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Abstract: Although the scale invariance is a main feature of growing networks, evidence from a few modelled networks show that the finite-size effect of network at a fixed time cannot be ignored. We propose a concept of time-dependent scale-free networks, and prove the criteria for the stability and scale-free of growing networks by the degree-growing Markov chain. Our results show the importance of rigorous theoretical analysis for the network science. [ABSTRACT FROM AUTHOR]

Abstract: We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature. [Copyright &y& Elsevier]

Abstract: Our aim is to point out an error in the proof of Lemma 2 in the paper “Fixed point theory in symmetric spaces with applications to probabilistic spaces” by T.L. Hicks, B.E. Rhoades [Nonlinear Analysis 36 (1999) 331–344], and to indicate a way to repair it. [Copyright &y& Elsevier]

Abstract: A lemma presented by Matkowski requires a proof. [Copyright &y& Elsevier]

This paper proposes a Cahn-Hilliard type inpainting model equipped with a nonlocal diffusion operator. A rigorous analysis of the well-posedness of the stationary solution is established using Schauder's fixed point theory. We construct a time stepping scheme based on the convex splitting method with the nonlocal term treated implicitly and the fidelity term treated explicitly. We prove the consistency, stability and convergence of the semidiscrete-in-time scheme. To the best of our knowledge, this is the first study to present such an analysis for semidiscrete-in-time problems of this model, which provides valuable guidance for parameter selection. Numerical experiments validate the effectiveness of the proposed nonlocal model, which shows superior performance compared to both local and classical total variation models in preserving fine textures and recovering image edges. [ABSTRACT FROM AUTHOR]

It is significant to investigate the transmission dynamics of vector-borne infection because it has a global impact, can help predict and prevent future outbreaks, is important for understanding the impact of climate change on public health, can lead to more effective control strategies, and can improve our comprehension of the dynamics of these infections. Our paper presents a new model for chikungunya virus infection, which considers treatment and vaccination, using the Atangana-Baleanu derivative within the framework of the Caputo definition. First of all, we examine the positivity and uniqueness of the solution for the model. Then, we find out the fundamental results of the suggested model, such as the steady-state without infection and the R 0 value that indicates endemicity pertaining to the system. Furthermore, we verify the local asymptotic stability of the infection-free steady-state. Through the application of fixed-point theory, we demonstrate the existence of the solution and propose a numerical methodology to investigate the dynamic behavior of the model. Finally, we performed simulations to demonstrate the effects of vaccination, transmission probability, treatment, and index of memory on the system's solution pathways. The findings of this research suggest the most sensitive parameters of the system responsible for the control and prevention of the infection. Emphasizing the significance of the memory index as an attractive parameter, we propose its consideration to the policy makers as a control parameter for the prevention of the infection. [ABSTRACT FROM AUTHOR]

In this manuscript, we are going to study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under the concept of conformable fractional order derivative (CFOD). Currently, most of real-world problems are considered under fractional order derivatives because of their stable and global behavior. First, we will investigate the model for qualitative theory including existence and uniqueness of solution and Ulam-Hyers stability. For qualitative theory, we will use fixed point theory. In addition, we use a numerical method to find the approximate solution of the proposed model. In the final part of the paper, we give a detailed discussion of its numerical results and its graphical presentation. [ABSTRACT FROM AUTHOR]

This paper discusses the periodicity and multi-periodicity in delayed Cohen–Grossberg-type neural networks (CGNNs) possessing impulsive effects, whose activation functions possess discontinuities and are allowed to be unbounded or nonmonotonic. Based on differential inclusion and cone expansion–compression fixed-point theory of set-valued mapping, several improved criteria are given to derive the positive solution with ω -periodicity and ω -multi-periodicity for delayed CGNNs under impulsive control. These ω -periodicity/ ω -multi-periodicity orbits are produced by impulses control. The analytical method and theoretical results presented in this paper are of certain significance to the design of neural network models or circuits possessing discontinuous neuron activation and impulsive effects in periodic environment. [ABSTRACT FROM AUTHOR]

