In this work, we prove a general and optimal decay estimates for the solution energy of a new thermoelastic Timoshenko system with viscoelastic law acting on the transverse displacement. Therefore, exponential and polynomial decay rates are obtained as particular cases. The result is obtained under the assumption of equal speed of wave propagation.

In this paper, the initial-boundary value problem of the original three-dimensional compressible Euler equations with (or without) time-dependent damping is considered. By considering a functional \(F(t,\alpha ,f)\) weighted by a general time-dependent parameter function \(\alpha \) and a general radius-dependent parameter function f, we show that if the initial value \(F|_{t=0}\) is sufficiently large

In this paper, we concern with the data interpolation by using extended cubic uniform B-splines with shape parameters. Two iterative formats, namely the progressive iterative approximation (PIA) and the weighted progressive iterative approximation (WPIA), are proposed to interpolate given data points. We study the optimal shape parameter and the optimal weight for the proposed methods by solving the

We consider normalized analytic function f on the open unit disk for which either \(Ref(z)/g(z)>0\), \(|f(z) /g(z) - 1|<1\) or \(Re(1-z^2) f(z) /z>0\) for some analytic function g with \(Re(1-z^2) g(z) /z>0\). We have obtained the radii for these functions to belong to various subclasses of starlike functions. The subclasses considered include the classes of starlike functions of order \(\alpha \)

Let p be an odd prime and \(H_k^{(n)}=\sum _{j=1}^k1/j^n\) denote the generalized harmonic number. In this paper, the authors establish a kind of congruences involving \(\sum _{k=1}^{p-1}k^mH_{k}^{(n)}\pmod {p^2}\), where m, n are positive integers. Furthermore, the authors prove a congruence for \(\sum _{k=1}^{p-1}k^{p-2}(H_{k}^{(2)})^2\pmod {p^2}\).

Let R be an artin algebra. The Auslander–Reiten formula for the category (mod-R)-mod of finitely presented functors is presented, which is extended from the Auslander–Reiten formula for the category mod-R of finitely presented modules.

Let A and B be Banach algebras with \(\sigma (B)\ne \emptyset \). Let \(\theta , \phi , \gamma \in \sigma (B)\) and \(\mathrm{Der}(A\times _\theta ^{\phi , \gamma }B)\) be the set of all linear mappings \(d: A\times B\rightarrow A\times B\) satisfying \(d((a, b)\cdot _\theta (x, y))=d(a, b)\cdot _\phi (x, y)+ (a, b)\cdot _\gamma d(x, y)\) for all \(a, x\in A\) and \(b, y\in B\). In this paper, we characterize

In this paper, we study the existence of multiple solutions for the following biharmonic problem $$\begin{aligned} \Delta ^2 u= & {} f(x,u) + g(x,u)\quad \hbox {in}\quad \Omega ,\\ u= & {} \Delta u =0 \quad \hbox {on}\quad \partial \Omega , \end{aligned}$$ where \(\Omega \subset {\mathbb {R}}^N, (N > 4)\) is a smooth bounded domain and \(f(x,\xi )\) is odd in \(\xi , g(x,\xi )\) is a perturbation term

By means of matrix decompositions, three determinants with their entries being binomial sums are evaluated in closed forms. Ten remarkable examples are illustrated as propositions, which present determinant identities about binomial coefficients and quotients of rising factorials, as well as orthogonal polynomials named after Hermite, Laguerre and Legendre.

We show that if the Hardy–Littlewood maximal operator is bounded on a separable Banach function space \(X({\mathbb {R}})\) and on its associate space \(X'({\mathbb {R}})\), then the space \(X({\mathbb {R}})\) has an unconditional wavelet basis. This result extends previous results by Soardi (Proc Am Math Soc 125:3669–3673, 1997) for rearrangement-invariant Banach function spaces with nontrivial Boyd

This paper aims to discuss the mathematical details in Lewis’ model by considering the analyticity and integrability conditions of characteristic functions and payoff functions of contingent claims. In his seminal paper, Lewis shows that it is much easier to compute the option value in the Fourier space than computing in terminal security price space. He computes the option value as an integral in

We study the asymptotic behavior of micropolar fluid flows in a thin domain of thickness \(\eta _\varepsilon \) with a periodic oscillating boundary with wavelength \(\varepsilon \). We consider the limit when \(\varepsilon \) tends to zero and, depending on the limit of the ratio of \(\eta _\varepsilon /\varepsilon \), we prove the existence of three different regimes. In each regime, we derive a

In this paper, for the incompressible nematic liquid crystal flows with heat effect and density-dependent viscosity coefficient in three-dimensional bounded domain, by using the elliptic regularity result of the Stokes equations and the linearization and iteration method, we investigate the local existence and uniqueness of strong solutions.

