recent paper [PRE 62, 4665 (2000)] (quant-ph/0203102) Manfredi and Feix proposed an alternative definition of quantum entropy based on Wigner phase-space distribution functions and discussed its properties. They proposed also some…
New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is useful to provide stability of viscous solutions and yields a…
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally,…
The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connections to the Kolmogorov's entropy, complexity and…
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
We derive new characterisations of the matrix $\mathrm{\Phi}$-entropy functionals introduced in [Electron.~J.~Probab., 19(20): 1--30, 2014]. Notably, all known equivalent characterisations of the classical $\Phi$-entropies have their matrix…
R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…