71,139 results on '"Type (model theory)"'
Search Results
2. Spatial dynamic analysis for COVID-19 epidemic model with diffusion and Beddington-DeAngelis type incidence
- Author
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Yantao Luo, Long Zhang, Zhidong Teng, Tao Zheng, and Xinran Zhou
- Subjects
Discrete mathematics ,Coronavirus disease 2019 (COVID-19) ,Applied Mathematics ,Homogeneity (statistics) ,Stability theory ,Reaction–diffusion system ,General Medicine ,Type (model theory) ,Diffusion (business) ,Epidemic model ,Analysis ,Mathematics ,Incidence (geometry) - Abstract
A diffusion SEIAR model with Beddington-DeAngelis type incidence is proposed to characterize the spread of COVID-19 with spatial transmission. First, the well-posedness of solution is studied. Second, the basic reproduction number \begin{document}$ \mathcal R_{0} $\end{document} is derived and served as a threshold value to determine whether COVID-19 will spread. Meanwhile, we consider the effect of diffusion on the spread of COVID-19 in spatial homogenous environment, by which we can obtain that if \begin{document}$ \mathcal R_{0} , then the infection-free steady state is globally asymptotically stable, while if \begin{document}$ \mathcal R_{0}>1 $\end{document} , then the endemic steady state is globally asymptotically stable. Furthermore, according to the official reporting data about COVID-19 in Wuhan, China, the actual value of \begin{document}$ \mathcal R_{0} $\end{document} is estimated, and comparing with other types of incidence, we find that the estimated peak with Beddington-DeAngelis type incidence is more close to the cases in reality. Finally, by numerical simulations, we can see that the diffusion behavior has evident impact on the spread of COVID-19 in spatial heterogeneity than homogeneity of environment.
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- 2023
3. New type i binary [72, 36, 12] self-dual codes from composite matrices and R1 lifts
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Serap Sahinkaya, Adrian Korban, and Deniz Ustun
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Ring (mathematics) ,Algebra and Number Theory ,Computer Networks and Communications ,Applied Mathematics ,Identity matrix ,Binary number ,Type (model theory) ,Microbiology ,Omega ,Lift (mathematics) ,Combinatorics ,Discrete Mathematics and Combinatorics ,Generator matrix ,Mathematics ,Group ring - Abstract
In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form \begin{document}$ [I_n \ | \ \Omega(v)], $\end{document} where \begin{document}$ I_n $\end{document} is the identity matrix and \begin{document}$ \Omega(v) $\end{document} is a composite matrix and search for binary self-dual codes with parameters \begin{document}$ [36,18, 6 \ \text{or} \ 8]. $\end{document} We next lift these codes over the ring \begin{document}$ R_1 = \mathbb{F}_2+u\mathbb{F}_2 $\end{document} to obtain codes whose binary images are self-dual codes with parameters \begin{document}$ [72,36,12]. $\end{document} Many of these codes turn out to have weight enumerators with parameters that were not known in the literature before. In particular, we find \begin{document}$ 30 $\end{document} new Type I binary self-dual codes with parameters \begin{document}$ [72,36,12]. $\end{document}
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- 2023
4. Balancing Constraints and Objectives by Considering Problem Types in Constrained Multiobjective Optimization
- Author
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Han Huang, Yi Xiang, Xiaowei Yang, and Jiahai Wang
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Mathematical optimization ,Computer science ,Existential quantification ,Context (language use) ,Type (model theory) ,Multi-objective optimization ,Computer Science Applications ,Human-Computer Interaction ,Constraint (information theory) ,Control and Systems Engineering ,Argument ,Benchmark (computing) ,Decomposition (computer science) ,Electrical and Electronic Engineering ,Software ,Information Systems - Abstract
Constrained multiobjective optimization problems widely exist in real-world applications. To handle them, the balance between constraints and objectives is crucial, but remains challenging due to non-negligible impacts of problem types. In our context, the problem types refer particularly to those determined by the relationship between the constrained Pareto-optimal front (PF) and the unconstrained PF. Unfortunately, there has been little awareness on how to achieve this balance when faced with different types of problems. In this article, we propose a new constraint handling technique (CHT) by taking into account potential problem types. Specifically, inspired by the prior work, problems are classified into three primary types: 1) I; 2) II; and 3) III, with the constrained PF being made up of the entire, part and none of the unconstrained counterpart, respectively. Clearly, any problem must be one of the three types. For each possible type, there exists a tailored mechanism being used to handle the relationships between constraints and objectives (i.e., constraint priority, objective priority, or the switch between them). It is worth mentioning that exact problem types are not required because we just consider their possibilities in the new CHT. Conceptually, we show that the new CHT can make a tradeoff among different types of problems. This argument is confirmed by experimental studies performed on 38 benchmark problems, whose types are known, and a real-world problem (with unknown types) in search-based software engineering. Results demonstrate that within both decomposition-based and nondecomposition-based frameworks, the new CHT can indeed achieve a good tradeoff among different problem types, being better than several state-of-the-art CHTs.
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- 2023
5. A new type of difference I-convergent sequence in IFnNS
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Izhar Khan Ali, Mobeen Ahmad, and A Vakeel Khan
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Pure mathematics ,Mathematics::General Mathematics ,Limit of a sequence ,Management Science and Operations Research ,Type (model theory) ,Mathematics - Abstract
In this paper, we introduce the notion of a generalized difference I-convergent (i.e.?m-I-convergent) and difference I-Cauchy (i.e.?m-I-Cauchy) sequence in intuitionistic fuzzy n-normed spaces. Further, we prove some results related to this notion. Also, we study the concepts of a generalized difference I*-convergent (i.e.?m-I*-convergent) sequence in intuitionistic fuzzy n-normed spaces and show the relation between them.
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- 2023
6. Semi-Supervised Learning With Label Proportion
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Hong Tao, Chenping Hou, Dewen Hu, Ningzhao Sun, Tingjin Luo, and Wenzhang Zhuge
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business.industry ,Computer science ,Supervised learning ,Semi-supervised learning ,Extension (predicate logic) ,Type (model theory) ,Machine learning ,computer.software_genre ,Computer Science Applications ,Submodular set function ,Consistency (database systems) ,ComputingMethodologies_PATTERNRECOGNITION ,Cardinality ,Computational Theory and Mathematics ,Minification ,Artificial intelligence ,business ,computer ,Information Systems - Abstract
The scarcity of labels is common and great challenge in traditional supervised learning. Semi-supervised learning (SSL) leverages unlabeled samples to alleviate the absence of label information. Similar with annotation, label proportion is another type of prior information and plays a significant role in classification tasks. Compared with the acquisition of labels, label proportion can be obtained more easily. For example, only a small number of patients have been diagnosed with or not with cancers in hospital database, while the proportion with cancer can be generally estimated by historical records. How to incorporate such prior information of label proportion is crucial but rarely studied in literature. Traditional SSL methods often ignore this prior information and will lead to performance degradation inevitably. To solve this problem, we propose a novel SSL with Label Proportion (SSLLP). Our approach encourages to preserve label consistency and label proportion by imposing the cardinality bound constraints. Our formulated problem equals to a mixed-integer constrained submodular minimization and it is difficult to be solved directly. Therefore, we transformed the original problem into a convex one by Lov $\acute{\text{a}}$ sz extension and designed an efficient solving algorithm. Extensive experimental results present the improved performance of our method over several state-of-the-art methods.
