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The maximum vibration transmissibility of paper honeycomb sandwich structures with different sizes of honeycomb core under various static stresses was investigated using the sine frequency sweep test. The effects of the cell length of the honeycomb, the thickness of the sandwich structure, and the static stress on the maximum vibration transmissibility were evaluated and a linear polynomial equation for evaluating the maximum vibration transmissibility was obtained. The results show that the maximum vibration transmissibility increases steadily with the increase in the cell length of the honeycomb, the thickness of the sandwich structure, and the static stress. The proposed equation for the maximum vibration transmissibility is suitable for predicting the maximum vibration transmissibility of paper honeycomb sandwich structures. In addition, the fitted three-dimensional diagrams of the effects of the factors on the maximum vibration transmissibility derived from the evaluation equation were shown to be in good agreement with the experimental results.

In this paper, we discuss the validity of the result of Khuangsatung and Kangtunyakarn [Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions, Filomat 32(1) (2018) 305–309].

In this short paper, we show that there does not exist a noncompact Type-I [Formula: see text]-solution of the Ricci flow with positive curvature in dimension 3.

A fractal tiling or [Formula: see text]-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. By substitution rule of tilings, this short paper presents a very simple strategy to create a great number of [Formula: see text]-tilings. The substitution tiling Equithirds is demonstrated to show how to achieve it in detail. The method can be generalized to every tiling that can be constructed by substitution rule.

In [A. J. Diesl, Classes of strongly clean rings, Ph.D. Dissertation, University of California, Berkely (2006); Nil clean rings, J. Algebra383 (2013) 197–211], a nil clean ring was defined as a ring for which every element is the sum of a nilpotent and an idempotent. In this short paper, we characterize nil clean commutative group rings.

In this paper, we present fuzzy data processing based on the Algebraic System of Aggregates (ASA) which operates with complex data structures called aggregates. An aggregate is a tuple of arbitrary tuples whose elements can be both crisp and fuzzy values. There are three categories of operations on aggregates in ASA: logical operations, ordering operations, and arithmetical operations. In this paper, we define the fuzzy case of ordering and logical operations. ASA has a practical value for data processing in various tasks where an object (process, phenomenon) of study needs to be defined through multiple measurable characteristics of its behavior changing in the course of time. In some cases, such characteristics cannot measured but only estimated with certain accuracy and thus, they are represented as fuzzy values. Application of ASA for processing of imprecise biomedical data is discussed in the paper as well.

The classical pricing theory requires that the simple sets of outcomes are extended, using the Kolmogorov Extension Theorem, to a sigma-algebra of measurable sets in an infinite-dimensional sample space whose elements are continuous paths; the process involved are represented by appropriate stochastic differential equations (using Itô calculus); a suitable measure for the sample space can be found by means of the Girsanov and Radon–Nikodym Theorems; the derivative asset valuation is determined by means of an expression using Lebesgue integration. It is known that if we replace Lebesgue’s by the generalized Riemann integration to obtain the expectation, the same result can be achieved by elementary methods. In this paper, we consider the Black–Scholes PDE subject to impulse action. We replace the process which follows a geometric Brownian motion by a process which has additional impulsive displacements at random times. Instead of constants, the volatility and the risk-free interest rate are considered as continuous functions which can vary in time. Using the Feynman–Ka[Formula: see text] formulation based on generalized Riemann integration, we obtain a pricing formula for a European call option which copes with many discontinuities. This paper seeks to develop techniques of mathematical analysis in derivative pricing theory which are less constrained by the standard assumption of lognormality of prices. Accordingly, the paper is aimed primarily at analysis rather than finance. An example is given to illustrate the main results.

Uncertain time series analysis is a method to predict future values based on imprecisely observed values. As a basic model of uncertain time series, an uncertain autoregressive model has been presented. However, the existing paper ignores the temporal dependence information embedded in time-series data. In dealing with this issue, this paper adds a least absolute shrinkage and selection operator penalty to the traditional uncertain autoregressive model and selects the optimum order of the model according to Akaike’s final prediction error criterion. Finally, two numerical examples are given to illustrate the effectiveness of the model and compare the results predicted by the uncertain autoregressive model with the principle of least squares.