The recent outbreak of rabies virus has affected numerous individuals in the community, highlighting the importance of studying the disease mathematically in epidemiology. In this paper, we develop a mathematical model for the spread of rabies disease using the harmonic mean incidence rate and determine the reproduction number R 0 using the next generation matrix approach. The fractional dynamics of the model incorporate the interaction between infected individuals and environmental factors. We analyze the model using both Atangana-Baleanu-Caputo (ABC) and Caputo-Fabrizio (CF) techniques, drawing on both modern and classical approaches. For qualitative investigation using fractional operators, we utilize the Banach fixed-point theory and derive the Hyers-Ulam stability concept. We assign values to the model parameters and utilize the Newton interpolation technique to obtain a numerical scheme. Additionally, we perform sensitivity analysis on the model. In conclusion, our findings provide important insights for the study of epidemics. [ABSTRACT FROM AUTHOR]

Fractional calculus plays an important role in the development of control strategies, the study of the dynamical transmission of diseases, and some other real-life problems nowadays. The time-fractional HIV/AIDS model is examined using a novel method in this paper. Based on the Atangana-concept Baleanu's of a derivative in the Caputo sense, the current modified fractional derivative operator uses singular and non-local kernels. This new modified fractional operator is given a numerical approximation and applied to the HIV/AIDS model. In the presence of this novel operator, we present some significant analysis for the HIV/AIDS epidemic model. The uniqueness and stability criteria of the model have been demonstrated using the Picard successive approximation approach and Banach's fixed point theory. The Laplace Adomian decomposition method (LADM) was used to obtain the numerical solution for the modified Atangana-Baleanu Caputo derivative model. The convergence analysis is verified for the proposed scheme. Finally, numerical results and simulations are derived with the proposed scheme for HIV/AIDS model. On the dynamics of HIV/AIDS transmission, the effects of many biological parameters are examined. [ABSTRACT FROM AUTHOR]

In this paper, we study the fractional integro-differential equation under the notion of fuzziness. We consider the fuzzy fractional Volterra-Fredholm integro-differential equation in the Caputo sense and show its existence and uniqueness by using fixed point theory. Further, we use the modified Adomian decomposition method (MADM) to determine the solution of the proposed problem. We provide some examples to support our method. We also provide graphical representation to visualize the behavior of the solutions. At the end of the paper, we present the conclusion part. [ABSTRACT FROM AUTHOR]

This paper investigates the multistability on a class of delayed neural networks with monotonically nondecreasing linear activation function. For n state neurons with 2 m + 1 piecewise linear activation function, we prove the neural networks have (2 m + 1) n equilibrium points, (m + 1) n of which are locally exponentially stable. Different from the traditional multistability analysis method such as fixed point theory, this paper only uses the character of activation functions, and can also handle the neural networks with disturbance term. The research results of this paper generalize the previous related research works and are easy to test. A numerical example is given to shown the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for the following fractional boundary value problem c D α u (t) = f (t , u (t)) , α ∈ (n , n + 1) , 0 ≤ t < + ∞ , u (0) = 0 , u ′ ′ (0) = 0 , ... , u (n) (0) = 0 , lim t → + ∞ c D α − 1 u (t) = β u (ξ). The considerations of this paper are based on the concept of a new family of measures of noncompactness in the space of functions C n , γ (R +) satisfying the Hölder condition and a fixed point theorem of Darbo type. We also provide an illustrative example in support of our existence theorems. Finally, to credibility, we apply successive approximation and homotopy perturbation method to find solution of the above problem with high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we propose the concept of fuzzy Meir–Keeler contractive mappings in fuzzy metric spaces, which covers fuzzy ψ -contractive mappings and fuzzy H -contractive mappings as special cases. With the aid of the proposed concept, we obtain some Meir–Keeler type fixed point theorems. The derived theorems improve and extend the corresponding ones developed by D. Mihet, D. Wardowski and V. Gregori, et al. And an example in the end of the paper illustrates the validity of our results. [ABSTRACT FROM AUTHOR]