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- 2023
7. Volumes of Polyhedra in Non-Euclidean Spaces of Constant Curvature
- Author
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V. A. Krasnov
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Statistics and Probability ,Hyperbolic space ,Applied Mathematics ,General Mathematics ,Dimension (graph theory) ,General Medicine ,Type (model theory) ,Combinatorics ,Constant curvature ,Polyhedron ,Non-Euclidean geometry ,Simple (abstract algebra) ,Tetrahedron ,Mathematics::Metric Geometry ,Mathematics - Abstract
Computation of the volumes of polyhedra is a classical geometry problem known since ancient mathematics and preserving its importance until present time. Deriving volume formulas for 3-dimensional non-Euclidean polyhedra of a given combinatorial type is a very difficult problem. Nowadays, it is fully solved for a tetrahedron, the most simple polyhedron in the combinatorial sense. However, it is well known that for a polyhedron of a special type its volume formula becomes much simpler. This fact was noted by Lobachevsky who found the volume of the so-called ideal tetrahedron in hyperbolic space (all vertices of this tetrahedron are on the absolute).In this survey, we present main results on volumes of arbitrary non-Euclidean tetrahedra and polyhedra of special types (both tetrahedra and polyhedra of more complex combinatorial structure) in 3-dimensional spherical and hyperbolic spaces of constant curvature K = 1 and K = -1, respectively. Moreover, we consider the new method by Sabitov for computation of volumes in hyperbolic space (described by the Poincare model in upper half-space). This method allows one to derive explicit volume formulas for polyhedra of arbitrary dimension in terms of coordinates of vertices. Considering main volume formulas for non-Euclidean polyhedra, we will give proofs (or sketches of proofs) for them. This will help the reader to get an idea of basic methods for computation of volumes of bodies in non-Euclidean spaces of constant curvature.
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- 2022
8. The new soliton solutions for long and short-wave interaction system
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Mohammad Bagher Ghaemi, Javad Vahidi, Sayyed Masood Zekavatmand, Hadi Rezazadeh, and Mühendislik ve Doğa Bilimleri Fakültesi
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Maple software ,Environmental Engineering ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Applied mathematics ,Ocean Engineering ,Extended Rational Sine-Cosine Method ,Soliton ,Type (model theory) ,Oceanography ,System of linear equations ,Extended Rational Sinh-Cosh Method ,Mathematics - Abstract
The goal of this paper is to discover modern soliton solutions to long and short-wave interaction system by procedures called extended rational sine-cosine and rational sinh-cosh methods. We assume that the equation has a hypothetical soliton solutions. By reorganizing the resulting equations, we obtain a system of equations. Using Maple software, we get unknown coefficients in the system and writing them in the original equation, we obtain new solition solutions of the equation. The results show that the soliton solutions generated by the method for the long and short-wave interaction system are bright, kink type, bright periodic and dark solutions. We provided 3-D figures to illustrate the solutions. Computational results indicate that the method employed in this paper is superior than some other methods used in the literature to solve the same system equations.
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- 2022
9. Two perishable inventory systems with one-way substitution
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David Perry, LQ Liqiang Liu, Ijbf Ivo Adan, Operations Planning Acc. & Control, and EAISI High Tech Systems
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Decision Sciences(all) ,021103 operations research ,Operations research ,Perishable items ,Computer science ,Substitution (logic) ,0211 other engineering and technologies ,Process (computing) ,General Decision Sciences ,02 engineering and technology ,Type (model theory) ,Management Science and Operations Research ,Poisson distribution ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Fluid model ,Markovian approximation ,Stochastic inventory system ,symbols ,0101 mathematics ,Constant (mathematics) - Abstract
Motivated by the ABO issue of the blood bank system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems-PIS A and PIS B, are correlated to each other through a one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four Poisson processes, which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items, an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items, an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. This one-way substitution of the issuing policy generates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis of PIS B is known from previous work. Thus, in this study we focus on the marginal performance analysis of PIS A. Based on a fluid formulation and a Markovian approximation for the one-way substitution demand process, we develop a unified approach to efficiently and accurately approximate the performance of the PIS A. The effectiveness of the approach is investigated by extensive numerical experiments.
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- 2022
10. Decentralized Mutual Damping Control of Cascaded-Type VSGs for Power and Frequency Oscillation Suppression
- Author
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Siqi Fu, Lang Li, Yao Sun, and Mei Su
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Lyapunov function ,Computer science ,Process (computing) ,Type (model theory) ,Term (time) ,Power (physics) ,symbols.namesake ,Control and Systems Engineering ,Transmission line ,Control theory ,Convergence (routing) ,symbols ,Electrical and Electronic Engineering ,Energy (signal processing) - Abstract
This paper reveals the power and frequency oscillation mechanism of the islanded cascaded-type virtual synchronous generators (VSGs), and proposes a decentralized mutual damping suppression method. In the proposed scheme, the mutual damping term is constructed via the decentralized manner with transmission line current. It contributes to increasing damping and accelerating the frequency convergence of cascaded-type VSGs in the dynamic process. As a result, the power and frequency oscillations are restrained, and the system dynamic performance is improved. Further, the system stability based on the Lyapunov energy function method is proved. Finally, the effectiveness of the proposed decentralized mutual damping control is verified by simulations and experimental results.
