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In the paper, we will present some important results from the theory of vector-valued invariant means. Discussing the results contained in the author’s paper Badora (Ann Pol Math 58:147–159, 1993), we will add new facts that were previously not published.

Let $G$ be a finite group. Denoting by ${\rm{cd}}(G)$ the set of the degrees of the irreducible complex characters of $G$, we consider the {\it character degree graph} of $G$: this is the (simple, undirected) graph whose vertices are the prime divisors of the numbers in ${\rm{cd}}(G)$, and two distinct vertices $p$, $q$ are adjacent if and only if $pq$ divides some number in ${\rm{cd}}(G)$. This paper completes the classification, started in [5] and [6], of the finite non-solvable groups whose character degree graph has a {\it cut-vertex}, i.e. a vertex whose removal increases the number of connected components of the graph. More specifically, it was proved in [6] that these groups have a unique non-solvable composition factor $S$, and that $S$ is isomorphic to a group belonging to a restricted list of non-abelian simple groups. In [5] and [6] all isomorphism types for $S$ were treated, except the case \(S\cong{\rm{PSL}}_2(2^a)\) for some integer $a\geq 2$; the remaining case is addressed in the present paper., arXiv admin note: text overlap with arXiv:2208.03519

In d dimensions, accurately approximating an arbitrary function oscillating with frequency $\lesssim k$ ≲ k requires $\sim k^{d}$ ∼ k d degrees of freedom. A numerical method for solving the Helmholtz equation (with wavenumber k) suffers from the pollution effect if, as $k\rightarrow \infty $ k → ∞ , the total number of degrees of freedom needed to maintain accuracy grows faster than this natural threshold. While the h-version of the finite element method (FEM) (where accuracy is increased by decreasing the meshwidth h and keeping the polynomial degree p fixed) suffers from the pollution effect, the hp-FEM (where accuracy is increased by decreasing the meshwidth h and increasing the polynomial degree p) does not suffer from the pollution effect. The heart of the proof of this result is a PDE result splitting the solution of the Helmholtz equation into “high” and “low” frequency components. This result for the constant-coefficient Helmholtz equation in full space (i.e. in $\mathbb {R}^{d}$ ℝ d ) was originally proved in Melenk and Sauter (Math. Comp79(272), 1871–1914, 2010). In this paper, we prove this result using only integration by parts and elementary properties of the Fourier transform. The proof in this paper is motivated by the recent proof in Lafontaine et al. (Comp. Math. Appl.113, 59–69, 2022) of this splitting for the variable-coefficient Helmholtz equation in full space use the more-sophisticated tools of semiclassical pseudodifferential operators.

A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper., Comments: 38 pages and 25 figures. To be published in Annali di Matematica Pura ed Applicata (1923 -). This paper covers until Section 7 of the previous version arXiv:1912.05774v3 [math.GT]. The contents of the remaining sections will be covered in a separate paper

Despite the benefits of a lean business system, many organisations struggle to implement and sustain lean initiatives. The purpose of this work was to explore in what way a leader’s deeper knowledge or different understandings of lean affects the lean implementation and its outcomes. The research methodology incorporated a survey of 757 participants. How respondents understood lean was assessed and later correlated to their extent of lean knowledge and specific understanding. This was supported by exploratory factor analysis and structural equation modelling. What caused participants to pursue lean knowledge was also assessed. Low lean knowledge and experience correlated with a system, tools and processes perspective of lean that was perceived to provide a low competitive advantage. Those of high lean knowledge had a much more holistic view of lean that encompassed both socio and technical aspects and also perceived greater competitive advantages from lean. Results showed 88% of people were (are) not at all familiar with lean, 9% of low knowledge and 3% of high knowledge. This paper promotes the importance of management knowledge in establishing a lean business system and exposes that many are actually self-deceived regarding their knowledge of lean. It identifies the need to develop lean education and recommends further research in this area. It also provides a conceptual framework for the implementation of lean with an emphasis on leadership learning. This paper contributes statistical evidence and a new perspective on the cause of lean success and failure.

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field.

In this paper, we focus on the existence of positive solutions to the following planar Schrödinger–Newton system with general critical exponential growth $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta {u}+u+\phi u =f(u)&{} \text{ in }\,\,\mathbb {R}^2, \\ \Delta {\phi }=u^2 &{} \text{ in }\,\, \mathbb {R}^2, \end{array} \right. \end{aligned}$$ - Δ u + u + ϕ u = f ( u ) in R 2 , Δ ϕ = u 2 in R 2 , where $$f\in C^1(\mathbb {R},\mathbb {R})$$ f ∈ C 1 ( R , R ) . We apply a variational approach developed in [36] to study the above problem in the Sobolev space $$H^1(\mathbb {R}^2)$$ H 1 ( R 2 ) . The analysis developed in this paper also allows to investigate the relation between a Riesz-type of Schrödinger–Newton systems and a logarithmic-type of Schrödinger–Poisson systems. Furthermore, this approach can overcome some difficulties resulting from either the nonlocal term with sign-changing and unbounded logarithmic integral kernel, or the critical nonlinearity, or the lack of monotonicity of $$\frac{f(t)}{t^3}$$ f ( t ) t 3 . We emphasize that it seems much difficult to use the variational framework developed in the existed literature to study the above problem.

