Results 1 to 10 of about 137,723 (315)
An Integral Representation of the Logarithmic Function with Applications in Information Theory [PDF]
Entropy, 2019 We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily computable exact formulas for quantities that involve expectations and higher moments of the logarithm of a positive ...
Neri Merhav, Igal Sason
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On integral representation of thetranslation operator
Mathematical Modelling and Analysis, 2012 The formulation in the explicit form of quantum expression of the one-dimensional translation operator as well as Hermitian operator of momentum and its eigenfunctions are presented.
Paulius Miškinis
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q-integral representation of the Al-Salam–Carlitz polynomials
Applied Mathematics Letters, 2009 We use the Andrews–Askey integral and the Leibniz rule for the q-difference operator to give the q-integral representation of the Al-Salam–Carlitz polynomials, which includes the q-integral representation of the Rogers–Szegö polynomials and the q ...
Mingjin Wang
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Integral representation of local functionals
Annali Di Matematica Pura Ed Applicata, 1993 We study conditions under which a functional $F(u,B)$ admits an integral representation of the form $$ F(u,B) = \int_B f ( x, D^ku(x) ) dx $
Giovanni Alberti
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Integrality of volumes of representations [PDF]
Mathematische Annalen, 2021 AbstractLetMbe an oriented complete hyperbolicn-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [3] we show that the volume of a representation$$\rho :\pi _1(M)\rightarrow \mathrm {Isom}^+({{\mathbb {H}}}^n)$$ρ:π1(M)→Isom+(Hn), properly normalized, takes integer values ifnis even and$$\ge
Michelle Bucher +2 more
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Some connections between various subclasses of univalent functions involving Pascal distribution series [PDF]
Journal of Mahani Mathematical Research, 2022 The main object of this paper is to define a new class of univalent functions and two subclasses of this class along with the Pascal distribution associated with convolution and subordination structures. We obtained a number of useful properties such as,
Rohollah Valizadeh +3 more
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Representational change is integral to reasoning
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 Reasoning is the derivation of new knowledge from old. The reasoner must represent both the old and new knowledge. This representation will change as reasoning proceeds. This change will not just be the addition of the new knowledge. We claim that therepresentationof the old knowledge will also often change as a side effect of the reasoning process ...
Alan Bundy, Xue Li
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SOME BASIC PROPERTIES OF THE NOISE REINFORCED BROWNIAN MOTION
Barekeng, 2022 Noise reinforced Brownian motion appears as the universal limit of the step reinforced random walk. This article aims to study some basic properties of the noise reinforced Brownian motion.
Herry Pribawanto Suryawan
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Some Useful Integral Representations for Information-Theoretic Analyses
Entropy, 2020 This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for ...
Neri Merhav, Igal Sason
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The Alternative Representation of the Bipolar Sugeno Integral [PDF]
Engineering and Technology Journal, 2022 In the context of decision support systems, bi-capacities were introduced as an extension of classical capacities. Many bipolar fuzzy integrals related to the bi-capacities have been presented in recent years.
Jabbar Abbas, Hossein Jafari
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