Authors:Noé Bárcenas; Daniel Juan-Pineda; Pablo Suárez-Serrato Pages: 119 - 127 Abstract: Abstract In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds. PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0099-5 Issue No:Vol. 23, No. 1 (2017)

Authors:Ralph L. Cohen; John D. S Jones Pages: 163 - 172 Abstract: Abstract Let R be a ring spectrum and \( \mathcal {E}\rightarrow X\) an R-module bundle of rank n. Our main result is to identify the homotopy type of the group-like monoid of homotopy automorphisms of this bundle, \(hAut^R(\mathcal {E})\) . This will generalize the result regarding R-line bundles proven by Cohen and Jones (Mex Bull Math, 2016). The main application is the calculation of the homotopy type of \(BGL_n(End ((\mathcal {L}))\) where \(\mathcal {L}\rightarrow X\) is any R-line bundle, and \(End^R(\mathcal {L})\) is the ring spectrum of endomorphisms. In the case when such a bundle is the fiberwise suspension spectrum of a principal bundle over a manifold, \(G \rightarrow P \rightarrow M\) , this leads to a description of the K-theory of the string topology spectrum in terms of the mapping space from M to \(BGL \left( \Sigma ^\infty (G_+)\right) \) . PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0136-4 Issue No:Vol. 23, No. 1 (2017)

Authors:A. Bahri; M. Bendersky; F. R. Cohen; S. Gitler Pages: 257 - 265 Abstract: Abstract In this note, it is shown that the Hilbert–Poincaré series for the rational homology of the free loop space on a moment-angle complex is a rational function if and only if the moment-angle complex is a product of odd spheres and a disk. A partial result is included for the Davis–Januszkiewicz spaces. The opportunity is taken to correct the result (Bahri et al., Proceedings of the Steklov Institute of Mathematics, Russian Academy of Sciences, vol. 286, pp. 219–223. doi:10.1134/S0081543814060121, 2014) which used a theorem from Berglund and Jöllenbeck (J Algebra 315:249–273, 2007). PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0124-8 Issue No:Vol. 23, No. 1 (2017)

Authors:Michael Wiemeler Pages: 501 - 509 Abstract: Abstract In this note we prove that equivariantly homeomorphic quasitoric manifolds are diffeomorphic. As a consequence we show that up to finite ambiguity the diffeomorphism type of certain quasitoric manifolds M is determined by their cohomology rings and first Pontrjagin classes. PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0091-0 Issue No:Vol. 23, No. 1 (2017)

Authors:Ahmad Moussavi; Kamal Paykan Abstract: Abstract Let R be a ring and \(\delta \) is a derivation of R. In this paper, it is proved that, under suitable conditions, the differential polynomial ring \(R[x;\delta ]\) has the same triangulating dimension as R. Furthermore, for a piecewise prime ring, we determine a large class of the differential polynomial ring which have a generalized triangular matrix representation for which the diagonal rings are prime. PubDate: 2017-08-02 DOI: 10.1007/s40590-017-0181-7

Authors:R. Peniche; M. C. Rodríguez-Vallarte; G. Salgado Abstract: Abstract We determine the canonical form of a Hamiltonian matrix \(X\in \mathfrak {sp}(2n,\mathbb {R})\) under symplectic similarity, and the canonical form of a matrix \(Y\in \mathfrak {o}(m)\) in the orthogonal Lie algebra under similarity. This is a well known problem, and it has been solved by means of different techniques. Our contribution is to provide a new solution through elementary linear algebra. As an application, a list of the non-equivalent two- and four-dimensional quadratic Hamiltonians is given. PubDate: 2017-07-29 DOI: 10.1007/s40590-017-0176-4

Authors:R. Abo-Zeid Abstract: Abstract In this paper, we determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of solutions of the difference equation: $$\begin{aligned} x_{n+1}=\frac{ax_{n}x_{n-2}}{-bx_{n}+ cx_{n-3}},\quad n=0,1,\ldots \end{aligned}$$ where a, b, c are positive real numbers and the initial conditions \(x_{-3},x_{-2},x_{-1},x_0\) are real numbers. PubDate: 2017-07-27 DOI: 10.1007/s40590-017-0180-8

