The elliptic integrals are of interest in various disciplines. While series solutions do exist for complete elliptic integrals, there are no deduced series solutions for Incomplete elliptic integrals, in terms of the special functions. This paper provides novel solutions of the Legendre forms of incomplete elliptic integrals of the first and second kinds in terms of the Euler’s gamma functions. The

In this note, we consider a hyperbolic system of equations in a domain made up of two components. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. We apply a control on the external boundary and, by means of

The Kuramoto–Sinelshchikov–Cahn–Hilliard equation models the spinodal decomposition of phase separating systems in an external field, the spatiotemporal evolution of the morphology of steps on crystal surfaces and the growth of thermodynamically unstable crystal surfaces with strongly anisotropic surface tension. In this paper, we prove the well-posedness of the Cauchy problem, associated with this

Leverages of magnetic cross-field, thermal radiation, second order chemical reaction on the unsteady three dimensional flow of electrically conducting Cu–Al\(_{2}\)O\(_{3}\)/water hybrid nanofluid flow past a bidirectionally stretchable melting surface are investigated in the present scrutiny. A comparative inspection of Cu–Al\(_{2}\)O\(_{3}\)/water hybrid nanofluid and Al\(_{2}\)O\(_{3}\)/water nanofluid

By applying Mountain Pass Lemma, Ekeland’s variational principle and Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\text {div}\left( a(x)\left| \nabla u\right| ^{p(x)-2}\nabla u\right) =\lambda b(x)\left| u\right| ^{q(x)-2}u, &{} x\in \varOmega \\ a(x)\left| \nabla u\right| ^{p(x)-2}\frac{\partial

In this paper, we initiate the study of impact of the existence of a unit vector \(\nu \), called a concurrent-recurrent vector field, on the geometry of a Riemannian manifold. Some examples of these vector fields are provided on Riemannian manifolds, and basic geometric properties of these vector fields are derived. Next, we characterize Ricci solitons on 3-dimensional Riemannian manifolds and gradient

In this paper, we introduce a new algorithm of multi-step inertial form for approximating a common solution of Split Generalized Mixed Equilibrium Problem (SGMEP) and Minimization Problem (MP) in real Hilbert spaces. Motivated by the multi-step inertial technique, we incorporate the multi-step inertial term to accelerate the convergence of the proposed method. Under standard and mild assumption of

The paper is devoted to prove the existence of solutions of a nonlinear integral equation in a WC-Banach algebra. Making use of the measure of weak noncompactness and the weak topology, we prove some fixed point theorems for operators not necessarily weakly sequentially continuous acting in WC-Banach algebra involving weakly compact operators.

In this article, we define the notions of strongly I-deferred Cesàro summable and \(\mu \)-deferred I-statistical convergence for real sequences and also introduce their corresponding sequence spaces \(DC_{_{(p,q)}}^{I}\) and \(_\mu DS_{_{(p,q)}}^{I},\) respectively. Additionally, some properties, based results and relations among numerous spaces have been established under a few restrictions.

In this research work, we consider the second-order viscoelastic equation with a weak internal damping, a time-varying delay term and nonlinear weights $$\begin{aligned} u_{tt}(t) + {\mathcal {A}} u(t) - \int _0^t g (t-s) {\mathcal {A}} u(s) ds + \mu _1 (t) u_t (t)+ \mu _2(t) u_t(t-\tau (t)) =0 \forall t>0 , \end{aligned}$$ together with suitable initial conditions. We first prove the existence of

We improve the boundedness of maximal function on the spaces defined by Choquet integrals associated to both Bessel and Riesz capacities. The capacities will be generalized to functionals as a means of proof.

