Scenario of Inflationary Cosmology from the Phenomenological Λ Models

Choosing the three phenomenological models of the dynamical cosmological term Λ, viz., , and Λ∼ρ where a is the cosmic scale factor, it has been shown by the method of numerical analysis for the considered non-linear differential equations that the three models are equivalent for the flat Universe k=0 and for arbitrary non-linear equation of state. The evolution plots for dynamical cosmological term Λ vs. time t and also the cosmic scale factor a vs. t are drawn here for k=0,+1. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.     

Identification of \mathrm{\ensuremath J^{\pi} = 19/2^+} and \mathrm{\ensuremath 23/2^+} isomeric states in 127Sb

The nucleus $\ensuremath {\rm ^{127}Sb}$ , which is on the neutron-rich periphery of the $\ensuremath \beta$ -stability region, has been populated in complex nuclear reactions involving deep-inelastic and fusion-fission processes with $\ensuremath {\rm {}^{136}Xe}$ beams incident on thick targets. The previously known isomer at 2325 keV in $\ensuremath {\rm {}^{127}Sb}$ has been assigned spin and parity $\ensuremath 23/2^+$ , based on the measured $\ensuremath \gamma$ - $\ensuremath \gamma$ angular correlations and total internal conversion coefficients. The half-life has been determined to be 234(12) ns, somewhat longer than the value reported previously. The 2194 keV state has been assigned $\ensuremath J^{\pi} = 19/2^+$ and identified as an isomer with $\ensuremath T_{1/2} = 14(1) {\rm ns}$ , decaying by two $\ensuremath E2$ branches. The observed level energies and transition strengths are compared with the predictions of a shell model calculation. Two $\ensuremath 15/2^+$ states have been identified close in energy, and their properties are discussed in terms of mixing between vibrational and three-quasiparticle configurations.     

Efficient Algorithms for Variants of Weighted Matching and Assignment Problems

Obtaining a matching in a graph satisfying a certain objective is an important class of graph problems. Matching algorithms have received attention for several decades. However, while there are efficient algorithms to obtain a maximum weight matching, not much is known about the maximum weight maximum cardinality, and maximum cardinality maximum weight matching problems for general graphs. Our contribution in this work is to show that for bounded weight input graphs one can obtain an algorithm for both maximum weight maximum cardinality (for real weights), and maximum cardinality maximum weight matching (for integer weights) by modifying the input and running the existing maximum weight matching algorithm. Also, given the current state of the art in maximum weight matching algorithms, we show that, for bounded weight input graphs, both maximum weight maximum cardinality, and maximum cardinality maximum weight matching have algorithms of similar complexities to that of maximum weight matching. Subsequently, we also obtain approximation algorithms for maximum weight maximum cardinality, and maximum cardinality maximum weight matching.      

Quasi-one dimensional graphite ribbon structures in the presence of a magnetic field and the on-site Coulomb correlation at half-filling

We have presented the role of the Coulomb interaction (U) and the magnetic field [(B)\vec]\vec{B} on the ground state properties of the quasi-one dimensional graphite ribbon structures at half-filling. Mean field Hartree-Fock Approximation is used to study the systems. To understand the boundary effects in graphite structures, we have compared the results of these systems with those of the square lattice ribbon structures. Studying the density of states, the Drude weight and the charge gap, we have drawn the U – B phase diagrams for the zigzag and the armchair graphite ribbons.     

A copper(II) complex of benzimidazole-based ligand: synthesis,structure, redox aspects and fluorescence properties

Employing 1-(2-methoxybenzyl)-2-(2-methoxyphenyl)-1H-benzimidazole (bpb) as a monodentate ligand, a new greenish-blue copper(II) complex, [Cu(bpb)₂(NO₃)₂] (1a), has been synthesized. 1a has been characterized analytically and spectroscopically. The X-ray crystal structure of 1a reveals that it adopts a cis disposition with respect to the ligands. The solid state structure of 1a is stabilized by intramolecular offset face-to-face π–π stacking. Non-covalent supramolecular edge-to-face C–H?π interactions with neighboring molecules give 1-D supramolecular chains that further lead to the formation of an assembled 3-D supramolecular metal-organic framework via hydrogen bonding interactions. 1a shows blue fluorescence most likely due to intramolecular offset face-to-face π–π stacking. At room temperature, 1a is one-electron paramagnetic. It shows a rhombic EPR spectrum with g₁ = 2.12, g₂ = 2.42, and g₃ = 2.52 in the solid state at liquid nitrogen temperature. In cyclic voltammetry, 1a displays a one-electron oxidative Cu(II)/Cu(III) couple. Our DFT calculations, corroborate the observed experimental results of 1a.     