We study the geometry of the scale-invariant Cassinian metric and prove sharp comparison inequalities between this metric and the hyperbolic metric in the case when the domain is either the unit ball or the upper half space. We also prove sharp distortion inequalities for the scale-invariant Cassinian metric under Möbius transformations.

In this work, we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional substantial derivatives are also introduced in both Riemann–Liouville and Caputo sense. Furthermore, we analyze fundamental properties of these operators. Finally

In this paper, we introduced the class \(\mathcal {S}_{T}^{*}(\lambda )\) of analytic functions which is related to starlike functions and generating function of generalized telephone numbers. By using bounds on some coefficient functionals for the family of functions with positive real part, we obtain for functions in the class \(\mathcal {S}_{T}^{*}(\lambda )\) several sharp coefficient bounds on

In this paper, we study the fattening effect of points over the complex numbers for del Pezzo surfaces \(\mathbb {S}_r\) arising by blowing-up of \(\mathbb {P}^2\) at r general points, with \( r \in \{1, \dots , 8 \}\). Basic questions when studying the problem of points fattening on an arbitrary variety are what is the minimal growth of the initial sequence and how are the sets on which this minimal

We study the optimal fractional Trudinger–Moser inequalities on \( \mathbb {R} \) when the integrands have the form \(\left( e^{\pi u^{2}}-1\right) \left| u\right| ^{2a}\) for some \(a\ge 0\). The equivalence of the subcritical and critical fractional Trudinger–Moser inequalities is set up in the spirit of Lam, Lu and Zhang. The existence of optimizers for the sharp subcritical fractional Trudinger–Moser

Let A and B be rings, U a (B, A)-bimodule and \(T=\begin{pmatrix}A&{}0\\ U&{}B\end{pmatrix}\) a triangular matrix ring. In this paper, we firstly construct a right recollement of stable categories of Ding injective B-modules, Ding injective T-modules and Ding injective A-modules and then establish a recollement of stable categories of these modules.

For a simple connected graph G, the Q-generating function of the numbers \(N_k\) of semi-edge walks of length k in G is defined by \(W_Q(t)=\sum \nolimits _{k = 0}^\infty {N_k t^k }\). This paper reveals that the Q-generating function \(W_Q(t)\) may be expressed in terms of the Q-polynomials of the graph G and its complement \(\overline{G}\). Using this result, we study some Q-spectral properties of

In this paper, we describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces \(K_1\) and \(K_2\). The novelty of our approach is that here we consider matrix representations computed with respect to bases of different type in \(K_1\) and \(K_2\) (for example, kernel basis in \(K_1\) and conjugate kernel basis in \(K_2\)). We thus

This paper deals with finite-time control problem for nonlinear fractional-order systems with order \(0<\alpha <1\). We first derive sufficient conditions for finite-time stabilization based on Caputo derivative calculus and Lyapunov-like function method. Then, by introducing a new type of the cost control function, we study guaranteed cost control problem for such systems. In terms of linear matrix

In this article, we present a new description of the integral second homology of crossed modules of groups and generalize two basic results on the integral second homology of groups for crossed modules. Using these, we strengthen some consequences on covering pairs and the universal relative central extensions of pairs of finite groups.

We deal with the Cauchy problem of three-dimensional incompressible magneto-micropolar fluid equations with a nonlinear damping term \(\alpha |{\mathbf {u}}|^{\beta -1}{\mathbf {u}}\ (\alpha >0\ \text {and}\ \beta \ge 1)\) in the momentum equations. By cancelation properties of the system under study, we show that there exists a unique global strong solution for any \(\beta \ge 4\). Our work extends

In this note, we establish a functional central limit theorem for the capacity of the range for a class of \(\alpha \)-stable random walks on the integer lattice \(\mathbb {Z}^d\) with \( d> 5\alpha /2\). Using similar methods, we also prove an analogous result for the cardinality of the range when \(d > 3\alpha / 2\).