In Enochs' relative homological dimension theory occur the so called (co)resolvent and (co)proper dimensions which are defined using proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some authors have been interested in relative homological dimensions defined by just exact sequences. In this paper, we contribute to the investigation of these relative homological dimensions. We first study the relation between these two kinds of relative homological dimensions and establish some "transfer results" under adjoint pairs. Then, relative global dimensions are studied which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories. At the end of the paper, relative derived functors are studied and generalizations of some known results of balance for relative homology are established., To appear in a Special Issue of Algebra Colloquium; proceedings of The International Conference on Algebra and Related Topics (ICART 2018)

This editorial paper is devoted to present the papers published in a special issue focused on modeling, qualitative analysis and simulation of the collective dynamics of living, self-propelled particles. A critical analysis of the overall contents of the issue is proposed, thus leading to a forward look to research perspectives.

This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples.

Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives.

It is much more practical to use the [Formula: see text]-norm than the minimum in defining the fuzzy graph. Hence, the concept of [Formula: see text]-fuzzy graph was introduced by Mordeson et al. in [J. N. Mordeson and S. Mathew, [Formula: see text]-norm Fuzzy Graphs, New Mathematics and Natural Computation 14(1) (2018) 129–143]. In this paper, we concentrate on the relatively new concept of fuzzy adjacency matrix of that [Formula: see text]-fuzzy graphs. The purpose of this paper is to further develop a product of this fuzzy adjacency matrix based on [Formula: see text]-fuzzy graphs. Moreover, two kinds of Boolean matrix are defined and relation between Normal Boolean matrix, product of adjacency matrix and 1-level cut Boolean matrix is obtained.

In this paper, we establish the error analysis for distributed pairwise learning with multi-penalty regularization, based on a divide-and-conquer strategy. We demonstrate with [Formula: see text]-error bound that the learning performance of this distributed learning scheme is as good as that of a single machine which could process the whole data. With semi-supervised data, we can relax the restriction of the number of local machines and enlarge the range of the target function to guarantee the optimal learning rate. As a concrete example, we show that the work in this paper can apply to the distributed pairwise learning algorithm with manifold regularization.

This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of the kinetic models developed in the last 10 years on the aforementioned topics so that overlapping with previous reviews can be avoided. Although the main focus of this paper lies on the mesoscopic models for collective dynamics, we provide a brief overview on the corresponding micro and macroscopic models, and discuss intermediate role of mesoscopic model between them. Moreover, we provide a number of selected challenging research perspectives for readers’ attention.

Molodtsov initiated the soft set theory, providing a general mathematical framework for handling uncertainties that we encounter in various real-life problems. The main object of this paper is to lay a foundation for providing a new soft algebraic tool for considering many problems that contain uncertainties. In this paper, we introduce a new kind of soft ring structure called [Formula: see text]-soft-intersectional ring based on some results of soft sets and intersection operations on sets. We also define [Formula: see text]-soft-intersectional ideal and [Formula: see text]-soft-intersectional subring, and investigate some of their properties using these new concepts. We obtain some results in ring theory based on [Formula: see text]-soft intersection sense and its application in ring structures. Furthermore, we provide relationships between soft-intersectional ring and [Formula: see text]-soft-intersectional ring, soft-intersectional ideal and [Formula: see text]-soft-intersectional ideal.

The aim of this paper is first to provide a presentation of the papers published in a special issue devoted to modeling, qualitative analysis, control and simulations of large systems of living entities, viewed as active particles, related to real-life applications, and subsequently to present some prospective ideas on possible future research programs for the development of mathematical tools to model living systems.

Many problems in applications are defined on a bounded interval. Therefore, wavelets and framelets on a bounded interval are of importance in both theory and application. There is a great deal of effort in the literature on constructing various wavelets on a bounded interval and exploring their applications in areas such as numerical mathematics and signal processing. However, many papers on this topic mainly deal with individual examples which often have many boundary wavelets with complicated structures. In this paper, we shall propose a method for constructing wavelets and framelets in [Formula: see text] from symmetric wavelets and framelets on the real line. The constructed wavelets and framelets in [Formula: see text] often have a few simple boundary wavelets/framelets with the additional flexibility to satisfy various desired boundary conditions. To illustrate our construction method, from several spline refinable vector functions, we present several examples of (bi)orthogonal wavelets and spline tight framelets in [Formula: see text] with very simple boundary wavelets/framelets.

