scholarly journals On the Uniqueness Theorem for Pseudo-Additive Entropies

Entropy ◽  
2017 ◽  
Vol 19 (11) ◽  
pp. 605 ◽  
Author(s):  
Petr Jizba ◽  
Jan Korbel
Keyword(s):  
Uniqueness Theorem ◽  
The Uniqueness Theorem

scholarly journals The uniqueness theorem for entanglement measures

2002 ◽  
Vol 43 (9) ◽  
pp. 4252-4272 ◽  
Author(s):  
Matthew J. Donald ◽  
Michał Horodecki ◽  
Oliver Rudolph
Keyword(s):  
Uniqueness Theorem ◽  
Entanglement Measures ◽  
The Uniqueness Theorem

scholarly journals On the uniqueness theorem

1970 ◽  
Vol 14 (3) ◽  
pp. 376-384 ◽  
Author(s):  
Helmut Bender
Keyword(s):  
Uniqueness Theorem ◽  
The Uniqueness Theorem

scholarly journals Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Y. S. Hamed
Keyword(s):  
Uniqueness Theorem ◽  
Difference Equations ◽  
Special Linear ◽  
Uncertain Variables ◽  
Important Theorem ◽  
Special Case ◽  
The Uniqueness Theorem

<p style='text-indent:20px;'>We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their <inline-formula><tex-math id="M1">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its <inline-formula><tex-math id="M2">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their <inline-formula><tex-math id="M3">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths.</p>

scholarly journals HORIZON MASS THEOREM

2005 ◽  
Vol 14 (12) ◽  
pp. 2219-2225 ◽  
Author(s):  
YUAN K. HA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uniqueness Theorem ◽  
Hawking Radiation ◽  
General Theorem ◽  
Positive Energy ◽  
Singularity Theorem ◽  
Area Theorem ◽  
Classical Black Holes ◽  
The Uniqueness Theorem

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes, neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: (i) the singularity theorem, (ii) the area theorem, (iii) the uniqueness theorem, (iv) the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.

THE UNIQUENESS THEOREM FOR COMPLEX-VALUED NEURAL NETWORKS WITH THRESHOLD PARAMETERS AND THE REDUNDANCY OF THE PARAMETERS

2008 ◽  
Vol 18 (02) ◽  
pp. 123-134 ◽  
Author(s):  
TOHRU NITTA
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Finite Group ◽  
Uniqueness Theorem ◽  
A Finite Group ◽  
Hidden Neurons ◽  
Complex Valued ◽  
Layered Complex ◽  
The Uniqueness Theorem

This paper will prove the uniqueness theorem for 3-layered complex-valued neural networks where the threshold parameters of the hidden neurons can take non-zeros. That is, if a 3-layered complex-valued neural network is irreducible, the 3-layered complex-valued neural network that approximates a given complex-valued function is uniquely determined up to a finite group on the transformations of the learnable parameters of the complex-valued neural network.

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