Background Automatic literature based discovery attempts to uncover new knowledge by connecting existing facts: information extracted from existing publications in the form of $$A \rightarrow B$$ A → B and $$B \rightarrow C$$ B → C relations can be simply connected to deduce $$A \rightarrow C$$ A → C . However, using this approach, the quantity of proposed connections is often too vast to be useful. It can be reduced by using subject$$\rightarrow$$ → (predicate)$$\rightarrow$$ → object triples as the $$A \rightarrow B$$ A → B relations, but too many proposed connections remain for manual verification. Results Based on the hypothesis that only a small number of subject–predicate–object triples extracted from a publication represent the paper’s novel contribution(s), we explore using BERT embeddings to identify these before literature based discovery is performed utilizing only these, important, triples. While the method exploits the availability of full texts of publications in the CORD-19 dataset—making use of the fact that a novel contribution is likely to be mentioned in both an abstract and the body of a paper—to build a training set, the resulting tool can be applied to papers with only abstracts available. Candidate hidden knowledge pairs generated from unfiltered triples and those built from important triples only are compared using a variety of timeslicing gold standards. Conclusions The quantity of proposed knowledge pairs is reduced by a factor of $$10^3$$ 10 3 , and we show that when the gold standard is designed to avoid rewarding background knowledge, the precision obtained increases up to a factor of 10. We argue that the gold standard needs to be carefully considered, and release as yet undiscovered candidate knowledge pairs based on important triples alongside this work.

Although I had not previously been aware of Jean Ginibre’s work on random matrices, beginning in 1978 I became an admirer of his many papers on nonlinear waves in collaboration with Giorgio Velo. Their papers were amazingly profound and inspirational. I subsequently met Jean and Giorgio many times. I especially remember the pleasant time Jean and I spent together at a meeting in 2001 at Hokkaido University dedicated to the memory of the great Tosio Kato. The present announcement is a very brief summary of some of my recent mathematical work, joint with Yilun Wu, concerning a simple model of galaxies.

In this paper, CFD-based results are presented on the estimation of losses in bends with validated numerical models for single-phase, incompressible Bingham fluids. Five fittings were investigated: $$90^\circ$$ 90 ∘ bends of different R/D ratios between 1 and 10. Bingham plastic fluids were studied with Hedström numbers in the wide range from 1 to $$10^9$$ 10 9 . Loss coefficients are given as the function of the generalized Reynolds number ($${\textrm{Re}_\textrm{gen}}=$$ Re gen = 0.1–17 800) and the generalized Dean number ($${\textrm{De}_\textrm{gen}}=$$ De gen = 0.1–12 600). The paper presents friction factors as well that were consistent with the literature. It was shown that at low generalized Dean numbers of $${\textrm{De}_\textrm{gen}}< 40$$ De gen < 40 , the losses of the bends were caused purely by the wall friction and can be estimated from the $${\textrm{De}_\textrm{gen}}$$ De gen . In a broad range of higher $${\textrm{Re}_\textrm{gen}}$$ Re gen and $${\textrm{De}_\textrm{gen}}$$ De gen numbers, the loss coefficients were separated at the basis of the Hedström numbers. This phenomenon was mainly observable in the case of high curvature and was attributed to the flow patterns. Our study investigated this range with the bend of $$R/D=1$$ R / D = 1 in detail: flow patterns in the bend and at the upstream side of the fitting were examined. An approximating equation and the fitting parameters were also given for loss coefficients.

In this paper, we study the L1-boundedness of Fourier integral operator T_{\phi,a} with rough symbol a\in L^{\infty}S^{m}_{\rho} and a new class of rough phase \phi. In this class, we extend the L^{\infty}\phi^{2} and non-degeneracy conditions to some generalized derivative estimation and some measure condition respectively. Our main result substantially extends and emproves some known results about L1-boundedness of Fourier integral operator. Moreover, the result in this paper can be used to prove the boundedness of the maximal wave operator.

A rooted directed tree $\mathscr T=(V, E)$ with can be extended to a directed graph $\mathscr T_\infty=(V_\infty, E_\infty)$ by adding a vertex $\infty$ to $V$ and declaring each vertex in $V$ as a parent of $\infty.$ One may associate with the extended directed tree a family of semigroup structures $\sqcup_{b}$ with extreme ends being induced by the join operation $\sqcup$ and the meet operation $\sqcap$. Each semigroup structure among these leads to a family of densely defined linear operators $W^{b}_{\lambda_u}$ acting on $\ell^2(V),$ which we refer to as weighted join operators at a given base point $b \in V_{\infty}$ with prescribed vertex $u \in V$. The extreme ends of this family are weighted join operators $W^{\mathsf{root}}_{\lambda_u}$ and weighted meet operators $W^{\infty}_{\lambda_u}$. In this paper, we systematically study these operators. We also present a more involved counter-part of weighted join operators on rootless directed trees. In both cases, the class of weighted join operators overlaps with the well-studied classes of complex Jordan operators and $n$-symmetric operators. An important half of this paper is devoted to the study of rank one extensions $W_{f, g}$ of weighted join operators, where $f \in \ell^2(V)$ and $g : V \to \mathbb C$ is unspecified. Unlike weighted join operators, these operators are not necessarily closed. We provide a couple of compatibility conditions involving the weight system $\lambda_u$ and $g$ to ensure closedness of $W_{f, g}$. We discuss the role of the Gelfand-triplet in the realization of the Hilbert space adjoint of $W_{f, g}$. Further, we describe various spectral parts of $W_{f, g}$ in terms of the weight system and the tree data. We also provide sufficient conditions for $W_{f, g}$ to be a sectorial operator. In case $\mathscr T$ is leafless, we characterize rank one extensions $W_{f, g}$, which admit compact resolvent., Comment: This is a slight revision of the previous version

