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

Similarity solutions are obtained for one-dimensional cylindrical shock wave in a self-gravitating, rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field in the presence of conductive and radiative heat fluxes. The total energy of the wave is non-constant. It is obtained that the increase in the Cowling number, in the parameters of radiative as well as conductive heat transfer

The problem of Moore–Gibson–Thompson equation with infinite memory and time delay terms is considered. Under suitable Lyapunov functionals with an appropriate assumptions on the kernel function and on the weight of the delay, we prove the well-posedness and the exponential stability of the system.

A condition that guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also presented.

We study both existence and stability of renormalized solutions for nonlinear parabolic problems with three lower order terms that have, respectively, growth with respect to u and to the gradient, whose model $$\begin{aligned}({\mathcal {P}})\ {\left\{ \begin{array}{ll} u_{t}-\varDelta _{p}u-\text {div}[c(t,x)|u|^{\gamma -1}u]+b(t,x)|\nabla u|^{\lambda }+d(t,x)|u|^{\iota }=\mu -\text {div}(E)\quad

It is proved that if G is an \(\mathfrak {X}\)-group of infinite rank whose proper subgroups of infinite rank are Baer groups, then so are all proper subgroups of G, where \(\mathfrak {X}\) is the class defined by N.S. Černikov as the closure of the class of periodic locally graded groups by the closure operations \(\varvec{\acute{P}}\), \(\varvec{\grave{P}}\) and \( \varvec{L}\). We prove also that

Let \({\mathfrak {X}}\) be a class of simple groups with a completeness property \(\pi ({\mathfrak {X}}) = \mathrm {char} \, {\mathfrak {X}}\). A formation is a class of finite groups closed under taking homomorphic images and finite subdirect products. Förster introduced the concept of \({\mathfrak {X}}\)-local formation in order to obtain a common extension of well-known Gaschütz–Lubeseder–Schmid

For sufficiently regular obstacles, we prove existence and uniqueness results for the obstacle problem related to an anisotropic parabolic equation.

Let G be a finite group and \(N \unlhd G\). The normal subgroup based power graph of G, \(\Gamma _N(G)\), is an undirected graph with vertex set \((G{\setminus }N) \cup \{e\}\) in which two distinct vertices a and b are adjacent if and only if \(aN = b^mN\) or \(bN = a^nN\), for some positive integers m and n. The aim of this paper is to characterize all pairs (G, N) of a finite group G and a proper

Let D be an integral domain. G. Picozza associated to a stable semistar operation \(\star \) on D, a semistar operation \(\star _1\) on the polynomial ring D[X]. We defined the notion of semistar accr domain. We prove that D is \({\widetilde{\star }}\)-Noetherian if and only D[X] is \(\star _1\)-accr. On the other hand, we prove that D satisfies the ascending chain condition on radical quasi-\({\widetilde{\star

In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis method is presented. The considered problem is formulated as a topology optimization one. The proposed process leads to a non-iterative reconstruction algorithm can be applied for large class of cost functional. The unknown shape of the term source support

This paper studies the existence of weak solutions and their asymptotic behaviour to the initial boundary value problem for a multidimensional nonlinear Bresse system. The existence of the solutions of the problem is obtained by appliying Galerkin method. Then, we obtain an explicit decay rate estimation dependent on both the strain-caused stress and the damping terms by using the multiplier method

Single hidden layer feedforward neural networks can represent multivariate functions that are sums of ridge functions. These ridge functions are defined via an activation function and customizable weights. The paper deals with best non-linear approximation by such sums of ridge functions. Error bounds are presented in terms of moduli of smoothness. The main focus, however, is to prove that the bounds

In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals

We presented a geometrical shock dynamics model to predict the behavior of weak converging shock waves in solid materials. Taking into consideration Mie–Grüneisen equation of state the analytical solution is obtained for the flow behind the converging shock-front propagating in solids. The analytical formaluas are also obtained for the shock velocity, pressure, density, particle velocity, temperature

This work discusses the existence of the limit as p goes to 1 of the nontrivial solutions to the one-dimensional problem: $$\begin{aligned} {\left\{ \begin{array}{ll} -\left( |u_x|^{p-2} u_x\right) _x = \lambda |{u}|^{{p}-2}{u} -|{u}|^{{q}-2}{u}&{} \quad 0< x < 1\\ u(0)=u(1)=0, &{} \end{array}\right. } \end{aligned}$$ where \(\lambda \) is a positive parameter and the exponents p, q satisfy \(1< p

Suppose \({\mathfrak R}\, \) is a 2,3-torsion free unital alternative ring having an idempotent element \(e_1\) \(\left( e_2 = 1-e_1\right) \) which satisfies \(x {\mathfrak R}\, \cdot e_i = \{0\} \Rightarrow x = 0\) \(\left( i = 1,2\right) \). In this paper, we aim to characterize the commuting maps. Let \(\varphi \) be a commuting map of \({\mathfrak R}\, \) so it is shown that \(\varphi (x) = zx

