Abstract The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black–Scholes equation for a European put option. The Liouville–Caputo derivative was used to improve the ordinary Black–Scholes equation. The analytic solution is a powerful tool for describing the behavior of the option price in the European style

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article by different authors [2] that was simultaneously under consideration at a different journal. The article also shows evidence of authorship manipulation and peer review manipulation. In addition, the identity of the third author could not be verified: the University of Mosul has confirmed that Ahmed

Abstract The use of surrogate modeling techniques to efficiently solve a single objective optimization (SOO) problem has proven its worth in the optimization community. However, industrial problems are often characterized by multiple conflicting and constrained objectives. Recently, a number of infill criteria have been formulated to solve multi-objective optimization (MOO) problems using surrogates

Abstract In this paper, new and optimal asymptotics on the decay of the coefficients for functions of limited regularity expanded in terms of Jacobi and Gegenbauer polynomial series are presented. For a class of functions with interior singularities, the decay of the coefficient is of the same asymptotic order for arbitrary \(\alpha ,\,\beta >-1\), which confirms that the decay of the coefficients

Abstract This paper is concerned with the solution of severely ill-conditioned linear tensor equations. These kinds of equations may arise when discretizing partial differential equations in many space-dimensions by finite difference or spectral methods. The deblurring of color images is another application. We describe the tensor Golub–Kahan bidiagonalization (GKB) algorithm and apply it in conjunction

Abstract In this paper, we propose a fast and stable evaluation method for the analytic derivatives of splines generated by the 7-direction quartic box-spline. We can maintain the spline structure by determining the derivative functions that can be represented as finite differences of box-splines defined by the sub-directions. Thus, the evaluation overhead can be reduced. We demonstrate that the first

Abstract We introduce an inexact variant of stochastic mirror descent (SMD), called inexact stochastic mirror descent (ISMD), to solve nonlinear two-stage stochastic programs where the second stage problem has linear and nonlinear coupling constraints and a nonlinear objective function which depends on both first and second stage decisions. Given a candidate first stage solution and a realization of

In this paper, the existence of solutions is obtained for the boundary value problems to the elastic beam equations with simply supports and impulsive effects. By using the variational method and spectral structure, under the condition ( n + δ ) 4 π 4 ≤ 2 G ( t , u ) u 2 ≤ ( n + 1 − δ ) 4 π 4 ( G ( t , u ) = ∫ 0 u g ( t , s ) d s , n is a positive integer) and other conditions, we give some new criteria

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness

This paper proposes an ω-periodic version of the Ellermeyer model of delayed chemostat. We obtain a sufficient condition ensuring the existence of a positive ω-periodic solution. Our proof is based on the application of the generalized continuation theorem. In addition, as a consequence of the implicit function theorem, we obtain a uniqueness result for sufficiently small delays.

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the “standard” Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the class of all “standard” Choquet integrals but the use

An important problem in Fuzzy OWL 2 ontology building is the definition of fuzzy membership functions for real-valued fuzzy sets (so-called fuzzy datatypes in Fuzzy OWL 2 terminology). In this paper, we present a tool, called Fudge, whose aim is to support the consensual creation of fuzzy datatypes by aggregating the specifications given by a group of experts. Fudge is freeware and currently supports

The application of mathematics, physics and engineering to medical research is continuously growing; interactions among these disciplines have become increasingly important and have contributed to an improved understanding of clinical and biological phenomena, with implications for disease prevention, diagnosis and treatment. This special issue presents examples of this synergy, with a particular focus

Abstract A synthetic drug transmission model with psychological addicts and time delay is proposed in this paper. By analyzing the corresponding characteristic equation and choosing the time delay as the bifurcation parameter, a set of sufficient criteria guaranteeing local stability of the synthetic drug addiction equilibrium and the appearance of a Hopf bifurcation of the model is established. Further

Abstract In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical

The original version of this article unfortunately contained an error in Acknowledgement section. The authors would like to correct the error with this erratum. The correct text should read as:

Abstract We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where the pattern resembles one of the bistable states, while the profile is close to the second bistable state outside this plateau. We show that the existence branches of such patterns generically form either an infinite

