In this paper, we study the dynamics of stochastic time-delayed predator–prey model with modified Leslie–Gower and ratio-dependent schemes including additional food for predator and prey with Michaelis–Menten type harvest. We introduce the effects of time delay, Michaelis–Menten type harvest and stochastic perturbation under the structure of the original model to make the model more consistent with

The purpose of this article is to present a novel idea of complex Pythagorean fuzzy threshold graphs \((\mathcal {CPFTG}_{s})\). We introduce the relation between vertex cardinality and threshold values of a \(\mathcal {CPFTG}\). We propose that \(\mathcal {CPFTG}_{s}\) are free from alternating \(4-cycle\) and these graphs can be built up repeatedly adding an isolated or a dominating vertex. We present

In this paper, new oscillation criteria for second-order half-linear difference equations with several variable advanced arguments are obtained, which improve the existing results. Our approach is better than the ones in the literature, only based on sequentially improved monotonicity of the nonoscillatory solutions. For we all know, this method is rare in the study of the oscillation of difference

A stochastic waterborne disease model is analyzed to reveal the effects of the white noise and telegraph noise. For this stochastic model, a critical quantity \(R_0^s\) is derived, which depends on not only model parameters but also environmental noises. If \(R_0^s>1\), then this model admits an ergodic stationary distribution. One of the most important contributions is the suitable Lyapunov function

This article deals with two different methods to solve a time fractional partial integro-differential equation. The fractional derivatives are defined here in Caputo sense. The model problem is solved using the Adomian decomposition method and homotopy perturbation method. Moreover, this paper proves the convergence analysis of the solution based on the present methods. Numerical evidences are illustrated

In this paper, we describe a new type of DNA codes over two noncommutative rings E and F of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over E and F. Using quasi self-duality, we can describe fixed GC-content constraint weight distributions and reverse-complement constraint minimum distributions of those codes.

In this paper, we calculate the Frobenius norm, and give upper and lower bounds for the spectral norm of r-circulant matrices whose entries are defined in terms of generalized bi-periodic Fibonacci numbers. We also provide explicit formulas for the computation of eigenvalues and determinants of these matrices.

In this paper, a new numerical iterative method based on the successive approximations method for solving nonlinear Hammerstein Volterra integral equations of the second kind is proposed. The main approximation tool is based on triangular functions. Also, the convergence analysis and numerical stability of the proposed method are proved. Finally, some numerical examples verify the theoretical results

Bluetongue, a midge-borne disease of ruminants caused by the bluetongue virus (BTV) can rapidly spread from one region (patch) to another by host and/or midge movements, making its control difficult. A multi-patch deterministic model for BTV is formulated and analysed to evaluate the effectiveness of vaccination, quarantine, insecticide spraying and the use of repellent control strategies in reducing

In the present study, a time-delayed SIR epidemic model with a logistic growth of susceptibles, Crowley–Martin type incidence, and Holling type III treatment rates is proposed and analyzed mathematically. We consider two explicit time-delays: one in the incidence rate of new infection to measuring the impact of the latent period, and another in the treatment rate of infectives to analyzing the effect

In this paper, we have considered an SIS epidemic model with arbitrary disease transmission function and arbitrary treatment control function. We have analyzed the model considering the disease transmission function as an increasing and decreasing function separately. To introduce heterogeneity in the system we have taken both the disease transmission function and treatment function as fuzzy numbers

In this paper, we apply the semi-tensor product of matrices and the real vector representation of quaternion matrix to solve quaternion matrix equations for the first time. We derive the expressions of the least squares Hermitian, Persymmetric and Bisymmetric solution for the quaternion matrix equation \(AXB=C\), respectively. Furthermore, we also put forward the equivalent conditions of existence

In this paper, we construct several infinite families of codes over the chain ring \(R={\mathbb {F}}_2[u]/\langle u^k\rangle \), i.e., \(R={\mathbb {F}}_2+u{\mathbb {F}}_2+\cdots +u^{k-1}{\mathbb {F}}_2, u^{k}=0\) by employing simplicial complexes. When the simplicial complexes are all generated by a single maximal element, we compute the homogeneous weight distributions of these classes of codes.

