The ladder graph \(L_n\) is the Cartesian product of a path on n vertices and a complete graph on two vertices. The Wiener index of a digraph is the sum of distances between all ordered pairs of vertices. In Knor et al. (Bounds in chemical graph theory - advances, 2017) the authors conjectured that the maximum Wiener index of a digraph whose underlying graph is \(L_n\) is \((8n^3+3n^2-5n+6)/3\). In

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that

In this paper, we investigate the dynamics of the following higher order difference equation $$\begin{aligned} x_{n+1}=A+B\frac{x_{n}}{x_{n-m}^{2}}, \end{aligned}$$ with A, B and initial conditions are positive numbers, and \(m\in \left\{ 2,3,\cdots \right\} \). Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related

In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The two algorithms are based on the conjugate gradient method. The corresponding search directions were obtained via a modified memoryless symmetric rank-one (SR1) update. Independent of the line search, the two directions were shown to be sufficiently descent and bounded. Moreover, the convergence of the algorithms

We study a higher-order Legendre reproducing kernel method (LRKM) for singular two-point boundary value problems (BVPs). Our method relies upon Legendre polynomials. We carry out error estimatation by using interpolation theory. Various numerical tests including linear and nonlinear problems are performed to reveal the stability and efficiency of the new scheme. Therewith, as an application of the

Here we solve the following system of difference equations $$ x^{(j)}_{n+1}=\frac{F_{m+2}+F_{m+1}x^{((j+1)mod(p))}_{n-k}}{F_{m+3} +F_{m+2}x^{((j+1)mod(p))}_{n-k}},\quad n,m, p, k \in N_0, j=\overline{1,p}, $$ where \(\left( F_{n}\right) _{n=0}^{+\infty }\) is the Fibonacci sequence. We give a representation of its general solution in terms of Fibonacci numbers and the initial values. Some theoretical

Diabetes is a disease which caused by socio-environmental and / or genetic factors. The negative effect of socio-environmental or lifestyle leads a susceptible individual to become a diabetic. On the one hand, social interaction wields a great deal of influence over lifestyle. On the other hand, genetic factors are the main cause of the birth diabetes genetic disorder. Considering these above mentioned

Wu et al. (Applied Mathematics and Computation 217(2011)8343-8353) constructed a gradient based iterative (GI) algorithm to find the solution to the complex conjugate and transpose matrix equation $$\begin{aligned} A_{1}XB_{1}+A_{2}\overline{X}B_{2}+A_{3}X^{T}B_{3}+A_{4}X^{H}B_{4}=E \end{aligned}$$ and a sufficient condition for guaranteeing the convergence of GI algorithm was given for an arbitrary

This paper deals with the concept of hierarchy of algebras and graphs. In the case of algebras, the work constitutes a generalization to any algebra of the concept of hierarchy that Tian gave for a particular type of them, evolution algebras, via concepts of occurrence and persistence. This new hierarchy proves to be invariant under isomorphism of algebras, which leads to a necessary condition for

An in-depth bifurcation analysis is carried out for the peristaltic transport of non-Newtonian fluid with heat and mass transfer through an axisymmetric channel. Based on the perturbation technique, analytical solutions for flow rate and stream function are presented. This function and its velocity fields build a nonlinear dynamic system in two spatial dimensions. We are then interested in identifying

Existence and uniqueness results are established for the general nonlinear fourth-order two-point boundary value problem with general linear homogeneous boundary conditions. The proofs are based on the Banach fixed-point theorem under the conditions that the nonlinear term is bounded and Lipschitz in a specific region. A fixed-point iterative method for finding the solution of the problem is also proposed

Oscillatory behavior of a hyperbolic delay partial dynamic equation with time and spatial variables defined on arbitrary time scales is studied in this article. The Green’s identity on an arbitrary time scale is presented. Using that identity and Riccati transformation, several oscillation criteria for the concern dynamic equation with Neumann boundary condition is established. Examples are provided

