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Journal articles on the topic 'Multi-semigroup'

Author: Grafiati
Published: 3 June 2025
Last updated: 19 July 2025

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1

Ding, Zhumin, Jiandong Yin, and Xiaofang Luo. "The multi-transitivity of free semigroup actions." Stochastics and Dynamics 20, no. 05 (2020): 2050040. http://dx.doi.org/10.1142/s0219493720500409.

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In this paper, we introduce the conceptions of multi-transitivity, [Formula: see text]-transitivity and [Formula: see text]-mixing property for free semigroup actions and give some equivalent conditions for a free semigroup action to be multi-transitive, multi-transitive with respect to vectors and strongly multi-transitive, respectively. For instance, we prove that a free semigroup action is multi-transitive or multi-transitive with respect to a vector if and only if its corresponding skew product system is multi-transitive or multi-transitive with respect to the same vector.
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2

Wang, Huoyun, Junyan Fang, and Xinlin Zhong. "Multi-transitivity of semigroup actions." Journal of Difference Equations and Applications 27, no. 9 (2021): 1263–79. http://dx.doi.org/10.1080/10236198.2021.1985483.

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3

Akın, Canan. "An application of fuzzy soft multisets to algebra." Filomat 34, no. 2 (2020): 399–408. http://dx.doi.org/10.2298/fil2002399a.

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In this paper, notions of multi and soft multi LA-?-semigroup are defined. Some generalizations of certain operations on the families of the soft and fuzzy soft multisets are introduced. A concept of fuzzy multi LA-?-semigroup is presented. The concept of fuzzy soft multisets is applied to L?-?-semigroups and various characteristics of these all structures defined on LA-?-semigroups are investigated. Some properties of generalized operations on multi soft and fuzzy multi soft LA-?-semigroups are studied.
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4

Zeng, Tiaoying. "Multi-transitivity and Δ-transitivity for semigroup actions". Topology and its Applications 226 (серпень 2017): 1–15. http://dx.doi.org/10.1016/j.topol.2017.04.030.

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5

Al-Adsani, Faryal Abdullah, and Ahmed Gamal Ibrahim. "Nonlocal Conformable Differential Inclusions Generated by Semigroups of Linear Bounded Operators or by Sectorial Operators with Impulses in Banach Spaces." Axioms 14, no. 4 (2025): 230. https://doi.org/10.3390/axioms14040230.

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This paper aims to explore sufficient conditions for the existence of mild solutions to two types of nonlocal, non-instantaneous, impulsive semilinear differential inclusions involving a conformable fractional derivative, where the linear part is the infinitesimal generator of a C0-semigroup or a sectorial operator and the nonlinear part is a multi-valued function with convex or nonconvex values. We provide a definition of the mild solutions, and then, by using appropriate fixed-point theorems for multi-valued functions and the properties of both the conformable derivative and the measure of noncompactness, we achieve our findings. We did not assume that the semigroup generated by the linear part is compact, and this makes our work novel and interesting. We give examples of the application of our theoretical results.
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Abughazalah, Nabilah, Majid Khan, Noor Munir, and Amna Zafar. "Optimum criterion for lightweight nonlinear confusion component with multi-criteria decision making." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 12399–410. http://dx.doi.org/10.3233/jifs-210524.

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In this article, we have designed a new scheme for the construction of the nonlinear confusion component. Our mechanism uses the notion of a semigroup, Inverse LA-semigroup, and various other loops. With the help of these mathematical structures, we can easily build our confusion component namely substitution boxes (S-boxes) without having specialized structures. We authenticate our proposed methodology by incorporating the available cryptographic benchmarks. Moreover, we have utilized the technique for order of preference by similarity to ideal solution (TOPSIS) to select the best nonlinear confusion component. With the aid of this multi-criteria decision-making (MCDM), one can easily select the best possible confusion component while selecting among various available nonlinear confusion components.
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7

Zhang, Xin, Zhaopeng Ding, and Yanxia Liu. "Reliability Analysis of Supply Chain System with the Multi-Suppliers and Single Demander." Journal of Systems Science and Information 9, no. 2 (2021): 192–202. http://dx.doi.org/10.21078/jssi-2021-192-11.

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Abstract The time-dependent solution of a kind of supply chain system with the multi-suppliers and single demander is investigated in this paper. By choosing state space and defining operator of system, we transfer model into an abstract Cauchy problem. We are devoted to studying the unique existence of the system solution and its exponential stability by using the theory of C 0-semigroup. We prove that the system operator generates C 0-semigroup by the theory of cofinal operator and resolvent positive operator. We derive that the system has a unique nonnegative dynamic solution exponentially converging to its steady-state one which is the eigenfunction corresponding eigenvalue 0 of the system operator.
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8

BRODERIX, KURT, DIRK HUNDERTMARK, and HAJO LESCHKE. "CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS." Reviews in Mathematical Physics 12, no. 02 (2000): 181–225. http://dx.doi.org/10.1142/s0129055x00000083.

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The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc.7 (1982) 447] to non-zero vector potentials and more general configuration spaces.
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9

Linesawat, Krittika, and Somsak Lekkoksung. "A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups." International Journal of Analysis and Applications 23 (March 7, 2025): 63. https://doi.org/10.28924/2291-8639-23-2025-63.