In this paper, we present some convergence results for various iterative algorithms built from Hardy-Rogers type generalized nonexpansive mappings and monotone operators in Hilbert spaces. We obtain some comparison results for the rates of convergence of these algorithms to the solution of variational inequality problem including Hardy–Rogers type generalized nonexpansive mappings and monotone operators

In this article, we enquire for a couple of weak and strong convergence results involving generalized \(\alpha \)-Reich-Suzuki non-expansive mappings in the setting of a hyperbolic metric space. Particularly, we make use of the recently proposed JF-iteration scheme to attain our theories and further, we attest that this algorithm has a faster convergence rate than that of \(M^*\) iteration. Additionally

In this paper, we present two new three-term conjugate gradient methods which can generate sufficient descent directions for the large-scale optimization problems. Note that this property is independent of the line search used. We prove that these three-term conjugate gradient methods are global convergence under the Wolfe line search. Numerical experiments and comparisons demonstrate that the proposed

In this paper, a class of nonconvex optimization with linearly constrained is considered. An inertial Bregman generalized alternating direction method of multiplies is investigated for solving the nonconvex optimization. The iterative schemes are formulated in the spirit of the proximal alternating direction method of multipliers and its inertial variant. The proximal term is introduced via Bregman

Let G be a graph with vertex set V(G). For \(u,v\in V(G)\), we write \(v\sim u\) if vertices v and u are adjacent. The Cartesian product of G and H, denoted by \(G\Box H\), is the graph with vertex set \(V(G)\times V(H)\), where \((x,u)\sim (y,v)\) if and only if \(x=y\) and \(u\sim v\) in H, or \(x\sim y\) in G and \(u=v\). The lexicographic product of G and H, denoted by G[H], is the graph with vertex

In this work, we introduce the \({\mathbb {F}}_qR\)-linear skew cyclic codes, wh ere \(q=p^s\) is a prime power and \(R={\mathbb {F}}_q+u{\mathbb {F}}_q\) with \(u^2=0\). We provide the algebraic structure of these codes. The dual codes of separable linear skew cyclic codes are also presented. Finally, by using the Gray map from \({\mathbb {F}}_qR\) to \({\mathbb {F}}_q\), we get some optimal linear

In this paper, we investigate the boundary value problem of a class of fractional (p, q)-difference Schrödinger equations. By applying Banach contraction mapping principle and a fixed point theorem in cones, we obtain the existence and uniqueness of solutions for the boundary value problem. An example illustrating the main results is also presented.

In this work, we introduce an inertial Halpern-type CQ algorithm for solving split feasibility problems in Hilbert spaces. The main advantages of the proposed algorithm are that the introduced stepsize is bounded away from zero and a strong convergence theorem for our method is established without assuming Lipschitz continuity of the gradient operator. Some preliminary numerical experiments are provided

In cryptography, rotation symmetric Boolean functions (RSBFs) have very significant research value. In this paper, based on the knowledge of integer splitting, a new class of even-variable RSBFs with optimal algebraic immunity (AI) was constructed. The new functions have a nonlinearity of \(2^{n-1}-\left( {\begin{array}{c}n-1\\ k\end{array}}\right) +2^{k-3}(k-3)(k-2) \), which is the highest among

We formulate a system of ordinary differential equations to model the contribution of antibiotic treatment and immune system to combat bacterial infections. We obtained threshold conditions that determine when the bacteria can be eliminated, which are consistent with biological phenomena. In order to minimize the bacterial population, we formulated an optimal control problem considering the action

