On the cubicity of bipartite graphs

A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.

Structure of 5'-O-acetyl-2',3'-O-isopropylideneuridine, C14H18N2O7

M r = 326.3, monoclinic, P21, a --= 6.510 (2), b=8.432 (2), c= 15.114 (2),a, /~= 101.42 (3) ° , Z = 2, V= 813.15 A 3, D x = 1-33 Mg m -3, F(000) = 172, 2(Cu Ka) = 1.5418/~,, g(Cu Ka) = 0.906 mm -~, final R = 6.4% for 1924 observed counter reflections. The conformation about the glycosidic bond is syn [torsion angle C(6)-N(1)-C(1')-O(4')=-103.9(3)°]. The sugar pucker is C(2')-exo,C(3')-endo (3Tz). The conformation about the C(4')-C(5') bond is gauche-trans. An uncommon intermolecular hydrogen bond involving the ribose-ring oxygen O(1') and the base-nitrogen N(3) stabilizes the crystal structure.

Electrical Discharge Resistant Characteristics of Epoxy Nanocomposites

This paper reports the electrical discharge resistant characteristics of epoxy nanocomposite systems with SiO2 and Al2O3 nano-fillers. A comparative study is performed between unfilled epoxy systems, nanoparticle filled epoxy systems and a bimodal system containing both micrometer and nanometer sized fillers of the same material. The samples are exposed to surface discharges and the levels of surface degradation are analyzed through SEM and surface roughness measurements. Significant variations were observed in the electrical discharge resistant characteristics between the different composite systems and it is seen that the introduction of nano-fillers to epoxy is advantageous in improving the electrical discharge resistance of epoxy.

Miniversal Deformations Of Dialgebras

We develop the theory of versal deformations of dialgebras and describe a method for constructing a miniversal deformation of a dialgebra.

A novel combustion process for the synthesis of fine particle α-alumina and related oxide materials

Synthesis of fine particle α-alumina and related oxide materials such as MgAl2O4, CaAl2O4, Y3Al5O12 (YAG), Image , β′-alumina, LaAlO3 and ruby powder (Image ) has been achieved at low temperatures (500°C) by the combustion of corresponding metal nitrate-urea mixtures. Solid combustion products have been identified by their characteristic X-ray diffraction patterns. The fine particle nature of α-alumina and related oxide materials has been investigated using SEM, TEM, particle size analysis and surface area measurements.

Kinetic mechanism of the interaction of D-cycloserine with serine hydroxymethyltransferase

The kinetic mechanism for the interaction of D-cycloserine with serine hydroxymethyltransferase (EC2.1.2.1) from sheep liver was established by measuring changes in the activity, absorbance, and circular dichoism (CD) of the enzyme. The irreversible inhibition of the enzyme was characterized by three detectable steps: an initial rapid step followed by two successive steps with rate constants of 5.4 X s-l and 1.4 X lo4 s-l. The first step was distinguished by a rapid disappearance of the enzyme absorbance peak at 425 nm, a decrease in the enzyme activity to 25% of the uninhibited velocity, and a lowering of the CD intensity at 432 nm to about 65% of the original value. The second step of the interaction was accompanied by a complete loss of enzyme.

Preparative solid state chemistry. Recent developments

A survey of recent developments in preparative solid state chemistry shows that, with a knowledge of structural chemistry and reactivity patterns of solids, it is possible to synthesize a variety of new solids possessing novel structures. A distinction is made between synthesis ofnew solids and synthesis of solids bynew methods. Three new routes to solid state synthesis are recognized: the precursor method, and topochemical methods involving redox and ion-exchange reactions. The low-temperature topochemical methods enable synthesis of metastable phases that are inaccessible by the high temperature route. Several illustrative examples of solid state synthesis from the recent literature are presented.

Planar pursuit-evasion with variable speeds, part 2, barrier sections

An iterative method of constructing sections of the game surfaces from the players'' extremal trajectory maps is discussed. Barrier sections are presented for aircraft pursuit-evasion at constant altitude, with one aircraft flying at sustained speed and the other varying its speed.

Global lopsided instability in a purely stellar galactic disc

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A(1), increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the groundstate lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N-body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global m = 1 instabilities, with almost zero pattern speed.

The Isolation and Characterization of β-N-Oxalyl-L-α,β-Diaminopropionic Acid: A Neurotoxin from the Seeds of Lathyrus sativus

A neurotoxic compound has been isolated from the seeds of Lathyrus sativus in 0.5% yield and characterized as β-N-oxalyl-L-α,β-diaminopropionic acid. The compound is highly acidic in character and forms oxalic acid and diaminopropionic acid on acid hydrolysis. The compound has a specific rotation of -36.9° and has apparent pK values in the order of 1.95, 2.95, and 9.25, corresponding to the two carboxyl and one amino functions, respectively. The compound has been synthesized by reacting an aqueous methanolic solution of the copper complex of L-α,β-diaminopropionic acid prepared at pH 4.5-5.0 with dimethyl oxalate under controlled pH conditions and isolating the compound by chromatography on a Dowex 50-H+ column after precipitating the copper. The compound induced severe neurological symptoms in day-old chicks at the level of 20 mg/chick, but not in rats or mice. It also inhibited the growth of several microorganisms and of the insect larva Corcyra cephalonica Staint. L-Homoarginine had no neural action in chicks. It is suggested that the neurotoxic compound is species specific in its action and may be related to "neurolathyrism" associated with the human consumption of L. sativus seeds.

Hydrogel-assisted synthesis of nanotubes and nanorods of US, ZnS and CuS, showing some evidence for oriented attachment

By carrying out the reaction of appropriate metal compounds with Na2S in the presence of a tripodal cholamide-based hydrogel, nanotubes and nanorods of CdS, ZnS and CuS have been obtained. The nanostructures have been characterized by transmission electron microscopy and spectroscopic techniques. Evidence is presented for the assembly of short nanorods to form one-dimensional chains.

Low Temperature Synthesis of Nano-Crystalline CaCu3Ti4O12 Through aFuel Mediated Auto-Combustion Pathway

A novel, cost effective,environment-friendly and energetically beneficial alternative method for the synthesis of giant dielectric pseudo-perovskite material CaCu3Ti4O12 (CCTO) is presented. The method involved auto-combustion of an aqueous precursor solution in oxygen atmosphere with the help of external fuels and is capable of producing high amount of CCTO at ultra-low temperature, in the combustion residue itself. The amount of phase generated was observed to be highly dependent on the combustion process i.e. on the nature and amount of external-fuels added for combustion. Two successful fuel combinations capable of producing reasonably higher amount of the desired compound were investigated. On a structural characterization grain size was observed to decrease drastically to nano-dimension compared to submicron-size that was obtained in a traditional sol-gel combustion and subsequent cacination method. Therefore, the method reported can produce nano-crystalline CaCu3Ti4O12 ceramic matrix at an ultra-low temperature and is expected to be applicable for other multifunctional perovskite oxide materials.

On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.