In this paper, an HIV infection model with eclipse phase, humoral immune response and immunological delay has been discussed. By studying the characteristic equations of the model, the local stability analysis of various equilibrium points has been explored. Treating the delay as the bifurcation parameter, it has been shown that the delay can destabilize the stability of the infected steady-state leading to Hopf bifurcation and periodic solutions. By using Lyapunov functionals and LaSalle’s invariance principle, the global stability analysis of the boundary equilibrium points has also been explored. It has also been shown numerically that the inclusion of the drug therapy in the model generates sporadic outbursts of virus called viral blips. In the end, numerical simulations have been employed to justify the analytical results proved in the paper. Biologically, the proposed model can explain the presence of viral blips in the system, during the introduction of HAART, as observed in the HIV-infected patient. These blips could mark the viral advancement in the system, thus resulting in complete immunological failure. One of the reasons for these viral blips can be the presence of delay in the activation of immunological response. But the development of drug-resistive virus could also be the reason for this sudden rise in viral loads. Moreover, the incorporation of the delay in the model generates oscillations and periodicity in the model, thus validating the long latency period seen in most HIV-infected patients. Also, a longer delay in the activation of immune response marks a viral advancement in the viral timeline resulting in viral blips, which signify the evolution of the virus.

Interval-valued Pythagorean fuzzy set is one of the successful extensions of the interval-valued intuitionistic fuzzy set for handling the uncertainties in the data. Under this environment, in this paper, we introduce the notion of induced interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (I-IVPFEOWA) aggregation operator. Some of its desirable properties namely, idempotency, boundedness, commutatively, monotonicity have also been proved. The main advantage of using the proposed operator is that this operator gives a more complete view of the problem to the decision-makers. The method proposed in this paper provides more general, more accurate and precise results as compared to the existing methods. Therefore this method play a vital role in real world problems. Finally, we apply the proposed operator to deal with multi-attribute group decision- making problems under interval-valued Pythagorean fuzzy information. The approach has been illustrated with a numerical example from the field of the decision-making problems to show the validity, practicality and effectiveness of the new approach.

Ranking of interval-valued intuitionistic fuzzy (IVIF) numbers is a most popular and elegant work in the area of decision-making of several real-world problems. Some limited methods have been presented concerning the ranking of IVIF sets in literature. In the present paper, we generalize the intuitionistic fuzzy (IF) number to interval-valued intuitionistic fuzzy number by defining interval membership and nonmembership functions instead of fixed-valued function and hence it will present uncertain situation better than IF numbers. It may also be applied in data analysis, industrial management, artificial intelligence, forecasting, time series and so on. In this paper, ranking methodology of IVIF numbers is presented, for this first we define the value and ambiguity of IVIF numbers. Proposed ranking method also is compared with existing ranking methods. Further, IVIF numbers are used to capture fuzziness and hesitation in transportation problem (TP), and we propose a new method to find optimal solutions of TP with IVIF number parameters and finally, a numerical example is given to demonstrate the proposed method.

In 1982, Drezner proposed the [Formula: see text]-centroid problem on the plane, in which two players, called the leader and the follower, open facilities to provide service to customers in a competitive manner. The leader opens the first facility, and the follower opens the second. Customers will each patronize the facility closer to them (with ties broken in favor of the first one), thereby deciding the market share of the two facilities. The goal is to find the best position for the leader’s facility so that its market share is maximized. The best algorithm of this problem is an [Formula: see text]-time parametric search approach, which searches over the space of market share values. In the same paper, Drezner also proposed a generalized version of [Formula: see text]-centroid problem by introducing a minimal distance constraint [Formula: see text], such that the follower’s facility is not allowed to be located within a distance [Formula: see text] from the leader’s. He proposed an [Formula: see text]-time algorithm for this generalized version by identifying [Formula: see text] points as the candidates of the optimal solution and checking the market share for each of them. In this paper, we develop a new parametric search approach searching over the [Formula: see text] candidate points, and present an [Formula: see text]-time algorithm for this generalized version, thereby closing the [Formula: see text] gap between the two bounds.

In this paper, we consider the following dual-gradient chemotaxis model [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary, [Formula: see text] and [Formula: see text]. The model was proposed to interpret the spontaneous aggregation of microglia in Alzheimer’s disease due to the interaction of attractive and repulsive chemicals released by the microglia. It has been shown in the literature that, when [Formula: see text], the solution of the model with homogeneous Neumann boundary conditions either blows up or asymptotically decays to a constant in multi-dimensions depending on the sign of [Formula: see text], which means there is no pattern formation. In this paper, we shall show as [Formula: see text], the uniformly-in-time bounded global classical solutions exist in multi-dimensions and hence pattern formation can develop. This is significantly different from the results for the case [Formula: see text]. We perform the numerical simulations to illustrate the various patterns generated by the model, verify our analytical results and predict some unsolved questions. Biological applications of our results are discussed and open problems are presented.