\({\mathbb {Z}}_2{\mathbb {Z}}_{4}\)-additive codes have been defined as a subgroup of \({\mathbb {Z}}_2^{r}\times {\mathbb {Z}}_4^{s}\) in [6] where \({\mathbb {Z}}_2\), \({\mathbb {Z}}_{4}\) are the rings of integers modulo 2 and 4 respectively and r and s are positive integers. In this study, we define a family of codes over the set \({\mathbb {Z}}_2[{\bar{\xi }}]^{r}\times {\mathbb {Z}}_4[\xi ]^{s}\)

In this paper, we develop a symmetric mixed covolume scheme for the nonlinear parabolic equations. The existence and uniqueness of the scheme are proved by using the lowest order Raviart–Thomas mixed element space on rectangular grids. We carry out a rigorous error estimates for the constructed scheme, establishing the first-order convergence for both velocity and pressure. Numerical examples are provided

In this work, we introduce two Bregman projection algorithms with self-adaptive stepsize for solving pseudo-monotone variational inequality problem in a Hilbert space. The weak and strong convergence theorems are established without the prior knowledge of Lipschitz constant of the cost operator. The convergence behavior of the proposed algorithms with various functions of the Bregman distance are presented

It is still a challenging task to get a satisfying numerical solution to the time-dependent Nernst-Planck (NP) equation, which satisfies the following three physical properties: solution nonnegativity, total mass conservation, and energy dissipation. In this work, we propose a structure-preserving finite element discretization for the time-dependent NP equation combining a reformulated Jordan-Kinderlehrer-Otto

We develop a mathematical model of the wild mosquito dispersal with impulsive releases of the sterile mosquitoes and obtain a threshold condition that determines the eradication and uniform persistence of the wild mosquitoes using Floquet theory and impulsive comparison theorem. The effect of the dispersal rate on dynamics is investigated by means of numerical simulation. Additionally, we investigate

The purpose of the present work is to introduce and study the concept of interval type-2 (IT2) fuzzy grammar which recognizes the given IT2 fuzzy languages. The relationship between IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars is discussed. Specifically, the results we obtained here are (i) IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy

We suggest the local analysis of a class of iterative schemes based on decomposition technique for solving Banach space valued nonlinear models. Earlier results used hypotheses up to the fourth derivative to establish convergence. But we only apply the first derivative in our convergence theorem. We also provide computable radius of convergence ball, error estimates and uniqueness of the solution results

This paper improves the modified multiwavelets bases of minimal search method for the fractional integro-differential equation. First, it shows the unique solvability of the equation. And then the Legendre multiwavelets are improved and the modified multiwavelets in reproducing kernel space are obtained. Subsequently, it is established a strict theory for obtaining the \(\varepsilon \)-approximate

Let \(\mathbb {F}_q\) denote the finite field of order q, and let \(\Lambda =(\lambda _1,\lambda _2,\cdots ,\lambda _\ell ),\) where \(\lambda _1,\lambda _2,\cdots ,\lambda _\ell \) are non-zero elements of \(\mathbb {F}_q.\) Let \(n =m_1+m_2+\cdots +m_\ell ,\) where \(m_1,m_2,\cdots ,m_\ell \) are arbitrary positive integers (not necessarily coprime to q). In this paper, we study algebraic structures

The second-order ordinary differential equation (ODE) often emerges from applied science, such as orbital mechanics, quantum mechanics, physical chemistry, electronics. As we all know, Runge-Kutta-Nyström (RKN) method is indispensable when solving the second-order ODE. In addition, there are also some intrinsic properties in these fields. How to preserve these properties must be considered when seeking

The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence

We consider the Cauchy problem for the Helmholtz equation defined in a rectangular domain. The Cauchy data are prescribed on a part of the boundary and the aim is to find the solution in the entire domain. The problem occurs in applications related to acoustics and is illposed in the sense of Hadamard. In our work we consider regularizing the problem by introducing a bounded approximation of the second

In this paper, we present a new predictor-corrector interior-point algorithm based on a wide neighborhood for semidefinite optimization. The proposed algorithm is a Mizuno-Todd-Ye predictor-corrector type and uses the Nesterov-Todd (NT) search direction in predictor step and a commutative class of search directions involving Helmberg-Kojima-Monteiro and NT directions in corrector step. We show that

