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Search Results: 1 - 10 of 779 matches for " Tatsuya Furuichi "
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Correction: The Zinc Transporter SLC39A13/ZIP13 Is Required for Connective Tissue Development; Its Involvement in BMP/TGF-β Signaling Pathways
Toshiyuki Fukada , Contributed equally to this work with: Toshiyuki Fukada, Natacha Civic, Tatsuya Furuichi
PLOS ONE , 2008, DOI: 10.1371/annotation/a6c35a12-e8eb-43a0-9d00-5078fa6da1bb
Abstract:
Characterizations of Generalized Entropy Functions by Functional Equations
Shigeru Furuichi
Advances in Mathematical Physics , 2011, DOI: 10.1155/2011/126108
Abstract: We will show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that Tsallis entropy function is characterized by a functional equation, which is a different form that used by Suyari and Tsukada, 2009, that is, in a proposition 2.1 in the present paper. We give an interpretation of the functional equation in our main theorem.
A mathematical review of the generalized entropies and their matrix trace inequalities
Shigeru Furuichi
Lecture Notes in Engineering and Computer Science , 2007,
Abstract:
Schr?dinger uncertainty relation with Wigner-Yanase skew information
Shigeru Furuichi
Physics , 2010, DOI: 10.1103/PhysRevA.82.034101
Abstract: We shall give a new Schr\"odinger type uncertainty relation for a quantity representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a mixed state.
Matrix trace inequalities on the Tsallis entropies
Shigeru Furuichi
Physics , 2010,
Abstract: Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addtition, some matrix trace inequalities related to the Tsallis relative entropy are studied.
On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics
Shigeru Furuichi
Physics , 2010, DOI: 10.1063/1.3063640
Abstract: We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the $q$-expectation value and the $q$-Gaussian distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the $q$-variance, as applications of the nonnegativity of the Tsallis relative entropy, without using the Lagrange multipliers method. In addition, we define a $q$-Fisher information and then prove a $q$-Cram\'er-Rao inequality that the $q$-Gaussian distribution with special $q$-variances attains the minimum value of the $q$-Fisher information.
Trace inequalities in nonextensive statistical mechanics
Shigeru Furuichi
Physics , 2005,
Abstract: In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.
On a parametrically extended entanglement-measure due to Tsallis relative entropy
Shigeru Furuichi
Physics , 2005,
Abstract: In the previous paper \cite{FYK}, we mainly studied the mathematical properties of Tsallis relative entropy with respect to the density operators. As an application of it, we adopt a parametrically extended entanglement-measure due to Tsallis relative entropy in order to measure the degree of entanglement. Then we study its properies with respect to the parameter $q$ appearing in Tsallis entropies. In addition, the relation between it and the relative entropy of entanglement is studied.
Precise estimates of bounds on relative operator entropies
Shigeru Furuichi
Physics , 2014,
Abstract: Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy.
A refinement of the arithmetic-geometric mean inequality
Shigeru Furuichi
Mathematics , 2009,
Abstract: We shall give a refinement of the arithmetic-geometric mean inequality.
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