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‎This paper addresses the problem of optimizing the reconstruction of links in a network in the aftermath of natural disasters or human errors‎, ‎such as landslides‎, ‎floods‎, ‎storms‎, ‎earthquakes‎, ‎bombing‎, ‎war‎, ‎etc‎. We aim to determine the optimal sequence for reconstructing the destroyed links within a specific time horizon, while simultaneously locating ‎‎(k)‎‎ portable emergency service centers (where ‎‎(k > 2) throughout the entire network. ‎In this paper‎, ‎the problem is considered in a tree structure‎. ‎A greedy algorithm and a heuristic method‎, ‎namely‎, ‎maximum radius‎, ‎are proposed to solve the problem‎. ‎We evaluate the performance of the proposed algorithms using randomly generated data‎. ‎The experimental results confirm the effectiveness of the proposed methods‎.

In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one. As the hyper-order is a crucial parameter that characterizes the growth of entire functions, it will be interesting to investigate this unexplored domain, as far as practible, with certain restriction on hyper order. Our results are the improvements of previous results reported in recent papers [12], [13]. We have provided a series of examples to demonstrate and validate the effectiveness of our proposed solutions.

In the paper industry, numerous studies have explored means of optimizing order allocation and cutting trim loss. However, enterprises may not adopt the resulting solutions because some widths of the inventory exceed or are less than those required for acceptable scheduling. To ensure that the results better suit the actual requirements, we present a new decision model based on the adjustment of scheduling and limitation of inventory quantity to differentiate trim loss and inventory distribution data. Differential analysis is used to reduce data filtering and the information is valuable for decision making. A numerical example is presented to illustrate the applicability of the proposed method. The results show that our proposed method outperforms the manual method regarding scheduling quantity and trim loss.

We improve a result in Silverman's paper (1999) and answer a question he posed. We also consider a similar problem and obtain sufficient conditions for starlikeness.

In 1997, J. A. Fridy gave conditions for noninclusion of ordinary and of absolute summability domains. In the present note, these conditions are interpreted in a natural topological context thus giving new proofs and also explaining why one of these conditions is too weak. Also an open question posed in Fridy's paper is answered.

Recommender systems are widely used in today’s world as they narrow down a huge number of options for a user in various fields. These recommender systems can also be significantly used by cab drivers also, since they can recommend the nearest location of passengers waiting for a cab. For the system to perform better, cluster formation is an essential step to be performed using the pick-up locations of the cab provided in the historical data. The recommendation is highly dependent on various other parameters also like timestamp, density of the area, clustering technique used, etc. This research paper aims to analyze the impact of varying minimum density of the pick-up data points on the accuracy of the recommendations by Clustering Based Cab Recommender System (CBCRS). Therefore, the research paper has a threefold objective: Firstly, to identify different clustering techniques for clustering the pickup locations. Secondly, the research paper proposes the design and development of a framework for CBCRS to cluster the cab pick-up data points along with recommending the nearest pick-up location of passengers to the cab drivers. Finally, the paper analyzes and evaluates the accuracy of CBCRS recommendation across varying densities of the pick-up data points as compared to the Partition-based Clustering Method, Density-based Clustering Method and Hierarchical Clustering Methods.

Assume that [Formula: see text] is a random variable whose moment generating function exists in a neighbourhood of the origin. In this paper, we study the probabilistic degenerate central Bell polynomials associated with [Formula: see text], as probabilistic extension of the degenerate central Bell polynomials. In addition, we investigate the probabilistic degenerate central factorial numbers of the second kind associated with [Formula: see text] and the probabilistic degenerate central Fubini polynomials associated with [Formula: see text]. The aim of this paper is to derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers.