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In this paper, we introduce the notion of multi-intuitionistic fuzzy sets in ordered semigroups. The concepts of multi-intuitionistic fuzzy subsemigroups, multi-intuitionistic fuzzy left (right, two-sided, interior) ideals of an ordered semigroup are introduced and some algebraic properties of multi-intuitionistic fuzzy subsemigroups and such their multi-intuitionistic fuzzy ideals are studied. Moreover, the relationships among their multi-intuitionistic fuzzy ideals are investigated. We prove that in regular, intra-regular, and semisimple ordered semigroups, the concepts of multi-intuitionistic fuzzy interior ideals and multi-intuitionistic fuzzy ideals coincide. Finally, the new multi-intuitionistic fuzzy sets are considered.
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10

Hu, Qing-Qing, Feng-Fei Jin, and Bao-Qiang Yan. "Boundary Stabilization of Heat Equation with Multi-Point Heat Source." Mathematics 9, no. 8 (2021): 834. http://dx.doi.org/10.3390/math9080834.

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In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations.
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11

SINGH, VIKRAM, RENU CHAUDHARY, and DWIJENDRA N. PANDEY. "A Study of Multi-Term Time-Fractional Delay Differential System with Monotonic Conditions." Kragujevac Journal of Mathematics 48, no. 2 (2024): 267–85. http://dx.doi.org/10.46793/kgjmat2402.267s.

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In this paper, the existence and uniqueness of mild solution for a class of multi-term time-fractional delay differential system have been discussed in ordered Banach space by enforcing monotone iterative technique. The generalized semigroup theory, fractional calculus and measure of noncompactness have been implemented to obtain the required results. A new set of sufficient conditions with the coefficients in the equations satisfying some monotonic properties has been obtained. Finally, an application is given to illustrate the obtained results.
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12

Möbus, Tim. "On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications." Quantum 8 (July 25, 2024): 1424. http://dx.doi.org/10.22331/q-2024-07-25-1424.

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The Trotter product formula and the quantum Zeno effect are both indispensable tools for constructing time-evolutions using experimentally feasible building blocks. In this work, we discuss assumptions under which quantitative bounds can be proven in the strong operator topology on Banach spaces and provide natural bosonic examples. Specially, we assume the existence of a continuously embedded Banach space, which relatively bounds the involved generators and creates an invariant subspace of the limiting semigroup with a stable restriction. The slightly stronger assumption of admissible subspaces is well-recognized in the realm of hyperbolic evolution systems (time-dependent semigroups), to which the results are extended. By assuming access to a hierarchy of continuously embedded Banach spaces, Suzuki-higher-order bounds can be demonstrated. In bosonic applications, these embedded Banach spaces naturally arise through the number operator, leading to a diverse set of examples encompassing notable instances such as the Ornstein-Uhlenbeck semigroup and multi-photon driven dissipation used in bosonic error correction.
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13

Sayed Ahmed, A. M., Hamdy M. Ahmed, Nesreen Sirelkhtam Elmki Abdalla, Assmaa Abd-Elmonem, and E. M. Mohamed. "Approximate controllability of Sobolev-type Atangana-Baleanu fractional differential inclusions with noise effect and Poisson jumps." AIMS Mathematics 8, no. 10 (2023): 25288–310. http://dx.doi.org/10.3934/math.20231290.

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<abstract><p>In this paper, we explore the approximative controllability of fractional stochastic differential inclusions (SDIs) of Sobolev-type with fractional derivatives in Atangana-Baleanu (AB) sense and Poisson jumps. Our findings are supported by the fixed point theorem, multi-valued map theory, compact semigroup theory and stochastic analysis principles. In the later part, an illustration is provided to clarify the established outcomes.</p></abstract>
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14

Bashir, Shahida, Ahmad N. Al-Kenani, Maria Arif, and Rabia Mazhar. "A new method to evaluate regular ternary semigroups in multi-polar fuzzy environment." AIMS Mathematics 7, no. 7 (2022): 12241–63. http://dx.doi.org/10.3934/math.2022680.

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<abstract> <p>Theory of $m$-polar fuzzy set deals with multi-polar information. It is used when data comes from $m$ factors $\left({m \ge 2} \right)$. The primary objective of this work is to explore a generalized form of $m$-polar fuzzy subsemigroups, which is $m$-polar fuzzy ternary subsemigroups. There are many algebraic structures which are not closed under binary multiplication that is a reason to study ternary operation of multiplication such as the set of negative integer is closed under the operation of ternary multiplication but not closed for the binary multiplication. This paper, presents several significant results related to the notions of $m$-polar fuzzy ternary subsemigroups, $m$-polar fuzzy ideals, $m$-polar fuzzy generalized bi-ideals, $m$-polar fuzzy bi-ideals, $m$-polar fuzzy quasi-ideals and $m$-polar fuzzy interior ideals in ternary semigroups. Also, it is proved that every $m$- polar fuzzy bi-ideal of ternary semigroup is an $m$-polar fuzzy generalized bi-ideal of ternary semigroup but converse is not true in general. Moreover, this paper characterizes regular and intra-regular ternary semigroups by the properties of $m$-polar fuzzy ideals, $m$-polar fuzzy bi-ideals.</p> </abstract>
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15

Salem, Ahmed, and Rania Al-Maalwi. "Fractional Evolution Equation with Nonlocal Multi-Point Condition: Application to Fractional Ginzburg–Landau Equation." Axioms 14, no. 3 (2025): 205. https://doi.org/10.3390/axioms14030205.

