L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

Catalytic Enantioselective 1,4-lodofunctionalizations of Conjugated Dienes

The first catalytic enantioselective 1,4-iodofunctionalizations of conjugated dienes have been developed. Starting from beta,gamma,delta,epsilon-unsaturated oximes and 4-Ns hydrazones, these N-iodosuccinimide-mediated reactions are catalyzed by newly modified tertiary aminothiourea derivatives and furnish Delta(2)-isoxazoline and Delta(2)-pyrazoline derivatives, respectively, containing an (E)-allyl iodide group at the quaternary stereogenic center generally in high yield and with excellent enantioselectivity (up to 98.5:1.5 er).

Tailoring energy absorption capacity of CNT forests through application of electric field

This study examines the effect of electric field on energy absorption capacity of carbon nanotube forests (CNTFs), comprising of vertically aligned multiwalled carbon nanotubes, under both quasistatic (strain rate, (epsilon) over dot = 10(-3) s(-1)) and dynamic ((epsilon) over dot = similar to 10(3) s(-1)) loading conditions. Under quasistatic condition, the CNTFs were cyclically loaded and unloaded while electric field was applied along the length of carbon nanotube (CNT) either throughout the loading cycle or explicitly during either the loading or the unloading segment. The energy absorbed per cycle by CNTF increased monotonically with electric field when the field was applied only during the loading segment: A 7 fold increase in the energy absorption capacity was registered at an electric field of 1 kV/m whereas no significant change in it was noted for other schemes of electro-mechanical loading. The energy absorption capacity of CNTF under dynamic loading condition also increased monotonically with electric field; however, relative to the quasistatic condition, less pronounced effect was observed. This intriguing strain rate dependent effect of electric field on energy absorption capacity of CNTF is explained in terms of electric field induced strengthening of CNTF, originating from the time dependent electric field induced polarization of CNT. (C) 2015 Elsevier Ltd. All rights reserved.

COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN CLUSTER CORES

Using high-resolution 3D and 2D (axisymmetric) hydrodynamic simulations in spherical geometry, we study the evolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGNs) jets. Condensation of cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative cooling with reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanical luminosity approximate to epsilon(M) over dot(acc)c(2); where (M) over dot(acc). is the mass accretion rate at 1 kpc) as small as 6 x 10(-5) is sufficient to reduce the cooling/accretion rate by similar to 10 compared to a pure cooling flow in clusters (with M-200 less than or similar to 7 x 10(14) M-circle dot). This value is much smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the fact that only a small fraction of gas at 1 kpc is accreted onto the supermassive black hole (SMBH). The feedback efficiency in earlier works was so high that the cluster core reached equilibrium in a hot state without much precipitation, unlike what is observed in cool-core clusters. We find hysteresis cycles in all our simulations with cold mode feedback: condensation of cold gas when the ratio of the cooling-time to the free-fall time (t(cool)/t(ff)) is less than or similar to 10 leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and overheating of the hot intracluster medium such that t(cool)/t(ff) > 10; further condensation of cold gas is suppressed and the accretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle. Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of core entropy t(cool)/t(ff). A smaller number of cycles is observed for higher efficiencies and for lower mass halos because the core is overheated to a longer cooling time. The 3D simulations show the formation of a few-kpc scale, rotationally supported, massive (similar to 10(11) M-circle dot) cold gas torus. Since the torus gas is not accreted onto the SMBH, it is largely decoupled from the feedback cycle. The radially dominant cold gas (T < 5 x 10(4) K; vertical bar v(r)vertical bar >vertical bar v(phi vertical bar)) consists of fast cold gas uplifted by AGN jets and freely infalling cold gas condensing out of the core. The radially dominant cold gas extends out to 25 kpc for the fiducial run (halo mass 7 x 10(14) M-circle dot and feedback efficiency 6 x 10(-5)), with the average mass inflow rate dominating the outflow rate by a factor of approximate to 2. We compare our simulation results with recent observations.

PERIODIC CONTROLS IN AN OSCILLATING DOMAIN: CONTROLS VIA UNFOLDING AND HOMOGENIZATION

An optimal control problem in a two-dimensional domain with a rapidly oscillating boundary is considered. The main features of this article are on two points, namely, we consider periodic controls in the thin periodic slabs of period epsilon > 0, a small parameter, and height O(1) in the oscillatory part, and the controls are characterized using unfolding operators. We then do a homogenization analysis of the optimal control problems as epsilon -> 0 with L-2 as well as Dirichlet (gradient-type) cost functionals.

