The motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions

In this work, using the weighted symmetric functions \(\sigma _{k}^{\infty }\) and the weighted Newton transformations \(T_{k}^{\infty }\) introduced by Case (Alias et al. Proc Edinb Math Soc 46(02):465–488, 2003), we derive some generalized integral formulae for close hypersurfaces in weighted manifolds. We also give some examples and applications of these formulae.

In this paper, we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations $$\begin{aligned} A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} 0, \\ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} F, \end{aligned}$$ where \(A_{k}\left( z\right) ,\ldots ,A_{0}\left( z\right) ,\) \(F\left( z\right) \) are meromorphic

We consider the irreducible representations each of dimension 2 of the necklace braid group \({\mathcal {N}}{\mathcal {B}}_n\) (\(n=2,3,4\)). We then consider the tensor product of the representations of \({\mathcal {N}}{\mathcal {B}}_n\) (\(n=2,3,4\)) and determine necessary and sufficient condition under which the constructed representations are irreducible. Finally, we determine conditions under

A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number of the form \(a(10^m-1)/9\), for some \(m\ge 1\) and \(1 \le a \le 9\). Let \(\left( P_n\right) _{n\ge 0}\) and \(\left( E_n\right) _{n\ge 0}\) be the sequence of Padovan and Perrin numbers, respectively. This paper deals with repdigits that can be written as the products of consecutive Padovan

Let R be a ring and let M be an R-module with \(S={\text {End}}_R(M)\). The module M is called quasi-dual Baer if for every fully invariant submodule N of M, \(\{\phi \in S \mid Im\phi \subseteq N\} = eS\) for some idempotent e in S. We show that M is quasi-dual Baer if and only if \(\sum _{\varphi \in \mathfrak {I}} \varphi (M)\) is a direct summand of M for every left ideal \(\mathfrak {I}\) of S

We shall consider measure algebras associated to locally compact groups, bounded operators between them and properties of the underlying measures. We take into account the second dual of measure algebras provided with the Arens products together with tools of Gélfand theory.

In this paper, we study the optimization problem (P) of minimizing a convex function over a constraint set with nonconvex constraint functions. We do this by given new characterizations of Robinson’s constraint qualification, which reduces to the combination of generalized Slater’s condition and generalized sharpened nondegeneracy condition for nonconvex programming problems with nearly convex feasible

Let D be an integrally closed domain, \(\{V_{\alpha }\}\) be the set of t-linked valuation overrings of D, and \(v_c\) be the star operation on D defined by \(I^{v_c} = \bigcap _{\alpha } IV_{\alpha }\) for all nonzero fractional ideals I of D. In this paper, among other things, we prove that D is a \(v_c\)-Noetherian domain if and only if D is a Krull domain, if and only if \(v_c = v\) and every prime

We study the following wave equation \(u_{tt}-\Delta u+\alpha (t)\left| u_{t}\right| ^{m(\cdot )-2}u_{t}=0\) with a nonlinear damping having a variable exponent m(x) and a time-dependent coefficient \(\alpha (t)\). We use the multiplier method to establish energy decay results depending on both m and \(\alpha \). We also give four numerical tests to illustrate our theoretical results using the conservative

This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the

In this paper, the Rayleigh beam system with two dynamical boundary controls is treated. Theoretically, the well-posedness of the weak solution is obtained. Later, we discretize the system by using the Implicit Euler scheme in time and the \(P^3\) Hermite finite element in space. In addition, we show the decay of the discrete energy and we establish some a priori error estimates. Finally, some numerical

In this paper, we aim to study the asymptotic behavior (when \(\varepsilon \;\rightarrow \; 0\)) of the solution of a quasilinear problem of the form \(-\mathrm{{div}}\;(A^{\varepsilon }(\cdot ,u^{\varepsilon }) \nabla u^{\varepsilon })=f\) given in a perforated domain \(\Omega \backslash T_{\varepsilon }\) with a Neumann boundary condition on the holes \(T_{\varepsilon }\) and a Dirichlet boundary

A t-frugal colouring of a graph G is an assignment of colours to the vertices of G, such that each colour appears at most t times in the neighbourhood of any vertex. A dichotomy theorem for the complexity of deciding whether a graph has a 1-frugal colouring with k colours was found by McCormick and Thomas, and then later extended to restricted graph classes by Kratochvil and Siggers. We generalize

In this paper, we investigate any non-invariant submanifold of a locally decomposable golden Riemannian manifold in the case that the rank of the set of tangent vector fields of the induced structure on the submanifold by the golden structure of the ambient manifold is less than or equal to the codimension of the submanifold.

In this paper, we describe the explicit structures of nonabelian tensor squares of nonabelian groups of order \(p^3q\), where p and q are distinct prime numbers and \(p>2\). Our method is based on determining the structures of their Schur multipliers by applying some well-known results and the presentations of groups, which leads us to obtain the orders of their nonabelian tensor squares.

Due to their practical applications, hulls of linear codes have been of interest and extensively studied. In this paper, we focus on constructions and bounds on quaternary linear codes with Hermitian hull dimension one. Optimal \([n,2]_4\) codes with Hermitian hull dimension one are constructed for all lengths \(n\ge 3\), such that \(n \equiv 1,2,4 \ (\mathrm{mod}\ 5)\). For positive integers \(n \equiv

The purpose of this paper to establish the semilocal convergence analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the \(\omega \) condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the

In this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. At the end, we use some numerical approximations based on finite difference techniques to validate the theoretical results.

