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The Last decade saw significant growth in the digital terrestrial television (DTT) subscribers. The High peak-to-average power ratio (PAPR) of the transmitted signal is implied by the large fluctuations in its amplitude, which is a serious issue in the contemporary and next generation DTT broadcasting systems. These large fluctuations prevent feeding the high power amplifier (HPA) at an operating point near its non-linear (NL) saturation region, thereby lowering its power efficiency. For a better future, energy-efficient green communications is the need of hour. This paper focuses on digital predistortion (DPD), which is among the widely used techniques for HPA linearization in order to minimize the NL effects. DPD technique requires a feedback signal. This paper proposes a novel adding signal-based digital predistortion, where the output of the HPA is gradually linearized by adding a signal at the input in an iterative manner. By Taylor series approximation, the DPD problem can be posed as a convex one. We prove that a tighter upper bound exists for the convergence factor and instead of directly solving the convex problem, we pick a convergence factor value within its bounds that offers a good trade-off between convergence speed and residual error value. The simulation results show that the proposed technique can quickly linearize the HPA with good convergence. [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]

This paper analyses the self-representations of Portuguese media professionals and their work practices. Utilizing data from a broader empirical study, this paper delves into the dynamics of influence among various actors within newsrooms. Based on journalists' perceptions of the content, the methods they use to assess the quality of the news are also identified. To address these enquiries, a survey was conducted among professionals engaged in the news production process. This sample comprised 72 individuals from various sectors of newsrooms, including photographers, designers, IT professionals, social media managers, and videographers. The main results indicate that seven out of ten respondents acknowledged their reliance on colleagues in newsrooms for success. Furthermore, the data suggest that there are no significant disparities among different professionals, with personal satisfaction emerging as the primary criterion for assessing the work quality. It is notable that almost twice as many women tend to indicate the low impact of the journalist on their work compared to male respondents. Moreover, most respondents stated that there is space for hybrid professionals in newsrooms. [ABSTRACT FROM AUTHOR]

In this article, we have studied the uniqueness problem of Dirichlet series, which is convergent in a right half-plane and having analytic continuation in the complex plane as a meromorphic function sharing some sets and values. Our first result partially improve a result of [Ann. Univ. Sci. Budapest., Sect. Comput., 48(2018), 117-128] by relaxing the sharing conditions. Most importantly, we have pointed out a number of big gaps in a recent paper [J. Contemp. Math. Anal., 56(2021), 80-86], which makes the existence of the paper under question. Finally, under a different approach, we have provided the corrected form of the result of [J. Contemp. Math. Anal., 56(2021), 80-86] as much as practicable. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical solution of the Brusselator system using a meshless method. A numerical scheme is derived employing the formulas of the Generalized Finite Difference Method, and the convergence of the approximate solution to the exact solution is examined. In order to demonstrate the applicability and accuracy of the method, several examples are proposed. [ABSTRACT FROM AUTHOR]

In this paper, we study a method of polynomial interpolation that lies in-between Lagrange and Hermite methods. The novelty is that we use very general nodal systems on the unit circle as well as on the bounded interval only characterized by a separation property. The way in which we interpolate consists in considering all the nodes for the prescribed values and only half for the derivatives. Firstly, we develop the theory on the unit circle, obtaining the main properties of the nodal polynomials and studying the convergence of the interpolation polynomials corresponding to continuous functions with some kind of modulus of continuity and with general conditions on the prescribed values for half of the derivatives. We complete this first part of the paper with the study of the convergence for smooth functions obtaining the rate of convergence, which is slightly slower than that when equidistributed nodal points are considered. The second part of the paper is devoted to solving a similar problem on the bounded interval by using nodal systems having good properties of separation, generalizing the Chebyshev–Lobatto system, and well related to the nodal systems on the unit circle studied before. We obtain an expression of the interpolation polynomials as well as results about their convergence in the case of continuous functions with a convenient modulus of continuity and, particularly, for differentiable functions. Finally, we present some numerical experiments related to the application of the method with the nodal systems dealt with. [ABSTRACT FROM AUTHOR]