This paper deals mainly with new very general fuzzy fixed point theorems in metric spaces and their application to fuzzy fractals. It is a natural continuation of our paper (2018) [1] which significantly generalizes and improves the results by Diamond, Kloeden and Pokrovskii (1997) [2] , where no application was given. Moreover, besides the existence, some further important properties of fixed point sets (in particular, fractals) like their weak local stability, called none-ejectivity in the sense of Browder (1965) [3] , will be established. [ABSTRACT FROM AUTHOR]

Wormhole propagation, arising in petroleum engineering, is used to describe the distribution of acid and the increase of porosity in carbonate reservoir under the dissolution of injected acid and plays a very important role in the product enhancement of oil and gas reservoirs. In this paper, a fully mixed virtual element method (VEM) is employed to discretize this problem, in which mixed VEM is used not only for the Darcy flow equations but also for approximation the concentration equation by introducing an auxiliary flux variable to guarantee full mass conservation. The stability, existence and uniqueness of solution of the associated mixed VEM are proved by fixed point theory. Also, we obtain unconditionally optimal error estimate for concentration and auxiliary flux variable of convection-diffusion equation, as well as for the velocity and pressure of Darcy equations in the L 2 norm. Finally, several numerical experiments are presented to support the theoretical analysis of convergence and to illustrate the applicability for solving actual problems. [ABSTRACT FROM AUTHOR]

• A new MEE criterion is defined with Cauchy kernel function. • CMEE-PCFF and CMEE-SCFF are designed in Cauchy kernel MEE criterion. • The fusion performance of proposed algorithms is analyzed from three aspects. With the help of Information Theory Learning (ITL) theory, a kind of increasingly popular non-Gaussian filtering method has been designed in the sense of the maximum correntropy (MC) criterion or minimum error entropy (MEE) criterion. In MC or MEE criterion, Gaussian kernel function is usually chosen as the kernel function. Compared to the Gaussian kernel function, the Cauchy kernel function has a wider range of action and is insensitive to the kernel parameters. In this paper, a new Cauchy kernel MEE criterion is defined. In the sense of the new defined criterion, two kinds of non-Gaussian centralized fusion filtering algorithms are proposed with the help of fixed-point theory, which are Cauchy kernel minimum error entropy parallel centralized fusion filter and Cauchy kernel minimum error entropy sequential centralized fusion filter. The propagation equation is used to calculate the prior estimates of the state and covariance, and then the fixed-point iteration is used to calculate the posterior estimates of the state and covariance. The convergence of the iteration process included in the two proposed methods is analyzed by using Banach fixed-point theorem. The final two experimental simulations verify the superior performance of the two proposed fusion filtering algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we present a dynamic model of syphilis. The goal of this work is to provide a mathematical model for syphilis disease that contains information about the suspect, infected, recovered, and exposed. Boundedness, positivity, and unique solutions at equilibrium points are used in the qualitative and quantitative study of a proposed model using the power law kernel. The Routh-Hurwitz stability criteria are used to address the model's local and global stability. Chaos control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium. Using Lyapunov function tests, the global stability of free and endemic equilibrium points is confirmed. The Lipschitz condition and fixed point theory are utilized to satisfy the requirements for the existence and uniqueness of the exact solution. The generalized form of the power law kernel is solved using a two-step Lagrange polynomial method to investigate the impact of the fractional operator using numerical simulations that illustrate the effects of various parameters on the illness. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some fixed point results for a pair of fuzzy dominated mappings satisfying contractive conditions on closed ball in multiplicative metric space. Some new fixed point results with graphic contraction on closed ball for a pair of fuzzy graph dominated mappings on multiplicative metric space have been established. Furthermore, we find a unique common solution for a system of non linear Voltera type integral equations and lastly we give an application to ensure the existence of common bounded solution of a functional equation in dynamic programming. [ABSTRACT FROM AUTHOR]