Abstract In this paper, we prove the existence of response solution (i.e., quasi-periodic solution with the same frequency as the forcing) for the quasi-periodically forced generalized ill-posed Boussinesq equation: $$\begin{aligned} \begin{aligned} y_{tt}(t,x)=\mu y_{xxxx}+y_{xx}+\left( y^{3}+\varepsilon f(\omega t,x)\right) _{xx},\,\, x\in [0, \pi ],\,\, \mu >0, \end{aligned} \end{aligned}$$subject

Abstract We derive time-averaged \(L^1\) estimates on Littlewood–Paley decompositions for linear advection–diffusion equations. For wave numbers close to the dissipative cutoff, these estimates are consistent with Batchelor’s predictions on the variance spectrum in passive scalar turbulent mixing.

Abstract This work focuses on multi-species Lotka–Volterra models with regime switching modulated by a continuous-time Markov chain involving a small parameter. The small parameter is used to reflect different rates of the switching among a large number of states representing the discrete events. Using perturbed Lyapunov function methods and the structure of the limit system as a bridge, stochastic

Abstract A new two-component nonlinear wave system is studied by the generalized perturbation (\(n,N\hbox {-}n\))-fold Darboux transformation, and various exotic localized vector waves are found. Firstly, the modulational instability is investigated to reveal the mechanism of appearance of rogue waves. Then based on the N-fold Darboux transformation, the generalized perturbation (\(n,N\hbox {-}n\))-fold

Abstract A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an objective function, an upper bound on the number of iterations (or function or derivative evaluations) required until a pth-order stationarity condition

In this paper, we develop an unconditionally stable linear numerical scheme for the N-component Cahn–Hilliard system with second-order accuracy in time and space. The proposed scheme is modified from the Crank–Nicolson finite difference scheme and adopts the idea of a stabilized method. Nonlinear multigird algorithm with Gauss–Seidel-type iteration is used to solve the resulting discrete system. We

Abstract New nonlinear integral inequalities (NII) are presented in this paper. Based on mathematical analysis technique, several estimation results are obtained, which not only complement the aforementioned results, but also generalize the inequalities to the more general nonlinearities. As an application, they can be employed to estimate the bound on the solutions of power integro-differential equations

Abstract In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold

Abstract In this paper, we present some new results on a class of tensors, which are defined by the solvability of the corresponding tensor complementarity problem. For such structured tensors, we give a sufficient condition to guarantee the nonzero solution of the corresponding tensor complementarity problem with a vector containing at least two nonzero components and discuss their relationships with

Abstract Nonlinear conjugate gradient methods are among the most preferable and effortless methods to solve smooth optimization problems. Due to their clarity and low memory requirements, they are more desirable for solving large-scale smooth problems. Conjugate gradient methods make use of gradient and the previous direction information to determine the next search direction, and they require no numerical

Abstract Block-coordinate descent is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at each iteration, which in practical terms usually restricts the quadratic term in the subproblem to be diagonal, thus losing most of the benefits of higher-order

Abstract Probability functions appearing in chance constraints are an ingredient of many practical applications. Understanding differentiability, and providing explicit formulae for gradients, allow us to build nonlinear programming methods for solving these optimization problems from practice. Unfortunately, differentiability of probability functions cannot be taken for granted. In this paper, motivated

Abstract We show that Hölder continuity of the gradient is not only a sufficient condition, but also a necessary condition for the existence of a global upper bound on the error of the first-order Taylor approximation. We also relate this global upper bound to the Hölder constant of the gradient. This relation is expressed as an interval, depending on the Hölder constant, in which the error of the

Abstract The notions of upper and lower global directional derivatives are introduced for dealing with nonconvex and nonsmooth optimization problems. We provide calculus rules and monotonicity properties for these notions. As a consequence, new formulas for the Dini directional derivatives, radial epiderivatives and generalized asymptotic functions are given in terms of the upper and lower global directional

Abstract This paper addresses Lipschitzian stability issues, that play an important role in both theoretical and numerical aspects of variational analysis, optimization, and their applications. We particularly concentrate on the so-called relaxed one-sided Lipschitz property of set-valued mappings with negative Lipschitz constants. This property has been much less investigated than more conventional