A note on tetrablock contractions

A commuting triple of operators (A, B, P) on a Hilbert space H is called a tetrablock contraction if the closure of the set E = {(a(11),a(22),detA) : A = GRAPHICS] with parallel to A parallel to <1} is a spectral set. In this paper, we construct a functional model and produce a set of complete unitary invariants for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations A - B* P = DPX1DP and B - A* P = DPX2DP where X-1, X-2 is an element of B(D-P) play a pivotal role. As a result of the functional model, we show that every pure tetrablock isometry (A, B, P) on an abstract Hilbert space H is unitarily equivalent to the tetrablock contraction (MG1*+G2z, MG2*+G1z, M-z) on H-DP*(2). (D), where G(1) and G(2) are the fundamental operators of (A*, B*, P*). We prove a Beurling Lax Halmos type theorem for a triple of operators (MF1*+F2z, MF2*+F1z, M-z), where epsilon is a Hilbert space and F-1, F-2 is an element of B(epsilon). We also deal with a natural example of tetrablock contraction on a functions space to find out its fundamental operators.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Effect of methylene group insertions on the structural rigidity of Aib containing helices

Nonprotein amino acids are being extensively used in the design of synthetic peptides to create new structure mimics. In this study we report the effect of methylene group insertions in a heptapeptide Boc-Ala(1)-Leu(2)-Aib(3)-Xxx(4)-Ala(5)-Leu(6)-Aib(7)-OMe which nicely folds into a mixed 3(10)-/-helical structure when Xxx= Ala. Analogs of this peptide have been made and studied by replacing central Xxx(4) residue with Glycine (-residue), -Alanine (-la), -aminobutyric acid (Gaba), and epsilon-aminocaproic acid (epsilon-Aca). NMR and circular dichroism were used to study the solution structure of these peptides. Crystals of the peptides containing alanine, -la, and Gaba reveal that increasing the number of central methylene (-CH2-) groups introduces local perturbations even as the helical structure is retained. (c) 2015 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 104: 720-732, 2015.

Role of (La, Gd) co-doping on the enhanced dielectric and magnetic properties of BiFeO3 ceramics

The effect of the La3+ and Gd3+ co-doping on the structure, electric and magnetic properties of BiFeO3 (BFO) ceramics are investigated. For the compositions (x=0 and 0 <= y <= 0.15) in the perovskite structured LaxGdyBi1-xFeO3 system, a tiny residual phase of Bi2Fe4O9 is noticed. Such a secondary phase is suppressed with the incorporation of `La' content (x). The magnitude of dielectric constant (epsilon(r) increases progressively by increasing the `La' content from x=0 to 0.15 with a remarkable decrease of dielectric loss. For x=0.15, the system LaxGdyBi1-x(x+y)FeO3 exhibits highest remanent magnetization (M-r) of 0.18 emu/g and coercive magnetic field (H-c) of similar to 1 Tin the presence of external magnetic field of 9 T at 300 K. The origin of enhanced dielectric and magnetic properties of LaxGdyBil (x+y)Fe03 and the role of doping elements, La3+, Gd3+ has been discussed. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Transgenic Drosophila model to study apolipoprotein E4-induced neurodegeneration

The epsilon 4 isoform of apolipoprotein E (ApoE4) that is involved in neuron-glial lipid metabolism has been demonstrated as the main genetic risk factor in late-onset of Alzheimer's disease. However, the mechanism underlying ApoE4-mediated neurodegeneration remains unclear. We created a transgenic model of neurodegenerative disorder by expressing epsilon 3 and epsilon 4 isoforms of human ApoE in the Drosophila melanogaster. The genetic models exhibited progressive neurodegeneration, shortened lifespan and memory impairment. Genetic interaction studies between amyloid precursor protein and ApoE in axon pathology of the disease revealed that over expression of hApoE in Appl-expressing neurons of Drosophila brain causes neurodegeneration. Moreover, acute oxidative damage in the hApoE transgenic flies triggered a neuroprotective response of hApoE3 while chronic induction of oxidative damage accelerated the rate of neurodegeneration. This Drosophila model may facilitate analysis of the molecular and cellular events implicated in hApoE4 neurotoxicity. (C) 2015 Elsevier B.V. All rights reserved.

HOMOGENIZATION OF A HYPERBOLIC EQUATION WITH HIGHLY CONTRASTING DIFFUSIVITY COEFFICIENTS

We study a hyperbolic problem in the framework of periodic homogenization assuming a high contrast between the diffusivity coefficients of the two components M-epsilon and B-epsilon of the heterogeneous medium. There are three regimes depending on the ratio between the size of the period and the amplitude a, of the diffusivity in B-epsilon. For the critical regime alpha(epsilon) similar or equal to epsilon, the limit problem is a strongly coupled system involving both the macroscopic and the microscopic variables. We also include the results in the non critical case.

