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A sinusoidally-driven conservative and dissipative system with signum nonlinearity is presented in this paper. The proposed system exhibits strange attractors, multistability, and megastability. The system exhibits both conservative and dissipative behaviors with the change of its parameters. The Lyapunov exponents, Lyapunov spectrum plots, bifurcation diagrams, and phase plots are used to show the special features of the proposed system. [ABSTRACT FROM AUTHOR]

The option-pricing problem is an important topic in modern finance. In this paper, we propose a stock model with varying stock diffusion based on uncertainty theory. The European option pricing formulas are derived from the proposed uncertain stock model, and some mathematical properties of these formulas are investigated. Moreover, extended uncertain stock models are introduced and discussed. Finally, numerical examples are given to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

We consider framed chord diagrams, i.e. chord diagrams with chords of two types. It is well known that chord diagrams modulo T-relations admit a Hopf algebra structure, where the multiplication is given by any connected sum with respect to the orientation. But in the case of framed chord diagrams a natural way to define a multiplication is not known yet. In this paper, we first define a new module which is generated by chord diagrams on two circles and factored by T-relations. Then we construct a 'parity' map from the module of framed chord diagrams into and a weight system on . Using the map and weight system we show that a connected sum for framed chord diagrams is not a well-defined operation. In the end of the paper we touch linear diagrams, the circle replaced by a directed line. [ABSTRACT FROM AUTHOR]

In this paper, forced convection of a turbulent flow of pure water, Al2O3/water nanofluid and Al2O3–Cu/water hybrid nanofluid (a new advanced nanofluid composited of Cu and Al2O3 nanoparticles) through a uniform heated circular tube is numerically analyzed. This paper examines the effects of these three fluids as the working fluids, a wide range of Reynolds number (10 000 ≤ Re ≤ 10 0000) and also the volume concentration (0% ≤ ϕ ≤ 2%) on heat transfer and hydrodynamic performance. The finite volume discretization method is employed to solve the set of the governing equations. The results indicate that employing hybrid nanofluid improves the heat transfer rate with respect to pure water and nanofluid, yet it reveals an adverse effect on friction factor and appears severely outweighed by pressure drop penalty. However, the average increase of the average Nusselt number (when compared to pure water) in Al2O3–Cu/water hybrid nanofluid is 32.07% and the amount for the average increase of friction factor would be 13.76%. [ABSTRACT FROM AUTHOR]

This paper is concerned with the diophantine problem of finding six integers such that the sum of any two of them is a perfect square. Till now, only one numerical example of such a sextuple has been published. In this paper, we obtain infinitely many examples of sextuples of integers such that the sum of any two of them is a perfect square. These examples include sextuples which have three or four or five distinct integers as well as sextuples in which all the integers are distinct. [ABSTRACT FROM AUTHOR]

The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries. Their various critical values are established and confirmed by numerical experiments demonstrating not only the loss of stability of an equilibrium point, but also other phenomena of transition to chaotic behavior. In addition, we suggest an active control method for synchronization of two chaotic fractional-order Rössler systems. Our theoretical analysis enables to synchronize them for any value of a free parameter under which the master system displays a chaotic behavior. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of uniform vertex fuzzy soft graphs, uniform edge fuzzy soft graphs, degree of a vertex, total degree of a vertex and complement fuzzy soft graphs with some examples. Also, we study regular and totally regular fuzzy soft graphs, and the conditions under which the complement of regular fuzzy soft graph becomes regular as well as totally regular are discussed. Also, we obtain some results related to regular, totally regular and complete fuzzy soft graphs. [ABSTRACT FROM AUTHOR]

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the structural and acoustic analysis of the orthotropic plate under the thermal environment. [ABSTRACT FROM AUTHOR]

A new type of high performance steel (HPS), designated WGJ steel, with high strength as well as improved fire and corrosion resistance, was recently developed by Wuhan Iron and Steel (Group) Company. This paper investigated the lateral-torsional buckling behavior of beams fabricated of WGJ steel through experimental and numerical analysis. Welded I-section beams were tested under concentrated loads, which indicated that lateral-torsional buckling was the dominant failure mode. A finite element model was established and validated by the experimental results. Parametric analyses were conducted to further understand the effect of steel strength on the lateral-torsional buckling capacity of steel beams. The numerical results were compared with design values obtained from the clauses in Eurocode 3 and GB50017. It is found that the design equations in GB50017 give less safe margins for the overall stability design of welded I-section beams fabricated of WGJ high performance steel, whereas Eurocode 3 appears to be more conservative in all conditions. [ABSTRACT FROM AUTHOR]