When we study the Karnaugh map in the switching theory course, we learn that the ones in the map are combined in rectangles whose length and width must be a power of two. The result is the logic function described as a sum of products. This paper shows that we can also make groups where the length and width of the rectangles are equal to three. This results in a logic function that is simpler than the sum of products in terms of logic gates, leading to more hardware-efficient circuits. This idea is extended later in the paper to other groups of elements. Finally, a new perspective on the Karnaugh map that integrates the proposed approach with the conventional one is provided. This can be used in switching theory courses to improve the explanation of the Karnaugh map.

In this paper, we proposed implementing a Deep Convolutional Neural Network. A relationship between a noisy character image to its clean counter-part are mapped using Deep Convolutional Neural Network.The overall process is divided into two stages: noise type classification and image denoising. Firstly, the noise type classification identifies the types of noise, and based on this noise type, a particular denoising model is selected, which increases the image denoising performance. The denoising network inputs a noisy image and a target of its clean corresponding image during the training. After the mapping function is trained, the generated model performs character image denoising. Then, on each band, a trained mapping function perform image denoising irrespective of the other band. Finally, each block is assembled to generate a clean image. In this paper, the MNIST and Char74K dataset of handwritten digits diluted with artificial noise divided into ten types are used for experimentation.. Our experimental results show that the proposed techniques perform better image denoising ascompared to the existing methods, both in terms of image noise type classification and image denoising. The overall Character recognition accuracy increased by 66% after performing the proposed denoising technique.

The majority of research work on triboelectric energy harvesting is on material science, manufacturing and electric circuit design. There is a lack of in-depth research into structural dynamics which is crucial for power generation in triboelectric energy harvesting. In this paper, a novel triboelectric energy harvester with a compact structure working in sliding mode is developed, which is in the form of a casing and an oscillator inside. Unlike most sliding-mode harvesters using single-unit films, the proposed harvester utilizes grating-patterned films which are much more efficient. A bistable mechanism consisting of two pairs of magnets is employed for broadening the frequency bandwidth. A theoretical model is established for the harvester, which couples the structural dynamics domain and electrical dynamics domain. This paper presents the first study about the nonlinear structural dynamics of a triboelectric energy harvester with grating-patterned films, which is also the first triboelectric energy harvester integrating grating-patterned films with a bistable magnetic system for power performance enhancement. Theoretical studies are carried out from the perspectives of both structural and electrical dynamics. Surface charge density and segment configuration of the films affect whether the electrostatic force influences the structural dynamics, which can be neglected under a low surface charge density. Differences in structural response and electrical output are found between a velocity-dependent model and Coulomb’s model for modelling the friction in the triboelectric energy harvesting system. The bistable mechanism can effectively improve the output voltage under low-frequency excitations. Additionally, the output voltage can also be obviously enhanced through increasing the number of the hollowed-out units of the grating-patterned films, which also results in a slight decrease in the optimal load resistance of the harvester. These findings enable innovative designs for triboelectric energy harvesters and provide fabrication guidelines in practical applications.

Throughout the centuries, nature has been a source of inspiration, with much still to learn from and discover about. Among many others, Swarm Intelligence (SI), a substantial branch of Artificial Intelligence, is built on the intelligent collective behavior of social swarms in nature. One of the most popular SI paradigms, the Particle Swarm Optimization algorithm (PSO), is presented in this work. Many changes have been made to PSO since its inception in the mid 1990s. Since their learning about the technique, researchers and practitioners have developed new applications, derived new versions, and published theoretical studies on the potential influence of various parameters and aspects of the algorithm. Various perspectives are surveyed in this paper on existing and ongoing research, including algorithm methods, diverse application domains, open issues, and future perspectives, based on the Systematic Review (SR) process. More specifically, this paper analyzes the existing research on methods and applications published between 2017 and 2019 in a technical taxonomy of the picked content, including hybridization, improvement, and variants of PSO, as well as real-world applications of the algorithm categorized into: health-care, environmental, industrial, commercial, smart city, and general aspects applications. Some technical characteristics, including accuracy, evaluation environments, and proposed case study are involved to investigate the effectiveness of different PSO methods and applications. Each addressed study has some valuable advantages and unavoidable drawbacks which are discussed and has accordingly yielded some hints presented for addressing the weaknesses of those studies and highlighting the open issues and future research perspectives on the algorithm.