We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Struct. 38 (26-27): 4585-4608 ’01). Depending on how different characteristic

In this work we are interested in the periodic solutions of the singular problem involving variable exponent with a homogeneous Dirichlet boundary conditions modeled as $$\begin{aligned} {\partial _t u}-\varDelta u =\displaystyle \frac{f}{u^{\gamma (t,x)}}\text { in }]0,T[\times \varOmega \end{aligned}$$ Where \(\varOmega \) is an open regular bounded subset of \({\mathbb {R}}^{N}\), \(T>0\) is the

According to Li and Zhao (Ukr Math J 64:102–109, 2012), a subgroup H of a finite group G is said to be \(S\Phi \)-supplemented in G if there exists a subnormal subgroup T of G such that \(G=HT\) and \(H\cap T\le \Phi (H)\), where \(\Phi (H)\) is the Frattini subgroup of H. In this paper, we extend the concept of \(S\Phi \)-supplemented subgroups, and give some criteria for (p-)hypercyclically embeddability

In this article we introduce the notion of relative uniform convergence of difference double sequence of positive linear functions. We define the difference double sequence spaces \(_2\ell _\infty (\varDelta , ru),~ _2c(\varDelta , ru),~ _2c_0(\varDelta , ru), _2{c_0}^B(\varDelta , ru),~_2c^B(\varDelta , ru), _2c^R(\varDelta , ru), ~_2{c_0}^R(\varDelta , ru)\) and study their topological properties

We use an approximation method to prove the existence of nontrivial weak solutions for two nonlocal inhomogeneous elliptic problems in a bounded domain \(\Omega \) of \({\mathbb {R}}^n \, (n\ge 1)\) under weak conditions on the diffusion coefficients M, \(N: (0,+\infty )\rightarrow {\mathbb {R}}\) and some hypotheses on the \(n\times n\) matrix function a and the functions f, \(g: \Omega \times {\mathbb

A group G is an N-barely transitive group (NBT-group) if G acts on an infinite set transitively and faithfully and all proper normal subgroups of G have finite orbits. We investigate the main properties and structure of NBT-groups. We give some examples in non-perfect and perfect case. Also we show that there does not exist a locally soluble perfect cofinitary NBT-group.

In the present paper we prove that every local and 2-local derivation of the complex finite dimensional simple Filippov algebra is a derivation. As a corollary we have the description of all local and 2-local derivations of complex finite dimensional semisimple Filippov algebras. All local derivations of the ternary Malcev algebra \(M_8\) are described. It is the first example of a finite-dimensional

In this paper a second order elliptic equation with nonsmooth coefficients is considered in grand-Sobolev classes \(W_{q)}^{2} \left( \varOmega \right) \) on a bounded n-dimensional domain \(\varOmega \subset R^{n} \) with a sufficiently smooth boundary \(\partial \varOmega \), generated by the norm of the grand-Lebesgue space \(L_{q)}\left( \varOmega \right) \). These spaces are non-separable and

In this paper we characterize, in terms of their conjugacy classes, linear groups G such that \(G/\zeta _k(G)\) belongs to a certain group class \(\mathfrak {X}\) for several natural choices of \(\mathfrak {X}\). Moreover, a description is given of linear groups with restrictions on layers.

The Shannon’s entropy function has a complementary dual function namely extropy and it facilitates the comparison of uncertainties of two random variables (see Lad et al. Stat Sci 30:40–58, 2015). Following the work of Lad et al. (Stat Sci 30:40–58, 2015), various generalizations/extensions of extropy measure are discussed in the literature analogous to that of Shannon’s entropy. Accordingly, a negative

In this paper, we study the boundedness and compactness of the Volterra integral operators from Dirichlet type spaces \({\mathcal {D}}^p_{p-2+s}\) into Hardy spaces \({\mathcal {H}}^q\) when \(1

We describe all central extensions of all 3-dimensional nontrivial complex Zinbiel algebras. As a corollary, we have a full classification of 4-dimensional nontrivial complex Zinbiel algebras and a full classification of 5-dimensional nontrivial complex Zinbiel algebras with 2-dimensional annihilator, which gives the principal step in the algebraic classification of 5-dimensional Zinbiel algebras.

We investigate the longitudinal and transversal vibrations of the viscoelastic beam with nonlinear tension and nonlinear delay term under the general decay rate for relaxation function. The existence theorem is proved by the Faedo–Galerkin method and using suitable Lyapunov functional to establish the general decay result.

