Improvement On Brooks Chromatic Bound For A Class Of Graphs

Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).

Application of z-COSY experiment and its variant for accurate chiral discrimination by H-1 NMR

We report the application of z-COSY experiment and a band selected version of it by employing a selective 90 degrees pulse entitled BASE-z-COSY for precise chiral discrimination, quantification of enantiomeric excess and the analyses of the H-1 NMR spectra of chiral molecules aligned in the chiral liquid crystalline solvent poly-gamma-benzyl-L-glutamate (PBLG). We have demonstrated their applicability for obtaining very high resolution in the H-1 NMR spectra of small organic molecules. It is well known that the commonly employed z-COSY experiment disentangles the spectral complexity, provides pure phase spectra with high resolution, aids in the complete spectral analyses, in addition to yielding information on relative signs of the Couplings. The BASE-z-COSY experiment possesses all these properties, permits the measure of enantiomeric excess, in addition to large saving of instrument time.

d-Regular Graphs of Acyclic Chromatic Index at Least d+2

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic 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). It was conjectured by Alon, Suclakov and Zaks (and earlier by Fiamcik) that a'(G) <= Delta+2, where Delta = Delta(G) denotes the maximum degree of the graph. Alon et al. also raised the question whether the complete graphs of even order are the only regular graphs which require Delta+2 colors to be acyclically edge colored. In this article, using a simple counting argument we observe not only that this is not true, but in fact all d-regular graphs with 2n vertices and d>n, requires at least d+2 colors. We also show that a'(K-n,K-n) >= n+2, when n is odd using a more non-trivial argument. (Here K-n,K-n denotes the complete bipartite graph with n vertices on each side.) This lower bound for Kn,n can be shown to be tight for some families of complete bipartite graphs and for small values of n. We also infer that for every d, n such that d >= 5, n >= 2d+3 and dn even, there exist d-regular graphs which require at least d+2-colors to be acyclically edge colored. (C) 2009 Wiley Periodicals, Inc. J Graph Theory 63: 226-230, 2010.

Strain-Temperature Discrimination Using a Single Fiber Bragg Grating

The out-diffusion of germanium from the core of a photosensitive fiber under elevated temperature is exploited to form a Fabry-Perot filter within a single fiber Bragg grating, by subjecting the diffused region to a single exposure using the standard phase-mask technique. A key aspect of our work is the measurement of the out-diffusion through energy dispersive X-ray analysis. Furthermore, we demonstrate the use of the above single-grating filter for discrimination and simultaneous measurement of strain and temperature. The proposed technique provides a significant advantage over other existing methods that require at least two gratings.

Non-destructive discrimination of Bell states by NMR using a single ancilla qubit

Discrimination of Bell states plays an important role in a number of quantum computational protocols such as teleportation and secret sharing. However, most of the protocols dealing with Bell state discrimination in the literature either involve performing correlated measurements or destroying the entanglement of the system. Here, we demonstrate an NMR-based experimental realization of a protocol for Bell state discrimination, following a scheme proposed by Gupta et al (quant-ph/0504183v1, 23 April 2005), which does not destroy the Bell state under consideration. Using the proposed protocol, one can deterministically distinguish the Bell states, without performing a measurement using the entangled basis. State discrimination is performed through two independent measurements on one ancilla qubit, which leaves the Bell states unchanged.

Modulation of lifetimes and diastereomeric discrimination in triplet-excited substituted butane-1,4-diones through intramolecular charge-transfer quenching

Triplet lifetimes have been determined for the diastereomers of a broad set of butane-l,4-dione derivatives (1-3). A remarkable dependence of lifetimes on conformational preferences is revealed in that the lifetimes are shorter for the meso diastereomers of 1-3 than those for the racemic ones. The intramolecular beta-phenyl quenching is promoted in the case of meso diastereomers by virtue of the gauche relationship between the excited carbonyl group and the beta-aryl ring, while a distal arrangement in the lowest energy conformation (H-anti) in racemic diastereomers prevents such a deactivation. The involvement of charge transfer in the intramolecular beta-phenyl quenching is suggested by the correlation of the triplet lifetimes of the meso diastereomers of compounds 2 with the nature of the substituent on the beta-phenyl rings. In the case of racemic diastereomers, beta-methoxy substitution on the beta-phenyl ring (2-OCH3, 3-OCH3) also led to a decrease of the triplet lifetimes when compared to those of the nonsubstituted compounds (2-H, 3-H). This shortening is accounted for by the deactivation of a small proportion of the excited molecules through beta-phenyl quenching. In addition to the above factors, the lifetimes in the case of meso diastereomers can further be controlled by increasing the energy spacing between the T-1 and T-2 states, since beta-phenyl quenching occurs from the latter for compounds 2 and 3. Through a rational conformational control, a surprisingly long triplet lifetime (300 ns) has been measured for the first time for a purely n,pi* triplet-excited beta-phenylpropiophenone dimer (1-rac).

