Some results between the properties of strongly topological gyrogroups and the properties of their remainders are established. In particular, if a strongly topological gyrogroup G is non-locally compact and G has a first-countable remainder, then \(\chi (G)\le \omega _{1}\), \(\omega (G)\le 2^{\omega }\) and \(|bG|\le 2^{\omega _{1}}\). Moreover, it is proved that the property of paracompact p-space

We provide optimality conditions in terms of Michel–Penot’s directional derivatives in locally Lipschitz vector equilibrium problem with set, inequality and equality constraints. Using this derivatives, we introduce three constraint qualifications (CQ1), (CQ1-s) and (CQ2-s), and then, we establish primal and dual Karush–Kuhn–Tucker necessary optimality conditions for a local weak efficient solution

The authors give sufficient conditions for the existence of at least three classical solutions to the nonlinear impulsive fractional boundary value problem with a p-Laplacian and Dirichlet conditions $$\begin{aligned} {\left\{ \begin{array}{ll} D^{\alpha }_{T^-}\varPhi _p(^cD^{\alpha }_{0^+}u(t))+|u(t)|^{p-2}u(t)= \lambda f(t,u(t)), &{}t\ne t_j,\ \ t\in (0,T),\\ \varDelta (D^{\alpha -1}_{T^-}\varPhi

In this article, we analyze a class of conformable non-instantaneous impulsive differential equations and obtain their solutions using the non-instantaneous impulsive Cauchy matrix. We derive a suitable formula for the solution of conformable nonhomogeneous linear non-instantaneous impulsive perturbed problems and we study its exponential stability. We also investigate nonlinear non-instantaneous impulsive

In this paper, we study the generalized quasilinear Schrödinger equation $$\begin{aligned} -\text {div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=(I_{\alpha }*|u|^{p})|u|^{p-2}u,\ \ \ x\in {{\mathbb {R}}}^N, \end{aligned}$$ where \(N\ge 3\), \(0<\alpha

In this paper, it is proved that the finite group G is solvable if \(\mathrm {cod}(\chi )< \chi ^{\alpha }(1)\) for any nonlinear irreducible character \(\chi \) of G where \(\alpha \approx 1.8876\).

In this paper, we prove the existence of infinitely many solutions for the following nonperiodic fractional Hamiltonian system $$\begin{aligned} \left\{ \begin{array}{l} _{t}D_{\infty }^{\alpha }(_{-\infty }D_{t}^{\alpha }u)(t)+L(t)u(t)=\nabla W(t,u(t)),\ t\in {\mathbb {R}}\\ u\in H^{\alpha }({\mathbb {R}}), \end{array}\right. \end{aligned}$$ where \(_{-\infty }D_{t}^{\alpha }\) and \(_{t}D^{\alpha

Clapp and Puppe (J. Reine Angew Math 418:1–29, 1991) proved that, if G is a torus or a p-torus, X is a path-connected G-space and Y is a finite-dimensional G-CW complex without fixed points, under certain cohomological conditions on X and Y, there is no equivariant map from X to Y. Also, Biasi and Mattos (Bull Braz Math Soc New Ser 37:127–137, 2006) proved that, again under certain cohomological conditions

A set S of vertices of a connected graph G is a doubly connected dominating set (DCDS) if every vertex not in S is adjacent to some vertex in S and the subgraphs induced by S and \(V-S\) are connected. The doubly connected domination number \(\gamma _{cc}(G)\) is the minimum size of such a set. The doubly connected domination subdivision number \(\hbox {sd}_{\gamma _{cc}}(G)\) is the minimum number

Let p(z) be a polynomial of degree n with zero of multiplicity s at the origin and the remaining zeros in \(|z|\ge k\) or in \(|z|\le k\), \(k>0\). In this paper, first we obtain inequalities about the dependence of |p(Rz)| on |p(rz)|, where \(|z|=1\), for \(r^2\le Rr\le k^2\) or \(k^2\le Rr \le R^2\). Further, another similar inequality for the class of polynomials having all zeros in \(|z|\ge k\)

In this paper, we study the extended trust-region subproblem with two linear inequality constraints (2-eTRS). Without any assumptions on the linear constraints, it is shown that its global optimal solution can be found by solving at most four trust-region subproblems. Finally, the efficiency of the proposed algorithm is compared with the branch and bound algorithm of Beck et al. (J Glob Optim 69(2):309–342

These are slightly expanded notes of lectures given in April 2019 at the Isfahan school and conference on representations of algebras. We recall the formalism of derived categories and functors and survey invariance results for the Hochschild (co)homology of differential graded algebras and categories.

