L-p-Integrability, Dimensions of Supports of Fourier Transforms and Applications

It is proved that there does not exist any non zero function in with if its Fourier transform is supported by a set of finite packing -measure where . It is shown that the assertion fails for . The result is applied to prove L-p Wiener Tauberian theorems for R-n and M(2).

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

REPRESENTING A CUBIC GRAPH AS THE INTERSECTION GRAPH OF AXIS-PARALLEL BOXES IN THREE DIMENSIONS

We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if their corresponding vertices are adjacent. In fact, we construct a representation in which any two intersecting boxes touch just at their boundaries.

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, nu of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrodinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and nonseparable integrable billiards, nu satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of m mod kn, given a particular k, for a set of quantum numbers, m, n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. (C) 2014 Elsevier Inc. All rights reserved.

Metal-organic chemical vapor-deposited cobalt oxide films as negative electrodes for thin film Li-ion battery

In this study, thin films of cobalt oxide (Co3O4) have been grown by the metal-organic chemical vapor deposition (MOCVD) technique on stainless steel substrate at two preferred temperatures (450 degrees C and 500 degrees C), using cobalt acetylacetonate dihydrate as precursor. Spherical as well as columnar microstructures of Co3O4 have been observed under controlled growth conditions. Further investigations reveal these films are phase-pure, well crystallized and carbon-free. High-resolution TEM analysis confirms that each columnar structure is a continuous stack of minute crystals. Comparative study between these Co3O4 films grown at 450 degrees C and 500 degrees C has been carried out for their application as negative electrodes in Li-ion batteries. Our method of electrode fabrication leads to a coating of active material directly on current collector without any use of external additives. A high specific capacity of 1168 micro Ah cm(-2) mu m(-1) has been measured reproducibly for the film deposited at 500 degrees C with columnar morphology. Further, high rate capability is observed when cycled at different current densities. The Co3O4 electrode with columnar structure has a specific capacity 38% higher than the electrode with spherical microstructure (grown at 450 degrees C). Impedance measurements on the Co3O4 electrode grown at 500 degrees C also carried out to study the kinetics of the electrode process. (C) 2014 Published by Elsevier B.V.

Demonstration of helicase activity in the nonstructural protein, NSs, of the negative-sense RNA virus, Groundnut bud necrosis virus

The nonstructural protein NSs, encoded by the S RNA of groundnut bud necrosis virus (GBNV) (genus Tospovirus, family Bunyaviridae) has earlier been shown to possess nucleic-acid-stimulated NTPase and 50 a phosphatase activity. ATP hydrolysis is an essential function of a true helicase. Therefore, NSs was tested for DNA helicase activity. The results demonstrated that GBNV NSs possesses bidirectional DNA helicase activity. An alanine mutation in the Walker A motif (K189A rNSs) decreased DNA helicase activity substantially, whereas a mutation in the Walker B motif resulted in a marginal decrease in this activity. The parallel loss of the helicase and ATPase activity in the K189A mutant confirms that NSs acts as a non-canonical DNA helicase. Furthermore, both the wild-type and K189A NSs could function as RNA silencing suppressors, demonstrating that the suppressor activity of NSs is independent of its helicase or ATPase activity. This is the first report of a true helicase from a negative-sense RNA virus.

Negative hyperconjugation and red-, blue- or zero-shift in X-Z center dot center dot center dot Y complexes

A generalized explanation is provided for the existence of the red-and blue-shifting nature of X-Z bonds (Z = H, halogens, chalcogens, pnicogens, etc.) in X-Z center dot center dot center dot Y complexes based on computational studies on a selected set of weakly bonded complexes and analysis of existing literature data. The additional electrons and orbitals available on Z in comparison to H make for dramatic differences between the H-bond and the rest of the Z-bonds. The nature of the X-group and its influence on the X-Z bond length in the parent X-Z molecule largely controls the change in the X-Z bond length on X-Z center dot center dot center dot Y bond formation; the Y-group usually influences only the magnitude of the effects controlled by X. The major factors which control the X-Z bond length change are: (a) negative hyperconjugative donation of electron density from X-group to X-Z sigma* antibonding molecular orbital (ABMO) in the parent X-Z, (b) induced negative hyperconjugation from the lone pair of electrons on Z to the antibonding orbitals of the X-group, and (c) charge transfer (CT) from the Y-group to the X-Z sigma* orbital. The exchange repulsion from the Y-group that shifts partial electron density at the X-Z sigma* ABMO back to X leads to blue-shifting and the CT from the Y-group to the sigma* ABMO of X-Z leads to red-shifting. The balance between these two opposing forces decides red-, zero- or blue-shifting. A continuum of behaviour of X-Z bond length variation is inevitable in X-Z center dot center dot center dot Y complexes.