In this paper, we consider a version of energy minimisation technique applied to images of a 2D fluid flow. The two Navier–Stokes equations describe the static flow of a 2D fluid in terms of velocity field, (u, v), pressure field, p and forcing field, f. Apart from these two Navier–Stokes equations, we have the incompressibility condition to evaluate the three parameters. While implementing this system

We establish sufficient conditions for 3-prime near-rings to be commutative rings. In particular, for a 3-prime near-ring R with a derivation d, we investigate conditions such as \(d([U,V])\subseteq Z(R)\), \(d(U)\subseteq Z(R)\), \(x_{o}d(R)\subseteq Z(R)\), and \(Ux_{o}\subseteq Z(R)\). As a by-product, we generalize and extend known results related to rings and near-rings. Furthermore, we discuss

In this work, we are concerned with a class of fractional equations of Kirchhoff type with potential. Using variational methods and a variant of quantitative deformation lemma, we prove the existence of a least energy sign-changing solution. Moreover, the existence of infinitely many solution is established.

Let M be a module over a commutative ring R. In this paper, we continue our study about the Zariski topology-graph \(G(\tau _T)\) which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of \(\mathrm{Spec}(M)\), we obtain useful characterizations for those modules M for which \(G(\tau _T)\) is a bipartite graph. Also, we prove that if \(G(\tau _T)\)

We prove the following: Let G and \(G'\) be two graphs on the same set V of v vertices, and let k be an integer, \(4\le k\le v-4\). If for all k-element subsets K of V, the induced subgraphs \(G_{\restriction K}\) and \(G'_{\restriction K}\) have the same numbers of 3-homogeneous subsets, the same numbers of \(P_4\)’s, and the same numbers of claws or co-claws, then \(G'\) is equal to G or to the complement

We consider ring extensions, whose set of all subextensions is stable under the formation of sums, the so-called \(\Delta \)-extensions. An integrally closed extension has the \(\Delta \)-property if and only it is a Prüfer extension. We then give characterizations of FCP \(\Delta \)-extensions, using the fact that for FCP extensions, it is enough to consider integral FCP extensions. We are able to

We construct a new series of \(n^2\)-dimensional axial algebras of Monster type \((2\eta ,\eta )\). They arise as subalgebras A of the Matsuo algebras \(M_\eta (^-O_{n+1}^+(3))\), generated by single and double axes. Also, we address the question of when these algebras are simple. While we do not solve this question, we formulate three concrete conjectures based on the calculation, using the computer

Let C be a nonempty closed convex subset of a real Hilbert space H and \(T: C\rightarrow CB(H)\) be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly

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 study the existence and uniqueness of solutions for fractional differential equations with nonlocal and fractional integral boundary conditions. New existence and uniqueness results are established using the Banach contraction principle. Other existence results are obtained using O’Regan fixed point theorem and Burton and Kirk fixed point. In addition, an example is given to demonstrate

The exponential timestepping Euler algorithm with a boundary test is adapted to simulate an expected of a function of exit time, such as the expected payoff of barrier options under the constant elasticity of variance (CEV) model. However, this method suffers from a high Monte Carlo (MC) statistical error due to its exponentially large exit times with unbounded samples. To reduce this kind of error

In this article, we define the bicomplex weighted Bergman spaces on the bidisk and their associated weighted Bergman projections, where the respective Bergman kernels are determined. We study also the bicomplex Bergman projection onto the bicomplex Bloch space.

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 notion of statistical convergence is more general than the classical convergence. Tauberian theorems via different ordinary summability means have been established by many researchers. In the present work, we have established some new Tauberian theorems based on post-quantum calculus via statistical Cesàro summability mean of real-valued continuous function of one variable under oscillating behavior

In this paper, we study nonparametric local linear estimation of the conditional density of a randomly censored scalar response variable given a functional random covariate. We establish under general conditions the pointwise almost sure convergence with rates of this estimator under \(\alpha \)-mixing dependence. Finally, to show interests of our results, on the practical point of view, we have conducted

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

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}}

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

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

We give an a-priori estimate near the boundary for solutions of a class of higher order degenerate elliptic problems in the general Besov-type spaces \(B^{s,\tau }_{p,q}\). This paper extends the results found in Hölder spaces \(C^s\), Sobolev spaces \(H^s\) and Besov spaces \(B^s_{p,q}\), to the more general framework of Besov-type spaces.

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

In this work, some new functional of Jensen-type inequalities are constructed using Shannon entropy, f-divergence, and Rényi divergence, and some estimates are obtained for these new functionals. Also using the Zipf–Mandelbrot law and hybrid Zipf–Mandelbrot law, we investigate some bounds for these new functionals. Furthermore, we generalize these new functionals for m-convex function using Lidstone

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

The problem of classification of \((P\hbox { and }Q)\)-polynomial association schemes, as a finite analogue of E. Cartan’s classification of compact symmetric spaces, was posed in the monograph “Association schemes” by E. Bannai and T. Ito in the early 1980s. In this expository paper, we report on some recent results towards its solution.

The aim of this paper is to explore some sufficient conditions for Aluthge transform of Toeplitz operators on the Bergman space to be unitary, average of unitaries and normal.

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

The Star graph \(S_n\), \(n\geqslant 2\), is the Cayley graph over the symmetric group \(\mathrm {Sym}_n\) generated by transpositions \((1~i),\,2\leqslant i \leqslant n\). This set of transpositions plays an important role in the representation theory of the symmetric group. The spectrum of \(S_n\) contains all integers from \(-(n-1)\) to \(n-1\), and also zero for \(n\geqslant 4\). In this paper

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

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

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