The GHP II Package with Applications

We present an advanced version of the Maple package GHP called GHPII. In it we provide a number of additional sophisticated tools to assist with problems formulated in the Geroch-Held-Penrose (ghp) formalism. The first part of this article discusses these new tools while in the second part we shall apply the ghp formalism, using the GHPII routines, to vacuum Petrov type D spacetimes and shear-free perfect fluids. We prove that for all shear-free perfect fluids with a barotropic equation of state, where two of the principal null directions are coplanar with the fluid four-velocity and vorticity then either the expansion or vorticity of the fluid must be zero.     

Stability analysis of a system of second‐order difference equations

In this paper, we study the boundedness character and persistence, existence and uniqueness of the positive equilibrium, local and global behavior, and the rate of convergence of positive solutions of the following system of rational difference equations where the parameters α_i,β_i,a_i,b_i for i∈{1,2} and the initial conditions x_?1,x₀,y_?1,y₀ are positive real numbers. Some numerical example are given to verify our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Null controllability in large time of a parabolic equation involving the Grushin operator with an inverse-square potential

We prove the null controllability in large time of the following linear parabolic equation involving the Grushin operator with an inverse-square potential

$$u_t-\Delta_{x} u-|x|^{2}\Delta_{y}u-\frac{\mu}{|x|^2}u=v1_\omega$$

in a bounded domain \({\Omega=\Omega_1\times \Omega_2\subset \mathbb{R}^{N_1}\times \mathbb{R}^{N_2} (N_1\geq 3, N_2\geq 1}\)) intersecting the surface {x = 0} under an additive control supported in an open subset \({\omega=\omega_1\times \Omega_2}\) of \({\Omega}\).

     

The Lipschitzianity of convex vector and set-valued functions

It is well known that every scalar convex function is locally Lipschitz on the interior of its domain in finite dimensional spaces. The aim of this paper is to extend this result for both vector functions and set-valued mappings acting between infinite dimensional spaces with an order generated by a proper convex cone C. Under the additional assumption that the ordering cone C is normal, we prove that a locally C-bounded C-convex vector function is Lipschitz on the interior of its domain by two different ways. Moreover, we derive necessary conditions for Pareto minimal points of vector-valued optimization problems where the objective function is C-convex and C-bounded. Corresponding results are derived for set-valued optimization problems.     

N‐Linked Glycosyl Auxiliary‐Mediated Native Chemical Ligation on Aspartic Acid: Application towards N‐Glycopeptide Synthesis

A practical approach towards N‐glycopeptide synthesis using an auxiliary‐mediated dual native chemical ligation (NCL) has been developed. The first NCL connects an N‐linked glycosyl auxiliary to the thioester side chain of an N‐terminal aspartate oligopeptide. This intermediate undergoes a second NCL with a C‐terminal thioester oligopeptide. Mild cleavage provides the desired N‐glycopeptide.     

Mechanical properties of metallic thin films: theoretical approach

The statistical moment method in statistical mechanics was developed to investigate themechanical properties of free-standing metallic thin films at ambient conditions includingthe anharmonicity effects of thermal lattice vibrations. Analytical expressions ofisothermal areal modulus B_T, Young’s modulusE and shearmodulus Gwere derived in terms of the power moments of the atomic displacements. Numericalcalculations have been performed for metallic Ni, Au and Al thin films, and compared withthose of bulk metals. This method is physically transparent and it successfully describedthe temperature effects on mechanical properties of metallic thin films.     

Effect of mutations to amino acid A301 and F361 in thermostability and catalytic activity of the β-galactosidase from <Emphasis Type="Italic">Bacillus subtilis</Emphasis> VTCC-DVN-12-01

Background

Beta-galactosidase (EC 3.2.1.23), a commercially important enzyme, catalyses the hydrolysis of β-1,3- and β-1,4-galactosyl bonds of polymer or oligosaccharidesas well as transglycosylation of β-galactopyranosides. Due to catalytic properties; β-galactosidase might be useful in the milk industry to hydrolyze lactose and produce prebiotic GOS. The purpose of this study is to characterize β-galactosidase mutants from B. subtilis.

Results

Using error prone rolling circle amplification (epRCA) to characterize some random mutants of the β-galactosidase (LacA) from B. subtilisVTCC-DVN-12-01, amino acid A301 and F361 has been demonstrated significantly effect on hydrolysis activity of LacA. Mutants A301V and F361Y had markedly reduced hydrolysis activity to 23.69 and 43.22 %, respectively. Mutants the site-saturation of A301 reduced catalysis efficiency of LacA to 20–50 %, while the substitution of F361 by difference amino acids (except tyrosine) lost all of enzymatic activity, indicating that A301 and F361 are important for the catalytic function. Interestingly, the mutant F361Y exhibited enhanced significantly thermostability of enzyme at 45–50 °C. At 45 °C, LacA-361Y retained over 93 % of its original activity for 48 h of incubation, whereas LacA-WT and LacA-301Vwere lost completely after 12 and 24 h of incubation, respectively. The half-life times of LacA-361Y and LacA-301 V were about 26.8 and 2.4 times higher, respectively, in comparison to the half-life time of LacA-WT. At temperature optimum 50 °C, LacA-361Y shows more stable than LacA-WT and LacA-301 V, retaining 79.88 % of its original activities after 2 h of incubation, while the LacA-WT and LacA-301 V lost all essential activities. The half-life time of LacA-361Y was higher 12.7 and 9.39 times than that of LacA-WT and LacA-301 V, respectively. LacA-WT and mutant enzymes were stability at pH 5–9, retained over 90 % activity for 72 h of incubation at 30 °C. However, LacA-WT showed a little bit more stability than LacA-301 V and LacA-361Y at pH 4.