The current paper is the analysis of an Anthroponotic Cutaneous Leishmania infection caused by a parasite known as Leishmania Tropica under the Caputo fractal-fractional operator. The problem has seven compartmental agents having two categories of human and vector population. By using the fixed point theory we show the existence and uniqueness of solutions of the system. Applying the methods of basic theorems of fractal-fractional calculus and the iterative numerical techniques of fractional Adams–Bashforth method for approximate solution. For the simulation of the model, we have considered different values for fractional-order ϱ and fractal dimension χ and compare the results with integer order for real data. The fractal-fractional calculus technique is applied as a beneficial technique to know about the real-world problem and also to controls the whole world situation of the aforesaid pandemic in the different continents and territories of the world. Finally, numerical simulations are performed to elaborate on the significance of the arbitrary order derivative. Our analysis indicates that the fractal-fractional order derivatives are more informative about the complexity of the dynamics of the proposed Leishmania model. [ABSTRACT FROM AUTHOR]

Abstract The present paper introduces and estimates the complexity of the fixed point property of a digital image (X, k) for any k − D C -self-map f of (X, k), where a k − D C -self-map f of (X, k) means a digitally k -continuous self-map of (X, k) with a digital version of the Banach contraction principle. To do this work, we need to study some properties of iterations of a k − D C -self-map f of (X, k) and to establish the notion of complexity of (X, k) denote by C ♯(X, k) (see Definition 7 in the present paper). According to C ♯(X, k), we can estimate complexity of the fixed point property of (X, k) for any k − D C -self-map f of (X, k). Based on this approach, the present paper investigates some relationships between the k -adjacency of (X, k) and C ♯(X, k). Furthermore, we prove that C ♯(X, k) is not a digital topological invariant. Besides, we develop the notions of uniform k -connectedness and strict k -connectivity to calculate C ♯(X, k) for some digital images (X, k). In the paper each (X, k) is assumed to be a k -connected and non-empty set and 2 ≤ | X |≨∞, where | X | means the cardinal number of the given set X. [ABSTRACT FROM AUTHOR]

Abstract In this paper, some new p -stability criteria and boundedness results of reaction–diffusion BAM neural networks are derived by way of fixed point theorem, Laplacian semigroup theory and L ∞-estimate technique, which are novel against those of the previous related literature. Since the T–S fuzzy impulsive reaction–diffusion neural networks was investigated by previous literature, the main difficulty of this paper is to find out a novel method to give simpler conclusions than existing results. Finally, a numerical example is presented to illustrate the effectiveness and feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract The theoretical part of the paper analyzes discretized Stokes systems with local Coulomb's slip boundary conditions. Solutions to discrete models are defined by means of fixed-points of an appropriate mapping. We prove the existence of a fixed-point, establish conditions guaranteeing its uniqueness and examine how they depend on the discretization parameter h and the slip coefficient κ. The second part of the paper is devoted to computational aspects. Numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the issue of multistability for competitive neural networks. First, a general class of continuous non-monotonic piecewise linear activation functions is introduced. Then, based on the fixed point theorem, the contraction mapping theorem and the eigenvalue properties of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks have exactly 5 n equilibrium points, among which 3 n equilibrium points are locally exponentially stable and the others are unstable. Moreover, it is revealed that the neural networks with non-monotonic piecewise linear activation functions introduced in this paper can have greater storage capacity than the ones with Mexican-hat-type activation function and nondecreasing saturated activation function. In addition, unlike most existing multistability results of neural networks with nondecreasing activation functions, the location of those obtained 3 n locally stable equilibrium points in this paper is more flexible. Finally, a numerical example is provided to illustrate and validate the theoretical findings via comprehensive computer simulations. [ABSTRACT FROM AUTHOR]

