Elementary Graphs with Respect to <Emphasis Type="Italic">f</Emphasis>-Parity Factors

This note concerns the f-parity subgraph problem, i.e., we are given an undirected graph G and a positive integer value function \({f : V(G) \rightarrow \mathbb{N}}\), and our goal is to find a spanning subgraph F of G with deg _F ≤ f and minimizing the number of vertices x with \({\deg_F(x) \not\equiv f(x) \, {\rm mod} \, {2}}\) . First we prove a Gallai–Edmonds type structure theorem and some other known results on the f-parity subgraph problem, using an easy reduction to the matching problem. Then we use this reduction to investigate barriers and elementary graphs with respect to f-parity factors, where an elementary graph is a graph such that the union of f-parity factors form a connected spanning subgraph.     

On the exterior algebra method applied to restricted set addition

In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erd?s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A$A$ of the p$p$-element group Z/pZ$\mathbb{Z}/p\mathbb{Z}$ (where p$p$ is a prime), at least min{p,m|A|−m²+1}$min\{p,m\left|A\right|-m^2+1\}$ different elements of the group can be written as the sum of m$m$ different elements of A$A$. In this note we present an easily accessible simplified version of their proof for the case m=2$m=2$, and explain how the method can be applied to obtain the corresponding inverse theorem.     

Review of recent developments in OR/MS research in disaster operations management

Potential consequences of disasters involve overwhelming economic losses, large affected populations and serious environmental damages. Given these devastating effects, there is an increasing interest in developing measures in order to diminish the possible impact of disasters, which gave rise to the field of disaster operations management (DOM). In this paper we review recent OR/MS research in DOM. Our work is a continuation of a previous review from Altay and Green (2006). Our purpose is to evaluate how OR/MS research in DOM has evolved in the last years and to what extent the gaps identified by Altay and Green (2006) have been covered. Our findings show no drastic changes or developments in the field of OR/MS in DOM since the publication of Altay and Green (2006). Additionally to our comparative analysis, we present an original evaluation about the most common assumptions in recent OR/MS literature in DOM. Based on our findings we provide future research directions in order to make improvements in the areas where lack of research is detected.     

Tree metrics and edge-disjoint S-paths

Given an undirected graph \(G=(V,E)\) with a terminal set \(S \subseteq V\) , a weight function on terminal pairs, and an edge-cost \(a: E \rightarrow \mathbf{Z}_+\) , the \(\mu \) -weighted minimum-cost edge-disjoint \(S\) -paths problem ( \(\mu \) -CEDP) is to maximize \(\sum \nolimits _{P \in \mathcal{P}} \mu (s_P,t_P) - a(P)\) over all edge-disjoint sets \(\mathcal{P}\) of \(S\) -paths, where \(s_P,t_P\) denote the ends of \(P\) and \(a(P)\) is the sum of edge-cost \(a(e)\) over edges \(e\) in \(P\) . Our main result is a complete characterization of terminal weights \(\mu \) for which \(\mu \) -CEDP is tractable and admits a combinatorial min–max theorem. We prove that if \(\mu \) is a tree metric, then \(\mu \) -CEDP is solvable in polynomial time and has a combinatorial min–max formula, which extends Mader’s edge-disjoint \(S\) -paths theorem and its minimum-cost generalization by Karzanov. Our min–max theorem includes the dual half-integrality, which was earlier conjectured by Karzanov for a special case. We also prove that \(\mu \) -EDP, which is \(\mu \) -CEDP with \(a = 0\) , is NP-hard if \(\mu \) is not a truncated tree metric, where a truncated tree metric is a weight function represented as pairwise distances between balls in a tree. On the other hand, \(\mu \) -CEDP for a truncated tree metric \(\mu \) reduces to \(\mu '\) -CEDP for a tree metric \(\mu '\) . Thus our result is best possible unless P = NP. As an application, we obtain a good approximation algorithm for \(\mu \) -EDP with “near” tree metric \(\mu \) by utilizing results from the theory of low-distortion embedding.     

Synthesis of three regioisomers of the pentasaccharide part of the Skp1 glycoprotein of Dictyostelium discoideum

Three regioisomers of the linear pentasaccharide part of the Skp1 glycoprotein, found in Dictyostelium discoideum, were prepared in the form of (2-trimethylsilyl)ethyl glycosides by means of 2+3 block syntheses using the disaccharide donor at the non-reducing end, and three different trisaccharide acceptors at the reducing end. Fucosylation of (2-trimethylsilyl)ethyl 3,4,6-tri-O-benzyl-β-d-galactopyranosyl-(1→3)-4,6-O-benzylidene-2-deoxy-2-NPhth-β-d-glucopyranoside with different fucosyl donors carrying an O-(2-naphthyl)methyl ether as a temporary-protecting group at positions C2, C3 or C4 gave rise to the protected core trisaccharides. After selective removal of the (2-naphthyl)methyl group, the resulting acceptors were glycosylated with the α(1→6) linked digalactosyl donor to yield the respective three regioisomeric pentasaccharides. Transformation of the phthalimido moiety into an N-acetyl group, followed by catalytic hydrogenation of the reducible-protecting groups furnished the free target pentasaccharides, which should be able to assist during the elucidation of the exact structure of the natural pentasaccharide.     

Misgivings from the theoretical foundation of the path‐following procedures based on the Elber–Karplus strategy

A mathematical proof against the theoretical foundation of the Elber–Karplus (EK) global reaction path‐following method and the improvements based on the EK strategy have been discussed. According to our arguments the minimization of the average value of the potential energy along a path to two energy minima never defines a reaction path (RP) unless in the chemically irrealistic situation where the points of the curve joining the two minima of reactants and products have constant energy values. Therefore, finding approximate RPs by EK‐strategies for large chemical systems or even in mathematical test examples is impossible or at least strongly doubtful (the larger the system the more doubtful). This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthesis of Ristriose

ABSTRACT

A new reducing trisaccharide 0-α-D-arabinofuranosyl-(1→ 2)-0-α-D-mannopyranosyl-(1→2)-0-D-glucopyranose (11), named ristriose, has been synthesized in twenty one steps, starting from D-glucose, D-mannose and D-arabinose, with an overall yield of 3.5 %.     

Synthesis of Sialyl Lewis X Analogues

Abstract

Sialyl Lewis X (SLe^x) analogs 2a and 2b were synthesised, where the N-acetyl-D-glucose and the D-galactose units of SLe^x 1 were replaced with an alkyl and a heteroalkyl spacer. Sulphate ester 6i was also synthesised from alcohol 6b and chlorosulphonic acid. A novel promoter, silver mercaptoethanesulphonate, was used to synthesise α-sialosides 2c. 7b and 7c.     

An integrated portable Raman sensor with nanofabricated gold bowtie array substrates for energetics detection

An integrated field-portable surface enhanced Raman scattering (SERS) sensing system has been developed and evaluated for quantitative analysis of energetics such as perchlorate (ClO(4)(-)) and trinitrotoluene (TNT) at environmentally relevant concentrations and conditions. The detection system consists of a portable Raman spectrometer equipped with an optical fiber probe that is coupled with novel elevated gold bowtie nanostructural arrays as a sensitive and reproducible SERS substrate. Using the standard addition technique, we show that ClO(4)(-) and TNT can be quantified at concentrations as low as 0.66 mg L(-1) (or ~6.6 μM) and 0.20 mg L(-1) (~0.9 μM), respectively, in groundwater samples collected from selected military sites. This research represents the first step toward the development of a field SERS sensor which may permit rapid, in situ screening and analysis for various applications including national security, chemical, biological and environmental detection.