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We revisit two old and apparently little known papers by Basuev (Teoret Mat Fiz 37(1):130-134, , Teoret Mat Fiz 39(1):94-105, ) and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials, which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results (Yuhjtman in J Stat Phys 160(6): 1684-1695, ) on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas, which improves by a factor of the order 10 on the current best lower bound recently obtained in de Lima and Procacci (J Stat Phys 157(3):422-435, ). [ABSTRACT FROM AUTHOR]

In this paper, we present several remarks on the paper by Yao et al. (citeyearcite.nine). The results presented in the present paper are interesting improvements on the main results of Yao et al. [ABSTRACT FROM AUTHOR]

In this paper, we first point out a gap in Yang (2012). Next, strong convergence theorem for the common solution for a finite family of φ -strongly accretive operator equations in Banach spaces is established without any bounded assumption, and we also give an example to show universality of the result of this paper, which improve and extend some recent results. [ABSTRACT FROM AUTHOR]

It is pointed out that a general theorem presented in Yu Miao and Shoufang Xu's paper has a serious gap. In this small note, a counterexample for this theorem is provided exhibiting a triangular array of real numbers and a sequence of independent identically distributed random variables for which its conclusion fails. An reformulation of Yu Miao and Shoufang Xu's general theorem is performed making this statement true. [ABSTRACT FROM AUTHOR]

A multi-modal search space can be defined as having multiple attraction basins - each basin has a single local optimum which is reached from all points in that basin when greedy local search is used. Optimization in multi-modal search spaces can then be viewed as a two-phase process. The first phase is exploration in which the most promising attraction basin is identified. The second phase is exploitation in which the best solution (i.e. the local optimum) within the previously identified attraction basin is attained. The goal of thresheld convergence is to improve the performance of search techniques during the first phase of exploration. The effectiveness of thresheld convergence has been demonstrated through applications to existing metaheuristics such as particle swarm optimization and differential evolution, and through the development of novel metaheuristics such as minimum population search and leaders and followers. [ABSTRACT FROM AUTHOR]

In this paper, we consider the quasi-convex feasibility problem (QFP), which is to find a common point of a family of sublevel sets of quasi-convex functions. By employing the Bregman projection mapping, we propose a unified framework of Bregman quasi-subgradient methods for solving the QFP. This paper is contributed to establish the convergence theory, including the global convergence, iteration complexity, and convergence rates, of the Bregman quasi-subgradient methods with several general control schemes, including the a-most violated constraints control and the s-intermittent control. Moreover, we introduce a notion of the Hölder-type bounded error bound property relative to the Bregman distance for the QFP, and use it to establish the linear (or sublinear) convergence rates for Bregman quasi-subgradient methods to a feasible solution of the QFP. [ABSTRACT FROM AUTHOR]

This paper presents numerical methods for solving the one-dimensional fractional reaction-diffusion equation with the fractional Caputo derivative. The proposed methods are based on transformation of the fractional differential equation to an equivalent form of a integro-differential equation. The paper proposes an improvement of the existing implicit method, and a new explicit method. Stability and convergence tests of the methods were also conducted. [ABSTRACT FROM AUTHOR]

The RSA (Rivest–Shamir–Adleman) cryptosystem is an asymmetric public key cryptosystem popular for its use in encryptions and digital signatures. However, the Wiener's attack on the RSA cryptosystem utilizes continued fractions, which has generated much interest in developing competitive factoring algorithms. A general-purpose integer factorization method first proposed by Lehmer and Powers formed the basis of the well-known Continued Fraction Factorization (CFRAC) method. Recent work on the one line factoring algorithm by Hart and its connection with Lehman's factoring method have motivated this paper. The emphasis of this paper is to explore the representations of  P Q  as continued fractions and the suitability of lower ordered convergences as representations of  a b . These simpler convergences are then prescribed to Hart's one line factoring algorithm. As an illustration, we demonstrate the working of our approach with two numbers: one smaller number and another larger number occupying 95 bits. Using our method, the fourth convergence finds the factors as the solution for the smaller number, while the eleventh convergence finds the factors for the larger number. The security of the RSA public key cryptosystem relies on the computational difficulty of factoring large integers. Among the challenges in breaking RSA semi-primes, RSA250, which is an 829-bit semi-prime, continues to hold a research record. In this paper, we apply our method to factorize RSA250 and present the practical implementation of our algorithm. Our approach's theoretical and experimental findings demonstrate the reduction of the search space and a faster solution to the semi-prime factorization problem, resulting in key contributions and practical implications. We identify further research to extend our approach by exploring limitations and additional considerations such as the difference of squares method, paving the way for further research in this direction. [ABSTRACT FROM AUTHOR]