In this paper, we study an age-structured hepatitis B virus model with DNA-containing capsids. We obtain the well-posedness of the model by reformulate the model as an abstract Cauchy problem, and we find a threshold number \(\mathfrak {R}_0\) for the existence of the steady states. The local stability of each steady states is established by linearizing the system and analyze the corresponding characteristic

In this work, interval programming problems are considered for financial investment and optimality criteria. An order relation, defined by Ishibuchi and Tanaka for maximization problems, is used to obtain the solution of the problems. A real-life example, related to investment, and its solution are given. Necessary and sufficient optimality criteria including weak and strongly solution for interval

The eccentric connectivity index of a graph G is \(\xi ^c(G) = \sum _{v \in V(G)}\varepsilon (v)\deg (v)\), and the eccentric distance sum is \(\xi ^d(G) = \sum _{v \in V(G)}\varepsilon (v)D(v)\), where \(\varepsilon (v)\) is the eccentricity of v, and D(v) the sum of distances between v and the other vertices. A lower and an upper bound on \(\xi ^d(G) - \xi ^c(G)\) is given for an arbitrary graph

In this paper, we prove some existence and uniqueness results for some elliptic quasilinear equation defined on the whole Euclidean space \( \mathbb {R}^N,\ N \ge 2\), involving the p(x)-Laplacian operator and whose nonlinearities can be discontinuous. Some new ideas and tools are used to reach our main results.

Let \(n >3\) and \( 0< k < \frac{n}{2} \) be integers. In this paper, we investigate some algebraic properties of the line graph of the graph \( {Q_n}(k,k+1) \) where \( {Q_n}(k,k+1) \) is the subgraph of the hypercube \(Q_n\) which is induced by the set of vertices of weights k and \(k+1\). The graph \( {Q_n}(k,k+1) \) has a close relation to Johnson graph \(J(n+1,k+1)\). In fact, it is the square

In this article, the problem of double-diffusive convection in a porous layer when the viscosity depends on the temperature and using Brinkman–Forchheimer model has been introduced by using the linear and nonlinear energy theories. For linear theory, the critical Rayleigh numbers have been derived and then numerically calculated. However, for nonlinear theory, the critical threshold was derived in

In this paper, we consider the nonlinear eigenvalue problems $$\begin{aligned} \begin{aligned}&u''''=\lambda h(t)f(u), \quad 00\) for \(s\ne 0\), and \(f_0=f_\infty =0\), \(f_0=\lim _{|s|\rightarrow 0}f(s)/s, \; f_\infty =\lim _{|s|\rightarrow \infty }f(s)/s\). We investigate the global structure of one-sign solutions by using bifurcation techniques.

In this paper, the minimum and maximum principle sufficiency properties for a nonsmooth variational inequality problem (NVIP) are studied. We discuss the relationship among the solution set of an NVIP and those defined by its dual problem and relevant gap functions. For a pseudomonotone NVIP, the weaker sharpness of its solution set has been shown to be sufficient for it to have minimum principle sufficiency

The exact Riemann solutions for a macroscopic production model under the equation of state given by the Chaplygin gas are solved explicitly for all possible Riemann initial data. It is discovered interestingly that a composite hyperbolic wave is involved in Riemann solution under some specially designated initial conditions, which is made up of a rarefaction wave and a delta contact discontinuity attached

A graph G is \((d_{1},d_{2},\ldots ,d_{k})\)-colorable if the vertex set of G can be partitioned into subsets \(V_{1}, V_{2},\ldots , V_{k}\) such that the subgraph \(G[V_{i}]\) induced by \(V_{i}\) has maximum degree at most \(d_{i}\) for \(i = 1, 2, \ldots , k\). Novosibirsk’s Conjecture (Sib lektron Mat Izv 3:428–440, 2006) says that every planar graph without 3-cycles adjacent to cycles of length

In this paper, we consider a nonlinear cancer invasion mathematical model with proliferation, growth and haptotaxis effects. We obtain lower bounds for the finite-time blow-up of solutions of the considered system with nonlinear diffusion operator when blow-up occurs. We have assumed both the Dirichlet and Neumann boundary conditions in \({\mathbb {R}}^n, n\ge 2\) to attain the desire result.

