Decompositions of a C-algebra by G. C. Rao, P. Sundarayya

“…Using this decomposition theorem, we prove that if a,b∈B(A) with a∧b=F, then Aa is isomorphic to Ab if and only if there exists an isomorphism φ on A such that φ(a)=b.…”
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Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces by Yekini Shehu, Jerry N. Ezeora

“…As an application, we prove strong convergence theorem for common zeroes of a finite family of m-accretive mappings of K to E. …”
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The Maxwell-Boltzmann-Euler System with a Massive Scalar Field in All Bianchi Spacetimes by Raoul Domingo Ayissi, Norbert Noutchegueme, Hugues Paulin Mbeutcha Tchagna

“…We clearly define function spaces, and we establish all the essential energy inequalities leading to the global existence theorem.…”
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Combined Effects in Singular Elliptic Problems in Punctured Domain by Imed Bachar, Habib Mâagli, Hassan Eltayeb

“…By means of properties of slowly regularly varying functions at zero and the Schauder fixed-point theorem, we establish the existence of a positive continuous solution for the suggested problem. …”
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Operator Theory on Hilbert Spaces. by Ampeire, Anitah

“…The proposal delves into the fundamental properties and characteristics of Hilbert spaces, the properties and classifications of operators, the implications of the Spectral Theorem for self-adjoint operators, and their applications in mathematics and related fields. …”
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Mean Square Consensus of General Linear Multiagent Systems with Communication Noises under Switching Topologies by Kairui Chen, Chuance Yan, Qijun Ren, Xianxian Zeng, Junwei Wang

“…By using the stochastic stability theorem, we show that mean square consensus is achieved in fixed topology case and switching topologies case, respectively. …”
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Indoor RFID localization algorithm based on adaptive bat algorithm by Liangbo XIE, Yuyang LI, Yong WANG, Mu ZHOU, Wei NIE

“…Aiming at the problem that long time-consuming and poor positioning accuracy using geometric method in the traditional UHF RFID indoor localization algorithm, an RFID indoor positioning algorithm based on adaptive bat algorithm (ABA) was proposed.Firstly, the phase of multiple frequency points was obtained by frequency hopping technology, and the location evaluation function of bat algorithm was established based on the angle information of multiple signal classification (MUSIC) algorithm and the distance information of clustering.Secondly, the bat location was initialized by tent reverse learning to increase the diversity of the population, and the adaptive weight factor was introduced to update the bat location.Finally, the target position was searched iteratively based on the position evaluation function to achieve fast centimeter level positioning.Experimental results show that the median localization error of the proposed algorithm is 7.74 cm, and the real-time performance is improved by 12 times compared with the traditional positioning algorithm based on the Chinese remainder theorem (CRT).…”
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Reflections on dipolar quantum fluids by Zwerger, Wilhelm

“…A tensorial generalization of the virial theorem and a number of further exact thermodynamic relations are derived. …”
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Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect by Wenjie Hu, Hua Zhao, Tao Dong

“…Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. …”
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A singularly perturbed HIV model with treatment and antigenic variation by Nara Bobko, Jorge P. Zubelli

“…Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. …”
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Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions by Brahim Ghrissi, Abdelkader Amara, Youcef Henka

“…We establish explicit criteria to guarantee both the existence and uniqueness of the solution, employing the Banach fixed point theorem. Additionally, we present two examples to enhance the illustration of our findings.…”
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Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions by Hui Li, Libo Wang, Minghe Pei

“…By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. …”
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Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays by Chao Liu, Yuanke Li

“…Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. …”
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Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems by M. I. Berenguer, D. Gámez, A. I. Garralda-Guillem, M. C. Serrano Pérez

“…The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.…”
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An Underdetermined Blind Source Separation Method with Application to Modal Identification by Gang Yu

“…Meanwhile, we provide the detailed theorem to explain the clustering features. Moreover, the TF coefficients of each modal are employed to reconstruct all monotone signals, which can benefit to individually identify the modal parameters. …”
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Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model by Ali Khalouta

“…We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called $\mathbb{J}$-decomposition method ($\mathbb{J}$-DM) which is a combined form of the $\mathbb{J}$-transform method and a new decomposition method to solve the proposed model. …”
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Fixed Point Theory and the Liouville–Caputo Integro-Differential FBVP with Multiple Nonlinear Terms by Shahram Rezapour, Ali Boulfoul, Brahim Tellab, Mohammad Esmael Samei, Sina Etemad, Reny George

“…Further, the Krasnoselskii and Leray–Schauder criteria give the existence property regarding solutions of the mentioned problem. For each theorem, we provide an example based on the required hypotheses and derive numerical data in the framework of tables and figures to show the consistency of results from different points of view.…”
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STUDY ON ELASTIC MECHANICAL PROPERTY OF NOVEL OBLIQUE CROSS-LIKE STRUCTURE WITH NEGATIVE POISSON’S RATIO (MT) by HAN Guang, QIE YanHui, BAN BaoWang

“…The analytical expressions of the equivalent elastic modulus, equivalent Poisson’s ratio and relative density of the structure are derived by using the energy method and Castigliano’s second theorem. The correctness of the analytical expression is verified by finite element simulation and experimental test. …”
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Dynamics of the Rumor-Spreading Model with Control Mechanism in Complex Network by Wei Zhang, Hongyong Deng, Xingmei Li, Huan Liu

“…Then, the basic reproductive number of the system and the unique existence of the solution are discussed, and the stability of the system is analyzed using the basic reproductive number, Lyapunov function, and Lienard and Chipart theorem; furthermore, the basic reproductive number may not be able to deduce the stability of the system and a counterexample is given. …”
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A ZigBee network anonymous authentication scheme based on Chebyshev chaotic mapping and CRT by Wei LIAO, Lesheng HE, Heng YIN, Shengtao YU, Jiarui QUAN

“…A ZigBee network anonymous authentication scheme based on Chebyshev chaotic mapping and Chinese remainder theorem (CRT) was proposed to solve the problems such as the incomplete reliability of ZigBee network trust center and the lack of identity authentication when accessing the network.The proposed scheme can not only realize two-way authentication of anonymous identity, but also ensure the security of key distribution when ZigBee network structure changes dynamically.It is mainly based on a ZigBee and NB-IoT wireless heterogeneous gateway, so that the server can effectively manage the nodes in the network through this gateway.From security analysis and comparison with other related literature, the proposed scheme has higher security, with anonymity and unlink ability.In addition, the results show that the proposed scheme has more advantages than other schemes on the computational overhead.…”
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