Dragon-King a is introduced in this paper as the manifestation of a disaster incident for a Smart Grid’s blackout for a day-ahead. The quintessential incident is being generated by an artificial black hole, it then spreads quickly into transmission lines. Consequently, it bursts into space-time transition regions. This paper reveals all the essential characteristics of the Dragon-King, it has non-isotropic stochastic kinematics. Regardless of its huge manifestation of unwanted phenomena, the Dragon-King is controllable. We also describe the mechanism of an updated complexity, spinning cosmic string and a messenger system in this paper. Furthermore, the control strategy of the feedback controller which ultimately leads to a stable normal operation is also reported in this paper.

This paper focuses on two very important questions: “what is the future of a hybrid mathematical structure of soft set in science and social science?” and “why should we take care to use hybrid structures of soft set?”. At present, these are the most fundamental questions; which encircle a few prominent areas of mathematics of uncertainties viz. fuzzy set theory, rough set theory, vague set theory, hesitant fuzzy set theory, IVFS theory, IT2FS theory, etc. In this paper, we review connections of soft set theory and hybrid structures in a non-technical manner; so that it may be helpful for a non-mathematician to think carefully to apply hybrid structures in his research areas. Moreover, we must express that we do not have any intention to nullify contributions of fuzzy set theory or rough set theory, etc. to mankind; but our main intention is to show that we must be careful to develop any new hybrid structure with soft set. Here, we have a short discussion on needs of artificial psychology and artificial philosophy to enrich artificial intelligence.

In this paper, we present the analysis of the discontinuous Galerkin dual-primal isogeometric tearing and interconnecting method (dG-IETI-DP) for the two-dimensional case where we only consider vertex primal variables. The dG-IETI-DP method is a combination of the dual-primal isogeometric tearing and interconnecting method (IETI-DP) with the discontinuous Galerkin (dG) method. We use the dG method only on the interfaces to couple different patches. This enables us to handle non-matching grids on patch interfaces as well as segmentation crimes (gaps and overlaps) between the patches. The purpose of this paper is to derive quasi-optimal bounds for the condition number of the preconditioned system with respect to the maximal ratio $H/h:=\max_k(H_k/h_k)$ of subdomain diameter and meshsize. We show that the constant is independent of $h_k$ and $H_k$, but depends on the ratio of meshsizes of neighbouring patches $h_\ell/h_k$., arXiv admin note: text overlap with arXiv:1601.01808

This paper presents a global study of the class [Formula: see text] of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the coalescence of a finite singularity and an infinite singularity. This class can be divided into two different families, namely, [Formula: see text] phase portraits possessing a finite saddle-node as the only finite singularity and [Formula: see text] phase portraits possessing a finite saddle-node and also a simple finite elemental singularity. Each one of these two families is given by a specific normal form. The study of family [Formula: see text] was reported in [Artés et al., 2020b] where the authors obtained [Formula: see text] topologically distinct phase portraits for systems in the closure [Formula: see text]. In this paper, we provide the complete study of the geometry of family [Formula: see text]. This family which modulo the action of the affine group and time homotheties is three-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the three-dimensional real projective space. The respective bifurcation diagram yields 631 subsets with 226 topologically distinct phase portraits for systems in the closure [Formula: see text] within the representatives of [Formula: see text] given by a specific normal form. Some of these phase portraits are proven to have at least three limit cycles.

Dynamical systems generated by continuous maps on compact metric spaces can have various properties, e.g. the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, the existence of an omega-limit set containing two minimal sets and other. In [Kočan et al., 2014] we consider six such properties and survey the relations among them for the cases of graph maps, dendrite maps and maps on compact metric spaces. In this paper, we consider fourteen such properties, provide new results and survey all the relations among the properties for the case of graph maps and all known relations for the case of dendrite maps. We formulate some open problems at the end of the paper.

In the paper, the theoretical study on some experimental and numerical results of grazing bifurcation for a soft impacting system are analyzed. After the conditions under which nonimpact period-1 orbit and grazing bifurcation exist are given, we prove that an impact period-1 orbit exists by the implicit function theorem. The details of these periodic orbits are also investigated, which also helps us numerically find them. The method in this paper is still efficient for the multiperiodic orbits with single impact.

