Special symplectic Lie groups and hypersymplectic Lie groups

A special symplectic Lie group is a triple $(G,\omega,\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure $\nabla$. In this paper starting from a special symplectic Lie group we show how to ``deform" the standard Lie group structure on the (co)tangent bundle through the left invariant affine structure $\nabla$ such that the resulting Lie group admits families of left invariant hypersymplectic structures and thus becomes a hypersymplectic Lie group. We consider the affine cotangent extension problem and then introduce notions of post-affine structure and post-left-symmetric algebra which is the underlying algebraic structure of a special symplectic Lie algebra. Furthermore, we give a kind of double extensions of special symplectic Lie groups in terms of post-left-symmetric algebras.Comment: 32 page

Lyapunov exponents for products of complex Gaussian random matrices

The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$ complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.Comment: 15 page

Identification and functional characterization of an N-terminal oligomerization domain for polycystin-2*

Autosomal dominant polycystic kidney disease (ADPKD), the most common inherited cause of kidney failure, is caused by mutations in either PKD1 (85%) or PKD2 (15%). The PKD2 protein, polycystin-2 (PC2 or TRPP2), is a member of the transient receptor potential (TRP) superfamily and functions as a non-selective calcium channel. PC2 has been found to form oligomers in native tissues suggesting that it may form functional homo- or heterotetramers with other subunits, similar to other TRP channels. Our experiments unexpectedly revealed that PC2 mutant proteins lacking the known C-terminal dimerization domain were still able to form oligomers and co-immunoprecipitate full-length PC2, implying the possible existence of a proximal dimerization domain. Using yeast two-hybrid and biochemical assays, we have mapped an alternative dimerization domain to the N terminus of PC2 (NT2-1-223, L224X). Functional characterization of this domain demonstrated that it was sufficient to induce cyst formation in zebrafish embryos and inhibit PC2 surface currents in mIMCD3 cells probably by a dominant-negative mechanism. In summary, we propose a model for PC2 assembly as a functional tetramer which depends on both C- and N-terminal dimerization domains. These results have significant implications for our understanding of PC2 function and disease pathogenesis in ADPKD and provide a new strategy for studying PC2 function

Beam Dynamics of Qi Storage Rings

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Measure representation and multifractal analysis of complete genomes

This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the $D_{q}$ spectra and related $C_{q}$ curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations considered as time series, exhibit strong long-range correlation. For substrings with length K=8, the $D_{q}$ spectra of all organisms studied are multifractal-like and sufficiently smooth for the $C_{q}$ curves to be meaningful. The $C_{q}$ curves of all bacteria resemble a classical phase transition at a critical point. But the 'analogous' phase transitions of chromosomes of non-bacteria organisms are different. Apart from Chromosome 1 of {\it C. elegans}, they exhibit the shape of double-peaked specific heat function.Comment: 12 pages with 9 figures and 1 tabl

Electronic Structure of a Hydrogenic Acceptor Impurity in Semiconductor Nano-structures

The electronic structure and binding energy of a hydrogenic acceptor impurity in 2, 1, and 0-dimensional semiconductor nano-structures (i.e. quantum well (QW), quantum well wire (QWW), and quantum dot (QD)) are studied in the framework of effective-mass envelope-function theory. The results show that (1) the energy levels monotonically decrease as the quantum confinement sizes increase; (2) the impurity energy levels decrease more slowly for QWWs and QDs as their sizes increase than for QWs; (3) the changes of the acceptor binding energies are very complex as the quantum confinement size increases; (4) the binding energies monotonically decrease as the acceptor moves away from the nano-structures’ center; (5) as the symmetry decreases, the degeneracy is lifted, and the first binding energy level in the QD splits into two branches. Our calculated results are useful for the application of semiconductor nano-structures in electronic and photoelectric devices

Calibration of the Gamma-RAy Polarimeter Experiment (GRAPE) at a Polarized Hard X-Ray Beam