This paper deals with the estimation of kurtosis on large datasets. It aims at overcoming two frequent limitations in applications: first, Pearson's standardized fourth moment is computed as a unique measure of kurtosis; second, the fact that data might be just samples is neglected, so that the opportunity of using suitable inferential tools, like standard errors and confidence intervals, is discarded. In the paper, some recent indexes of kurtosis are reviewed as alternatives to Pearson’s standardized fourth moment. The asymptotic distribution of their natural estimators is derived, and it is used as a tool to evaluate efficiency and to build confidence intervals. A simulation study is also conducted to provide practical indications about the choice of a suitable index. As a conclusion, researchers are warned against the use of classical Pearson’s index when the sample size is too low and/or the distribution is skewed and/or heavy-tailed. Specifically, the occurrence of heavy tails can deprive Pearson’s index of any meaning or produce unreliable confidence intervals. However, such limitations can be overcome by reverting to the reviewed alternative indexes, relying just on low-order moments.

In this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.

In this paper we deal with construction and analysis of a multiwavelet spectral element scheme for a generalized Cauchy type problem with Caputo fractional derivative. Numerical schemes for this type of problems, often suffer from the draw-back of spurious oscillations. A common remedy is to render the problem to an equivalent integral equation. For the generalized Cauchy type problem, a corresponding integral equation is of nonlinear Volterra type. In this paper we investigate wellposedness and convergence of a stabilizing multiwavelet scheme for a, one-dimensional case (in [a, b] or [0, 1]), of this problem. Based on multiwavelets, we construct an approximation procedure for the fractional integral operator that yields a linear system of equations with sparse coefficient matrix. In this setting, choosing an appropriate threshold, the number of non-zero coefficients in the system is substantially reduced. A severe obstacle in the convergence analysis is the lack of continuous derivatives in the vicinity of the inflow/ starting boundary point. We overcome this issue through separating a J (mesh)-dependent, small, neighborhood of a (or origin) from the interval, where we only take $$L_2$$ L 2 -norm. The estimate in this part relies on Chebyshev polynomials, viz. As reported by Richardson( Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms, Oxford University, UK, 2012) and decreases, almost, exponentially by raising J. At the remaining part of the domain the solution is sufficiently regular to derive the desired optimal error bound. We construct such a modified scheme and analyze its wellposedness, efficiency and accuracy. The robustness of the proposed scheme is confirmed implementing numerical examples.

In this paper we investigate, from a graph theoretical point of view, the notion of acceptability in Dung semantics for abstract argumentation frameworks. We advance the state of the art by introducing and analyzing combinatorial structures exploited for taming, in particular cases, the exponential blowout of acceptance algorithms. We conclude the paper by a series of observations allowing to deepen the intuition with respect to the practical use of Dung acceptance based semantics.

In the previous paper Bello-Cruz et al. (J Optim Theory Appl 188:378–401, 2021), we showed that the quadratic growth condition plays a key role in obtaining Q-linear convergence of the widely used forward–backward splitting method with Beck–Teboulle’s line search. In this paper, we analyze the property of quadratic growth condition via second-order variational analysis for various structured optimization problems that arise in machine learning and signal processing. This includes, for example, the Poisson linear inverse problem as well as the $$\ell _1$$ ℓ 1 -regularized optimization problems. As a by-product of this approach, we also obtain several full characterizations for the uniqueness of optimal solution to Lasso problem, which complements and extends recent important results in this direction.

The collective behaviour of fish schools, shoals and other swarms in nature has long inspired researchers to develop solutions for optimization problems. Instinct influences the behaviour of fish to group into schools to increase safety, enhance foraging success, and promote breeding. According to these instinctive behaviours, several fish-inspired algorithms have been introduced to solve hard problems. This paper presents a comprehensive survey of fish-inspired heuristics, exploring their evolution within the context of general optimization problems. To our knowledge, this survey is the first to cover both main fish-inspired heuristics in the literature, namely, the artificial fish swarm algorithm (AFSA) and Fish school search (FSS), in addition to other algorithms inspired by specific fish species. The review covers more than 50 papers published in the Web of Science and IEEE databases since 2000. We first review the basic fish heuristics, highlighting their advantages and drawbacks, and then detail attempts in the literature to improve their behaviour to solve complex, multi-objective and high-dimensional problems in several domains. Our work is intended to provide guidance for researchers and practitioners for the purpose of further advancing research in the area of fish-inspired heuristics. We aspire to encourage their utilization in various fields for global optimization and in real-life applications. The survey findings indicate that fish-inspired heuristics are very alive in recent literature and still have great potential. Several challenges and future research directions are also identified among the findings of this survey, which can help to enhance this vibrant line of research.