The paper concludes the series of the research works on the interdisciplinary analytical approach (the so-called bifurcation-fractal analytics) to forecast the dynamics of pulse systems on the basis of modified bifurcation diagrams. These diagrams are intended to integrate incompatible-in-traditional-spaces images (mainly transients from the phase space and evolution pictures from the parametric space) in order to analyze whether the running transient converges towards the domain of a desirable behavior taking into account its qualitative and quantitative characteristics. The interdisciplinary context of the analytics appears because the novel mathematical images need physical meaning and further this research should be continued for proposing the expedient engineering decision. Here, the advantages to forecast the evolutionary tendencies in different scales of the modified bifurcation diagrams are illustrated by computer-based simulations. Translations of the mathematical images into their physical implementations follow the principle of the bifurcation poker and the principle of the spatial nonuniformity. The experimental results to verify these principles are presented. Variants of engineering proposals are commented in comparison with traditional abilities of the small-signal design. The results systematized in the paper confirm that fundamental obstacles to forecast abnormal evolutionary changes in the dynamics of pulse energy converters are absent. Prospects of the outcome from the experience accumulated in engineering to similar problem statements independently of a pulse system nature are finally discussed. And the regulatory hypothesis on local climate dynamics is considered in this connection. This discussion is quite suitable here because a local climate system can be described as a converter of the solar energy under a specific pulse control realized by the astronomic forcing and there are circumstances, in which electrotechnical simulations can remain a unique way to accelerate the research on prerequisites and sequels of the forthcoming climate changes. Then the bifurcation-fractal analytics provides an initial theoretical foundation to this research.

Directed fuzzy networks are introduced in this paper. They are normalized node capacitated networks and provide a good platform to model different types of complicated flows in nature. A directed fuzzy network version of Menger’s theorem and the celebrated Max flow Min cut theorem are also provided. Since the maximum flow through minimum number of directed internally disjoint paths is important in quality of service (QoS) problems in networking, the results in this paper can be applied to a wide variety of problems.

In this paper, we consider an interval coverage problem. We are given [Formula: see text] intervals of the same length on a line [Formula: see text] and a line segment [Formula: see text] on [Formula: see text]. Each interval has a nonnegative weight. The goal is to move the intervals along [Formula: see text] such that every point of [Formula: see text] is covered by at least one interval and the maximum moving cost of all intervals is minimized, where the moving cost of each interval is its moving distance times its weight. Algorithms for the “unweighted” version of this problem have been given before. In this paper, we present a first-known algorithm for this weighted version and our algorithm runs in [Formula: see text] time. The problem has applications in mobile sensor barrier coverage, where [Formula: see text] is the barrier and each interval is the covering interval of a mobile sensor.

We propose that businesses, government, and not-for-profit entities could benefit from a better understanding of organizational behavior through the lens of a contemporary global culture model. Human resourcing and partnering decisions could be improved by using global culture to ensure a better organizational-fit as well as to reduce the risk of destructive relationship dependencies. For an extreme-limits example, a company could inadvertently hire a terrorist or a social loafer seeking to steal competitive intelligence. A big data approach supported by a socio-cultural framework could help in hypothesis testing which is essential for advancing the body of knowledge in organizational behavior. This paper will make a scholarly contribution by identifying literature relevant to collecting and analyzing organizational big data that could explain beneficial socio-cultural behavior. This paper will explore how sources of qualitative big data could be collected and then analyzed to measure organizational-fit factors relevant for decision-making.

The recent research evolution on big data has brought exciting aspiration to mathematicians, computer scientists and business professionals alike. However, the lack of a sound mathematical foundation presents itself as a real challenge amidst the swarm of big data marketing activities. This paper intends to propose a possible mathematical theory as a foundation for big data research. Specifically, we propose the concept of the adjective “big” as a mathematical operator, furthermore, the concept of so-called “big” logically and naturally fits the concept of being “linguistics variable” as per fuzzy logic research community for decades. The consequence of adopting such a mathematical modeling can be profoundly considered as an abstraction of the technologies, systems, tools for data management and processing that transforms data into big data. In addition, the concept of infinity of the big data is based on the theory of calculus and the set theory. Furthermore, the concept of relativity of the big data, as we find out, is based on the operations of the fuzzy subsets theory. The proposed approach in this paper, we hope, can facilitate and open up more opportunities for big data research and developments on big data analytics, business analytics, big data intelligence, big data computing as well as big data science.

In this paper, we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler–Lagrange equations for the height function of the graph are derived. This is the natural generalisation of the well-known linearisation in the Monge gauge for initially flat surfaces. We discuss energy perturbations of point constraints and point forces acting on the surface. We establish existence and uniqueness results for weak solutions on spheres and on tori. Algorithms for the computation of numerical solutions in the general setting are provided. We present numerical examples which highlight the behaviour of the surface deformations in different settings at the end of the paper.

