Showing papers in "Arabian Journal of Mathematics in 2020"

Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

Abstract: This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

A Dai–Liao conjugate gradient method via modified secant equation for system of nonlinear equations

Abstract: In this paper, we propose a Dai–Liao (DL) conjugate gradient method for solving large-scale system of nonlinear equations. The method incorporates an extended secant equation developed from modified secant equations proposed by Zhang et al. (J Optim Theory Appl 102(1):147–157, 1999) and Wei et al. (Appl Math Comput 175(2):1156–1188, 2006) in the DL approach. It is shown that the proposed scheme satisfies the sufficient descent condition. The global convergence of the method is established under mild conditions, and computational experiments on some benchmark test problems show that the method is efficient and robust.

Forward–backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators

Abstract: In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an $$\alpha $$-inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorithm and prove that the generated sequence converges strongly to a common element of a fixed points set of a nonexpansive mapping and zero points set of the sum of monotone operators. We apply our main result both to equilibrium problems and convex programming.

Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Abstract: In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.

Lie symmetry analysis of some conformable fractional partial differential equations

Abstract: In this article, Lie symmetry analysis is used to investigate invariance properties of some nonlinear fractional partial differential equations with conformable fractional time and space derivatives. The analysis is applied to Korteweg–de Vries, modified Korteweg–de Vries, Burgers, and modified Burgers equations with conformable fractional time and space derivatives. For each equation, all the vector fields and the Lie symmetries are obtained. Moreover, exact solutions are given to these equations in terms of solutions of ordinary differential equations. In particular, it is shown that the fractional Korteweg–de Vries can be reduced to the first Painleve equation and to the fractional second Painleve equation. In addition, a solution of the fractional modified Korteweg–de Vries is given in terms of solutions of the fractional second Painleve equation.

Almost $$*$$∗ -Ricci soliton on paraKenmotsu manifolds

Abstract: We consider almost $$*$$ -Ricci solitons in the context of paracontact geometry, precisely, on a paraKenmotsu manifold. First, we prove that if the metric g of $$\eta $$ -Einstein paraKenmotsu manifold is $$*$$ Ricci soliton, then M is Einstein. Next, we show that if $$\eta $$ -Einstein paraKenmotsu manifold admits a gradient almost $$*$$ -Ricci soliton, then either M is Einstein or the potential vector field collinear with Reeb vector field $$\xi $$ . Finally, for three-dimensional case we show that paraKenmotsu manifold is of constant curvature $$-1$$ . An illustrative example is given to support the obtained results.

Study of a boundary value problem for fractional order $$\psi $$ ψ -Hilfer fractional derivative

Abstract: This manuscript is devoted to the existence theory of a class of random fractional differential equations (RFDEs) involving boundary condition (BCs). Here we take the corresponding derivative of arbitrary order in $$\psi $$ -Hilfer sense. By utilizing classical fixed point theory and nonlinear analysis we establish some basic results of the qualitative theory such as existence, uniqueness and stability of solutions to the considered boundary value problem of RFDEs. Further, for the justification of our analysis we provide two examples.

The $$M^{X}/M/c$$ M X / M / c Bernoulli feedback queue with variant multiple working vacations and impatient customers: performance and economic analysis

Abstract: The present paper deals with an $$M^{X}/M/c$$ Bernoulli feedback queueing system with variant multiple working vacations and impatience timers which depend on the states of the servers. Whenever a customer arrives at the system, he activates an random impatience timer. If his service has not been completed before his impatience timer expires, the customer may abandon the system. Using certain customer retention mechanism, the impatient customer can be retained in the system. After getting incomplete or unsatisfactory service, with some probability, each customer may comeback to the system as a Bernoulli feedback. Using the probability generating functions (PGFs), we derive the steady-state solution of the model. Then, we obtain useful performance measures. Moreover, we carry out an economic analysis. Finally, numerical study is performed to explore the effects of the model parameters on the behavior of the system.

