Ulam-Hyers Stability of Trigonometric Functional Equation with Involution by Jaeyoung Chung, Chang-Kwon Choi, Jongjin Kim

“…Let S and G be a commutative semigroup and a commutative group, respectively, C and R+ the sets of complex numbers and nonnegative real numbers, respectively, and σ:S→S or σ:G→G an involution. …”
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Compact Hermitian operators on projective tensor products of Banach algebras by T. K. Dutta, H. K. Nath, H. K. Sarmah

“…We prove that (i) every compact Hermitian operator T1 on U gives rise to a compact Hermitian operator T on U⊗pV having the properties that ‖T1‖=‖T‖ and sp(T1)=sp(T); (ii) if U and V are separable and U has Hermitian approximation property (HAP), then U⊗pV is also separable and has HAP; (iii) every compact analytic semigroup (CAS) on U induces the existence of a CAS on U⊗pV having some nice properties. …”
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Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems by Tao Hao, Juan Li

“…We get the related dynamic programming principle (DPP) with the help of the stochastic backward semigroup which was introduced by Peng in 1997. By making use of a new, more direct approach, we prove that our nonlocal Hamilton-Jacobi-Bellman (HJB) equation has a unique viscosity solution in the space of continuous functions of at most polynomial growth. …”
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Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear part satisfies the Carathëodory condition and is bounded by some suitable functions. …”
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Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses by Hasanen A. Hammad, Manuel De la Sen

“…Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). …”
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On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation by Chunyan Huang

“…The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup e-a+it-Δα to overcome the derivative in the nonlinear term.…”
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Generalized Derivations on Prime Near Rings by Asma Ali, Howard E. Bell, Phool Miyan

“…The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.…”
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Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces by Haibo Lin, Eiichi Nakai, Dachun Yang

“…If χ has the volume regularity Property (P), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from ερa,p(χ) to ε̃ρa,p(χ) without invoking any regularity of considered kernels. …”
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The Order of Hypersubstitutions of Type (2,1) by Tawhat Changphas, Wonlop Hemvong

“…Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of 𝑀-solid varieties. …”
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Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects by Xiaoyan Wang, Yuming Chen, Junyuan Yang

“…We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. …”
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Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations by Aimin Liu, Yongjian Liu, Qun Liu

“…The condition of being uniformly exponentially stable of the strongly continuous semigroup {Tt}t≥0 is essentially removed, which is generated by the linear densely defined operator A∶D(A)⊂L2(ℙ,ℍ)→L2(ℙ,ℍ), only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. …”
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An Equivalence between the Limit Smoothness and the Rate of Convergence for a General Contraction Operator Family by Maxim J. Goldberg, Seonja Kim

“…For example, At is a diffusion semigroup (with T=0,∞). For W a finite measure space and w∈W, select real-valued hw∈L2X, defined everywhere, with hwL2X≤1. …”
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Estimates for Unimodular Multipliers on Modulation Hardy Spaces by Jiecheng Chen, Dashan Fan, Lijing Sun, Chunjie Zhang

“…Finally, we investigate the boundedness of the operator eit|Δ|α/2 for α>0 and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroup eit|Δ|α/2.…”
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Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces by Sha He, Taotao Zheng, Xiangxing Tao

“…Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. …”
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Controllability and Observability of Nonautonomous Riesz-Spectral Systems by Sutrima Sutrima, Christiana Rini Indrati, Lina Aryati

“…In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a C0-quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.…”
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Intra-group mutual authentication key agreement protocol based on Chinese remainder theorem in VANET system by Haibo ZHANG, Zhou CHEN, Hongwu HUANG, Xiaofan HE

“…Aiming at the problem that vehicles in the vehicular ad-hoc network (VANET) system were vulnerable to malicious attacks when communicating with each other on the public network, a mutual authentication key agreement protocol in the VANET was proposed.A dynamic vehicle group was established by the Chinese remainder theorem to adapt to the rapid changes in the VANET topology.Signature information was used by both parties in communication to quickly authenticate the identity of the message sender, and key agreement was conduct through the semigroup of Chebyshev chaotic mapping.The pseudonym update and private key update mechanism were adopted to protect the privacy and security of the vehicle’s identity.The identities of malicious vehicles were tracked accurately by using signature information, and were revoked quickly by modifying the public key information.In addition, the semantic security of the protocol was proved by the BAN logic model.The simulation results show that the proposed protocol can effectively reduce the communication consumption and significantly reduce the computational consumption compared with the existing similar literature.…”
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Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations by Mohamed Hannabou, Mohamed Bouaouid, Khalid Hilal

“…/dtα is the vectorial conformable fractional derivative of order α∈0,1 in a Banach space X and A is the infinitesimal generator of a semigroup Ttt≥0 on X. The element x0 is a fixed vector in X and f, g are given functions. …”
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Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations by Răzvan O. Moşincat, Ciprian Preda, Petre Preda

“…We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {𝑇(𝑡)}𝑡≥0). The novelty of our approach consists in the fact that we do not assume the T(t)-invariance of the unstable manifolds. …”
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Global Analysis of a Discrete Nonlocal and Nonautonomous Fragmentation Dynamics Occurring in a Moving Process by E. F. Doungmo Goufo, S. C. Oukouomi Noutchie

“…Our system involving transport and nonautonomous fragmentation processes, where in addition, new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of forward propagators associated with evolution semigroup theory and perturbation theory. The full generator is considered as a perturbation of the pure nonautonomous fragmentation operator. …”
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On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems by Ahmed Fadili, Hamid Bounit

“…We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates a C0-semigroup. Next, a necessary and sufficient condition for Lp-admissibility p∈1,∞ of the system's control operator is given in terms of the UMD-property of its underlying control space for a wider class of Volterra integrodifferential equations when the leading operator is not necessarily a generator, which provides a generalization of a result known to hold for the standard Cauchy problem (Bounit et al., 2010, Proposition 3.2).…”
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