Mixed norm estimates for the Riesz transforms on the Heisenberg group

In this paper we prove weighted mixed norm estimates for Riesz transforms on the Heisenberg group and Riesz transforms associated to the special Hermite operator. From these results vector-valued inequalities for sequences of Riesz transforms associated to generalised Grushin operators and Laguerre operators are deduced.

Renormalization group invariants and sum rules in the deflected mirage mediation supersymmetry breaking

We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.

Binary group III-nitride based heterostructures: band offsets and transport properties

In the last few years, there has been remarkable progress in the development of group III-nitride based materials because of their potential application in fabricating various optoelectronic devices such as light emitting diodes, laser diodes, tandem solar cells and field effect transistors. In order to realize these devices, growth of device quality heterostructures are required. One of the most interesting properties of a semiconductor heterostructure interface is its Schottky barrier height, which is a measure of the mismatch of the energy levels for the majority carriers across the heterojunction interface. Recently, the growth of non-polar III-nitrides has been an important subject due to its potential improvement on the efficiency of III-nitride-based opto-electronic devices. It is well known that the c-axis oriented optoelectronic devices are strongly affected by the intrinsic spontaneous and piezoelectric polarization fields, which results in the low electron-hole recombination efficiency. One of the useful approaches for eliminating the piezoelectric polarization effects is to fabricate nitride-based devices along non-polar and semi-polar directions. Heterostructures grown on these orientations are receiving a lot of focus due to enhanced behaviour. In the present review article discussion has been carried out on the growth of III-nitride binary alloys and properties of GaN/Si, InN/Si, polar InN/GaN, and nonpolar InN/GaN heterostructures followed by studies on band offsets of III-nitride semiconductor heterostructures using the x-ray photoelectron spectroscopy technique. Current transport mechanisms of these heterostructures are also discussed.

Continuum in the X-Z-Y Weak Bonds: Z= Main Group Elements

The Continuum in the variation of the X-Z bond length change from blue-shifting to red-shifting through zero-shifting in the X-Z---Y complex is inevitable. This has been analyzed by ab-initio molecular orbital calculations using Z= Hydrogen, Halogens, Chalcogens, and Pnicogens as prototypical examples. Our analysis revealed that, the competition between negative hyperconjugation within the donor (X-Z) molecule and Charge Transfer (CT) from the acceptor (Y) molecule is the primary reason for the X-Z bond length change. Here, we report that, the proper tuning of X-and Y-group for a particular Z-can change the blue-shifting nature of X-Z bond to zero-shifting and further to red-shifting. This observation led to the proposal of a continuum in the variation of the X-Z bond length during the formation of X-Z---Y complex. The varying number of orbitals and electrons available around the Z-atom differentiates various classes of weak interactions and leads to interactions dramatically different from the H-Bond. Our explanations based on the model of anti-bonding orbitals can be transferred from one class of weak interactions to another. We further take the idea of continuum to the nature of chemical bonding in general. (C) 2015 Wiley Periodicals, Inc.

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.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.