SUB1 Plays a Negative Role during Starvation Induced Sporulation Program in Saccharomyces cerevisiae

Saccharomyces cerevisiae Sub1 is involved in several cellular processes such as, transcription initiation, elongation, mRNA processing and DNA repair. It has also been reported to provide cellular resistance during conditions of oxidative DNA damage and osmotic stress. Here, we report a novel role of SUB1 during starvation stress-induced sporulation, which leads to meiosis and spore formation in diploid yeast cells. Deletion of SUB1 gene significantly increased sporulation efficiency as compared to the wild-type cells in S288c genetic background. Whereas, the sporulation functions of the sub1(Y66A) missense mutant were similar to Sub1. SUB1 transcript and protein levels are downregulated during sporulation, in highly synchronized and sporulation proficient wild-type SK1 cells. The changes in Sub1 levels during sporulation cascade correlate with the induction of middle sporulation gene expression. Deletion of SUB1 increased middle sporulation gene transcript levels with no effect on their induction kinetics. In wild-type cells, Sub1 associates with chromatin at these loci in a temporal pattern that correlates with their enhanced gene expression seen in sub1. cells. We show that SUB1 genetically interacts with HOS2, which led us to speculate that Sub1 might function with Set3 repressor complex during sporulation. Positive Cofactor 4, human homolog of Sub1, complemented the sub1. sporulation phenotype, suggesting conservation of function. Taken together, our results suggest that SUB1 acts as a negative regulator of sporulation.

Average Overlap for Clustering Incomplete Data using Symmetric Non-Negative Matrix Factorization

Clustering techniques which can handle incomplete data have become increasingly important due to varied applications in marketing research, medical diagnosis and survey data analysis. Existing techniques cope up with missing values either by using data modification/imputation or by partial distance computation, often unreliable depending on the number of features available. In this paper, we propose a novel approach for clustering data with missing values, which performs the task by Symmetric Non-Negative Matrix Factorization (SNMF) of a complete pair-wise similarity matrix, computed from the given incomplete data. To accomplish this, we define a novel similarity measure based on Average Overlap similarity metric which can effectively handle missing values without modification of data. Further, the similarity measure is more reliable than partial distances and inherently possesses the properties required to perform SNMF. The experimental evaluation on real world datasets demonstrates that the proposed approach is efficient, scalable and shows significantly better performance compared to the existing techniques.

Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

Universal anomalous dimensions at large spin and large twist

In this paper we consider anomalous dimensions of double trace operators at large spin (l) and large twist (tau) in CFTs in arbitrary dimensions (d >= 3). Using analytic conformal bootstrap methods, we show that the anomalous dimensions are universal in the limit l >> tau >> 1. In the course of the derivation, we extract an approximate closed form expression for the conformal blocks arising in the four point function of identical scalars in any dimension. We compare our results with two different calculations in holography and find perfect agreement.

Baryon squishing in synthetic dimensions by effective SU(M) gauge fields

The ``synthetic dimension'' proposal A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (''flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles with SU(M) symmetric interactions] experiencing an SU(M) Zeeman field at each lattice site and a non-Abelian SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For M particles, concomitantly, the SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (''squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU(M) random flux model, inconceivable in conventional experimental systems.

epsilon-expansions near three dimensions from conformal field theory

We formally extend the CFT techniques introduced in arXiv: 1505.00963, to phi(2d0/d0-2) theory in d = d(0) dimensions and use it to compute anomalous dimensions near d(0) = 3, 4 in a unified manner. We also do a similar analysis of the O(N) model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the phi(3) theory in d(0) = 6 is qualitatively different.

Analytic bootstrap at large spin

We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension Delta(phi). It is known that such theories will contain an in finite sequence of large spin operators with twists approaching 2 Delta(phi) + 2n for each integer n. By considering the case where such operators are separated by a twist gap from other operators at large spin, we analytically determine the n, Delta(phi) dependence of the anomalous dimensions. We find that for all n, the anomalous dimensions are negative for Delta(phi) satisfying the unitarity bound. We further compute the first subleading correction at large spin and show that it becomes universal for large twist. In the limit when n is large, we find exact agreement with the AdS/CFT prediction corresponding to the Eikonal limit of a 2-2 scattering with dominant graviton exchange.