This work is concerned with the bifurcational analysis of nonlinear dissipative systems affected by time delay. This issue typically arises when testing highly nonlinear energy dissipation devices, commonly used in vibration control of civil structures, and carried out experimentally via a hybrid technique known as Real-Time Dynamic Substructuring (RTDS) simulation. Unfortunately, the RTDS simulation is affected by time delay in the control feedback loop due to the actuator response, sensor reading and numerical processing. In essence, this paper focuses on studying the nonlinear dynamics induced by the interaction of a dynamical system with the nonlinear damper affected by the presence of time delay. Given the complexity of the system, numerical analysis is carried out in the context of bifurcational behavior, and bifurcation diagrams are computed using a continuation method. The bifurcational analysis presented here, provides a characterization of delay-induced nonlinear phenomena created by the interaction of the dynamical system with a delayed nonlinear response of the dissipation device. Nonlinear dynamics are also identified and characterized for different damper types when varying the damper model parameters, leading to the identification of system conditions at which the testing arrangement and test specimens can exhibit undesired dynamics. [ABSTRACT FROM AUTHOR]

This paper is aimed to study spherically symmetric anisotropic dissipative quark star for tilted observer. The corresponding field equations as well as dynamical equations are formulated. We consider the MIT bag model for quark stars and investigate numerical solution of the field equations by imposing the shear-free condition. It is found that all the expected physical properties are present related to stellar fluid distribution. Finally, we analyze stability of the compact object by analyzing splitting of the fluid distribution. It is found that radial velocity does not change its sign during evolution of the system implying that the system does not undergo splitting and remains stable. [ABSTRACT FROM AUTHOR]

In this paper, we provide the noncommutative Sprott models. We demonstrate, that effectively, each of them is described by a system of three complex, ordinary and nonlinear differential equations. Apart from that, we find for such modified models the corresponding (noncommutative) jerk dynamics as well as we study numerically as an example, the deformed Sprott-A system. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach based on the intuitionistic fuzzy combined ordered weighted averaging (IFCOWA) operator to solve multiple attribute group decision making (MAGDM) problems under fuzzy environment. Firstly, we introduce the new methods for determining the attribute weights and the order inducing variable of the proposed operator. With the intuitionistic fuzzy cross-entropy of aggregated attribute value to the optimum and the poorest information measures, the sort vector is constructed to derive the weights of attributes. Moreover, the order inducing variable of the attributes is obtained from their score values, by which the inducing order is roughly determined. Finally, two numerical examples about the venture investment problems are illustrated to demonstrate the applicability and efficiency of the raised approach in group decision making problem. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the effect of channel noise on synchronization transitions induced by time delay in adaptive scale-free Hodgkin-Huxley neuronal networks with spike-timing-dependent plasticity (STDP). It is found that synchronization transitions by time delay vary as channel noise intensity is changed and become most pronounced when channel noise intensity is optimal. This phenomenon depends on STDP and network average degree, and it can be either enhanced or suppressed as network average degree increases depending on channel noise intensity. These results show that there are optimal channel noise and network average degree that can enhance the synchronization transitions by time delay in the adaptive neuronal networks. These findings could be helpful for better understanding of the regulation effect of channel noise on synchronization of neuronal networks. They could find potential implications for information transmission in neural systems. [ABSTRACT FROM AUTHOR]

In this paper, a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave. [ABSTRACT FROM AUTHOR]

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data. [ABSTRACT FROM AUTHOR]

In this paper, an aircraft model was tested in the wind tunnel with different degrees of yaw-roll coupling at different angles of attack. The dynamic increments of yawing and rolling moments are compared to study the coupling effects on damping characteristics. The characteristic time constants are calculated to study the changes of flow field structure related to coupling ratios. The damping characteristics and time lag effects of aerodynamic loads calculated by dynamic derivative method are also compared with experimental results to estimate the applicability of linear superposition principle at large angles of attack. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of the interaction between transverse cold jets on slender body in front of or between X-shape rudders with rudders in the oncoming free stream is presented. Firstly, the flow field at different jet conditions is simulated and analyzed. Then, the total force and moment amplification factors of the corresponding slender body with jet at different locations are analyzed and compared with those results of non-jet flow. Numerical results show that interactions take a great effect to the configuration of the flow field around rudders and the pressure distribution on slender surface. Moreover, the force and moment amplification changes regularly along with the location of jet nozzle. [ABSTRACT FROM AUTHOR]

