Authors:Najoua Gamara; Akram Makni Abstract: We give new estimates on the capacity of a condenser in the first Heisenberg group. As an application, we establish new lower and upper bounds for the first eigenvalue of the Kohn–Laplace operator for a regular bounded open domain of the Heisenberg group. PubDate: 2018-04-23 DOI: 10.1007/s40840-018-0628-7

Authors:Saminathan Ponnusamy; Victor V. Starkov Abstract: One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them. PubDate: 2018-04-18 DOI: 10.1007/s40840-018-0626-9

Authors:J. N. Alonso Álvarez; J. M. Fernández Vilaboa; R. González Rodríguez Abstract: In this paper, we introduce the notion of weak nonassociative Doi–Hopf module and give the Fundamental Theorem of Hopf modules in this setting. Also, we prove that there exists a categorical equivalence that admits as particular instances the ones constructed in the literature for Hopf algebras, weak Hopf algebras, Hopf quasigroups and weak Hopf quasigroups. PubDate: 2018-04-16 DOI: 10.1007/s40840-018-0624-y

Authors:Weihong Xie; Haibo Chen; Hongxia Shi Abstract: This paper is dedicated to studying the multiplicity of positive solutions for the following Schrödinger–Poisson problem $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+u+\phi u=\lambda Q(x) u ^{q-2}u+ K(x) u ^4u, \quad &{}\hbox {in} \ \mathbb {R}^3,\\ -\Delta \phi =u^2, \quad &{}\hbox {in} \ \mathbb {R}^3,\\ \end{array}\right. \end{aligned}$$ where \(4<q<6 \) or \(q=2\) , \(\lambda >0\) is a parameter, K(x) and Q(x) satisfy some mild assumptions. With minimax theorems and Ljusternik–Schnirelmann theory, we investigate the relation between the number of positive solutions and the topology of the set where K(x) attains its global maximum for small \(\lambda \) . PubDate: 2018-04-11 DOI: 10.1007/s40840-018-0623-z

Authors:D. K. Thomas; S. Abdul Halim Abstract: The authors have retracted this article because the article contains major flaws in the proof of the main results. The results of the paper are invalid, since the assumption that the functionals considered are rotationally invariant is not valid. All authors have agreed to this retraction. PubDate: 2018-04-01 DOI: 10.1007/s40840-018-0620-2

Authors:Wenwen Zhang; Jian-Liang Wu Abstract: A graph G is of class 1 if its edges can be colored with k colors such that adjacent edges receive different colors, where k is the maximum degree of G. It is proved here that every planar graph is of class 1 if its maximum degree is at least 6 and any 6-cycle contains at most two chords. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0376-5

Authors:Limonka Lazarova; Biljana Jolevska-Tuneska; İnci Aktürk; Emin Özc̣ağ Abstract: The composition of the distributions \(x^\lambda \) and \(x_+^\mu \) is evaluated for \(\lambda = -1,-2,\ldots \quad \mu >0\) and \(\lambda \mu \in {{\mathbb {Z}}}^- .\) Further results are deduced. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0342-2

Authors:Yilun Shang Abstract: Let G be a simple connected graph on n vertices. The distance Estrada index DEE(G) of G is defined as the sum of \(e^{\lambda _i(D)}\) over \(1\le i\le n\) , where \(\lambda _1(D),\lambda _2(D),\) \(\ldots ,\) \(\lambda _n(D)\) are the eigenvalues of its distance matrix D. In this paper, we establish lower and upper bounds to DEE(G) for almost all bipartite graphs G. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0306-6

Authors:Fortuné Massamba; Ange Maloko Mavambou Abstract: In this paper, we study a class of almost contact manifolds, namely locally conformal almost manifolds. We investigate subclasses of such manifolds and prove that some of them contain the class of bundle-like metric structures. Under some conditions, we prove that the class of conformal changes of almost cosymplectic structures is a subclass of (almost)-cosymplectic structures. Examples are also obtained. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0309-3

