In this paper, a weakly dissipative viscoelastic plate equation with an infinite memory is considered. We show a general energy decay rate for a wide class of relaxation functions. To support our theoretical findings, some numerical illustrations are presented at the end. The numerical solution is computed using the popular finite element method in space, combined with time-stepping finite differences

This paper is an extension and generalization of some previous works, such as the study of M. Benalili and A. Lansari. Indeed, these authors, in their work about the finite co-dimension ideals of Lie algebras of vector fields, restricted their study to fields \(X_0\) of the form \(X_0=\sum _{i=1}^{n}( \alpha _i \cdot x_i+\beta _i\cdot x_i^{1+m_i}) \frac{\partial }{\partial x_i}\), where \(\alpha _i

In this paper, a finite fractured aquifer, bounded by a stream and impervious layers on the other sides, has been considered. Variation in the level of groundwater is analyzed in confined aquifer for the unsteady flow. The governing differential equation for piezometric head involves the Caputo–Fabrizio fractional derivative operator with respect to time and is based on dual-porosity model with the

In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of \(CAT\left( 0\right) \) spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert

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

For a map \(f:X\rightarrow Y\), there is the relative model \(M(Y)=(\Lambda V,d)\rightarrow (\Lambda V\otimes \Lambda W,D)\simeq M(X)\) by Sullivan model theory (Félix et al., Rational homotopy theory, graduate texts in mathematics, Springer, Berlin, 2007). Let \(\mathrm{Baut}_1X\) be the Dold–Lashof classifying space of orientable fibrations with fiber X (Dold and Lashof, Ill J Math 3:285–305, 1959])

In this paper, we investigate some kind of Dynkin game under g-expectation induced by backward stochastic differential equation (short for BSDE). The lower and upper value functions \(\underline{V}_t=ess\sup \nolimits _{\tau \in {\mathcal {T}_t}} ess\inf \nolimits _{\sigma \in {\mathcal {T}_t}}\mathcal {E}^g_t[R(\tau ,\sigma )]\) and \(\overline{V}_t=ess\inf \nolimits _{\sigma \in {\mathcal {T}_t}}

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

The graph \(G'\) obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor is called a 1-fold of G. A sequence \(G_0, G_1, G_2, \ldots , G_k\) of graphs such that \(G_0=G\) and \(G_i\) is a 1-fold of \(G_{i-1}\) for each \(i=1, 2, \ldots , k\) is called a uniform k-folding of G if the graphs in the sequence are all singular or all nonsingular. The fold

The authors discover a new identity concerning differentiable mappings defined on \(\mathbf{m }\)-invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized-\(\mathbf{m }\)-\(((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))\)-convex mappings by involving an extended generalized Mittag–Leffler function are presented

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

We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the Arnowitt–Deser–Misner (ADM) phase space and the ADM Hamiltonian of general relativity are, what constitutes a dynamical system, and subsequently present a nascent attempt to draw a formal analogy between the notions

Gravitational microlensing is a powerful method to search for and characterize exoplanets, and it was first proposed by Paczyński in 1986. We provide a brief historical excursus of microlensing, especially focused on the discoveries of free-floating planets (FFPs) in the Milky Way. We also emphasize that, thanks to the technological developments, it will allow to estimate the physical parameters (in

The masses and radii of neutron stars are discussed in general relativity and scalar-tensor theory of gravity and the differences are compared with the current uncertainties stemming from the nuclear equation of state in the relativistic mean-field framework. It is shown that astrophysical and gravitational wave observations of radii of neutron stars with masses \(M \lesssim 1.4 M_{\odot }\) constrain

The objective of this paper is to investigate the validity conditions for the generalized second law of thermodynamics, and the universal relations for multi-horizon dynamical spacetime. It is found that there are three horizons of McVittie universe termed as event horizon, cosmological apparent horizon, and virtual horizon. The mass-dependent and mass-independent area product relations are formulated

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

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 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

Zhou et al. and Huang et al. have proposed the modified shift-splitting (MSS) preconditioner and the generalized modified shift-splitting (GMSS) for non-symmetric saddle point problems, respectively. They have used symmetric positive definite and skew-symmetric splitting of the (1, 1)-block in a saddle point problem. In this paper, we use positive definite and skew-symmetric splitting instead and present