In this article, we deal with the existence result for nonlinear parabolic equations of the form $$\begin{aligned} \frac{\partial u}{\partial t}-{\text {div}}\>\mathcal {A}(x,t,u,\nabla u)-\hbox {div}\Phi (x,t,u)= f \quad \text {in }{\Omega _T=\Omega \times (0,T)}, \end{aligned}$$ with initial datum and source term which are only summable. The main term in the equation which contains the space derivatives

The main aim of this paper is to describe the closure of a finitely generated subgroup of a finitely generated free group in the proabelian topology. Our approach depends heavily on the description of the abelian kernel of a finite inverse semigroup.

In this paper, we give some necessary and sufficient conditions for a family of linear bounded operators to be a dual K-g-Bessel sequence of a given K-g-frame and, particularly, we determine a method to examine the uniqueness of the dual K-g-Bessel sequences associated with a K-g-frame. We also study the redundancy of K-g-frames and some new properties of exact K-g-frames are presented.

In this paper, we introduce two algorithms for finding a common solution of the monotone inclusion problem and the fixed point problem for a relatively nonexpansive mapping in reflexive Banach spaces. The weak convergence results for both algorithms are established without the prior knowledge of the Lipschitz constant of the mapping. An application to the variational inequality problem is considered

Frieze patterns are defined by objects of a category of Dyck paths, to do that, it is introduced the notion of diamond of Dynkin type \({\mathbb {A}}_{n}\). Such diamonds constitute a tool to build integral frieze patterns.

In this paper, we extend the Minkowski integral inequality on time scales by \( \varDelta \varDelta \)-integral and the inverse Minkowski inequality over the set of constant sign functions. We get similar results by replacing \( \varDelta \varDelta \)-integral with \( \varDelta \nabla \), \( \nabla \varDelta \) and \( \nabla \nabla \)-integrals. For application, we give another proof of the Hardy inequality

Let \(C^2[0, 1]\) be the Banach space of all (real or complex valued) functions that have continuous derivatives \(f'\), \(f''\) on the closed unit interval [0, 1], equipped with norm \(\Vert f\Vert = |f(0)| + |f'(0)| + \Vert f''\Vert _{\infty }\), where \(\Vert \cdot \Vert _{\infty }\) is the usual supremum norm. In this paper, we investigate the algebraic reflexivity of the group of isometries, and

We present a treatment of the non-Markovian character of memory by incorporating different forms of Mittag-Leffler (ML) function, which generally arises in the solution of a fractional master equation, as different memory functions in the Generalized Kolmogorov-Feller Equation (GKFE). The cross-over from the short time (stretched exponential) to long time (inverse power law) approximations of the ML

In this paper, first we consider some partitioned matrices having some special kind of blocks, and we obtain their eigenvalues and eigenvectors. From these, we deduce several results on the eigenvalues of partitioned matrices in the literature. Next we consider an extension of a generalized join of graphs introduced by Hedetniemi (On classes of graphs defined by special cutsets of lines. In: Many facets

We obtain a new boundedness criterion for the difference of two composition operators from a weighted Bergman space \(A^p_{\alpha }\) into a Lebesgue space \(L^q(\mu )\), where \(0< q < p\) and \(\alpha > -1\). As a consequence, we provide a direct proof that such a bounded difference operator is necessarily compact. We also characterize compact differences of composition operators from \(A^p_{\alpha

In this paper, we have considered the van der Waals equation of state to study the one-dimensional spherically symmetric self-gravitating interstellar gas clouds. The transport equation for the acceleration waves is obtained. The evolution and propagation of the characteristic shock are considered to study its interaction with the acceleration wave. The amplitudes of the reflected and the transmitted

In the present work, we prove an existence and uniqueness result of solutions to a quasilinear elliptic problem with nonlinear singular terms in the weighted Sobolev space. The equation that we consider is the following $$\begin{aligned} -\Delta _{p(\cdot )}^{\omega } u+\beta (u)=\frac{f(x)}{u^{\alpha }}, \end{aligned}$$ where \(\alpha \ge 1\), \(\beta \) is a continuous non decreasing surjective real

