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

Irregularity of a graph is an invariant measuring how much the graph differs from a regular graph. Albertson index is one measure of irregularity, defined as the sum of \(|deg(u)-deg(v)|\) over all edges uv of the graph. Motivated by a recent result on the irregularity of Fibonacci cubes, we consider irregularity polynomials and determine them for Fibonacci and Lucas cubes. These are graph families

A Roman dominating function on a graph G is a function \(f:V(G)\rightarrow \{0,1,2\}\) satisfying the condition that every vertex u for which \(f(u) = 0\) is adjacent to at least one vertex v for which \(f(v) =2\). A Roman dominating function f is called a restrained Roman dominating function if the induced subgraph of G by the vertices with label 0 has no isolated vertex. The weight of a restrained

In this paper, we study the following Chern–Simons–Schrödinger equation $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta u+\omega u+\lambda \Big (\frac{h^{2}(|x|)}{|x|^{2}}+ \int _{|x|}^{+\infty }\frac{h(s)}{s}u^{2}(s)\hbox {d}s\Big )u=g(u) \quad \text{ in }\ {\mathbb {R}}^{2},\\ \displaystyle u\in H_r^1({\mathbb {R}}^{2}), \end{array}\right. } \end{aligned}$$ where \(\omega ,\lambda

In this paper, we introduce semi-doubly stochastic (\({\mathcal {SDS}}\)) operators on \(L^1(X,\mu )\). The Ryff’s theorem extended to sigma-finite measure space using semi-doubly stochastic operators on \(L^1(X,\mu )\).

The Duhamel product for two suitable functions f and g is defined as follows: $$\begin{aligned} (f\circledast g)(x)={\frac{\mathrm{{d}}}{\mathrm{d}x}} {\textstyle \int \limits _{0}^{x}} f(x-t)g(t)\mathrm{{d}}t. \end{aligned}$$ We consider the integration operator J, \(Jf(x)={\textstyle \int \limits _{0}^{x}} f(t)\mathrm{{d}}t\), on the Frechet space \(C^{\infty }\) of all infinitely differentiable

In Lorentz–Minkowski space, we prove that the conjugate surface of a maximal graph over a convex domain is also a graph. We provide three proofs of this result that show a suitable correspondence between maximal surfaces in Lorentz–Minkowski space and minimal surfaces in Euclidean space.

Graph burning is a deterministic discrete-time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number of a graph G is the minimum number of steps in a graph burning process for G. It is shown that the graph burning problem is NP-complete even for trees and path forests. In this paper, we first determine the burning numbers of path forests

We study the existence and nonexistence of global weak solutions to the semilinear parabolic differential inequality $$\begin{aligned} \partial _t u-\Delta u \ge |u|^p,\quad (t,x)\in (0,\infty )\times B^c, \end{aligned}$$ where \(p>1\), B is the closed unit ball in \({\mathbb {R}}^N\) (\(N\ge 2\)) and \(B^c\) is its complement, under the semilinear dynamical boundary conditions $$\begin{aligned} \partial

Let \(K_n-C_{k}\) denote the graph obtained from the complete graph \(K_n\) by deleting k edges of a cycle \(C_k\), that is, a nearly complete graph. In this paper, we completely determine the structure of the sandpile group of \(K_{n}-C_{k}\) for \(3\le k\le n-2\).

In this paper, we introduce a space of \(\theta \)-admissible distributions denoted by \({\mathcal {A}}_\theta ^*\) as well as the notion of \(\theta \)-admissible operators. We study the regularity properties of the classical conditional expectation acting on \({\mathcal {A}}_\theta ^*\) and acting on \({\mathcal {L}}({\mathcal {A}}_\theta ,{\mathcal {A}}_\theta ^*)\) which is the space of linear

Let \(p\ge 1, \ell \in \mathbb {N}, \alpha ,\beta >-1\) and \(\varpi =(\omega _0,\omega _1, \ldots , \omega _{\ell -1})\in \mathbb {R}^{\ell }\). Given a suitable function f, we define the discrete–continuous Jacobi–Sobolev norm of f as: $$\begin{aligned} \Vert f \Vert _{{\scriptscriptstyle \mathsf {s}},{\scriptscriptstyle p}}:= \left( \sum _{k=0}^{\ell -1} \left| f^{(k)}(\omega _{k})\right| ^{p} +

Sums of the form \(\sum _{n\ge 0} (-1)^nq^{(n-1)n/2} x^n \) are called partial theta functions. In his lost notebook, Ramanujan recorded many identities for those functions. In 2003, Warnaar found an elegant formula for a sum of two partial theta functions. Subsequently, Andrews and Warnaar established a similar result for the product of two partial theta functions. In this note, I discuss the relation

In this paper, the Touchard-based Laguerre–Gould–Hopper polynomials are introduced by using operational techniques. We investigate many properties of such polynomials. In particular, generating functions, series definitions, integral representations, and summation formulas are analyzed. Further, we derive some new identities satisfied by these polynomials by using umbral calculus methods.