Understanding the spatial correlation of urban traffic state is essential for identifying the evolution patterns of urban traffic state. However, the distribution of traffic state always has characteristics of large spatial span and heterogeneity. This paper adapts the concept of community detection to the correlation network of urban traffic state and proposes a new perspective to identify the spatial correlation patterns of traffic state. In the proposed urban traffic network, the nodes represent road segments, and an edge between a pair of nodes is added depending on the result of significance test for the corresponding correlation of traffic state. Further, the process of community detection in the urban traffic network (named GWPA- K-means) is applied to analyze the spatial dependency of traffic state. The proposed method extends the traditional K-means algorithm in two steps: (i) redefines the initial cluster centers by two properties of nodes (the GWPA value and the minimum shortest path length); (ii) utilizes the weight signal propagation process to transfer the topological information of the urban traffic network into a node similarity matrix. Finally, numerical experiments are conducted on a simple network and a real urban road network in Beijing. The results show that GWPA- K-means algorithm is valid in spatial correlation analysis of traffic state. The network science and community structure analysis perform well in describing the spatial heterogeneity of traffic state on a large spatial scale. [ABSTRACT FROM AUTHOR]

A WH-packet is a system of vectors which is analogous to Aldroubi's model for explicit expression of vectors (including frame vectors) in terms of a series associated with a given frame. In this paper, we study frame properties of WH-packet type system for matrix-valued wave packet frames in the function space . A necessary and sufficient condition for WH-packets of matrix-valued wave packet frames in terms of a bounded below operator is given. We present sufficient conditions for both lower and upper frame conditions on scalars associated with WH-packet of matrix-valued wave packet frames. Finally, a Paley-Wiener type perturbation theorem for WH-packet of matrix-valued wave packet frames is given. Several examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of image segmentation, an improved adaptive level set method is proposed based on level set evolution without re-initialization method and adaptive distance preserving level set evolution method. A new definition of weight coefficient in evolution equations is the main innovation of this paper. The improved method can detect certain object boundaries, interior and exterior contours of an object, edges of multi-objects and weak boundaries of an object by synthetic and real images numerical experiments. Numerical results show that the improved adaptive level set method has faster segmentation speed and higher segmentation accuracy compared with the previous two methods, especially in weak boundaries and edges of multi-objects segmentation problems. [ABSTRACT FROM AUTHOR]

In this brief paper, we study the constraint consensus problem of heterogeneous multi-agent systems. First, we provide an invariant set, which can be exactly obtained by solving linear equations. Then, a virtual system is defined on this invariant set such that it is the largest common embedded system of all the individual agents. Afterwards, a linear consensus protocol is proposed with the corresponding constraint consensus criterion. In particular, the above virtual system can reveal all the asymptotic dynamical behaviors if heterogeneous multi-agent systems achieve consensus. Finally, an example with numerical simulations is given to illustrate the validity of our criterion. [ABSTRACT FROM AUTHOR]

In this paper, we construct new exact solutions of the reaction-diffusion equation with time dependent variable coefficients by employing the mathematical computation via the Painlevé test. We describe the behaviors and their interactions of the obtained solutions under certain constraints and various variable coefficients. [ABSTRACT FROM AUTHOR]

Link prediction in complex networks has become a common focus of many researchers. But most existing methods concentrate on neighbors, and rarely consider degree heterogeneity of two endpoints. Node degree represents the importance or status of endpoints. We describe the large-degree heterogeneity as the nonequilibrium between nodes. This nonequilibrium facilitates a stable cooperation between endpoints, so that two endpoints with large-degree heterogeneity tend to connect stably. We name such a phenomenon as the nonequilibrium cooperation effect. Therefore, this paper proposes a link prediction method based on the nonequilibrium cooperation effect to improve accuracy. Theoretical analysis will be processed in advance, and at the end, experiments will be performed in 12 real-world networks to compare the mainstream methods with our indices in the network through numerical analysis. [ABSTRACT FROM AUTHOR]

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction . The disease-free equilibrium is stable locally and globally whenever . If , then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented. [ABSTRACT FROM AUTHOR]