Exponential finite difference methods for solving Newell–Whitehead–Segel equation

Abstract: This work presents two different finite difference methods to compute the numerical solutions for Newell–Whitehead–Segel partial differential equation, which are implicit exponential finite difference method and fully implicit exponential finite difference method. Implicit exponential methods lead to nonlinear systems. Newton method is used to solve the resulting systems. Stability and consistency are discussed. To illustrate the accuracy of the proposed numerical methods, some examples are delivered at the end.

A note on Eneström–Kakeya theorem for a polynomial with quaternionic variable

Abstract: In this paper, we present certain results concerning the location of the zeros of polynomials with quaternionic variable which generalize and refine some known Enestrom–Kakeya type bounds for the zeros of polynomials.

Solving Yosida inclusion problem in Hadamard manifold

Abstract: We consider a Yosida inclusion problem in the setting of Hadamard manifolds We study Korpelevich-type algorithm for computing the approximate solution of Yosida inclusion problem The resolvent and Yosida approximation operator of a monotone vector field and their properties are used to prove that the sequence generated by the proposed algorithm converges to the solution of Yosida inclusion problem An application to our problem and algorithm is presented to solve variational inequalities in Hadamard manifolds

An exploration of quintic Hermite splines to solve Burgers’ equation

Abstract: An innovative scheme of collocation having quintic Hermite splines as base functions has been followed to solve Burgers’ equation. The scheme relies on approximation of Burgers’ equation directly in non-linear form without using Hopf–Cole transformation (Hopf in Commun Pure Appl Math 3:201–216, 1950; Cole in Q Appl Math 9:225–236, 1951). The significance of the numerical technique is demonstrated by comparing the numerical results to the exact solution and published results (Asaithambi in Appl Math Comput 216:2700–2708, 2010; Mittal and Jain in Appl Math Comput 218:7839–7855, 2012). Five problems with different initial conditions have been examined to validate the efficiency and accuracy of the scheme. Euclidean and supremum norms have been reckoned to scrutinize the stability of the numerical scheme. Results have been demonstrated in plane and surface plots to indicate the effectiveness of the scheme.

Nonexistence of $$\mathcal {P}\mathcal {R}$$PR-semi-slant warped product submanifolds in paracosymplectic manifolds

Abstract: In the present paper, we prove that there does not exist any $$\mathcal {P}\mathcal {R}$$-semi-slant warped product submanifolds in paracosymplectic manifolds. In addition, by presenting a non-trivial example we find that there is no proper $$\mathcal {P}\mathcal {R}$$-semi-slant warped product submanifold other than $$\mathcal {P}\mathcal {R}$$-semi-invariant warped products.

On compact and bounded embedding in variable exponent Sobolev spaces and its applications

Abstract: For a weighted variable exponent Sobolev space, the compact and bounded embedding results are proved. For that, new boundedness and compact action properties are established for Hardy’s operator and its conjugate in weighted variable exponent Lebesgue spaces. Furthermore, the obtained results are applied to the existence of positive eigenfunctions for a concrete class of nonlinear ode with nonstandard growth condition.

On dynamic coloring of certain cycle-related graphs

Abstract: Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. A dynamic k-coloring is also called a conditional (k, 2)-coloring. The smallest integer k such that G has a dynamic k-coloring is called the dynamic chromatic number $$\chi _d(G)$$ of G. In this paper, we investigate the dynamic chromatic number for the line graph of sunlet graph and middle graph, total graph and central graph of sunlet graphs, paths and cycles. Also, we find the dynamic chromatic number for Mycielskian of paths and cycles and the join graph of paths and cycles.

Non-static spherically symmetric spacetimes and their conformal Ricci collineations

Abstract: For a perfect fluid matter, we present a study of conformal Ricci collineations (CRCs) of non-static spherically symmetric spacetimes. For non-degenerate Ricci tenor, a vector field generating CRCs is found subject to certain integrability conditions. These conditions are then solved in various cases by imposing certain restrictions on the Ricci tensor components. It is found that non-static spherically symmetric spacetimes admit 5, 6 or 15 CRCs. In the degenerate case, it is concluded that such spacetimes always admit infinite number of CRCs.