Conclusions

Our findings demonstrated that the amino acids A301V and F361 play important role in hydrolysis activity of β -galactosidase from B. subtilis. Specially, amino acid F361 had noteworthy effect on both catalytic and thermostability of LacA enzyme, suggesting that F361 is responsible for functional requirement of the GH42 family.

     

Bottom-Up Synthesis,Dispersion and Properties of Rectangular-Shaped Graphene Quantum Dots

Carbon nanomaterials have attracted the attention of the scientific community for more than 30 years now; first with fullerene, then with nanotubes and now with graphene and graphene related materials. Graphene quantum dots (GQDs) are nanoparticles of graphene that can be synthesized following two approaches, namely top-down and bottom-up methods. The top-down synthesis used harsh chemical and/or physical treatments of macroscopic graphitic materials to obtain nanoparticles, while the second is based on organic chemistry through the synthesis of polycyclic aromatic hydrocarbons exhibiting various sizes and shapes that are perfectly controlled. The main drawback of this approach is related to the low solubility of carbon materials that prevents the synthesis of nanoparticles containing more than few hundreds of sp² carbon atoms. Here we report on the synthesis of a family of rectangular-shaped graphene quantum dots containing up to 162 sp² carbon atoms. These graphene quantum dots are not functionalized on their periphery in order to keep the maximum similarity with nanoparticles of pure graphene. We chose water with sodium deoxycholate surfactant to study their dispersion and their optical properties (absorption, photoluminescence and photoluminescence excitation). The electronic structure of the particles and of their aggregates are studied using Tight-Binding (TB). We observe that the larger particles ( GQD 3 and GQD 4 ) present a slightly better dispensability than the smaller ones, probably because the larger GQDs can accommodate more surfactant molecules on each side, which helps to stabilize their dispersion in water.     

Rotationally resolved electronic spectroscopy of water clusters of 7-azaindole

The rotationally resolved electronic spectra of the electronic origin of the 7-azaindole-(H(2)O)(1) and of the 7-azaindole-(H(2)O)(2) clusters have been measured in a molecular beam. From the rotational constants the structures in the S(0) and S(1) electronic states were determined as cyclic with the pyrrolo NH and the pyridino N atoms being bridged by one and two water molecules, respectively. Excited state lifetimes of about 10 ns for both clusters have been found. In the spectrum of the 7-azaindole-(H(2)O)(2) cluster a splitting of the rovibronic band is observed, which can be traced back to a large amplitude motion, involving the out-of-plane hydrogen atoms of the water chain. Both the changes of the rotational constants upon electronic excitation and the orientation of the transition dipole point to a solvent induced state reversal between the L(a) and the L(b) states upon microsolvation.     

Energetics and mechanism of the decomposition of trifluoromethanol

The thermal instability of alpha-fluoroalcohols is generally attributed to a unimolecular 1,2-elimination of HF, but the barrier to intramolecular HF elimination from CF3OH is predicted to be 45.1 +/- 2 kcal/mol. The thermochemical parameters of trifluoromethanol were calculated using coupled-cluster theory (CCSD(T)) extrapolated to the complete basis set limit. High barriers of 42.9, 43.1, and 45.0 kcal/mol were predicted for the unimolecular decompositions of CH2FOH, CHF2OH, and CF3OH, respectively. These barriers are lowered substantially if cyclic H-bonded dimers of CF3OH with complexation energies of approximately 5 kcal/mol are involved. A six-membered ring dimer has an energy barrier of 28.7 kcal/mol and an eight-membered dimer has an energy barrier of 32.9 kcal/mol. Complexes of CF3OH with HF lead to strong H-bonded dimers, trimers and tetramers with complexation energies of approximately 6, 11, and 16 kcal/mol, respectively. The dimer, CH3OH:HF, and the trimers, CF3OH:2HF and (CH3OH)2:HF, have decomposition energy barriers of 26.7, 20.3, and 22.8 kcal/mol, respectively. The tetramer (CH3OH:HF)2 gives rise to elimination of two HF molecules with a barrier of 32.5 kcal/mol. Either CF3OH or HF can act as catalysts for HF-elimination via an H-transfer relay. Because HF is one of the decomposition products, the decomposition reactions become autocatalytic. If the energies due to complexation for the CF3OH-HF adducts are not dissipated, the effective barriers to HF elimination are lowered from approximately 20 to approximately 9 kcal/mol, which reconciles the computational results with the experimentally observed stabilities.