In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Brinkman type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation relate to the heat and substance concentration, of a viscous fluid in a porous media with physical boundary conditions. The model problem is rewritten in terms of a first-order system, without the pressure, based on the introduction of the strain tensor and a nonlinear pseudo-stress tensor in the fluid equations. After a variational approach, the resulting weak model is then augmented using appropriate redundant penalization terms for the fluid equations along with a standard primal formulation for the heat and substance concentration. Then, it is rewritten as an equivalent fixed-point problem. Well-posedness results for both the continuous and the discrete schemes are stated, as well as the respective convergence result under certain regularity assumptions combined with the Lax-Milgram theorem, and the Banach and Brouwer fixed-point theorems. In particular, Raviart-Thomas elements of order k are used for approximating the pseudo-stress tensor, piecewise polynomials of degree ≤ k and ≤ k + 1 are utilized for approximating the strain tensor and the velocity, respectively, and the heat and substance concentration are approximated by means of Lagrange finite elements of order ≤ k + 1. Optimal a priori error estimates are derived and confirmed through some numerical examples that illustrate the performance of the proposed semi-augmented mixed-primal scheme. [ABSTRACT FROM AUTHOR]

A mathematical model describing the HIV/AIDS transmission dynamics in the existence of an aware community using fractional differential operator having Mittag–Leffler kernel is presented and investigated in this paper. By using the fixed point theorem, the existence and uniqueness conditions of the model are obtained. We have used a novel technique known as the iterative Laplace transform approach to obtain the approximate solution of the mathematical model of HIV/AIDS based on the Atagana-Baleanu operator.We investigate the necessary conditions for the disease control in order to determine the role of unaware infective in the spread of HIV/AIDS. The numerical simulations and plots are demonstrated for different values of fractional order. Moreover, we have compared the obtained numerical results based on the Atagana-Baleanu operator with the values obtained using the Caputo operator for the suggested model. We believe that Atangana-Baleanue fractional derivative and the suggested algorithm are expected to be used in future to formulate and analyse many generalised fractional models. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as classical solutions for a class of associated linear partial differential equations (PDEs) defined on [ 0 , T ] × R d × P 2 (R d) , for any T > 0 , P 2 (R d) being the Wasserstein space (i.e. the space of probability measures on R d with a finite second-order moment). The martingale problem is addressed by a fixed point argument on a suitable complete metric space, under some mild regularity assumptions on the coefficients that covers a large class of interaction. Also, new well-posedness results in the strong sense are obtained from the previous analysis. Under additional assumptions, we then prove the existence of the associated density and investigate its smoothness property. In particular, we establish some Gaussian type bounds for its derivatives. We eventually address the existence and uniqueness for the related linear Cauchy problem with irregular terminal condition and source term. [ABSTRACT FROM AUTHOR]

Let Π be a finite lattice of integer points in a box of R n and f an increasing mapping in terms of the componentwise ordering from Π to itself. The well-known Tarski's fixed point theorem asserts that f has a fixed point in Π. A simple expansion of f from Π to a larger lattice C of integer points in a box of R n yields that the smallest point in C is always a fixed point of f (an expanded Tarski's fixed point problem). By introducing an integer labeling rule and applying a cubic triangulation of the Euclidean space, we prove in this paper that the expanded Tarski's fixed point problem is in the class PPA when f is given as an oracle. It is shown in this paper that Nash equilibria of a bimatrix game can be reformulated as fixed points different from the smallest point in C of an increasing mapping from C to itself. This implies that the expanded Tarski's fixed point problem has at least the same complexity as that of the Nash equilibrium problem. As a byproduct, we also present a homotopy-like simplicial method to compute a Tarski fixed point of f . The method starts from an arbitrary lattice point and follows a finite simplicial path to a fixed point of f . [ABSTRACT FROM AUTHOR]

