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.

It is an important question whether it is possible to put a geometry on a given manifold or not. It is well known that any simply connected closed manifold admitting a real projective structure must be a sphere. Therefore, any simply connected manifold M which is not a sphere \((\dim M \ge 4)\) does not admit a real projective structure. Cooper and Goldman gave an example of a 3-dimensional manifold

Some characterizations of products of two projections on a Hilbert space are generalized to the case of products of a finite number of projections on a Hilbert \(C^*\)-module. An example is constructed to show that in the Hilbert \(C^*\)-module case, \(\mathfrak {X}\) and its subset \(\mathfrak {X}_\bot \) can be different, where \(\mathfrak {X}\) denotes the set of all products of two projections

This article proposes various sufficient controllability criteria for a class of networked higher dimensional systems under the influence of impulses exhibited by their state functions. The conditions obtained are characterised in terms of impulse matrices, inner coupling matrix, network topology and the system matrices. It is demonstrated that Kalman’s rank condition and Popov–Belevitch–Hautus (PBH)-rank

Let R and S be rings and \(_RC_S\) a semidualizing bimodule. For a subcategory \({\mathcal {X}}\) of the Auslander class \({\mathcal {A}}_C(S)\) containing all projective and C-injective modules, we show that a module \(N\in {\mathcal {A}}_C(S)\) if and only if there exists an exact sequence \(\cdots \rightarrow X_i\rightarrow \cdots \rightarrow X_1\rightarrow X_0\rightarrow X^0\rightarrow X^1\rightarrow

In this paper, we show that for almost every \(m>0\), the solution to the semi-linear Klein–Gordon equation associated with the harmonic oscillator, with small initial data, exists over a longer time interval than the one given by local existence theory, using the normal form method. A similar result for the quadratic wave equation is also obtained.

Let \({\mathcal {M}}\) be a finite von Neumann algebra with no central summands of type \(I_{1}\). Assume that \(\delta :{\mathcal {M}}\rightarrow {\mathcal {M}}\) is a nonlinear map satisfying \(\delta ([[A,B],C])=[[\delta (A),B],C]+[[A,\delta (B)],C]+[[A,B],\delta (C)]\) for any \(A,B,C\in {\mathcal {M}}\) with \(ABC=0\). Then, we prove that there exists an additive derivation \(d:{\mathcal {M}}\rightarrow

We are concerned with the existence and multiplicity of nontrivial solutions to the following double phase problems: $$\begin{aligned} \left\{ \begin{array}{ll} -\mathrm{div}(|\nabla u|^{p-2}\nabla u+\alpha (x)|\nabla u|^{q-2}\nabla u)+V(x)|u|^{\gamma -2}u=f(x,u),&{}\ \mathrm{in}\ \Omega ,\\ u=0,&{}\ \mathrm{on}\ {\partial \Omega ,} \end{array}\right. \end{aligned}$$ applying the mountain pass theorem

Let G be a finite p-group. Assume that \(\nu (G)\) and \(\nu _c(G)\) denote the number of conjugacy classes of non-normal subgroups and non-normal cyclic subgroups of G, respectively. In this paper, we completely classify the finite p-groups with \(\nu _c=p\) or \(p+1\) for an odd prime number p. Also, we classify the groups G with \(\nu (G)=\nu _c(G)=p^i, i\ge 1\).

Let R be a commutative ring with identity and \({\mathbb {N}}_0\) be the additive monoid of nonnegative integers. We say that a function \(t : {\mathbb {N}}_0 \times {\mathbb {N}}_0 \rightarrow R\) is a twist function on R if t satisfies the following three properties for all \(n, m, q \in {\mathbb {N}}_0\): (i) \(t(0,q) = 1\), (ii) \(t(n,m) = t(m,n)\), and (iii) \(t(n,m) \cdot t(n + m, q) = t (n,

For two frames \(\{\phi _i\}_{i \in {\mathcal {I}}}\) and \(\{\psi _i\}_{i\in {\mathcal {I}}}\), the family \(\{\phi _i\}_{i \in \sigma } \cup \{\psi _i\}_{i \in \sigma ^c}\) is called a weaving, where \({\mathcal {I}}\) is a countable index set and \(\sigma \subset {\mathcal {I}}\). Two frames \(\{\phi _i\}_{i \in {\mathcal {I}}}\) and \(\{\psi _i\}_{i\in {\mathcal {I}}}\) are called woven if all

Let \(f:I\rightarrow {\mathbb {R}}\) be an operator convex function of class \( C^{1}\left( I\right) \). If \((A_{t})_{t\in T}\) is a bounded continuous field of selfadjoint operators in \({\mathcal {B}}\left( H\right) \) with spectra contained in I defined on a locally compact Hausdorff space T with a bounded Radon measure \(\mu \), such that \(\int _{T}{\mathbf {1}}d\mu \left( t\right) =\mathbf {1

Using compositions of the weighted core–EP inverse and Moore–Penrose inverse, we solve new systems of operator equations and define three new weighted generalized inverses of a bounded linear operator between two Hilbert spaces, which are called the W-MPCEP inverse, W-CEPMP inverse and W-MPCEPMP inverse. The W-MPCEP inverse extends the notion of the MPCEP inverse for an operator. We give operator matrix

