On the geometric–arithmetic index by decompositions-CMMSE

The concept of geometric–arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. There are many papers studying different kinds of indices (as Wiener, hyper–Wiener, detour, hyper–detour, Szeged, edge–Szeged, PI, vertex–PI and eccentric connectivity indices) under particular cases of decompositions. The main aim of this paper is to show that the computation of the geometric-arithmetic index of a graph G is essentially reduced to the computation of the geometric-arithmetic indices of the so-called primary subgraphs obtained by a general decomposition of G. Furthermore, using these results, we obtain formulas for the geometric-arithmetic indices of bridge graphs and other classes of graphs, like bouquet of graphs and circle graphs. These results are applied to the computation of the geometric-arithmetic index of Spiro chain of hexagons, polyphenylenes and polyethene.     

Immobilization and Stabilization of Beta-Xylosidases from Penicillium janczewskii

β-Xylosidases are critical for complete degradation of xylan, the second main constituent of plant cell walls. A minor β-xylosidase (BXYL II) from Penicillium janczewskii was purified by ammonium sulfate precipitation (30% saturation) followed by DEAE-Sephadex chromatography in pH 6.5 and elution with KCl. The enzyme presented molecular weight (MW) of 301 kDa estimated by size exclusion chromatography. Optimal activity was observed in pH 3.0 and 70–75 °C, with higher stability in pH 3.0–4.5 and half-lives of 11, 5, and 2 min at 65, 70, and 75 °C, respectively. Inhibition was moderate with Pb⁺² and citrate and total with Cu⁺², Hg⁺², and Co⁺². Partially purified BXYL II and BXYL I (the main β-xylosidase from this fungus) were individually immobilized and stabilized in glyoxyl agarose gels. At 65 °C, immobilized BXYL I and BXYL II presented half-lives of 4.9 and 23.1 h, respectively, therefore being 12.3-fold and 33-fold more stable than their unipuntual CNBr derivatives (reference mimicking soluble enzyme behaviors). During long-term incubation in pH 5.0 at 50 °C, BXYL I and BXYL II glyoxyl derivatives preserved 85 and 35% activity after 25 and 7 days, respectively. Immobilized BXYL I retained 70% activity after 10 reuse cycles of p-nitrophenyl-β-D-xylopyranoside hydrolysis.

     

Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach

Consider a finite collection \(\{\xi _k\}_{k=1}^p\) of vectors in the space \(\mathbb {R}^n\). The \(\xi _k\)’s are not to be seen as position points but as directions. This work addresses the problem of computing the ellipsoidal cone of minimal volume that contains all the \(\xi _k\)’s. The volume of an ellipsoidal cone is defined as the usual n-dimensional volume of a certain truncation of the cone. The central axis of the ellipsoidal cone of minimal volume serves to define the central direction of the datapoints, whereas its volume can be used as measure of dispersion of the datapoints.     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

Convergence of Asymptotic Systems of Non-autonomous Neural Network Models with Infinite Distributed Delays

In this paper, we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.     

Linear representations of formal loops

A representation of an object in a category is an abelian group in the corresponding comma category. In this paper, we derive the formulas describing linear representations of objects in the category of formal loops and formal loop homomorphisms and apply them to obtain a new approach to the representation theory of formal Moufang loops and Malcev algebras based on Moufang elements. Certain ‘non-associative Moufang symmetry’ of groups is revealed.     

Multi-poly-Bernoulli numbers and polynomials with a <Emphasis Type="Italic">q</Emphasis> parameter

We introduce themulti-poly-Bernoulli numbers and polynomialswith a q parameter, which are generalizations of the poly-Bernoulli numbers and polynomials with a q parameter, respectively.We give several combinatorial identities and properties of these new numbers and polynomials.     

Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films

We use the method of \(\Gamma \)-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach in Golovaty et al. (J Nonlinear Sci 25(6):1431–1451, 2015) where we considered a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary conditions on the lateral boundary of the film when the surface is not closed. We establish a general convergence result to an energy defined on the surface that involves a somewhat surprising remnant of the normal component of the tensor gradient. Then we exhibit one effect of curvature through an analysis of the behavior of minimizers to the limiting problem when the substrate is a frustum.