With optimized design and modern brushless operation, wound rotor synchronous machines are resurrecting as a strong contender in many applications presently dominated by permanent magnet machines. Considering the notion, this paper introduces a novel brushless synchronous machine topology that utilizes sub-harmonic magnetomotive force (MMF) of its stator winding for desirable brushless operation. It is significant to state that the sub-harmonic MMF component that is used in this novel topology is one-fourth of the fundamental MMF component, whereas, in previous practices, it was half. Moreover, the stator of the machine uses a new winding arrangement of two sets of balanced three-phase windings wound in two layers to produce the fundamental and the sub-harmonic MMF. To achieve the brushless excitation, the rotor utilizes an additional winding that is used to induce the electromotive force (EMF) by the sub-harmonic MMF component of the stator. This novel two-layer stator winding topology permits the utilization of maximum allowable space in the stator to house conductors in all of its 48 slots, which was not the case in previous papers. To validate the performance, and feasibility, an 8-pole 48-slot brushless wound rotor synchronous motor is designed, and a 2-D finite element analysis simulation is conducted, where the topology shows immense potential in terms of better torque performance.

We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes our formulas generalize the classical hook-length formula and Stanley's formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its $q$-analogues, which were studied in previous papers of the series., Comment: 26 pages, 3 figures. This is the fourth paper in the series "Hook formulas for skew shapes", v2. expanded final remarks, added section 6.4 with a generalization of the Okounkov-Olshanski formula, fixed typos

Traditionally, the literature on statistical inference with left-truncated samples assumes the independence of truncation variable on lifetime. Alternatively, this paper considers an approach of using a copula for dependent truncation. When considering maximum likelihood estimation and goodness-of-fit procedures, key challenges are the absence of the explicit form of the inclusion probability and truncated distribution functions. This paper shows that, under the copula model, the inclusion probability and truncated distribution functions are expressed as univariate integrals of some functions. With aid of these expressions, we propose computational algorithms to maximize the log-likelihood and to perform goodness-of-fit tests. Simulations are conducted to examine the performance of the proposed method. Real data from a field reliability study on the brake pad lifetimes are analyzed for illustration. Relevant computational programs are made available in the R package “depend.truncation”.

This paper presents a new class of regression models for continuous data restricted to the interval $(0,1)$, such as rates and proportions. The proposed class of models assumes a beta distribution for the variable of interest with regression structures for the mean and dispersion parameters. These structures consider covariates, unknown regression parameters, and parametric link functions. Link functions depend on parameters that model the relationship between the random component and the linear predictors. The symmetric and assymetric Aranda-Ordaz link functions are considered in details. Depending on the parameter values, these link functions refer to particular cases of fixed links such as logit and complementary log-log functions. Joint estimation of the regression and link function parameters is performed by maximum likelihood. Closed-form expressions for the score function and Fisher's information matrix are presented. Aspects of large sample inferences are discussed, and some diagnostic measures are proposed. A Monte Carlo simulation study is used to evaluate the finite sample performance of point estimators. Finally, a practical application that employs real data is presented and discussed., Comment: Accepted paper

In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good candidates having C2 regularity. On the other hand, if the data points present discontinuities, the classical spline approximations produce Gibbs oscillations. In a recent paper, we have introduced a new nonlinear spline approximation avoiding the presence of these oscillations. Unfortunately, this new reconstruction loses the C2 regularity. This paper introduces a new nonlinear spline that preserves the regularity at all the joint points except at the end points of an interval containing a discontinuity, and that avoids the Gibbs oscillations. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was funded by the Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18, by the national research project MMTM2015-64382-P and PID2019-108336GB-I00 (MINECO/FEDER), by grant MTM2017-83942 funded by Spanish MINECO and by grant PID2020-117211GB-I00 funded by MCIN/AEI/10.13039/501100011033.

The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adopts the traditional full steepest descent direction or Newton-like direction as a search direction to generate an iterate on which a certain thresholding is performed. Traditional hard thresholding discards a large part of a vector, and thus some important information contained in a dense vector has been lost in such a thresholding process. Recent study (Zhao in SIAM J Optim 30(1): 31–55, 2020) shows that the hard thresholding should be applied to a compressible vector instead of a dense vector to avoid a big loss of information. On the other hand, the optimal k-thresholding as a novel thresholding technique may overcome the intrinsic drawback of hard thresholding, and performs thresholding and objective function minimization simultaneously. This motivates us to propose the so-called partial gradient optimal thresholding (PGOT) method and its relaxed versions in this paper. The PGOT is an integration of the partial gradient and the optimal k-thresholding technique. The solution error bound and convergence for the proposed algorithms have been established in this paper under suitable conditions. Application of our results to the sparse optimization problems arising from signal recovery is also discussed. Experiment results from synthetic data indicate that the proposed algorithm is efficient and comparable to several existing algorithms.