In this paper, the split common fixed point problem for quasi-pseudo-contractive mappings is studied in Hilbert spaces. By using the hybrid projection method, a new algorithm and some strong convergence theorems are established under suitable assumptions. Our results not only improve and generalize some recent results but also give an affirmative answer to an open question.

We are concerned with the following elliptic equation with a general nonlocal integrodifferential operator \({\mathcal {L}}_K\)$$\begin{aligned} \begin{aligned} \left\{ \begin{array}{ll} -{\mathcal {L}}_Ku=\lambda u+f(x,u), &{}\quad \text {in}\quad \Omega ,\\ u=0, &{} \quad \text {in}\quad {\mathbb {R}}^n{\setminus }\Omega , \end{array}\right. \end{aligned} \end{aligned}$$ where \(\Omega \) be an open-bounded

In this paper, we consider a differential inclusion governed by a set-valued nonexpansive mapping and study the asymptotic behavior (weak and strong convergence) of its solutions with various assumptions on this mapping. Then for a set-valued nonexpansive mapping, we define the corresponding resolvent (proximal) operator as a set-valued mapping and study some of its elementary properties. Subsequently

In this paper we investigate some reliability measures, including super-connectivity, cyclic edge connectivity, etc., in the folded hypercubes.

The aim of this article is to determine entirely the Jordan automorphisms of generalized matrix rings of Morita contexts. Necessary and sufficient conditions are obtained for an \(\mathcal {R}\)-linear map on a general Morita context to be a Jordan homomorphism. Moreover, some conditions are studied, under which, any Jordan automorphism of a general Morita context is either an automorphism or an anti-automorphism

Boundary value problems for fractional elliptic equations with parameter in Banach spaces are studied. Uniform \(L_{p}\)-separability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives. Particularly, it is proven that the fractional elliptic operators generated by these equations are positive and also are generators of the analytic semigroups

In this paper, we study the existence and multiplicity of solutions for a class of equations involving a nonlocal term and the biharmonic operator with critical exponent. By new techniques, multiplicity results are established together with variational method. It is worth noting that the method of this paper is obviously different from the existing literature.

We show that all non-trivial solutions of complex differential equation \(f''+ A(z)f'+B(z)f = 0\) are of infinite order if coefficients A(z) and B(z) are of special type and establish a relation between the hyper-order of these solutions and the orders of coefficients A(z) and B(z). We have also extended these results to higher order complex differential equations.

Let G be a nontrivial connected graph with a vertex-coloring c: \(V(G)\rightarrow \{1,2,\ldots ,q\},q\in N\). For a set \(S\subseteq V(G)\) and \(|S|\ge 2\), a subtree T of G satisfying \(S\subseteq V(T)\) is said to be an S-Steiner tree or simply S-tree. The S-tree T is called a vertex-rainbow S-tree if the vertices of \(V(T)\setminus S\) have distinct colors. Let k be a fixed integer with \(2\le

In this paper, we prove that \(cmo^{p}(\mathbb {R}^{n})\) and \(\Lambda _{n(\frac{1}{p}-1)}\), the dual spaces of local Hardy space \(h^{p}(\mathbb {R}^{n})\), are coincide with equivalent norms for \(\frac{n}{n+1}

In this paper, we study the nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. Global bifurcation of nontrivial solutions of this problem is investigated. We prove the existence of two families of unbounded continua of the set of solutions to this problem bifurcating from points and intervals of the line of trivial solutions

In this paper, we study the following nonlinear Schrödinger–Bopp–Podolsky system $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+V(x)u+q\phi u=f(u)&{}\\ -\Delta \phi +a^2\Delta ^2\phi =4\pi u^2 \end{array} \right. \ \,\mathrm{in }\,{\mathbb {R}}^3, \end{aligned}$$ where \(a>0\), \(q>0\) and \(V\in {\mathcal {C}}({\mathbb {R}}^3,{\mathbb {R}})\). By means of the variational methods, we prove the