In this paper, we introduce the unbalanced crown graphs \({\mathcal {C}}_{m,n}\), and compute all graded Betti numbers of edge ideals of these graphs in terms of associated numerical data. As a consequence, we determine the regularity and the projective dimension of edge ideals of these graphs. Also, the Hilbert series of the cover ideals of these graphs is obtained.

This paper is devoted to study the geometry of vector bundle manifolds equipped with spherically symmetric metrics. We will compute the curvature tensor, the sectional curvature, the Ricci curvature tensor and the scalar curvature. We will then characterize spherically symmetric metrics of constant sectional curvature. Moreover, we will establish some rigidity results regarding the scalar curvature

For a Hausdorff zero-dimensional topological space X and a totally ordered field F with interval topology, let \(C_c(X,F)\) be the ring of all F-valued continuous functions on X with countable range. It is proved that if F is either an uncountable field or countable subfield of \({\mathbb {R}}\), then the structure space of \(C_c(X,F)\) is \(\beta _0X\), the Banaschewski Compactification of X. The

Let \({\mathcal {M}}\) be a factor von Neumann algebra on a complex separable Hilbert space \({\mathcal {H}}\) with \(\dim {\mathcal {M}}>1\). We proved that if \(\varPhi :{\mathcal {M}}\rightarrow {\mathcal {M}}\) is a second nonlinear mixed Jordan triple derivable mapping, that is, $$\begin{aligned} \varPhi (A\circ B\bullet C)=\varPhi (A)\circ B\bullet C+A\circ \varPhi (B)\bullet C+A\circ B\bullet

A new formula expressing explicitly the integrals, antidifference, of discrete orthogonal polynomials \(\{P_{n}(x):\) Hahn, Meixner, Kravchuk, and Charlier\(\}\) of any degree in terms of \(P_{n}(x)\) themselves are proved. Other formulae for the expansion coefficients of general-order difference integrations \(\nabla ^{-s}f(x),\,\Delta ^{-s}f(x),\) \(\nabla ^{-s}[x^{\ell }\nabla ^{q}f(x)]\,\) and

Cluster structures have been established on numerous algebraic varieties. These lectures focus on the Grassmannian variety and explain the cluster structures on it. The tools include dimer models on surfaces, associated algebras, and the study of associated module categories.

In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as an introduction to recent work by Barnard–Carroll–Zhu and Demonet–Iyama–Reading–Reiten–Thomas.

The class of close-to-convex functions are univalent and so its subclasses. For normalised analytic functions defined on the unit disk, four subclasses of close-to-convex functions are considered and Hermitian-Toeplitz determinants for these classes are investigated. All the results presented in this article are sharp.

The purpose of this paper is to study the existence of mild solutions and approximate controllability for measure driven evolution system with nonlocal conditions. First, we obtain the existence of mild solutions and approximate controllability for the concerned problem by constructing new Green’s function and control function involving Gramian controllability operator. This research relies on Schauder’s

Let \(\mathcal {A}\) be a unital algebra and \(\mathcal {M}\) be a unital \(\mathcal {A}\)-bimodule. We characterize the linear mappings \(\delta \) and \(\tau \) from \(\mathcal {A}\) into \(\mathcal {M}\), satisfying \(\delta (A)B+A\tau (B)=0\) for every \(A,B \in \mathcal {A}\) with \(AB=0\) when \(\mathcal {A}\) contains a separating ideal \(\mathcal {T}\) of \(\mathcal {M}\), which is in the algebra

In this paper, we show that a matrix algebra \(\mathcal {LM}_{I}^{p}(\mathbb {C})\) is pseudo-contractible if and only if I is finite. In addition, for each non-empty set I, we show that \(\mathcal {LM}_{I}^{p}(\mathbb {C})\) is always pseudo-amenable. Amenability, approximate biprojectivity and approximate biflatness of upper triangular algebras with respect to \(\mathcal {LM}_{I}^{p}(\mathbb {C})\)

