A short proof of a theorem on degree sets of graphs

For a finite simple graph G, we denote the set of degrees of its vertices, known as its degree set, by D(G). Kapoor, Polimeni and Wall [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] have determined the least number of vertices among graphs with a given degree set. We give a very short proof of this result.     

End-to-end single cyanato and thiocyanato bridged Cu(II) polymers with a new tridentate Schiff base ligand: crystal structure and magnetic properties

A new tridentate Schiff base ligand HL (L = C14H19N2O), derived from the condensation of benzoylacetone and 2-dimethylaminoethylamine in a 1:1 ratio, reacts with copper(ii) acetate and cyanate, thiocyanate or azide, to give rise to several end-to-end polymeric complexes of formulae [CuL(mu(1,3)-NCO)]n 1, [CuL(mu(1,3)-NCS)]n 2 and the complex 3 has two crystallographically independent units of formula [CuL(N3)] in the asymmetric unit cell. Complex 3 exists in dimeric form rather than as a polymeric chain. Compound 1 is the first report of a singly end-to-end cyanate bridged polymeric chain of Cu(II) with a Schiff base as a co-ligand. There are many examples of double NCS bridged polymeric chains, but fewer singly bridged ones such as compound 2. We have characterized these complexes by analytical, spectroscopic, structural and variable temperature magnetic susceptibility measurements. The coordination geometry around the Cu(II) centers is distorted square pyramidal for 1 and 2 and square planar for complex 3. The magnetic susceptibility data show slight antiferromagnetic coupling for the polymers having J values -0.19 and -0.57 cm(-1) for complexes 1 and 2 respectively. The low values of J are consistent with the equatorial-axial disposition of the bridges in the polymers.     

State-resolved unimolecular dissociation of cis-cis HOONO: Product state distributions and action spectrum in the 2nuOH band region

Nascent OH fragment product state distributions arising from unimolecular dissociation of room temperature HOONO, initiated by excitation in the region of the 2nu(OH) band, are probed using laser-induced fluorescence at sub-Doppler resolution. Phase-space simulations of the measured OH rotational distributions are consistent with the dissociation dynamics being statistical and confirm that all major features in the room temperature action spectrum belong to the cis-cis conformer. The phase-space simulations also allow us to estimate the HO-ONO bond dissociation energy of cis-cis HOONO to be D(0)=19.9+/-0.5 kcal/mol, which when combined with the known heat-of-formation data for the OH and NO(2) fragments gives DeltaH(f) (0)(cis-cis HOONO)=-2.5 kcal/mol. In addition to fragment energy release, spectral features in the cis-cis HOONO action spectrum are examined with respect to their shifts upon (15)N isotope substitution and through ab initio spectral simulation using a two-dimensional dipole surface that takes into account the influence of HOON torsional motion on the OH stretching overtone. The two-dimensional spectral simulations, using CCSD(T)/cc-pVTZ dipole surface, qualitatively reproduces features appearing in the action spectrum and suggest that the strong broad feature occurring approximately 570 cm(-1) to the blue of the cis-cis HOONO 2nu(OH) peak, likely involve excitation of HOON-torsion/OH-stretch combination bands originating from thermally populated excited torsional states. A closer examination of the predictions of the two-dimensional model with experiments also reveals its limitations and suggests that a more elaborate treatment, one which includes several additional modes, will likely be required in order to fully explain the room temperature action spectrum. Ab initio calculations of the HOON torsional potential at the CCSD(T)/cc-pVTZ level of theory are also presented and confirm that cis-perp configuration does not correspond to a bound localized minimum on the HOONO potential energy surface.     

Octahedral CuII and NiII complexes manifesting with N′-[1-(pyridin-2-yl)ethylidene] acetohydrazide: Structural outlooks and spectral characteristics

A tridentate hydrazone precursor, N′-[1-(pyridin-2-yl)ethylidene]acetohydrazide (L) (1:1 refluxed product of acetichydrazide and 2-acetylpyridine), produced two octahedral Cu^II and Ni^II derivatives, [CuL₂]·NO₃ (1) and [NiL₂]·ClO₄·H₂O (2). Both are subjected to X-ray diffraction system, and structural investigation shows that the central metal atom (Cu^II or Ni^II) adopts a distorted octahedral geometry with N₄O₂ donor sets by coordination of a pair of independent hydrazone precursors. Besides X-ray study, IR and UV-vis spectra, thermal analysis and room temperature magnetic moments are utilized for establishing significant characteristics of both complexes. It is apparent that the M-N_pyridine bonds are slightly longer than the M-N_imino bonds, Cu1-N1 and Cu1-N4 [2.300(2) and 2.038(2) ?] for 1 and Ni1-N1 and Ni1-N4 [2.075(2) and 2.084(1) ?] for 2, Cu1-N2 and Cu1-N5 [2.062(1) and 1.932(1) ?] for 1 and Ni1-N2 and Ni1-N5 [2.008(2) and 1.975(2) ?] for 2, respectively. As per our observation, the effective magnetic moment value (μ_eff) is found to be 1.77 B.M. for 1 and 3.06 BM for 2, respectively.     