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- 2022
11. Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue
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Alon Eden, Michal Feldman, Kira Goldner, Anna R. Karlin, and Amos Fiat
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FOS: Computer and information sciences ,050101 languages & linguistics ,Class (set theory) ,General Mathematics ,05 social sciences ,Parameterized complexity ,02 engineering and technology ,Type (model theory) ,Management Science and Operations Research ,Matroid ,Submodular set function ,Separable space ,Computer Science Applications ,Combinatorics ,Combinatorial auction ,Computer Science - Computer Science and Game Theory ,0202 electrical engineering, electronic engineering, information engineering ,Common value auction ,020201 artificial intelligence & image processing ,0501 psychology and cognitive sciences ,Mathematics ,Computer Science and Game Theory (cs.GT) - Abstract
We study combinatorial auctions with interdependent valuations. In such settings, each agent $i$ has a private signal $s_i$ that captures her private information, and the valuation function of every agent depends on the entire signal profile, ${\bf s}=(s_1,\ldots,s_n)$. The literature in economics shows that the interdependent model gives rise to strong impossibility results, and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple single-parameter settings (mostly single item auctions, or matroid feasibility constraints). Both bodies of literature focus largely on valuations satisfying a technical condition termed {\em single crossing} (or variants thereof). We consider the class of {\em submodular over signals} (SOS) valuations (without imposing any single-crossing type assumption), and provide the first welfare approximation guarantees for multi-dimensional combinatorial auctions, achieved by universally ex-post IC-IR mechanisms. Our main results are: $(i)$ 4-approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; $(ii)$ 4-approximation for any combinatorial auction with multi-dimensional signals and {\em separable}-SOS valuations; and $(iii)$ $(k+3)$- and $(2\log(k)+4)$-approximation for any combinatorial auction with single-dimensional signals, with $k$-sized signal space, for SOS and strong-SOS valuations, respectively. All of our results extend to a parameterized version of SOS, $d$-SOS, while losing a factor that depends on $d$., To appear in the 20th ACM conference on Economics and Computation (ACM EC '19)
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- 2023
12. Automorphisms of the k-Curve Graph
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Shuchi Agrawal, Roberta Shapiro, Marissa Loving, J. Robert Oakley, Tarik Aougab, Yassin Chandran, and Yang Xiao
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Surface (mathematics) ,Conjecture ,General Mathematics ,010102 general mathematics ,Geometric Topology (math.GT) ,Natural number ,0102 computer and information sciences ,Type (model theory) ,Automorphism ,01 natural sciences ,Mapping class group ,Combinatorics ,Mathematics - Geometric Topology ,010201 computation theory & mathematics ,FOS: Mathematics ,Isotopy ,Mathematics - Combinatorics ,Graph (abstract data type) ,Combinatorics (math.CO) ,0101 mathematics ,Mathematics - Abstract
Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of such curves admitting representatives that intersect at most k times. We prove that the automorphism group of the k-curve graph of a surface S is isomorphic to the extended mapping class group for all k sufficiently small with respect to the Euler characteristic of S. We prove the same result for the so-called systolic complex, a variant of the curve graph whose complete subgraphs encode the intersection patterns for any collection of systoles with respect to a hyperbolic metric. This resolves a conjecture of Schmutz Schaller., Comment: 33 pages, 23 figures, 1 table. Incorporated referee comments. To appear in the Michigan Mathematical Journal
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- 2023
13. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure
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Michael Schwarz, Matthias Keller, Melchior Wirth, and Bobo Hua
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Pure mathematics ,Continuum (topology) ,Applied Mathematics ,General Mathematics ,Type (model theory) ,Measure (mathematics) ,Dirichlet distribution ,Functional Analysis (math.FA) ,Mathematics - Spectral Theory ,Mathematics - Functional Analysis ,Sobolev space ,Elliptic operator ,symbols.namesake ,Mathematics - Analysis of PDEs ,Bounded function ,FOS: Mathematics ,symbols ,Spectral Theory (math.SP) ,Eigenvalues and eigenvectors ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.
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- 2023
14. Порядок слов в эритажном русском : влияние типа клаузы и языка окружения
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Sabine Zerbian, Maria Martynova, Yulia Zuban, Natalia Gagarina, and Luka Szucsich
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Linguistics and Language ,Historical Linguistics ,Linguistics, general ,Russian ,Type (model theory) ,Regional and Cultural Studies ,Syntax ,Language and Linguistics ,Linguistics ,Developmental and Educational Psychology ,Historical linguistics ,Narrative ,Saint petersburg ,ddc:400 ,Psychology ,400 Sprache ,Word order - Abstract
Heritage speakers (HSs) are known to differ from monolingual speakers in various linguistic domains. The present study focuses on the syntactic properties of monolingual and heritage Russian. Using a corpus of semi-spontaneous spoken and written narratives produced by HSs of Russian residing in the US and Germany, we investigate HSs’ word order patterns and compare them to monolingual speakers of Russian from Saint Petersburg. Our results show that the majority language (ML) of HSs as well as the clause type contribute to observed differences in word order patterns between speaker groups. Specifically, HSs in Germany performed similarly to monolingual speakers of Russian while HSs in the US generally produced more SVO and less OVS orders than the speakers of the latter group. Furthermore, HSs in the US produced more SVO orders than both monolingual speakers and HSs in Germany in embedded clauses, but not in main clauses. The results of the study are discussed with the reference to the differences between main and embedded clauses as well as the differences between the MLs of the HSs., Deutsche Forschungsgemeinschaft, Projekt DEAL
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- 2023
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15. Linear Forms in Polylogarithms
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Noriko Hirata-Kohno, Makoto Kawashima, and Sinnou David
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Physics ,Rational number ,Mathematics - Number Theory ,Degree (graph theory) ,Wronskian ,Field (mathematics) ,Type (model theory) ,Algebraic number field ,Theoretical Computer Science ,Combinatorics ,Mathematics (miscellaneous) ,FOS: Mathematics ,Number Theory (math.NT) ,Polylogarithmic function ,Algebraic number - Abstract
Let $r, \,m$ be positive integers. Let $x$ be a rational number with $0 \le x, Comment: Corrected typos
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- 2022
16. Finite-Time Stabilization of Switched Systems Under Mode-Dependent Event-Triggered Impulsive Control
- Author
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Taixiang Zhang, Xiaodi Li, and Shiji Song
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FTCS scheme ,Lyapunov function ,Computer science ,Mode (statistics) ,Type (model theory) ,Stability (probability) ,Computer Science Applications ,Human-Computer Interaction ,Constraint (information theory) ,symbols.namesake ,Dwell time ,Nonlinear system ,Control and Systems Engineering ,Control theory ,symbols ,Electrical and Electronic Engineering ,Software - Abstract
This article studies the event-triggered finite-time stabilization problem of nonlinear switched systems in which the time derivatives of Lyapunov functions of modes are indefinite. Based on a mode-dependent average dwell time constraint and event-triggered impulsive control (ETIC) strategy, a new type of the mode-dependent event-triggered mechanism (MDETM) which can efficiently avoid Zeno behavior for switched systems is presented. Some Lyapunov-based criteria for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained, respectively, where a relationship between the prescribed bound and event-triggered mechanism is established. Then, we apply these proposed ETIC strategies to impulsive switched systems and design a class of LMI-based MDETMs to guarantee the FTS/FTCS property. Finally, the effectiveness of presented ETIC strategies is illustrated by two examples.
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- 2022
17. Dimensions of the popcorn graph
- Author
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Haipeng Chen, Jonathan M. Fraser, Han Yu, EPSRC, The Leverhulme Trust, University of St Andrews. Pure Mathematics, and University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
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Thomae function ,Popcorn function ,Assouad dimension ,Mathematics::Number Theory ,General Mathematics ,T-NDAS ,Dimension (graph theory) ,Type (model theory) ,Diophantine approximation ,Assouad spectrum ,Mathematics - Metric Geometry ,Probability theory ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Mathematics::Metric Geometry ,Number Theory (math.NT) ,QA Mathematics ,QA ,28A80, 11B57 ,Mathematics ,Discrete mathematics ,Mathematics::Combinatorics ,Box dimension ,Mathematics - Number Theory ,Real analysis ,Applied Mathematics ,Spectrum (functional analysis) ,Metric Geometry (math.MG) ,Function (mathematics) ,Mathematics - Classical Analysis and ODEs ,Graph (abstract data type) - Abstract
The 'popcorn function' isThe `popcorn function' is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erd\H{o}s inequality from probability theory., Comment: 13 pages, 2 figures
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- 2022
18. Interval Type-2 Fuzzy Application for Diet Journaling
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Joshua M. Krbez and Adnan Shaout
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General Computer Science ,Computer science ,Journaling file system ,020208 electrical & electronic engineering ,0202 electrical engineering, electronic engineering, information engineering ,Interval (graph theory) ,020201 artificial intelligence & image processing ,02 engineering and technology ,Type (model theory) ,Arithmetic ,Fuzzy logic - Abstract
In this article, an improved system is constructed using interval type-2 fuzzy sets (IT2FS) and a fuzzy logic controller (FLC) with non-singleton inputs. The primary purpose is to better model nutritional input uncertainty which is propagated through the Type-2 FLC. To this end, methods are proposed to (1) model nutrient uncertainty in food items, (2) extend the nutritional information of a food item using an IT2FS representation for each nutrient incorporating the uncertainty in the extension process, (3) accumulate uncertainties for IT2FS inputs using fuzzy arithmetic, and (4) build IT2FS antecedents for FLC rules based on dietary reference intakes (DRIs). These methods are then used to implement a web application for diet journaling that includes a client-side Type-2 non-singleton Interval Type-2 FLC. The produced application is then compared with the previous work and shown to be more suitable. This is the first known work on diet journaling that attempts to model uncertainty for all anticipated measurement error.