In this article, a boundary value problem for a nonlinear system of singularly perturbed two second order differential equations in which only the first equation is multiplied by a small positive parameter is considered. The first component of the solution exhibits boundary layers whereas the second component exhibits less-severe layers. A numerical method composed of a classical finite difference

Based on the study of the plankton population system, a diffusive toxic plankton model with Tissiet type functional response function and predation delay is proposed. Firstly, the sufficient conditions for locally asymptotic stability of the diffusion system without delay at the positive equilibrium are given, the existence conditions of Hopf bifurcation caused by diffusion are given, and the conditions

The fractional differential equation has been used to describe many phenomenons in almost all applied sciences, such as fluid flow in porous materials, anomalous diffusion transport, acoustic wave propagation in viscoelastic materials, and others. In some cases, it is complicated to find the analytical solution of a fractional differential equation, so there are some special techniques to approximate

Graph invariants provide an outstanding tool for investigation of abstract structures of graphs. They contain global and general information about a graph and its particular substructures. In this paper, the graph invariants such as vertex connectivity, metric dimension, minimum vertex degree, independence number, domination number, Laplacian energy and Zagreb indices of line graph of zero-divisor

In this paper, we constructed a fitted mesh finite difference method for solving a class of time-dependent singularly perturbed turning point convection-diffusion problems whose solution exhibits an interior layer. The diffusion coefficient in the underlying PDE is a quadratic function of the space variable and contains a perturbation parameter. While such problems have been studied in the case of

The objectives of this paper are to survey and extend results on several classes of asymptotically good quasi-twisted codes over finite field with a low index, namely double circulant codes, double negacirculant codes, four circulant codes and four negacirculant codes. For a given length, we summarize the enumerations of the self-dual and LCD codes and supplement some expansion results. The existence

A graph is called Hamilton-connected if there exists a Hamiltonian path between every pair of its vertices. Determining whether or not a graph is Hamilton-connected is an NP-complete problem. In this paper, we present two methods to show Hamilton-connectivity in graphs. The first method uses the vertex connectivity and Hamiltoniancity of graphs, and, the second is the definition-based constructive

In this paper we import a novel approach to solve the non-linear fourth order boundary value problem. The basic strategy depends on integral operator equation which includes Green’s function and fixed point iteration. To ensure the method, three illustrations were conferred. From the residual or absolute error calculations, it is shown that the S-iteration for contraction operator gives fast convergence

The concept of energy of a graph was first introduced by I. Gutman [5] in 1978. The energy E(G) of a simple graph G is defined to be the sum of the absolute values of the eigenvalues of G. The tree dendrimer d(n, k) is a finite connected cycle free graph, also known as Bethe lattice. The each vertex in d(n, k) is connected to \((k-1)\). It is a rooted tree, with all other vertices arranged in shells

This paper studies the single-machine due-date assignment problem with past-sequence-dependent setup times (denoted by \(ST_{psd}\)). Under common due-date (denoted by CON-DD) assignment, slack due-date (denoted by SLK-DD) and different due-date (denoted by DIF-DD) assignment, the objective function is to minimize the linear weighted sum of earliness-tardiness, number of early and delayed jobs, and

In this contribution, two delayed commensalism models with noise coupling and interval biological parameters are constructed, in which the positive and negative intrinsic growth rates of commensal species are respectively considered. Two sets of sufficient conditions for the persistence and extinction of each species are obtained as well as the existence of a unique ergodic stationary distribution

Monotone inclusion problems are crucial to solve engineering problems and problems arising in different branches of science. In this paper, we propose a novel two-step inertial Douglas-Rachford algorithm to solve the monotone inclusion problem of the sum of two maximally monotone operators based on the normal S-iteration method (Sahu, D.R.: Applications of the S-iteration process to constrained minimization

In this paper, we consider the existence of extremal solutions for a type of fractional compartment models. By use of a new comparison result, some new sufficient conditions for the existence of solutions are established by combining the monotone iterative technique and the methods of lower and upper solutions. Finally, an example is presented to illustrate the validity of our main results.