In this paper, we solve the difference equation xn+1 = α xnxn-1 - 1 , n = 0, 1, . . . , where α > 0 and the initial values x-1, x0 are real numbers. We find some invariant sets and discuss the global behavior of the solutions of that equation. We show that when α > 2 3 √ 3 , under certain conditions there exist solutions, that are either periodic or converging to periodic solutions. We show also the existence of dense solutions in the real line. Finally, we show that when α < 2 3 √ 3 , one of the negative equilibrium points attracts all orbits with initials outside a set of Lebesgue measure zero.

Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency in particular are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in non-smooth dynamical systems is of the special scientists’ interest. In this paper we study the type-III intermittency route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We apply relatively new mathematical tool – continuous wavelet transform CWT – for investigation this phenomenon. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate intermittency route to chaos, to distinguish and analyze the laminar and turbulent phases.

The gap between software design and implementation often results in a lack of clarity and precision. Formal languages, based on mathematical rules, logic, and symbols, are invaluable for specifying and verifying system designs. Various semi-formal and formal languages, such as JSON, XML, predicate logic, and regular expressions, along with formal models like Turing machines, serve specific domains. This paper introduces a new specification formal language, ObTFL (Object Transaction Formal Language), developed for general-purpose distributed systems, such as specifying the interactions between servers and IoT devices and their security protocols. The paper details the syntax and semantics of ObTFL and presents three real case studies—federated learning, blockchain for crypto and bitcoin networks, and the industrial PCB board with machine synchronization—to demonstrate its versatility and effectiveness in formally specifying the interactions and behaviors of distributed systems.

Scholars of English Literature unanimously say that J.R.R. Tolkien influenced C.S. Lewis’s writings. For the first time, we have investigated this issue mathematically by using an original multi-dimensional analysis of linguistic parameters, based on surface deep language variables and linguistic channels. To set our investigation in the framework of English Literature, we have considered some novels written by earlier authors, such as C. Dickens, G. MacDonald and others. The deep language variables and the linguistic channels, discussed in the paper, are likely due to writers’ unconscious design and reveal connections between texts far beyond the writers’ awareness. In summary, the capacity of the extended short-term memory required to readers, the universal readability index of texts, the geometrical representation of texts and the fine tuning of linguistic channels within texts—all tools largely discussed in the paper—revealed strong connections between The Lord of the Rings (Tolkien), The Chronicles of Narnia, The Space Trilogy (Lewis) and novels by MacDonald, therefore agreeing with what the scholars of English Literature say.

This paper explores the mathematical dynamics of consumer spending during a financial crisis using opponent process theory (OPT). Traditionally applied in psychology, OPT explains how initial emotional responses are followed by counteracting reactions to restore equilibrium. This study models the short-term boost in consumer spending and subsequent economic adjustments. Utilizing differential equations to represent these processes, this paper provides insights into the interplay between immediate policy effects and longer-term economic consequences. We focus on the United States (US) response to the 2008 Global Financial Crisis in this study. Results show evidence of diminishing response from prolonged stimuli due to demand saturation, resource allocation inefficiencies, and agent adaptation. Monetary stimuli may inflate debt/prices, outweighing benefits, and structural issues persist despite stimuli. Confidence and expectations impact response because perceived ineffectiveness weakens impact over time. Thus, while stimuli can initially boost activity, their sustained impact demands careful consideration of economic dynamics and agents’ responses.

Let $ R $ be a commutative ring with the identity $ 1_{R} $, and let $ R^* $ be the multiplicative group of units in $ R $. An element $ a\in R^* $ is called an exceptional unit if there exists a $ b\in R^* $ such that $ a+b = 1_{R} $. We set $ R^{**} $ to be the set of all exceptional units in $ R $. In this paper, we consider the residue-class ring $ \mathbb{Z}_n $. For any positive integers $ n, s $, and $ c\in\mathbb{Z}_n $, let $ {\mathcal N}_{s}(n, c): = \sharp\big\{(x_1, ..., x_s)\in (\mathbb{Z}_n^{**})^s : x_1+...+x_s\equiv c \pmod n\big\} $. In 2016, Sander (J.Number Theory 159 (2016)) got a formula for $ {\mathcal N}_{2}(n, c) $. Later on, Yang and Zhao (Monatsh. Math. 182 (2017)) extended Sander's theorem to finite terms by using exponential sum theory. In this paper, using matrix theory, we present an explicit formula for $ {\mathcal N}_{s}(n, c) $. This extends and improves earlier results.