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This paper is devoted to studying the existence and uniqueness of mild solutions for semilinear fractional evolution equations with the Hilfer–Katugampola fractional derivative and under the nonlocal multi-point condition. The analysis is based on analytic semigroup theory, the Krasnoselskii fixed-point theorem, and the Banach fixed-point theorem. An application to a time-fractional real Ginzburg–Landau equation is also given to illustrate the applicability of our results. Furthermore, we determine some conditions to make the control (Bifurcation) parameter in the Ginzburg–Landau equation sufficiently small.
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16

Gu, Caihong, and Yanbin Tang. "Global solution to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity." Networks and Heterogeneous Media 18, no. 1 (2022): 109–39. http://dx.doi.org/10.3934/nhm.2023005.

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<abstract><p>In this paper, we consider the global existence, regularizing decay rate and asymptotic behavior of mild solutions to Cauchy problem of fractional drift diffusion system with power-law nonlinearity. Using the properties of fractional heat semigroup and the classical estimates of fractional heat kernel, we first prove the global-in-time existence and uniqueness of the mild solutions in the frame of mixed time-space Besov space with multi-linear continuous mappings. Then, we show the asymptotic behavior and regularizing-decay rate estimates of the solution to equations with power-law nonlinearity by the method of multi-linear operator and the classical Hardy-Littlewood-Sobolev inequality.</p></abstract>
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17

Davvaz, B. "Structure and order: A concise overview of ordered semi(hyper)groups." Quarterly Journal of Research and Planning in Higher Education 6, no. 1 (2025): 111–46. https://doi.org/10.61838/kman.jahla.6.1.9.

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This paper explores a hierarchy of algebraic structures beginning with ordered semigroups and extending through their generalizations and fuzzifications. An ordered semigroup is a semigroup equipped with a partial order that is compatible with its binary operation. Building on this foundation, we investigate fuzzy ideals within ordered semigroups, where fuzzy set theory introduces gradation and uncertainty into ideal theory. We then extend the framework to ordered semihypergroups, where the binary operation is replaced by a hyperoperation mapping element pair to subsets, allowing the modeling of systems with multi-valued outputs under an order-preserving structure. From there, we examine methods for constructing ordered semigroups derived from ordered semihypergroups, using representative elements and congruences to recover associativity in a classical sense. Finally, we introduce the fuzzification of ordered semihypergroups, integrating fuzzy logic into hyperoperations to develop fuzzy hyperideals, hyperfilters and explore their properties. This comprehensive study highlights the interplay between order, hyperstructure, and fuzziness, providing a generalized framework for both theoretical advancement and practical applications in areas involving uncertainty and complex relationships.
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18

Azhini, M., H. M. Kenari, and R. Saadati. "Strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in multi-Banach space." Proceedings - Mathematical Sciences 127, no. 4 (2017): 657–72. http://dx.doi.org/10.1007/s12044-017-0351-6.

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19

Alarcon, Eduardo A., Marcos R. Batista, Alysson Cunha, Jesus C. Da Mota, and Ronaldo A. Santos. "APPLICATION OF THE SEMIGROUP THEORY TO A COMBUSTION PROBLEM IN A MULTI-LAYER POROUS MEDIUM." Journal of Applied Analysis & Computation 13, no. 6 (2023): 3107–35. http://dx.doi.org/10.11948/20220333.

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20

Bazarra, N., J. R. Fernández, and R. Quintanilla. "A dual-phase-lag porous-thermoelastic problem with microtemperatures." Electronic Research Archive 30, no. 4 (2022): 1236–62. http://dx.doi.org/10.3934/era.2022065.

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<abstract><p>In this work, we consider a multi-dimensional dual-phase-lag problem arising in porous-thermoelasticity with microtemperatures. An existence and uniqueness result is proved by applying the semigroup of linear operators theory. Then, by using the finite element method and the Euler scheme, a fully discrete approximation is numerically studied, proving a discrete stability property and a priori error estimates. Finally, we perform some numerical simulations to demonstrate the accuracy of the approximation and the behavior of the solution in one- and two-dimensional problems.</p></abstract>
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21

Wang, Shaoli, and Xinyu Song. "Global properties for an age-structured within-host model with Crowley–Martin functional response." International Journal of Biomathematics 10, no. 02 (2017): 1750030. http://dx.doi.org/10.1142/s1793524517500309.

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Based on a multi-scale view, in this paper, we study an age-structured within-host model with Crowley–Martin functional response for the control of viral infections. By means of semigroup and Lyapunov function, the global asymptotical property of infected steady state of the model is obtained. The results show that when the basic reproductive number falls below unity, the infection dies out. However, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium which is globally asymptotically stable. This model can be deduced to different viral models with or without time delay.
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22

Yuan, Xiaolin, Guojian Ren, Mingze Li, and Yongguang Yu. "New asymptotic stability conditions for nonlinear stochastic systems driven by fractional Brownian motion." Filomat 38, no. 18 (2024): 6355–69. https://doi.org/10.2298/fil2418355y.