In this study, we extended the applicability of a derivative-free algorithm to encompass the solution of operators that may be either differentiable or non-differentiable. Conditions weaker than the ones in earlier studies are employed for the convergence analysis. The earlier results considered assumptions up to the existence of the ninth order derivative of the main operator, even though there are no derivatives in the algorithm, and the Taylor series on the finite Euclidian space restricts the applicability of the algorithm. Moreover, the previous results could not be used for non-differentiable equations, although the algorithm could converge. The new local result used only conditions on the divided difference in the algorithm to show the convergence. Moreover, the more challenging semi-local convergence that had not previously been studied was considered using majorizing sequences. The paper included results on the upper bounds of the error estimates and domains where there was only one solution for the equation. The methodology of this paper is applicable to other algorithms using inverses and in the setting of a Banach space. Numerical examples further validate our approach. [ABSTRACT FROM AUTHOR]

This study deepens and further concretizes an analysis conducted in a prior study highlighting Romania's goals and objectives in comparison with the sustainable development principles established through the adoption of the European Green Deal (EGD) at the European Union (EU) level. The second section of this paper presents this study's methodology, aiming to highlight the quantification of the compatibility of the targets of Romania's pertinent strategies with the EGD after evoking the principles of sustainable development (SD) and—in this context—the importance of achieving the objectives set by the EGD. The third section of this paper presents our findings, and the final section offers conclusions drawn from our analysis. [ABSTRACT FROM AUTHOR]

Copyright of Ekonomika is the property of Society of Economists 'Ekonomika' and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In February 2007, the FASB issued Statement 159 to provide entities the discretion to select financial instruments to be measured at fair value in the balance sheet. Entities quickly identified an opportunity to exploit Statement 159's transition provisions to transfer unrealized losses directly to stockholders' equity, bypassing the income statement. This paper describes the events surrounding the issuance of Statement 159 and examines the reasons why the FASB issued a standard that had the potential to reduce financial statement comparability and provide a mechanism for earnings manipulation. The paper contributes to historical research in three areas: convergence of U.S. GAAP with IFRS, changes in accounting standards, and the FASB's Conceptual Framework. [ABSTRACT FROM AUTHOR]

The paper presents an iterative scheme called the general tensor regular splitting iterative (GTRS) method for solving the multilinear PageRank problem, which is based on a (weak) regular splitting technique and further accelerates the iterative process by introducing a parameter. The method yields familiar iterative schemes through the use of specific splitting strategies, including fixed-point, inner-outer, Jacobi, Gauss-Seidel and successive overrelaxation methods. The paper analyzes the convergence of these solvers in detail. Numerical results are provided to demonstrate the effectiveness of the proposed method in solving the multilinear PageRank problem. [ABSTRACT FROM AUTHOR]

Systems engineering (SE) solves the most complex problems, bringing together societal issues, theoretical engineering, and the transformation of theory into products and services to better humanity and reduce suffering. In industry, the effort to transform theoretical concepts into practical solutions begins with the product life cycle concept stage, where systems engineering estimates and derives technologies, costs, and schedules. It is crucial to have a successful concept stage as today's industries focus on producing the most capable technologies at an affordable cost and faster time to market than ever before. The research of this paper utilizes a transdisciplinary SE process model in the concept stage to develop and propose training for early-in-career engineers, effectively bridging the gap from university learning to industry practice. With a focus on the concept stage of the product life cycle and the industry's demands of expeditiously proposing complex technical solutions, the paper aims to create an efficient learning program. The main objective of this research is to create a learning program to bring up-to-speed early-in-career engineers using a transdisciplinary SE process model, with six key components: (1) disciplinary convergence—creating a collective impact; (2) TD collaboration; (3) collective intelligence; (4) TD research integration; (5) TD engineering tools; and (6) analysis and TD assessment. The research will then conclude with a case study piloting the TD learning program and analyzing its effectiveness, ultimately aiming to enhance early-in-career engineers' skills in proposing technical solutions that meet customer demands and drive business profitability. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a finite difference scheme that estimates the solution of space fractional diffusion equation with the Caputo fractional derivative. The proposed scheme's stability, and convergence are proved. To assess the efficiency of this program, a set of tests is carried out. The results of these tests demonstrate the reliability and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