In this paper, we explore the numerical analysis of the microscale heat equation. We present the characteristics of numerical solutions obtained through both semi- and fully-discrete linear finite element methods. We establish a priori estimates and error bounds for both semi-discrete and fully-discrete finite element approximations. Additionally, the existence and uniqueness of the semi-discrete and fully-discrete finite element approximations have been confirmed. The study explores error bounds in various spaces, comparing the semi-discrete to the exact solutions, the semidiscrete against the fully-discrete solutions, and the fully-discrete solutions with the exact ones. A practical algorithm is introduced to address the system emerging from the fully-discrete finite element approximation at every time step. Additionally, the paper presents numerical error calculations to further demonstrate and validate the results. [ABSTRACT FROM AUTHOR]

This paper examines the concepts and practical applications of the spanning tree protocol (STP). It also covers per-VLAN spanning tree (PVST), multiple spanning tree (MST), and rapid STP (RSTP). Moreover, practical scenarios are presented to help the reader understand the concepts and implementations of these protocols. This study analyzes protocols using seven metrics. All protocols have been evaluated using these metrics in both small and big topology scenarios to obtain the best results. In addition, all metrics are mentioned in the introduction chapter, and the way used to apply tests on the metrics is described in the methodology chapter. Based on the experiments, different STPs performance are compared, including STP, RSTP, PVST, and MST. In summary, findings show that STP is easy to use and performs well overall, but it consistently has high latency issues. RSTP is suitable for small networks and has quick convergence, but it cannot handle as much load as STP. PVST performed the best in the experiments, as it demonstrated high scalability and the ability to handle a lot of pressure, although it requires strong hardware. However, MST did not perform as well as expected, as it struggled with delay problems and high jitter. In conclusion, it is recommended to use RSTP for simple networks that require fast convergence with dependable delay and capacity, or STP for networks that require good scaling and bandwidth. PVST is an excellent option for those who can afford high-performance hardware, while MST is suitable for simple networks or those with outdated hardware. [ABSTRACT FROM AUTHOR]

In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q -symmetric starlike and q -symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q -analogue Salagean integral operator, the p -valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p -valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ , q -neighborhoods for p -valent functions are defined. In relation to symmetric δ , q -neighborhoods of q -symmetric p -valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q -symmetric inequalities of analytic functions with negative coefficients is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). [ABSTRACT FROM AUTHOR]

Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors. Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid. The uncertain parameters mainly exist in the form of intervals. This method requires a lot of calculation and is often difficult to achieve efficiently. In order to solve this problem, this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty. Based on the non-probabilistic reliability index method, the extreme value of the limit state function is obtained using the properties of Bernstein polynomials, thus avoiding the need for a lot of sampling to solve the reliability analysis problem. The method is applied to numerical examples and engineering applications such as experiments, and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method, especially for some reliability problems with higher nonlinearity. Moreover, this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems. [ABSTRACT FROM AUTHOR]

Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas [Math. Progam. 1992] has inspired intensive attention in analyzing its theoretical convergence properties. This paper is devoted to the linear convergence rate of the semi-proximal GADMM (sPGADMM) for solving linearly constrained convex composite optimization problems. The semi-proximal terms contained in each subproblem possess the abilities of handling with multi-block problems efficiently. We initially present some important inequalities for the sequence generated by the sPGADMM, and then establish the local linear convergence rate under the assumption of calmness. As a by-product, the global convergence property is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a distributed interval optimization problem whose local functions are interval functions rather than scalar functions. Focusing on distributed interval optimization, this paper presents a distributed primal-dual algorithm. A criterion is introduced under which linear convergence to the Pareto solution of distributed interval optimization problems can be achieved without strong convexity. Lastly, a numerical simulation is presented to illustrate the linear convergence of the algorithm that has been proposed. [ABSTRACT FROM AUTHOR]