Transgenic Drosophila model to study apolipoprotein E4-induced neurodegeneration

The epsilon 4 isoform of apolipoprotein E (ApoE4) that is involved in neuron-glial lipid metabolism has been demonstrated as the main genetic risk factor in late-onset of Alzheimer's disease. However, the mechanism underlying ApoE4-mediated neurodegeneration remains unclear. We created a transgenic model of neurodegenerative disorder by expressing epsilon 3 and epsilon 4 isoforms of human ApoE in the Drosophila melanogaster. The genetic models exhibited progressive neurodegeneration, shortened lifespan and memory impairment. Genetic interaction studies between amyloid precursor protein and ApoE in axon pathology of the disease revealed that over expression of hApoE in Appl-expressing neurons of Drosophila brain causes neurodegeneration. Moreover, acute oxidative damage in the hApoE transgenic flies triggered a neuroprotective response of hApoE3 while chronic induction of oxidative damage accelerated the rate of neurodegeneration. This Drosophila model may facilitate analysis of the molecular and cellular events implicated in hApoE4 neurotoxicity. (C) 2015 Elsevier B.V. All rights reserved.

HOMOGENIZATION OF A HYPERBOLIC EQUATION WITH HIGHLY CONTRASTING DIFFUSIVITY COEFFICIENTS

We study a hyperbolic problem in the framework of periodic homogenization assuming a high contrast between the diffusivity coefficients of the two components M-epsilon and B-epsilon of the heterogeneous medium. There are three regimes depending on the ratio between the size of the period and the amplitude a, of the diffusivity in B-epsilon. For the critical regime alpha(epsilon) similar or equal to epsilon, the limit problem is a strongly coupled system involving both the macroscopic and the microscopic variables. We also include the results in the non critical case.

Numerical Investigations for Leakage and Windage Heating in Straight-Through Labyrinth Seals

The ability to quantify leakage flow and windage heating for labyrinth seals with honeycomb lands is critical in understanding gas turbine engine system performance and predicting its component life. Variety of labyrinth seal configurations (number of teeth, stepped or straight, honeycomb cell size) are in use in gas turbines, and for each configuration, there are many geometric factors that can impact a seal's leakage and windage characteristics. This paper describes the development of a numerical methodology aimed at studying the effect of honeycomb lands on leakage and windage heating. Specifically, a three-dimensional computational fluid dynamics (CFD) model is developed utilizing commercial finite volume-based software incorporating the renormalization group (RNG) k-epsilon turbulence model with modified Schmidt number. The modified turbulence model is benchmarked and fine-tuned based on several experiments. Using this model, a broad parametric study is conducted by varying honeycomb cell size, pressure ratio (PR), and radial clearance for a four-tooth straight-through labyrinth seal. The results show good agreement with available experimental data. They further indicate that larger honeycomb cells predict higher seal leakage and windage heating at tighter clearances compared to smaller honeycomb cells and smooth lands. However, at open seal clearances larger honeycomb cells have lower leakage compared to smaller honeycomb cells.

Archean tectonics and crustal evolution of the Biligiri Rangan Block, southern India

The Southern Granulite Terrain in India is a collage of crustal blocks ranging in age from Archean to Neoproterozoic. This study investigate the tectonic evolution of one of the northernmost block- the Biligiri Block (BRB) through a multidisciplinary approach involving field investigation, petrographic studies, LA-ICPMS zircon U-Pb geochronology, Hf isotopic analyses, metamorphic P-T phase diagram computations, and crustal thickness modeling. The garnet bearing quartzofeldspathic gneiss from the central BRB preserve Mesoarchean magmatic zircons with ages between 3207 and 2806 Ma and positive epsilon Hf value (+2.7) which possibly indicates vestiges of a Mesoarchean primitive continental crust. The occurrence of quartzite-iron formation intercalation as well as ultramafic lenses along the western boundary of the BRB is interpreted to indicate that the Kollegal structural lineament is a possible paleo-suture. Phase diagram computation of a metagabbro from the southwestern periphery of the Kollegal suture zone reveals high-pressure (similar to 18.5 kbar) and medium-temperature (similar to 840 degrees C) metamorphism, likely during eastward subduction of the Western Dharwar oceanic crust beneath the Mesoarchean BRB. In the model presented here, slab subduction, melting and underplating processes generated arc magmatism and subsequent charnockitization within the BRB between ca. 2650 Ma and ca. 2498 Ma. These results thus reveal Meso- to Neoarchean tectonic evolution of the BRB. The spatial variation of crustal thickness, derived from flexure inversion technique, provides additional constraints on the tectonic linkage of the BRB with its surrounding terrains. In conjunction with published data, the Moyar and the Kollegal suture zones are considered to mark the trace of ocean closure along which the Nilgiri and Biligiri Rangan Blocks accreted on to the Western Dharwar Craton. (C) 2016 Elsevier B.V. All rights reserved.