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This paper is concerned with the asymptotic stability for nonlinear stochastic systems driven by fractional Brownian motion (fBm) with Hurst parameter H ? (1/2, 1). First, some new asymptotic stability conditions are given for nonlinear stochastic systems with fBm by using the characteristic of the mild solution, the fBm, and the semigroup. Then, the results obtained are extended to the linear case, and some asymptotic stability conditions are derived. Furthermore, the methods proposed are utilized to solve the consensus control problem of the stochastic multi-agent systems (SMAS) with fBm. Finally, simulations are provided to illustrate the effectiveness of the proposed theoretical results.
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23

Liu, Ya-Qiang, Jun-Wei Wang, and Chang-Yin Sun. "A Lyapunov-based design of dynamic feedback compensator for linear parabolic MIMO PDEs." IMA Journal of Mathematical Control and Information 37, no. 2 (2019): 455–74. http://dx.doi.org/10.1093/imamci/dnz008.

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Abstract This paper discusses dynamic feedback compensator design for a linear parabolic partial differential equation (PDE) with multiple inputs and multiple outputs. Actuating control inputs are provided by actuators distributed over partial areas (or active at specified positions) of the spatial domain, and observation outputs are taken from the non-collocated sensors distributed over partial areas of the spatial domain. An observer-based dynamic feedback compensator is constructed via the observer-based feedback control technique to exponentially stabilize the multi-input–multi-output PDE in the spatial $\mathscr{L}^2$ norm. By constructing an appropriate Lyapunov function candidate and using two variants of Poincaré–Wirtinger inequality, sufficient conditions on the existence of such observer-based dynamic feedback compensator are developed and presented in terms of linear matrix inequalities. The well posedness of the closed-loop coupled PDEs is also analyzed within the framework of $C_0$ semigroup theory. Finally, numerical simulation results are given to show the effectiveness of the proposed method.
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24

Delgado, F., and S. M. Gusein-Zade. "POINCARÉ SERIES FOR SEVERAL PLANE DIVISORIAL VALUATIONS." Proceedings of the Edinburgh Mathematical Society 46, no. 2 (2003): 501–9. http://dx.doi.org/10.1017/s0013091502000652.

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AbstractWe compute the (generalized) Poincaré series of the multi-index filtration defined by a finite collection of divisorial valuations on the ring $\mathcal{O}_{\mathbb{C}^2,0}$ of germs of functions of two variables. We use the method initially elaborated by the authors and Campillo for computing the similar Poincaré series for the valuations defined by the irreducible components of a plane curve singularity. The method is essentially based on the notions of the so-called extended semigroup and of the integral with respect to the Euler characteristic over the projectivization of the space of germs of functions of two variables. The last notion is similar to (and inspired by) the notion of the motivic integration.AMS 2000 Mathematics subject classification: Primary 14B05; 16W70
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25

ZHOU, FUJUN, and JUNDE WU. "Stability and bifurcation analysis of a free boundary problem modelling multi-layer tumours with Gibbs–Thomson relation." European Journal of Applied Mathematics 26, no. 4 (2015): 401–25. http://dx.doi.org/10.1017/s0956792515000108.

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Of concern is the stability and bifurcation analysis of a free boundary problem modelling the growth of multi-layer tumours. A remarkable feature of this problem lies in that the free boundary is imposed with nonlinear boundary conditions, where a Gibbs–Thomson relation is taken into account. By employing a functional approach, analytic semigroup theory and bifurcation theory, we prove that there exists a positive threshold value γ* of surface tension coefficient γ such that if γ > γ* then the unique flat stationary solution is asymptotically stable under non-flat perturbations, while for γ < γ* this unique flat stationary solution is unstable and there exists a series of non-flat stationary solutions bifurcating from it. The result indicates a significant phenomenon that a smaller value of surface tension coefficient γ may make tumours more aggressive.
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26

Qiao, Xing, Dan Ma, and Shuang Guo. "Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function." Axioms 14, no. 2 (2025): 113. https://doi.org/10.3390/axioms14020113.

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The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary focus of research. A mathematical model of a five-robot system, equipped with early warning capabilities, is developed using Markov process theory and the supplementary variable method in this paper. A model of an abstract Cauchy problem system is developed, employing semigroup theory to investigate the well-posedness of solutions for this five-robot system. The stability of the system is verified using analytical methods, confinal correlation theory, and modern functional analysis techniques. Several key reliability indicators are presented using the eigenvector method. Numerical simulations and comparative methods effectively demonstrate the efficacy of the proposed eigenvector method. Firstly, the innovation of this paper lies in the combination of qualitative and quantitative analyses to improve and enrich the theory and methods of repairable systems. Secondly, mathematical analysis methods and the mathematical software are employed to provide both analytical and numerical solutions for the system.
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27

Henríquez, Fernando, and Carlos Jerez-Hanckes. "Multiple traces formulation and semi-implicit scheme for modelling biological cells under electrical stimulation." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 2 (2018): 659–703. http://dx.doi.org/10.1051/m2an/2018019.