This paper discusses the classifier ensemble problem with sparsity and diversity learning, which is a central issue in machine learning. The current approach for reducing the size and increasing the accuracy of a classifier ensemble is to formulate it as a convex quadratic programming problem, which is a relaxation problem, and then solve it by using the existing methods for convex quadratic programming or by computing closed-form solutions. This paper presents a novel computational approach for solving the classifier ensemble problem with sparsity and diversity learning without any recourse to relaxation problems and their associated methods. We first show that the classifier ensemble problem can be expressed as a minimization problem for the sum of certain convex functions over the intersection of fixed point sets of quasi-nonexpansive mappings. Next, we propose fixed point optimization algorithms for solving the minimization problem and show that the algorithms converge to the solution of the minimization problem. It is shown that the proposed algorithms can directly solve the classifier ensemble problem with sparsity and diversity learning. Finally, we compare the performance of the proposed sparsity and diversity learning methods against an existing method in classification experiments using data sets from the UCI machine learning repository and the LIBSVM. The experimental results show that the proposed methods have higher classification accuracies than the existing method. [ABSTRACT FROM AUTHOR]

Calculating and analyzing the number of spanning trees of graphs (network models) is an important and interesting research project in wide variety of fields, such as mathematics, physics, theoretical computer science, chemistry and so on. The number of spanning trees of graphs (models) displays amounts of information on its structural features and also on some relevant dynamical properties, in particular network security, random walks and percolation. In this paper, firstly, due to lots of graphs (models) are built on the basis of various simple and small elements (components), we provide primarily some helpful network-operation, such as link-operation and merge-operation, to generate more realistic and complicated graphs (models). Secondly, considering reliability of fault-tolerance to random faults and of intrusion-tolerance to selectively remove attacks, synchronization capability and diffusion properties of networks, we present an iterative method (algorithm) for computing the total number of spanning trees. As a pellucid example, we apply our method to tree space and cycle space, notice that it is proved to be indeed a better tool. In order to reflect more widely practical meanings, we study its applications in graph theory, including ladder-graph with zero clustering coefficient, wheel-graph having nonzero clustering coefficient as constituent ingredients of maximal planar graphs. In the rest of this paper, we make a brief summary that the method described by us can be designed a program (algorithm) for obtaining easily the exact number of spanning trees of some models. [ABSTRACT FROM AUTHOR]

This paper provides a new model framework to study interval-valued dynamical systems with length constraints. We use impulses instead of switching points to control the length of solutions to interval-valued differential equation under gH -differentiability. Firstly, we consider a class of interval-valued differential equation with impulses. Then, we study interval-valued differential equation with impulses relative to length constraints. Applying fixed point theory in metric space, we prove some existence results. Several examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

