Search

In the present paper, we obtain a Halanay inequality on time scales with unbounded coefficient for a dynamic problem, which extends a result of Wen et al. (J. Math. Anal. Appl., 347 (2008), 169–178.) to the inequality of integral type on time scales. Moreover, we list two dynamic problems to which the Halanay inequality obtained above can be applied and prove the zero solution of two delay dynamic problems are asymptotically stable. Moreover, it is worth mentioning that the Halanay inequality obtained in the present paper is more precise than the results in [3, 14, 17].

An open problem proposed by Rhoades is the following. Is there a contractive condition which guarantees the existence of a fixed point, but does not require the mapping to be continuous at the point? In this paper, we generalize a celebrated result of Eshaghi et al., [On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), 569–578], which allows us to find a new solution to this open problem. Furthermore we show that a claim of the aforementioned paper, that Banach’s fixed point theorem cannot be applied in their application, is incorrect. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresponding functional equation.

A graph Γ is called a bi-circulant if it admits a cyclic group as a group of automorphisms acting semiregularly on the vertices of Γ with two orbits. The characterization of tetravalent edgetransitive bi-circulants was given in several recent papers. In this paper, a classification is given of connected tetravalent vertex-transitive bi-circulants of order twice an odd integer.

The main motive of the paper is to look on rectifying and osculating curves on a smooth surface. In this paper we find the normal and geodesic curvature for a rectifying curve on a smooth surface and we also prove that geodesic curvature is invariant under the isometry of surfaces such that rectifying curves remain. We find a sufficient condition for which an osculating curve on a smooth surface remains invariant under isometry of surfaces and also we prove that the component of the position vector of an osculating curve α(s) on a smooth surface along any tangent vector to the surface at α(s) is invariant under such isometry.

Let $$\mathcal{\widetilde{O}}$$ (B) be the category of (open) subcategories of a topological groupoid B: In this paper we study Cat-valued sheaves over category $$\mathcal{\widetilde{O}}$$ (B): The paper introduces a notion of categorical union, such that the categorical union of subcategories is a subcategory. We use this definition of categorical unions to define a categorical cover of a topological category. Instead of assuming a Grothendieck topology, we define Cat-valued sheaves in terms of the categorical cover defined in this paper. The main result is the following. For a fixed category C, the categories of local functorial sections from B to C define a Catvalued sheaf on $$\mathcal{\widetilde{O}}$$ (B): Replacing C with a categorical group G; we find a CatGrp-valued sheaf on $$\mathcal{\widetilde{O}}$$ (B): We also relate and distinguish our construction with the notion of stacks.

The aim of the paper is to investigate the boundary value problem of the evolution equation Lu = K (x,t) ut - Δu + a (x,t) u = f (x,t). The characteristic property of this type of equations is the failure of the Petrovski’s “A” condition when coefficients are constant [1]. In this case, Cauchy problem is incorrect in the sense of Hadamard. Hence in this paper, the space, guaranteeing the correctness of the boundary value problem in the sense of Hadamard, is selected by adding some additional conditions to the coefficients of the equation.

Let M ⊑ B(X) be an algebra with nontrivial idempotents or nontrivial projections if M is a *-algebra and ZM = ℂI. In this paper, the notion of (strong) 2-local Lie automorphism normalized property is introduced and it is proved that if M has 2-local Lie automorphism normalized property and Φ: M → M is an almost additive surjective 2-local Lie isomorphism with idempotent decomposition property, then → = Ψ + τ, where Ψ is an automorphism of M or the negative of an anti-automorphism of M and τ is a homogenous map from M into ℂI. Moreover, it is proved that nest algebras on a separable complex Hilbert space II with dimII >2 and factor von Neumann algebras on a separable complex Hilbert space H with dimH > 2 have strong 2-local Lie automorphism normalized property.

In this paper, we inspect the global asymptotic stability (GAS) of Ebola–epidemic using a modified Susceptible-Infected-Deceased-Pathogen (SIDP) model with perturbation. The feasible region is obtained, and we determine the basic reproduction number using the next-generation matrix method. The GAS of the disease-free and endemic equilibria are discuss and provide parameter conditions for which the stability exists. We show theoretically that the contaminated environmental Ebola human–deceased transmission model is GAS with and without probability. Numerical simulation to support our theoretical findings are presented.

In this paper, we propose a new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems without pseudomonotonicity of the bifunction f in a real Hilbert space. When setting the solution of dual equilibrium problem is nonempty, we obtain a strong convergence theorem which is generated by the iterative scheme. Moreover, we also receive a new linesearch iterative scheme for finding a solution of the split equilibrium problem in suitable assumptions, and report some numerical results to illustrate the convergence of the proposed scheme.