Let \(X = \{X_1,X_2, \ldots ,X_m\}\) be a system of smooth vector fields in \({{\mathbb R}^n}\) satisfying the Hörmander’s finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space \(\mathbb G\) associated to system X$$\begin{aligned} \left( \frac{1}{\int _{B_R} K(x)\; dx} \int _{B_R} |u|^{t} K(x) \; dx \right) ^{1/t} \le C\, R \left( \frac{1}{\int

In this paper, we investigate a mixed fractional integral boundary value problem with p(t)-Laplacian operator. Firstly, we derive the Green function through the direct computation and obtain the properties of Green function. For \(p(t)\ne \) constant, under the appropriate conditions of the nonlinear term, we establish the existence result of at least one positive solution of the above problem by means

In this paper, we prove the existence and uniqueness results of entropy solutions to a class of nonlinear parabolic p(u)-Laplacian problem with Fourier-type boundary conditions and \(L^1\)-data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.

The Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

We establish asymptotic stability estimates for solutions to evolution problems with singular convection term. Such quantitative estimates provide a measure with respect to the time variable of the distance between the solution to a parabolic problem from the one of the its elliptic stationary counterpart.

We extend the algebraic construction of finite dimensional varying exponent \(L^{p(\cdot )}\) space norms, defined in terms of Cauchy polynomials to a more general setting, including varying exponent \(L^{p(\cdot )}\) spaces. This boils down to reformulating the Musielak–Orlicz or Nakano space norm in an algebraic fashion where the infimum appearing in the definition of the norm should become a (uniquely

The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case \(1< q, p_1, p_2<\infty \) with \(q \ge \max (p_1,p_2)\).

We study the existence of fast homoclinic orbits for the following damped vibration system \(\ddot{u}(t)+q(t)\dot{u}(t)+\nabla V(t,u(t))=0\); where \(q\in C(\mathbb {R},\mathbb {R})\) and \(V\in C^{1}(\mathbb {R}\times \mathbb {R}^{N},\mathbb {R})\) is of the type V(t,x)=-K(t,x)+W(t,x). A map K is not a quadratic form in x and W(t, x) is superquadratic in x.

In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes et al. (Adv Calc Var 10:357–380, 2017) that “the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area” under the weaker restriction that the boundary of the domain is diffeomorphic

We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.

A Lagrangian version of the classical 1+1-dimensional Korteweg capillarity system is shown to encapsulate as a particular reduction an integrable Boussinesq equation. The associated integrability of the corresponding Eulerian capillarity system is set down. In turn, hidden integrability cases of the generalised Boussinesq equation are recorded associated with reduction of the Eulerian system to the

The Boltzmann equation for charge transport in monolayer graphene is numerically solved by using a discontinuous Galerkin method. The numerical fluxes are based on a uniform non oscillatory reconstruction. The numerical scheme has been tested by simulating the electron dynamics in a graphene field effect transistor. To the best of our knowledge the presented simulations are the first ones using a full

This notes studies the inhomogeneous non-linear Schrödinger equations with a harmonic potential $$\begin{aligned} i\partial _tu +\Delta u-|x|^2u+|x|^{b}|u|^{p-1}u=0. \end{aligned}$$ Indeed, following the methods of Fukuizumi and Ohta (Differ Integral Equ 16(6):691–706, 2003), Ohta (Funccialaj Ekvacioj 61:135–143, 2018), the non-linear and strong instability of standing waves are obtained in the two

The motivation of this study is to analyze the structure of the Riemann solutions for compressible hyperbolic system, so called logotropic system, with a Coulomb-type friction. The classical wave solutions of the Riemann problem (RP) for the logotropic system are structured explicitly for all cases. The system considered in this problem is hyperbolic in nature and the characteristic fields associated

In the present paper, we use a Lie group of transformations to obtain a class of similarity solutions to a problem of cylindrically symmetric strong shock waves propagating through one-dimensional, unsteady, and isothermal flow of a self-gravitating ideal gas under the influence of azimuthal magnetic field. The density of the ambient medium is assumed to be non-uniform ahead of the shock. The generators

Feng (Complexity, Art. 5139419, 2020) studied a thermoelastic laminated Timoshenko beam, where the heat conduction is given by Cattaneo’s law, as well as established the exponential and polynomial stabilities depending on the stability number \(\chi _\tau \). In this short paper, we consider the same system and show a lack of exponential stability when the stability number \(\chi _\tau \ne 0\), by

The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is to evaluate the possible gap between the energy equality and the energy inequality deduced for a weak solution. This kind of analysis is new and the result is a natural continuation and improvement of a result obtained by the same authors in Crispo et al. (Some new properties of a suitable weak solution to the Navier–Stokes

The power graph \({\mathcal {P}}_{G}\) of a finite group G is the graph whose vertex set is G, two distinct vertices are adjacent if one is a power of the other. The order supergraph \({\mathcal {S}}_{G}\) of \({\mathcal {P}}_G\) is the graph with vertex set G, and two distinct vertices x, y are adjacent if o(x)|o(y) or o(y)|o(x). In this paper, we study the independence number of \({\mathcal {S}}_{G}\)