The purpose of this paper is to solve the problem of the sharp estimation of the modulus of the third Taylor coefficient on the class of holomorphic bounded nonvanishing in the unit disk functions (hereafter referred to as the class of bounded nonvanishing functions). The problem of sharp estimation of the moduli of all Taylor coefficients depending on the coefficient number on this class is usually called the Krzyz problem. Consider the class of normalized holomorphic bounded functions in the unit disk (hereafter referred to as the class of bounded functions). The coefficient problem on this class is posed as follows: find the necessary and sufficient conditions to impose on a sequence of complex numbers so that the power series with coefficients from this sequence is the Taylor series of some function from the class of bounded functions. In this paper, by means of the solution of the coefficient problem for the class of bounded functions, we solve the problem of obtaining the sharp estimates of moduli of the first three Taylor coefficients on the class of bounded functions. It is pointed out that it is possible to visualize the first three coefficient bodies of the subclass of the class of bounded functions, consisting of functions with real coefficients. Next, we solve the problem of obtaining the sharp upper estimation of the modulus of the third Taylor coefficient on the class of bounded nonvanishing functions, by reducing it to the functional over the class of bounded functions. On the basis of the above-mentioned estimates on the class of bounded functions, it was possible to obtain a functional that majorizes the original one. The problem is then reduced to the problem of finding the conditional maximum of the function of three real variables with inequality-type constraints, which made it possible to apply standard methods of differential calculus to obtain this main result.

Neyman’s 1923 paper introduced the potential outcomes framework and the foundations of randomization-based inference. We discuss the influence of Neyman’s paper on four introductory to intermediate-level textbooks by Berkeley faculty members (Scheffé; Hodges and Lehmann; Freedman, Pisani, and Purves; and Dunning). These examples illustrate that Neyman’s key insights can be explained in intuitive and interesting ways to audiences at all levels, including undergraduates in introductory statistics courses. We have found Freedman, Pisani, and Purves’s box-of-tickets model to be a valuable expository tool, and we also find their intuitive explanation of Neyman’s variance result helpful: It is a “minor miracle” that in randomized experiments, the two-sample zz-test is conservative because of “two mistakes that cancel.” All four books take a more positive view of Neyman’s results than Neyman himself did. We encourage educators and researchers to explore ways to communicate Neyman’s ideas that are helpful for their own audiences.

This paper investigates rumor propagation in a multilingual environment, taking into account language usage variations. Firstly, a 2I2S2R model is proposed within a heterogeneous network framework that incorporates both immunologic and cross-transmitted mechanisms. Secondly, the paper calculates the basic reproduction number $ R_0 $ by the next-generation matrix method. Thirdly, the local asymptotic stability and the global asymptotic stability are further explored, which indicate that whether the rumor continuously spreads or becomes extinct is determined by the threshold. Finally, the numerical simulation and sensitivity analysis are given to illustrate the effectiveness of theoretical results and the influence of model parameters on rumor spreading.

Abstract In this paper we propose an algorithm for testing whether the independent observations come from finite-variance distribution. The preliminary knowledge about the data properties may be crucial for its further analysis and selection of the appropriate model. The idea of the testing procedure is based on the simple observation that the empirical cumulative even moment (ECEM) for data from finite-moments distribution tends to some constant whereas for data coming from heavy-tailed distribution, the ECEM exhibits irregular chaotic behavior. Based on this fact, in this paper we parameterize the regular/irregular behavior of the ECEM and construct a new test statistic. The efficiency of the testing procedure is verified for simulated data from three heavy-tailed distributions with possible finite and infinite variances. The effectiveness is analyzed for data represented in time domain. The simulation study is supported by analysis of real vibration signals from rotating machines. Here, the analyses are provided for data in both the time and time-frequency domains.