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

We have investigated effect of geometric optics as the rotation of polarization vector of light in spacetime of gravitational compact object in the fourth-order theory of conformal Weyl gravity. The Pineault–Roeder method is applied to the rotating Weyl metric, and analytical results are obtained in the limit of weak field and or slow rotation. For the photon traveling parallel to the symmetry axes

Let R a commutative ring with identity and M be a unitary R-module. In this paper, we investigate some properties of n-absorbing submodules of M as a generalization of 2-absorbing submodules. We also define the classical n-absorbing submodule, a proper submodule N of an R-module M is called a classical n-absorbing submodule if whenever \(a_1 a_2\ldots a_{n+1} m\in N\) for \(a_1, a_2,\ldots , a_{n+1}\in

A massive star undergoes a continual gravitational collapse when the pressures inside the collapsing star become insufficient to balance the pull of gravity. The Physics of gravitational collapse of stars is well studied. Using general relativistic techniques, one can show that the final fate of such a catastrophic collapse can be a black hole or a naked singularity, depending on the initial conditions

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.

Let P(z) be a polynomial of degree n which does not vanish in \(|z|<1\). Then it was proved by Hans and Lal (Anal Math 40:105–115, 2014) that$$\begin{aligned} \Bigg |z^s P^{(s)}+\beta \dfrac{n_s}{2^s}P(z)\Bigg |\le \dfrac{n_s}{2}\Bigg (\bigg |1+\dfrac{\beta }{2^s}\bigg |+\bigg | \dfrac{\beta }{2^s}\bigg |\Bigg )\underset{|z|=1}{\max }|P(z)|, \end{aligned}$$for every \(\beta \in \mathbb C\) with \(|\beta

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

We develop a generic spacetime model in general relativity which can be used to build any gravitational model within general relativity. The generic model uses two types of assumptions: (a) geometric assumptions in addition to the inherent geometric identities of the Riemannian geometry of spacetime and (b) assumptions defining a class of observers by means of their four-velocity \(u^{a}\) which is

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

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

The matrix representation of operators in Hilbert spaces is a useful tool in applications. It is important to present the matrix representation by sequences other than orthonormal bases. In this paper, we extend the matrix representation of operators using g-frames and investigate their invertibility and stability.

Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum \(\sum _{i=1}^m \rho _i h(\lambda _i)\) and the integral \(\int ^{b}_{a} \rho (\lambda ) h(\gamma (\lambda ))d\lambda \) where h is an n-convex function.

The rotation of the galactic halos is a fascinating topic which is still waiting to be addressed. Planck data have shown the existence of a temperature asymmetry towards the halo of several nearby galaxies, such as M31, NGC 5128, M33, M81 and M82. However, the cause of this asymmetry is an open problem. A possibility to explain the observed effect relies on the presence of “cold gas clouds” populating

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

Motivated by recent investigations, in this paper we introduce (p, q)-Szász-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.

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

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

Linearization criteria for two-dimensional systems of second-order ordinary differential equations (ODEs) have been derived earlier using complex symmetry analysis. For such systems, the linearizable form, linearization criteria and symmetry group classification are presented. In this paper, we extend the complex approach to obtain a complex-linearizable form of two-dimensional systems of third-order

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

This paper reviews the concept of pp-waves and plane waves in classical general relativity theory. The first four sections give discussions of some algebraic constructions and symmetry concepts which will be needed in what is to follow. The final sections deal with the definitions of such wave solutions, their associated geometrical tensors in space–time and their Killing, homothetic, conformal and

Renormalization scheme of quantum electrodynamics (QED) at high temperatures is used to calculate the effective parameters of relativistic plasma in the early universe. Renormalization constants of QED play the role of effective parameters of the theory and can be used to determine the collective behavior of the medium. We explicitly show that the dielectric constant, magnetic reluctivity, Debye length

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

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.