For the sake of precise simulation, and proper controlling of the performance of the proton exchange membrane fuel cells (PEMFCs) generating systems, robust and neat mathematical modelling is crucially needed. Principally, the robustness and precision of modelling strategy depend on the accurate identification of PEMFC’s uncertain parameters. Hence, in the last decade, with the noteworthy computational development, plenty of meta-heuristic algorithms (MHAs) are applied to tackle such problem, which have attained very positive results. Thus, this review paper aims at announcing novel inclusive survey of the most up-to-date MHAs that are utilized for PEMFCs stack’s parameter identifications. More specifically, these MHAs are categorized into swarm-based, nature-based, physics-based and evolutionary-based. In which, more than 350 articles are allocated to attain the same goal and among them only 167 papers are addressed in this effort. Definitely, 15 swarm-based, 7 nature-based, 6 physics-based, 2 evolutionary-based and 4 others-based approaches are touched with comprehensive illustrations. Wherein, an overall summary is undertaken to methodically guide the reader to comprehend the main features of these algorithms. Therefore, the reader can systematically utilize these techniques to investigate PEMFCs’ parameter estimation. In addition, various categories of PEMFC’s models, several assessment criteria and many PEMFC commercial types are also thoroughly covered. In addition to that, 27 models are gathered and summarized in an attractive manner. Eventually, some insights and suggestions are presented in the conclusion for future research and for further room of improvements and investigations.

This preface introduces the special issue on Dynamic Games for Modeling and Control of Epidemics. It showcases 12 papers with timely contributions to dynamic games and their applications to the modeling, analysis, and control of epidemics. The papers in this collection connect dynamic games and epidemic models to address the recent challenges related to screening, containment, and mitigation strategies for epidemics. This collection covers broad application areas in networks, human behaviors, and epidemiology as well as a diverse range of dynamic game methods, including evolutionary games, differential games, and mean-field games.

In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner, i.e., only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set.

This paper treats comprehensively the construction of problems from nonlinear dynamics and constrained optimization amenable to parameter continuation techniques and with particular emphasis on multi-segment boundary-value problems with delay. The discussion is grounded in the context of the COCO software package and its explicit support for community-driven development. To this end, the paper first formalizes the COCO construction paradigm for augmented continuation problems compatible with simultaneous analysis of implicitly defined manifolds of solutions to nonlinear equations and the corresponding adjoint variables associated with optimization of scalar objective functions along such manifolds. The paper uses applications to data assimilation from finite time histories and phase response analysis of periodic orbits to identify a universal paradigm of construction that permits abstraction and generalization. It then details the theoretical framework for a COCO-compatible toolbox able to support the analysis of a large family of delay-coupled multi-segment boundary-value problems, including periodic orbits, quasiperiodic orbits, connecting orbits, initial-value problems, and optimal control problems, as illustrated in a suite of numerical examples. The paper aims to present a pedagogical treatment that is accessible to the novice and inspiring to the expert by appealing to the many senses of the applied nonlinear dynamicist. Sprinkled among a systematic discussion of problem construction, graph representations of delay-coupled problems, and vectorized formulas for problem discretization, the paper includes an original derivation using Lagrangian sensitivity analysis of phase-response functionals for periodic-orbit problems in abstract Banach spaces, as well as a demonstration of the regularizing benefits of multi-dimensional manifold continuation for near-singular problems.

The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.

Tests on infill masonry walls have been widely performed by many researchers and for a long time with the main purpose of characterising the infill performance under earthquake-type excitations. However, most of these works deal with laboratory tests on purpose-built specimens. More recently, vibration-based tests have been also adopted to investigate the influence of the non-structural elements on the dynamic behaviour of buildings, with the advantage that this kind of tests can be performed both on laboratory specimens and on in-situ buildings. However, differently from classical infill tests (i.e., monotonic or cyclic lateral load tests, out of plane tests, etc.), a limited number of works is available in the literature discussing the outcomes and possible procedures for testing infilled structures with vibration-based methods aimed to investigate the role of the non-structural components. This paper presents a literature review of research works dealing with vibration-based tests performed on RC frame structures with the main target of discussing the influence of non-structural components on the dynamics of buildings. Tests on infilled buildings performed during the construction, in operating conditions and after the damage occurred due to earthquake shakings, are discussed. Furthermore, a comprehensive review about papers discussing vibration-based tests performed on infill masonry walls is presented and in-depth investigated with the aim of finding possible correlations between the dynamic test outcomes and the infill geometric and mechanical properties. From this study it comes out the need of further experimental data on both undamaged and damaged infills in order to get more reliable correlations.

In the last decade, the application of membrane-inspired evolutionary algorithms in real-life problems has attracted much attention due to their flexibility and parallelizability. Almost seven years have passed since the first membrane algorithms survey paper was published in 2014. Considering the importance and ongoing research on such algorithms and their applications in various disciplines, this paper presents a comprehensive review of the published literature and suggests future directions. This review aims to summarize and analyze membrane algorithms based on the used nature-inspired algorithm, membrane structure, membrane rules, and their merits and demerits. Furthermore, an extensive bibliography about their real-world applications is presented.

The version of record is available online at: http://dx.doi.org/10.1007/s10623-021-00988-z According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that, if the minimum distance of the code is larger than a certain threshold then the TA property implies the rest. Silverberg et al. ask if there is some kind of tracing capability left when the minimum distance falls below the threshold. Under different assumptions, several papers have given a negative answer to the question. In this paper, further progress is made. We establish values of the minimum distance for which Reed-Solomon codes do not posses the separating property. This work has been supported by the Spanish Government Grant TCO-RISEBLOCK (PID2019-110224RB-I00) MINECO .