In order to address the convergence issue in fuzzy power flow calculations, this paper proposes an analytical approach based on the Levenberg–Marquardt method, aiming to improve the convergence of the fuzzy Newton power flow method. Firstly, a detailed analysis is conducted on the convergence theorem and convergence behavior of the fuzzy Newton method, revealing its poor convergence when the initial values are not properly selected. The Levenberg–Marquardt method is then selected as a means to enhance the convergence of the fuzzy Newton power flow calculations, specifically to tackle the problem of initial value deviation. Since the Jacobian matrix has a significant impact on the convergence region of the power flow, this paper reconstructs the Jacobian matrix based on the Levenberg–Marquardt method, effectively enlarging the convergence region. Through validation experiments on the IEEE 118 standard nodes and simulation comparative analysis, the results confirm the method's effectiveness in resolving the problem of initial value deviation and notably enlarging the convergence region, thereby improving the convergence of power flow calculations. [ABSTRACT FROM AUTHOR]

This paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on an inverse polynomial technique. The proposed method is proven to be consistent, stable, and convergent. We also demonstrate the consistency property of the One-stage scheme and the Two-stage scheme, as well as the stability property of the proposed method. To validate the accuracy of our approach, we conduct several numerical experiments and present the results graphically. Our findings show that the proposed method outperforms existing approaches in terms of accuracy and efficiency. Additionally, we discuss the implications of our results for future research in this field. Overall, this paper provides a valuable contribution to the numerical solution of IVPs and lays the groundwork for further exploration in this area. [ABSTRACT FROM AUTHOR]

In the present paper, we consider a special class of third-order polynomial evolutionary equations. These equations, via Lie theory admit the same one-parameter point transformations which leave the equations invariant. Reductions with these invariant functions lead to highly nonlinear third-order ordinary differential equations. We use a power series to establish interesting solutions to the reduced equations, whereby recurrence relations occur and convergence of the series may be tested. Finally, the conserved vectors of the class are constructed. [ABSTRACT FROM AUTHOR]

As data-based research activities and outcomes increase and ontact or non-face-to-face activities become common, the demand for easy utilization of resources, tools, functions, and easily accessible information required for research in the R&D sector has increased accordingly. With the rapid increase in the demand for collaborative research based on online platforms, research support institutions strive to provide venues for research activities that merge various information and functions. ScienceON, an integrated science & technology (S&T) knowledge infrastructure service developed and operated by the Korea Institute of S&T Information (KISTI), supports open collaboration by connecting and merging all the information, functions, and infrastructure required for research activities. This paper describes the online research activity support tool provided by ScienceON and the remarkable results achieved through this activity. Specifically, the excellent creation of the following flow of meta-material research activities in the ontact space is elucidated. First, the papers required for a meta-material analysis are retrieved, virtual simulation is conducted with the experimental data extracted from the papers, and research data are accumulated. ScienceON's tools for supporting ontact research activity will play a role as an important service in the era of digital transformation and open science. [ABSTRACT FROM AUTHOR]

In this paper, an improved zeroing neural network (ZNN) model is proposed to obtain the positive definite solutions of the continuous coupled Lyapunov matrix equations (CLMEs) associated with continuous‐time Markovian jump (CMJ) systems. To achieve this, a general ZNN model is established by constructing a matrix‐valued error function. Then, to accelerate the convergence rate of the proposed ZNN model, the latest estimation is introduced to obtain an improved ZNN model. Some convergence conditions have been derived for the presented improved ZNN model through Lyapunov theory. Comparisons among the improved ZNN model and the existing results are conducted to illustrate the advantages of the proposed improved ZNN model in numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed approximate subgradient-type method for minimizing a sum of differentiable and non-differentiable convex functions subject to nondifferentiable convex functional constraints in a Euclidean space. We establish the convergence of the sequence generated by our method to an optimal solution of the problem under consideration. Moreover, we derive a convergence rate of order O(N1−a) for the objective function values, where a ∈ (0.5, 1). Finally, we provide a numerical example illustrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

For µ ≥ −1/2, and under appropriate conditions on the sequence {Mp}∞p=0 of weights, the elements, the (weakly, weakly*, strongly) bounded subsets, and the (weakly, weakly*, strongly) convergent sequences in the dual of a space Kµ of type Hankel-K{Mp} can be represented by distributional derivatives of functions and measures in terms of iterated adjoints of the differential operator x−1Dx and the Bessel operator Sµ = x−µ−1/2 Dx x 2µ+1Dxx−µ−1/2. In this paper, such representations are compiled, and new ones involving adjoints of suitable iterations of the Zemanian differential operator Nµ = xµ+1/2Dxx−µ−1/2 are proved. Prior to this, new descriptions of the topology of the space Kµ are given in terms of the latter iterations. [ABSTRACT FROM AUTHOR]

