Related papers: On the modified entropy equation
The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized…
This paper is concerned with the qualitative properties of the solutions of mixed integro-differential equation \begin{equation}\label{eq 1} \left\{ \arraycolsep=1pt \begin{array}{lll} (-\Delta)_x^{\alpha} u+(-\Delta)_y u+u=f(u)\quad \ \…
A new transform method for solving boundary value problems for linear and integrable nonlinear PDEs recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation…
In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue measure. We propose a non-linear exponential transform of…
The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps…
We tackle the inverse problem of reconstructing an unknown finite measure $\mu$ from a noisy observation of a generalized moment of $\mu$ defined as the integral of a continuous and bounded operator $\Phi$ with respect to $\mu$. When only a…
We investigate the integral \[\int_0^\infty \cosh^\mu\!t\,K_\nu(z\cosh t)\,dt \qquad \Re(z)>0,\] where $K$ denotes the modified Bessel function, for non-negative integer values of the parameters $\mu$ and $\nu$. When the integers are of…
We show that $h_\infty(X+Y)\leq h_\infty(Z+W)$, where $X, Y$ are independent log-concave random variables, and $Z, W$ are exponential random variables having the same respective $\infty$-R\'enyi entropies. Analogs for integer-valued…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
We describe meromorphic solutions to the equations $f^n(z)+\left(f'\right)^n(z)=e^{\alpha z+\beta}$ and $f^n(z)+f^n(z+c)=e^{\alpha z+\beta}$ ($c\neq0$) over the complex plane $\mathbf{C}$ for integers $n\geq1$.
We present the modified relative entropy of entanglement (MRE) in order to both improve the computability for the relative entropy of entanglement and avoid the problem that the entanglement of formation seems to be greater than…
This paper is devoted to the proof of two related results. The first one asserts that if $\mu$ is a Radon measure in $\mathbb R^d$ satisfying $$\limsup_{r\to 0} \frac{\mu(B(x,r))}{r}>0\quad \text{ and }\quad…
We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…
Considering the general quantum corrections to the area law of black hole entropy and adopting the viewpoint that gravity interprets as an entropic force, we derive the modified forms of MOND theory of gravitation and Einstein field…
The problem of precise evaluation of perturbative QCD predictions at moderate energies is addressed. In order to improve stability of the predictions with respect to change of the renormalization scheme it is proposed to replace the…
According to the formal holographic principle, a modification to the assumption of holographic principle in Verlinder's investigation of entropy force is obtained. A more precise relation between entropy and area in the holographic system…
We present an observation about the proposal that four-dimensional modification of general relativity may explain the observed cosmic acceleration today. Assuming that the thermodynamical nature of gravity theory continues to hold in…
In this work, we derive a generalized modified Friedmann equation based on an entropy-area relation that incorporates established modifications, such as volumetric, linear, and logarithmic terms, in addition to novel entropic modifications…
We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…