We establish relations of Gorenstein homological properties of modules and rings linked by a fixed quasi-Frobenius bimodule. Particularly, let \(R\subset S\) be a strongly separable quasi-Frobenius extension. The left Gorenstein global dimensions and the left finitistic Gorenstein projective dimensions of rings S and R are equal. Moreover, R is left-Gorenstein (Cohen–Macaulay finite, Cohen–Macaulay

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y, respectively, and \( \rho , \tau :I\longrightarrow A\), \( S, T :I\longrightarrow B \) be maps on a non-empty set I whose ranges are closed under multiplication and contain exponential functions. In this paper, we first show that if \(\Vert S(p)\Vert _{Y}=\Vert \rho (p)\Vert _{X}\), \(\Vert T(p)\Vert _Y=\Vert \tau (p)\Vert

The present paper makes a research on the optimal cash holding problem in the continuous time under a class of utility functions, and verifies that the limit of the optimal cash holding strategy under a class of utility functions is equal to the optimal cash holding strategy under the power utility function. An empirical analysis is stated at the end of this paper.

A set D of vertices in a graph G is a locating-dominating set if for every two vertices u, v of \(V-D\) the sets \(N_{G}(u)\cap D\) and \(N_{G}(v)\cap D\) are non-empty and different. The locating-domination number \(\gamma _{L}(G)\) is the minimum cardinality of a locating-dominating set of G. A graph G is \(\gamma _{L}\)-dot-critical if contracting any edge of G decreases its locating-domination

Let (a, b, c) be a primitive Pythagorean triple. Set \(a = m^2-n^2 \), \(b=2mn\) , and \(c=m^2+n^2\) with m and n positive coprime integers, \( m>n \) and \(m \not \equiv n \pmod 2 \). A famous conjecture of Jeśmanowicz asserts that the only positive integer solution to the Diophantine equation \(a^x+b^y=c^z\) is \((x,y,z)=(2,2,2).\) A solution \((x,y,z) \ne (2,2,2)\) of this equation is called an

In this addendum, an example is given to show that there is an error in the proof of Theorem 4.17 in “Semi-Rothberger and related spaces” (Sabah and Khan in Bull Iran Math Soc 43(6):1969–1987, 2017). Then, the author proves the correct version of this theorem.

An undirected graph \(G=(V,A)\) by a set V of n nodes, a set A of m edges, and a set \(D\subseteq V\) consists of h demand nodes are given. Peeters (Eur J Oper Res 104:299–309, 1998) presented the absolute 1-center problem, which finds a point x placed on nodes or edges of the graph G with the property that the cost distance from the most expensive demand node to x is as cheap as possible. In the absolute

Let G be a locally compact abelian group, \(\phi \) be a topological isomorphism on G, and L be a uniform lattice in G. We provide a development of the \(L^{ 1} (G/\phi (L)) \) function-valued product on \( L^{ p} (G)\) called \((\phi (L),p)\)-bracket product, where \( 1

In this paper, we study the concomitants of m-generalized order statistics (m-GOS) from the bivariate Cambanis family as an extension of several recent papers. This study can also be applied to the model of m-dual generalized order statistics (m-DGOS) as a parallel model of m-GOS. Some information measures, namely the Shannon entropy, Kullback-Leibler (KL) distance, and Fisher information number (FIN)

In this article, we introduce generalized reverse derivations in semirings and present conditions that lead to the commutativity of additively inverse semirings.

In this essay, a method is presented for approximating the optimal control problem (OCP) with nonlinear delay differential equations using global collocation at Legendre–Gauss–Radau points. This OCP models the spread of the computer virus. The operational matrices and collocation method together with hybrid Legendre polynomials and block-pulse functions are applied to discretize the model and convert

For a connected graph \(G=(V, E)\) of order at least two, a total monophonic set of a graph \(G\) is a monophonic set \(S\) such that the subgraph \(G[S]\) induced by \(S\) has no isolated vertices. The minimum cardinality of a total monophonic set of \(G\) is the total monophonic number of \(G\) and is denoted by \({m}_{t}(G)\). The number of extreme vertices and support vertices of \(G\) is its extreme-support