This paper proposes a conceptual revisiting of population dynamics to include heterogeneous behaviors of individuals, mutations, and selection. The first part of the paper focuses on the derivation of a general mathematical structure which permits to describe systems composed of individuals whose interactions are stochastic. Hybrid models where some of the populations follow a deterministic dynamics are also discussed. The second part deals with two specific applications, namely the effect of the cellular aging in the virus infection process and the dynamics of virus mutation and competition with the immune system. Sample simulations are presented and classical models of population dynamics are critically analyzed in light of the proposed approach.

This paper addresses some preliminary steps toward the modeling and qualitative analysis of swarms viewed as living complex systems. The approach is based on the methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlocal, nonlinearly additive and modeled by theoretical tools of stochastic game theory. Collective learning theory can play an important role in the modeling approach. We present a kinetic equation incorporating the Cucker–Smale flocking force and stochastic game theoretic interactions in collision operators. We also present a sufficient framework leading to the asymptotic velocity alignment and global existence of smooth solutions for the proposed kinetic model with a special kernel. Analytic results on the global existence and flocking dynamics are presented, while the last part of the paper looks ahead to research perspectives.

In theoretical ecology and community ecology, it is still unclear how phylogenetic community structure and species distributions are linked together. In this paper, a neutral model for evaluating phylogenetic constraints on species diversity and distribution patterns is developed to address these issues. To accomplish this, temporal species distribution and diversity patterns are evaluated and simulated by considering the impact of phylogenetic relatedness of species in a lattice landscape with square grids. A continuous patch for the resultant distributional range map of a species is defined as a group of grids in which the interior grids are adjacent to each other while the edge grids of the patch are isolated from other remaining grids in the range map. The adjacency or isolation of a grid with respect to another grid follows the von Neumann neighborhood criterion. The hypothesis tested is: phylogenetically closely related species tend to avoid each other (phylogenetic dilution), which produces a phylogenetic overdispersion pattern. In this case, all species have similar species abundances and distribution-patch size patterns. In contrast, if closely related species tend to associate together (phylogenetic concentration), a phylogenetic clustering pattern emerges: phylogenetically distinct species tend to have higher abundances and more large distribution patches. Using simulations, this paper presents results which demonstrate the reverse phenomenon: if it is assumed that phylogenetic relatedness of species is modeled as a dilution effect, the resultant distributional maps for evolutionarily distinct species present significantly increased numbers of continuous large patches. An evolutionarily distinct clade tends to have significantly higher relative abundance than other clades in all simulations. It was also found that if phylogenetic relatedness of species is modeled as a concentration effect, the simulated distributional map of each species would present a similar percentage of large patches for both evolutionarily unique and common clades for many cases when the community size is large enough. However, being similar to dilution effect, the resultant species relative abundance for evolutionarily unique clade is significantly higher than that for evolutionarily common clade. In conclusion, evolutionary distinct species will have more chances to survive with high populations and less fragmented distributional range in environments where the phylogenetic dilution effect is functioning. It is hoped that these results contributed to clarifying the complex associations generated by phylogenetic community structure in future ecological and evolutionary studies.

We in this paper derive necessary and sufficient conditions for the system of the periodic discrete-time coupled Sylvester matrix equations AkXk + YkBk = Mk, CkXk+1 + YkDk = Nk (k = 1, 2) over the quaternion algebra to be consistent in terms of ranks and generalized inverses of the coefficient matrices. We also give an expression of the general solution to the system when it is solvable. The findings of this paper generalize some known results in the literature.

Experience-based reasoning (EBR) is a paradigm used in almost every human activity as a part of human reasoning. However, EBR has not been seriously studied from a logical viewpoint. This paper will attempt to fill this gap by providing a unified logical approach to EBR. More specifically, this paper first examines EBR and inference rules. Then it proposes eight different rules of inference for EBR, which cover all possible EBRs from a logical viewpoint. These eight different rules of inference constitute the fundamentals for all EBR paradigms, and therefore will be the theoretical foundation for EBR. The proposed approach will facilitate research and development of EBR, human reasoning, and common sense reasoning.