Indium-mediated vic-diallylation/propargylation of phenacyl bromides: a facile synthesis of 4-arylocta-1,7-dien-4-ol derivatives

Phenacyl bromides undergo smooth vic-diallylation and dipropargylation with allyl and propargyl indium reagents generated in situ from metallic indium and allyl or propargyl bromide to produce 4-arylocta-1,7-dien-4-ol derivatives in good yields. Phenacyl chloride and azide also participated effectively in bis-allylation. Similar results are also obtained from in situ generated allyl or propargyl zinc bromide.     

An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Membrane Disruption and Enhanced Inhibition of Cell‐Wall Biosynthesis: A Synergistic Approach to Tackle Vancomycin‐Resistant Bacteria

Resistance to glycopeptide antibiotics, the drugs of choice for life‐threatening bacterial infections, is on the rise. In order to counter the threat of glycopeptide‐resistant bacteria, we report development of a new class of semi‐synthetic glycopeptide antibiotics, which not only target the bacterial membrane but also display enhanced inhibition of cell‐wall biosynthesis through increased binding affinity to their target peptides. The combined effect of these two mechanisms resulted in improved in vitro activity of two to three orders of magnitude over vancomycin and no propensity to trigger drug resistance in bacteria. In murine model of kidney infection, the optimized compound was able to bring bacterial burden down by about 6 logs at 12 mg kg^?1 with no observed toxicity. The results furnished in this report emphasize the potential of this class of compounds as future antibiotics for drug‐resistant Gram‐positive infections.     

A Spirocyclohexyl Nitroxide Amino Acid Spin Label for Pulsed EPR Spectroscopy Distance Measurements

Site‐directed spin labeling and EPR spectroscopy offer accurate, sensitive tools for the characterization of structure and function of macromolecules and their assemblies. A new rigid spin label, spirocyclohexyl nitroxide α‐amino acid and its N‐(9‐fluorenylmethoxycarbonyl) derivative, have been synthesized, which exhibit slow enough spin‐echo dephasing to permit accurate distance measurements by pulsed EPR spectroscopy at temperatures up to 125 K in 1:1 water/glycerol and at higher temperatures in matrices with higher glass transition temperatures. Distance measurements in the liquid nitrogen temperature range are less expensive than those that require liquid helium, which will greatly facilitate applications of pulsed EPR spectroscopy to the study of structure and conformation of peptides and proteins.     

A Rational Approach Towards Determination of Optical Ionicity and Non-covalent Interactions in Fullerene-Calix[4]arene Host-Guest Complexes

The present article reports the host-guest complexation of a calix[4]arene derivative, namely 4-iso-propyl-calix[4]arene (1), with fullerenes (both C₆₀ and C₇₀) in toluene and benzonitrile solutions. It is observed that the charge-transfer (CT) absorption bands are located in the ground state for the C₆₀ and C₇₀ complexes of 1. By utilizing the CT absorption bands, various important physicochemical parameters like the oscillator strength, resonance energy, transition dipole moment, electronic coupling element and solvent reorganization energies have been estimated for the C₆₀-1 and C₇₀-1 complexes. The CT transition energy is very helpful for determining the vertical ionization potential of 1 in solution. Jobs method of continuous variation was used to establish 1:1 stoichiometry for the fullerene complexes of 1. The most fascinating feature of the present study is that 1 binds C₇₀ preferentially compared to C₆₀ as obtained from binding constant (K) data. The effect of solvent on the complexation of fullerenes (C₆₀ and C₇₀) with 1 is clearly observed from the trend in the K values: in toluene and whereas in benzonitrile, and . Molecular mechanics force field (MMMF) calculations reveal fascinating features regarding the binding pattern of fullerenes towards 1 in vacuo in terms of enthalpy of formation. MMMF calculations establish that during C₇₀-1 complexation, C₇₀ is directed in an end-on manner rather than the traditional side-on pattern.