The number of edges in a bipartite graph of given radius

Vizing established an upper bound on the size of a graph of given order and radius. We find a sharp upper bound on the size of a bipartite graph of given order and radius.     

Temperature,concentration and salt effect on F68 tri-block copolymer in aqueous solution: Rheological study

The rheology of the aqueous solution of poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) (PEO?PPO?PEO) triblock copolymer, Pluronic F68 in the presence of KF was studied in the temperature range from 15 to 60°C. The variation of the shear stress according to the shear rate shows that independently from the temperature and concentration, the F68 solutions exhibit a Newtonian behavior. The results show that the Critical Micelle Temperature of Pluronic F68 in a KF aqueous solution decreases with the increase in the salt concentration.     

Changes in the morphology of interstellar ice analogues after hydrogen atom exposure

The morphology of water ice in the interstellar medium is still an open question. Although accretion of gaseous water could not be the only possible origin of the observed icy mantles covering dust grains in cold molecular clouds, it is well known that water accreted from the gas phase on surfaces kept at 10 K forms ice films that exhibit a very high porosity. It is also known that in the dark clouds H(2) formation occurs on the icy surface of dust grains and that part of the energy (4.48 eV) released when adsorbed atoms react to form H(2) is deposited in the ice. The experimental study described in the present work focuses on how relevant changes of the ice morphology result from atomic hydrogen exposure and subsequent recombination. Using the temperature-programmed desorption (TPD) technique and a method of inversion analysis of TPD spectra, we show that there is an exponential decrease in the porosity of the amorphous water ice sample following D-atom irradiation. This decrease is inversely proportional to the thickness of the ice and has a value of ?(0) = 2 × 10(16) D-atoms cm(-2) per layer of H(2)O. We also use a model which confirms that the binding sites on the porous ice are destroyed regardless of their energy depth, and that the reduction of the porosity corresponds in fact to a reduction of the effective area. This reduction appears to be compatible with the fraction of D(2) formation energy transferred to the porous ice network. Under interstellar conditions, this effect is likely to be efficient and, together with other compaction processes, provides a good argument to believe that interstellar ice is amorphous and non-porous.     

Spanning cycles of nearly cubic graphs

The fact that a cubic hamiltonian graph must have at least three spanning cycles suggests the question of whether every hamiltonian graph in which each point has degree at least 3 must have at least three spanning cycles. We answer this in the negative by exhibiting graphs on n=2m+1, m≥5, points in which one point has degree 4, all others have degree 3, and only two spanning cycles exist.     

Trees with Equal Domination and Restrained Domination Numbers

Let G = (V,E) be a graph and let S V. The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), is the minimum cardinality of a DS of G, while the restrained domination number of G, denoted by γ_r(G), is the minimum cardinality of a RDS of G. The graph G is γ-excellent if every vertex of G belongs to some minimum DS of G. A constructive characterization of trees with equal domination and restrained domination numbers is presented. As a consequence of this characterization we show that the following statements are equivalent: (i) T is a tree with γ(T)=γ_r(T); (ii) T is a γ-excellent tree and T ≠ K₂; and (iii) T is a tree that has a unique maximum packing and this set is a dominating set of T. We show that if T is a tree of order n with ℓ leaves, then γ_r(T) ≤ (n + ℓ + 1)/2, and we characterize those trees achieving equality.     

Rheological Properties of L64 Tri-block Copolymer in Aqueous and <Emphasis Type="Italic">p</Emphasis>-xylene Solutions

The rheological properties of Pluronic L64 in aqueous solutions at various temperatures and concentrations have been investigated. Changes in temperature and concentration cause structural and rheological modifications in Pluronic L64 in aqueous solutions as well as the appearance of a micellization process. For concentrations between 10 and 20 mg/mL, the Pluronic L64 showed a Newtonian or liquid-like behavior at various temperatures. However, for concentrations ranging between 30 and 40 mg/mL, the solutions showed a Newtonian behavior for temperatures below 55°C and a non-Newtonian behavior at 60°C. In p-xylene solutions, the solution exhibits a Newtonian behavior for all the concentrations and temperatures studied. It is believed that the Newtonian behavior of the binary Pluronic L64/p-xylene is due to the nonformation of complex conformations as direct or reverse micelles.     

Alkaline hydrolysis of ethiofencarb: Kinetic study and mechanism degradation

The present paper deals with the hydrolysis of ethiofencarb [2‐ethylthiomethyl(phenyl)‐N‐methylcarbamate] in alkaline solution. The reaction kinetics has been investigated using spectrophotometric and liquid chromatographic techniques. The rate constants were determined following a proposed first‐order kinetic model. The positive activation entropy Δ S^≠ = +100.07 J mol^?1 K^?1 and the absence of general basic catalysis indicated an E1cB hydrolytic mechanism, involving the formation of methyl isocyanate. This result was confirmed by the fact that ethiofencarb fits well into Brönsted and Hammett lines, obtained for a series of substituted N‐methylcarbamate whose decomposition in aqueous media was established to follow an E1cB mechanism. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 45: 118–124, 2013     

The influence of CHx coating on the optical properties of porous silicon

In this work, we report a study on the influence of CH_x thickness layer on optical properties of CH_x/PS/Si structures. The hydrocarbon groups were deposited by plasma of methane–argon mixture.The properties of these structures are investigated by photoluminescence (PL), reflection and spectral response measurements from where a different behavior depending on CH_x layer thickness has been observed.The entire total reflection spectrum is modulated by Fabry–Pérot fringes that are a result of thin film interference. As the CH_x layer thickness increases, the amplitude of the interferences decreases and a positive shift of the maximum peak is observed.The PL spectra from CH_x/PS samples with two CH_x layer thicknesses show more intense luminescence than that observed from PS sample and the existence of an optimum thickness CH_x that gives the maximum PL intensity. The spectral response spectra show the presence of an intense peak at 450 nm. Finally, the results point out the importance of CH_x coating in optoelectronic applications.