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- 2022
19. Some novel integration techniques to explore the conformable M-fractional Schrödinger-Hirota equation
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M. Asif, Mohammad Mirzazadeh, Kamyar Hosseini, Lanre Akinyemi, M. Raheel, and Asim Zafar
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Environmental Engineering ,Current (mathematics) ,Wave propagation ,Ocean Engineering ,Conformable matrix ,Type (model theory) ,Oceanography ,Differential operator ,Nonlinear system ,symbols.namesake ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,symbols ,Applied mathematics ,Soliton ,Nonlinear Sciences::Pattern Formation and Solitons ,Schrödinger's cat ,Mathematics - Abstract
The current study deals with exact soliton solutions for Schrodinger-Hirota (SH) equation via two modified integration methods. Those methods are known as the improved ( G ′ / G ) -expansion method and the Kudryashov method. This model is a generalized version of the nonlinear Schrodinger (NLS) equation with higher order dispersion and cubic nonlinearity. It can be considered as a more accurate approximation than the NLS equation in explaining wave propagation in the ocean and optical fibers. A novel derivative operator named as the conformable truncated M-fractional is used to study the above mentioned model. The obtained results can be used in describing the Schrodinger-Hirota equation in some better way. Moreover the obtained results are verified through symbolic computational software. Also, the obtained results show that the suggested approaches have broaden capacity to secure some new soliton type solutions for the fractional differential equations in an effective way. In the end, the results are also explained through their graphical representations.
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- 2022
20. Distributed Integral-Type Edge Event- and Self-Triggered Synchronization for Nonlinear Multiagent Systems
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Chengxi Zhang, Bo Li, Ming-Zhe Dai, Henry Leung, and Peng Dong
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Computer science ,Multi-agent system ,Function (mathematics) ,Type (model theory) ,Lipschitz continuity ,Synchronization ,Computer Science Applications ,Human-Computer Interaction ,Nonlinear system ,Control and Systems Engineering ,Control theory ,Enhanced Data Rates for GSM Evolution ,Electrical and Electronic Engineering ,Software ,Event (probability theory) - Abstract
This article presents integral-type edge event- and self-triggered policies for Lipschitz nonlinear multiagent systems, in which only edge states are employed by all controllers. An integral-type triggering function is designed to determine event instants, and the considered system can achieve Zeno-free triggering. An integral-type edge self-triggered policy is then designed to avoid sensors' continuous measurements. Compared to traditional event-triggered schemes, the proposed strategies have relaxed triggering conditions and lowered the event frequencies. Also, the proposed edge self-triggered algorithm can avoid the requirement for continuous measurement error monitoring. Numerical simulations are given to demonstrate the effectiveness of the theoretical conclusions.
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- 2022
21. Minimising the expected commute time
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Saul D. Jacka and Ma Elena Hernández-Hernández
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Statistics and Probability ,Stochastic control ,Diffusion (acoustics) ,Applied Mathematics ,010102 general mathematics ,Control (management) ,Markov chain Monte Carlo ,Sense (electronics) ,Type (model theory) ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Reflection (mathematics) ,Modeling and Simulation ,symbols ,Applied mathematics ,Point (geometry) ,0101 mathematics ,QA ,Mathematics - Abstract
Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to 1 and then return (the so-called commute time from 0 to 1). We consider the static and dynamic versions of this problem where the control mechanism is related to the diffusion’s drift via the corresponding scale function. In the static version the diffusion’s drift can be chosen at each point in [0,1], whereas in the dynamic version we are only able to choose the drift at each point at the time of first visiting that point. The dynamic version leads to a novel type of stochastic control problem.
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- 2022
22. Observer Design for Sampled-Data Systems via Deterministic Learning
- Author
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Jingtao Hu, Weiming Wu, Cong Wang, and Bing Ji
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Radial basis function network ,Observer (quantum physics) ,Computer Networks and Communications ,Computer science ,Process (computing) ,Type (model theory) ,Computer Science Applications ,Nonlinear system ,Artificial Intelligence ,Control theory ,Trajectory ,State (computer science) ,Software ,Sampled data systems - Abstract
A unified approach is proposed to design sampled-data observers for a certain type of unknown nonlinear systems undergoing recurrent motions based on deterministic learning in this article. First, a discrete-time implementation of high-gain observer (HGO) is utilized to obtain state trajectory from sampled output measurements. By taking the recurrent estimated trajectory as inputs to a dynamical radial basis function network (RBFN), a partial persistent exciting (PE) condition is satisfied, and a locally accurate approximation of nonlinear dynamics can be realized along the estimated sampled-data trajectory. Second, an RBFN-based observer consisting of the obtained dynamics from the process of deterministic learning is designed. Without resorting to high gains, the RBFN-based observer is shown capable of achieving correct state observation. The novelty of this article lies in that, by incorporating deterministic learning with the discrete-time HGO, the nonlinear dynamics can be accurately approximated along the estimated trajectory, and such obtained knowledge can then be utilized to realize nonhigh-gain state estimation for the same or similar sampled-data systems. Simulation is performed to validate the effectiveness of the proposed approach.
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- 2022
23. A Novel Attack Detection for Linear Systems With Unknown-But-Bounded Noises
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Ben Niu, Hao Liu, Shaodong Wang, and Yuzhe Li
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Optimization problem ,Intersection (set theory) ,Computer science ,Linear system ,Type (model theory) ,Computer Science Applications ,Human-Computer Interaction ,Matrix (mathematics) ,Control and Systems Engineering ,Bounded function ,Electrical and Electronic Engineering ,Replay attack ,Algorithm ,Software - Abstract
This article proposes a novel attack detection approach based on zonotopes for linear parameter-varying (LPV) systems with unknown-but-bounded (UBB) noises. The following three types of attacks are considered: 1) denial-of-service (DoS) attacks; 2) replay attacks (RAs); and 3) false-data-injection (FDI) attacks. In order to reduce the conservativeness, a free-weighting matrix is introduced, which can be computed by solving an optimization problem. Moreover, the radius of the intersection zonotope can be guaranteed to be limited as well. Furthermore, it is not necessary to acquire the knowledge about the specific type of attack in advance. Finally, a numerical example is given to illustrate the validity of the given method.