Abstract Taking advantage of recent developments in the theory of generalized differentiation of multifunctions, we present in a unified manner a general iterative procedure for solving generalized equations. This procedure is based on a certain type of approximation of functions called point-based approximation together with a linearization of the multifunctions. Our theorem encompasses the Newton

Abstract This article discusses periodic and Poisson stable points of control affine systems. The main result states that the Poisson stability and the periodicity are equivalent concepts for states with closed semi-orbits. This is applied to providing a sufficient condition for the existence of periodic trajectories. Almost periodicity of invariant control systems on Lie groups is specially studied

Abstract In this paper, the connectedness and path-connectedness of solution sets for weak generalized symmetric Ky Fan inequality problems with respect to addition-invariant set are studied. A class of weak generalized symmetric Ky Fan inequality problems via addition-invariant set is proposed. By using a nonconvex separation theorem, the equivalence between the solutions set for the symmetric Ky

Abstract We consider an optimal control problem governed by a system of nonlinear difference equations. We obtain the existence of the optimal control as well as first-order optimality conditions of Pontryagin type by using the Dubovitskii–Milyutin formalism. Also, we give the necessary and sufficient conditions for global optimality.

Abstract In this work, we focus on bicooperative games, a variation of the classic cooperative games, and investigate the conditions for the coefficients of the bisemivalues—a generalization of semivalues for cooperative games—necessary and / or sufficient in order to satisfy some properties, including among others, desirability relation, balanced contributions, null player exclusion property and block

We investigate the global existence and analyticity of mild solution to the three‐dimensional generalized Hall‐magnetohydrodynamics (MHD) system in this work. We prove the global existence and analyticity of solutions in the corresponding critical spaces. The work extends global existence and analyticity of solutions to Hall‐MHD system in Duan and MHD system in Wang and Ye and Zhao, to the generalized

In this paper, we consider the combined quasi‐neutral and inviscid limits of the two‐fluid compressible Navier–Stokes–Poisson system in the unbounded domain R 2 × T with the ill‐prepared initial data. We prove that the weak solutions of the compressible Navier–Stokes–Poisson system converge to the strong solution of the incompressible Euler equation as long as the latter exists. Moreover, the convergence

In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh–Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on the asymptotic synchronization of this neuron network at a uniform exponential rate provided that the boundary coupling strength and the stimulating signal exceed

In this work, we show that two distance functions independently defined on the space of subcopulas are topological equivalent. In this process, we also defined another distance functions equivalent to the first two distances. Moreover, all metric spaces of subcopulas with fixed domain under the supremum distance are metric subspaces under this new distance function. We also prove that the Sklar correspondence

Abstract Using some fixed point theorems for contractive mappings, including α-γ-Geraghty type contraction, α-type F-contraction, and some other contractions in \(\mathcal{F}\)-metric space, this research intends to investigate the existence of solutions for some Atangana–Baleanu fractional differential equations in the Caputo sense.

Abstract This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam

Abstract In this study, a novel sequential optimality condition for general continuous optimization problems is established. In the context of mathematical programs with equilibrium constraints, the condition is proved to ensure Clarke stationarity. Originally devised for constrained nonsmooth optimization, the proposed sequential optimality condition addresses the domain of the constraints instead

Abstract We extend some results of nonsmooth analysis from the Euclidean context to the Riemannian setting. Particularly, we discuss the concepts and some properties, such as the Clarke generalized covariant derivative, upper semicontinuity, and Rademacher theorem, of locally Lipschitz continuous vector fields on Riemannian settings. In addition, we present a version of the Newton method for finding

Abstract In this paper, we study a class of subdifferential evolution inclusions involving history-dependent operators. First, we improve an existence and uniqueness theorem and prove the continuous dependence result in the weak topologies. Next, we establish the existence of optimal solution to an optimal control problem for the evolution inclusion. Finally, we illustrate the results by an example

