A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). Let Delta = Delta(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K-n,K-n. Alon, McDiarmid and Reed observed that a'(K-p-1,K-p-1) = p for every prime p. In this paper we prove that a'(K-p,K-p) <= p + 2 = Delta + 2 when p is prime. Basavaraju, Chandran and Kummini proved that a'(K-n,K-n) >= n + 2 = Delta + 2 when n is odd, which combined with our result implies that a'(K-p,K-p) = p + 2 = Delta + 2 when p is an odd prime. Moreover we show that if we remove any edge from K-p,K-p, the resulting graph is acyclically Delta + 1 = p + 1-edge-colorable. (C) 2009 Elsevier B.V. All rights reserved.

Growth of Mycobacterium smegmatis in minimal and complete media

The growth patterns of Mycobacterium smegmatis SN2 in a minimal medium and in nutrient broth have been compared. The growth was monitored by absorbancy (Klett readings), colony forming units, wet weight and content of DNA, RNA and protein. During the early part of the growth cycle, the bacteria had higher wet weight and macromolecular content in nutrient broth than in minimal media. During the latter half of the growth cycle however, biosynthesis stopped much earlier in nutrient broth and the bacteria had a much lower content of macromolecules than in the minimal medium. In both the media, a general pattern of completing biosynthesis rapidly in the initial phase and a certain amount of cell division at a later time involving the distribution of preformed macromolecules was seen. The possible adaptive significance of this observation has been discussed.

Nucleotide sequence and expression inE. coli of the complete P4 type VP4 from a G2 serotype human rotavirus

The complete sequence of a P4 type VP4 gene from a G2 serotype human rotavirus, IS2, isolated in India has been determined. Although the IS2 VP4 is highly homologous to the other P4 type alleles, it contained acidic amino acid substitutions at several positions that make it acidic among the P4 type alleles that are basic. Moreover, comparative sequence analysis revealed unusual polymorphism in members of the P4 type at amino acid position 393 which is highly conserved in members of other VP4 types. To date, expression of complete VP4 inE. coli has not been achieved. In this study we present successful expression inE. coli of the complete VP4 as well as VP8* and VP5* cleavage subunits in soluble form as fusion proteins of the maltose-binding protein (MBP) and their purification by single-step affinity chromatography. The hemagglutinating activity exhibited by the recombinant protein was specifically inhibited by the antiserum raised against it. Availability of pure VP4 proteins should facilitate development of polyclonal and monoclonal antibodies (MAbs) for P serotyping of rotaviruses.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Optimal multicommodity flow through the complete graph with random edge capacities

We consider a multicommodity flow problem on a complete graph whose edges have random, independent, and identically distributed capacities. We show that, as the number of nodes tends to infinity, the maximumutility, given by the average of a concave function of each commodity How, has an almost-sure limit. Furthermore, the asymptotically optimal flow uses only direct and two-hop paths, and can be obtained in a distributed manner.

Cubic and ultimate groups of complete symmetry

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

The change of complete symmetry of the crystals during the phase transitions in ferroelectrics and ferromagnetics

The extension of the superposition principle of the symmetries (P. Curie principle of symmetry) for the case of complete symmetry is given. The enumeration of all crystallographical groups of complete symmetry is presented, the number of elements having complete symmetry for each class of the crystals being indicated. The change of complete symmetry of the crystals under the phase transitions is obtained by superimposing the elements of complete symmetry of polar or axial vectors on the one hand, and the elements of complete symmetry of the crystals on the other. The tables of complete symmetry changes for the cubic, rhombic, monoclinic and triclinic crystals during the ferroelectric and ferromagnetic phase transitions are given.

Arithmetically Cohen-Macaulay bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.

Computing complete test graphs for hierarchical systems

Conformance testing focuses on checking whether an implementation. under test (IUT) behaves according to its specification. Typically, testers are interested it? performing targeted tests that exercise certain features of the IUT This intention is formalized as a test purpose. The tester needs a "strategy" to reach the goal specified by the test purpose. Also, for a particular test case, the strategy should tell the tester whether the IUT has passed, failed. or deviated front the test purpose. In [8] Jeron and Morel show how to compute, for a given finite state machine specification and a test purpose automaton, a complete test graph (CTG) which represents all test strategies. In this paper; we consider the case when the specification is a hierarchical state machine and show how to compute a hierarchical CTG which preserves the hierarchical structure of the specification. We also propose an algorithm for an online test oracle which avoids a space overhead associated with the CTG.

Complete Pick positivity and unitary invariance

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S) (z, w) = (1 - z (w) over tilde)(-1) for |z|, |w| < 1, by means of (1/k(S))(T,T*) >= 0, we consider an arbitrary open connected domain Omega in C-n, a complete Pick kernel k on Omega and a tuple T = (T-1, ..., T-n) of commuting bounded operators on a complex separable Hilbert space H such that (1/k)(T,T*) >= 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with T. Moreover, the characteristic function is then a complete unitary invariant for a suitable class of tuples T.

The complete primary structure of a unique mannose/glucose-specific lectin from field bean (Dolichos lab lab)

The complete amino acid sequence of two non identical subunits of the glucose/mannose-specific lectin from Dolichos lab lab (field bean) has been determined by sequential Edman analyses of the intact subunits and peptides derived by enzymatic and chemical cleavage. Peptides were purified by reverse phase high performance liquid chromatography and ion pair chromatography. The D. lab lab lectin is a glycoprotein having two polypeptide chains of 132 and 105 amino acid residues. The amino acid sequence of the D. Lab lab lectin is compared with the various lectins of the family Leguminosae. The D. lab lab lectin is the only species of the tribe Phaseoleae that contains two nonidentical subunits of almost equal size and that shows a specificity to glucose/ mannose. The lectin shows a greater homology to the glucose/mannose specific lectins, especially concanavalin A. The unique subunit architecture of the D. lab lab lectin indicates the presence of new post translational cleavage sites.

Synthetic studies directed towards the potent cytotoxic natural product ottelione A: stereoselective construction of the complete framework

A stereoselective strategy for the rapid acquisition of the complete framework (dideoxyottelione A) of the promising cytotoxic agent ottelione A, with four contiguous stereogenic centres on a hydrindane skeleton and a sensitive 4-methylenecyclohex-2-enone functionality, from the readily available Diels-Alder adduct of 1,2,3,4-tetrachloro-5,5-dimethoxycyclopentadiene and norbornadiene, is delineated.

Synthetic studies towards novel terpenic natural products kelsoene and poduran: Construction of the complete 4-5-5-fused tricarbocyclic core

A common synthetic approach to the recently reported sesquiterpene kelsoene 1 and the tetraterpene poduran 5, bearing a novel tricyclo[6.2.0.0(2,6)]decane framework, from commercially available 1,5-COD and leading to the first construction of the carbocyclic core present in these natural products is delineated.

A Complete Characterization of an Optimal Timer Based Selection Scheme

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.