In this paper, we define a new area-type filter algorithm based on the trust-region method. A relaxed trust-region quadratic correction subproblem is proposed to compute the trial direction at the current point. Consider the objective function and the constraint violation function at the current point as a point pair. We divide the point pairs into different partitions by the dominant region of the filter and calculate the contributions of the point pairs to the area of the filter separately. Different from the conventional filter, we define the contribution as the filter acceptance criterion for the trial point. The nonmonotone area-average form is also adopted in the filter mechanism. In this paper, monotone and nonmonotone methods are proposed and compared with the numerical values. Furthermore, the algorithm is proved to be convergent under some reasonable assumptions. The numerical experiment shows the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Source localization is widely used in many areas including GPS, but the influence of possible noises cannot be overlooked. Many optimization methods have been attempted to mitigate different kinds of noises. However, the stability of the solution, even the number of global solutions, is not fully known. Only local convergence or stability for the optimization problem is known in simple L1 or L2 settings. In this paper, we prove that the number of possible two‐dimensional source locations with three measurements in L2 setting is at most 5. We also showed the sufficient and necessary condition for the number of the solutions being 1, 2, 3, 4, and 5, where the measurement triangle is isosceles and the measurement distance for the two isosceles triangles is the same. [ABSTRACT FROM AUTHOR]

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system's state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a novel group self-supervised learning approach designed to improve visual representation learning. This new method aimed to rectify the limitations observed in conventional self-supervised learning. Traditional methods tended to focus on embedding distortion-invariant in single-view features. However, our belief was that a better representation can be achieved by creating a group of features derived from multiple views. To expand the siamese self-supervised architecture, we increased the number of image instances in each crop, enabling us to obtain an average feature from a group of views to use as a distortion, invariant embedding. The training efficiency has greatly increased with rapid convergence. When combined with a robust linear protocol, this group self-supervised learning model achieved competitive results in CIFAR-10, CIFAR-100, Tiny ImageNet, and ImageNet-100 classification tasks. Most importantly, our model demonstrated significant convergence gains within just 30 epochs as opposed to the typical 1000 epochs required by most other self-supervised techniques. [ABSTRACT FROM AUTHOR]

In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish convergence and stability of Jungck -modified three-step iterations for three nonself mappings in a Banach space. The results obtained in this paper extend and improve the recent ones announced by Khan et al., Olatinwo, Hussain et al. and many papers. [ABSTRACT FROM AUTHOR]

The authors study the complete convergence and complete moment convergence for weighted sums of m-extended negatively dependent (m-END) random variables. The results obtained in this paper extend and improve the corresponding results of Wu, Zhai and Peng [Y. F. Wu, M. Q. Zhai and J. Y. Peng, On the complete convergence for weighted sums of extended negatively dependent random variables, Journal of Mathematical Inequalities, 13 (1) (2019), 251–260] and Zarei and Jabbari [H. Zarei and H. Jabbari, Complete convergence of weighted sums under negative dependence, Statistical Papers, 52 (2011), 413–418]. [ABSTRACT FROM AUTHOR]