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition \(0=t_0

In this paper, we present a fast boundary integral equation method for the numerical conformal mapping and its inverse of bounded multiply connected regions onto a disk and annulus with circular slits regions. The method is based on two uniquely solvable boundary integral equations with Neumann-type and generalized Neumann kernels. The integral equations related to the mappings are solved numerically

In this paper, we study some ternary Diophantine equations of the form \(Aa^n+Bb^n=Cc^m\), where \(m \in \{2,3\} \), and \(n\geqslant 7 \) is a prime. In fact, we completely solve some particular cases: \(A=5^{\alpha }, ~B=64,~ C=3\), when \(m=2\); \(A=2^{\alpha },~ B=27, ~C \in \{7,13\}\), when \(m=3\).

Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle. In this regard, not only we obtain new properties in weaving frame theory related to dual frames but also we bring up new approaches for manufacturing pairs of woven frames. Specifically

We show that if the following delay differential equation of rational coefficients $$\begin{aligned} w^k(z)\sum _{\mu =1}^se_\mu (z)w(z+c_\mu )+a(z)\frac{w^{(n)}(z)}{w(z)}= \frac{\sum _{i=0}^pa_i(z)w^i}{\sum _{j=0}^qb_j(z)w^j} \end{aligned}$$ admits a transcendental entire solution w of hyper-order less than one, then it reduces into a delay differential equation of rational coefficients $$\begin{aligned}

Fourth-order tensors play a fundamental role in signal processing, wireless communication systems, image processing, data analysis and higher-order statistics. In this paper, we introduce a Z-identity tensor and establish two Z-eigenvalue inclusion sets for fourth-order tensors, which are sharper than some existing results. Numerical examples are proposed to verify the efficiency of the obtained results

In this paper, we show that the Carathéodory function \(\varphi _{\mathrm{Ne}}(z)=1+z-z^3/3\) maps the open unit disk \(\mathbb {D}\) onto the interior of the nephroid, a 2-cusped kidney-shaped curve, $$\begin{aligned} \left( (u-1)^2+v^2-\frac{4}{9}\right) ^3-\frac{4 v^2}{3}=0, \end{aligned}$$ and introduce new Ma–Minda-type function classes \(\mathcal {S}^*_{\mathrm{Ne}}\) and \(\mathcal {C}_{\mathrm{Ne}}\)

Let G be a locally compact abelian group and \(\Lambda \) be a closed subgroup of the dual group \({\widehat{G}}\). In this paper we investigate modulation preserving operators with respect to \(\Lambda \) and give a characterization of them in terms of modulation-range operators.

The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked numerous new investigations in the theory of formal languages by various researchers, among whom is Şerbănuţă. Recently, a decade-old conjecture by Şerbǎnuţǎ on the M-ambiguity of words has disproved, leading to new possibilities in the study of such words. In this paper, we investigate how selective repeated duplications of

In this paper, we study the existence and concentration of ground state solution for the Choquard equation $$\begin{aligned} \left\{ \begin{array}{ll} \begin{aligned} &{}-\Delta u+V(x)u=\left( \int _{{\mathbb {R}}^N}\frac{A(\epsilon y)|u(y)|^p}{|x-y|^\mu }\mathrm{d}y\right) A(\epsilon x)|u|^{p-2}u~~\text {in}~{\mathbb {R}}^{N},\\ &{}u\in H^1({\mathbb {R}}^N), \end{aligned} \end{array} \right. \end{aligned}$$

In this paper, by the affine analogue of the fundamental theorem for Euclidean planar curves, we classify the affine curves with constant affine curvatures. Note that we use the fully affine group and not the equi-affine subgroup consisting of area-preserving affine transformations. (Caution: much of the literature omits the “equi-” in their treatment.) According to the equivariant method of moving

Let \({\mathscr {A}}=m_1p_1+ \cdots +m_np_n\) be a fat point subscheme of \({\mathbb {P}}^2\), and let \(I({\mathscr {A}})\), which is called a fat point ideal, be its corresponding ideal in \({\mathbb {K}}[{\mathbb {P}}^2]\). In this note, we identify those fat point ideals in \({\mathbb {K}} [{\mathbb {P}}^2]\) for which their Waldschmidt constants are less than 5 / 2.

By introducing new deformations on symbolic Cantor sets and ultrametric spaces, we prove that doubling ultrametric spaces admit bilipschitz embedding into Cantor sets. If in addition the spaces are uniformly perfect, we show that they are quasisymmetrically equivalent to Cantor sets. Moreover, we provide a new proof for a recent work of Heer regarding quasimöbius uniformization of Cantor set.