In this manuscript, we will study \({\tilde{o}}\)-convergence in (partially) ordered vector spaces and we will study a kind of convergence in a vector space V. A vector space V is called semi-order vector space (in short semi-order space), if there exist an ordered vector space W and an operator T from V into W. In this way, we say that V is semi-order space with respect to \(\{W, T\}\). A net \(\{x_\alpha

In this paper, we present the notion of approximate solutions for vector variational inequalities in Banach spaces, which extends the existing approximate solutions. It is shown that, under the cone subconvexlikeness, our new approximate solutions can be characterized by the approximate solutions of linear scalar problem by means of the convex separation theorem. For the nonconvex cases, based on the

In this work, we construct a class of Hermite-type interpolation basis functions based on the sixth-order ordinary differential equation \({S^{(6)}}(\mathrm{{t}}) - {\tau }^4{S^{(2)}}(t) = 0\). Using them, we propose a kind of \(C^2\) tension interpolation splines with a local tension parameter \(\tau _i\). For \(C^2\) interpolation, the given interpolant has \(O(h^2)\) convergence. Some applications

In this paper, we construct the monotonicity-preserving Lax–Wendroff (MP-Lax–Wendroff) scheme based on the MP scheme as proposed by Suresh and Huynh [11], which is a high-order and high-resolution method for hyperbolic conservation laws. It is well known that the total-variation-diminishing (TVD) methods possess the order reduction at smooth extremum points. However, the MP scheme not only preserves

We establish some new inequalities for K-g-frames in Hilbert \(C^{*}\)-modules using the Moore–Penrose inverse of the adjointable operator K and a parameter \(\lambda \). It turns out that the results which we obtained can lead to some known results if we choose particular values for K and \(\lambda \). We also give a double inequality for K-g-frames in Hilbert \(C^{*}\)-modules with the help of two

In this paper, we consider the notion of quasi-multipliers to the general topological algebra setting, not necessarily normed or locally convex. We discuss the quasi-uniform and quasi-strong operator topologies on the algebra QM(A) of all bilinear and jointly continuous quasi-multipliers on A and study their various properties.

This paper deals with qualitative properties of solutions in a parabolic equation with nonstandard growth conditions and singular medium void. For the sublinear source, we prove that all solutions are global. For the linear source, the solutions are global provided that the measure of domain is small. For the superlinear source, the solutions blow up at infinite time given the initial data belonging

This work studies the approximate controllability of a class of second-order retarded semilinear differential equations with nonlocal conditions and with delays in control. First, we deduce the existence of mild solutions using cosine family and fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz. Controllability of the system is shown using an approximate and

Recently, Daghigh et al. proposed some isogeny-based key agreement protocols in Bull. Iran. Math. Soc. 43 (2017), no. 4, 77-88. They claimed that their key exchange protocols based on supersingular isogenies provide the same security level as the Jao et al.’s protocol SIDH. This paper addresses first a vulnerability of these protocols to a key manipulation attack. Hence, unlike the security claims

In this paper, we study the category \(\mathbb {C} (\mathrm{{Rep}}(\mathcal {Q}, \mathfrak {A}))\) of complexes of representations of quiver \(\mathcal {Q}\) with values in an abelian category \(\mathfrak {A}\). We develop a method for constructing some model structures on \(\mathbb {C} (\mathrm{{Rep}}(\mathcal {Q}, \mathfrak {A}))\) based on componentwise notion. Moreover, we also show that these

In this paper, we verify a relation between the symmetric continuity of lower semicontinuous extended seminorms on a locally convex cone with respect to the symmetric topology and barreledness of the locally convex cone. The assertion, whether a barreled cone is upper-barreled or not, was posed as a question in Ranjbari and Saiflu (J Math Anal Appl 332(2):1097–1108, 2007). We show that a barreled locally

In this paper, we show that every homogeneous Finsler metric is a weakly stretch metric if and only if it reduces to a weakly Landsberg metric. This yields an extension of Tayebi–Najafi’s result that proved the result for the class of stretch Finsler metrics. Let \(F:=\alpha \phi (\beta /\alpha )\) be a homogeneous weakly stretch \((\alpha ,\beta )\)-metric on a manifold M. We show that if \(\phi \)

In this paper some subdifferentials of distance function from a closed subset in points outside of the target set are introduced in the context of Riemannian manifolds. The subdifferential regularities of distance function \(d_{S}\) and normal regularities of enlargements of a set S are also studied in this setting.

