Research on a 3D Predator-Prey Evolutionary System in Real Estate Market by Yujing Yang, Wenzhe Tang

“…The local stability conditions and complex dynamics are investigated, and the existence of chaos is discussed in the sense of Marotto theorem; bifurcation diagrams, Lyapunov exponents, sensitivity analysis for initial values, and time history figure of the system are mapped out and discussed. …”
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Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach by KumSong Jong, HuiChol Choi, KyongJun Jang, SunAe Pak

“…Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fixed-point theorems such as the Leray-Schauder nonlinear alternative, the Schauder fixed-point theorem, and the Banach contraction mapping principle and the properties of the Gauss hypergeometric function are used to prove our main results. …”
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Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions by Bashir Ahmad, Juan J. Nieto

“…The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.…”
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On the two-loop BSM corrections to $$h\longrightarrow \gamma \gamma $$ h ⟶ γ γ in a triplet extension of the SM by Giuseppe Degrassi, Pietro Slavich

“…We focus on the two-loop corrections controlled by the quartic scalar couplings, and obtain explicit and compact formulas for the $$h \gamma \gamma $$ h γ γ amplitude by means of a low-energy theorem that connects it to the derivative of the photon self-energy w.r.t. the Higgs field. …”
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KENAS BINMORE'AS: SOCIALINIS KONTRAKTAS LOŠIMŲ TEORIJOS KONTEKSTE by Nida Vasiliauskaitė

“…Binmore tries to reformulate the famous Rawlsian original position theorem in terms of game theory and for this purpose introduces a strict distinction between personal and empathetic preferences. …”
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Floer homology and non-fibered knot detection by John A. Baldwin, Steven Sivek

“…These results rely on our main technical theorem, which gives a complete classification of genus-1 knots in the 3-sphere whose knot Floer homology in the top Alexander grading is 2-dimensional. …”
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The Kronecker Summation Method for Robust Stabilization Applied to a Chemical Reactor by Radek Matušů, Jana Závacká, Roman Prokop, Monika Bakošová

“…The paper focuses on robust stabilization where the suitable parameters of a simple continuous-time PI controller are determined through a combination of the Kronecker summation method, sixteen plant theorem, and an algebraic approach to control design in the ring of proper and stable rational functions. …”
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Adaptive Neural Control of Hypersonic Vehicles with Actuator Constraints by Changxin Luo, Humin Lei, Dongyang Zhang, Xiaojun Zou

“…Secondly, on the basis of the implicit function theorem, the radial basis function neural network (RBFNN) is introduced to approximate the uncertain items of the model. …”
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Culture of Critical Discourse on Education and Science by M. B. Sapunov, Kh. G. Tkhagapsoev

“…In particular, the researchers actively use the methodological potential of such concepts as “converted form”, “red tapes”, “Goodhart’s law”, “Thomas theorem” that are implemented as conceptual tools to comprehend and describe the specificity of educational system. …”
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A new condition for Root Clustering in PMI regions by Mohamed Hechmi BOUAZIZI

“…This paper also provides an extension to the classical theorem of Cyparissos Stephanos, which formulates the relationship between the eigenvalues of two matrices and those of composite matrices of their Kronecker products. …”
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Fraïssé limit via forcing by Mohammad Golshani

“…A Fra\"{i}ss\'{e} limit, denoted $Flim(\mathcal{K})$, of aFra\"{i}ss\'{e} class $\mathcal{K}$ is the unique\footnote{The existence and uniqueness follows from Fra\"{i}ss\'{e}'s theorem, See \cite{hodges}.} countable ultrahomogeneous (every isomorphism of finitely-generated substructures extends to an automorphism of $Flim(\mathcal{K})$) structure into which every member of $\mathcal{K}$ embeds.Given a Fraïssé class K and an infinite cardinal κ, we define a forcing notion which adds a structure of size κ using elements of K, which extends the Fraïssé construction in the case κ=ω.…”
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Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications by Thabet Abdeljawad, Qasem M. Al-Mdallal, Mohamed A. Hajji

“…Then, existence and uniqueness theorems for the Caputo (CFC) and Riemann (CFR) type initial difference value problems by using Banach contraction theorem are proved. …”
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Finite-Time Adaptive Tracking Control for a Class of Pure-Feedback Nonlinear Systems with Disturbances via Decoupling Technique by Qiangqiang Zhu, Ben Niu, Shengtao Li, Peiyong Duan, Dong Yang

“…By properly modeling the nonaffine function, the design difficulty of the pure feedback structure is overcome without using the median value theorem. In our design procedure, an finite-time adaptive controller is elaborately developed using the decoupling technology, which eliminates the limitation assumption on the partial derivatives of nonaffine functions. …”
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Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification by Oscar Castillo, Juan R. Castro, Patricia Melin, Antonio Rodriguez-Diaz

“…In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs) for this purpose. …”
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Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions by Douglas R. Anderson, Christopher C. Tisdell

“…We form new existence results for solutions to the continuous BVP with our methods involving linear interpolation of the data from the discrete BVP, combined with a priori bounds and the convergence Arzela-Ascoli theorem. Thus, our use of discrete BVPs to yield results for the continuous BVP may be considered as a discrete approach to continuous BVPs.…”
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Evaluation Formulas for Generalized Conditional Wiener Integrals with Drift on a Function Space by Dong Hyun Cho

“…In this paper we derive a translation theorem for a generalized Wiener integral and then prove that Y is a generalized Brownian motion process with drift a. …”
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Three-Party Stochastic Evolutionary Game Analysis of Reward and Punishment Mechanism for Green Credit by Qingfeng Zhu, Kaimin Zheng, Yilin Wei

“…We gave sufficient conditions for the stability of strategy based on the stability discriminant theorem of Ito^'s stochastic differential equation (SDE). …”
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A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative by Belaynesh Melkamu, Benyam Mebrate

“…The solution of the proposed model, which is carried out using a fixed-point theorem and an iterative method, exists and is unique. …”
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Security & safety issues and endogenous security for intelligent connected vehicles by JIA Hongying, LI Yufeng

“…Based on a comprehensive analysis the integrated security problem of intelligent connected vehicle (ICV) and limitations of existing security defense methods, guided by the endogenous security existence theorem, a dynamics heterogeneous redundancy (DHR) based endogenous security construction technology was proposed to solve the triple security overlap problem with integrated construction effects, achieving known and unknown threat defense without relying on prior knowledge. …”
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Weighted Couple-Group Consensus Analysis of Heterogeneous Multiagent Systems with Cooperative-Competitive Interactions and Time Delays by Xingcheng Pu, Chaowen Xiong, Lianghao Ji, Longlong Zhao

“…By using graph theory, general Nyquist criterion and Gerschgorin disc theorem, the time delay upper limit that the system may allow is obtained. …”
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