In 1989, Bakhtin proved a version of the Banach contraction principle in the context of b-metric spaces. More precisely, let (X, d; s) be a complete b-metric space with parameter s ⩾ 1 and let T a contractive map on X, that is a self-map T of X satisfying d(Tx, Ty) ⩽ λd(x, y), ∀x, y ∈ X, (Bλ) with some λ ∈ [0, 1). Bakhtin proved that if λ ∈ [0, 1 s), then T has a unique fixed point. In the two last decades many research papers were produced by many authors in the setting of b-metric spaces. In 2021, the author published a note on the Banach contraction principle in b-metric spaces in Divilgaciones Mat'ematicas dealing with some complements to Bakhtin results. The aim of this paper is to provide other complements. In particular, we discuss the remaining case where λ ∈ [1 s, 1). We give an evaluation of the order of convergence for the iterative Picard process and a posteriori error estimate for this process and we estimate the diameter of the T-orbits. We investigate well-posedness of the fixed problem of a map T satisfying Bλ when X is Torbitally complete and we establish two shadowing properties for these maps without requiring completeness of X. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalization of a recent result of Tam (2018) which is for iterates of a set-valued paracontracting operators in a finite-dimensional space. Our result in this paper is obtained for operators in a metric space such that every its bounded and closed set is compact. We establish a convergence of inexact iterates of the set-valued operator by taking into account computational errors. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new class of variational inequalities involving two operators, which is called the general variational inequality. We have shown that the general variational inequalities are equivalent to the fixed point problem using the projection technique. This equivalent fixed point formulation is used to discuss the existence of solution as well as to investigate several iterative methods for solving general variational inequalities. Some applications of the associated dynamical system coupled with finite difference are explored. Convergence analysis of the proposed methods is considered under suitable conditions. Since general variational inequalities include the variational inequalities, complementarity problems and nonlinear equations as special cases, our results continued to hold for these problems. The techniques and ideas of this paper be starting point for the future research. [ABSTRACT FROM AUTHOR]

This paper introduces a variant version of the Aquila Optimizer (AO) for efficiently solving high-dimensional computationally expensive problems. Traditional optimization techniques struggle with problems characterized by expensive objective functions and a large number of variables. To address this challenge, this paper proposes a Surrogate Model-based Aquila Optimizer (SMAO) that leverages machine learning techniques to approximate the objective function. SMAO utilizes Radial Basis Functions (RBFs) to build an accurate and efficient surrogate model. By iteratively optimizing the surrogate model, the search process is directed toward the global optimum while significantly reducing the computational cost compared to traditional optimization methods. To evaluate and compare the performance of SMAO with the surrogate model-based versions of the Gazelle Optimization Algorithm Gazelle Optimization Algorithm (GOA), Reptile Search Algorithm (RSA), Prairie Dog Optimization (PDO), and Fick's Law Optimization Algorithm (FLA), they are analyzed on a set of benchmark test functions with dimensions varying from 30 to 200. According to the reported results, SMAO has a higher performance compared to others in terms of achieving the nearest solutions to an optimum, early convergence, and accuracy. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the strong Cesaro summability of difference sequence spaces through fusion of modulus function. On the newly established sequence space, linear structure is imposed and a paranorm is established. Apart from various inclusion relations, a new variant of statistical convergence is investigated. [ABSTRACT FROM AUTHOR]

The analysis of oscillatory properties of fractional circuits is still an open problem due to the multi-valuedness and non-locality of fractional operators. In this paper, the complex path integral approach is applied to achieve the impulsive response of fractional order RLCα circuit, which possesses the advantages of high precision and fast convergence as well as providing a novel way to the theoretical analysis of fractional order RLCα circuit. On this basis, the order dependent oscillation criterion (critical damping criterion) for fractional order RLCα circuit is successfully solved by adopting dimensionless analysis, and verified by the above proposed high accurate algorithm. Lastly, two examples are provided to validate and to show the advantages of the above conclusions. It should be highlighted that the approaches and conclusions of this paper are important supplements to the fractional order equivalent circuit modellings, and have important application values in engineering, viscoelastic materials and some other fields. [ABSTRACT FROM AUTHOR]

Slope instability issues could cause severe damage and endanger the population, especially when dams are concerned. Over the past years, more and more refined numerical approaches have been proposed to evaluate the slope stability. However, a criterion based on the lack of numerical convergence is generally considered to compute the safety factor with this kind of approaches, which may result in a dramatic increase in the overall computation time for the probabilistic assessment of the safety factor (e.g., using Monte Carlo simulations that require the automation of a large number of simulations). This paper proposes an original approach coupling the shear strength reduction technique with the second-order work criterion. This approach is implemented in the open finite element software Cast3M, version 22.0. The relevance and efficiency of the developed approach is illustrated with two case studies: a heuristic slope and an existing earth dam. Safety factors similar to those calculated by classical approaches are obtained, but without pushing the calculation to the point of non-convergence. Among other advantages described in the paper, the proposed approach makes it possible to compute safety factors using a rational and physically based criterion, while facilitating probabilistic calculations. [ABSTRACT FROM AUTHOR]

