Related papers: New identities for the Shannon function and applic…
Baez, Fritz, and Leinster derived a method for characterizing Shannon entropy in classical systems. In this method, they considered a functor from a certain category to the monoid of non-negative real numbers with addition as a map from…
In this paper our aim is to establish new integral representations for the Fox--Wright function ${}_p\Psi_q[^{(\alpha_p,A_p)}_{(\beta_q,B_q)}|z]$ when $$\mu=\sum_{j=1}^q\beta_j-\sum_{k=1}^p\alpha_k+\frac{p-q}{2}=-m,\;\;m\in\mathbb{N}_0.$$…
Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on…
The objective of this paper is to derive symmetric property of (h,q)-Zeta function with weight alpha. By using this property, we give some interesting identities for (h,q)-Genocchi polynomials with weight alpha. As a result, our…
We analyze systematically composable composite entropy of two Tsallis subsystems with different q indices. H-theorem and thermal balance relation are commented.
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
Information entropies give a genuine way to characterize quantitatively an incompatibility in quantum measurements. Together with the Shannon entropy, few families of parametrized entropies have found use in various questions. It is also…
There is an asymptotic relationship between the multiplicative relations among multinomial coefficients and the (additive) recurrence property of Shannon entropy known as the chain rule. We show that both types of identities are…
We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden-Thompson's trace inequality…
In this letter, the (q,h)-analogue of Newton's binomial formula is obtained in the (q,h)-deformed quantum plane which reduces for h=0 to the q-analogue. For (q=1,h=0), this is just the usual one as it should be. Moreover, the h-analogue is…
The partition functions $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, and $Q(n,m,p)$, the number of integer partitons of $n$ into exactly $m$ distinct parts with each part at most…
After a brief introduction to Heun type functions we note that the actual solutions of the eigenvalue equation emerging in the calculation of the one loop contribution to QCD from the Belavin-Polyakov-Schwarz-Tyupkin instanton and the…
The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a constant, an…
We develop potential theory including a Bernstein-Walsh type estimate for functions of the form $p(z)q(f(z))$ where $p,q$ are polynomials and $f$ is holomorphic. Such functions arise in the study of certain ensembles of probability measures…
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…
The complete elliptic integrals are generalized by using the generalized trigonometric functions with two parameters. It is shown that a particular relation holds for the generalized integrals. Moreover, as an application of the integrals,…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip…
There is a natural pluripotential-theoretic extremal function V_{K,Q} associated to a closed subset K of C^m and a real-valued, continuous function Q on K. We define random polynomials H_n whose coefficients with respect to a related…