Uniqueness and Asymptotic Behavior of Positive Solutions for a Fractional-Order Integral Boundary Value Problem by Min Jia, Xin Liu, Xuemai Gu

“…Our analysis relies on Schauder's fixed-point theorem and upper and lower solution method.…”
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Distributed Event-Triggered Output Synchronization of Complex-Valued Memristive Reaction-Diffusion Complex Networks with Spatial Sampled-Data by Tiane Chen, Zaihe Cheng

“…First, by using the separate method, set value mapping, and intermediate value theorem, the complex-valued memristive reaction-diffusion complex networks can be transferred into two semi-uncertain real-valued reaction-diffusion complex networks. …”
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The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator by Jevgeņijs Carkovs, Jolanta Goldšteine, Kārlis Šadurskis

“…We propose a stochastic approximation algorithm for quantitative analysis of the above model based on the probabilistic limit theorem. If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion. …”
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Manipulation Game Considering No-Regret Strategies by Julio B. Clempner

“…The existence of an optimal solution is demonstrated via the Weierstrass theorem. The game is modeled as a three-level Stackelberg framework based on Markov chains. …”
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Global dynamics of a general class of multi-group epidemic models with latency and relapse by Xiaomei Feng, Zhidong Teng, Fengqin Zhang

“….$ In particular, a matrix-theoretic method is used to provethe global stability of the disease-free equilibrium when $R_0\leq1,$while a new combinatorial identity (Theorem 3.3 in Shuai and vanden Driessche [29]) in graph theory is applied to provethe global stability of the endemic equilibrium when $R_0>1.…”
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Entanglement wedge reconstruction using the Petz map by Chi-Fang Chen, Geoffrey Penington, Grant Salton

“…From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.…”
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Null Controllability of a Nonlinear Age Structured Model for a Two-Sex Population by Amidou Traoré, Okana S. Sougué, Yacouba Simporé, Oumar Traoré

“…Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after Kakutani’s fixed-point theorem.…”
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Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator by Jinhua Wang, Hongjun Xiang, ZhiGang Liu

“…By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. …”
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Population Dynamic Study of Prey-Predator Interactions with Weak Allee Effect, Fear Effect, and Delay by Ye Xuan Li, Hua Liu, Yu Mei Wei, Ming Ma, Gang Ma, Jing Yan Ma

“…Next, according to the Sotomayor theorem, the cross-sectional conditions of transcritical bifurcation and Hopf bifurcation are obtained. …”
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Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection by Francesco Salvarani, Gabriel Turinici

“…We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. …”
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Modelling and Simulation of the Spread of HBV Disease. by Niyirora, Ignatius

“…It was guided by specific objectives that were to find out the disease-free equilibrium of the spread of Hepatitis B Virus, to determine sensitivity analysis on Ro to ascertain which parameter is most sensitive and that should be targeted by way of intervention and to examine the local stability of the model equation using the modified implicit function theorem. The first result of our simulations confirms that the disease-free equilibrium is globally asymptotically stable when Ro 1. …”
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Recognition and Simulation of Exercise Mode Based on Energy Consumption Model by Yulei Li

“…Based on the kinetic energy theorem, the student movement energy expenditure is estimated. …”
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On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces by Isra Al-Shbeil, Houari Bouzid, Benali Abdelkader, Alina Alp Lupas, Mohammad Esmael Samei, Reem K. Alhefthi

“…We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. …”
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Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation by I. J. Cabrera, J. Harjani, K. B. Sadarangani

“…Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results.…”
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Observer-Based Sliding Mode Control for Path Tracking of a Spherical Robot by Majid Taheri Andani, Zahra Ramezani, Saeed Moazami, Jinde Cao, Mohammad Mehdi Arefi, Hassan Zargarzadeh

“…Then a modified sliding mode controller is proposed for the robot’s tracking control in the presence of uncertainties. Next, the Lyapunov theorem is utilized to analyse the overall stability of the proposed scheme, including the convergence of the observer estimation and the trajectory tracking errors. …”
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Tensor weight structures and t-structures on the derived categories of schemes by Dubey, Umesh V., Sahoo, Gopinath

“…First, we show that the bijection [12, Theorem 4.10] restricts to give a bijection between the set of compactly generated $\otimes ^c$-weight structures and the set of compactly generated tensor t-structures. …”
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Physical layer security of NOMA-D2D cooperative wireless system by Yifan DING, Guangqiu LI, Hui LI

“…Aiming at the physical layer security (PLS) application requirement of massive user equipments access in the future, the PLS model combining with non-orthogonal multiple access (NOMA), device-to-device (D2D) and relay cooperation was proposed.The model was composed of base station with transmit antenna selection (TAS), NOMA far cellular user of base station and D2D transmitter, D2D receiver and passive eavesdropper, the D2D transmitter was also assumed two roles of NOMA near user of base station and decode-and-forward relay.The approximate expressions for the secrecy outage probability, non-zero secrecy capacity probability and asymptotic secrecy outage probability of NOMA-D2D cooperative wireless system under two TAS schemes were derived by using Gaussian-Chebyshev Quadrature theorem.Numerical and simulation results verify the accuracy of PLS performance analysis of NOMA-D2D cooperative wireless system.The results also show that increasing the power allocated to far cellular user under constant total power of base station can effectively improve PLS performance of NOMA-D2D cooperative wireless system.…”
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Double-dual n-types over Banach spaces not containing ℓ1 by Markus Pomper

“…The proof makes use of Henson's language for normed space structures and uses ideas from mathematical logic, most notably the Löwenheim-Skolem theorem.…”
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Multiple Positive Solutions for a Coupled System of p-Laplacian Fractional Order Two-Point Boundary Value Problems by K. R. Prasad, B. M. B. Krushna

“…This paper establishes the existence of at least three positive solutions for a coupled system of p-Laplacian fractional order two-point boundary value problems, D0+β1(ϕp(D0+α1u(t)))=f1(t,u(t),v(t)), t∈(0,1), D0+β2(ϕp(D0+α2v(t)))=f2(t,u(t),v(t)), t∈(0,1), u(0)=D0+q1u(0)=0, γu(1)+δD0+q2u(1)=0, D0+α1u(0)=D0+α1u(1)=0, v(0)=D0+q1v(0)=0, γv(1)+δD0+q2v(1)=0, D0+α2v(0)=D0+α2v(1)=0, by applying five functionals fixed point theorem.…”
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The SSIM index is not a metric and it is badly evaluate the similarity of images by V. V. Starovoitov

“…This article debunks some of the myths that have arisen around this index. A theorem is proved which states that the SSIM index and any of its linear transformations are not metric functions. …”
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