Addressing the challenges posed by pollutants is necessary to achieve the Sustainable Development Goals (SDGs) target 12 or achieve sustainable production and consumption patterns. Convergence assessment of air pollution provides information which can be beneficial to how to handle that air pollution across different countries. Nitrogen oxides (NOx) are one of the most popular air pollutants. However, the current empirical literature on environmental economics largely ignores the convergence of per capita NOx. For this reason, this study investigates the stochastic convergence of aggregate and fuel-specific per capita NOx emissions in 20 OECD countries. This paper employs a recently introduced panel stationarity test that considers both smooth and sharp structural changes in the data generation process. The panel results show that the convergence hypothesis is rejected only for NOx from light-oil consumption. However, country-specific results reveal substantial evidence for divergence in the sample countries when NOx emissions per capita generated through diesel consumption, light-oil consumption, and natural gas consumption are considered. Besides, we find that most of the series have convergent behaviour for aggregate NOx, NOx from biomass consumption, NOx from hard-coal consumption, NOx from heavy-oil consumption, and NOx from the process. The policy implications of the empirical results for proper environmental management are elucidated in the paper. Actions taken based on the convergence findings will likely lead to a decrease in NOx emissions per capita as the countries will converge towards a lower level of NOx emissions per capita, in line with SDG's target 12. [ABSTRACT FROM AUTHOR]

In this paper, the exponential convergence of delayed inertial Cohen-Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results. [ABSTRACT FROM AUTHOR]

Over the last-decade, global scale datasets of atmospheric water vapor isotopologues (HDO) have become available from different remote-sensing instruments. Due to the observational geometry and the spectral ranges that are used, only few satellites sample water isotopologues in the lower troposphere, where the bulk of hydrological processes within the atmosphere take place. Here, we compare three satellite HDO datasets, two from the Tropospheric Emission Spectrometer (TES retrieval version 4 and 5) and one from SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY), with results from the atmospheric global circulation model ECHAM4 (European Center HAMburg 4). We examine a list of known isotopologue effects to qualitatively benchmark the various observational datasets. TES version 5 (TESV5), TES version 4 (TESV4), SCIAMACHY, ECHAM, and ECHAM convoluted with averaging kernel of TES version 5 (ECHAMAK5) successfully reproduced a number of established isotopologue effects such as the latitude effect, the amount effect, and the continental effect, but to different extent. The improvement of TES version 5 over version 4 was confirmed by the steeper latitudinal gradient at higher latitudes in agreement with SCIAMACHY. Other features of the water isotopologue cycle such as the seasonally varying signal in the tropics due to the movement of the Inter Tropical Convergence Zone (ICTZ) are captured in TESV5 and SCIAMACHY. We suggest that the qualitative and quantitative tests carried out in this study could become benchmark tests for evaluation of future satellite isotopologue datasets. [ABSTRACT FROM AUTHOR]