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- 2022
24. An analytical solution for the Caputo type generalized fractional evolution equation
- Author
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Panumart Sawangtong and Wannika Sawangtong
- Subjects
Mellin transform ,Laplace transform ,Generalized Mellin transform ,Generalization ,Mathematics::Optimization and Control ,Mathematics::Classical Analysis and ODEs ,General Engineering ,Fractional Green’s functions ,Type (model theory) ,Caputo type generalized fractional derivative ,Engineering (General). Civil engineering (General) ,Generalized Laplace transform ,Mathematics::Numerical Analysis ,Fractional calculus ,Fractional evolution equations ,Evolution equation ,Applied mathematics ,TA1-2040 ,Fractional differential ,Variety (universal algebra) ,Mathematics - Abstract
The Caputo type generalized fractional evolution equation is studied in this paper. Since the Caputo type generalized fractional derivative is well-known for being the generalization of Caputo fractional derivatives, this article’s studies contribute to the solving of a variety of fractional differential equations in the sense of Caputo type generalized fractional derivative and Caputo fractional derivative. Moreover, the fractional Green’s functions for those fractional differential equations are obtained. The generalized Laplace transform and generalized Mellin transform are used to effectively and successfully achieve the desired results. Importantly, the generalized Mellin transform is firstly proposed here.
- Published
- 2022
25. Linear theory for a mixed operator with Neumann conditions
- Author
-
Edoardo Proietti Lippi, Serena Dipierro, and Enrico Valdinoci
- Subjects
General Mathematics ,Operator (physics) ,010102 general mathematics ,Spectral properties ,Linear system ,Type (model theory) ,01 natural sciences ,010305 fluids & plasmas ,0103 physical sciences ,Applied mathematics ,Preprint ,0101 mathematics ,Logistic function ,Eigenvalues and eigenvectors ,Mathematics - Abstract
We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann condition that we take into account comprises, as a particular case, the one that has been recently introduced in [S. Dipierro, X. Ros-Oton, E. Valdinoci, Rev. Mat. Iberoam. (2017)]. Also, the results that we present here find a natural application to a logistic equation motivated by biological problems that has been recently considered in [S. Dipierro, E. Proietti Lippi, E. Valdinoci, preprint (2020)].
- Published
- 2022
26. A maximum-margin multisphere approach for binary Multiple Instance Learning
- Author
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Matteo Avolio, Antonio Fuduli, and Annabella Astorino
- Subjects
Fixed-center margin maximization ,Information Systems and Management ,General Computer Science ,Basis (linear algebra) ,Computer science ,Heuristic ,Multiple Instance Learning ,Binary number ,Management Science and Operations Research ,Type (model theory) ,Industrial and Manufacturing Engineering ,Machine Learning ,Set (abstract data type) ,Support vector machine ,Spherical separation ,Margin (machine learning) ,Modeling and Simulation ,Benchmark (computing) ,Algorithm - Abstract
We propose a heuristic approach for solving binary Multiple Instance Learning (MIL) problems, whose objective is to categorize bags of instances. Considering the case with two classes of instances, on the basis of the standard MIL assumption, a bag is classified positive if it contains at least a positive instance and negative if all its instances are negative. Inspired by a well-established MIL Support Vector Machine type approach, our technique is based on iteratively separating the bags by means of successive maximum-margin spheres. Such spheres, whose number is automatically determined, are generated by computing, for each of them, the optimal radius in correspondence to a prefixed center. Numerical results are presented on a set of benchmark test problems, showing the effectiveness of our approach.
- Published
- 2022
27. Adaptive and Optimal Point-Wise Estimations for Densities in Garch-Type Model by Wavelets
- Author
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Cong Wu
- Subjects
Computational Mathematics ,Wavelet ,Autoregressive conditional heteroskedasticity ,Applied mathematics ,Point (geometry) ,Type (model theory) ,Mathematics - Published
- 2022
28. Metrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type Method
- Author
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Mohammed Harunor Rashid
- Subjects
Computational Mathematics ,Convergence (routing) ,Applied mathematics ,Type (model theory) ,Mathematics - Published
- 2022
29. Sobolev-type inequalities on variable exponent Morrey spaces of an integral form
- Author
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Takao Ohno and Tetsu Shimomura
- Subjects
Morrey space ,Mathematics::Functional Analysis ,Pure mathematics ,variable exponent ,Variable exponent ,Applied Mathematics ,General Mathematics ,Mathematics::Analysis of PDEs ,Mathematics::Classical Analysis and ODEs ,Order (ring theory) ,Integral form ,Type (model theory) ,Sobolev space ,Riesz potential ,Maximal operator ,Sobolev's inequality ,Algebra over a field ,maximal functions ,Variable (mathematics) ,Mathematics - Abstract
The aim of this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on variable exponent Morrey spaces of an integral form. As an application of the boundedness of the maximal operator, we establish Sobolev-type inequalities for Riesz potentials $$I_{\alpha (\cdot )}f$$ of variable order $$\alpha (\cdot )$$ of functions f in variable exponent Morrey spaces of an integral form.
- Published
- 2022
30. Generalized Fractal Jensen–Mercer and Hermite–Mercer type inequalities via h-convex functions involving Mittag–Leffler kernel
- Author
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Saad Ihsan Butt, Saba Yousaf, Adnan Aslam, Peng Xu, and Tariq Javed Zia
- Subjects
Pure mathematics ,Hermite polynomials ,Mathematics::Classical Analysis and ODEs ,General Engineering ,Function (mathematics) ,Type (model theory) ,Engineering (General). Civil engineering (General) ,Fractional calculus ,Fractal ,26D15 ,Kernel (statistics) ,26A51 ,Differentiable function ,TA1-2040 ,26A33 ,Convex function ,Mathematics - Abstract
In this paper, we present generalized Jensen-Mercer inequality for a generalized h-convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h-convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature.