Development of recombinant coat protein antibody based IC-RT-PCR for detection and discrimination of sugarcane streak mosaic virus isolates from Southern India

Sugarcane streak mosaic virus (SCSMV), causes mosaic disease of sugarcane and is thought to belong to a new undescribed genus in the family Potyviridae. The coat protein (CP) gene from the Andhra Pradesh (AP) isolate of SCSMV (SCSMV AP) was cloned and expressed in Escherichia coli. The recombinant coat protein was used to raise high quality antiserum. The CP antiserum was used to develop an immunocapture reverse transcription-polymerase chain reaction (IC-RT-PCR) based assay for the detection and discrimination of SCSMV isolates in South India. The sequence of the cloned PCR products encoding 3'untranslated region (UTR) and CP regions of the virus isolates from three different locations in South India viz. Tanuku (Coastal Andhra Pradesh), Coimbatore (Tamil Nadu) and Hospet (Karnataka) was compared with that of SCSMV AP The analysis showed that they share 89.4, 89.5 and 90% identity respectively at the nucleotide level. This suggests that the isolates causing mosaic disease of sugarcane in South India are indeed strains of SCSMV In addition, the sensitivity of the IC-RT-PCR was compared with direct antigen coating-enzyme linked immunosorbent assay (DAC-ELISA) and dot-blot immunobinding assays and was found to be more sensitive and hence could be used to detect the presence of virus in sugarcane breeding, germplasm centres and in quarantine programs.

Discrimination of Nuclear Grade Steel Samples Subjected to Different Heat Treatment Procedures Based on Acoustic Emission (AE) Data Profiling at Crack Initiation

The present work is an attempt to study crack initiation in nuclear grade, 9Cr-1Mo ferritic steel using AE as an online NDE tool. Laboratory experiments were conducted on 5 heat treated Compact Tension (CT) specimens made out of nuclear grade 9Cr-1Mo ferritic steel by subjecting them to cyclic tensile load. The CT Specimens were of 12.5 mm thickness. The Acoustic emission test system was setup to acquire the data continuously during the test by mounting AE sensor on one of the surfaces of the specimen. This was done to characterize AE data pertaining to crack initiation and then discriminate the samples in terms of their heat treatment processes based on AE data. The AE signatures at crack initiation could conclusively bring to fore the heat treatment distinction on a sample to sample basis in a qualitative sense.Thus, the results obtained through these investigations establish a step forward in utilizing AE technique as an on-line measurement tool for accurate detection and understanding of crack initiation and its profile in 9Cr-1Mo nuclear grade steel subjected to different processes of heat treatment.

Protein Model Discrimination Using Mutational Sensitivity Derived from Deep Sequencing

A major bottleneck in protein structure prediction is the selection of correct models from a pool of decoys. Relative activities of similar to 1,200 individual single-site mutants in a saturation library of the bacterial toxin CcdB were estimated by determining their relative populations using deep sequencing. This phenotypic information was used to define an empirical score for each residue (Rank Score), which correlated with the residue depth, and identify active-site residues. Using these correlations, similar to 98% of correct models of CcdB (RMSD <= 4 angstrom) were identified from a large set of decoys. The model-discrimination methodology was further validated on eleven different monomeric proteins using simulated RankScore values. The methodology is also a rapid, accurate way to obtain relative activities of each mutant in a large pool and derive sequence-structure-function relationships without protein isolation or characterization. It can be applied to any system in which mutational effects can be monitored by a phenotypic readout.