How Do Glassy Domains Grow?

We construct equations for the growth kinetics of structural glass within mode-coupling theory, through a nonstationary variant of the three-density correlator defined by G. Biroli et al. Phys. Rev. Lett. 97, 195701 (2006)]. We solve a schematic form of the resulting equations to obtain the coarsening of the three-point correlator chi(3)(t, t(w)) as a function of waiting time tw. For a quench into the glass, we find that chi(3) attains a peak value similar to t(w)(0.5) at t - t(w) similar to t(w)(0.8), providing a theoretical basis for the numerical observations of Parisi J. Phys. Chem. B 103, 4128 (1999)] and Kob and Barrat Phys. Rev. Lett. 78, 4581 (1997)]. The aging is not ``simple'': the t(w) dependence cannot be attributed to an evolving effective temperature.

Model Pseudoconvex Domains and Bumping

The Levi geometry at weakly pseudoconvex boundary points of domains in C-n, n >= 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping outward a pseudoconvex, finite- type Omega subset of C-3 in such a way that: (i) pseudoconvexity is preserved, (ii) the (locally) larger domain has a simpler defining function, and (iii) the lowest possible orders of contact of the bumped domain with partial derivative Omega, at the site of the bumping, are realized. When Omega subset of C-n, n >= 3, it is, in general, hard to meet the last two requirements. Such well-controlled bumping is possible when Omega is h-extendible/semiregular. We examine a family of domains in C-3 that is strictly larger than the family of h-extendible/semiregular domains and construct explicit models for these domains by bumping.

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C (0) interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H (2), H (1) and L (2) norms. L (a) norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

Totally geodesic discs in strongly convex domains

We prove that every isometry from the unit disk Delta in , endowed with the Poincar, distance, to a strongly convex bounded domain Omega of class in , endowed with the Kobayashi distance, is the composition of a complex geodesic of Omega with either a conformal or an anti-conformal automorphism of Delta. As a corollary we obtain that every isometry for the Kobayashi distance, from a strongly convex bounded domain of class in to a strongly convex bounded domain of class in , is either holomorphic or anti-holomorphic.

Domains in complex surfaces with a noncompact automorphism group - II

Let X be an arbitrary complex surface and D subset of X a domain that has a noncompact group of holomorphic automorphisms. A characterization of those domains D that admit a smooth real analytic, finite type, boundary orbit accumulation point and whose closures are contained in a complete hyperbolic domain D' subset of X is obtained.

Condition R and proper holomorphic maps between equidimensional product domains

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as a product of proper mappings between the factor domains. (C) 2013 Elsevier Inc. All rights reserved.

Understanding the role of domain-domain linkers in the spatial orientation of domains in multi-domain proteins

Inter-domain linkers (IDLs)' bridge flanking domains and support inter-domain communication in multi-domain proteins. Their sequence and conformational preferences enable them to carry out varied functions. They also provide sufficient flexibility to facilitate domain motions and, in conjunction with the interacting interfaces, they also regulate the inter-domain geometry (IDG). In spite of the basic intuitive understanding of the inter-domain orientations with respect to linker conformations and interfaces, we still do not entirely understand the precise relationship among the three. We show that IDG is evolutionarily well conserved and is constrained by the domain-domain interface interactions. The IDLs modulate the interactions by varying their lengths, conformations and local structure, thereby affecting the overall IDG. Results of our analysis provide guidelines in modelling of multi-domain proteins from the tertiary structures of constituent domain components.

Nodal domains of the equilateral triangle billiard

We characterize the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of the nodal loop count and the nodal counting function are shown to contain information about the classical periodic orbits using the semiclassical trace formula. We believe that the results belong generically to non-separable systems, thus extending the previous works which are concentrated on separable and chaotic systems.

Model domains in C-3 with abelian automorphism group

It is shown that every hyperbolic rigid polynomial domain in C-3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight.