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive convergence analysis and derive optimal iteration parameters aimed at minimizing the spectral radius of the iteration matrix. Through numerical experiments, we validate the efficiency of both iteration methods. [ABSTRACT FROM AUTHOR]

Dynamic Pattern Synthesis (DPS) provides a new longitudinal method for evaluating the impacts of macroeconomic and public policy interventions. Situated within complexity theory and critical realism, it has evolved from the established methods of Cluster Analysis and Configurational Modelling approaches. Dynamic Pattern Synthesis identifies case convergence and divergence (using quantitative techniques), while remaining close to the qualitative uniqueness of each case. In this paper, the DPS approach is used to consider macroeconomic convergence across Sub-Saharan Africa during the Millennium Development Goals, and the possible impacts of IMF interventions in stimulating long-term macroeconomic outcomes. The findings reveal a high degree of economic instability experienced across the region and varying responses to an external shock. The importance of 'outliers' and inconsistency in country convergence are also observed. The DPS method highlights the importance of individual country experiences in relation to external shocks. When factoring in IMF interventions, the findings highlight multiple paths to a given policy outcome, rather than a single optimal economic strategy. This opens up the debate on policy issues associated with economic complexity, including how best to create an overall environment of stability that might promote convergence and reduce the instability that undermines planning and investment. [ABSTRACT FROM AUTHOR]

Gender-related issues feature prominently on the EU's agenda and in policies such as the Gender Equality Strategy 2020–2025 which identifies gender equality as a core principle of the EU. Within the broader convergence discourse which examines whether candidate countries are converging with the EU, prompted by Turkey's withdrawal from the Council of Europe Istanbul Convention and the Sofagate incident, this paper conducts a gender-centric convergence analysis in the case Turkey. To this end, it uses five gender-focused indices compiled by the Varieties of Democracy (V-Dem) project. The empirical results from the convergence tests do not provide evidence supporting convergence in terms of these five gender-related indices. The findings of the present study concur with the existing relevant literature and should be viewed in the broader context of Turkey's democratic backsliding and de-Europeanization process. [ABSTRACT FROM AUTHOR]

This paper considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced. [ABSTRACT FROM AUTHOR]

In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numerical solution are presented. Then, the proposed algorithm is proved to be second-order convergence in temporal and fourth-order spatial convergence using the discrete energy method. Finally, some numerical experiments validate the effectiveness of the conservative algorithm and confirm the accuracy of the theoretical results for different choices of the fractional-order α. [ABSTRACT FROM AUTHOR]

The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective. [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]

The paper is devoted to the study of the uniqueness and certain qualitative properties of the solution of a class of integral equations with sum-difference kernel on the positive half-line and with a convex nonlinearity. This class of equations arises in a particular case in the dynamical theory of -adic closed-open strings for the scalar field of tachyons. Such equations also play a very important role in the study of the existence and uniqueness of solutions of nonlinear integral equations in the mathematical theory of the geographical distribution of an epidemic within the framework of the Diekmann–Kaper model. We prove the uniqueness theorem for the solution of the equation under consideration for a class of nonnegative (nonzero) and bounded functions on , thereby obtaining a definitive solution of Vladimirov's open problem on the uniqueness of rolling solutions of nonlinear -adic equations. Under an additional constraint on the kernel of the equation, we also prove that the solution is a concave function on whose derivative belongs to the space . At the end of the paper, we give specific model equations from the above-mentioned applications, to which our results are applied. [ABSTRACT FROM AUTHOR]