Thermal-aware virtual machine (VM) placement has emerged as a critically significant research domain in response to the escalating demand for energy-efficient and dependable cloud data centers. Addressing the imperative need for resource optimization and reduced energy consumption, the virtual machine placement problem seeks to strategically allocate VMs to physical servers while adhering to stringent thermal constraints. This paper intricately surveys the state-of-the-art techniques employed in thermal-aware VM placement, encompassing both static and dynamic approaches. Our comprehensive analysis delves into influential factors, including workload characteristics, server heterogeneity, and advanced thermal management techniques. By elucidating the intricacies of these considerations, our review offers a nuanced understanding of the complex VM placement landscape. Importantly, we spotlight key challenges and identify open research issues, presenting a roadmap for future investigations. This review paper stands as a pivotal resource, providing invaluable insights for researchers and practitioners navigating the evolving landscape of thermal-aware virtual machine placement in cloud data centers.

The aim of this paper is to introduce the cyclic-Fibonacci hybrid sequence and give some properties. By taking into account the cyclic-Fibonacci hybrid sequence modulo $m$, the method will be given to determine the period lengths of this sequence according to the different $m$ values. In the final part of this paper, we study the cyclic-Fibonacci hybrid sequence in groups and then we calculate the cyclic-Fibonacci hybrid lengths of polyhedral groups $(2,2,2)$, $(2,n,2)$ and $(n,2,2)$ as applications of the results produced.

In manufacturing industries, reliability analysis of cutting tools is of paramount importance, as their frequent failures may result in enhanced downtime of production lines, leading to reduced throughput, enhanced process cycle times, and low profits. There are numerous factors that govern the desired operations of cutting tools, e.g., tool cutting speed, feed, depth of cut, and many others. Existing literature on cutting tools’ reliability estimation emphasizes mainly three variables, as mentioned earlier while neglecting other important factors. Including a greater number of factors in the process of estimating reliability increases the number of covariates, hence rendering the data acquisition costlier and estimation models highly complex. This work initially utilizes Analytical Hierarchy Process (AHP) to assess the importance of various factors that are responsible for the cutting tool’s performance, followed by the reliability estimation of the cutting tools using proportional hazards model (PHM) considering the four “critical to reliability” factors as obtained through AHP as covariates. The proposed method also helps in determining the relationship of these sub-factors with the hazard rate and reliability of the cutting tools. Experimental results are then used to verify the model’s predictions through response surface methodology (RSM) and Weibull fit. Furthermore, the paper also presents a proposed technique to estimate the required number of cutting tools for one machine per day and the number of job completions that can be an essential takeaway for various industries. Thus, this research paper proposes an integrated AHP-RSM-PHM based approach for a comprehensive reliability analysis of cutting tools.

This paper investigates the complexities surrounding uncertain portfolio selection in cases where security returns are not well-represented by historical data. Uncertainty in security returns is addressed by treating them as uncertain variables. Portfolio selection models are developed using the quadratic-entropy of these uncertain variables, with entropy serving as a standard measure of diversification. Additionally, the study underscores the superior risk estimation accuracy of Average Value-at-Risk (AVaR) compared to variance. The research concentrates on the computational challenges of portfolio optimization in uncertain environments, utilizing the Mean-AVaR-Quadratic Entropy paradigm to meet investor requirements and assuage concerns. Two illustrative examples are provided to show the efficiency of the proposed models in this paper.

Devising a financial trading strategy that allows for long-term gains is a very common problem in finance. This paper aims to formulate a mathematically rigorous framework for the problem and compare and contrast the results obtained. The main approach considered is based on Dynamic Bayesian Networks (DBNs). Within the DBN setting, a long-term as well as a short-term trading strategy are considered and applied on twelve equities obtained from developed and developing markets. It is concluded that both the long-term and the medium-term strategies proposed in this paper outperform the benchmark buy-and-hold (B&H) trading strategy. Despite the clear advantages of the former trading strategies, the limitations of this model are discussed along with possible improvements.