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 \(r\in R\), \(R(1 - e)re\subseteq J(R)\)

Following Frink’s characterization of completely regular spaces, we say that a regular \(T_1\)-space is an RC-space whenever the family of all regular open sets constitutes a regular normal base. Normal spaces are RC-spaces and there exist completely regular spaces which are not RC-spaces. So the question arises, which of the known examples of completely regular and not normal spaces are RC-spaces

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

The reflexive property for rings was introduced by Mason and play roles in noncommutative ring theory. A ring R is called reflexive if for \(a, b \in R\), \(aRb = 0\) implies \(bRa = 0\). Recently, Kheradmand et al. introduced the notion of RNP (reflexive-nilpotents-property) rings by restricting the reflexive property to nilpotent elements. In this article, we study reflexive-nilpotents-property skewed

Let \(L^2(\mu )\) denote the separable Hilbert space associated with a \(\sigma \)-finite atomic measure \(\mu \). In this paper, we determine necessary and sufficient conditions for boundedness of weighted composition transformation on \(L^2(\mu )\) and give a characterization of antinormal weighted composition operators on \(L^2(\mu )\).

We study the asymptotic properties of the spectral density estimator (a periodogram) of a linear spatial process with alpha mixing innovations. A periodogram is a natural estimate of the spectral density. Under some conditions, a relation between the periodograms of innovations and that of the linear process is established in a spatial case. As the estimator of periodogram is inconsistent, a linear

In this paper, we investigate the \({\mathcal {A}}\)-valued Cauchy–Schwarz inequality and its reverse in a 2-semi inner product \( {\mathcal {A}}\)-module over a locally \(C^*\)-algebra \( {\mathcal {A}}\).

In this article, global asymptotic stability of solutions of non-homogeneous differential-operator equations of the third order is studied. It is proved that every solution of the equations decays exponentially under the Routh–Hurwitz criterion for the third order equations.

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.

In the present paper, we first characterize real hypersurfaces in the complex quadric \(Q^{m}\) by giving an inequality in terms of the scalar curvature and the Mean curvature vector field. We also obtain the condition under which this inequality becomes an equality. Further, we develop two extremal inequalities involving the normalized \(\delta \)-Casorati curvatures and the extrinsic generalized

In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by introducing two different classes of elementary topical functions. Next, we use this pseudo-metric d to investigate the non-expansivity and some properties of topical functions. Finally, the characterizations of fixed points of topical functions are given, and a relation between the pseudo-metric d and the

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

Let \(\nu _{d,n}: \mathbb {P}^n\rightarrow \mathbb {P}^r\), \(r=\left( {\begin{array}{c}n+d\\ n\end{array}}\right) \), be the order d Veronese embedding. For any \(d_n\ge \cdots \ge d_1>0\) let \(\check{\eta }(n,d;d_1,\ldots ,d_n)\subseteq \mathbb {P}^r\) be the union of all linear spans of \(\nu _{d,n}(S)\) where \(S\subset \mathbb {P}^n\) is a finite set which is the complete intersection of hypersurfaces

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

We take a ring \(R = \mathbb F_2+s\mathbb F_2+s^2\mathbb F_2\). We consider a Gray map on this ring, discuss self-dual codes, define various weight enumerators over the ring, and discuss equivalence class of codes over the ring. We construct self-dual codes of Type I and Type II over the given ring for different lengths.

A class of coupled Schrödinger equations is investigated. First, in the stationary case, the existence of ground states is obtained and a sharp Gagliardo–Nirenberg inequality is discussed. Second, in the energy critical radial case, global well-posedness and scattering for small data are proved.

Assuming the source of energy momentum tensor as perfect fluid, a classification of static cylindrically symmetric spacetimes in f(R) theory of gravity by conformal vector fields (CVFs) is presented. For the classification purpose, we put different conditions on metric coefficients to obtain solutions in f(R) theory of gravity. By means of some algebraic and direct integration techniques, it is shown

The class of stretch metrics contains the class of Landsberg metrics and the class of R-quadratic metrics. In this paper, we show that a regular non-Randers type \((\alpha , \beta )\)-metric with vanishing S-curvature is stretchian if and only if it is Berwaldian. Let F be an almost regular non-Randers type \((\alpha , \beta )\)-metric. Suppose that F is not a Berwald metric. Then, we find a family