For an edge-colored graph G, a set F of edges of G is called a proper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned different colors. An edge-colored graph is proper disconnected if for each pair of distinct vertices of G there exists a proper edge-cut separating them. For a connected graph G, the proper disconnection number of G, denoted by pd(G), is the minimum

In this paper, we mainly study the geometric model of the derived category of gentle one-cycle algebras provided by Opper, Plamondon and Schroll. We provide a realization of AAG-invariant on the surface, which is slightly different from the realization in their paper, and deduce a standard form of marked surfaces of gentle one-cycle algebras under derived equivalences. As an application, we classify

Due to the Nevanlinna theory, the paper gives the general structure of transcendental meromorphic solutions of a certain ordinary differential equation with rational coefficients. As an application, the meromorphic solutions of the FitzHugh–Nagumo system are obtained in explicit form.

In this paper, we obtain error bound for pseudo-binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein’s method. We also discuss approximation results for weighted sums of independent random variables. We demonstrate our results through some applications in finance and runs in statistics.

The notion of R-dual in general Hilbert spaces was first introduced by Casazza et al. (J Fourier Anal Appl 10:383–408, 2004), with the motivation to obtain a general version of the duality principle in Gabor analysis. On the other hand, the space \(L^2({{\mathbb {R}}}_+)\) of square integrable functions on the half real line \({\mathbb {R}}_{+}\) admits no traditional wavelet or Gabor frame due to

We consider two types of continued fraction expansions of the generating functions of Cauchy numbers. One type has been often studied by many authors, but another has not. In this paper, we give several continued fraction expansions of hypergeometric Cauchy numbers, shifted Cauchy numbers and leaping Cauchy numbers. In special cases, continued fraction expansions of the classical Cauchy numbers of

We call the solution of a kind of weighted Laplace equation complex-valued kernel \(\alpha \)-harmonic mappings. In this paper, some geometric properties of the complex-valued kernel \(\alpha \)-harmonic mappings, such as area, fully starlikeness and fully convexity of order \(\gamma \), \(\gamma \in [0,1)\), are explored. Furthermore, for a class of given boundary function, the Radó–Kneser–Choquet-type

This paper is concerned with the regularity criteria in terms of the middle eigenvalue of the deformation (strain) tensor \(\mathcal {D}(u)\) to the 3D Navier–Stokes equations in Lorentz spaces. It is shown that a Leray–Hopf weak solution is regular on (0, T] provided that the norm \(\Vert \lambda _{2}^{+}\Vert _{L^{p,\infty }(0,T; L ^{q,\infty }(\mathbb {R}^{3}))} \) with \( {2}/{p}+{3}/{q}=2\) \((

We provide sufficient conditions for the existence of one positive solution for a fourth--order beam equation with a discontinuous nonlinear term. Also a multiplicity result is established. They are based on a recent generalization of the Krasnosel’skiĭ fixed point theorem in cones.

Most important examples of null hypersurfaces in a Lorentzian manifold admit an integrable screen distribution, which determines a spacelike foliation of the null hypersurface. In this paper, we obtain conditions for a codimension two spacelike submanifold contained in a null hypersurface to be a leaf of the (integrable) screen distribution. For this, we use the rigging technique to endow the null

In this paper, we provide some exact formulas for the projective dimension and regularity of powers of edge ideals of some vertex-weighted rooted forests. These formulas are functions of the weight of vertices and the number of edges.

Let \(({\mathcal {C}},{\mathbb {E}},{\mathfrak {s}})\) be an extriangulated category with a proper class \(\xi \) of \({\mathbb {E}}\)-triangles. In a previous work, we introduced and studied the \(\xi \)-\({\mathcal {G}}\)projective and the \(\xi \)-\({\mathcal {G}}\)injective dimension for any object in \({\mathcal {C}}\). In this paper, we first give some characterizations of \(\xi \)-\({\mathcal

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by reducing them to different but isomorphic interpretations of an abstract notion, viz. the universal property, which is based on a pair of axioms.

For solving large sparse linear complementarity problems effectively, by utilizing the parametric method, the acceleration strategy and the relaxation technique to the modulus-based matrix splitting (MMS) iteration method, we develop the accelerated relaxation MMS (ARMMS) iteration method, which generalizes the generalized accelerated MMS (GAMMS) and the relaxation MMS (RMMS) ones proposed recently

Phase transitions in a model of van der Waals fluid flows in a nozzle with discontinuous cross-sectional area are investigated. The model admits a physically unstable elliptic region which causes phase transitions, and a jump in cross-sectional area which causes stationary contact waves. Compositions between waves in different characteristic fields are constructed differently in subsonic or supersonic

In this article, we study the following Kirchhoff–Schrödinger–Poisson system with pure power nonlinearity $$\begin{aligned} \left\{ \begin{array}{ll} -\Bigl (a+b \displaystyle \int _{\mathbb {R}^3}|\nabla u|^2{\text {d}}x\Bigr )\Delta u+V(x) u+K(x) \phi u= h(x)|u|^{p-1}u, &{}x\in \mathbb {R}^3, \\ -\Delta \phi =K(x)u^2, &{}x\in \mathbb {R}^3, \end{array} \right. \end{aligned}$$ where a, b are positive