Local linear conditional cumulative distribution function with mixing data

Abstract: This paper investigates a conditional cumulative distribution of a scalar response given by a functional random variable with an $$\alpha $$ -mixing stationary sample using a local polynomial technique. The main purpose of this study is to establish asymptotic normality results under selected mixing conditions satisfied by many time-series analysis models in addition to the other appropriate conditions to confirm the planned prospects.

An extension of the Bessel–Wright transform in the class of Boehmians

Abstract: In this paper, we first construct a suitable Boehmian space on which the Bessel–Wright transform can be defined and some desired properties are obtained in the class of Boehmians. Some convergence results are also established.

Some algebraic structures on the generalization general products of monoids and semigroups

Abstract: For arbitrary monoids A and B, in Cevik et al. (Hacet J Math Stat 2019:1–11, 2019), it has been recently defined an extended version of the general product under the name of a higher version of Zappa products for monoids (or generalized general product) $$A^{\oplus B}$$ $$_{\delta }\bowtie _{\psi }B^{\oplus A}$$ and has been introduced an implicit presentation as well as some theories in terms of finite and infinite cases for this product. The goals of this paper are to present some algebraic structures such as regularity, inverse property, Green’s relations over this new generalization, and to investigate some other properties and the product obtained by a left restriction semigroup and a semilattice.

On a function involving generalized complete (p, q)-elliptic integrals

Abstract: Motivated by the work of Alzer and Richards (Anal Math 41:133–139, 2015), here authors study the monotonicity and convexity properties of the function $$\begin{aligned} \Delta _{p,q} (r) = \frac{{E_{p,q}(r) - \left( {r'} \right) ^p K_{p,q}(r) }}{{r^p }} - \frac{{E'_{p,q}(r) - r^p K'_{p,q}(r) }}{{\left( {r'} \right) ^p }}, \end{aligned}$$where $$K_{p,q}$$ and $$E_{p,q}$$ denote the complete (p, q)-elliptic integrals of the first and second kind, respectively.

Approximation by (p,q) Szász-beta–Stancu operators

Abstract: Motivated by recent investigations, in this paper we introduce (p, q)-Szasz-beta–Stancu operators and investigate their local approximation properties in terms of modulus of continuity. We also obtain a weighted approximation and Voronovskaya-type asymptotic formula.

New Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions

Abstract: In this paper, we proved two new Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions using the left and right fractional integrals independently. Also, we have two new Riemann–Liouville fractional trapezoidal type identities for differentiable functions. Using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalize the results given by Iscan (Hacet J Math Stat 46(6):935–942, 2014).

Applications of a version of the de Rham lemma to the existence theory of a weak solution to the Maxwell–Stokes type equation

Abstract: In this paper, we show the existence of a weak solution to the Maxwell–Stokes type equation with a potential satisfying the Dirichlet condition, under the hypothesis that the domain has no holes, using a version of the de Rham lemma that was proved in our previous paper. We also give the regularity of weak solutions.

A closed-form solution to the inverse problem in interpolation by a Bézier-spline curve

Abstract: A geometric construction of a Bezier curve is presented by a unifiable way from the mentioned literature with some modification. A closed-form solution to the inverse problem in cubic Bezier-spline interpolation will be obtained. Calculations in the given examples are performed by a Maple procedure using this solution.