The exploration of closed-form solutions for nonlinear partial differential equations (NLPDEs) is an attractive subject in the different branches of mathematical and biological sciences. In this paper, we have applied a modified exp-function method to calculate closed-form solutions of a degenerate parabolic equation arising in the spatial diffusion of biological populations. The model assists us to comprehend the dynamical process of population variations in population models and delivers prized guesses. It is shown that the obtained solutions are more general and fresh and can be helpful to analyze the inner mechanism of other nonlinear biological models. Moreover, 2D and 3D graphical demonstrations together with the numerical data strengthen the effectiveness of the rummage-sale procedure. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm. [ABSTRACT FROM AUTHOR]

In this paper, several finite element models of an equine stifle joint with varying meniscal properties and attachments are compared to understand the effects of meniscal attachment complexity and material property changes on bone stresses. We found that the complexity in the meniscal attachment is critical when evaluating tensile stresses in the bone. We also demonstrate that simplified material properties may be justified when the relationship between each material property and the desired output variables is well understood. The choice of the most efficient, and yet appropriate, meniscal modeling method depends on the goals of the model. [ABSTRACT FROM AUTHOR]

Implementing parallel software for QR factorizations to achieve scalable performance on massively parallel manycore systems requires a comprehensive design that includes algorithm redesign, efficient runtime systems, synchronization and communication reduction, and analytical performance modeling. This paper presents a piece of tiled communication-avoiding QR factorization software that is able to scale efficiently for matrices with general dimensions. We design a tiled communication-avoiding QR factorization algorithm and implement it with a fully distributed dynamic scheduling runtime system to minimize both synchronization and communication. The whole class of communication-avoiding QR factorization algorithms uses an important parameter of D (i.e., the number of domains), whose best solution is still unknown so far and requires manual tuning and empirical searching to find it. To that end, we introduce a simplified analytical performance model to determine an optimal number of domains D. The experimental results show that our new parallel implementation is faster than a state-of-the-art multicore-based numerical library by up to 30%, and faster than ScaLAPACK by up to 30 times with thousands of CPU cores. Furthermore, using the new analytical model to predict an optimal number of domains is as competitive as exhaustive searching, and exhibits an average performance difference of 1%. [ABSTRACT FROM AUTHOR]

To understand the interaction between the oscillated body and oncoming vortex, some numerical studies have been conducted on a system including two parallel D-cylinder and one oscillated foil in this paper. It is found that the distance between parallel D- cylinder and oscillated foil would play a key role in affecting the change regulation of thrust generation of oscillated foil, and the kinematics of oscillated foil would determine the value of propulsive thrust, the gap between two parallel D-cylinder would only affect the hydrodynamic performance of oscillated foil at intermediate conditions. [ABSTRACT FROM AUTHOR]

In this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates. [ABSTRACT FROM AUTHOR]

In this paper, the large time behavior of the solution to the initial-boundary problems for the one-dimensional compressible gas-liquid drift-flux model with slip is studied. Under some suitable smallness conditions upon the initial data, the optimal pointwise upper and lower decay estimates on masses as well as the sharpest decay rates for the norms in terms of the velocity function are obtained. This result generalizes the one in [On the large time behavior of the compressible gas-liquid drift-flux model with slip, Math. Models Methods Appl. Sci. 25 (2015) 2175-2215] by Evje and Wen. The key of the proof is to derive some new global-in-time weighted estimates. Our method can also be easily adopted to the study on the large time behavior of the solution to the one-dimensional compressible Naiver-Stokes equations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the uniform regularity of solutions to the three-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the compressible Euler system for vanishing viscosity and surface tension. It is shown that there exists a unique strong solution to the free boundary problem for the compressible Navier-Stokes system in a finite time interval which is independent of the viscosity and the surface tension. The solution is uniformly bounded both in and a conormal Sobolev space. It is also shown that the boundary layer for the density is weaker than the one for the velocity field. Based on such uniform estimates, the asymptotic limits, to the free boundary problem for the ideal compressible Euler system with or without surface tension as both the viscosity and the surface tension tend to zero, are established by a strong convergence argument. [ABSTRACT FROM AUTHOR]