The Gamma-RAy Polarimeter Experiment (GRAPE) is a concept for an astronomical hard X-ray Compton polarimeter operating in the 50 - 500 keV energy band. The instrument has been optimized for wide-field polarization measurements of transient outbursts from energetic astrophysical objects such as gamma-ray bursts and solar flares. The GRAPE instrument is composed of identical modules, each of which consists of an array of scintillator elements read out by a multi-anode photomultiplier tube (MAPMT). Incident photons Compton scatter in plastic scintillator elements and are subsequently absorbed in inorganic scintillator elements; a net polarization signal is revealed by a characteristic asymmetry in the azimuthal scattering angles. We have constructed a prototype GRAPE module containing a single CsI(Na) calorimeter element, at the center of the MAPMT, surrounded by 60 plastic elements. The prototype has been combined with custom readout electronics and software to create a complete "engineering model" of the GRAPE instrument. This engineering model has been calibrated using a nearly 100% polarized hard X-ray beam at the Advanced Photon Source at Argonne National Laboratory. We find modulation factors of 0.46 +/- 0.06 and 0.48 +/- 0.03 at 69.5 keV and 129.5 keV, respectively, in good agreement with Monte Carlo simulations. In this paper we present details of the beam test, data analysis, and simulations, and discuss the implications of our results for the further development of the GRAPE concept.Comment: 35 pages, 14 figures, accepted for publication in NIM-

Electroexcitation of the Δ+(1232)\Delta^{+}(1232) at low momentum transfer

We report on new p$(e,e^\prime p)\pi^\circ$ measurements at the $\Delta^{+}(1232)$ resonance at the low momentum transfer region. The mesonic cloud dynamics is predicted to be dominant and rapidly changing in this kinematic region offering a test bed for chiral effective field theory calculations. The new data explore the low $Q^2$ dependence of the resonant quadrupole amplitudes while extending the measurements of the Coulomb quadrupole amplitude to the lowest momentum transfer ever reached. The results disagree with predictions of constituent quark models and are in reasonable agreement with dynamical calculations that include pion cloud effects, chiral effective field theory and lattice calculations. The reported measurements suggest that improvement is required to the theoretical calculations and provide valuable input that will allow their refinements

Partial Wave Analysis of J/ψ→γ(K+K−π+π−)J/\psi \to \gamma (K^+K^-\pi^+\pi^-)

BES data on $J/\psi \to \gamma (K^+K^-\pi^+\pi^-)$ are presented. The $K^*\bar K^*$ contribution peaks strongly near threshold. It is fitted with a broad $0^{-+}$ resonance with mass $M = 1800 \pm 100$ MeV, width $\Gamma = 500 \pm 200$ MeV. A broad $2^{++}$ resonance peaking at 2020 MeV is also required with width $\sim 500$ MeV. There is further evidence for a $2^{-+}$ component peaking at 2.55 GeV. The non-$K^*\bar K^*$ contribution is close to phase space; it peaks at 2.6 GeV and is very different from $K^{*}\bar{K^{*}}$.Comment: 15 pages, 6 figures, 1 table, Submitted to PL

Fine mapping of the tomato yellow leaf curl virus resistance gene Ty-2 on chromosome 11 of tomato

Resistances to begomoviruses, including bipartite tomato mottle virus and monopartite tomato yellow leaf curl virus (TYLCV), have been introgressed to cultivated tomato (Solanumlycopersicum) fromwild tomato accessions. A major gene, Ty-2 from S. habrochaites f. glabratum accession ‘‘B6013,’’ that confers resistance to TYLCV was previously mapped to a 19-cMregion on the long arm of chromosome 11. In the present study, approximately 11,000 plants were screened and nearly 157 recombination events were identified between the flankingmarkersC2_At1g07960 (82.5 cM, physical distance 51.387 Mb) and T0302 (89 cM, 51.878 Mb). Molecular marker analysis of recombinants and TYLCV evaluation of progeny from these recombinants localized Ty-2 to an approximately 300,000-bp interval between markers UP8 (51.344 Mb) and M1 (51.645 Mb). No recombinants were identified between TG36 and C2_At3g52090, a region of at least 115 kb, indicating severe recombination suppression in this region. Due to the small interval, fluorescence in situ hybridization analysis failed to clarify whether recombination suppression is caused by chromosomal rearrangements. Candidate genes predicted based on tomato genome annotation were analyzed by RT-PCR and virus-induced gene silencing. Results indicate that the NBS gene family present in the Ty-2 region is likely not responsible for the Ty-2-conferred resistance and that two candidate genes might play a role in the Ty-2-conferred resistance. Severalmarkers very tightly linked to the Ty-2 locus are presented and useful for marker-assisted selection in breeding programs to introgress Ty-2 for begomovirus resistance