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We model the electrical behavior of several biological cells under external stimuli by extending and computationally improving the multiple traces formulation introduced in Henríquez et al. [Numer. Math. 136 (2016) 101–145]. Therein, the electric potential and current for a single cell are retrieved through the coupling of boundary integral operators and non-linear ordinary differential systems of equations. Yet, the low-order discretization scheme presented becomes impractical when accounting for interactions among multiple cells. In this note, we consider multi-cellular systems and show existence and uniqueness of the resulting non-linear evolution problem in finite time. Our main tools are analytic semigroup theory along with mapping properties of boundary integral operators in Sobolev spaces. Thanks to the smoothness of cellular shapes, solutions are highly regular at a given time. Hence, spectral spatial discretization can be employed, thereby largely reducing the number of unknowns. Time-space coupling is achieved via a semi-implicit time-stepping scheme shown to be stable and second order convergent. Numerical results in two dimensions validate our claims and match observed biological behavior for the Hodgkin–Huxley dynamical model.
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28

Jourdain, Benjamin, and Julien Reygner. "A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data." Journal of Hyperbolic Differential Equations 13, no. 03 (2016): 441–602. http://dx.doi.org/10.1142/s0219891616500144.

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This paper is devoted to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions or, more generally, nonconstant monotonic bounded functions as initial data. Under a uniform strict hyperbolicity assumption on the characteristic fields, we construct a multi-type version of the sticky particle dynamics and we obtain the existence of global weak solutions via a compactness argument. We then derive a [Formula: see text] stability estimate on the particle system which is uniform in the number of particles. This allows us to construct nonlinear semigroups solving the system in the sense of Bianchini and Bressan [Vanishing viscosity solutions of nonlinear hyperbolic systems, Ann. of Math. (2) 161(1) (2005) 223–342]. We also obtain that these semigroup solutions satisfy a stability estimate in Wasserstein distances of all order, which extends the classical [Formula: see text] estimate and generalizes to diagonal systems a result by Bolley, Brenier and Loeper [Contractive metrics for scalar conservation laws, J. Hyperbolic Differ. Equ. 2(1) (2005) 91–107] in the scalar case. Our results are established without any smallness assumption on the variation of the data, and we only require the characteristic fields to be Lipschitz continuous and the system to be uniformly strictly hyperbolic.
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29

Gondolf, Paul, Tim Möbus, and Cambyse Rouzé. "Energy preserving evolutions over Bosonic systems." Quantum 8 (December 4, 2024): 1551. https://doi.org/10.22331/q-2024-12-04-1551.

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The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to the code-space – an invariant subspace protected against certain types of errors. In this paper, we investigate perturbations of quantum dynamical semigroups that operate on continuous variable (CV) systems and admit an invariant subspace. First, we prove a generation theorem for quantum Markov semigroups on CV systems under the physical assumptions that (i) the generator is in GKSL form with corresponding jump operators defined as polynomials of annihilation and creation operators; and (ii) the (possibly unbounded) generator increases all moments in a controlled manner. Additionally, we show that the level sets of operators with bounded first moments are admissible subspaces of the evolution, providing the foundations for a perturbative analysis. Our results also extend to time-dependent semigroups and multi-mode systems. We apply our general framework to two settings of interest in continuous variable quantum information processing. First, we provide a new scheme for deriving continuity bounds on the energy-constrained capacities of Markovian perturbations of quantum dynamical semigroups. Second, we provide quantitative perturbation bounds for the steady state of the quantum Ornstein-Uhlenbeck semigroup and the invariant subspace of the photon dissipation used in bosonic error correction.
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30

Beybalaev, Vetlugin D., Abutrab A. Aliverdiev, Amuchi Z. Yakubov, Said A. Ninalalov, and Anise A. Amirova. "Mathematical Model of Heat Conduction for a Semi-Infinite Body, Taking into Account Memory Effects and Spatial Correlations." Fractal and Fractional 7, no. 3 (2023): 265. http://dx.doi.org/10.3390/fractalfract7030265.

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One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-similar) environments. In a fractal medium, in contrast to an ordinary continuous medium, a randomly wandering particle moves away from the reference point more slowly since not all directions of motion become available to it. The slowdown of the diffusion process in fractal media is so significant that physical quantities begin to change more slowly than in ordinary media.This effect can only be taken into account with the help of integral and differential equations containing a fractional derivative with respect to time. Here, the problem of heat and mass transfer in media with a fractal structure was posed and analytically solved when a heat flux was specified on one of the boundaries. The second initial boundary value problem for the heat equation with a fractional Caputo derivative with respect to time and the Riesz derivative with respect to the spatial variable was studied. A theorem on the semigroup property of the fractional Riesz derivative was proved. To find a solution, the problem was reduced to a boundary value problem with boundary conditions of the first kind. The solution to the problem was found by applying the Fourier transform in the spatial variable and the Laplace transform in time. A computational experiment was carried out to analyze the obtained solutions. Graphs of the temperature distribution dependent on the coordinate and time were constructed.
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31

Al-Masarwah, Anas, Mohammed Alqahtani, and Majdoleen Abu Qamar. "Groups and Structures of Commutative Semigroups in the Context of Cubic Multi-Polar Structures." Symmetry 14, no. 7 (2022): 1493. http://dx.doi.org/10.3390/sym14071493.