This paper deals with an analysis of the free vibration of nonprismatic thin-walled beams, with a special focus on the effect of a change in the support point location on the eigenfrequencies of the systems. A change in the support point location is understood here as occurring within the same fixed cross-section of the beam where the latter is supported. The original elements of this study are a thin-walled beam model and a method of solving differential equations, not previously used by other authors. The equations describing the model used in this paper were derived using the momentless theory of shells and the Vlasov theory assumptions. The displacement equations were derived relative to an arbitrary rectilinear reference axis. In most works known to the authors the equations describing the vibration of the nonprismatic thin-walled beam do not take into account the effects due to the curvature of the axis formed by the shear centers. The recursive algorithm was used to solve the obtained differential equations with variable coefficients. The algorithm enables one to solve the analyzed displacement equations in the form of series relative to the orthogonal Gegenbauer polynomials. For special values of the parameter defining the order of the polynomials the Gegenbauer polynomials became Chebyshev or Lagrange polynomials. In the provided numerical example, the effect of a change in the support point location within the fixed cross-section is examined. It is also analyzed which of the approximation polynomials (Chebyshev or Lagrange polynomials) yield more precise results for a small approximation base. In order to verify the model and the effectiveness of the adopted solution method, the results obtained using this method are compared with the results yielded by FEM. The results obtained showed a significant effect of the position of the support point, within a fixed section, on the eigenfrequencies values of the thin-walled systems.

The discrete event simulation with simultaneous events is discussed. Discrete models are treated as some points in the general space of models. The main topic of this paper is the convergence of sequences of continuous models to the corresponding discrete event model. It is pointed out that the discrete event models may represent some singularities in the space of models. This fact is related to the problem of validity of discrete event simulation. The models presented here are not the topic of the paper. These are known models, used as examples. The model of the “chicken game” and multiple elastic collisions are considered. It is shown that if a discrete event model is some special limit case of a sequence of continuous models with finite event duration, then that limit model is a singularity. It may provide results very different from the expected limit value of the results from the converging sequence of models.

AIMD and RED are two dominant algorithms for controlling Internet congestion. So this paper explores the periodic solutions and complex dynamical phenomena in the state-dependent round-trip delayed AIMD/RED network congestion model with heterogeneous flows, and its improved model. We first use the semi-analytical and semi-numerical method, known as the harmonic balance method with alternating frequency/time (HB-AFT) domain technique, to derive the analytical approximations of periodic oscillations of the system. The obtained results are compared with the numerical results by WinPP, and they show good consistency. At the same time, this suggests that the method used in this paper is correct and valid. Then for the sake of making the system more realistic, we improve the model by using the hyperbolic tangent function. We obtain the approximate solutions, and find some rich dynamical behaviors of this delayed heterogeneous system, including Period-1 to torus, Period-1 to Period-2 to Period-3 motions and two kinds of mechanisms of chaos, i.e. the windows of Period-2 and Period-3 orbits to chaos, where to the best knowledge of the authors, the former route has never been reported. The periodic oscillations may induce synchronization and further congestion, where chaotic oscillation usually means that the system is unstable and may even collapse. Hence, we need to avoid these abundant dynamics discovered in this paper because they are undesirable and harmful. The derived results can help researchers better understand the performance of the AIMD/RED system, and they can be a guide for choosing parameters in a suitable range in order to maintain the network stability and optimize system performance.

As a kind of classical fractal network models, Sierpinski Gasket and its extended network models have attracted the attention of many scholars because of their many applications in real-world networks. Based on the classical Sierpinski Gasket, this paper proposes a joint Sierpinski Gasket model, which can be used not only to study the topology and dynamic properties of Sierpinski Gasket itself, but also to study the Sierpinski Gasket under special conditions, such as the residual Sierpinski Gasket after damage. Since the mean time to absorption (MTA) on the network is a basic dynamic property related to the random walk, in this paper, we study the expression of MTA on the proposed general joint Sierpinski Gasket model, and find that the MTA is determined by the number of iterations [Formula: see text] and two variables determined by the mode variable [Formula: see text], which can be solved by matrix algorithm. Therefore, using the expression of MTA on the general joint Sierpinski Gasket model, we calculate the analytical expressions of the MTA on a general example of the joint Sierpinski Gasket model and three Sierpinski Gaskets with varying degrees of damage and do the corresponding numerical simulation to verify the correctness of the conclusion.