By applying the Brouwer fixed point theorem, we prove an existence result of solutions for strongly pseudomonotone quasi-variational inequalities which extends an analogous result in Kocvara and Outrata (Optim Methods Softw 5:275–295, 1995). The result is based on a new result concerning continuity property of solutions to a parametric variational inequality. Examples are given to illustrate our results

Let G be a finite group and \(\mathfrak {s}(G)\) denote the number of subgroups of G. Aivazidis and Müller proved that if G is a non-cyclic p-group of order \(p^{\lambda }\), then \(\mathfrak {s}(G)\ge 6\) whenever \(p^{\lambda }=2^3\); \(s(G)\ge (p+1)(\lambda -1)+2\) whenever \(p^{\lambda }\ne 2^3\). In this paper, we generalize the results of Aivazidis and Müller on all finite non-cyclic nilpotent

In this paper, we propose two new methods to solve large-scale systems of differential equations, which are based on the Krylov method. In the first one, the exact solution with the exponential projection technique of the matrix. In the second, we get a new problem of small size, by dropping the initial problem, and then we solve it in ways, such as the Rosenbrock and the BDF. Some theoretical results

This paper focuses on the role of hyperbolicity on pattern formation in the subcritical regime for a class of hyperbolic models with cross-diffusion. A weakly nonlinear analysis up to the fifth order is employed to describe the time evolution of the pattern amplitude close to the instability threshold. The effects of the inertial times on the pattern formation as well as on the transient subcritical

Let b be a non-constant function in the unit ball of \(H^{\infty }\). We characterize the universal interpolating sequences and the uniqueness sequences for the de Branges–Rovnyak space \({{\mathcal {H}}}(b)\), a Hilbert space contractively contained in \(H^2\).

For modules over group rings we introduce the following numerical parameter. We say that a module A over a ring R has finite r-generator property if each f.g. (finitely generated) R-submodule of A can be generated exactly by r elements and there exists a f.g. R-submodule D of A, which has a minimal generating subset, consisting exactly of r elements. Let FG be the group algebra of a finite group G

We introduce and investigate the so-called D-regularly nil clean rings by showing that these rings are, in fact, a non-trivial generalization of the classical \(\pi \)-regular rings (in particular, of the von Neumann regular rings and of the strongly \(\pi \)-regular rings). Some other close relationships with certain well-known classes of rings such as exchange rings, clean rings, nil-clean rings

Let G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice \(\mathcal {L}(H)\) embeds in \(\mathcal {L}(G)\). It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

Let G be a finite group. A subgroup H of G is called a \({\mathbb {P}}\)-subnormal subgroup whenever \(H=G\) or there exists a chain of subgroups \(H=H_0\le H_1\le \cdots \le H_t=G\) such that \(|H_i:H_{i-1}|\) is a prime for every \(i\in \{1, 2, \ldots t\}\). In the present paper, we study finite groups in which some 2-maximal subgroups or cyclic subgroups are \({\mathbb {P}}\)-subnormal subgroups

Let G be a finite group. A collection \(\Pi =\{H_1,\dots ,{H_r}\}\) of subgroups of G, where \(r>1\), is said a non-trivial partition of G if every non-identity element of G belongs to one and only one \(H_i\), for some \(1\leqslant i\leqslant r\). We call a group G that does not admit any non-trivial partition a partition-free group. In this paper, we study a partition-free group G whose all proper

In this paper, we attain the multifractal Hewitt–Stromberg dimension functions of Moran measures associated with homogeneous Moran fractals and show that the multifractal Hewitt–Stromberg measures are mutually singular for which the multifractal functions do not necessarily coincide. In particular, we give a positive answer to questions posed in Attia and Selmi (J Geom Anal 31:825-862, 2021) and discuss

We fix a Finsler norm F and, using the anisotropic curvature flow, we prove that in the plane the anisotropic maximum curvature \(k^F_{\max }\) of a smooth Jordan curve is such that \( k^F_{\max }(\gamma )\ge \sqrt{\kappa /A}\), where A is the area enclosed by \(\gamma \) and \(\kappa \) the area of the unitary Wulff shape associated to the anisotropy F.

