Ladder operators for isospectral oscillators

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.Comment: 13 page

Use of vibrational spectroscopy to study 1,3-dimethyl-5-nitrobenzene: A combined theoretical and experimental approach

The FTIR and FT-Raman spectra of 1,3-dimethyl-5-nitrobenzene (DMNB) have been recorded in the range 4000‒400 cm−1 and 3500‒100 cm−1, respectively. The molecular structures, fundamental vibrational frequencies and intensity of the vibrational bands have been investigated and interpreted theoretically with the use of structural optimizations and normal coordinate force field calculations based on density functional theory (DFT) with 6-31G(d,p) basis set. The vibrational assignments have been made from potential energy distribution (PED). The theoretically simulated vibrational spectra of the molecule show excellent agreement with the experimental spectra. The hyper conjugative interaction energy (E(2)) and electron densities of donor (i) and acceptor (j) bonds have been calculated using NBO analysis. The electronic transition has been studied using UV-Visible analysis of the title molecule with B3LYP/6-31G(d,p) level of theory. The microscopic non-linear optical (NLO) behaviour of the title compound has also been calculated. In addition, the 1H and 13C NMR chemical shifts values of DMNB in the ground state for B3LYP/6-31G(d,p) method have also been calculated using gauge independent atomic orbital (GIAO) method

Spectroscopic characterization and natural bond orbital analysis of 2-(trifluoromethyl) phenylacetonitrile based on DFT calculations

The experimental Fourier transform infrared (FT-IR) and Fourier transform Raman (FT-Raman) spectra of 2-(trifluoromethyl)phenylacetonitrile (2TFMP) have been recorded in the spectral region 4000‒400 cm−1 and 3500‒100 cm−1, respectively. Also the title molecule has been characterized by 13C NMR and 1H NMR spectroscopes. The geometry optimization and frequency calculations have been performed at B3LYP/6-311+G (d,p) level.  A detailed interpretation of FT-IR and FT-Raman spectra aided by the potential energy distributions (PEDs) for the calculated frequencies has been reported. Results of this study showed that there is a good correlation between the experimental and computational results. The HOMO-LUMO energy gap explains the charge transfer interactions in the molecule. NBO (natural bond orbital) computations have been utilized to evaluate the stabilities which occur from charge delocalization and inter-molecular interactions have been studied using DFT calculation

Topical steroid induced Cushing’s syndrome-a rare entity

The topical steroid therapy is the commonest mode of treatment for Psoriasis. When the therapy is overused, it can cause unusual side effects like Cushing’s syndrome which is very rarely reported and we are reporting such a case. Treatment with maintenance dose of steroids is necessary based on basal cortisol levels to avert hypocortisolemic crisis in Cushing’s syndrome, however in some select asymptomatic cases maintenance dose of steroids can be withdrawn and only stress dose be given in spite of low basal serum cortisol. We managed such a case and it is reported because of its rarity in clinical practice. This can alert the clinicians to avoid prescribing steroids as maintenance dose for a long time in asymptomatic Cushing’s syndrome with low morning cortisol and thereby reducing the side effects of long-term steroids on them

Centrality scaling in large networks

Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks, however, it is computationally costly, and its measurement for networks with millions of nodes is near impossible. By introducing a multiscale decomposition of shortest paths, we show that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling vs L, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of 5.5*10^6 nodes and 2.7*10^7 links

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

Self interacting Brans Dicke cosmology and Quintessence

Recent cosmological observations reveal that we are living in a flat accelerated expanding universe. In this work we have investigated the nature of the potential compatible with the power law expansion of the universe in a self interacting Brans Dicke cosmology with a perfect fluid background and have analyzed whether this potential supports the accelerated expansion. It is found that positive power law potential is relevant in this scenario and can drive accelerated expansion for negative Brans Dicke coupling parameter $\omega$. The evolution of the density perturbation is also analyzed in this scenerio and is seen that the model allows growing modes for negative $\omega$.Comment: 8pages, 5 figures, PRD style, some changes are made, figures added, reference added. To be published in Int. J. Mod. Phys.

rac-6-Eth­oxy-3,3a,4,9b-tetra­hydro-1,3-diphenyl-1H-chromeno[4,3-c]isoxazole-3a-carbonitrile

The title compound, C25H22N2O3, with three stereogenic centres, crystallizes in a centrosymmetric space group as a racemate. The pyran ring adopts a sofa conformation and the five-membered isoxazole ring exhibits an envelope conformation. The dihedral angle between the benzene ring and the mean plane through the near coplanar atoms of the pyran ring is 10.54 (9)°. In the crystal, no significant intermolecular interactions are observed

Structural disorder, magnetism, and electrical and thermoelectric properties of pyrochlore Nd2Ru2O7

Polycrystalline Nd2Ru2O7 samples have been prepared and examined using a combination of structural, magnetic, and electrical and thermal transport studies. Analysis of synchrotron X-ray and neutron diffraction patterns suggests some site disorder on the A-site in the pyrochlore sublattice: Ru substitutes on the Nd-site up to 7.0(3)%, regardless of the different preparative conditions explored. Intrinsic magnetic and electrical transport properties have been measured. Ru 4d spins order antiferromagnetically at 143 K as seen both in susceptibility and specific heat, and there is a corresponding change in the electrical resistivity behaviour. A second antiferromagnetic ordering transition seen below 10 K is attributed to ordering of Nd 4f spins. Nd2Ru2O7 is an electrical insulator, and this behaviour is believed to be independent of the Ru-antisite disorder on the Nd site. The electrical properties of Nd2Ru2O7 are presented in the light of data published on all A2Ru2O7 pyrochlores, and we emphasize the special structural role that Bi3+ ions on the A-site play in driving metallic behaviour. High-temperature thermoelectric properties have also been measured. When considered in the context of known thermoelectric materials with useful figures-of-merit, it is clear that Nd2Ru2O7 has excessively high electrical resistivity which prevents it from being an effective thermoelectric. A method for screening candidate thermoelectrics is suggested.Comment: 19 pages, 10 figure