Results 11 to 20 of about 74 (74)
Entropy- A Tale of Ice and Fire
Annals of the West University of Timisoara: Mathematics and Computer Science, 2023 In this review paper, we recall, in a unifying manner, our recent results concerning the Lie symmetries of nonlinear Fokker-Plank equations, associated to the (weighted) Tsallis and Kaniadakis entropies.
Hirica Iulia-Elena +3 more
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A new refinement of Jensen’s inequality with applications in information theory
Open Mathematics, 2020 In this paper, we present a new refinement of Jensen’s inequality with applications in information theory. The refinement of Jensen’s inequality is obtained based on the general functional in the work of Popescu et al.
Xiao Lei, Lu Guoxiang
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F‐Manifolds and geometry of information
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 777-792, October 2020., 2020 Abstract The theory of F‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s. The focus of this paper consists in the demonstration that various
Noémie Combe, Yuri I. Manin
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Refinement of the Jensen integral inequality
Open Mathematics, 2016 In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
Sever Dragomir Silvestru +2 more
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Majorization, “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law
Open Mathematics, 2018 In this paper, we consider the definition of “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences.
Latif Naveed +2 more
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International Journal of Stochastic Analysis, Volume 16, Issue 3, Page 209-231, 2003., 2003 Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst‐case design settings, the disturbance is considered random with imprecisely known probability distribution.
Phil Diamond +2 more
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New bounds for Shannon, Relative and Mandelbrot entropies via Hermite interpolating polynomial
Demonstratio Mathematica, 2018 To procure inequalities for divergences between probability distributions, Jensen’s inequality is the key to success. Shannon, Relative and Zipf-Mandelbrot entropies have many applications in many applied sciences, such as, in information theory, biology
Mehmood Nasir +3 more
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Weighted additive information measures
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 417-423, 1990., 1990 We determine all measurable functions I, G, L : [0, 1] → ℝ satisfying the functional equation for P ∈ Γn, Q ∈ Γm and for a fixed pair (n, m), n ≥ 3, m ≥ 3, where G(0) = L(0) = 0 and G(1) = L(1) = 1. This functional equation has interesting applications in information theory.
Wolfgang Sander
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A measure of mutual divergence among a number of probability distributions
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 3, Page 597-607, 1987., 1986 The principle of optimality of dynamic programming is used to prove three major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.
J. N. Kapur, Vinod Kumar, Uma Kumar
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International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 3, Page 545-550, 1986., 1986 In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degree β. Here, we find the general solution of the functional equation (2) on an open domain, without using 0‐probability and 1‐probability.
Pl. Kannappan, P. K. Sahoo
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