The paper presents a study related to the two-phase analysis of pulsatile blood flow through a narrowed stenosed artery with radiation and the chemical effects. In the model, a vertical artery is considered in which the flow of blood is assumed vertical upward and the direction of an external applied magnetic is in the radial direction of the flow. To understand the behavior of blood flow, graphs of

We establish some functional analytic properties for the \(\bar{\partial }\)-Neumann operator \(N_s\) on the intersection of two bounded weakly q-convex domains with \(\mathcal {C}^2\)-boundaries in \(\mathbb {C}^n\). Attention is focussed on questions of \(L^2\)-existence and compactness of \(N_s\) for all \(s\ge q\). Sobolev and boundary regularity for the \(\bar{\partial }\)-equation are consequently

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let \(A\ \)be a commutative ring with a nonzero identity \(1\ne 0.\) A proper ideal \(P\ \)of \(A\ \)is said to be a weakly 1-absorbing prime ideal if for every nonunits \(x,y,z\in A\ \)with \(0\ne xyz\in P,\ \)then \(xy\in P\) or \(z\in P.\ \)In addition to give many properties and characterizations of weakly 1-absorbing

The purpose of this paper is to study the multiplicity of periodic solutions for a class of non-autonomous second-order damped vibration systems. New results are obtained by using Fountain theorem. These results improve the related ones in the literature.

A supersymmetric extension of a two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this superalgebra into 63 equivalence classes is performed. For some of the subalgebras, it is found that the invariants have a non-standard structure. For six selected subalgebras

The goal of this article is to study a thermoelastic Timoshenko system with viscoelastic law acting on the shear force and thermoelastic dissipation acting on the bending moment. We prove a general decay as well as an explicit decay estimate for solution energy, from which the exponential and polynomial decay results are only special cases. The result is obtained without imposing equal-wave-speed condition

Di Crescenzo and Longobardi (J Appl Prob 39, 434–440, 2002), introduced the concept of past entropy for measuring uncertainty contained in past lifetime of random variables. By analogous to past entropy, Krishnan et al. (J Korean Stat Soc, 49, 457–474, 2020) defined the concept of past extropy. In this work, we propose nonparametric estimator for the past extropy, where the observations under consideration

We study the fourth order semilinear suspension bridge problem with restoring force h(u) and linear damping \(\delta u_{t}\). Using the multiplier method, we first establish the observability inequality of the corresponding system without damping term. Then we show an equivalence between observability and exponential stabilization of this system by using an appropriate decomposition technique and the

Let \({{\mathcal {S}}}\subseteq {{\mathbb {Z}}}^m \oplus T\) be a finitely generated and reduced monoid. In this paper we develop a general strategy to study the set of elements in \({\mathcal {S}}\) having at least two factorizations of the same length, namely the ideal \({\mathcal {L}}_{{\mathcal {S}}}\). To this end, we work with a certain (lattice) ideal associated to the monoid \({\mathcal {S}}\)

In this article, we study the delta shock wave for zero-pressure gasdynamics system with energy conservation laws in the frame of \(\alpha \)-solutions defined in the setting of distributional products. By reformulating the system, we construct within a convenient space of distributions, all solutions which include discontinuous solutions and Dirac delta measures. We also establish the generalized

If \(I\subset {\mathbb {R}}\) is a bounded interval, we prove the boundedness of Calderón singular operator and of Hardy-Littlewood Maximal operator in the generalized weighted Grand Lebesgue spaces \(L_p^{p),{\delta }}(I)\), \(1

The reversed aging intensity function is defined as the ratio of the instantaneous reversed hazard rate to the baseline value of the reversed hazard rate. It analyzes the aging property quantitatively, the higher the reversed aging intensity, the weaker the tendency of aging. In this paper, a family of generalized reversed aging intensity functions is introduced and studied. Those functions depend