Gold-catalyzed 1,2-difunctionalizations of aminoalkynes using only N- and O-containing oxidants

We report two viable routes for the 1,2-difunctionalization of aminoalkynes using only oxidants. In the presence of a gold catalyst, nitrones enable the oxoamination of aminoalkynes 1 to form 2-aminoamides 2. With a suitable gold catalyst, nitrosobenzenes implement an alkyne/nitroso metathesis of the same substrates to give 2-oxoiminylamides 3. These two novel oxidations also provide 1,2-aminoalcohols with opposite regioselectivity via NaBH(4) reduction in situ.     

Low-temperature magnetization relaxation in magnetic molecular solids

The low temperature relaxation of the magnetization in molecular magnetic solids such as Fe₈ is studied using Monte Carlo simulations. A set of rate equations is then developed to understand the simulations, and the results are compared. The simulations show that the magnetization of an initially saturated sample deviates as a square-root in time at short times, as observed experimentally, and this law is derived from the rate equations analytically.     

Degree of approximation of functions in the Hölder metric by Borel’s means

After establishing the Fourier character of the series the authors have studied the degree of approximation of functions associated with the same series in the Hölder metric using Borel’s mean.     

Synthesis of 1-Isonicotinoyl-3-Methyl-4-(Substituted AZO) Pyrazol-5-Ones

Isonicotinic acid hydrazide (INH) and their derivatives are generally used as antitubercular agent. We synthesised 1-isonicotinoyl-3-methyl-4-(substituted azo) pyrazol-5-one and their derivatives. Their Rf values, chemical analyses and IR spectra were recorded, The compounds had shown significant central nervous system stimulant activity.     

Problems on matchings and independent sets of a graph

Let $G$ be a finite simple graph. For $X?V\left(G\right)$, the difference of $X$, $d\left(X\right)?\left|X\right|?\left|N\left(X\right)\right|$ where $N\left(X\right)$ is the neighborhood of $X$ and $max\{d\left(X\right):X?V\left(G\right)\}$ is called the critical difference of $G$. $X$ is called a critical set if $d\left(X\right)$ equals the critical difference and $\ker \left(G\right)$ is the intersection of all critical sets. $\mathrm{diadem}\left(G\right)$ is the union of all critical independent sets. An independent set $S$ is an inclusion minimal set with$d\left(S\right)>0$ if no proper subset of $S$ has positive difference.A graph $G$ is called a König–Egerváry graph if the sum of its independence number $\alpha \left(G\right)$ and matching number $\mu \left(G\right)$ equals $\left|V\left(G\right)\right|$.In this paper, we prove a conjecture which states that for any graph the number of inclusion minimal independent set $S$ with $d\left(S\right)>0$ is at least the critical difference of the graph.We also give a new short proof of the inequality $\left|\ker \left(G\right)\right|+\left|\mathrm{diadem}\left(G\right)\right|\le 2\alpha \left(G\right)$.A characterization of unicyclic non-König–Egerváry graphs is also presented and a conjecture which states that for such a graph $G$, the critical difference equals $\alpha \left(G\right)?\mu \left(G\right)$, is proved.We also make an observation about $\ker \left(G\right)$ using Edmonds–Gallai Structure Theorem as a concluding remark.     

An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X₁,…,X_g⊆V with each group X_i having a requirement r_i between 0 and |X_i|, the goal is to find a minimum cost set of edges whose removal separates each group X_i into at least r_i disconnected components. We give a tight Θ(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk⋅logg) approximation ratio for general graphs, where .     

Molecular alignment of biphenyl derivatives -a computational analysis

Molecular alignment of some biphenyl derivatives likes 4'-Nitro-2-biphenylamine (NBPA), 4-Acetyl-3'-chlorobiphenyl (ACBP) and 4-Acetyl-3'-florobiphenyl (AFBP) has been examined. The CNDO/2 method has been employed to compute the net atomic charge and atomic dipole-moment components at each atomic centre. Configurational energy has been computed using a modified Rayleigh- Schrodinger perturbation method at an interval of 0.1 A° in translation and 1° in rotation, and corresponding probabilities have been calculated using MB-statistics. A comparative study of molecular parameters like the total energy, the binding energy and the total dipole moment etc., has been made. On the basis of the stacking and the in-plane interaction energy calculations, all the possible geometrical arrangements between molecular pairing have been obtained. The investigation suggests that a strong intermolecular interaction energy between a pair of NBPA molecules, and the specific minimum energy configuration, determines the alignment of molecules with respect to one another. An attempt has been made to correlate the liquid crystalline properties exhibited by this class of molecules, and thereby develop a molecular model for the liquid crystallinity.     

Molecular ordering of Fluoro-Nematogen in a dielectric medium at phase-transition temperature: a statistical–mechanical approach based on computer simulation

A molecular-ordering study of p-phenylene-4-methoxy benzoyl 4-trifluoromethylbenzoate (FLUORO) in a dielectric medium (benzene) has been carried out on the basis of statistical mechanics and computer simulation. The atomic net charge and atomic dipole moment at each atomic centre has been evaluated using the CNDO/2 method. The modified Rayleigh–Schrodinger perturbation theory with multicentered–multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while ‘6-exp’ potential function has been assumed for the short-range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium at the phase-transition temperature (506?K), using the MB-formula. The flexibility of various interacting configurations was studied in terms of variation of probability due to departure from the most probable configuration. It has been observed that in dielectric medium the energies/probabilities are redistributed, and there is considerable rise in the probability of interaction, although the order of preference remains the same. The results are discussed in the light of experimental observations.     

Inter- and Intra-Molecular Hydrogen Bonding in Bis(2-amino-5-fluoro-3-methylphenyl)disulfide

Abstract  Bis(2-amino-5-fluoro-3-methylphenyl)disulfide was obtained by oxidation of 2-amino-5-fluoro-3-methylbenzenethiol and was characterized by elemental analysis, IR and ¹H-NMR spectroscopy. The X-ray structure was determined. Crystal data: C₁₄H₁₄N₂F₂S₂: Monoclinic, P2₁ /n, a = 11.8268(3), b = 9.5770(3), c = 12.3977(3) ?, β = 98.079(2)°, V = 1390.29(7) ?, Z = 4. The supramolecular structure arises because the NH₂ groups form three center S···H···F hydrogen bonds and two center N–H···F and N–H···S hydrogen bonds. Index Abstract  Inter- and Intra-Molecular Hydrogen Bonding in Bis(2-amino-5-fluoro-3-methylphenyl)disulfide J. E. Drake¹, M. B. Hursthouse², M. E. Light², R. Maheshwari³, K.G. Ojha³, R. Ratnani^3* Bis(2-amino-5-fluoro-3-methylphenyl)disulfide is linked into a three-dimensional frame work by a combination of intermolecular N–H···F and N–H···N and intramolecular N–H···S hydrogen bonds. The supramolecular structure arises because the NH₂ groups form three center S···H···F hydrogen bonds and two center N–H···F and N–H···S hydrogen bonds.