A novel plate-type acoustic metamaterial with a high sound transmission loss (STL) in the low-frequency range (1000 Hz) is designed, theoretically proven and then experimentally verified. The thin plates with large modulus used in this paper mean that we do not need to apply tension to the plates, which is more applicable to practical engineering, the achievement of noise reduction is better and the installation of plates is more user-friendly than that of the membranes. The effects of different structural parameters of the plates on the sound-proofed performance at low-frequencies were also investigated by experiment and finite element method (FEM). The results showed that the STL can be modulated effectively and predictably using vibration theory by changing the structural parameters, such as the radius and thickness of the plate. Furthermore, using unit cells of different geometric sizes which are responsible for different frequency regions, the stacked panels with thickness 16 mm and weight 5 kg/m2 showed high STL below 2000 Hz. The acoustic metamaterial proposed in this study could provide a potential application in the low-frequency noise insulation. [ABSTRACT FROM AUTHOR]

In this paper, a class of difference equations with variable-time impulses is considered. By applying comparison principle, we shall show that difference equations with variable-time impulse can be reduced to the corresponding difference equations with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the difference equations with variable-time impulses. Furthermore, we use a series of sufficient criteria to illustrate the same stability properties between variable-time impulsive difference equations and the fixed-time ones. We then establish several sufficient conditions guaranteeing the global exponential stability of variable-time impulsive difference equations by comparison principle. As an application, global exponential stability of discrete-time neural networks with variable-time impulses is discussed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Local bifurcations occur in power systems, causing changes in power system dynamic behaviors. These local bifurcations include the saddle-node bifurcation, Hopf bifurcation, and structureinduced bifurcation. This paper presents a new type of bifurcation that can occur in the optimal power flow (OPF) problem. This new type of bifurcation, termed pseudo-pitchfork bifurcation, involves bifurcations of the feasible components of the OPF problem and the disappearance of local optimal power flow solutions. The main features of this special type of bifurcation are demonstrated on several power systems with different loading condition parameters and different constraint parameters. Then the computation consideration and physical meaning of the pseudo-pitchfork bifurcation are roughly discussed. It is also demonstrated that a pseudopitchfork bifurcation occurring between feasible components can help us interpret the loss or birth of optimal power flow solutions and can lead to powerful numerical methods for computing high-quality optimal power flow solutions. [ABSTRACT FROM AUTHOR]

We consider the process of hemodialysis performed by means of a hollow fiber dialyzer with a special focus on the dynamics of the light solutes (including metabolic waste products) through the porous fibers membrane. The model we illustrate here completes the one formulated in a previous paper in which solutes concentrations in the dialyzate were neglected. Exploiting the large difference between the characteristic time of the processes in the machine and the relaxation time to equilibrium in the body, we confine our study to the case of constant input data in order to emphasize the role of the solute transport mechanisms. Numerical solutions show that diffusion is dominant at the early stage of filtration. [ABSTRACT FROM AUTHOR]

This paper considers a class of three-dimensional systems constructed by a rotating planar symmetric cubic vector field. To study its periodic orbits including homoclinic orbits, which may be knotted in space, we classify the types of periodic orbits and then calculate their exact parametric representations. Our study shows that this class of systems has infinitely many distinct types of knotted periodic orbits, which lie on three families of invariant tori. Numerical examples of -torus knot periodic orbits have also been provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the symmetry and monotonicity properties for positive solutions of fractional Laplacian equations. Especially, we consider the following fractional Laplacian equation with homogeneous Dirichlet condition: Here is a domain (bounded or unbounded) in which is convex in -direction. is the nonlocal fractional Laplacian operator which is defined as Under various conditions on and on a solution it is shown that is strictly increasing in in the left half of , or in . Symmetry (in ) of some solutions is proved. [ABSTRACT FROM AUTHOR]

This paper deals with an equivalent system to the nonlinear differential equation of Liénard type , where the range of the function is bounded. Sufficient conditions are obtained for the system to have at least one limit cycle. The proofs of our results are based on phase plane analysis of the system with the Poincaré-Bendixon theorem. Moreover, to show that these sufficient conditions are suitable in some sense, we also establish the results that the system has no limit cycles. Finally, some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the local existence and uniqueness of the solution with discontinuous density for the inhomogeneous non-resistive magnetohydrodynamics (MHD) equations on a bounded domain or , if the initial data with satisfies . [ABSTRACT FROM AUTHOR]