The COVID-19 pandemic has affected all Sustainable Development Goals (SDGs), leading to setbacks in various Latin American countries. In Brazil, progress in technological development and the adoption of sustainable practices by organizations has been significantly hindered. Yet, there remains a limited understanding of the long-term impacts on the country’s development, and a structured national plan for recovery and resuming progress toward the SDGs is lacking. This paper aims to investigate the repercussions of COVID-19 on SDGs 9 (industry, innovation, and infrastructure) and 12 (sustainable consumption and production) in the context of a latecomer country such as Brazil. This study adopted the Delphi-based scenario and Fuzzy Delphi approach and involved the participation of 15 sustainability experts with extensive experience in the Brazilian industrial sector. The findings elucidate the long-term impacts of the pandemic on these SDGs, focusing on Brazil’s socioeconomic landscape and developmental challenges. The pandemic worsened pre-existing issues, hindering infrastructure modernization, technological investment, and sustainable practices. Insufficient research funding, industry modernization, and small business integration further impede progress. Additionally, the paper identifies implications for research, companies, and public policies, aiming to provide actionable insights for fostering sustainable development in the post-pandemic era.

This research paper explores the behavior analysis of a repairable 2-out-of-4 system utilizing an evolutionary algorithm approach. The 2-out-of-4 system configuration is a critical setup widely employed in various engineering applications, necessitating thorough understanding and optimization for reliability and performance enhancement. By integrating evolutionary algorithms with system analysis, this paper aims to optimize system parameters, such as redundancy allocation and maintenance scheduling, to improve reliability and availability. The proposed methodology offers a novel approach to address the challenges associated with the complex behavior of repairable 2-out-of-4 systems, providing insights for system designers and engineers.

Cholera, as an endemic disease around the world, has imposed great harmful effects on human health. In addition, from a microscopic viewpoint, the interference of random factors exists in the process of virus replication. However, there are few theoretical studies of viral infection models with biologically reasonable stochastic effects. This paper studied a stochastic cholera model used to describe transmission dynamics in China. In this paper, we adopted a special method to simulate the effect of environmental perturbations to the system instead of using linear functions of white noise, i.e., the transmission rate of environment to human was satisfied Ornstein–Uhlenbeck processes, which is a more practical and interesting. First, it was theoretically proved that the solution to the stochastic model is unique and global, with an ergodic stationary distribution. Moreover, by solving the corresponding Fokker–Planck equation and using our developed algebraic equation theory, we obtain the exact expression of probability density function around the quasi-equilibrium of the stochastic model. Finally, several numerical simulations are provided to confirm our analytical results.

In this paper, our study is divided into two parts. The first part involves analyzing a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo derivatives. The also system incorporates the Caputo derivatives in the initial conditions, which adds a layer of complexity and realism to the problem. We focus on proving the existence of a unique solution for this system, and highlighting the robustness and applicability of fractional derivatives in modeling complex physical phenomena. In the second part of the paper, we employ conformable fractional derivatives, as defined by Khalil, to examine another system consisting of two coupled evolution equations. By the Tanh method, we derive new progressive waves. The connection between these two parts lies in the use of fractional calculus to extend and enhance classical problems.

Purpose – This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results. Design/methodology/approach – This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results. Findings – This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results. Originality/value – This article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

Purpose – This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results. Design/methodology/approach – This paper considered theoretical and numerical methodologies. Findings – This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures. Originality/value – The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

Purpose – Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L2α (K), where K=0,+∞×0,+∞[. Design/methodology/approach – The author has employed the results developed by Titchmarsh, of reference number [1]. Findings – In this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform. Originality/value – To the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.