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In recent years, the m-polar fuzziness structure and the cubic structure have piqued the interest of researchers and have been commonly implemented in algebraic structures like groupoids, semigroups, groups, rings and lattices. The cubic m-polar (CmP) structure is a generalization of m-polar fuzziness and cubic structures. The intent of this research is to extend the CmP structures to the theory of groups and semigroups. In the present research, we preface the concept of the CmP groups and probe many of its characteristics. This concept allows the membership grade and non-membership grade sequence to have a set of m-tuple interval-valued real values and a set of m-tuple real values between zero and one. This new notation of group (semigroup) serves as a bridge among CmP structure, classical set and group (semigroup) theory and also shows the effect of the CmP structure on a group (semigroup) structure. Moreover, we derive some fundamental properties of CmP groups and support them by illustrative examples. Lastly, we vividly construct semigroup and groupoid structures by providing binary operations for the CmP structure and provide some dominant properties of these structures.
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32

Kozlovskaya, Tatyana A. "Multi-groups." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 87 (2024): 34–43. http://dx.doi.org/10.17223/19988621/87/4.

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In the present paper we define homogeneous algebraic systems. Particular cases of these systems are semigroup (monoid, group) systems. These algebraic systems were studied by J. Loday, A. Zhuchok, T. Pirashvili, and N. Koreshkov. Quandle systems were introduced and studied by V. Bardakov, D. Fedoseev, and V. Turaev. We construct some group systems on the set of square matrices over a field k. Also, we define rack systems on the set V x G , where V is a vector space of dimension n over k and G is a subgroup of GLn(k). Finally, we find the connection between skew braces and dimonoids.
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33

Fayolle, Guy, Philippe Flajolet, and Micha Hofri. "On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel." Advances in Applied Probability 18, no. 2 (1986): 441–72. http://dx.doi.org/10.2307/1427308.

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We analyse a stack protocol of the Capetanakis–Tsybakov–Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a non-commutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration semigroup we show that for arrival rates smaller than a fixed threshold, the mean CRI duration for n initial colliders is asymptotically proportional to n. Ergodicity conditions are also demonstrated.
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34

Fayolle, Guy, Philippe Flajolet, and Micha Hofri. "On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel." Advances in Applied Probability 18, no. 02 (1986): 441–72. http://dx.doi.org/10.1017/s0001867800015846.

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We analyse a stack protocol of the Capetanakis–Tsybakov–Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a non-commutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration semigroup we show that for arrival rates smaller than a fixed threshold, the mean CRI duration for n initial colliders is asymptotically proportional to n. Ergodicity conditions are also demonstrated.
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35

Sun, Ruoci. "Complete integrability of the Benjamin–Ono equation on the multi-soliton manifolds." Communications in Mathematical Physics 383, no. 2 (2021): 1051–92. http://dx.doi.org/10.1007/s00220-021-03996-1.

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AbstractThis paper is dedicated to proving the complete integrability of the Benjamin–Ono (BO) equation on the line when restricted to every N-soliton manifold, denoted by $$\mathcal {U}_N$$ U N . We construct generalized action–angle coordinates which establish a real analytic symplectomorphism from $$\mathcal {U}_N$$ U N onto some open convex subset of $${\mathbb {R}}^{2N}$$ R 2 N and allow to solve the equation by quadrature for any such initial datum. As a consequence, $$\mathcal {U}_N$$ U N is the universal covering of the manifold of N-gap potentials for the BO equation on the torus as described by Gérard–Kappeler (Commun Pure Appl Math, 2020. 10.1002/cpa.21896. arXiv:1905.01849). The global well-posedness of the BO equation on $$\mathcal {U}_N$$ U N is given by a polynomial characterization and a spectral characterization of the manifold $$\mathcal {U}_N$$ U N . Besides the spectral analysis of the Lax operator of the BO equation and the shift semigroup acting on some Hardy spaces, the construction of such coordinates also relies on the use of a generating functional, which encodes the entire BO hierarchy. The inverse spectral formula of an N-soliton provides a spectral connection between the Lax operator and the infinitesimal generator of the very shift semigroup.
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36

Fornaro, Simona, Giorgio Metafune, Diego Pallara, and Roland Schnaubelt. "Multi-dimensional degenerate operators in $L^p$-spaces." Communications on Pure and Applied Analysis 21, no. 6 (2022): 2115. http://dx.doi.org/10.3934/cpaa.2022052.

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<p style='text-indent:20px;'>This paper is concerned with second-order elliptic operators whose diffusion coefficients degenerate at the boundary in first order. In this borderline case, the behavior strongly depends on the size and direction of the drift term. Mildly inward (or outward) pointing and strongly outward pointing drift terms were studied before. Here we treat the intermediate case equipped with Dirichlet boundary conditions, and show generation of an analytic positive <inline-formula><tex-math id="M2">\begin{document}$ C_0 $\end{document}</tex-math></inline-formula>-semigroup. The main result is a precise description of the domain of the generator, which is more involved than in the other cases and exhibits reduced regularity compared to them.</p>
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37

Mohamed, Esmail Basher. "On Folding of Groups." June 30, 2012. https://doi.org/10.5281/zenodo.821467.

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The aim of our study is to give a definition of the folding of groups and study the folding of some types of groups such as cyclic groups and dihedral groups, also we discussed the folding of direct product of groups. Finally the folding of semigroups are investigated.
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38

Cong, Nguyen Dinh. "Semigroup property of fractional differential operators and its applications." Discrete & Continuous Dynamical Systems - B, 2022, 0. http://dx.doi.org/10.3934/dcdsb.2022064.