Quantitative models may exhibit sophisticated behaviour that includes having multiple steady states, bistability, limit cycles, and period-doubling bifurcation. Such behaviour is typically driven by the numerical dynamics of the model, where the values of various numerical parameters play the crucial role. We introduce in this paper natural correspondents of these concepts to reaction systems modelling, a framework based on elementary set theoretical, forbidding/enforcing-based mechanisms. We construct several reaction systems models exhibiting these properties. [ABSTRACT FROM AUTHOR]

In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier-Stokes equations with no flow. In this paper, such models with acoustic losses are applied to an acoustic metamaterial. Metamaterials are structures formed by smaller, usually periodic, units showing remarkable physical properties when observed as a whole. Acoustic losses are relevant in metamaterials in the millimeter scale. In addition, their geometry is intricate and challenging for numerical implementation. The results are compared with existing measurements. [ABSTRACT FROM AUTHOR]

Discontinuities are a common feature of physical models in engineering and biological systems, e.g. stick-slip due to friction, electrical relays or gene regulatory networks. The computation of basins of attraction of such nonsmooth systems is challenging and requires special treatments, especially regarding numerical integration. In this paper, we present a numerical routine for computing basins of attraction (BA) in nonsmooth systems with sliding, (so-called Filippov systems). In particular, we extend the Simple Cell Mapping (SCM) method to cope with the presence of sliding solutions by exploiting an event-driven numerical integration routine specifically written for Filippov systems. Our algorithm encompasses a method for dynamic construction of the cell state space so that a lower number of integration steps are required. Moreover, we incorporate an adaptive strategy of the simulation time to render more efficiently the computation of basins of attraction. We illustrate the effectiveness of our algorithm by computing basins of attraction of a sliding control problem and a dry-friction oscillator. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the Thomas-Fermi model for the electron gas in Rindler space. We have observed that if the uniform acceleration is along -direction, then there is -symmetry in space. For the sake of mathematical simplicity, we have therefore assumed a two-dimensional spatial structure in Rindler space. It has been shown that in two-dimensional spatial coordinates, the electrons are distributed discontinuously but in a periodic manner in a number of rectangular strip-like domains along -direction. Some of them are having void structure, with no electrons inside such rectangular strips, while some are filled up with electrons. We call the latter type domain as the normal zone. We have also given physical interpretation for such exotic type electron distribution in Rindler space. [ABSTRACT FROM AUTHOR]

This paper proposes a preference index for ranking the most applicable vague data, i.e. closed intervals and LR-fuzzy numbers. In this approach, first a preference degree is suggested to compare two closed intervals. Then, we extended the proposed criterion from the space of closed intervals into the the space of fuzzy numbers. Using some theorems and lemmas, it will be proved that the extended preference degrees will satisfy many common and desired properties based on the proposed axiomatic definitions introduced for similarity measures. Some numerical examples are also used to illustrate the proposed ranking methods. Moreover, the proposed methods are examined to compare other existing methods and the feasibility and effectiveness of the proposed methods will be cleared via some numerical comparisons. Comparative examples show that the proposed method overcomes certain unreasonable and shortcomings exhibited by some existing methods in some common situations. [ABSTRACT FROM AUTHOR]

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For , the disease-free equilibrium is stable both locally and globally and for , the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented. [ABSTRACT FROM AUTHOR]

Graphene is an atomic scale honeycomb lattice made of the carbon atoms. Graph theory has given scientific expert an assortment of helpful apparatuses, for example, topological indices. A topological index of a graph is a number with the property that for each graph isomorphic to In this paper, we exhibit correct expressions for some topological indices for para-line graph of honeycomb networks and graphene. [ABSTRACT FROM AUTHOR]

Cyclic hypergroups are of great importance due to their applications to many fields in mathematics. In this paper, we classify all commutative single power cyclic hypergroups of order three and period two. Moreover, we prove some new interesting properties regarding cyclic hypergroups. [ABSTRACT FROM AUTHOR]

In this paper, we consider dominating sets and such that and are disjoint and there exists a perfect matching between them. Let denote the cardinality of smallest such sets in (provided they exist, otherwise ). This concept was introduced in [W. F. Klostermeyer, M. E. Messinger and A. Angeli Ayello, An eternal domination problem in grids, Theory Appl. Graphs 4(1) (2017) 23pp.] in the context of studying a certain graph protection problem. We characterize the trees for which equals a certain graph protection parameter and for which , where is the independence number of . We also further study this parameter in graph products, e.g., by giving bounds for grid graphs, and in graphs of small independence number. [ABSTRACT FROM AUTHOR]