- Published
- 2022
31. A New Conservative Allen-Cahn Type Ohta-Kawaski Phase-Field Model for Diblock Copolymers and Its Numerical Approximations
- Author
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Shuang Geng, Tongmao Li, Qiongwei Ye, and Xiaofeng Yang
- Subjects
Materials science ,Field (physics) ,Condensed matter physics ,Applied Mathematics ,Mechanical Engineering ,Phase (matter) ,Copolymer ,Type (model theory) - Published
- 2022
32. Quasi Type-1 PLL With Tunable Phase Detector for Unbalanced and Distorted Three-Phase Grid
- Author
-
Mohamed Benbouzid, Hafiz Ahmed, Zoheir Tir, Seifeddine Ben Elghali, Anant Kumar Verma, Aix Marseille Université (AMU), Pronostic-Diagnostic Et CommAnde : Santé et Energie (PECASE), Laboratoire d'Informatique et Systèmes (LIS), and Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Phase-locked loop ,Physics ,[SPI]Engineering Sciences [physics] ,Three-phase ,Energy Engineering and Power Technology ,Electrical and Electronic Engineering ,Type (model theory) ,Topology ,Grid ,Phase detector ,ComputingMilieux_MISCELLANEOUS - Abstract
International audience
- Published
- 2022
33. A Unified Carrier-Based Pulsewidth Modulation for Three-Phase Vienna-Type Rectifiers
- Author
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Li Zhang, Yan Xing, Hao Zhao, Zhe Zhang, Yuhang Zou, and Zhongshu Zheng
- Subjects
Correctness ,Three-phase ,Computer science ,Component (UML) ,Electrical and Electronic Engineering ,Type (model theory) ,Topology ,Pulse-width modulation ,Expression (mathematics) ,Voltage - Abstract
Compared with space-vector PWM (SV-PWM) schemes, carrier-based PWM (CB-PWM) schemes feature less digital calculation burden. Unfortunately, since different CB-PWM schemes were not represented by a unified expression and the relationship between the injected zero-sequence components (ZSCs) and the switching-state sequences is not revealed, the CB-PWM has poor flexibility in designing the switching-state sequences. In this article, a unified carrier-based PWM (UCB-PWM) is proposed to unify the expressions of different CB-PWM schemes. The ZSC of the proposed UCB-PWM is classified into a basic ZSC (B-ZSC) and a redundant ZSC (R-ZSC). The B-ZSC is a shared component of all CB-PWM schemes, and the dwelling time of redundant small vectors can be distributed by injecting different R-ZSCs. Also, the neutral-point (NP) voltage balance control based on either continuous PWM (CPWM) or discontinuous PWM (DPWM) can be achieved by injecting R-ZSCs. Besides, not only the existing carrier-based DPWM schemes but also new carrier-based DPWM schemes are derived by the proposed UCB-PWM. Finally, experimental results verify the correctness and advantages of the proposed UCB-PWM.
- Published
- 2022
34. Synchronization of Timescale-Type Nonautonomous Neural Networks With Proportional Delays
- Author
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Qiang Xiao, Tingwen Huang, and Zhigang Zeng
- Subjects
Artificial neural network ,Computer science ,Direct method ,Type (model theory) ,Exponential transformation ,Computer Science Applications ,Term (time) ,Human-Computer Interaction ,Control and Systems Engineering ,Control theory ,Synchronization (computer science) ,Key (cryptography) ,Electrical and Electronic Engineering ,Software - Abstract
Synchronization of a class of drive-response timescale-type nonautonomous proportional-delayed neural networks (TNPNNs) is addressed in this article. The key technique to cope with the proportional term is using comparison principle. By timescale theory, inequality technique, and comparison principle, criteria of synchronization are obtained. The method used in this article is effective to cope with TNPNNs and it is a direct approach as well by eliminating the conventional exponential transformation. The obtained results are verified with three examples.
- Published
- 2022
35. Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy
- Author
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Xiyuan Ma, Thomas Welsh Archibald, and Roberto Rossi
- Subjects
Mathematical optimization ,Information Systems and Management ,General Computer Science ,0211 other engineering and technologies ,Time horizon ,02 engineering and technology ,Management Science and Operations Research ,Type (model theory) ,Industrial and Manufacturing Engineering ,0502 economics and business ,FOS: Mathematics ,Leverage (statistics) ,Mathematics - Optimization and Control ,Mathematics ,050210 logistics & transportation ,021103 operations research ,Series (mathematics) ,Inventory ,05 social sciences ,stochastic lot-sizing ,Function (mathematics) ,non-stationary demand ,Reorder point ,Optimization and Control (math.OC) ,(,s,Q,) policy ,Modeling and Simulation ,Heuristics ,Integer (computer science) - Abstract
This paper addresses the single-item single-stocking location non-stationary stochastic lot-sizing problem under a reorder point – order quantity control strategy. The reorder points and order quantities are chosen at the beginning of the planning horizon. The reorder points are allowed to vary with time and we consider order quantities either to be a series of time-dependent constants or a fixed value; this leads to two variants of the policy: the ( s t , Q t ) and the ( s t , Q ) policies, respectively. For both policies, we present stochastic dynamic programs (SDP) to determine optimal policy parameters and introduce mixed integer non-linear programming (MINLP) heuristics that leverage piecewise-linear approximations of the cost function. Numerical experiments demonstrate that our solution method efficiently computes near-optimal parameters for a broad class of problem instances.
- Published
- 2022
36. Birational geometry of varieties fibred into complete intersections of codimension two
- Author
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Aleksandr V. Pukhlikov
- Subjects
General Mathematics ,Complete intersection ,Fibered knot ,14E05, 14E07 ,Birational geometry ,Codimension ,Type (model theory) ,Combinatorics ,Base (group theory) ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,FOS: Mathematics ,Projective space ,Algebraic Geometry (math.AG) ,General position ,Mathematics - Abstract
In this paper we prove the birational superrigidity of Fano-Mori fibre spaces $\pi\colon V\to S$, every fibre of which is a complete intersection of type $d_1\cdot d_2$ in the projective space ${\mathbb P}^{d_1+d_2}$, satisfying certain conditions of general position, under the assumption that the fibration $V/S$ is sufficiently twisted over the base (in particular, under the assumption that the $K$-condition holds). The condition of general position for every fibre guarantees that the global log canonical threshold is equal to one. This condition bounds the dimension of the base $S$ by a constant that depends on the dimension $M$ of the fibre only (as the dimension $M$ of the fibre grows, this constant grows as $\frac12 M^2$). The fibres and the variety $V$ itself may have quadratic and bi-quadratic singularities, the rank of which is bounded from below., Comment: 86 pages, the final version
- Published
- 2022
37. A novel quasi-type-1 PLL based on frequency-fixed complex filter for three phase grid synchronization
- Author
-
Zizhao Wang, Junyou Yang, Tianhe Gao, Yunlu Li, and Yan Xu
- Subjects
Computer science ,Harmonic ,Grid synchronization ,Type (model theory) ,Power converter ,Topology ,TK1-9971 ,Phase-locked loop ,General Energy ,Three-phase ,Complex filter ,Electrical engineering. Electronics. Nuclear engineering - Abstract
In practical applications of distributed generation, accurate phase and frequency detection of grid voltages is the critical aspect for the control of power converter. Thanks for its similarity and robustness, phase-locked loop (PLL) has been widespread. However, under distorted grid conditions with polluted harmonics, the accuracy of phase detection may be deteriorated. It is still a challenge to maintain the accuracy of phase detection and dynamic performance at same time. In this paper, to tackle this issue, a novel quasi-type-1 (QT1) structure based PLL is proposed. QT1-PLL incorporated with complex filter can meet the requirement of filtering capability, dynamic response and robustness. The utilization of complex filter based on frequency-fixed structure and feed-forward phase compensation path can eliminate the phase error oriented from frequency deviation. The results of comparative experiments confirm the effectiveness of the proposed PLL.