Neutrosophic soft sets are a mathematical model put forward to overcome uncertainty with the contribution of a parameterization tool and neutrosophic logic by considering of information a falsity membership function, an indeterminacy membership function and a truth membership function. This set theory which is a very successful mathematical model, especially as it handles information in three different

Computing topological indices of molecular structures is a fundamental and classical topic. In organic chemistry, hexagonal and quadrilateral molecular structures are very common. The detour index \(\omega (G)\) of a connected graph G is defined as \(\omega (G)=\sum \nolimits _{\{u,v\}\subseteq V(G)}l_{G}(u,v)\), where \(l_{G}(u,v)\) denotes the detour distance between vertices u and v. In this study

The connective eccentricity index (CEI) of a connected graph G is defined as \(\xi ^{ee}(G)=\sum _{u\in V_G}[d_G(u)/\varepsilon _G(u)]\), where \(d_G(u)\) and \(\varepsilon _G(u)\) are the degree and eccentricity, respectively, of the vertex \(u\in V_G\) of G. In this paper, graphs with the maximum CEI are characterized from the class of all connected graphs of a fixed order and size. Graphs having

In this paper, a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten type prey harvesting is investigated. It is shown that the model exhibits several bifurcations of codimension 1 viz. Neimark–Sacker bifurcation, transcritical bifurcation and flip bifurcation on varying one parameter. Bifurcation theory and center manifold theory are used to establish the conditions for the existence

In this paper, we study a pseudo-parabolic equation with the Caputo fractional derivative. By applying the properties of Mittag–Leffler functions and the method of eigenvalue expansion, under a suitable definition of mild solution of our problem, we obtain the existence result and \(L^p\) regularity of the mild solution by using some Sobolev embeddings. Finally, we also give some examples to illustrate

Our contribution is the development of novel representations and investigations of main properties of the MPCEP inverse. Precisely, we present representations of the MPCEP inverse which involve appropriate Moore–Penrose inverses, projections and full-rank decompositions, as well as limit and integral representations. Determinantal representations for the MPCEP inverse are also established. We study

In this work, a class of bilateral free boundary problem is considered. This identification problem is formulated as a shape optimization problem via the definition of a cost functional. The existence of an optimal solution for the optimization problem is proved. An augmented Lagrangian approach is used to facilitate the computation of the shape derivatives. A numerical approach is proposed to solve

In this work, we study the average Steiner 3-eccentricity on block graphs with a fixed block order sequence. Two graph transformations are present on block graphs. Relying on the transformations, we establish both the lower bound and the upper bound for the average Steiner 3-eccentricity on block graphs with a fixed block order sequence. Finally, we devise an \(O(n^{2})\) algorithm to calculate the

This paper investigates the dynamics of the stochastic predator–prey model with a Crowley–Martin functional response function driven by Lévy noise. First, the existence, uniqueness and boundedness of a global positive solution is proven. Next, the persfor an optimal conditions. Finally, the theoretical results are reinforced by some numerical simulations. We illustrated the sufficient conditions to

Let Q(G), \({{\mathcal {D}}(G)}\) and \({{\mathcal {D}}}^Q(G)={{\mathcal {D}}iag(Tr)} + {{\mathcal {D}}(G)}\) be, respectively, the signless Laplacian matrix, the distance matrix and the distance signless Laplacian matrix of graph G, where \({{\mathcal {D}}iag(Tr)}\) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of Q(G) and \({{\mathcal {D}}}^Q(G)\) will be denoted by

The present study aims to introduce new methods to achieve optimal matching in fuzzy graphs and classify the fuzzy sizes of the edges and vertices of a matching called “matching number”. Matching numbers in a fuzzy graph are not only a direct tool in improving existing matching optimization algorithms, but also can be used to build optimization algorithms based on the vertices of a matching. Thus,