This paper discusses the asymptotic behavior of the stochastic evolutionary system under the Markov-modulated Poisson perturbations in an averaging schema. Such a perturbation process combines the Poisson process with the Markov process that modulates the intensity of jumps. This allows us to model systems with transitions between different modes or rare but significant jumps. Initially, the asymptotic properties of the Markov-modulated Poisson perturbation are investigated. For this purpose, we build the generator for the limit process solving the singular perturbation problem for the original process. Then we introduce a compensated Poisson process with a zero mean value, and it is used to center the jumps. The stochastic evolutionary system perturbed by the compensated Poisson process with an additional jump size function is described. We build the generator for an evolution process and investigate its asymptotic properties. Solving the singular perturbation problem we obtain the form of the limit process and its generator. This allows us to formulate and prove the theorem about weak convergence of the evolution process to the averaged one. The limit process for the stochastic evolutionary system at increasing time intervals is determined by the solution of a deterministic differential equation. The obtained result makes it possible to study the rate of convergence of the perturbed process to the limit one, as well as to consider stochastic approximation and optimization procedures for problems in which the system is described by an evolutionary equation with the Markov-modulated Poisson perturbation. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive synchronization of a class of nonlinear multiple neural networks (MNNs) with multi-delays was considered under a dynamic event-based mechanism. To achieve a more comprehensive synchronization outcome and mitigate the conservativeness of impulsive control due to predetermined time sequences, we integrated a dynamic event-triggered strategy. This approach formed a novel control framework for generalized MNNs, where impulsive inputs were applied only under specific conditions governed by event-triggering rules. Towards the above objectives, the impulsive jumping system, resulting from dynamic component, and matrix measure method were invoked to directly increase the computational simplicity and extensibility of the study. As the outcome, the synchronization criteria for the MNNs could be achieved, and the exponential convergence rate is resolved by considering both the generalized comparison principle regarding impulsive systems and the variable parameter formula. Moreover, Zeno-freeness of the achieved triggering regulation is ensured. Finally, two numerical examples confirmed the validity of the designed approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behaviour of a family of random free-discontinuity energies E ε defined in a randomly perforated domain, as ε goes to zero. The functionals E ε model the energy associated to displacements of porous random materials that can develop cracks. To gain compactness for sequences of displacements with bounded energies, we need to overcome the lack of equi-coerciveness of the functionals. We do so by means of an extension result, under the assumption that the random perforations cannot come too close to one another. The limit energy is then obtained in two steps. As a first step, we apply a general result of stochastic convergence of free-discontinuity functionals to a modified, coercive version of E ε . Then the effective volume and surface energy densities are identified by means of a careful limit procedure. [ABSTRACT FROM AUTHOR]

This paper aims to extend a Krylov subspace technique based on an incomplete orthogonalization of Krylov tensors (as a multidimensional extension of the common Krylov vectors) to solve generalized Sylvester tensor equations via the Einstein product. First, we obtain the tensor form of the quasi-GMRES method, and then we lead to the direct variant of the proposed algorithm. This approach has the great advantage that it uses previous data in each iteration and has a low computational cost. Moreover, an upper bound for the residual norm of the approximate solution is found. Finally, several experimental problems are given to show the acceptable accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, a singularly perturbed one-dimensional initial boundary value problem of a quasilinear Sobolev-type equation is presented. The nonlinear term of the problem is linearized by Newton's linearization method. Time derivatives are discretized by implicit Euler's method on nonuniform step size. A uniform trigonometric B-spline collocation method is used to treat the spatial variable. The convergence analysis of the scheme is proved, and the accuracy of the method is of order two in space and order one in time direction, respectively. To test the efficiency of the method, a model example is demonstrated. Results of the scheme are presented in tabular, and the figure indicates the scheme is uniformly convergent and has an initial layer at t = 0. [ABSTRACT FROM AUTHOR]

Robust approach is a special scalarization method to deal with multiobjective optimization problems in the worst-case. In this paper, we propose a new non-monotone gradient type algorithm for solving unconstrained multiobjective optimization problems by the conjugate technique and the robust approach. The proposed method has a memory gradient property since the search direction is constructed by using the current descent direction and the past multi-step iterative descent directions. For this, the search direction is called a memory gradient search direction. The step-size is computed by the non-monotone linear search. A lower bound of the stepsize is presented under some mild conditions. Then the iterative sequence generated by the proposed method is proved to be convergent to a Pareto critical point of the multiobjective optimization problem under some mild conditions. Numerical experiments are reported to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inexact projected gradient method equipped with a nonmonotone line search rule for smooth constrained multiobjective optimization. In this method, a new nonmonotone line search technique proposed here is employed and the relative errors on the search direction is admitted. We demonstrate that this method is well-defined. Then, we prove that each accumulation point of the sequence generated by this method is Pareto stationary and analyze the convergence rate of the algorithm. When the objective function is convex, the convergence of the sequence to a weak Pareto optimal point of the problem is established. [ABSTRACT FROM AUTHOR]