- Published
- 2022
38. Efficient top/bottom-k fraction estimation in spatial databases using bounded main memory
- Author
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Zhuojun Duan, Jinbao Wang, Donghua Yang, and Xixian Han
- Subjects
Multidisciplinary ,Point of interest ,Database ,Computer science ,Bounded function ,Spatial database ,Fraction (mathematics) ,Space (commercial competition) ,Type (model theory) ,computer.software_genre ,computer ,Auxiliary memory ,Variety (cybernetics) - Abstract
Spatial databases store objects with their locations and certain types of attached items. A variety of modern applications have been developed by leveraging the utilization of locations and items in spatial objects, such as searching points of interest, hot topics, or users' attitude in specified spatial regions. In many scenarios, the high and low-frequency items in a spatial region are worth noticing, considering they represent the majority's interest or eccentric users' opinion. However, existing works have yet to identify such items in an interactive manner, despite the significance of the endeavor in decision-making systems. This study recognizes a novel type of analytical query, called top/bottom-k fraction query, to discover such items in spatial databases. To achieve fast query response, we propose a multilayered data summary that is spread out across the main memory and external memory. A memory-based estimation method for top/bottom-k fraction queries is proposed. To maximize the use of the main memory space, we design a data summary tuning method to dynamically allocate memory space among different spatial partitions. The proposed approach is evaluated with real-life datasets and synthetic datasets in terms of estimation accuracy. Evaluation results demonstrate the effectiveness of the proposed data summary and corresponding estimation and tuning algorithms.
- Published
- 2022
39. Stochastic evolution equations with Wick-polynomial nonlinearities
- Author
-
Milica Žigić, Tijana Levajković, Stevan Pilipović, and Dora Seleši
- Subjects
Statistics and Probability ,Polynomial ,Class (set theory) ,Wick product ,11B83 ,infinitesimal generator ,47J35 ,37L55 ,Type (model theory) ,01 natural sciences ,0103 physical sciences ,FOS: Mathematics ,$C_0-$semigroup ,Applied mathematics ,Hida–Kondratiev spaces ,Uniqueness ,Infinitesimal generator ,0101 mathematics ,stochastic nonlinear evolution equations ,60G20 ,Mathematics ,60H40 ,Probability (math.PR) ,010102 general mathematics ,White noise ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Nonlinear system ,60H15 ,010307 mathematical physics ,Statistics, Probability and Uncertainty ,Catalan numbers ,Mathematics - Probability - Abstract
We study nonlinear parabolic stochastic partial differential equations with Wick-power and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fujita equation, the stochastic Fisher-KPP equation and the stochastic FitzHugh-Nagumo equation among many others. By implementing the theory of $C_0-$semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this class of SPDEs. In particular, we also treat the linear nonautonomous case and provide several applications featured as stochastic reaction-diffusion equations that arise in biology, medicine and physics.
- Published
- 2023
40. Cubature rules for unitary Jacobi ensembles
- Author
-
J. F. van Diejen and E. Emsiz
- Subjects
Pure mathematics ,General Mathematics ,Numerical analysis ,010102 general mathematics ,Lie group ,65D32, 15B52, 28C10, 43A75 ,010103 numerical & computational mathematics ,Numerical Analysis (math.NA) ,Type (model theory) ,01 natural sciences ,Chebyshev filter ,Unitary state ,Mathematics::Numerical Analysis ,Symmetric function ,Computational Mathematics ,Hyperplane ,Mathematics - Classical Analysis and ODEs ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,Mathematics - Numerical Analysis ,0101 mathematics ,Analysis ,Mathematics ,Symplectic geometry - Abstract
We present Chebyshev type cubature rules for the exact integration of rational symmetric functions with poles on prescribed coordinate hyperplanes. Here the integration is with respect to the densities of unitary Jacobi ensembles stemming from the Haar measures of the orthogonal and the compact symplectic Lie groups., Comment: 10 pages, 1 table
- Published
- 2023
- Full Text
- View/download PDF
41. Diamond distances in Nottingham algebras
- Author
-
Marina Avitabile, Sandro Mattarei, Avitabile, M, and Mattarei, S
- Subjects
Pure mathematics ,Algebra and Number Theory ,Applied Mathematics ,media_common.quotation_subject ,Graded Lie algebra ,Modular Lie algebra ,Field (mathematics) ,Thin Lie algebra ,Group Theory (math.GR) ,Mathematics - Rings and Algebras ,Primary 17B50, secondary 17B70, 17B65 ,Type (model theory) ,Central series ,Infinity ,Nottingham group ,MAT/02 - ALGEBRA ,Rings and Algebras (math.RA) ,Lie algebra ,FOS: Mathematics ,Mathematics - Group Theory ,G110 Pure Mathematics ,Mathematics ,media_common - Abstract
Nottingham algebras are a class of just-infinite-dimensional, modular, $\mathbb{N}$-graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series. Homogeneous components of a Nottingham algebra have dimension one or two, and in the latter case they are called diamonds. The first diamond occurs in degree $1$, and the second occurs in degree $q$, a power of the characteristic. Many examples of Nottingham algebras are known, in which each diamond past the first can be assigned a type, either belonging to the underlying field or equal to $\infty$. A prospective classification of Nottingham algebras requires describing all possible diamond patterns. In this paper we establish some crucial contributions towards that goal. One is showing that all diamonds, past the first, of an arbitrary Nottingham algebra $L$ can be assigned a type, in such a way that the degrees and types of the diamonds completely describe $L$. At the same time we prove that the difference in degrees of any two consecutive diamonds in any Nottingham algebra equals $q-1$. As a side-product of our investigation, we classify the Nottingham algebras where all diamonds have type $\infty$., 22 pages
- Published
- 2023
42. Dynamics of an atom cavity field system in interacting Fock space
- Author
-
Prasanta Kumar Das and Arpita Chatterjee
- Subjects
Physics ,Quantum Physics ,Physics and Astronomy (miscellaneous) ,Field (physics) ,010308 nuclear & particles physics ,General Mathematics ,Dynamics (mechanics) ,State vector ,Atom (order theory) ,FOS: Physical sciences ,State (functional analysis) ,Type (model theory) ,01 natural sciences ,Fock space ,Field system ,Quantum mechanics ,0103 physical sciences ,81V80 ,010306 general physics ,Quantum Physics (quant-ph) - Abstract
In this paper, we investigate one-time passing of a $V$-type three-level atom through a single-mode interacting field in a cavity. We extend the idea of elementary Jaynes-Cummings model by assuming that the field vector belongs to interacting Fock space. In the process, we arrive at a state vector which will be analyzed to study the nonclassicality of the evolved state of the system., Comment: 14 pages, 5 figures
- Published
- 2023
- Full Text
- View/download PDF
43. Multiple positive solutions for a p-Laplace Benci–Cerami type problem (1<2), via Morse theory
- Author
-
Giuseppina Vannella
- Subjects
Pure mathematics ,Laplace transform ,Computer Science::Information Retrieval ,Applied Mathematics ,General Mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,58E05, 35J60, 35J92, 35B20 ,Boundary (topology) ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Type (model theory) ,Domain (mathematical analysis) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Mathematics - Analysis of PDEs ,Bounded function ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,p-Laplace equations ,Morse theory ,perturbation results ,critical groups ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let us consider the quasilinear problem \[ (P_\varepsilon) \ \ \left\{ \begin{array}{ll} - \varepsilon^p \Delta _{p}u + u^{p-1} = f(u) & \hbox{in} \ \Omega \newline u>0 & \hbox{in} \ \Omega \newline u=0 & \hbox{on} \ \partial \Omega \end{array} \right. \] where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary, $N\geq 2$, $1< p < 2$, $\varepsilon >0$ is a parameter and $f: \mathbb{R} \to \mathbb{R}$ is a continuous function with $f(0)=0$, having a subcritical growth. We prove that there exists $\varepsilon^* >0$ such that, for every $\varepsilon \in (0, \varepsilon^*)$, $(P_\varepsilon)$ has at least $2{\mathcal P}_1(\Omega)-1$ solutions, possibly counted with their multiplicities, where ${\mathcal P}_t(\Omega)$ is the Poincar\'e polynomial of $\Omega$. Using Morse techniques, we furnish an interpretation of the multiplicity of a solution, in terms of positive distinct solutions of a quasilinear equation on $\Omega$, approximating $(P_\varepsilon)$., Comment: to be published in "Communications in Contemporary Mathematics"
- Published
- 2023
44. Decision model to identify the optimum retaining wall type for restricted highway projects sites
- Author
-
Ibrahim M. Mahdi, Hisham Arafat, Ahmed M. Ebid, and Anwar F. El-Kadi
- Subjects
Computer science ,Management of Technology and Innovation ,Strategy and Management ,Building and Construction ,Type (model theory) ,Retaining wall ,Decision model ,Civil engineering - Abstract
Choosing the suitable soil retaining system is the key to optimizing the design of the restricted sites highway projects. Many parameters are involved in identifying the optimum choice. This research approaches a decision support system (DSS) to determine the level of suitability of each alternative in order to identify the most optimal choice. In this approach, an integration of the value engineering (VE) hypothesis with the analytical hierarchy process (AHP) is implemented to form the DSS to determine the relative importance of the factors affecting selection. This research includes four of the most applied retaining wall types: cemented sand, stone gravity wall, RC cantilever wall and the mechanically stabilized wall (MSW). The developed DSS was verified via four case studies of highway projects in the construction stage. In three out of the four case studies, the optimal choice was in accordance with the proposed DSS. The research also showed that fully slopped embankments are the optimum choice for unrestricted sites up to a certain land cost, beyond which fully retained embankments became the optimum choice.