Let p be a prime such that \(p^m \equiv 1\pmod {4}\), and \(\mathcal{R}=\mathbb F_{p^m}+u\mathbb F_{p^m}\). For any non-square unit \(\lambda \) of \(\mathcal{R}\), the Hamming and b-symbol distances of all \(\lambda \)-constacyclic codes of length \(4p^s\) over \(\mathcal{R}\) are completely determined. As examples, several good codes with new parameters are constructed. We also identified all Maximum

We construct a class of \({\mathbb {Z}}_p{\mathbb {Z}}_p[v]\)-additive cyclic codes, where p is a prime number and \(v^2=v\). We determine the asymptotic properties of the relative minimum distance and rate of this class of codes. We prove that, for any positive real number \(0<\delta <1\) such that the p-ary entropy at \(\frac{k+l}{2}\delta \) is less than \(\frac{1}{2}\), the relative minimum distance

This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified L1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete

Linear barycentric rational interpolants, instead of customary polynomial interpolants, have been recently used to design the efficient numerical integrators for ODEs. In this way, the BDF-type methods based on these interpolants have been introduced as a general class of the methods in this type with better accuracy and stability properties. In this paper, we introduce an extension of them equipped

Given a graph G and an integer \(k\ge 2\). A spanning subgraph F of a graph G is said to be a \(P_{\ge k}\)-factor of G if each component of F is a path of order at least k. A graph G is called a \(P_{\ge k}\)-factor uniform graph if for any two distinct edges \(e_{1}\) and \(e_{2}\) of G, G admits a \(P_{\ge k}\)-factor including \(e_{1}\) and excluding \(e_{2}\). More recently, Zhou and Sun (Discret

A signed Italian dominating function on a graph \(G=(V,E)\) is a function \(f: V\rightarrow \{-1, 1, 2\}\) satisfying the condition that for every vertex u, \(f[u]\ge 1\). The weight of the signed Italian dominating function, f, is the value \(f(V)=\sum _{u\in V}f(u)\). The signed Italian dominating number of a graph G, denoted by \(\gamma _{sI}(G)\), is the minimum weight of a signed Italian dominating

Human mobility has been significantly influencing public health since time immemorial. A susceptible-infected-deceased epidemic reaction diffusion network model using asymptotic transmission rate is proposed to portray the spatial spread of the epidemic among two cities due to population dispersion. Qualitative behaviour including global attractor and persistence property are obtained. We also study

This paper investigates the high-order efficient numerical method with the corresponding stability and convergence analysis for the generalized fractional Oldroyd-B fluid model. Firstly, a high-order compact finite difference scheme is derived with accuracy \(O\left( \tau ^{\min {\{3-\gamma ,2-\alpha }\}}+h^{4}\right) \), where \(\gamma \in (1,2)\) and \(\alpha \in (0,1)\) are the orders of the time

Let \(G=(V,E)\) be a graph without isolated vertices. A set \(D\subseteq V\) is said to be a dominating set of G if for every vertex \(v\in V\setminus D\), there exists a vertex \(u\in D\) such that \(uv\in E\). A set \(D\subseteq V\) is called a semitotal dominating set of G if D is a dominating set and every vertex in D is within distance 2 from another vertex of D. For a given graph G, the semitotal

Topological indices are widely used for characterizing molecular graphs, establishing relationships between structure and properties of molecules. In this article we discuss adjacency matrix and three topological indices: Wiener index, Laplacian energy and Zagreb indices of zero-divisor graphs of \(\mathbb {Z}_n\). We also provide a MATLAB code for Laplacian energy and Zagreb indices of \(\varGamma

In this paper, a new iterative algorithm of a Halpern-type is constructed. The sequence generated by the algorithm is proved to converge strongly to a common solution of two generalized equilibrium problems and a common J-fixed point of two continuous J-pseudo-contractive maps in a uniformly smooth and uniformly convex real Banach space. Furthermore, a numerical example is given to illustrate the implementability