This paper studies the analytical solution to the Fractional Differential Equations (FDEs) under uncertainty. Fuzzy differential equations are one of the emerging topics in the present era of research, where we have found an effective combination of FDEs with fuzziness. The Homotopy Analysis Transform Method (HATM) with the Caputo fractional derivative is applied in this work to find the analytical fuzzy solution of two fuzzy FDEs. One of the interesting parts of this study is that we have found upper and lower fuzzy solutions for both fuzzy FDEs. The different graphical representations that have been presented for both examples show that there is a symmetry relation between the upper and lower-cut fuzzy solutions. In this method, the region and rate of convergence of the solution series are controlled by the auxiliary parameter r-cut. This paper shows that the proposed method is reliable and efficient in determining the fuzzy solutions of the FDEs in applied mathematics and engineering [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameterized three-operator splitting algorithm to solve nonconvex minimization problems with the sum of three non-convex functions, where two of them have Lipschitz continuous gradients. We establish the convergence of the proposed algorithm under the KurdykaŁojasiewicz assumption by constructing a suitable energy function with a non-increasing property. As applications, we employ the proposed algorithm to solve low-rank matrix recovery and image inpainting problems. Numerical results demonstrate the efficiency and effectiveness of the proposed algorithm compared to other algorithms. [ABSTRACT FROM AUTHOR]

The level-set subdifferential error bound (LSEB) is weaker than the Kurdyka-Łojasiewicz (KL) property and can replace it to establish linear convergence for various first-order algorithms. In this paper, we mainly study the behaviour of the level-set subdifferential error bound via Moreau envelopes under suitable assumptions. We provide an example that the Moreau envelope does not have the KL property but has the LSEB when the original function does not satisfy the KL property but only the LSEB. [ABSTRACT FROM AUTHOR]

Nowadays, textual information grows exponentially on the Internet. Text summarization (TS) plays a crucial role in the massive amount of textual content. Manual TS is time-consuming and impractical in some applications with a huge amount of textual information. Automatic text summarization (ATS) is an essential technology to overcome mentioned challenges. Non-negative matrix factorization (NMF) is a useful tool for extracting semantic contents from textual data. Existing NMF approaches only focus on how factorized matrices should be modeled, and neglect the relationships among sentences. These relationships provide better factorization for TS. This paper suggests a novel non-negative matrix factorization for text summarization (NMFTS). The proposed ATS model puts regularizes on pairwise sentences vectors. A new cost function based on the Frobenius norm is designed, and an algorithm is developed to minimize this function by proposing iterative updating rules. The proposed NMFTS extracts semantic content by reducing the size of documents and mapping the same sentences closely together in the latent topic space. Compared with the basic NMF, the convergence time of the proposed method does not grow. The convergence proof of the NMFTS and empirical results on the benchmark data sets show that the suggested updating rules converge fast and achieve superior results compared to other methods. [ABSTRACT FROM AUTHOR]

The vehicle routing problem with time windows (VRPTW) is a classical optimization problem. There have been many related studies in recent years. At present, many studies have generally analyzed this problem on the two-dimensional plane, and few studies have explored it on spherical surfaces. In order to carry out research related to the distribution of goods by unmanned vehicles and unmanned aerial vehicles, this study carries out research based on the situation of a three-dimensional sphere and proposes a three-dimensional spherical VRPTW model. All of the customer nodes in this problem were mapped to the three-dimensional sphere. The chimp optimization algorithm is an excellent intelligent optimization algorithm proposed recently, which has been successfully applied to solve various practical problems and has achieved good results. The chimp optimization algorithm (ChOA) is characterized by its excellent ability to balance exploration and exploitation in the optimization process so that the algorithm can search the solution space adaptively, which is closely related to its outstanding adaptive factors. However, the performance of the chimp optimization algorithm in solving discrete optimization problems still needs to be improved. Firstly, the convergence speed of the algorithm is fast at first, but it becomes slower and slower as the number of iterations increases. Therefore, this paper introduces the multiple-population strategy, genetic operators, and local search methods into the algorithm to improve its overall exploration ability and convergence speed so that the algorithm can quickly find solutions with higher accuracy. Secondly, the algorithm is not suitable for discrete problems. In conclusion, this paper proposes an improved chimp optimization algorithm (MG-ChOA) and applies it to solve the spherical VRPTW model. Finally, this paper analyzes the performance of this algorithm in a multi-dimensional way by comparing it with many excellent algorithms available at present. The experimental result shows that the proposed algorithm is effective and superior in solving the discrete problem of spherical VRPTW, and its performance is superior to that of other algorithms. [ABSTRACT FROM AUTHOR]