Authors:Salah Boulaaras; Mohamed El Amine Bencheikh Le Hocine; Mohamed Haiour Abstract: Abstract The main propose of this paper is to provide an error estimate on uniform norm of the parabolic quasi-variational inequalities system related to management of energy production problems, using semi-implicit time scheme with Galerkin spatial methods. Moreover, a new proof of the existence and uniqueness of the solution are given by the introduction of a constructive presented algorithm. Furthermore, an optimally \(L^{\infty }\) -asymptotic behavior in maximum norm is given. The approach is based on the subsolution concept and discrete regularity. PubDate: 2017-07-24 DOI: 10.1007/s40590-017-0177-3

Authors:R. Nikandish; M. J. Nikmehr; N. Kh. Tohidi Abstract: Abstract Let R be a commutative ring with identity and \(\mathbb {A}(R)\) be the set of ideals with non-zero annihilator. The strongly annihilating-ideal graph of R is defined as the graph \(\mathrm {SAG}(R)\) with the vertex set \(\mathbb {A}(R)^*=\mathbb {A}(R){\setminus }\{0\}\) and two distinct vertices I and J are adjacent if and only if \(I\cap \mathrm {Ann}(J)\ne (0)\) and \(J\cap \mathrm {Ann}(I)\ne (0)\) . We show that if R is a reduced ring with finitely many minimal primes, then \(\mathrm {SAG}(R)\) is weakly prefect and an explicit formula for the vertex chromatic number of \(\mathrm {SAG}(R)\) is given. Furthermore, strongly annihilating-ideal graphs with finite clique numbers are studied. Finally, we classify that all rings whose \(\mathrm {SAG}(R)\) are planar. PubDate: 2017-07-21 DOI: 10.1007/s40590-017-0179-1

Authors:Sergio Santiago Chan Castro; Alejandro Waldemar Cobá Magaña; Jesús Efrén Pérez Terrazas Abstract: Abstract Let \(\Lambda \) be an Artin algebra and \(\mathcal {C}\) a full subcategory of \(\Lambda \) -mod closed under direct summands and closed under extensions. It is known that if \(\mathcal {C}\) is functorially finite, then it has almost split sequences. Here we review an example of a covariantly finite subcategory that has right almost split morphisms except for one isomorphism class, and we compute its almost split sequences. PubDate: 2017-07-14 DOI: 10.1007/s40590-017-0174-6

Authors:S. Pirbavafa; S. M. Vaezpour Abstract: In this paper, as applications of best proximity point theorems, we obtain new existence theorems of an equilibrium pair in free abstract economies. Also, we state examples which guarantee that the similar results cannot be employed for this type of free abstract economies. PubDate: 2017-07-11 DOI: 10.1007/s40590-017-0175-5

Authors:Robert Laterveer Abstract: Abstract This small note presents in any dimension a family of cubics that have finite-dimensional motive (in the sense of Kimura). As an illustration, we verify a conjecture of Voevodsky for these cubics and a conjecture of Murre for the Fano variety of lines of these cubics. PubDate: 2017-07-07 DOI: 10.1007/s40590-017-0173-7

Authors:B. I. Dave Abstract: Abstract In the present work, we establish a general inverse series relations which unify the polynomials of Askey–Wilson, q-Racah, and q-Konhauser. The q-extensions of Riordan’s inverse series relations [Combinatorial Identities, John Wiley and Sons, Inc. 1968] are obtained by means of the main two theorems. Then we emphasize on the special cases, namely the q-Bessel function together with a q-Neumann expansion, and an inverse pair associated with the partition identities. PubDate: 2017-06-27 DOI: 10.1007/s40590-017-0172-8

Authors:Daniel Juan-Pineda; Alejandra Trujillo-Negrete Abstract: Abstract We construct two models for the classifying space for the family of infinite cyclic subgroups of the fundamental group of the Klein bottle. These examples do not fit in general constructions previously done, for example, for hyperbolic groups. PubDate: 2017-06-22 DOI: 10.1007/s40590-017-0171-9