Authors:Mojtaba Bakherad Abstract: In this paper, we employ some operator techniques to establish some refinements and reverses of the Callebaut inequality involving the geometric mean and Hadamard product under some mild conditions. In particular, we show $$\begin{aligned}&K\left( \frac{M^{2t-1}}{m^{2t-1}},2\right) ^{r{^\prime }} \sum _{j=1}^n(A_j\sharp _{s}B_j)\circ \sum _{j=1}^n(A_j\sharp _{1-s}B_j)\\&\qquad +\left( \frac{t-s}{t-1/2}\right) \left( \sum _{j=1}^n(A_j\sharp _{t}B_j)\circ \sum _{j=1}^n(A_j\sharp _{1-t}B_j) \!-\!\sum _{j=1}^n(A_j\sharp B_j)\circ \sum _{j=1}^n(A_j\sharp B_j)\!\right) \\&\quad \le \sum _{j=1}^n(A_j\sharp _{t}B_j)\circ \sum _{j=1}^n(A_j\sharp _{1-t} B_j), \end{aligned}$$ where \(A_j, B_j\in {\mathbb {B}}({\mathscr {H}})\,\,(1\le j\le n)\) are positive operators such that \(0<m{^\prime } \le B_j\le m <M \le A_j\le M{^\prime }\,\,(1\le j\le n)\) , either \(1\ge t\ge s>{\frac{1}{2}}\) or \(0\le t\le s<\frac{1}{2}\) , \(r{^\prime }=\min \left\{ \frac{t-s}{t-1/2},\frac{s-1/2}{t-1/2}\right\} \) and \(K(t,2)=\frac{(t+1)^2}{4t}\,\,(t>0)\) . PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0364-9

Authors:Tudor Bînzar; Cristian Lăzureanu Abstract: In this paper, a pair of noncommutative isometric semigroups on a Hilbert space is considered. The existence and uniqueness of Wold-type decompositions for this pair are studied and connections with the noncommutative Wold decomposition for the product semigroup generated by this pair are given. Also, characterizations for the product semigroup to be a standard semigroup are presented. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0379-2

Authors:Phan Quoc Khanh; Vo Si Trong Long Abstract: We propose a pure topological notion of a finite-intersection map (FI-map), which captures the idea of a typical generalized KKM-map, with no use of any generalized convexity structure and prove its full characterizations in terms of recent generalized KKM and connectedness structures. We establish an intersection point theorem in terms of FI-maps. Then, a half of the paper is devoted to apply this result to obtain characterizations of the existence of solutions in optimization. First, we discuss a general model of variational relations. Then, we move on to more particular, but typical and important cases: equilibrium problems, saddle points, constrained minimization, and Nash equilibria. We include discussions and examples to illustrate that our results improve or extend many recent contributions in the literature. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0370-y

Authors:Rashad M. EL-Sagheer Abstract: Accelerated life testing is widely used in product life testing experiments since it provides significant reduction in time and cost of testing. In this article, we assume that the lifetime of items under use condition follows the two-parameter distributions having power hazard function, and partially accelerated life tests based on progressive type-II censored samples are considered. The maximum likelihood, Bayes, and parametric bootstrap methods are used for estimating the unknown parameters. Based on normal approximation to the asymptotic distribution of MLEs, the approximate confidence intervals for the parameters are derived. Two bootstrap confidence intervals are also proposed. The classical Bayes estimates cannot be obtained in explicit form, so we propose to apply the Markov chain Monte Carlo (MCMC) technique. Gibbs within the Metropolis–Hasting algorithm has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and the highest posterior density credible intervals of the unknown parameters have been computed. Finally, analysis of a simulated data set has also been presented to illustrate the proposed estimation methods developed here. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0311-9