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<p style='text-indent:20px;'>We establish partial semigroup property of families of Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction of multi-term fractional differential systems to single-term and multi-order systems. As an application we obtain existence and uniqueness of solution to multi-term Caputo fractional differential systems.</p>
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39

Wang, JinRong, Ahmed Gamal Ibrahim, and Donal O’Regan. "Global attracting solutions to Hilfer fractional differential inclusions of Sobolev type with noninstantaneous impulses and nonlocal conditions." Nonlinear Analysis: Modelling and Control 24, no. 5 (2019). http://dx.doi.org/10.15388/na.2019.5.6.

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In this paper, we establish the existence of decay mild solutions on an unbounded interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and involving the Hilfer derivative. Our argument uses fixed point theorems, semigroup theory, multi-functions and a measure of noncompactness on the space of piecewise weighted continuous functions defined on an unbounded interval. An example is provided to illustrate our results.
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40

Debbouche, Amar, and Delfim F. M. Torres. "Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions." Fractional Calculus and Applied Analysis 18, no. 1 (2015). http://dx.doi.org/10.1515/fca-2015-0007.

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AbstractIn We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given.
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41

Moreillon, Philippe. "Density of the Free Additive Convolution of Multi-cut Measures." International Mathematics Research Notices, October 23, 2024. http://dx.doi.org/10.1093/imrn/rnae229.

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Abstract We consider the free additive convolution semigroup $\lbrace \mu ^{\boxplus t}:\,t\ge 1\rbrace $ and determine the local behavior of the density of $\mu ^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study the free additive convolution of two multi-cut probability measures and show that its density decays either as a square root or as a cubic root at any endpoint of its support. The probability measures considered in this paper satisfy a power law behavior with exponents strictly between $-1$ and $1$ at the endpoints of their supports.
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42

Theodosiadis, E. K. "Explicit Multi-slit Loewner Flows and Their Geometry." Computational Methods and Function Theory, October 14, 2024. http://dx.doi.org/10.1007/s40315-024-00567-y.

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AbstractIn this paper we present explicit solutions to the radial and chordal Loewner PDEs and we make an extensive study of their geometry. Specifically, we study multi-slit Loewner flows, driven by the time-dependent point masses $$\mu _{t}:=\sum _{j=1}^{n}b_j \delta _{\{\zeta _j e^{iat}\}}$$ μ t : = ∑ j = 1 n b j δ { ζ j e iat } in the radial case and $$\nu _t:=\sum _{j=1}^{n}b_j\delta _{\{k_j\sqrt{1-t}\}}$$ ν t : = ∑ j = 1 n b j δ { k j 1 - t } in the chordal case, where all the above parameters are chosen arbitrarily. Furthermore, we investigate their close connection to the semigroup theory of holomorphic functions, which also allows us to map the chordal case to the radial one.
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43

Wästlund, Johan. "Two-Person Symmetric Whist." Electronic Journal of Combinatorics 12, no. 1 (2005). http://dx.doi.org/10.37236/1941.

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We introduce a two-person perfect information model of trick taking games. A set of cards is distributed between two players, and play proceeds in tricks with the obligation to follow suit, as in many real-world card games. We assume that in each suit, the two players have the same number of cards. Under this assumption, we show how to assign a value from a certain semigroup to each single-suit card distribution in such a way that the outcome of a multi-suit deal under optimal play is determined by the sum of the values of the individual suits.
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44

Bietti, Alberto, Joan Bruna, and Loucas Pillaud‐Vivien. "On learning Gaussian multi‐index models with gradient flow part I: General properties and two‐timescale learning." Communications on Pure and Applied Mathematics, July 15, 2025. https://doi.org/10.1002/cpa.70006.

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AbstractWe study gradient flow on the multi‐index regression problem for high‐dimensional Gaussian data. Multi‐index functions consist of a composition of an unknown low‐rank linear projection and an arbitrary unknown, low‐dimensional link function. As such, they constitute a natural template for feature learning in neural networks. We consider a two‐timescale algorithm, whereby the low‐dimensional link function is learnt with a non‐parametric model infinitely faster than the subspace parametrizing the low‐rank projection. By appropriately exploiting the matrix semigroup structure arising over the subspace correlation matrices, we establish global convergence of the resulting Grassmannian gradient flow dynamics, and provide a quantitative description of its associated “saddle‐to‐saddle” dynamics. Notably, the timescales associated with each saddle can be explicitly characterized in terms of an appropriate Hermite decomposition of the target link function.
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45

Jury, Michael T., and Robert T. W. Martin. "Lebesgue Decomposition of Non-Commutative Measures." International Mathematics Research Notices, September 5, 2020. http://dx.doi.org/10.1093/imrn/rnaa231.

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Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.
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46

Geredeli, Pelin G. "An inf-sup approach to $$C_0$$-semigroup generation for an interactive composite structure-Stokes PDE dynamics." Journal of Evolution Equations 24, no. 3 (2024). http://dx.doi.org/10.1007/s00028-024-00978-3.