Rings having normality in terms of the Jacobson radical

Abstract: A ring R is defined to be J-normal if for any $$a, r\in R$$ and idempotent $$e\in R$$, $$ae = 0$$ implies $$Rera\subseteq J(R)$$, where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly normal rings and left min-abel rings. It is proved that R is J-normal if and only if for any idempotent $$e\in R$$ and for any $$r\in R$$, $$R(1 - e)re\subseteq J(R)$$ if and only if for any $$n\ge 1$$, the $$n\times n$$ upper triangular matrix ring $$U_{n}(R)$$ is a J-normal ring if and only if the Dorroh extension of R by $${\mathbb {Z}}$$ is J-normal. We show that R is strongly regular if and only if R is J-normal and von Neumann regular. For a J-normal ring R, it is obtained that R is clean if and only if R is exchange. We also investigate J-normality of certain subrings of the ring of $$2\times 2$$ matrices over R.

Menon-type identities concerning additive characters

Abstract: By considering even functions ( $$\hbox {mod}\ n$$ ), we generalize a recent Menon-type identity by Li and Kim, involving additive characters of the group $${\mathbb {Z}}_n$$ . We use a different approach, based on certain convolutional identities. Some other applications, including related formulas for Ramanujan sums, are discussed as well.

Spectrally accurate approximate solutions and convergence analysis of fractional Burgers’ equation

Abstract: In this paper, a new numerical technique implements on the time-space pseudospectral method to approximate the numerical solutions of nonlinear time- and space-fractional coupled Burgers’ equation This technique is based on orthogonal Chebyshev polynomial function and discretizes using Chebyshev–Gauss–Lobbato (CGL) points Caputo–Riemann–Liouville fractional derivative formula is used to illustrate the fractional derivatives matrix at CGL points Using the derivatives matrices, the given problem is reduced to a system of nonlinear algebraic equations These equations can be solved using Newton–Raphson method Two model examples of time- and space-fractional coupled Burgers’ equation are tested for a set of fractional space and time derivative order The figures and tables show the significant features, effectiveness, and good accuracy of the proposed method

Two-valenced association schemes and the Desargues theorem

Abstract: The main goal of the paper is to establish a sufficient condition for a two-valenced association scheme to be schurian and separable. To this end, an analog of the Desargues theorem is introduced for a noncommutative geometry defined by the scheme in question. It turns out that if the geometry has enough many Desarguesian configurations, then under a technical condition, the scheme is schurian and separable. This result enables us to give short proofs for known statements on the schurity and separability of quasi-thin and pseudocyclic schemes. Moreover, by the same technique, we prove a new result: given a prime p, any $$\{1,p\}$$ -scheme with thin residue isomorphic to an elementary abelian p-group of rank greater than two, is schurian and separable.

Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices

Abstract: It is known that if $$A\in \mathscr {L}(\mathscr {X})$$ and $$B\in \mathscr {L}(\mathscr {Y})$$ are Banach operators with the single-valued extension property, SVEP, then the matrix operator $$M_\mathrm{{C}}=\begin{pmatrix} A &{} C \\ 0&{} B \\ \end{pmatrix} $$ has SVEP for every operator $$C\in \mathscr {L}(\mathscr {Y},\mathscr {X}),$$ and hence obeys generalized Browder’s theorem This paper considers conditions on operators A, B, and $$M_0$$ ensuring generalized Weyl’s theorem and property (Bw) for operators $$M_\mathrm{{C}}$$ Moreover, certain conditions are explored on Banach space operators T and S so that $$T\oplus S$$ obeys property (gw)

Penalized Partial Least Square applied to structured data

Abstract: Nowadays, data analysis applied to high dimension has arisen. The edification of high-dimensional data can be achieved by the gathering of different independent data. However, each independent set can introduce its own bias. We can cope with this bias introducing the observation set structure into our model. The goal of this article is to build theoretical background for the dimension reduction method sparse Partial Least Square (sPLS) in the context of data presenting such an observation set structure. The innovation consists in building different sPLS models and linking them through a common-Lasso penalization. This theory could be applied to any field, where observation present this kind of structure and, therefore, improve the sPLS in domains, where it is competitive. Furthermore, it can be extended to the particular case, where variables can be gathered in given a priori groups, where sPLS is defined as a sparse group Partial Least Square.