In this study, the second kind Volterra integral equations (VIEs) are considered. An algorithm based on the two-point Taylor formula as a special case of the Hermite interpolation is proposed to approximate the solution of such problems. The method can be applied for solving both the linear and nonlinear VIEs and systems of nonlinear VIEs. The convergence analysis and the error estimate of the method

In this paper, we investigate a stochastic multi-stage model to evaluate the influence of treatment intensification with the integrase inhibitor raltegravir on viral load and 2-LTR dynamics in HIV patients under suppressive therapy. Firstly, it is proven that the model has a unique global positive solution. Secondly, by constructing a Lyapunov function, we establish sufficient conditions for the existence

In this research, we discuss balancing two essential ecosystem services, known as resilience and yield, in a harvested two predators one prey system. We study how these two ecosystem services respond to different types of harvesting plans applied to the system. In individual harvesting, we observe that prey harvesting is suitable for generating more yield while either predator harvesting gives more

The aim of this paper is twofold: (a) to revisit the results in Iqbal et al. (Numer Algorithms 1–21, 2019. https:doi.org/10.1007/s11075-019-00854-z) and prove some convergence and stability results for the subclass of multivalued contractive operators under some mild conditions (b) to introduce a multivalued Reich-Suzuki type \(\alpha \)-nonexpansive mappings and present some fixed point results for

In order to study the impact of random environments during the spread of the disease, we propose a novel stochastic SIQS model on scale-free networks, which introduces stochastic perturbations to the infected rates. We first obtain the existence of global positive solutions. Moreover, by constructing appropriate stochastic Lyapunov functions, we prove sufficient conditions for extinction and persistence

Food-webs consisting of three or more species exhibit very complex dynamics in ecosystems which mainly depend on the various traits of prey and predator. In presence of predator, prey adopted optimal strategies to avoid predation and to increase their survival. The antipedator behaviour exhibited by prey against predator’s fear; have potential to change the qualitative dynamics of food web systems

In this paper, we consider an inverse source problem for a fractional pseudo-parabolic equation. We show that the problem is severely ill-posed (in the sense of Hadamard) and the Tikhonov regularization method is proposed to solve the problem. In addition, we present numerical examples to illustrate applicability and accuracy of the proposed method to some extent.

In this paper, we consider a two-predator–one-prey population model that incorporates both the inter-specific competition between two predator populations and the intra-specific competition within each predator population. We investigate the dynamics of this model by addressing the existence, local and global stability of equilibria, uniform persistence as well as saddle-node and Hopf bifurcations

Give a graph G, we color its all edges. If any two adjacent edges gets the different colors, then we call this color a proper edge coloring of G. Give a proper edge coloring of G, if only two colors alternately appear on a cycle, then the cycle is called bichromatic. Acyclic edge coloring of a graph G means that there are no bichromatic cycles in G. The acyclic chromatic index of a graph G is the minimum

Suppose \([3]=\{0,1,2,3\}\) and \([3^{-}]=\{-1,1,2,3\}\). An outer independent signed double Roman dominating function (OISDRDF) of a graph \(\Gamma \) is function \(l:V({\Gamma })\rightarrow [3^{-}]\) for which (i) each vertex t with \(l(t)=-1\) is joined to at least two vertices labeled a 2 or to at least one vertex z with \(l(z)=3\), (ii) each vertex t with \(l(t)=1\) is joined to at least a vertex

In this paper, a new conjugacy condition is established to solve unconstrained optimization problems based on a new quasi-Newton equation. We present a modified Dai–Liao conjugate gradient method to solve unconstrained optimization problems with a new value of the parameter t based on the new conjugacy condition. The presented algorithm has the following properties: (i) the modified Dai–Liao conjugate