We study the existence and approximation of fixed points for the recently introduced class of mappings called enriched Suzuki nonexpansive mappings in the setting of Banach spaces. We use the modified K-iteration process to establish the main results of the paper. The class of enriched Suzuki nonexpansive operators is an important class of nonlinear operators that includes properly the class of Suzuki nonexpansive operators as well as enriched nonexpansive operators. Various assumptions are imposed on the domain or on the operator to establish the main convergence theorems. Eventually, a numerical example of enriched Suzuki nonexpansive operators is used to show the effectiveness of the studied iteration scheme. The main outcome of the paper is new and essentially suggests a new direction for researchers who are working on fixed point problems in a Banach space setting. Our results improve and extend some main results due to Hussain et al. [ABSTRACT FROM AUTHOR]

We explore coupling to a configurable subsurface reactive transport code as a flexible and extensible approach to biogeochemistry in land surface models; our goal is to facilitate testing of alternative models and incorporation of new understanding. A reaction network with the CLM-CN decomposition, nitrification, denitrification, and plant uptake is used as an example. We implement the reactions in the open-source PFLOTRAN code, coupled with the Community Land Model (CLM), and test at Arctic, temperate, and tropical sites. To make the reaction network designed for use in explicit time stepping in CLM compatible with the implicit time stepping used in PFLOTRAN, the Monod substrate rate-limiting function with a residual concentration is used to represent the limitation of nitrogen availability on plant uptake and immobilization. To achieve accurate, efficient, and robust numerical solutions, care needs to be taken to use scaling, clipping, or log transformation to avoid negative concentrations during the Newton iterations. With a tight relative update tolerance to avoid false convergence, an accurate solution can be achieved with about 50% more computing time than CLM in point mode site simulations using either the scaling or clipping methods. The log transformation method takes 60-100% more computing time than CLM. The computing time increases slightly for clipping and scaling; it increases substantially for log transformation for half saturation decrease from 10-3 to 10-9 mol m-3, which normally results in decreasing nitrogen concentrations. The frequent occurrence of very low concentrations (e.g. below nanomolar) can increase the computing time for clipping or scaling by about 20%; computing time can be doubled for log transformation. Caution needs to be taken in choosing the appropriate scaling factor because a small value caused by a negative update to a small concentration may diminish the update and result in false convergence even with very tight relative update tolerance. As some biogeochemical processes (e.g., methane and nitrous oxide production and consumption) involve very low half saturation and threshold concentrations, this work provides insights for addressing nonphysical negativity issues and facilitates the representation of a mechanistic biogeochemical description in earth system models to reduce climate prediction uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme for the integration of the periodic nonlinear Schrödinger equation and rigorously prove convergence rates at low regularity. The new integrator has decisive advantages over standard schemes at low regularity. In particular, it is able to handle initial data in Hs for 0 < s ≤ 1. The key feature of the integrator is its ability to distinguish between low and medium frequencies in the solution and to treat them differently in the discretization. This new approach requires a well-balanced filtering procedure which is carried out in Fourier space. The convergence analysis of the proposed scheme is based on discrete (in time) Bourgain space estimates which we introduce in this paper. A numerical experiment illustrates the superiority of the new integrator over standard schemes for rough initial data. [ABSTRACT FROM AUTHOR]