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AbstractIn this work, we investigate the existence and uniqueness properties of a composite structure (multilayered)–fluid interaction PDE system which arises in multi-physics problems, and particularly in biofluidic applications related to the mammalian blood transportation process. The PDE system under consideration consists of the interactive coupling of 3D Stokes flow and 3D elastic dynamics which gives rise to an additional 2D elastic equation on the boundary interface between these 3D PDE systems. By means of a nonstandard mixed variational formulation, we show that the PDE system generates a $$C_0$$ C 0 -semigroup on the associated finite energy space of data. In this work, the presence of the pressure term in the 3D Stokes equation adds a great challenge to our analysis. To overcome this difficulty, we follow a methodology which is based on the necessarily non-Leray-based elimination of the associated pressure term, via appropriate nonlocal operators. Moreover, while we express the fluid solution variable via decoupling of the Stokes equation, we construct the elastic solution variables by solving a mixed variational formulation via a Babuska–Brezzi approach.
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47

Faiz, Muhammad Khan, Khan Madad, and Ihsanullah. "Classification of Ordered Semigroups Through Neutrosophic Generalized bi-ideals with Applications." October 2, 2022. https://doi.org/10.5281/zenodo.7135401.

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An icebreaking theory known as neutrosophic theory opened a new direction for researchers of philosophy, logics, set theory and probability/statistics. Neutrosophy put the point base for a entire household of new mathematical speculations that summarized classical and fuzzy correspondence theories. In this article, we introduced the conception of neutrosophic fuzzy ideal theory of ordered semigroups based on belongs to relation and quasi-coincident with relation. Particularly, neutrosophic fuzzy generalized bi-ideal (resp. bi-ideal) of type (∈, ∈ ∨q) have been developed and detail symposium on multi-dimension of the neutrosophic said ideals in ordered semigroup has given. Further, a verity of depictions of ordered semigroups in expression of (∈, ∈ ∨q)- fuzzy generalized bi-ideals have been constructed and several related examples have been formulated. Finally, the lower parts of neutrosophic (∈, ∈ ∨q)-fuzzy generalized bi-ideals were proposed and ordered semigroups have been discussed by the properties of these newly developed neutrosophic fuzzy generalized bi-ideals. 
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48

Raeymaekers, Joris. "A note on ensemble holography for rational tori." Journal of High Energy Physics 2021, no. 12 (2021). http://dx.doi.org/10.1007/jhep12(2021)177.

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Abstract We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theories, which results in a weighted average over all modular invariants. In the simplest case, when the chiral algebra is primitive (in a sense we explain), the weights in this ensemble average are all equal. In the non-primitive case the ensemble weights are governed by a semigroup structure on the space of modular invariants.These observations can be viewed as evidence for a holographic duality between the ensemble of CFTs and an exotic gravity theory based on a compact U(1) × U(1) Chern-Simons action. In the bulk description, the extended chiral algebra arises from soliton sectors, and including these in the path integral on thermal AdS3 leads to the vacuum character of the chiral algebra. We also comment on wormhole-like contributions to the multi-boundary path integral.
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49

Hasan, Sameer Qasim. "Observability of Fractional-Order Impulsive Control Integro-Differential System with Nonlocal Initial Condition." Journal of Southwest Jiaotong University 55, no. 1 (2020). http://dx.doi.org/10.35741/issn.0258-2724.55.1.4.

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The article describes a new concept for initial and exactly observability of nonlocal fractional-order impulsive control integro-differential system. This is based on the concepts of the abstract Cauchy problem, which depended on some necessary and sufficient conditions. These conditions established on the semigroup theory of bounded operators as a dynamical operator system, which generated by bounded linear operators. Moreover, invertible operators play a primary role, and we presented a necessary condition for some nonlinear multi variables functions. Thus, all these operators were treated in nonlinear functional analysis to guaranty the initial observable and exactly observability. Therefore, from the mild solution of the system and exactly homogenous part, we proved the equivalent concepts between the initial observability and exactly the observability. Thus, our approach in this article is to prove the uniqueness of initial nonlocal values with admissible control, which belongs to the second-order Lebesgue integrable. The interest of observability results in this article lies by proving a unique fixed point, which is nonlocal initial values that are described in the proposal formula by using Banach’s fixed point theory. The processing observability for complexly systems (such as this system) with all components and properties was established and can be used for many control system applications.
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50

Ohkitani, K., and R. Vanon. "Self-similar source-type solutions to the three-dimensional Navier–Stokes equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 478, no. 2258 (2022). http://dx.doi.org/10.1098/rspa.2021.0527.

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We formalize a systematic method of constructing forward self-similar solutions to the Navier–Stokes equations in order to characterize the late stage of decaying process of turbulent flows. (i) In view of critical scale-invariance of type 2 we exploit the vorticity curl as the dependent variable to derive and analyse the dynamically scaled Navier–Stokes equations. This formalism offers the viewpoint from which the problem takes the simplest possible form. (ii) Rewriting the scaled Navier–Stokes equations by Duhamel principle as integral equations, we regard the nonlinear term as a perturbation using the Fokker–Planck evolution semigroup. Systematic successive approximations are introduced and the leading-order solution is worked out explicitly as the Gaussian function with a solenoidal projection. (iii) By iterations the second-order approximation is estimated explicitly up to solenoidal projection and is evaluated numerically. (iv) A new characterization of nonlinear term is introduced on this basis to estimate its strength N quantitatively. We find that N = O ( 10 − 2 ) for the three-dimensional Navier–Stokes equations. This should be contrasted with N = O ( 10 − 1 ) for the Burgers equations and N ≡ 0 for the two-dimensional Navier–Stokes equations. (v) As an illustration we explicitly determine source-type solutions to the multi-dimensional Burgers equations. Implications and applications of the current results are given.
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