Purpose – The aims of this paper is to prove that every semisimple Jordan algebra bundle is locally trivial and establish the decomposition theorem for locally trivial Jordan algebra bundles using the decomposition theorem of Lie algebra bundles. Design/methodology/approach – Using the decomposition theorem of Lie algebra bundles, this paper proves the decomposition theorem for locally trivial Jordan algebra bundles. Findings – Findings of this paper establish the decomposition theorem for locally trivial Jordan algebra bundles. Originality/value – To the best of the author’s knowledge, all the results are new and interesting to the field of Mathematics and Theoretical Physics community.

In the paper, we introduce a new class of noncyclic $\varphi$-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp\'{i}nola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic $\varphi$-contractions as a consequence of our main theorems.

The decision-making process for computational offloading is a critical aspect of mobile edge computing, and various offloading decision strategies are strongly linked to the calculated latency and energy consumption of the mobile edge computing system. This paper proposes an offloading scheme based on an enhanced sine-cosine optimization algorithm (SCAGA) designed for the "edge-end" architecture scenario within edge computing. The research presented in this paper covers the following aspects: (1) Establishment of computational resource allocation models and computational cost models for edge computing scenarios; (2) Introduction of an enhanced sine and cosine optimization algorithm built upon the principles of Levy flight strategy sine and cosine optimization algorithms, incorporating concepts from roulette wheel selection and gene mutation commonly found in genetic algorithms; (3) Execution of simulation experiments to evaluate the SCAGA-based offloading scheme, demonstrating its ability to effectively reduce system latency and optimize offloading utility. Comparative experiments also highlight improvements in system latency, mobile user energy consumption, and offloading utility when compared to alternative offloading schemes.

This paper is concerned with the periodic solutions for a coupled system of wave equations with x-dependent coefficients. Such a model arises naturally when two waves propagate simultaneously in the nonisotrpic media. In this paper, for the periods having the form T=2a−1b(a,bare positive integers) $T=\frac{2a-1}{b}\left(a,b \text{are\,positive\,integers}\right)$ and some types of boundary conditions, we obtain the existence of the time periodic solutions and analyze the asymptotic behaviors as the coupled parameter goes to zero, when the nonlinearities are superlinear and monotone, by using the variational method. In particular, the condition ess inf η ϱ(x) > 0 is not required.

This paper focused on the point-of-interest (POI) recommendation task. Recently, graph representation learning-based POI recommendation models have gained significant attention due to the powerful modeling capacity of graph structural data. Despite their effectiveness, we have found that recent methods struggle to effectively utilize information from POIs that have not been checked in, which could limit their performance. Hence, in this paper, we proposed a new model, named the multi-contextual graph contrastive learning (MCGCL) model, which introduces the contrastive learning into graph representation learning-based methods. First, MCGCL extracts interactions between POIs under different contextual factors from user check-in records using predefined graph structure information. Next, it samples important POI sets from different contextual factors using a random walk-based method. Then, it introduces a new contrastive learning loss that incorporates contextual information into traditional contrastive learning to enhance its ability to capture contextual information. Finally, MCGCL employs a graph neural network (GNN) model to learn representations of users and POIs. Extensive experiments on real-world datasets have demonstrated the effectiveness of MCGCL on the POI recommendation task compared to representative POI recommendation approaches.

This paper explores the synergy between fuzzy set theory and genetic algorithms in the domain of epidemic modeling, shedding light on the broader challenges inherent in infectious diseases. In response to the evolving landscape of epidemiology, the study advocates for sophisticated modeling techniques to better understand and predict dynamic scenarios. The research thoroughly investigates the global stability of equilibrium solutions within a fuzzy epidemic model, accompanied by an inventive parameter estimation methodology. Utilizing Lyapunov functions, the paper establishes global stability outcomes for both disease-free and endemic equilibria. The novel approach, integrating continued fraction theory and a genetic algorithm, is applied to fit real-world epidemic data, offering insights crucial for public health planning and control measures. By addressing unexplored facets and bridging gaps in previous research, the paper contributes to a more comprehensive understanding of epidemic dynamics, providing a foundation for effective public health strategies in the face of infectious diseases.