- Published
- 2023
- Full Text
- View/download PDF
45. Regional Controllability for Caputo Type Semi-Linear Time-Fractional Systems
- Author
-
Ali Boutoulout, Asmae Tajani, and Fatima Zahrae El Alaoui
- Subjects
Controllability ,Matematik ,Pure mathematics ,Regional Controllability,Fractional Calculus,Caputo Time-Fractional Systems,Fixed PointTheorems,HUM Approach,Compact Operators ,Applied Mathematics ,Fixed-point theorem ,Type (model theory) ,Compact operator ,Time complexity ,Mathematics ,Analysis ,Fractional calculus - Abstract
The main purpose of this paper, is to study the regional controllability concept of a semi-linear time-fractionaldiffusion systems involving Caputo derivative of order α ∈ (0,1). The main result is obtained by using anextension of the Hilbert Uniqueness Method (HUM) in addition to a fixed point technique and under severalassumptions on the data of the considered equation. At the end, some numerical simulations are given toillustrate the efficiently of our result.
- Published
- 2022
46. Combination of Concave and Convex Paraboloids: Theoretical Model of New-type Daylighting System
- Author
-
Yusuke Tsuji and Hirotaka Suzuki
- Subjects
Mathematical optimization ,Regular polygon ,Type (model theory) ,Daylighting ,Mathematics - Published
- 2022
47. Bayesian Risk With Bregman Loss: A Cramér–Rao Type Bound and Linear Estimation
- Author
-
H. Vincent Poor, Michael Fauss, and Alex Dytso
- Subjects
Linear estimation ,Applied mathematics ,Library and Information Sciences ,Type (model theory) ,Bayesian risk ,Cramér–Rao bound ,Computer Science Applications ,Information Systems ,Mathematics - Published
- 2022
48. An Equivalent Circuit/System by Design Approach to the Design of Reflection-Type Dual-Band Circular Polarizers
- Author
-
Luigi Boccia, Andrea Massa, Giandomenico Amendola, Emilio Arnieri, Francesco Greco, and Marco Salucci
- Subjects
Physics ,Optics ,business.industry ,law ,Reflection (physics) ,Equivalent circuit ,Multi-band device ,Electrical and Electronic Engineering ,Polarizer ,Type (model theory) ,business ,law.invention - Published
- 2022
49. Generalization of Darbo-type theorem and application on existence of implicit fractional integral equations in tempered sequence spaces
- Author
-
Syed Abdul Mohiuddine, Anupam Das, Abdullah Alotaibi, and Bhuban Chandra Deuri
- Subjects
47H08 ,Pure mathematics ,Sequence ,Work (thermodynamics) ,Generalization ,45G15 ,General Engineering ,Type (model theory) ,Fixed point ,Engineering (General). Civil engineering (General) ,Measure (mathematics) ,Integral equation ,Sequence space ,TA1-2040 ,46B45 ,47H10 ,Mathematics - Abstract
The aim of this work is to give some fixed point results based on the technique of measure of noncompactness which extend the classical Darbo’s theorem. With the help of our Darbo-type theorem, we obtain the existence of solution of implicit fractional integral equations in C ( I , l p α ) (collection of all continuous functions from I = [ 0 , a ] ( a > 0 ) to l p α ), where l p α is a tempered sequence space. Finally, we present a numerical example to see the validity and practicability of our existence result.
- Published
- 2022
50. Effects of lossy mediums for resonator-coupled typewireless power transfer system using conventional single- and dual-spiral resonators
- Author
-
Nur Syafiera Azreen Norodin, Masashi Hotta, and Kousuke Nakamura
- Subjects
Physics ,business.industry ,wireless power transfer ,power transmission efficiency ,spiral resonator ,Lossy compression ,Type (model theory) ,electromagnetic coupling ,Electronic, Optical and Magnetic Materials ,Dual (category theory) ,Resonator ,Optoelectronics ,Wireless power transfer ,Electrical and Electronic Engineering ,Spiral (railway) ,business ,lossy mediums - Abstract
To realize a stable and efficient wireless power transfer (WPT) system that can be used in any environment, it is necessary to inspect the influence of environmental interference along the power transmission path of the WPT system. In this paper, attempts have been made to reduce the influence of the medium with a dielectric and conductive loss on the WPT system using spiral resonators for resonator-coupled type wireless power transfer (RC-WPT) system. An important element of the RC-WPT system is the resonators because they improve resonant characteristics by changing the shape or combination of spiral resonators to confine the electric field that mainly causes electrical loss in the system as much as possible inside the resonator. We proposed a novel dual-spiral resonator as a candidate and compared the basic characteristics of the RC-WPT system with conventional single-spiral and dual-spiral resonators. The parametric values of the spiral resonators, such as the quality factors and the coupling coefficients between resonators with and without a lossy medium in the power transmission path, were examined. For the lossy mediums, pure water or tap water filled with acryl bases was used. The maximum transmission efficiency of the RC-WPT system was then observed by tuning the matching condition of the system. Following that, the transmission efficiency of the system with and without lossy medium was investigated. These inspections revealed that the performance of the RC-WPT system with the lossy medium using the modified shape spiral resonator, which is the dual-spiral resonator proposed in our laboratory, outperformed the system using the conventional single-spiral resonator.
- Published
- 2022
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