Acyclic edge coloring of subcubic graphs

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 it is denoted by a′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors.

Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.

Effect of compatibilization on mechanical and thermal properties of polypropylene–soy flour composites

A new biobased composite was developed by adding soy flour (SF) to polypropylene (PP). This composite shows an enhanced tensile strength and modulus but decrease in elongation at break. The compatibilizer (coupling agent) appears to have a synergistic effect on tensile strength. The presence of the compatibilizer improves the dispersion of SF in the PP matrix. The addition of glycerol plasticizer to the composite improves the processability resulting in improved performance, as compared to composites without glycerol plasticizer. The optimal compatibilizer content appears to be 6%.

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.

High-level expression of biologically active glycoprotein hormones in Pichia pastoris strains—selection of strain GS115, and not X-33, for the production of biologically active N-glycosylated 15N-labeled phCG

The methylotrophic yeast Pichia pastoris is widely used for the production of recombinant glycoproteins. With the aim to generate biologically active 15N-labeled glycohormones for conformational studies focused on the unravelling of the NMR structures in solution, the P. pastoris strains GS115 and X-33 were explored for the expression of human chorionic gonadotropin (phCG) and human follicle-stimulating hormone (phFSH). In agreement with recent investigations on the N-glycosylation of phCG, produced in P. pastoris GS115, using ammonia/glycerol-methanol as nitrogen/carbon sources, the N-glycosylation pattern of phCG, synthesized using NH4Cl/glucose–glycerol–methanol, comprised neutral and charged, phosphorylated high-mannose-type N-glycans (Man8–15GlcNAc2). However, the changed culturing protocol led to much higher amounts of glycoprotein material, which is of importance for an economical realistic approach of the aimed NMR research. In the context of these studies, attention was also paid to the site specific N-glycosylation in phCG produced in P. pastoris GS115. In contrast to the rather simple N-glycosylation pattern of phCG expressed in the GS115 strain, phCG and phFSH expressed in the X-33 strain revealed, besides neutral high-mannose-type N-glycans, also high concentrations of neutral hypermannose-type N-glycans (Manup-to-30GlcNAc2). The latter finding made the X-33 strain not very suitable for generating 15N-labeled material. Therefore, 15N-phCG was expressed in the GS115 strain using the new optimized protocol. The 15N-enrichment was evaluated by 15N-HSQC NMR spectroscopy and GLC-EI/MS. Circular dichroism studies indicated that 15N-phCG/GS115 had the same folding as urinary hCG. Furthermore, 15N-phCG/GS115 was found to be similar to the unlabeled protein in every respect as judged by radioimmunoassay, radioreceptor assays, and in vitro bioassays.

Aggregation and mesomorphic properties of 'double-headed' carbohydrate amphiphiles

Sugar-based amphiphiles, consisting of two sugar head groups and an alkylene chain within the molecules, are synthesized and their aggregation and mesomorphic properties are evaluated. The hydrophilic sugar head groups, constituted with beta-D-glucopyranoside units, and the lyophilic alkylene units, are coupled to a glycerol backbone to afford the 'double-headed' sugar amphiphiles. Aggregation studies in aqueous solutions provided their critical micellar concentrations and the aggregation numbers. Mesophase characterizations by polarizing optical microscopy and differential scanning calorimetry (DSC) revealed the phase-transition behaviour of these new 'double-headed' glycolipids.

Heat transfer to newtonian fluids in coiled pipes in laminar flow

Data on pressure drop and heat transfer to aqueous solutions of glycerol flowing in different types of coiled pipes are presented for laminar flow in the range of NRe from 80 to 6000. An empirical correlation is set up which can account the present data as well as the data available in literature within ±10 per cent deviation. Conventional momentum and heat transfer analogy equation is used to analyse the present data.

Heats of combustion of some symmetrical dialkyl ureas and their corresponding alkyl carbamates

The standard heats of combustion of the disubstituted ureas, N, N′-diheptyl urea, N, N′-dioctyl urea and N, N′-didecyl urea and the carbamates,n-heptyl ammoniumn-heptyl carbamate,n-octylammoniumn-octyl carbamate andn-decyl ammoniumn-decyl carbamate have been determined. The values found are 2353±1·3, 2658·4±1·1, 3268·5±1·7, 2349·8±1·6, 2654·4±1·2, 3264·6±1·8, K.cals. mole−1 respectively. The heats of formation of these compounds have been calculated.

Intraseasonal response of mixed layer temperature and salinity in the Bay of Bengal to heat and freshwater flux

Buoy and satellite data show pronounced subseasonal oscillations of sea surface temperature (SST) in the summertime Bay of Bengal. The SST oscillations are forced mainly by surface heat flux associated with the active break cycle of the south Asian summer monsoon. The input of freshwater (FW) from summer rain and rivers to the bay is large, but not much is known about subseasonal salinity variability. We use 2002-2007 observations from three Argo floats with 5 day repeat cycle to study the subseasonal response of temperature and salinity to surface heat and freshwater flux in the central Bay of Bengal. About 95% of Argo profiles show a shallow halocline, with substantial variability of mixed layer salinity. Estimates of surface heat and freshwater flux are based on daily satellite data sampled along the float trajectory. We find that intraseasonal variability of mixed layer temperature is mainly a response to net surface heat flux minus penetrative radiation during the summer monsoon season. In winter and spring, however, temperature variability appears to be mainly due to lateral advection rather than local heat flux. Variability of mixed layer freshwater content is generally independent of local surface flux (precipitation minus evaporation) in all seasons. There are occasions when intense monsoon rainfall leads to local freshening, but these are rare. Large fluctuations in FW appear to be due to advection, suggesting that freshwater from rivers and rain moves in eddies or filaments.

Reaction of dialkyl 2-butynoate with aniline and formaldehyde: revision of the structure of the product

Dimethyl 3-(aryl)-3,6-dihydro-2H-1,3-oxazine4,5-dicarboxylate structure assigned for the products obtained in the Bronsted acid catalyzed reaction of dimethyl but-2-ynoates with anilines and an excess of formaldehyde in methanol has been revised to methyl 1-(aryl)-3-(methoxymethyl)-4,5-dioxopyrrolidine-3-carboxylate. (C) 2010 Elsevier Ltd. All rights reserved.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

Analysis of Flux Fringing for High-Frequency AC Inductor Design

Design of high-frequency inductors for purposes like Active Front End (AFE) converter filters involves analytical calculations based on methods like area product approach and accurate graphical methods. Once a core with an area product is selected the subsequent calculations of inductance and peak operating flux requires the estimation of reluctance of the magnetic circuit. This in turn demands an estimate of the fringing that will happen in the air gap of the inductor. In this paper we have looked at analytical methods for evaluating fringing flux and compared it with results from finite element method. Different levels of details of modelling the inductor is first considered for this purpose. The end results are compared with experimental measurements of inductance. It is shown that simple fringing flux model can provide accurate models for the inductor design.