This paper is concerned with the dynamical behaviors of a model of syphilis transmission disturbed by both white noises and telegraph noises. Multiple infections and treatment stages are considered, which include and extend the existing ones. The existence and ergodicity of the stationary distribution are obtained by constructing a suitable Lyapunov function, which determines a critical value \(R_0^*\)

We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional diffusion equations. Those linear systems are Toeplitz-like. By making use of diagonal-plus-Toeplitz splitting iteration technique, a sine-transform-based splitting preconditioner is proposed

The aim of this work is to study global dynamics of target-mediated drug disposition (TMDD) models and their solutions by nonstandard finite difference (NSFD) schemes. Firstly, we use comparison principles and the Lyapunov stability theory for ODEs to establish positivity, boundedness, local and global asymptotic stability of the TMDD models. Secondly, positivity-preserving NSFD schemes are proposed

In the spread of infectious diseases, media reports have played a positive role. However, in the process of game communication, there are not only positive but also negative media reports. Therefore, in this paper, we establish a model with positive and negative media reports to analyze the role of media reports in the process of game communication. First, we study its positivity and boundedness, and

A new \(C^0\) nonconforming quasi three degree element with 13 freedoms is introduced to solve biharmonic problem. The given finite element space consists of piecewise polynomial space \(P_3\) and some bubble functions. Different from non-\(C^0\) nonconforming scheme, a smoother discrete solution can be obtained by this method. Compared with the existed 16 freedoms finite element method, this scheme

In this paper, two linearized schemes for time fractional nonlinear wave equations (TFNWEs) with the space fourth-order derivative are proposed and analyzed. To reduce the smoothness requirement in time, the considered TFNWEs are equivalently transformed into their partial integro-differential forms by the Riemann–Liouville integral. Then, the first scheme is constructed by using piecewise rectangular

In this paper, we consider the numerical solutions of two generalized nonlinear matrix equations. Newton’s method is applied to compute one of the generalized nonlinear matrix equations and a generalized Stein equation is obtained, then we adapt the generalized Smith method to find the maximal Hermitian positive definite solution. Furthermore, we consider the properties of the solution for the generalized

This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane–Emden type. Also, convergence analysis and error analysis with an upper bound of the absolute error for the proposed method are discussed. The proposed method is capable to remove the singular behaviour of the problems

In this study, we prove some convergence results for generalized \(\alpha \)-Reich–Suzuki non-expansive mappings via a fast iterative scheme. We validate our result by constructing a numerical example. Also, we compare our results with the other well known iterative schemes. Finally, we calculate the approximate solution of nonlinear fractional differential equation.

Given a commutative ring R with identity, a matrix \(A\in M_{s\times l}(R)\), and linear codes \(\mathcal {C}_1, \dots , \mathcal {C}_s\) over R of the same length, this article considers the hull of the matrix-product code \([\mathcal {C}_1 \dots \mathcal {C}_s]\,A\). Consequently, it introduces various sufficient conditions (as well as some necessary conditions in certain cases) under which \([\mathcal

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the system exponentially converges to zero when the time tends to infinity provided that the time-delay is small and the damping term satisfies reasonable conditions. Lastly

This article presents a study of Leslie–Gower predator–prey system to investigate the dynamics of disease transmission among predator species. The system includes the harvesting of infected predator. The positivity, boundedness of the solutions and permanence of the system are taken into consideration. The stability and Hopf bifurcation analyses around biologically feasible equilibria are scrutinized

For large-scale non-autonomous Stratonovich stochastic differential equations, we study a very general parallel waveform relaxation process which is on the basis of stochastic Runge–Kutta (SRK) method of mean-square order 1.0 in this literature. The convergence of the whole parallel numerical iterative scheme can be guaranteed and the scheme provides better properties in terms of decreasing the load

In this paper, we study the global asymptotic stability of following system of difference equations with quadratic terms: \(x_{n+1}=A+B\frac{y_{n}}{y_{n-1}^{2}}\), \(y_{n+1}=A+B\frac{x_{n}}{x_{n-1}^{2}}\) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