In this paper, the vibration of a stacked multilayered graphene/black phosphorus (G/BP) heterostructure is investigated via the mesh-free method. The shape function and its derivatives are addressed by the moving least squares (MLS) approach. Optimization of the sequential quadratic programming method is adopted to calculate the distance between the arbitrary layers. Therefore, coefficients of the van der Waals (vdW) interaction between arbitrary layers of heterostructures are obtained. Then the frequencies and mode shapes of the multilayered G/BP heterostructure, considering the vdW interaction between arbitrary layers, are compared with considering only the vdW interaction among adjacent layers. The effects of the number of layers and aspect ratio of the G/BP heterostructure on the frequencies are investigated. The results demonstrate that coefficients of the vdW interaction, considering the arbitrary layers, are larger than those considering only adjacent layers. The difference between natural frequencies considering arbitrary layers and those considering adjacent layers is not clear for the low-order cases. Alternatively, the difference between natural frequencies obtained considering arbitrary layers and those considering adjacent layers are obvious for high-order cases. This paper provides a useful method to optimize the vdW interaction between multilayered G/BP heterostructures and can adequately simulate their vibration behaviors.

The relationship between currencies in foreign exchange markets has been a topic of significance in economics. Previous studies have focused more on correlations between currencies. However, the detection of causality can reveal their inherent laws. Although the traditional Granger causality test can identify causality, it cannot take into account the nature and intensity of the causality. Thus, the objective of this paper is to identify the causalities of currencies from the perspective of dynamics. In this paper, we select 25 currencies (with the US dollar (USD) as the numeraire) from foreign exchange markets, as they occupy large shares in their regions. To detect the causalities of the foreign exchange markets, we combine PC (pattern causality) theory and complex networks to construct directed and weighted causality networks, in which the nodes represent the currencies and the directed edges represent the causal intensities. Furthermore, we study the symmetry of each causality and quantify the symmetry degree. The results demonstrate that causalities exist between currencies that differ in terms of nature and intensity. The positive causality network exhibits substantial robustness, which can be regarded as the dominant causal relationship in the foreign exchange markets, although a few exceptions are encountered, such as the dominant negative and disordered causalities between currency pairs. In addition, the dominant causalities between most currencies are symmetric in terms of nature, and they also exhibit symmetry in terms of intensity. Furthermore, by gradually deleting the network by thresholding according to the edge weights, we identify the important driving currencies of the markets. This paper may provide valuable information for investors and supervisory departments.

In this paper, we consider an SI epidemic model incorporating additive Allee effect and time delay. The primary purpose of this paper is to study the dynamics of the above system. Firstly, for the model without time delay, we demonstrate the existence and stability of equilibria for three different cases, i.e. with weak Allee effect, with strong Allee effect, and in the critical case. We also investigate the existence and uniqueness of Hopf bifurcation and limit cycle. Secondly, for the model with time delay, the stability of equilibria and the existence of Hopf bifurcation are discussed. All the above show that both additive Allee effect and time delay have vital effects on the prevalence of the disease.

In this paper, we study infinite families of orthogonal exponentials of some self-affine measures. The digit set [Formula: see text] and any [Formula: see text] expanding integer matrix [Formula: see text] can generate a self-affine measure [Formula: see text]. Let [Formula: see text] and [Formula: see text] be the transposed conjugate of [Formula: see text], where [Formula: see text] and the elements of [Formula: see text] come from [Formula: see text]. In this paper, we prove the following results. For [Formula: see text], [Formula: see text] is a spectral measure. For [Formula: see text], there are infinite families of orthogonal exponentials, but none of them forms an orthogonal basis in [Formula: see text].

This paper focuses on the Hölder continuity and the Box Dimension to the [Formula: see text]th Hadamard Fractional Integral (HFI) on a given interval [Formula: see text]. We use [Formula: see text] to denote it. In this paper, two different methods are used to study this problem. By using the approximation method, we obtain that for [Formula: see text] with [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text] is [Formula: see text]th Hölder continuous in [Formula: see text] with [Formula: see text], and is [Formula: see text]th Hölder continuous on [Formula: see text]. Moreover, the Box Dimension of the graph of [Formula: see text] on the interval [Formula: see text] is less than or equal to [Formula: see text]. If [Formula: see text], then [Formula: see text] is locally [Formula: see text]th Hölder continuous in [Formula: see text] with the same [Formula: see text], and the Box Dimension of [Formula: see text] on [Formula: see text] is less than or equal to [Formula: see text]. By using another method, we imply that, for [Formula: see text] with [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text] is [Formula: see text]th Hölder continuous, and thus the Box Dimension of the graph of [Formula: see text] is no more than [Formula: see text]; if [Formula: see text], then [Formula: see text] is locally [Formula: see text]th Hölder continuous in [Formula: see text], and is [Formula: see text]th Hölder continuous at [Formula: see text]. Then the Box Dimension of the graph to [Formula: see text] on [Formula: see text] is less than or equal to [Formula: see text]. We also give two examples to show that the above Hölder indexes given by the second method are optimal.