A finite group G is called \(\psi \)-divisible if \(\psi (H)|\psi (G)\) for any subgroup H of G, where \(\psi (H)\) and \(\psi (G)\) are the sum of element orders of H and G, respectively. In this paper, we classify the finite groups whose subgroups are all \(\psi \)-divisible. Since the existence of \(\psi \)-divisible groups is related to the class of square-free order groups, we also study the sum

In this paper, we explicitly find all the solutions of the exponential Diophantine equation \(F_{n+1}^x + F_{n}^x - F_{n-1}^x = F_{m}\), in nonnegative integers (m, n, x), where \(F_{n}\) is the nth Fibonacci number.

For a connected graph G, the Mostar index Mo(G) and the irregularity irr(G) are defined as \(Mo(G)=\sum _{uv\in E(G)}|n_u-n_v|\) and \( irr (G)=\sum _{uv\in E(G)}|d_u-d_v|\), respectively, where \(d_u\) is the degree of the vertex u of G and \(n_u\) denotes the number of vertices of G which are closer to u than to v for an edge uv. In this paper, we focus on the difference \(\Delta M(G)=Mo(G)- irr

On a real hypersurface M of a complex quadric we have an almost contact metric structure induced by the Kählerian structure of the ambient space. Therefore, on M we have the Levi-Civita connection \(\nabla \) and, for any non-null real number k, the so called kth generalized Tanaka Webster connection \({\hat{\nabla }}^{(k)}\). We introduce the notions of \(({\hat{\nabla }}^{(k)},\nabla )\)-Codazzi

In the present paper, we show that \(\vartheta \)-convergent double series spaces \({\mathcal {CS}}_\vartheta \) and the series space \(\mathcal {BV}\) of double sequences of bounded variation are BDK-spaces and investigate their \(AK(\vartheta )\)-space property, where \(\vartheta \in \{p,bp,r\}\).

In this paper, we consider digraphs with possible loops and the particular case of oriented graphs, i.e. loopless digraphs with at most one oriented edge between every pair of vertices. We provide an upper bound for the largest singular value of the skew Laplacian matrix of an oriented graph, the largest singular value of the skew adjacency matrix of an oriented graph and the largest singular value

In this study, we propose nonemptiness and boundedness of the solution set for a bifunction variational inequality problem with P-strict feasibility in reflexive Banach spaces. As a novel concept, P-strict feasibility for a bifunction variational inequality is introduced. Moreover, it is proved that a pseudomonotone bifunction variational inequality has a nonempty and bounded solution set if and only

We study the root distribution of some univariate polynomials satisfying a recurrence of order two with linear polynomial coefficients. We show that the set of non-isolated limits of zeros of the polynomials is either an arc, or a circle, or an interval, or a “lollipop.” As an application, we discover a sufficient and necessary condition for the universal real-rootedness of the polynomials, subject

Examining the asymptotic growth behavior of holomorphic and meromorphic functions has significant importance in complex analysis. Estimations of upper bounds for the rate of growth of entire functions are mostly guaranteed. However, the analog estimations for lower bounds of the rate of growth are not always attainable. In this paper, we give the lower rate of growth of the generalized Hadamard product

The main purpose of this paper is twofold. First, a class of polyharmonic mappings with positive Jacobian and being univalent in the unit disk \({\mathbb {D}}\) are constructed. Second, we state and prove several theorems about the radius of univalence of a class of polyharmonic mappings, which gives a partial generalized answer to the radius problem posed by Abu Muhanna (Complex Var Elliptic Equ 53:745–751

Suppose w is a sense-preserving harmonic mapping of the unit disk \({\mathbb D}\) such that \(w({\mathbb D})\subseteq {\mathbb D}\) and w has a zero of order \(p\ge 1\) at \(z=0\). In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of \({\mathbb D}\), we further generalize this result.

In this paper, we generalize the notion of the ergodic shadowing property to the iterated function systems and prove some related theorems on this notion. In addition, we give an example to show that there is an iterated function system which has the ergodic shadowing property but not weakly mixing. Moreover, we show that ergodic shadowing property implies the average shadowing property for iterated