Mathematics最新文献_第3页

Strong Convergence of Euler-Type Methods for Nonlinear Fractional Stochastic Differential Equations without Singular Kernel 无奇异核的非线性分式随机微分方程欧拉型方法的强收敛性

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-16 DOI: 10.3390/math12182890

Zakaria Ali, Minyahil Abera Abebe, Talat Nazir

引用次数: 0

Stochastic Differential Games and a Unified Forward–Backward Coupled Stochastic Partial Differential Equation with Lévy Jumps 随机微分博弈和带列维跳跃的统一前后耦合随机偏微分方程

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-16 DOI: 10.3390/math12182891

Wanyang Dai

{"title":"Stochastic Differential Games and a Unified Forward–Backward Coupled Stochastic Partial Differential Equation with Lévy Jumps","authors":"Wanyang Dai","doi":"10.3390/math12182891","DOIUrl":"https://doi.org/10.3390/math12182891","url":null,"abstract":"We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents {γ1,γ2,…} under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer 由 Maxwell-Cattaneo 热弹性层包裹的热弹性半空间中的瑞利波

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-16 DOI: 10.3390/math12182885

Stan Chiriţă, Ciro D’Apice

{"title":"Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer","authors":"Stan Chiriţă, Ciro D’Apice","doi":"10.3390/math12182885","DOIUrl":"https://doi.org/10.3390/math12182885","url":null,"abstract":"This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

HyperCLR: A Personalized Sequential Recommendation Algorithm Based on Hypergraph and Contrastive Learning HyperCLR：基于超图和对比学习的个性化序列推荐算法

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-16 DOI: 10.3390/math12182887

Ruiqi Zhang, Haitao Wang, Jianfeng He

{"title":"HyperCLR: A Personalized Sequential Recommendation Algorithm Based on Hypergraph and Contrastive Learning","authors":"Ruiqi Zhang, Haitao Wang, Jianfeng He","doi":"10.3390/math12182887","DOIUrl":"https://doi.org/10.3390/math12182887","url":null,"abstract":"Sequential recommendations aim to predict users’ next interactions by modeling their interaction sequences. Most existing work concentrates on user preferences within these sequences, overlooking the complex item relationships across sequences. Additionally, these studies often fail to address the diversity of user interests, thus not capturing their varied latent preferences effectively. To tackle these problems, this paper develops a novel recommendation algorithm based on hypergraphs and contrastive learning named HyperCLR. It dynamically incorporates the time and location embeddings of items to model high-order relationships in user preferences. Moreover, we developed a graph construction approach named IFDG, which utilizes global item visit frequencies and spatial distances to discern item relevancy. By sampling subgraphs from IFDG, HyperCLR can align the representations of identical interaction sequences closely while distinguishing them from the broader global context on IFDG. This approach enhances the accuracy of sequential recommendations. Furthermore, a gating mechanism is designed to tailor the global context information to individual user preferences. Extensive experiments on Taobao, Books and Games datasets have shown that HyperCLR consistently surpasses baselines, demonstrating the effectiveness of the method. In particular, in comparison to the best baseline methods, HyperCLR demonstrated a 29.1% improvement in performance on the Taobao dataset.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Properties of the Hyperbolic Distribution 论双曲线分布的性质

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-16 DOI: 10.3390/math12182888

Roman V. Ivanov

引用次数: 0

C-Semigroups and Their Induced Order C 族半群及其诱导有序

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-16 DOI: 10.3390/math12182889

Daniel Marín-Aragón, Raquel Tapia-Ramos

引用次数: 0

Applications of the Hahn-Banach Theorem, a Solution of the Moment Problem and the Related Approximation 哈恩-巴拿赫定理的应用、矩问题的解法及相关近似法

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-15 DOI: 10.3390/math12182878

Octav Olteanu

引用次数: 0

Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric 配备距离度量的有序集合中的定点定理和随机定点定理

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-15 DOI: 10.3390/math12182877

Himanshu Baranwal, Ravindra Kishor Bisht, Arya Kumar Bedabrata Chand, Jen-Chih Yao

引用次数: 0

Mathematical Formulations for Predicting Pressure Drop in Solid–Liquid Slurry Flow through a Straight Pipe Using Computational Modeling 利用计算建模预测固液浆液流经直管时压降的数学公式

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-15 DOI: 10.3390/math12182879

Tanuj Joshi, Abhinav Gupta, Om Parkash, Ralph Kristoffer B. Gallegos, Nay Lin Oo, Gopal Krishan

引用次数: 0

Multi-Type Self-Attention-Based Convolutional-Neural-Network Post-Filtering for AV1 Codec 用于 AV1 编解码器的基于卷积神经网络的多类型自注意后过滤技术

IF 2.4 3区数学

Mathematics Pub Date : 2024-09-15 DOI: 10.3390/math12182874

Woowoen Gwun, Kiho Choi, Gwang Hoon Park

{"title":"Multi-Type Self-Attention-Based Convolutional-Neural-Network Post-Filtering for AV1 Codec","authors":"Woowoen Gwun, Kiho Choi, Gwang Hoon Park","doi":"10.3390/math12182874","DOIUrl":"https://doi.org/10.3390/math12182874","url":null,"abstract":"Over the past few years, there has been substantial interest and research activity surrounding the application of Convolutional Neural Networks (CNNs) for post-filtering in video coding. Most current research efforts have focused on using CNNs with various kernel sizes for post-filtering, primarily concentrating on High-Efficiency Video Coding/H.265 (HEVC) and Versatile Video Coding/H.266 (VVC). This narrow focus has limited the exploration and application of these techniques to other video coding standards such as AV1, developed by the Alliance for Open Media, which offers excellent compression efficiency, reducing bandwidth usage and improving video quality, making it highly attractive for modern streaming and media applications. This paper introduces a novel approach that extends beyond traditional CNN methods by integrating three different self-attention layers into the CNN framework. Applied to the AV1 codec, the proposed method significantly improves video quality by incorporating these distinct self-attention layers. This enhancement demonstrates the potential of self-attention mechanisms to revolutionize post-filtering techniques in video coding beyond the limitations of convolution-based methods. The experimental results show that the proposed network achieves an average BD-rate reduction of 10.40% for the Luma component and 19.22% and 16.52% for the Chroma components compared to the AV1 anchor. Visual quality assessments further validated the effectiveness of our approach, showcasing substantial artifact reduction and detail enhancement in videos.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0