This paper is a review, which focuses on our work, while including an analysis of many works of other researchers in the field of quaternionic regularization. The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel (KS) variables and Euler (Rodrigues-Hamilton) parameters are analyzed. These models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point particle. This paper also covers some applications of these models. Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics. However, the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author. More general (compared with the KS equations) quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented. These equations are derived with the assumption that the KS bilinear relation was not satisfied. The main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented, together with regular equations in the KS variables and Euler parameters, derived by the aforementioned theory. We also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters, developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.

In the paper we will focus on weakly Światkowski functions. We say that f satisfies the weak Świa̧tkowski condition (or f is a weakly Świa̧tkowski function) if for all $$x_1, x_2$$ x 1 , x 2 with $$f(x_1)< f(x_2)$$ f ( x 1 ) < f ( x 2 ) there is a point x between $$x_1$$ x 1 and $$x_2$$ x 2 such that $$f(x_1) f ( x 1 ) < f ( x ) < f ( x 2 ) . This definition is a modification of the Świa̧tkowski condition, in which point x mentioned above has to be a point of continuity of f. In the paper we will examine some properties of weakly Świa̧tkowski functions and consider lineability and algebrability of some families of functions related to them.

The main goal of this paper is to investigate the properties and connections of neatly and semistrictly quasiconvex functions, especially when they appear in constrained and unconstrained optimization problems. The lower global subdifferential, recently introduced in the literature, plays an essential role in this study. We present several optimality conditions for constrained and unconstrained nonsmooth neatly/semistrictly quasiconvex optimization problems in terms of lower global subdifferentials. To this end, for a constrained optimization problem, we present some characterizations for the normal and tangent cones and the cone of feasible directions of the feasible set. Some relationships between the Greenberg-Pierskalla, tangentially and lower global subdifferentials of neatly and semistrictly quasiconvex functions are also given. The mentioned relationships show that the outcomes of this paper generalize some results existing in the literature.

Z-complementary pairs (ZCPs) are well-known, but few work has dedicated to their aperiodic cross-correlation. One objective of this paper is to propose a novel class of sequence pairs, called ``preferred Z-complementary pairs (PZCPs)'', where each sequence pair has Z-complementary property, and the aperiodic cross-correlation between the two sequences in each pair are zeros within a certain region. Some constructions of PZCPs from Golay complementary pairs (GCPs) are presented. Another objective of this paper is to apply PZCPs to design Doppler resilient waveforms combined with equal sums of powers (ESPs). Simulation results show that the proposed waveform has good Doppler tolerance. Mathematics Subject Classification (2000) 06E30 · 11T71 · 94A60

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed method's capability using the implicit gradient method for compressible flows., Comment: arXiv admin note: substantial text overlap with arXiv:2106.01738

In this paper, motivated by the competitive performance of the proximal stochastic variance reduction gradient (Prox-SVRG) method, a novel general inertial Prox-SVRG (GIProx-SVRG) algorithm is proposed for solving a class of nonconvex finite sum problems. More precisely, Nesterov’s momentum trick-based extrapolation accelerated step is incorporated into the framework of Prox-SVRG method. The GIProx-SVRG algorithm possesses more general accelerated expression and thus can potentially achieve accelerated convergence speed. Moreover, based on the supermartingale convergence theory and the error bound condition, we establish a linear convergence rate for the iterate sequence generated by the GIProx-SVRG algorithm. We observe that there is no theory in which the general extrapolation technique is incorporated into the Prox-SVRG method, whereas we establish such a theory in this paper. Experimental results demonstrate the superiority of our method over state-of-the-art methods.

Equal channel angular drawing (ECAD) represents the most successful severe plastic deformation (SPD) technique for continuous industrial manufacturing of longer wires, with a constant cross-section, characterized by smaller diameters and better mechanical properties (i.e. high strains and hardness) mainly attributed to the grain size refinement. In this paper an advanced innovative concept to impose SPD, on commercial 1370 pure aluminium wires (Al 99.7%), is proposed to improve the flexibility of the classic manufacturing method of ECAD by controlling and regulating process parameters in real time to obtain several combinations of mechanical properties and to increase manufacture productivity. This paper provides a preliminary analysis of mechanical and microstructural changes occurring during ECAD process and, preserving the principle of the ECAD method, describes an innovative concept of plastic deformation showing the potential improvements to practice. The proposed manufacturing system has been validated by finite element analysis (FEA) implementing a flow stress empirical model, that includes the influence of the grain size change, for the material behaviour and two customized user-subroutines for predicting grain refinement and hardness variation. The study demonstrates the possibility to renew the classic industrial techniques within an Industry 4.0 ecosystem.

In this paper, we establish the a priori$C^{2}$ C 2 estimates for solutions of a class of obstacle problem for Hessian equations on Riemannian manifolds. Some applications are also discussed. The main contribution of this paper is the boundary estimates for second-order derivatives.