This paper explores the multifaceted world of IoT, exploring its historical evolution, core definitions, enabling technologies, architectural considerations, communication models and future predictions. Moreover, the paper critically scrutinises the potential benefits and challenges associated with IoT adoption. This study employed a systematic literature review (SLR) methodology to review existing literature between January 2020 and January 2024 on IoT technology. 20 relevant studies out of an initial pool of 45,312 studies were reviewed. The study followed the established Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) framework to ensure a rigorous and unbiased selection process. Findings revealed the lack of a universally accepted definition for IoT and significant variations in architectural models across scholarly works. Moreover, the study acknowledges the complex and ever-evolving nature of IoT technology, recognising its early stages of development. This dynamic technological landscape calls for continuous exploration of future research. Findings will provide valuable insights for academics, researchers, and industry professionals interested in the understanding the intricate technical landscape of IoT and its development. Moreover, by providing insights into growth predictions, benefits, and existing challenges, this will empower stakeholders to navigate the evolving IoT landscape and contribute to its future progress.

The strong geodetic number of a graph and its edge counterpart are recent variations of the pioneering geodetic number problem. Covering every vertex and edge of $ G $, respectively, using a minimum number of vertices and the geodesics connecting them, while ensuring that one geodesic is fixed between each pair of these vertices, is the objective of the strong geodetic number problem and its edge version. This paper investigates the strong geodetic number of the lexicographic product involving graph classes that include complete graph $ K_{m} $, path $ P_{m} $, cycle $ C_{m} $ and star $ K_{1, \, m} $ paired with $ P_{n} $ and with $ C_{n} $. Furthermore, the parameter is studied in the lexicographic product of, arbitrary trees with diameter-2 graphs whose geodetic number is equal to 2, $ K_{n}-e $ with $ K_{2} $ and their converses. Upper and lower bounds for the parameter are established for the lexicographic product of general graphs and in addition, the edge variant of the aforementioned problem is studied in certain lexicographic products. The strong geodetic parameters considered in this paper have pivotal applications in social network problems, thereby making them indispensable in the realm of graph theoretical research. This work contributes to the expansion of the current state of research pertaining to strong geodetic parameters in product graphs.

The study of Large Language Models (LLMs), as an interdisciplinary discipline involving multiple fields such as computer science, artificial intelligence, and linguistics, has diverse collaborations within its field. In this study, papers related to LLMs in the SSCI and SCI sub-collections of the Web of Science core database from January 2020 to April 2024 are selected, and a mixed linear regression model is used to assess the impact of scientific collaborations on the application of LLMs. On this basis, the paper further considers factors such as financial support and dominant countries to deeply explore the heterogeneous impact of scientific collaborations on the application of LLMs. The findings show that (1) excessive involvement of academic institutions limits the research and application of LLMs, and the number of authors does not have a significant effect on the application of LLMs; (2) with or without financial support, the role played by scientific collaborations in the application of LLMs does not significantly change; and (3) differences in the dominant countries of scientific collaborations have a slightly heterogeneous effect on the role of LLMs applications, which are mainly reflected in the number of collaborators.

This paper introduces a novel numerical scheme, the conformable finite difference method (CFDM), for solving time-fractional gas dynamics equations. The method was developed by integrating the finite difference method with conformable derivatives, offering a unique approach to tackle the challenges posed by time-fractional gas dynamics models. The study explores the significance of such equations in capturing physical phenomena like explosions, detonation, condensation in a moving flow, and combustion. The numerical stability of the proposed scheme is rigorously investigated, revealing its conditional stability under certain constraints. A comparative analysis is conducted by benchmarking the CFDM against existing methodologies, including the quadratic B-spline Galerkin and the trigonometric B-spline functions methods. The comparisons are performed using $ {L}_{2} $ and $ {L}_{\infty } $ norms to assess the accuracy and efficiency of the proposed method. To demonstrate the effectiveness of the CFDM, several illustrative examples are solved, and the results are presented graphically. Through these examples, the paper showcases the capability of the proposed methodology to accurately capture the behavior of time-fractional gas dynamics equations. The findings underscore the versatility and computational efficiency of the CFDM in addressing complex phenomena. In conclusion, the study affirms that the conformable finite difference method is well-suited for solving differential equations with time-fractional derivatives arising in the physical model.