Trace Formulae for Curvature of Jet Bundles over Planar Domains

For a domain Omega in C and an operator T in B-n(Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E-T over Omega corresponding to T. The Hermitian holomorphic vector bundle E-T is obtained as a pull-back of the tautological bundle S(n, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are rather intricate. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

PROPER HOLOMORPHIC MAPS BETWEEN BOUNDED SYMMETRIC DOMAINS REVISITED

We prove that a proper holomorphic map between two nonplanar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively.

Quadrature Domains in C-n

We prove two density theorems for quadrature domains in , . It is shown that quadrature domains are dense in the class of all product domains of the form , where is a smoothly bounded domain satisfying Bell's Condition R and is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in C-2.

Combined toxicity of two crystalline phases (anatase and rutile) of Titania nanoparticles towards freshwater microalgae: Chlorella sp

In view of the increasing usage of anatase and rutile crystalline phases of titania NPs in the consumer products, their entry into the aquatic environment may pose a serious risk to the ecosystem. In the present study, the possible toxic impact of anatase and rutile nanoparticles (individually and in binary mixture) was investigated using freshwater microalgae, Chlorella sp. at low exposure concentrations (0.25, 0.5 and 1 mg/L) in freshwater medium under UV irradiation. Reduction of cell viability as well as a reduction in chlorophyll content were observed due to the presence of NPs. An antagonistic effect was noted at certain concentrations of binary mixture such as (0.25, 0.25), (0.25, 0.5), and (0.5, 0.5) mg/L, and an additive effect for the other combinations, (0.25, 1), (0.5, 0.25), (0.5, 1), (1, 0.25), (1, 0.5), and (1, 1) mg/L. The hydrodynamic size analyses in the test medium revealed that rutile NPs were more stable in lake water than the anatase and binary mixtures at 6 h, the sizes of anatase (1 mg/L), rutile NPs (1 mg/L), and binary mixture (1, 1 mg/L) were 948.83 +/- 35.01 nm, 555.74 +/- 19.93 nm, and 1620.24 +/- 237.87 nm, respectively]. The generation of oxidative stress was found to be strongly dependent on the crystallinity of the nanoparticles. The transmission electron microscopic images revealed damages in the nucleus and cell membrane of algal cells due to the interaction of anatase NPs, whereas rutile NPs were found to cause chloroplast and internal organelle damages. Mis-shaped chloroplasts, lack of nucleus, and starch-pyrenoid complex were noted in binary-treated cells. The findings from the current study may facilitate the environmental risk assessment of titania NPs in an aquatic ecosystem. (C) 2015 Elsevier B.V. All rights reserved.

The beta hairpin structure within ribosomal protein S5 mediates interplay between domains II and IV and regulates HCV IRES function

Translation initiation in Hepatitis C Virus (HCV) is mediated by Internal Ribosome Entry Site (IRES), which is independent of cap-structure and uses a limited number of canonical initiation factors. During translation initiation IRES-40S complex formation depends on high affinity interaction of IRES with ribosomal proteins. Earlier, it has been shown that ribosomal protein S5 (RPS5) interacts with HCV IRES. Here, we have extensively characterized the HCV IRES-RPS5 interaction and demonstrated its role in IRES function. Computational modelling and RNA-protein interaction studies demonstrated that the beta hairpin structure within RPS5 is critically required for the binding with domains II and IV. Mutations disrupting IRES-RPS5 interaction drastically reduced the 80S complex formation and the corresponding IRES activity. Computational analysis and UV cross-linking experiments using various IRES-mutants revealed interplay between domains II and IV mediated by RPS5. In addition, present study demonstrated that RPS5 interaction is unique to HCV IRES and is not involved in 40S-3 ` UTR interaction. Further, partial silencing of RPS5 resulted in preferential inhibition of HCV RNA translation. However, global translation was marginally affected by partial silencing of RPS5. Taken together, results provide novel molecular insights into IRES-RPS5 interaction and unravel its functional significance in mediating internal initiation of translation.