With low damping in the edge-wise of the wind turbine blade, significant damage can be caused by the high-amplitude vibrations resulting from environmental loads. This paper proposes the use of a tuned cable-inerter system (TCIS) to mitigate the edge-wise vibration of the blades by exploiting the bending deformation of the blade. Firstly, the TCIS is studied analytically, and a reduce-order blade-TCIS model is established for describing the dynamic behavior. A closed-form solution allowing for parameter optimization is then derived based on the fixed-point theory. Subsequently, a coupling wind turbine model with the TCIS is established. By employing the NREL 5MW wind turbine as a benchmark model, the feasibility of the TCIS is verified in both frequency and time domain. The simulation results show that the TCIS performs superior in reducing the blade response with smaller stroke, compared with the traditional tuned mass damper (TMD) and tuned mass damper with inerter (TMDI). The investigation on feasibility of TCIS in blade vibration control shows potential value for utilization in the narrow spaces of wind turbine blades without additional weight on the blade. Furthermore, the closed-form solution offers an analytical method for rapid and effective parameters optimization. • Exploration of the feasibility of TCIS in rotating wind turbine blades. • Closed-form solutions for the optimal design of TCIS parameters are derived through fixed-point theory. • The coupled model between the entire wind turbine and TCIS is established. • The TCIS outperforms the classic DVAs in vibration control with a smaller stroke. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, the authors have proposed the qualitative properties for the solution of the Hilfer implicit fractional differential equations (HIFDE) of order 1 < ϱ ≤ 2 involving nonlocal boundary conditions using fixed point theory. By imposing the growth conditions on a non-linear function the sufficient condition existence of a solution for the assumed problem is given by using Schaefer's fixed point theorem. The result for the existence and uniqueness of the solution has been established utilizing the Banach contraction principle using the Lipschitz property and following the existence and uniqueness result, a priori bound of the solution is also given. In addition to existence and uniqueness results, the Ulam-Hyers and Generalized Ulam-Hyers stability analysis for the solutions of HIFDE is also provided. Some examples are presented in order to demonstrate the applications of our findings. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algorithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtaining capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested networks. A set of computational tests on realistic small- and large-scale transit networks under various congestion levels are reported, and the characteristics of the proposed method are analyzed. [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence of the traveling waves of the equations describing a diffusive SEIR model with non-local reaction between the infected and the susceptible. The existence of traveling waves depends on the basic reproduction rate S − ∞ β / γ and the minimal speed. We use the Schauder fixed point theorem and the Laplace transform to get the existence and non-existence of traveling waves in our paper. We also give some numerical results of the minimal wave speed. [ABSTRACT FROM AUTHOR]

The present paper studies both the fixed point property ( FPP for brevity) and the almost fixed point property ( AFPP for short) for Marcus-Wyse ( M -, for short) topological spaces by using an M -retract. Under M -topology, let S N M ( x ) be the smallest open neighborhood of x . In this paper we prove that every M -connected subspace of S N M ( x ) has the FPP . Let S C M 4 be a simple closed M -curve with four elements in Z 2 . Besides, consider an M -topological plane ( X , γ X ) (see Definition 5 ) such that S N M ( x ) ⊂ ( X , γ X ) , where x is a double even point or an even point. Then, proving that S C M 4 is an M -retract of ( X , γ X ) , we propose that every M -topological plane does not have the AFPP . Finally, the present paper proves the following: consider M -connected spaces ( X i , γ X i ) , where X i ⊂ Z , 2 ≤ | X i | ≨ ∞ , i ∈ { 1 , 2 } . Then the Cartesian product as an M -topological subspace ( X 1 × X 2 , γ X 1 × X 2 ) does not have the AFPP . [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence of the traveling waves of the equations describing a diffusive SEIR model with non-local reaction between the infected and the susceptible. The existence of traveling waves depends on the minimal speed c ∗ and basic reproduction rate β / γ . We use the Laplace transform and the Schauder fixed point theorem to get the existence and non-existence of traveling waves in our paper. We also give some numerical results of the minimal wave speed. [ABSTRACT FROM AUTHOR]

The paper considers a general neural networks model with variable-time impulses. It is shown that each solution of the system intersects with every discontinuous surface exactly once via several new well-proposed assumptions. Moreover, based on the comparison principle, this paper shows that neural networks with variable-time impulse can be reduced to the corresponding neural network with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the variable-time impulsive neural networks. Furthermore, a series of sufficient criteria are derived to ensure the existence and global exponential stability of periodic solution of variable-time impulsive neural networks, and to illustrate the same stability properties between variable-time impulsive neural networks and the fixed-time ones. The new criteria are established by applying Schaefer’s fixed point theorem combined with the use of inequality technique. Finally, a numerical example is presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, a predator–prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington–DeAngelis functional response and nonlinear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the main parameter, we mainly investigate the existence, stability and exact number of positive solutions when m is large and other parameters meet a certain range of conditions. Meanwhile, some numerical simulations are applied to illustrate the analytical results. The main techniques used in this paper include the fixed point index theory, the super-sub solution method, the Lyapunov-Schmidt reduction procedure and the perturbation principle. [ABSTRACT FROM AUTHOR]