Abstract This article investigates stability conditions for set optimization problems with the set less order relation in the senses of Panilevé–Kuratowski and Hausdorff convergence. Properties of various kinds of convergences for elements in the image space are discussed. Taking such properties into account, formulations of internal and external stability of the solutions are studied in the image

Abstract We study nonlinear hyperbolic conservation laws posed on a differential \((n+1)\)-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms depending on a parameter (the unknown variable)—a class of equations proposed by LeFloch and Okutmustur (Far East J. Math. Sci. 31:49–83, 2008). Our main result is a proof of the convergence of the finite volume

Abstract In this paper we provide a priori error estimates with explicit constants for both the \(L^2\)-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently obtained for spline spaces of maximal smoothness. The presented error estimates are in agreement with the numerical evidence found in the literature that smoother

Abstract The purpose of this article is to propose an algorithm for finding an approximate solution of a split variational inclusion problem for monotone operators. By using inertial method, we get a new and simple algorithm for such a problem. Under standard assumptions, we study the strong convergence theorem of the proposed algorithm. As application, we study the split feasibility problem in real

Abstract We consider integer linear programs whose solutions are binary matrices and whose (sub-)symmetry groups are symmetric groups acting on (sub-)columns. Such structured sub-symmetry groups arise in important classes of combinatorial problems, e.g. graph coloring or unit commitment. For a priori known (sub-)symmetries, we propose a framework to build (sub-)symmetry-breaking inequalities for such

In the present article, the idea of using the variable-order fractional-derivative thermoviscoelastic constitutive laws in dynamic stress and vibration analysis of the engineering structures, the required implementation backgrounds, and the relevant numerical solution procedures are investigated for the first time. In this regard, dynamic 3D stress and displacement fields and radial/transverse vibrations

In the work, the psychophysical model of the signal detection theory with the nine outcomes (PMSDT9) for a quantitative description of the solution of the sensory problem of detecting an alternating differential signal was proposed. Unlike the classical model, PMSDT9 has the three probability density functions of the subjective intensity and the sign of the differential signal (instead of the two)

This paper deals with a reaction–diffusion system modeling predator–prey interaction with additive Allee effect. We first analyze nonnegative constant equilibrium solutions and study the stability of the unique positive solution. Then we investigate the steady state bifurcation and Hopf bifurcation from the unique positive constant solution, respectively. The main tools used here include the bifurcation

In this paper, we propose and study the dynamics of a non-autonomous biocontrol model concerned with native consumer A, biocontrol agent B and their common predator L. We assume that some parameters in our proposed model are nonnegative functions instead of being bounded below by positive reals. This assumption is more realistic but makes mathematical proofs more challenging. We first study the positive

Following our previous paper Dombi and Jónás (2019) [16], we will now present new inequalities using the general Poincaré formula for λ-additive measures. These inequalities represent bounds for the well-known Poincaré formula of probability theory.

In this work, we consider a partial differential equation that extends the well-known Fermi–Pasta–Ulam–Tsingou chains from nonlinear dynamics. The continuous model under consideration includes the presence of both a damping term and a polynomial function in terms of Riesz space-fractional derivatives. Initial and boundary conditions on a closed and bounded interval are considered in this work. The

We consider a modification of the well studied Hamiltonian Mean-Field model with cosine potential by introducing a hard-core point-like repulsive interaction and propose a numerical integration scheme to integrate its dynamics. Our results show that the outcome of the initial violent relaxation is altered, and also that the phase-diagram is modified with a critical temperature at a higher value than

Abstract The Moreau envelope, also known as Moreau–Yosida regularization, and the associated proximal mapping have been widely used in Hilbert and Banach spaces. They have been objects of great interest for optimizers since their conception more than half a century ago. They were generalized by the notion of the D-Moreau envelope and D-proximal mapping by replacing the usual square of the Euclidean

Abstract This paper considers higher-order necessary conditions for Henig-proper, positively proper and Benson-proper solutions. Under suitable constraint qualifications, our conditions are of the Karush–Kuhn–Tucker rule. The conditions include higher-order complementarity slackness for both the objective and the constraining maps. They are in a nonclassical form with a supremum expression on the right-hand