In this paper, we consider the title simultaneous Pell equations, where $$a\ge 2,b \ge 1$$ are positive integers and p is an odd prime. Particularly, we give all the solutions when $$2\le a\le 1000$$ and $$1\le b\le 1000$$ .

In recent years, researchers have studied the use of different iteration processes from fixed point theory for the generation of complex fractals. Examples are the Mann, the Ishikawa, the Noor, the Jungck-Mann and the Jungck-Ishikawa iterations. In this paper, we present a generalisation of complex fractals, namely Mandelbrot, Julia and multicorn sets, using the Jungck-CR implicit iteration scheme. This type of iteration does not reduce to any of the other iterations previously used in the study of complex fractals; thus, this generalisation gives rise to new fractal forms. We prove a new escape criterion for a polynomial of the following form zm − az + c, where a, c ∈ ℂ, and present some graphical examples of the obtained complex fractals.

This paper discusses the antiperiodic boundary value problem for first-order impulsive differential inclusions. By using Martelli’s fixed point theorem with upper and lower solutions method, we establish the existence results.

In this paper, we study the restricted injective dimensions of complexes. Some new characterizations of the restricted injective dimensions are obtained. In particular, it is shown that the restricted injective dimensions can be computed in terms of the restricted injective resolutions. As applications, we get some results on the behavior of the restricted injective dimensions under change of rings. In addition, a characterization of almost Cohen-Macaulay ring is obtained.

In this paper, we carry the obtained results for a certain class of Moufang-Klingenberg planes co-ordinatized by the local alternative ring of dual numbers, over to a class of Moufang-Klingenberg planes coordinatized by the plural algebra of order m which is a local alternative ring. So, we show that its collineation group is transitive on quadrangles and therefore that coordinatization of the planes is independent of the choice of the coordinatization quadrangle. Moreover, by a conjugacy class we discuss the definition of cross-ratio of four distinct points on the projective lines for the planes.

In this paper, a new extension for Delannoy numbers is presented. Also, several identities such as generating function and recurrence relations for these numbers are obtained.

In this paper, we establish some results on algebraic polynomials in the complex plane that are inspired by some classical Bernstein-type inequalities that relate the sup-norm of a polynomial to that of its derivative on the unit circle. The obtained results relate the Lγ-norm of the polar derivative and the polynomial.

The author in [7] conjectured the following inequality; If a and b are nonnegative real numbers with a + b = 1/2, then the inequality 1/2 ≤ a(2b)k+ b(2a)k ≤ 1 holds for 0 ≤ k ≤ 1. In this paper, we shall prove the conjecture affirmatively and give the upper and lower estimation of the power exponential functions ab + ba for the nonnegative real numbers a and b with a + b = 2. Moreover, we pose some inequalities with power exponential functions.

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. Let p be a prime. In this paper, we proved that there is only one connected heptavalent symmetric graphs of order 40p, it is a vertex primitive graph of order 40.3 = 120 admitting S7 as its full automorphism group.

Let ℌ be a Hilbert space, and let K(ℌ) be the C*-algebra of compact operators on ℌ. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert K(ℌ)-module by employing the Birkhoff-James orthogonality. Among other things, we present a characterization of transitive relation of the norm-parallelism for elements in a certain Hilbert K(ℌ)-module. We also give some characterizations of the Schatten p-norms and the operator norm-parallelism for matrices.

In this paper, after introducing the notion of relative ideals in ordered semigroups, some important properties of these ideals are studied. Then notions of relatively prime and relatively weakly prime ideals are defined and some vital results have been proved. We also find some conditions under which relative ideals become left, right and two-sided ideals in any regular ordered semigroup. Finally, the notion of maximal and minimal relative ideals are introduced and some of their properties are studied.