In this paper, we modify the general iterative method to approximate a common element of the set of solutions of split variational inclusion problem and the set of common fixed points of a finite family of k -strictly pseudo-contractive nonself mappings. Strong convergence theorem is established under some suitable conditions in a real Hilbert space, which also solves some variational inequality problems. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors. Finally, some examples to study the rate of convergence and some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

Two distinct research approaches have been proposed for assigning extensional semantics to higher-order logic programming. The former approach [11] uses classical domain-theoretic tools while the latter [1] builds on a fixed-point construction defined on a syntactic instantiation of the source program. The relationships between these two approaches had not been investigated until now. In this paper we demonstrate that for a very broad class of programs, namely the class of definitional programs introduced by W.W. Wadge, the two approaches coincide with respect to ground atoms that involve symbols of the program. On the other hand, we argue that if existential higher-order variables are allowed to appear in the bodies of program rules, the two approaches are in general different. The results of the paper contribute to a better understanding of the semantics of higher-order logic programming. [ABSTRACT FROM AUTHOR]

The implied volatility is the unique volatility value that makes the celebrated Black–Scholes formula yields a traded option’s price. Implied volatilities at varying strike prices and maturities form the implied volatility surface. Empirically, this surface is never flat. The local-volatility (LV) model is an option model that attempts to fit the implied volatility surface. It is popular because the preference freedom of the Black–Scholes model is retained. A tree consistent with the implied volatility surface generated by an LV model is known as implied tree. Past attempts to construct the implied tree, however, are prone to having invalid transition probabilities. In fact, this problem occurs even when the volatility surface is flat as in the Black–Scholes model. This paper unearths a potentially fundamental reason for that failure: the trees contain repelling fixed points. As efficient and valid trees for general LV models remain elusive despite decades of research, this paper turns to separable LV models. An efficient and valid binomial tree is then built for such models. Our novel tree is named the waterline tree because its upper part (the part that is above the water, so to speak) matches the moments of the price, whereas the lower part matches the moments of its logarithmic price. This break from traditional trees ensures that only attracting fixed points remain. Numerical results confirm the excellent performance of the waterline tree. [ABSTRACT FROM AUTHOR]

In this paper, we firstly introduce a model of four-point boundary value problem for generalized singular Lane–Emden systems on whole line. By establishing Green’s function G ( t , s ) for problem − ( ρ ( t ) x ′ ( t ) ) ′ = 0 , lim t → − ∞ x ( t ) − k x ( ξ ) = 0 , lim t → + ∞ x ( t ) − l x ( η ) = 0 , we prove that G ( t , s ) ≥ 0 under some assumptions which actually generalize a corresponding result in Liu (2004). We then obtain sufficient conditions to guarantee existence of positive solutions of this kind of models. Finally, three examples are given at the end of the paper to illustrate main theorems. [ABSTRACT FROM AUTHOR]

Our understanding of climate change is dominated by quantified scientific knowledge, with science and politics usually seen as operating separately and autonomously from one another. By investigating a particular fact box in the IPCC’s Fourth Assessment Report (AR4), this paper challenges the assumption that science and policy can be clearly delineated. The so-called “Bali Box” gained a prominent role in negotiations leading up to the Copenhagen Conference in 2009, as it was widely seen as providing a “fixed point” – a quantified scientific answer to the question of equitable effort-sharing between North and South. This understanding of the Bali Box triggered a backlash, however, when the hybrid character of the box as an assemblage of science, political considerations and moral judgements became evident to actors in the negotiations. The paper employs the notion of boundary objects to analyse the history of the Bali Box, and argues that climate politics will benefit from a richer understanding of the interplay between science and policy. Moving beyond characterizations that place the Bali Box on either side of a clear boundary between the scientific and the political, we suggest focusing instead on what the Box as a hybrid product is doing, i.e. how it simplifies and quantifies, what it covers and what it leaves outside. [ABSTRACT FROM AUTHOR]