Copyright of Revista INVI is the property of Universidad de Chile and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The concepts of internet banking and mobile banking have led to changes in people's financial behavior in terms of earning, consuming, and saving. This new concept, which entered the market quite recently, was used at the beginning of the new digital technology in various types of activities, banking operations, and nowadays these services are used by all people who want to save through banks or create new sources of income, as well as to make quick currency exchanges without going to credit institutions. The main purpose of this paper is to analyze people's behavior toward new digital technologies, e-banking adoption, and non-banking financial institutions internet services. The objectives pursued are: whether e-banking users are homogeneous in their characteristics in the EU 27 and which users have the most convergent or divergent behavior in the EU 27. Statistical data taken from Eurostat 2023 was used for the Sigma convergence analysis, the time series taken into consideration being from 2004 to 2022. The results showed that the changes in the procedural-fiscal-financial sphere are the ones that fully reflect the two principles underlying the tax evolution: digitization and simplification. These results confirm that people are adopting the new digital technology and change their behavior from consumer to prosumer. The study shows that all most categories adopted e-banking using new digital technologies when it comes to consumption and saving, with few exceptions that should be carefully supported. Plain Language Summary: E-Banking convergence and the adopter's behaviour within the EU Countries The concepts of internet banking and mobile banking have led to changes in people's financial behavior in terms of earning, consuming, and saving. This new concept, which entered the market quite recently, was used at the beginning of the new digital technology in various types of activities, banking operations, and nowadays these services are used by all people who want to save through banks or create new sources of income, as well as to make quick currency exchanges without going to credit institutions. The main purpose of this paper is to analyze people's behavior towards new digital technologies, e-banking adoption, and non-banking financial institutions internet services. The objectives pursued are: whether e-banking users are homogeneous in their characteristics in the EU 27 and which users have the most convergent or divergent behavior in the EU 27. Statistical data taken from Eurostat 2023 was used for the Sigma convergence analysis, the time series taken into consideration being from 2004 to 2022. The results showed that the changes in the procedural-fiscal-financial sphere are the ones that fully reflect the two principles underlying the tax evolution: digitization and simplification. These results confirm that people are adopting the new digital technology and change their behavior from consumer to prosumer. The study shows that all most categories adopted e-banking using new digital technologies when it comes to consumption and saving, with few exceptions that should be carefully supported. Digital transformation is not just about buying new, modern equipment, or retrieving data quickly and securely, but also about the technical implementation of state-of-the-art IT systems. It should be noted that digitization has had important effects on both public and private organizations and people, which can be translated as follows: time saved in people's interaction with public and private organizations; efficiency in administrative processes; transparency in their work. The economic environment becomes much more attractive and leads to investment and innovation in all areas. The digitization of all public or private services would also strengthen the administrative capacity of the whole population. Through studies, research, and future studies, it is essential to analyze and demonstrate that new digital technologies and their use could lead to the elimination of tax fraud, increased public confidence in local or central government and confidence in business. Finally, we can say that it is essential that new research in the field of digitization and e-banking use strengthens the literature reviews and explains at a higher level the answers to all research questions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of successive over relaxation-based alternately linearized implicit iteration method for computing the minimal nonnegative solution of nonsymmetric algebraic Riccati equations. Under certain conditions, we prove the convergence of the iterative method. Finally, numerical examples are given to show the iterative method is efficient. [ABSTRACT FROM AUTHOR]

Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute. Exploring the convergence properties of such methods is crucial in their development. The convergence behavior of such approaches and determining their practical applicability require conducting local as well as semi-local convergence analysis. In this study, we explore the convergence properties of a sixth-order derivative-free method. Previous local convergence studies assumed the existence of derivatives of high order even when the method itself was not utilizing any derivatives. These assumptions imposed limitations on its applicability. In this paper, we extend the local analysis by providing estimates for the error bounds of the method. Consequently, its applicability expands across a broader range of problems. Moreover, the more important and challenging semi-local convergence not investigated in earlier studies is also developed. Additionally, we survey recent advancements in this field. The outcomes presented in this paper can be proved valuable to practitioners and researchers engaged in the development and analysis of derivative-free numerical algorithms. Numerical tests illuminate and validate further the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is aimed at efficient numerical implementation of the fractional-order generalization of the stochastic Stokes–Darcy model, which has important scientific, applied, and economic significance in hydrology, the oil industry, and biomedicine. The essence of this generalization of the stochastic model is the introduction of fractional time derivatives in the sense of Caputo's definition to take into account long-term changes in the properties of media. An efficient numerical method for the implementation of the fractional-order Stokes–Darcy model is proposed, which is based on the use of a higher-order approximation formula for the fractional derivative, higher-order finite difference relations, and a finite element approximation of the problem in the spatial direction. In the paper, a rigorous theoretical analysis of the stability and convergence of the proposed numerical method is carried out, which is confirmed by numerous computational experiments. Further, the proposed method is applied to the implementation of the fractional-order stochastic Stokes–Darcy model using an ensemble technique, in which the approximation is carried out in such a way that the resulting systems of linear equations have the same coefficient matrix for all realizations. Furthermore, evaluation of the discrete fractional derivatives is carried out with the use of parallel threads. The efficiency of applying both approaches has been demonstrated in numerical tests. [ABSTRACT FROM AUTHOR]

Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks, where one task is nested inside the other. In machine learning and computer vision fields, despite the different motivations and mechanisms, a lot of complex problems, such as hyper-parameter optimization, multi-task and meta learning, neural architecture search, adversarial learning and deep reinforcement learning, actually all contain a series of closely related subproblms. In this paper, we first uniformly express these complex learning and vision problems from the perspective of BLO. Then we construct a best-response-based single-level reformulation and establish a unified algorithmic framework to understand and formulate mainstream gradient-based BLO methodologies, covering aspects ranging from fundamental automatic differentiation schemes to various accelerations, simplifications, extensions and their convergence and complexity properties. Last but not least, we discuss the potentials of our unified BLO framework for designing new algorithms and point out some promising directions for future research. A list of important papers discussed in this survey, corresponding codes, and additional resources on BLOs are publicly available at: https://github.com/vis-opt-group/BLO. [ABSTRACT FROM AUTHOR]

The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper, we investigate the asymptotic behavior and the variational stability of the subgame perfect Nash equilibrium (SPNE) in one-leader one-follower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE-outcomes of perturbed games is an SPNE-outcome of the original game. We fully positively answer when the follower's best reply correspondence is single-valued. When the follower's best reply correspondence is not single-valued, the answer is positive only for the SPNE-outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable non-restrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. [ABSTRACT FROM AUTHOR]

Performance requirements necessitate control designs that assure not only transient response specifications but also steady-state accuracy. Monotonic convergence of the tracking error is crucial for an efficient control design to prevent the performance degradation caused by overshooting. This needs a balanced consideration of both reaching conditions and the monotonic convergence, in the context of sliding mode control. In this paper, the dynamic behaviour of the dead-beat sliding mode control is characterized and the signum function is replaced by employing a non-switching one, in order to reduce chattering. The paper conducts a thorough analysis of monotonic convergence of both the switching and the non-switching error dynamics. By deriving the conditions for monotonic convergence, the control parameters can be strategically chosen to ensure monotonic convergence of the tracking error. Numerical and experimental results are presented to validate effectiveness of the proposed control scheme, which evaluate the tracking performance achieved by both the switching and the non-switching control methods. • The DBSMC approach uses a dead-beat reaching law for the global sliding-mode. • Both the switching and non-switching attractive laws are proposed. • The monotonic convergence is characterized by the MD-region and the SS-band. • The calculation of convergence steps of the DBSMC schemes is provided. [ABSTRACT FROM AUTHOR]

The conventional approach of the local convergence analysis of an iterative method on R m , with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives may not be part of the proposed method(s). In this way, the method(s) can face several limitations, particularly the use of higher-order derivatives and a lack of information about a priori computable error bounds on the solution distance or uniqueness. In this paper, we address these drawbacks by conducting the local convergence analysis within the broader framework of a Banach space. We have selected an important family of high convergence order methods to demonstrate our technique as an example. However, due to its generality, our technique can be used on any other iterative method using inverses of linear operators along the same line. Our analysis not only extends in R m spaces but also provides convergence conditions based on the operators used in the method, which offer the applicability of the method in a broader area. Additionally, we introduce a novel semilocal convergence analysis not presented before in such studies. Both forms of convergence analysis depend on the concept of generalized continuity and provide a deeper understanding of convergence properties. Our methodology not only enhances the applicability of the suggested method(s) but also provides suitability for applied science problems. The computational results also support the theoretical aspects. [ABSTRACT FROM AUTHOR]

In this paper, the simplified modulus-based matrix splitting iteration method was extended to solve the nonlinear complementarity problem, and the convergence conditions were presented from the spectral radius and the matrix norm. Then, for the special cases of this method, we provided some concrete convergence conditions as well as the quasi-optimal parameter matrix. Moreover, some numerical examples were illustrated to show the validity of the convergence results. [ABSTRACT FROM AUTHOR]

Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. [ABSTRACT FROM AUTHOR]