The 2-distance vertex-distinguishing index \(\chi '_\mathrm{d2}(G)\) of a graph G is the minimum number of colors required for a proper edge coloring of G such that any pair of vertices at distance two have distinct sets of colors. It was conjectured that every subcubic graph G has \(\chi '_{\mathrm{d2}}(G)\le 5\). In this paper, we confirm this conjecture for subcubic graphs with maximum average degree

The adjacent vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that the edge coloring set on any pair of adjacent vertices is distinct. The minimum number of colors required for an adjacent vertex distinguishing edge coloring of G is denoted by \(\chi _{a}'(G)\). It is observed that \(\chi _a'(G)\ge \Delta (G)+1\) when G contains two adjacent vertices of degree \(\Delta

By means of critical point theory, we study the existence and multiplicity of homoclinic solutions of the damped second-order difference equation $$\begin{aligned} \Delta ^{2}u(n-1)-c\Delta u(n-1)-a(n)u(n)+f(n,u(n))=0 ,\quad n\in {\mathbb {Z}}, \end{aligned}$$ where \(c>-1\) is a constant, \(a: {\mathbb {Z}}\rightarrow (0,+\infty )\) and \(f: {\mathbb {Z}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}\)

A finite p-group G is called a NDC-group if \(G'/{G' \cap N}\) is cyclic or \(N/{N \cap Z(G)}\) is cyclic for every normal subgroup N in G. In this paper, first we give some properties of NDC-groups and in particular, we give the order of \(G'Z(G)/Z(G)\) for a NDC-group G so that we could investigate the structure of NDC-groups. Next, some necessary and sufficient conditions for a p-group G whose quotient

In this manuscript, a conjecture related to the estimate on the fifth coefficient of Bazilevič functions is settled for the range \(1\le \alpha \le \alpha ^*(\approx 2.049)\). However, for \(\alpha >\alpha ^*\), a non-sharp bound on the same is also derived. At the end of this manuscript, sharp upper bound on the functional \(|a_2a_3-a_4|\) is also obtained.

In this paper we give an estimate for the difference between the moduli of two roots of a polynomial with integer coefficients in terms of its degree and Mahler measure. An application of this estimate implies a stronger version of a recent result of Gómez Ruiz and Luca. In passing, we prove an estimate for the distance between two algebraic numbers in terms of their degrees and Mahler measures. For

Using the notion of the integral weight, we characterize all entire functions that transform a Bloch-type space \({\mathcal {B}}^{\mu _1}\) into another space of the same kind \({\mathcal {B}}^{\mu _2}\) by superposition for very general weights \(\mu _1\) and \(\mu _2\), satisfying a growth condition.

Using the Gallagher–Koyama approach, we reduce the exponent in the error term of the prime geodesic theorem for real hyperbolic manifolds with cusps.

We establish some inequalities between the global double Roman domination number \(\gamma _\mathrm{gdR}(G)\) and double Roman domination number \(\gamma _\mathrm{dR}(G)\) of graphs G. We also completely characterize the trees T with \(\gamma _\mathrm{gdR}(T)=\gamma _\mathrm{dR}(T)+k\) for \(k\in \{0,1,2,3\}\), which partially answer an open problem posed by Shao et al. (J Discrete Math Sci Cryptogr

The greatest power of a prime p dividing the natural number n will be denoted by \(n_p\). For a set of primes \(\pi \) and a natural number n we will denote \(n_{\pi }=\prod _{p\in \pi }n_p\). Let G be a finite group with trivial center, and \(p,q>5\) be distinct prime divisors of |G|. We prove that if for every nonunity conjugacy classes size \(\alpha \), it is true that \(\alpha _{\{p,q\}}\in \{p^n

A subgroup H of a finite group G is weakly supplemented in G if there exists a proper subgroup K of G such that \(G=HK\). In the paper, we present some sufficient and necessary conditions for a finite group to be p-nilpotent and solvable by using some weakly supplemented minimal subgroups. As applications, we extend some known results.

The paper is concerned with the study of some partial neutral functional integrodifferential equations with nondense domain. Using the integrated resolvent operator theory, we derive some results concerning the existence and regularity of solutions. Finally, an example is given to illustrate our theory.

In this paper, we investigate the existence and precise expression form of entire solutions to the two certain Fermat-type differential–difference equations. We also give several examples to supplement our results. Moreover, our results generalize some previous results.

We study a pursuit differential game of many pursuers and one evader in the plane. We are given a compact convex subset of \({\mathbb {R}}^2\), and the pursuers and evader move in this set. They cannot leave this set during the game. Control functions of players are subject to coordinate-wise integral constraints. If the state of a pursuer coincides with that of evader at some time, then we say that