In this paper we investigate the compact operators under Orlicz function, named noncommutative Orlicz sequence space (denoted by Sϕ(ℌ)), where ℌ is a complex, separable Hilbert space. We will show that the space generalizes the Schatten classes Sp(ℌ) and the classical Orlicz sequence space respectively. After getting some relations of trace and norm, we will give some operator inequalities, such as Holder inequality and some other classical operator inequalities. Also we will give the dual space and reflexivity of Sϕ(ℌ) which generalizes the results of Sϕ(ℌ). Finally, as an application, we will show that the Toeplitz operator $${T_{1 — {{\left| z \right|}^2}}}$$ on the Bergman space $$L_\alpha ^2\left(\mathbb{R} \right)$$ belongs to some Sϕ(ℌ), and the norm satisfies $$1 = \sum\limits_{n \ge 0} {\varphi \left({{1 \over {\left({n + 2} \right){{\left\| {{T_{1 — {{\left| z \right|}^2}}}} \right\|}_\varphi}}}} \right)} $$ . Especially, if ϕ(T) = ∣T∣p, p > 1, the norm is $${\left\| {{T_{1 — {{\left| z \right|}^2}}}} \right\|_p} = {\left[{\sum\limits_{n \ge 0} {{1 \over {{{\left({n + 2} \right)}^p}}}}} \right]^{{1 \over p}}} = {\left({\zeta \left(p \right) — 1} \right)^{{1 \over p}}}$$ , where ζ(p) is the Riemann function.

In this paper, we define the notions of centrally-extended reverse derivations and centrally-extended generalized reverse derivations and discuss the relationship between these mappings and the reverse derivations as well as the generalized reverse derivations. Also, we give some commutativity results.

Let $$\mathfrak{F}$$ denote a class of groups. A maximal subgroup M of G is called $$\mathfrak{F}$$ -abnormal provided G/MG ∉ $$\mathfrak{F}$$ . We say that (K, H) is an $$\mathfrak{F}$$ -abnormal pair of G provided K is a maximal $$\mathfrak{F}$$ -abnormal subgroup of H. Let Σ = {G0 ≤ G1 ≤ G2 ≤ … ≤ Gn} be a subgroup series of G. A subgroup H of G is said to be Σ- $$\mathfrak{F}$$ -embedded in G if H either covers or avoids every $$\mathfrak{F}$$ -abnormal pair (K, H) such that Gi−1≤ K < H ≤ Gi for some i ∈ {0, 1, …, n}. In this paper, some new characterizations of p-supersoluble and p-soluble are given by discussing the properties of Σ- $$\mathfrak{F}$$ -embedded of subgroups.

In this paper, in considering aspects of the geometric mean sequence, offers new results connecting generalized Tribonacci and third-order Horadam numbers which are established and then proved independently.

A Grassmannian fusion frame is an optimal configuration of subspaces of a given vector space, that are useful in some applications related to representing data in signal processing. Grassmannian fusion frames are robust against noise and erasures when the signal is reconstructed. In this paper, we present an approach to construct optimal Grassmannian fusion frames based on a given Grassmannian frame. We also analyse an algorithm for sparse fusion frames which was introduced by Calderbank et al. and present necessary and sufficient conditions for the output of that algorithm to be an optimal Grassmannian fusion frame.

Let $$H(p,tK_{1,m}^ * )$$ be a connected unicyclic graph with p + t(m + 1) vertices obtained from the cycle Cp and t copies of the star K1, m by joining the center of K1, m to each one of t consecutive vertices of the cycle Cp through an edge, respectively. When t = p, the graph is called a dandelion graph and when t ≠ p, the graph is called a broken dandelion graph. In this paper, we prove that the dandelion graph $$H(p,pK_{1,m}^ * )$$ and the broken dandelion graph $$H(p,tK_{1,m}^ * )$$ (0 < t < p) are determined by their Laplacian spectra when m ≠ 2 and p is even.

Let λ be a reflexive Banach sequence lattice and X be a Banach lattice. In this paper, we show that the positive injective tensor product $$\lambda {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over \otimes } _{\left| \varepsilon \right|}}X$$ is a Grothendieck space if and only if X is a Grothendieck space and every positive linear operator from λ* to X** is compact.

In this paper we discuss a new approach to discuss Stokes flow past porous bodies of arbitrary shape using the Darcy [1] model and Saffman [2] boundary conditions.

In this paper, we characterize the *-Jordan semi-triple derivable mappings (i.e. a mapping Φ from * algebra $$\mathcal{A}$$ into $$\mathcal{A}$$ satisfying Φ(AB*A) = Φ(A)B*A + AΦ(B)*A + AB* Φ(A) for every A, B $$\mathcal{A}$$ ) in the finite dimensional case and infinite dimensional case.

In this paper, we consider a class of fractional Sturm-Liouville problems, in which the second order derivative is replaced by the Caputo fractional derivative. The Laplace transform method is applied to obtain algebraic equations. Then, the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems are obtained numerically. We provide a convergence analysis for given method. Finally, the simplicity and efficiency of the numerical method is shown by some examples.

This paper describes the construction of a natural Hermitian holomorphic line bundle on the stratified moduli space of complex representations of a finite quiver, which are semistable with respect to a fixed rational weight and have a fixed type. It is shown that the curvature of this Hermitian line bundle on each stratum of the moduli space is essentially the Kahler form of that stratum.