Authors:Yuji Liu; Patricia J. Y. Wong Abstract: Abstract We present a new method to convert the boundary value problems for impulsive fractional differential equations involving Caputo fractional derivatives to integral equations. This method is used to solve a classes of boundary value problems for impulsive fractional differential equations. Moreover, some new results on the existence of solutions of anti-periodic boundary value problems for impulsive fractional differential systems are established (see Sect. 3). Our analysis relies on the well known Schauder’s fixed point theorem. Some examples and comments on recent published papers are given to illustrate the differences between our main theorems and known results. PubDate: 2017-06-08 DOI: 10.1007/s40590-017-0170-x

Authors:Dmitry Fedchenko; Nikolai Tarkhanov Abstract: Abstract We prove that if u is a locally Lipschitz continuous function on an open set \(\mathcal {X} \subset \mathbb {R}^{n+1}\) satisfying the nonlinear heat equation \(\partial _t u = \Delta ( u ^{p-1} u)\) , \(p > 1\) , weakly away from the zero set \(u^{-1} (0)\) in \(\mathcal {X}\) , then u is a weak solution to this equation in all of \(\mathcal {X}\) . PubDate: 2017-06-03 DOI: 10.1007/s40590-017-0169-3

Authors:Ali Shojaei-Fard Abstract: Abstract The article applies Connes–Kreimer Hopf algebra of Feynman diagrams and theory of graphons to build an operational calculus machinery on the basis of measure theory for Green’s functions of quantum field theory. PubDate: 2017-05-10 DOI: 10.1007/s40590-017-0166-6

Authors:Iz-iddine EL-Fassi; Abdellatif Chahbi; Samir Kabbaj Abstract: Abstract Let \((S,\cdot )\) be a semigroup, \(\mathbb {C}\) be the set of complex numbers, and let \(\sigma ,\tau \in Hom(S,S)\) satisfy \(\tau \circ \tau =\sigma \circ \sigma =id.\) We show that any solution \(f:S \rightarrow \mathbb {C}\) of the functional equation $$\begin{aligned} f(x\sigma (y))+\chi (y)f(\tau (y)x)=2f(x)f(y), \quad x,y \in S, \end{aligned}$$ has the form \(f=(m+\chi \, m\circ \sigma \circ \tau )/2\) , where m is a multiplicative function on S and \(\chi :S\rightarrow (\mathbb {C}\backslash \{0\},\cdot )\) is a character on S (i.e., \(\chi (xy)=\chi (x)\chi (y)\) for all \(x,y\in S\) ) which satisfies \(\chi (x\tau (x))=1\) for all \(x\in S\) . PubDate: 2017-05-09 DOI: 10.1007/s40590-017-0168-4

Authors:Gauhar Rahman; Praveen Agarwal; Shahid Mubeen; Muhammad Arshad Abstract: Abstract This paper is devoted to the study of fractional calculus with an integral and differential operators containing the following family of extended Mittag–Leffler function: $$\begin{aligned} E_{\alpha ,\beta }^{\gamma ;c}(z; p)=\sum \limits _{n=0}^{\infty }\frac{B_p(\gamma +n, c-\gamma )(c)_{n}}{B(\gamma , c-\gamma )\Gamma (\alpha n+\beta )}\frac{z^n}{n!}, (z,\beta , \gamma \in \mathbb {C}), \end{aligned}$$ in its kernel. Also, we further introduce a certain number of consequences of fractional integral and differential operators containing the said function in their kernels. PubDate: 2017-04-25 DOI: 10.1007/s40590-017-0167-5

Authors:Ernesto Lupercio; Elias Micha Abstract: Abstract In his note we briefly analyze the rôle of the oeuvre of Mexican mathematician Samuel Gitler and his influence in twentieth and twenty-first century mathematics. PubDate: 2017-03-11 DOI: 10.1007/s40590-017-0163-9