Authors:Hafiz Fukhar-ud-din; Khairul Saleh Abstract: We study a one-step iterative scheme to establish strong convergence theorems and \(\triangle \) -convergence theorems for a finite family of generalized nonexpansive mappings on a nonlinear domain. Our results generalize and extend several relevant results in the literature. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0310-x

Authors:Aref Jeribi; Najib Kaddachi; Bilel Krichen Abstract: In this paper, we establish some new fixed point theorems for a \(2\times 2\) block operator matrix defined on nonempty, bounded, closed, and convex subsets of Banach algebras, where the inputs are multi-valued mappings. The obtained results are then applied to a coupled system of perturbed functional differential inclusions of initial and boundary value problems in order to prove the existence of solutions under a Carathéodory condition. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0374-7

Authors:A. R. Vahidi; E. Babolian; Z. Azimzadeh Abstract: In this paper, a new form of the homotopy perturbation method has been adopted for solving nonlinear Duffing’s equations, which yields the Maclaurin series of the exact solution. The Laplace transformation is applied to the truncated Maclaurin series, and then the Padé approximation with fast convergence rate and high accuracy is used for the solution derived from the Laplace transformation. Illustrative examples are given to demonstrate the efficiency and the simplicity of the proposed method. PubDate: 2018-04-01 DOI: 10.1007/s40840-015-0191-4

Authors:Bahman Khosravi Abstract: In this paper first we study and characterize the Cayley graph of Rees matrix semigroups (completely simple semigroups). Then we investigate Cayley D-saturated property of these graphs and we study the Cayley D-saturated property of Rees matrix semigroups. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0361-z

Authors:Mansoor Saburov; Mohd Ali Khameini Ahmad Abstract: One of the most frequently asked question in the p-adic lattice models of statistical mechanics is that whether a root of a polynomial equation belongs to domains \({\mathbb {Z}}_p^{*}, \ {\mathbb {Z}}_p{\setminus }{\mathbb {Z}}_p^{*}, \ {\mathbb {Z}}_p, \ {\mathbb {Q}}_p{\setminus }{\mathbb {Z}}_p^{*}, \ {\mathbb {Q}}_p{\setminus }({\mathbb {Z}}_p{\setminus }{\mathbb {Z}}_p^{*}), \ {\mathbb {Q}}_p{\setminus }{\mathbb {Z}}_p, \ {\mathbb {Q}}_p \) or not. However, this question was open even for lower-degree polynomial equations. In this paper, we give local descriptions of roots of cubic equations over the p-adic fields for \(p>3\) . PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0401-8

Authors:Tadeusz Antczak Abstract: In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of this method is established. Further, the exactness property of a vector exact penalty function method is defined and analyzed in the context of the introduced vector exponential penalty function method. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto solutions of the considered nondifferentiable multiobjective programming problem and the associated vector penalized optimization problem with the vector exact exponential penalty function. This equivalence is established for nondifferentiable vector optimization problems with inequality constraints in which involving functions are r-invex. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0340-4

Authors:Salah Mecheri Abstract: In this paper, we introduce the class of quasi-nM-hyponormal operators and study various properties. We show that every quasi-nM-hyponormal operator is subscalar of order 2n; in particular, every M-hyponormal operator is subscalar of order two. Consequently, if the spectrum of T has a nonempty interior in \(\mathbb {C}\) , then T has a nontrivial invariant subspace. We also examine the hyperinvariant subspace problem for quasi-nM-hyponormal operators. Finally, we consider some of the spectral properties of this class and show that they share many spectral properties with normal operators on Hilbert spaces, mainly concerning Fredholm theory and local spectral theory. We are primarily interested in isolated points of the spectra of quasi-nM-hyponormal operators as well as the isolated points of the approximate point spectra. These properties lead to the concept of a polaroid-type operator, which when combined with the single-valued extension property, an important property in local spectral theory, produces a general framework for several versions of Weyl-type theorems. PubDate: 2018-04-01 DOI: 10.1007/s40840-016-0377-4