Toughness and Vertex Degrees

We study theorems giving sufficient conditions on the vertex degrees of a graph G to guarantee G is t‐tough. We first give a best monotone theorem when , but then show that for any integer , a best monotone theorem for requires at least nonredundant conditions, where grows superpolynomially as . When , we give an additional, simple theorem for G to be t‐tough, in terms of its vertex degrees.     

Heterogeneous Spatial Dynamical Regression in a Hilbert-Valued Context

This article introduces a Hilbert-valued spatially dynamic regression model. The spatially heterogeneous functional trend is modeled by functional multiple regression, with varying regression operators. The spatial autoregressive Hilbertian model of order one (SARH(1) model, see [37 Ruiz-Medina , M.D. 2011 . Spatial autoregressive and moving average Hilbertian processes . J. Multivariate Anal. 102 : 292 – 305 .[Crossref] , [Google Scholar]]) is considered to represent the spatial correlation and dynamics displayed by the functional error term. The RKHS theory is applied in the construction of suitable bases for projection and regularization of the associated estimation problems. The performance of the proposed Hilbert-valued modeling and estimation methodology is illustrated with a real-data example, related to financing decisions from firm panel data.     

The admissible interval for the invariant factors of a product of matrices

It is well known that Littlewood-Richardson sequences give a combinatorial characterization for the invariant factors of a product of two matrices over a principal ideal domain. Given partitions a and c, let LR(a,c) be the set of partitions b for which at least one Littlewood - Richardson sequence of type (a,b,c) exists. I. Zaballa has shown in [20] that LR(a, c) has a minimal element w and a maximal element n, with respect to the order bf majorization, depending only on a and c;. In generalLR(a, c) is not the whole interval [w, n]. Here a combinatorial algorithm is provided for constructing all the elements of LR(a, c). This algorithm consists in starting with the minimal Littlewood-Richardson sequence of shape c/a and successively modifying it until the maximal Littlewood - Richardson sequence of shape c/a is achieved. Also explicit bijections between Littlewood - Richardson sequences of conjugate shape and weight and between Littlewood - Richardson sequences of dual shape and equal weight are presented. The bijections are denned by means of permutations of Littlewood - Richardson sequences.     

NSD随机变量序列的完全收敛性

本文利用NSD随机变量序列的性质、矩不等式及三级数定理,在一定的矩条件下,得到了NSD随机变量序列的完全收敛性.所得结果推广了 Chow与Lai[15,16]与Jajte[17]的独立序列的结果.     

2D representation of protein secondary structure sequences and its applications

In terms of the classification of the protein secondary structures, we propose a 2D representation of protein secondary structure sequences. The representation are used to display, analyze, and compare the secondary structure sequences. Based on this representation, we assign the structural class to the protein, and verify the advantage or disadvantage of the methods of predicted protein second structure.     

PTreeRec: Phylogenetic Tree Reconstruction based on genome BLAST distance

Phylogenetic Tree Reconstruction (PTreeRec) is a web-based tool for automatic phylogeny inferences from whole-genome sequences, which accepts files of DNA sequences in the FASTA format and allows users to save the output tree file, and displays the inferred tree through an applet in a web browser. PTreeRec involves three basic steps. First, regions of maximal segment pairs (MSPs) based on an all-against-all pairwise comparison of genomes are located. Second, a distance matrix is calculated from MSP scores or coverage. Finally, a phylogenetic tree is reconstructed by the neighbor-joining method.     

The sufficiency of arithmetic progressions for the Conjecture

Define by if is odd and if is even. The Conjecture states that the -orbit of every positive integer contains . A set of positive integers is said to be sufficient if the -orbit of every positive integer intersects the -orbit of an element of that set. Thus to prove the Conjecture it suffices to prove it on some sufficient set. Andaloro proved that the sets are sufficient for and asked if is also sufficient for larger values of . We answer this question in the affirmative by proving the stronger result that is sufficient for any nonnegative integers and with i.e. every nonconstant arithmetic sequence forms a sufficient set. We then prove analagous results for the Divergent Orbits Conjecture and Nontrivial Cycles Conjecture.

     

Parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences

We show that a linear partial differential operator with constant coefficients P(D) is surjective on the space of E-valued (ultra-)distributions over an arbitrary convex set if E^′ is a nuclear Fréchet space with property (DN). In particular, this holds if E is isomorphic to the space of tempered distributions S^′ or to the space of germs of holomorphic functions over a one-point set H({0}). This result has an interpretation in terms of solving the scalar equation P(D)u=f such that the solution u depends on parameter whenever the right-hand side f also depends on the parameter in the same way. A suitable analogue for surjective convolution operators over is obtained as well. To get the above results we develop a splitting theory for short exact sequences of the form

0XYZ0,