We consider vector-valued Banach function algebras on a compact Hausdorff space. Then, we define the subalgebras generated by vector-valued polynomials and rational functions, and determine their maximal ideal spaces and Šilov boundaries. We finally make use the results for a certain category of these algebras such as vector-valued Lipschitz algebras, vector-valued Dales–Davie algebras (algebras of

In this paper, we study existence, dependence, and optimal control results concerning solutions to a class of hemivariational inequalities for stationary Navier–Stokes equations but without making use of the theory of pseudo-monotone operators. To do so, we consider a classical assumption, due to Rauch, which constrains us to make a slight change on the definition of a solution. The Rauch assumption

In this paper, we study a nonlinear inverse problem for a third-order partial differential equation with integral conditions. This inverse problem is formulated as an auxiliary inverse problem which, in turn, is reduced to the operator equation in a specified Banach space using the method of spectral analysis. Finally, the existence and uniqueness of this operator equation is proved by applying the

This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s41980-019-00232-4.

In this paper, we introduce the irreducible \(\alpha \)-Nekrasov matrices and irreducible \(\alpha \)-S-Nekrasov matrices as the extended irreducible Nekrasov matrices and we analyze the relationships among the involved matrices and irreducible H-matrices.

The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers \(k^2\), in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions

Throughout this article, we fix a group G and a commutative ring \(\Bbbk \). This is an exposition on 2-equivalences between a 2-category of small \(\Bbbk \)-categories with pseudo G-actions and a 2-category of G-graded small \(\Bbbk \)-categories, which generalizes (Asashiba in Appl Categor Sturct 25(8):3278–3296, 2017). This article is a translation of some parts of Ch. 4 and 5 in the book (Asashiba

Let \({\mathcal {A}}\) and \({\mathcal {B}}\) be two factors with dim\({\mathcal {A}}>4\). In this article, it is proved that a bijective map \(\Phi : {\mathcal {A}}\rightarrow {\mathcal {B}}\) satisfies \(\Phi ([A\bullet B, C])=[\Phi (A)\bullet \Phi (B), \Phi (C)]\) for all \(A, B, C\in {\mathcal {A}}\) if and only if \(\Phi \) is a linear \(*\)-isomorphism, or a conjugate linear \(*\)-isomorphism

Let \({\mathcal {R}}\) be a semiprime ring with center \(Z({\mathcal {R}})\) and with extended centroid C and let \(\sigma : {\mathcal {R}} \rightarrow {\mathcal {R}}\) be an automorphism. Assume that \(\tau : {\mathcal {R}} \rightarrow {\mathcal {R}} \) is an anti-homomorphism, such that the image of \(\tau \) has small centralizer. It is proved that the following are equivalent: (1) \(x^{\sigma }x^{\tau

We study the load-balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined clients, in a way that the total traveling cost is a minimum, and the vehicle loads are balanced. The unbalanced loads cause the decrease of distribution quality

In this paper, we present a modified SP iteration with the inertial technical term for three quasi-nonexpansive multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. The strong convergence theorems are given using CQ and shrinking projection methods with our modified iteration. Finally, we test some numerical experiments to illustrate that our inertial

For a non-empty set X denote the full transformation semigroup on X by T(X) and suppose that \(\sigma \) is an equivalence relation on X. For every \(f\in T(X)\), the kernel of f is defined to be \(\ker f =\{(x, y)\in X\times X\mid f(x) = f(y)\}\). Evidently, \(E(X, \sigma )=\{f\in T(X) \mid \sigma \subseteq \ker f\}\) is a subsemigroup of T(X). Also, the subset \(RE(X, \sigma )\) of \(E(X, \sigma

We introduce and study the notions of restricted projective, injective and flat complexes of modules. It is shown in the paper that a complex C of modules is restricted projective if and only if for each \(m\in \mathbb {Z}\) the module \(C^{m}\) is restricted projective. A similar result for restricted injective complexes is also given. As an application, we characterize the complex of strongly torsion-free

Based on the Schur complements, two upper bounds for the infinity norm of the inverse of doubly strictly diagonally dominant (DSDD) matrices are presented. As applications, an error bound for linear complementarity problems of DB-matrices and a lower bound for the smallest singular value of matrices are given.

In this paper, we study a generalized convex vector equilibrium problem with cone and set constraints in real Banach spaces. We provide some basic characterizations on generalized convexity for the first- and second-order directional derivatives. We obtain Kuhn–Tucker second-order necessary and sufficient optimality conditions for efficiency to such problem under suitable assumptions on the generalized

Let \(G=(V,E)\) be a simple graph. A set \(M\subseteq E\) is a matching if no two edges in M have a common vertex. The matching number, denoted \(\beta (G)\) (or \(\beta \)), is the maximum size of a matching in G. A double Roman dominating function (DRDF) on a graph G is a function f: \(V\longrightarrow \{0,1,2,3\}\) satisfying the conditions that for every vertex u of weight \(f(u)\in \left\{ 0,1\right\}