The present paper dealt with the study of solitons of Lorentzian Kähler space-time manifolds. In this paper, we have discussed different conditions for solitons to be steady, expanding, or shrinking in terms of isotropic pressure, the cosmological constant, energy density, nonlinear equations, and gravitational constant in pseudo-quasi-conformally flat and pseudo-$ W_8 $ flat Lorentzian Kähler space-time manifolds.

The filled function method is a deterministic algorithm for finding a global minimizer of global optimization problems, and its effectiveness is closely related to the form of the constructed filled function. Currently, the filled functions mainly have three drawbacks in form, namely, parameter adjustment and control (if any), inclusion of exponential or logarithmic functions, and properties that are discontinuous and non-differentiable. In order to overcome these limitations, this paper proposed a parameter-free filled function that does not include exponential or logarithmic functions and is continuous and differentiable. Based on the new filled function, a filled function method for solving unconstrained global optimization problems was designed. The algorithm selected points in the feasible domain that were far from the global minimum point as initial points, and improved the setting of the step size in the stage of minimizing the filled function to enhance the algorithm's global optimization capability. In addition, tests were conducted on 14 benchmark functions and compared with existing filled function algorithms. The numerical experimental results showed that the new algorithm proposed in this paper was feasible and effective.

This research paper investigated weighted Milne-type inequalities utilizing Riemann-Liouville fractional integrals across diverse function classes. A key contribution lies in the establishment of a fundamental integral equality, facilitated by the use of a nonnegative weighted function, which is pivotal for deriving the main results. The paper systematically proved weighted Milne-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. The obtained results not only contribute to the understanding of Milne-type inequalities but also offer insights that pave the way for potential future research in the considered topics. Furthermore, it is evident that the results obtained encompass numerous findings that were previously presented in various studies as special cases.

Recently, Baktash et al. (2008) proved the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) and the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. In this note, we correct the proofs.

Researching different solutions of nonlinear models has been interesting in different fields of science and application. In this study, we investigated different solutions of fourth-order nonlinear Ablowitz– Kaup–Newell–Segur wave equation. We have used the sine-Gordon expansion method (SGEM) during this research. We have given the 2D, 3D, and contour graphs acquired from the values of the solutions obtained using strong SGEM.

We extend the Boltzmann’s ideas that describe the evolution to the equilibrium of many body systems to the multifractal decomposition of the unitary interval 𝕀, in terms of sets Jα conformed by points with the same pointwise dimension, and obtain the D(α) singularity spectrum.

We give an affirmative answer to the following question: are Mann and Ishikawa iterations equivalent under the assumptions that \(\lim_{n\rightarrow\infty }\alpha_{n}\neq0\;\) and \(\lim_{n\rightarrow\infty}\beta_{n}\neq0\)?

We give an affirmative answer to the following question: are Mann and Ishikawa iterations equivalent under the assumptions that \(\lim_{n\rightarrow\infty }\alpha_{n}\neq0\;\) and \(\lim_{n\rightarrow\infty}\beta_{n}\neq0\)?

In this note we show that a result previously obtained by us [An equivalence between the convergences of Ishikawa, Mann and Picard iterations, Math. Commun., 8, pp.~15--22, 2003], holds under weaker assumptions.

In this note we show that a result previously obtained by us [An equivalence between the convergences of Ishikawa, Mann and Picard iterations, Math. Commun., 8, pp.~15--22, 2003], holds under weaker assumptions.