In this paper we study the a. e. exponential strong (C, 1, 0) summability of of the 2-dimensional trigonometric Fourier series of the functions belonging to L (log+L)2.

In this paper, we study reiterated homogenization problems for equations −div(A(x/e, x/e2)∇ue) = f (x). We introduce auxiliary functions and obtain the representation formula satisfied by ue and homogenized solution u0. Then we utilize this formula in combination with the asymptotic estimates of Neumann functions for operators and uniform regularity estimates of solutions to obtain convergence rates in Lp for solutions as well as gradient error estimates for Neumann problems.

Let G be a connected graph with n vertices, m edges and having distance signless Laplacian eigenvalues ρ1≥ ρ2 ≥ … ≥ ρn≥ 0. For any real number α ≠ 0, let $${m_\alpha }\left( G \right) = \sum\nolimits_{i = 1}^n {\rho _i^\alpha } $$ be the sum of αth powers of the distance signless Laplacian eigenvalues of the graph G. In this paper, we obtain various bounds for the graph invariant mα(G), which connects it with different parameters associated to the structure of the graph G. We also obtain various bounds for the quantity DEL(G), the distance signless Laplacian-energy-like invariant of the graph G. These bounds improve some previously known bounds. We also pose some extremal problems about DEL(G).

In this paper, we define the concepts of ϕ-contraction in probabilistic generalized Menger space. We prove that ϕ-contraction mappings in probabilistic generalized Menger space have a unique fixed point. Also we prove some fixed point theorems related this concept. Some examples are given to support the obtained results.

In this paper, we deal with the Schrodinger’s problems, in the first part we study the theoretical side, we show the existence of at least three weak solutions, our main tools are based on variational inequalities, more precisely, using the three critical points theorem due to Ricceri, existence and multiplicity results are established. In the second part, we are interested in the application side, more exactly, we examine some computational problems on the discretization of finite elements of the p(x)-Laplacian, we propose a quasi-Newton minimization approach for the solution, our numerical tests show that these algorithms are able to resolve the problems with p(x)-Laplacian, for different values of p(x).

In this paper, we are interested in considering the following singular elliptic problem with concaveconvex nonlinearities $$\left\{ {\begin{array}{*{20}{l}} { - \Delta u - \frac{\mu }{{|x{|^2}}}u = f(x)|u{|^{p - 2}}u + g(x)|u{|^{q - 2}}u,}&{in\;\;\Omega \backslash \{ 0\} ,} \\ {u = 0,}&{on\;\;2\Omega ,} \end{array}} \right.$$ where Ω ⊂ ℝN(N ≥ 3) is a smooth bounded domain with 0 ∈ Ω, $$0 < \mu < \bar\mu = \frac{{{{(N - 2)}^2}}}{4}$$, 1 < q < 2 < p < 2* and $$2* = \frac{{2N}}{{N - 2}}$$ is the Sobolev critical exponent, the coefficient functions f, g may change sign on Ω. By the Nehari method, we obtain two solutions, and one of them is a ground state solution. Under some stronger conditions, we point that the two solutions are positive solutions by the strong maximum principle.

In this paper we prove some normality criteria for a family of meromorphic functions, which involves the zeros of certain differential polynomials generated by the members of the family., This work has been communicated for publication. arXiv admin note: text overlap with arXiv:1305.6214

In this paper, we investigate two optimization problems related to a quasilinear elliptic equation with p-Laplacian, logistic-type growth rate function such that the admissible set is a class of rearrangements of a fixed function. Under some suitable assumptions, we prove existence and representation of the maximizers and existence, uniqueness and representation of the minimizer. Also, when the domain of the equation is a ball, we show that the maximizer is unique and symmetric.

In this paper we present a method to generate new fractal interpolation curves. We ensure that attractors of nonlinear iterated function systems (IFSs) constructed by Geraghty contractions are graphs of some continuous functions which interpolate the given data. In particular, we give an explicit illustrative example to demonstrate the effectiveness of obtained results. Concerning IFSs, our methods and results extend known results from the literature.

