Authors:William Browder Pages: 75 - 78 Abstract: A space is defined to be “n-spheroidal” if it has the homotopy type of an n-dimensional CW-complex X with \(H_{n}(X; \mathbb {Z})\) not zero and finitely generated. A group G is called “n-spheroidal” if its classifying space K(G, 1) is n-spheroidal. Examples include fundamental groups of compact manifold K(G, 1)s. Moreover, the class of groups G, which are n-spheroidal for some n, is closed under products, free products, and group extensions. If Y is a space with \(\pi _{1}(Y)\) n-spheroidal, and if \(H_{k}(Y;\mathbb {F}_{p})\) is non-zero and finitely generated, and if \(H_{i}(Y;\mathbb {F}_{p}) = 0\) for \(i>k\) , then \(H_{n+k}(\overline{Y};\mathbb {F}_{p}) \ne 0\) for \(\overline{Y}\) a finite sheeted covering space of Y. Hence, dim \((Y) \ge n+k\) . Thus, it follows that if dim \((Y) < n\) , and if \(H_{k}(Y;\mathbb {F}_{p}) \ne 0\) and \(H_{i}(Y;\mathbb {F}_{p}) = 0\) for \(i>k>0\) , then \(H_{k}(Y;\mathbb {F}_{p})\) is not finitely generated. Similar results follow for \(Y\subset K(G,1)\) . PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0137-3 Issue No:Vol. 23, No. 1 (2017)

Authors:Kee Yuen Lam Pages: 79 - 86 Abstract: This paper is a summary of my talk given at the event “Sam 80” which was a meeting held at El Colegio Nacional in Mexico (2013) to celebrate Professor Samuel Gitler’s 80th birthday. The main purpose of that talk was to present an affirmative answer to the Yuzvinsky Conjecture in the case of square matrices (explained below). I would like to dedicate this write-up to Sam’s memory, to express my appreciation for his warm friendship throughout our 46 years of acquaintance. PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0130-x Issue No:Vol. 23, No. 1 (2017)

Authors:Noé Bárcenas; Daniel Juan-Pineda; Pablo Suárez-Serrato Pages: 119 - 127 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:Suyoung Choi; Shizuo Kaji; Stephen Theriault Pages: 153 - 161 Abstract: We give p-local homotopy decompositions of the suspensions of real toric spaces for odd primes p. Our decomposition is compatible with the one given by Bahri, Bendersky, Cohen, and Gitler for the suspension of the corresponding real moment-angle complex, or more generally, the polyhedral product. As an application, we obtain a stable rigidity property for real toric spaces. PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0090-1 Issue No:Vol. 23, No. 1 (2017)

Authors:Ralph L. Cohen; John D. S Jones Pages: 163 - 172 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: 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:Bogdan Gheorghe; Daniel C. Isaksen Pages: 389 - 397 Abstract: We study the stable motivic homotopy groups \(\pi _{s,w}\) of the 2-completion of the motivic sphere spectrum over \(\mathbb {C}\) . When arranged in the (s, w)-plane, these groups break into four different regions: a vanishing region, an \(\eta \) -local region that is entirely known, a \(\tau \) -local region that is identical to classical stable homotopy groups, and a region that is not well-understood. PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0094-x Issue No:Vol. 23, No. 1 (2017)

Authors:Iván D. Castrillón; Enrique Reyes Pages: 399 - 412 Abstract: If a simplicial complex \(\Delta \) is vertex decomposable, then the n-sphere moment angle complex \(\mathcal {Z}_{\Delta ^{\vee }}(D^{n},S^{n-1})\) has the homotopy type of the wedges of spheres, where \(\Delta ^{\vee }\) is the Alexander dual of \(\Delta \) . Furthermore, if \(\Delta \) is pure vertex decomposable, then its Stanley–Reisner ring \(k[\Delta ]\) is Cohen–Macaulay. Consequently, the vertex decomposable property is an interesting property from combinatorial, algebraic and topological point of view. In this paper, we characterize the pure vertex decomposable simplicial complexes associated to graphs whose 5-cycles have at least 4 chords. PubDate: 2017-04-01 DOI: 10.1007/s40590-016-0147-1 Issue No:Vol. 23, No. 1 (2017)

Authors:Michael Wiemeler Pages: 501 - 509 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:Sergio Santiago Chan Castro; Alejandro Waldemar Cobá Magaña; Jesús Efrén Pérez Terrazas 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: 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: 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: 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: 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: 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: 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: 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: 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: 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