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions for a Minkowski-curvature Dirichlet problem with indefinite weight. By figuring the shape of unbounded continua of solutions, we show the existence and multiplicity of positive solutions with respect to the parameter \(\lambda \). In particular, we obtain the existence of at least three positive

In this paper, we are working with convolutions on the positive half-line, for Lebesgue integrable functions. Six new convolutions are introduced. Factorization identities for these convolutions are derived, upon the use of Fourier sine and cosine transforms and Hermite functions. Such convolutions allow us to consider systems of convolution type equations on the half-line. Using two different methods

In this paper, we obtain the formula of scalar curvature for Kropina metrics. Then we prove that a Kropina metric of isotropic scalar curvature must be of isotropic S-curvature. We also focus on Yamabe problem in Kropina metrics and give a negative answer to the Yamabe problem on Kropina metrics with isotropic S-curvature. It turns out that C-reducible metrics do not satisfy Yamabe problem.

Some characterizations for the boundedness, compactness and essential norm of a class of product-type operators \(T^n_{u,v,\varphi }\) from the Bloch space and little Bloch space into Zygmund-type spaces are given in this paper.

The net Laplacian matrix \(N_{\dot{G}}\) of a signed graph \(\dot{G}\) is defined as \(N_{\dot{G}}=D_{\dot{G}}^{\pm }-A_{\dot{G}}\), where \(D_{\dot{G}}^{\pm }\) and \(A_{\dot{G}}\) denote the diagonal matrix of net-degrees and the adjacency matrix of \(\dot{G}\), respectively. In this study, we give two upper bounds for the largest eigenvalue of \(N_{\dot{G}}\), both expressed in terms related to

Recently, Phuong and Thin (Ukrain Math J 67(7), 2015) proved some fundamental theorems for holomorphic curves on the annuli with target being fixed hyperplanes. In this paper, we consider the same problems in the case of target being fixed hypersurfaces.

It is shown that if A is an object in an exactly definable category \({\mathcal {C}}\) such that A has finite pure Goldie dimension and that every pure monomorphism \(A\rightarrow A\) is an isomorphism, then its endomorphism ring \(\hbox {End}_{{\mathcal {C}}}(A)\) is semilocal. Also, it is proved that every subobject of a pure quotient finite dimensional pure injective object of an exactly definable

In this paper, we define a (1, 3)-tensor field T(X, Y)Z on Kenmotsu manifolds and give a necessary and sufficient condition for T to be a curvature-like tensor. Next, we present some properties related to the curvature-like tensor T and prove that \(M^{2m+1}\) is an \(\eta \)-Einstein–Kenmotsu manifold if and only if \(\sum ^{m}_{j=1}T( \varphi (e_j), e_j) X = 0\). Besides, we define a (1, 4)-tensor

In this work, we are interested in introducing a new generalization of lifting modules, namely SSP-lifting modules. This definition generalizes two concepts lifting modules and SSP-modules (modules with sum of each two summands is a summand). We show that every direct summand of an SSP-lifting module inherits the property, while a direct summand of a SIP-extending module is not SIP-extending, in general

In this article, we construct new explicit formulas for the Drazin inverse of \(P+Q\) under some conditions, where P and Q are singular square matrices over skew fields. These formulas generalize some recent results in literature. By using these formulas, we establish new results for the Drazin inverse of \(2\times 2\) block matrix under some assumptions over skew fields. Finally, illustrative numerical

This article is devoted to studying the topological structure of a solution set for Clarke subdifferential type fractional non-instantaneous impulsive differential inclusion driven by Poisson jumps. Initially, for proving the solvability result, we use a nonlinear alternative of Leray–Schauder fixed point theorem, Gronwall inequality, stochastic analysis, a measure of noncompactness, and the multivalued

In the present paper, we propose the modification of the Baskakov–Kantorovich operators based on \(\mu \)-integral. Such operators are connected with exponential functions. We estimate moments and establish some direct results in terms of modulus of continuity.