In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with \(div^2W(\nabla f,\nabla f)=0\) is rigid. Moreover, we show that a four-dimensional radially flat gradient shrinking Ricci soliton with \(\text {div}^2W^\pm (\nabla f,\nabla f)=0\) is either Einstein or a finite quotient of \({\mathbb {R}}^4\), \({\mathbb {S}}^2\times {\mathbb {R}}^2\) or \({\mathbb {S}}^3\times

Chen et al. (Appl Math Lett 17:281–285, 2004) conjectured that for even m, \(R(T_n,W_m)=2n-1\) if the maximum degree \(\varDelta (T_n)\) is small. However, they did not state how small it is. Related to this conjecture, it is also interesting to know which tree \(T_n\) causes the Ramsey number \(R(T_n,W_m)\) to be greater than \(2n-1\) whenever m is even. In this paper, we determine the Ramsey number

Under a previously studied condition on the argument of the Selberg zeta function on the critical line, we reach the critical exponent \(\frac{1}{2}\) in the error term of the prime geodesic theorem for the modular group PSL(2,\( \mathbb {Z}\)) outside a set of finite logarithmic measure. We also prove a conditional prime geodesic theorem of Hejhal’s type in this setting without the latter exclusion

A set of vertices W of a graph G is a resolving set if every vertex of G is uniquely determined by its vector of distances to W. In this paper, the Maker–Breaker resolving game is introduced. The game is played on a graph G by Resolver and Spoiler who alternately select a vertex of G not yet chosen. Resolver wins if at some point the vertices chosen by him form a resolving set of G, whereas Spoiler

In this paper, we prove the global well-posedness of the 3-D generalized incompressible Navier–Stokes equations in critical Besov spaces under a polynomial smallness assumption on the initial data. Moreover, we construct a class of initial data with large vertical component, which satisfies that polynomial condition but cannot satisfy the exponential condition in Liu (2020).

The Balaban index and sum-Balaban index of a connected (molecular) graph G are defined as $$\begin{aligned} J(G)&=\frac{m}{\mu +1} \sum _{uv\in E(G)}\frac{1}{\sqrt{\sigma _{G}(u)\sigma _{G}(v)}}~ \text{ and }\\ SJ(G)&=\frac{m}{\mu +1} \sum _{uv\in E(G)}\frac{1}{\sqrt{\sigma _{G}(u)+\sigma _{G}(v)}}, \end{aligned}$$ respectively, where m is the number of edges, \(\mu \) is the cyclomatic number, \(\sigma

This paper concerns with the geometric study of fixed points of a self-mapping on a metric space. We establish new generalized contractive conditions which ensure that a self-mapping has a fixed disc or a fixed circle. We introduce the notion of a best proximity circle and explore some proximal contractions for a non-self-mapping as an application. Necessary illustrative examples are presented to highlight

In this paper, we consider simple connected weighted graphs in which the edge weights are positive numbers. We obtain several upper bounds on the spectral radius and the signless Laplacian spectral radius of irregular weighted graphs, which extend some known results for irregular unweighted graphs.

We study the existence of radial solutions for the p-Laplacian Neumann problem with gradient term of the type $$\begin{aligned} \left\{ \begin{array}{l} -\Delta _{p}u=f(|x|,u,x\cdot \nabla u)\quad \text {in} ~\varOmega ,\\ \displaystyle \frac{\partial u}{\partial \mathbf{n} }=0\quad \text {on}~ \partial \varOmega , \end{array} \right. \end{aligned}$$ where \(\Delta _pu=\text {div}(|\nabla u|^{p-2}\nabla

We are concerned with the blowup phenomena of a dissipative Dullin–Gottwald–Holm equation which can describe unidirectional propagation of surface waves in a shallow water regime. A “local-in-space” blowup criterion is obtained by delicate analysis on the evolution of some linear combinations of the solution u and its derivative \(u_x\). The result is the improvement of E. Novruzov’s theorem on the

In this paper, we study the Korovkin-type theorem for modified Meyer–König and Zeller operators via A-statistical convergence and power series summability method. The rate of convergence for this new summability methods is also obtained with the help of the modulus of continuity. Further, we establish Voronovskaya-type and Grüss–Voronovskaya-type theorems for A-statistical convergence.

An ideal on \(\mathbb N\) is a family of subsets of \(\mathbb N\) closed under the operations of taking finite unions and subsets of its elements. The \(\mathcal {I}\)-open sets of topological spaces, which are determined by an ideal \(\mathcal {I}\) on \(\mathbb N\) and the topology of the spaces, are a basic concept of ideal topological spaces. However, it encounters some difficulties in the study

The present work is intended to investigate optimal control for time-dependent variational–hemivariational inequalities in which the constraint set depends on time. Based on the existence, uniqueness and boundedness of the solution to the inequality, we deliver two continuous dependence results with respect to the time, and then, an existence result for an optimal control problem is presented. Finally

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