In this study, we have investigated local and global dynamics of a modified Leslie–Gower predator–prey model with Monod–Haldane functional response, where prey is subjected to quadratic harvesting. It is found that the solutions of the proposed system are positive and bounded uniformly. The feasible equilibrium points are also obtained for some suitable and predefined conditions. It is observed that

The fractional-order Bagley–Torvik equation has many applications in the field of life science and engineering. In this paper, we develop a new scheme based on the existing finite element method for the numerical solution of the Bagley–Torvik equation of order (0, 2). We adopt the formulation of the equation in a simple and generalized way. The existence and uniqueness of the solution and its error

The widespread problem of water pollution due to enhanced concentration of anthropogenic effluents is becoming a global issue. Public environmental awareness may be a plausible factor for the control of toxicants in the aquatic medium. The present paper is devoted to study the impact of awareness among human on reduction of environmental toxins affecting planktonic system. The provision of awareness

A compact quadratic spline collocation (QSC) method for the time-fractional Black–Scholes model governing European option pricing is presented. Firstly, after eliminating the convection term by an exponential transformation, the time-fractional Black–Scholes equation is transformed to a time-fractional sub-diffusion equation. Then applying \(L1 - 2\) formula for the Caputo time-fractional derivative

In a graph \(G=(V,E)\), a vertex \(v\in V\) is said to ve-dominate the edges incident on v as well as the edges adjacent to these incident edges on v. A set \(D\subseteq V\) is called a double vertex-edge dominating set if every edge of the graph is ve-dominated by at least two vertices of D. Given a graph G, the double vertex-edge dominating problem, namely Min-DVEDS is to find a minimum double vertex-edge

We discuss the superconvergence analysis of the Galerkin finite element method for the singularly perturbed coupled system of both reaction–diffusion and convection–diffusion types. The superconvergence study is carried out by using linear finite element, and it is shown to be second-order (up to a logarithmic factor) uniformly convergent in the suitable discrete energy norm. We have conducted some

Boreal forest in Canada has two main recurrent disturbances: one is fire and the other one is spruce budworm. The defoliation by spruce budworm, Choristoneura fumiferana (Clem.) (Lepidoptera: Tortricidae) was first started in British Columbia of Canada in 1957 near Liard River. Budworm outbreaks were observed in the 1960’s to 1970’s and from the mid 1980’s to the present. Spruce budworm disturbance

A limited memory q-BFGS (Broyden–Fletcher–Goldfarb–Shanno) method is presented for solving unconstrained optimization problems. It is derived from a modified BFGS-type update using q-derivative (quantum derivative). The use of Jackson’s derivative is an effective mechanism for escaping from local minima. The q-gradient method is complemented to generate the parameter q for computing the step length

In the present paper, a new fixed point iterative method is introduced based on Green’s function and it’s successfully applied to approximate the solution of boundary value problems. A strong convergence result is proved for the integral operator by using the proposed method. It is also showed that the newly defined iterative method has a better rate of convergence than the Picard–Green’s, Mann–Green’s

In this paper, we discuss the numerical solution of a class of linear integral equations of the second kind over an infinite interval. The method of solution is based on the reduction of the problem to a finite interval by means of a suitable family of mappings so that the resulting singular equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. Several selected numerical

In this paper, we study \((1+2^{s-1}u)\)-constacyclic codes and a class of skew \((1+2^{s-1}u)\)-constacyclic codes of odd length over the ring \(R= {\mathbb {Z}}_{2^s}+u{\mathbb {Z}}_{2^s}\), \(u^2=0\), where \(s \ge 3\) is an odd integer. We have obtained the algebraic structure of \((1+2^{s-1}u)\)-constacyclic codes over R. Three new Gray maps from R to \({\mathbb {Z}}_2+u{\mathbb {Z}}_2\) have

Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called