Let Tl(n) denote the number of l-regular partition triples of n. In this paper, we consider the arithmetic properties of T7(n). An infinite family of congruences modulo powers of 7 and several congruences modulo 7 are established. For instance, we prove that for all n ≥ 0 and α ≥ 1, $${T_7}\left( {{7^{2\alpha }}n + \frac{{3 \times {7^{2\alpha }} - 3}}{4}} \right) \equiv 0\;(\bmod {7^\alpha })$$

Let R be a finite commutative ring with nonzero identity and U(R) be the set of all units of R. The graph Γ is the simple undirected graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u in U(R) such that x + uy is a unit in R. Also, $$\overline{\Gamma}$$ denotes the complement of Γ. In this paper, we find the domination number γ of Γ as well as $$\overline{\Gamma}$$ and characterize all γ-sets in Γ and $$\overline{\Gamma}$$. Also, we obtain the bondage number of Γ. Further, we obtain the values of some domination parameters like independent, strong and weak domination numbers of $$\overline{\Gamma}$$.

The concept of the Schur multiplier of a Lie algebra was introduced by Batten et al. (1996). This concept was extended to that of a c-nilpotent multiplier of a Lie algebra, and then further extended to a theory of a c-nilpotent multiplier of a pair of Lie algebras, by the author and others. In this paper we present some new inequalities for the dimension of the c-nilpotent multiplier of a pair of Lie algebras. We also give a necessary and sufficient condition for the c-nilpotent multiplier of a pair of Lie algebras to embed into the c-nilpotent multiplier of their quotient. Finally we provide a sufficient condition for the c-nilpotent multiplier of a pair of Lie algebras to be finite dimensional.

In this paper, we study the dilation of g-frame generators and the dual g-frame generators for an abstract wavelet system. By the semi-orthogonality of a special unitary system, we prove the dual g-frame generators can be dilated to a pair of dual g-Riesz basis generators for some larger Hilbert space. We first show the existence of the dual g-frame generators with the same structure of a g-frame generator for a unitary system. We then get a sufficient and necessary condition for the existing of the dual g-frame generators for unitary groups on a subspace.

Let Tc := D(x - c)((x - c)D + 2II) be a second-order linear differential operator, where c is an arbitrary complex number, $$D: = \frac{d}{{dx}}$$ and II represents the identity on the linear space of polynomials with complex coefficients. The aim of this paper is to describe all of the Tc-classical orthogonal polynomials. Two canonical situations appear: the Laguerre $$\{L_n^{(2)}\}_{n\geq0}$$ and the Jacobi $$\{P_n^{(\alpha-2,2)}\}_{n\geq0}$$

In this paper, we prove an analogue of a time-frequency localization theorem for orthonormal sequences in $$L_{{\mu _\alpha }}^2({\mathbb{R}_ + })$$. As a consequence, we obtain an analogue of Shapiro’s Umbrella theorem for the Hankel-Gabor transform Vg. We also prove a mean dispersion inequality for Vg. Finally, we get a strong version of the uncertainty inequality for orthonormal sequences of $$L_{{\mu _\alpha }}^2({\mathbb{R}_ + })$$.

Let X be a K3 surface and let H be a very ample line bundle on X of sectional genus g ≤ 9. In this paper, we characterize the destabilizing sheaf of the Lazarsfeld-Mukai bundle EC,Z of rank 2 associated with a smooth curve C ∈ |H| and a base point free divisor Z on C with h0(OC(Z)) = 2, in the case where it is not H-slope stable.

In this paper we completely characterize when the commutator and semi-commutator of two monomial-type Toeplitz operators on the Fock space over ℂn have finite rank. In sharp contrast to Bergman space over the unit ball case, it turns out that there are many other cases on the Fock space for (semi-)commuting Toeplitz operators.

In this paper we study the following fourth-order elliptic equations of Kirchhoff type $$\Delta^2u - (a+b\int_{\mathbb{R}^N} | \triangledown u|^2dx)\Delta u + V(x)u=f(x, u), \;\;x\in\mathbb{R}^N,$$ where Δ2 := Δ(Δ) is the biharmonic operator, a, b > 0 are constants, V ∈ C(ℝN, ℝ) and f ∈ C(ℝN × ℝ, ℝ). Under some appropriate assumptions on V(x) and f(x, u), new results on the existence of infinitely many high energy solutions for the above equation are obtained via Symmetric Mountain Pass Theorem.

In this paper, we study the following Choquard equations with small perturbation f$$-\Delta u + V(x)u = (I_\alpha * |u|^p)|u|^{p-2}u+f(x), x\in \mathbb{R}^N.$$ where N ≥ 3 and Iα denotes the Riesz potential. As is known that the above equation has a ground state uα and a bound state vα by fibering maps (see [22] or [23]), our aim is to show that for fixed $$p \in (1,\frac{N}{N-2})$$, uα and vα converge to a ground state and a bound state of the limiting local problem respectively, as α → 0.