Membrane Organization and Dynamics of the G-Protein-Coupled Serotonin<Subscript>1A</Subscript> Receptor Monitored Using Fluorescence-Based Approaches

The G-protein-coupled receptor (GPCR) superfamily represents one of the largest classes of molecules involved in signal transduction across the plasma membrane. Fluorescence-based approaches have provided valuable insights into GPCR functions such as receptor–receptor and receptor–ligand interactions, real-time assessment of signal transduction, receptor dynamics on the plasma membrane, and intracellular trafficking of receptors. This has largely been possible with the use of fluorescent probes such as the green fluorescent protein (GFP) from the jellyfish Aequoria victoria and its variants. We discuss the potential of fluorescence-based approaches in providing novel information on the membrane organization and dynamics of the G-protein-coupled serotonin_1A receptor tagged to the enhanced yellow fluorescent protein (EYFP). These authors contributed equally to the work.     

Velocity-dependent inertial induction and secular retardation of the earth’s rotation

According to the model of inertial induction proposed earlier, the inertia force consists of an acceleration-dependent term which comes out as identically equal to -ma. Besides, there is a velocity-dependent term which is exceedingly small to be easily detected. However, it has been shown that this results in a cosmological red shift of light coming from distant stars and galaxies; the magnitude of the red shift agrees very well with the observed values. Though this model yields correct results when applied to photons it needs modification before applying to other bodies. A modified form of the inertial induction model is now proposed where the proposed velocity-dependent inertia forces, when applied to the solar system, yields correct order of magnitude for the secular retardation of the earth’s rotation. Moreover, a combined model using the velocity term and the tidal friction also does not suggest any close proximity of the moon to the earth in the past. When the model is applied to the case of Phobos, a secular acceleration of the order of magnitude of 10⁻³ deg yr⁻² is obtained.     

Molecular interaction of organic dyes in bulk and confined media

Molecular interactions of five thiazine dyes with increasing alkyl substitution have been studied in aqueous and microemulsion media at 303 K within a concentration range of (1.35–7.00) × 10^?4 M. The dimerization constant (K_d) values for the five dyes are ranged between 1.761 and 6.258 × 10³ l mol^?1 in bulk water media, where as in microemulsion media, K_d's are ranged between 1.760 and 4.110 × 10³ l mol^?1. Thionine (with no methyl substitution) and azure A (with two methyl substitution) displayed slightly larger K_d values in microemulsion water pools compared to bulk water while other dyes recorded significant drop in K_d values. The influence of microemulsion media on the molecular interaction of dyes has been explained in terms of electrostatic and hydrophobic factors. The monomer and the dimer spectra are explained in terms of molecular exciton model and the optical absorption parameters of both the species are reported in bulk and confined media.     

Immobilization of bio-macromolecules on self-assembled monolayers: methods and sensor applications

Attachment of biomolecules on gold, silicon or glass surfaces has direct implications for the development of novel biosensors in the context of nanoscale detection of pathogens and other metabolites related to issues of human health. In this critical review, we have highlighted the current developments in various techniques of immobilization of biomolecules, specifically biological macromolecules on surfaces through the modification of a functional self-assembled monolayer. The utility of such immobilized biomolecules in the area of biosensing in nanoscale has been surveyed. Merits and demerits of some of the methods with reference to sensitivity of detection and practical use have been discussed (221 references).     

On the density of integral sets with missing differences from sets related to arithmetic progressions

For a given set M of positive integers, a problem of Motzkin asks for determining the maximal density μ(M) among sets of nonnegative integers in which no two elements differ by an element of M. The problem is completely settled when |M|?2, and some partial results are known for several families of M for |M|?3, including the case where the elements of M are in arithmetic progression. We consider some cases when M either contains an arithmetic progression or is contained in an arithmetic progression.