Induced Representation Method in the Theory of Electron Structure and Superconductivity by V. G. Yarzhemsky

“…It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. …”
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Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“…This study investigates the dynamics of turbulent systems through the lens of four fundamental theorems. The first theorem establishes a spectral decomposition of the velocity correlation function, shedding light on the coherent and incoherent structures within turbulent flows. …”
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New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness by Wei-Shih Du

“…By exploiting these results, we prove some new coincidence point and fixed point theorems which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, Kikkawa-Suzuki's fixed point theorem, and some well known results in the literature. …”
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Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems by Jie Yang, Haibo Chen, Senli Liu

“…Moreover, infinitely many pairs of solutions are provided by applying the Fountain Theorem, Dual Fountain Theorem, and Krasnoselskii’s genus theory.…”
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An Augmented Lagrangian Algorithm for Solving Semiinfinite Programming by Qian Liu, Changyu Wang

“…For this algorithm, we establish a perturbation theorem under mild conditions. As a corollary of the perturbation theorem, we obtain the global convergence result, that is, any accumulation point of the sequence generated by the algorithm is the solution of SIP. …”
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Distributed energy efficient beamforming algorithm for multicell multiuser downlink system by Wen-yang CHEN, Shi-wen HE, Yong-ming HUANG, Lv-xi YANG

“…A distributed energy efficient beamforming algorithm was studied for multicell multiuser downlink communication system.Firstly,the energy efficient optimization problem was first considered as the maximization of the ratio between the system sum rate and the system power consumption.The fractional programming optimization target was then transformed into a subtractive form via using the fractional programming theorem.Secondly,the problem was decomposed into some subproblems that can be solved respectively by introducing the concept of the interference temperature in cognitive radio networks.Finally,an effective distributed energy efficient beamforming algorithm was proposed by exploiting the Lagrangian duality theorem and optimization theorem.Compared to the classical energy efficient optimization algorithm,the proposed algorithm can achieve an obvious energy efficiency performance gain.…”
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Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations by Jun Zhang, Ti-Jun Xiao, Jin Liang

“…An application is also given to illustrate the abstract existence theorem.…”
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Some special cases on Stolarsky’s means by Cesare Palmisani

“…In this paper we observe that one-parameter Stolarsky’s means (SM) are deduced from both the Mean Value Theorem for derivatives (MVTD) and the Mean Value Theorem for definite integrals (MVTI), and we study their elementary properties as the parameter varies. …”
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Quaternary Boundary Optimal Control Problem for Quaternary Nonlinear Elliptic System with Constraints by Alaa S. Khneab, Jamil Amir Al-hawasy, Ion Chryssoverghi

“…Furthermore, the necessary condition theorem (NCTH) and the sufficient condition theorem (SCTH) for optimality are presented and proved. …”
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CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System by Jun Yu, Bo Ren, Ping Liu, Jia-Li Zhou

“…A nonauto-Bäcklund transformation (BT) theorem includes two fields f and v1 is obtained by using the CTE method. …”
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Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems by Mohamed Hannabou, Khalid Hilal, Ahmed Kajouni

“…We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. …”
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Fixed points and self-reference by Raymond M. Smullyan

“…It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. …”
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On almost increasing sequences and its applications by Hikmet S. Özarslan

“…We prove a general theorem on |N¯,pn;δ|k summability factors, which generalizes a theorem of Bor (1994) on |N¯,pn|k summability factors, under weaker conditions by using an almost increasing sequence.…”
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Hodographic study of plane micropolar fluid flows by Indrasena Adluri

“…Results are summarized in the form of a theorem, some flow problems are investigated as applications of this theorem and exact solutions and geometry of the flow are obtained in each case.…”
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Compatible mappings and common fixed points by Gerald Jungck

“…Properties of this weakened commutativity are derived and used to obtain results which generalize a theorem by Park and Bae, a theorem by Hadzic, and others.…”
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Local properties of Fourier series by Hüseyin Bor

“…A theorem on local property of |N¯,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N¯,pn|k summability factors of Fourier series have been proved.…”
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent by Mohammed El Mokhtar ould El Mokhtar

“…By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial solutions.…”
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Recognition of non-drilled polar codes based on soft decision by Zhaojun WU, Zhaogen ZHONG, Limin ZHANG, Bo DAN

“…In order to solve the problem of the blind recognition of polar codes, the theorem 1 and theorem 2 were proved firstly, which reflects the relationship between length and rate of actual polar codes, and then theorem 3 which could distinguish frozen bit and information bit positions was also proved.Based on these three theorems, the codewords matrixes and Kronecker matrixes were constructed by traversing the possible code length values.Then the information bits were traversed to detect the check relationship between the codewords and the suspected dual space.In order to detect the check relationship, log likelihood ratio was introduced, based on its characteristics and optimal criteria, the code rate and information bit positions were estimated.The simulation results show that the conclusions of the three theorems are consistent with the results.At the same time, the proposed algorithm has a strong error tolerance.Under 6.5 dB and code length of 1024, the rate of recognition can reach more than 98%.…”
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Horizon causality from holographic scattering in asymptotically dS3 by Victor Franken, Takato Mori

“…This statement is formalized by the connected wedge theorem, which can be proven using general relativity within AdS3 but also argued for using quantum information theory on the boundary, suggesting that the theorem applies to any holographic duality. …”
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A note on defect stability in d = 4 − ε by William H. Pannell

“…For surface defects Michel’s theorem survives almost untouched, and we explore bulk models for which the symmetry preserving defect is the unique stable point. …”
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