Background In the global effort to discover biomarkers for cancer prognosis, prediction tools have become essential resources. TCR (T cell receptor) repertoires contain important features that differentiate healthy controls from cancer patients or differentiate outcomes for patients being treated with different drugs. Considering, tools that can easily and quickly generate and identify important features out of TCR repertoire data and build accurate classifiers to predict future outcomes are essential. Results This paper introduces GENTLE (GENerator of T cell receptor repertoire features for machine LEarning): an open-source, user-friendly web-application tool that allows TCR repertoire researchers to discover important features; to create classifier models and evaluate them with metrics; and to quickly generate visualizations for data interpretations. We performed a case study with repertoires of TRegs (regulatory T cells) and TConvs (conventional T cells) from healthy controls versus patients with breast cancer. We showed that diversity features were able to distinguish between the groups. Moreover, the classifiers built with these features could correctly classify samples (‘Healthy’ or ‘Breast Cancer’)from the TRegs repertoire when trained with the TConvs repertoire, and from the TConvs repertoire when trained with the TRegs repertoire. Conclusion The paper walks through installing and using GENTLE and presents a case study and results to demonstrate the application’s utility. GENTLE is geared towards any researcher working with TCR repertoire data and aims to discover predictive features from these data and build accurate classifiers. GENTLE is available on https://github.com/dhiego22/gentle and https://share.streamlit.io/dhiego22/gentle/main/gentle.py.

Fluid dynamic equations are used to model various phenomena arising from physics, engineering, astrophysics, geophysics. One feature is that they take place at different time and length scales and it is important to understand which phenomena occur according to the use of single scales or to the interactions of them. From a mathematical point of view, these various physical behaviours give rise to different singular limits and, consequently to a different analysis of the asymptotic state of the governing equations. In this paper we will analyse a very simplified model given by a linearised continuity equation and by the classical momentum equation which include terms that take into account of rotation and we will show, according to the values of different scales, that the asymptotic behaviour of the model will be those of an incompressible fluid or of a geostrophic flow. Finally we point out, that the set of equations analysed in the paper may also fit in the artificial compressibility approximation methods.

Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Furthermore, the conic-segmentation SVM (CS-SVM) is a natural multiclass analogue of the standard binary SVM, as CS-SVM models are dealing with the situation where the exact values of the data points are known. This paper studies CS-SVM when the data points are uncertain or mislabelled. With some properties known for the distributions, a chance-constrained CS-SVM approach is used to ensure the small probability of misclassification for the uncertain data. The geometric interpretation is presented to show how CS-SVM works. Finally, we present experimental results to investigate the chance constrained CS-SVM's performance., Accepted paper for Annals of Mathematics and Artificial Intelligence

Let $G$ be a finite group, and let ${\rm{cd}}(G)$ denote the set of degrees of the irreducible complex characters of $G$. Define then the character degree graph $\Delta(G)$ as the (simple undirected) graph whose vertices are the prime divisors of the numbers in ${\rm{cd}}(G)$, and two distinct vertices $p$, $q$ are adjacent if and only if $pq$ divides some number in ${\rm{cd}}(G)$. This paper continues the work, started in [7], toward the classification of the finite non-solvable groups whose degree graph possesses a cut-vertex, i.e., a vertex whose removal increases the number of connected components of the graph. While, in [7], groups with no composition factors isomorphic to ${\rm{PSL}}_2(t^a)$ (for any prime power $t^a\geq 4$) were treated, here we consider the complementary situation in the case when $t$ is odd and $t^a> 5$. The proof of this classification will be then completed in the third and last paper of this series ([8]), that deals with the case $t=2$.

In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann–Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the $\Delta ^{2}$ Δ 2 , which will be useful to obtain the convexity results. We examine the correlation between the positivity of $({}^{\mathrm{RL}}_{w_{0}}\Delta ^{\alpha} \mathrm{f} )( \mathrm{t})$ ( w 0 RL Δ α f ) ( t ) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of $(2,3)$ ( 2 , 3 ) , $\mathscr{H}_{\mathrm{k},\epsilon}$ H k , ϵ and $\mathscr{M}_{\mathrm{k},\epsilon}$ M k , ϵ . The decrease of these sets allows us to obtain the relationship between the negative lower bound of $({}^{\mathrm{RL}}_{w_{0}}\Delta ^{\alpha} \mathrm{f} )( \mathrm{t})$ ( w 0 RL Δ α f ) ( t ) and convexity of the function on a finite time set $\mathrm{N}_{w_{0}}^{\mathrm{P}}:=\{w_{0}, w_{0}+1, w_{0}+2,\dots , \mathrm{P}\}$ N w 0 P : = { w 0 , w 0 + 1 , w 0 + 2 , … , P } for some $\mathrm{P}\in \mathrm{N}_{w_{0}}:=\{w_{0}, w_{0}+1, w_{0}+2,\dots \}$ P ∈ N w 0 : = { w 0 , w 0 + 1 , w 0 + 2 , … } . The numerical part of the paper is dedicated to examinin the validity of the sets $\mathscr{H}_{\mathrm{k},\epsilon}$ H k , ϵ and $\mathscr{M}_{\mathrm{k},\epsilon}$ M k , ϵ for different values of k and ϵ. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.

In this paper, we establish several new inequalities for q-differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We also show that the inequalities proved in this paper generalize the results given in earlier works. Moreover, we give some examples in order to demonstrate our main results.