Local theta lifting of generalized Whittaker models associated to nilpotent orbits

Let $(G,\tilde{G})$ be a reductive dual pair over a local field {\Fontauri k} of characteristic 0, and denote by $V$ and $\tilde{V}$ the standard modules of $G$ and $\tilde{G}$, respectively. Consider the set $Max Hom(V,\tilde{V})$ of full rank elements in $Hom(V,\tilde{V})$, and the nilpotent orbit correspondence $\mathcal{O} \subset \mathfrak{g}$ and $\Theta (\mathcal{O})\subset \tilde{\mathfrak{g}}$ induced by elements of $Max Hom(V,\tilde{V})$ via the moment maps. Let $(\pi,\mathscr{V})$ be a smooth irreducible representation of $G$. We show that there is a correspondence of the generalized Whittaker models of $\pi$ of type $\mathcal{O}$ and of $\Theta (\pi)$ of type $\Theta (\mathcal{O})$, where $\Theta (\pi)$ is the full theta lift of $\pi$. When $(G,\tilde{G})$ is in the stable range with $G$ the smaller member, every nilpotent orbit $\mathcal{O} \subset \mathfrak{g}$ is in the image of the moment map from $Max Hom (V,\tilde{V})$. In this case, and for {\Fontauri k} non-Archimedean, the result has been previously obtained by M\oe{}glin in a different approach.Comment: To appear in Geometric and Functional Analysi

Phase transitions and spin excitations of spin-1 bosons in optical lattice

We investigate ground state properties of spin-1 bosonic system trapped in optical lattice with extended standard basis operator (SBO) method. For both ferromagnetic ($U_20$) systems, we analytically figure out the symmetry properties in Mott-insulator and superfluid phases, which would provide a deeper insight into the MI-SF phase transition process. Then by applying self-consistent approach to the method, we include the effect of quantum and thermal fluctuations and derive the MI-SF transition phase diagram, which is in quantitative agreement with recent Monte-Carlo simulation at zero temperature, and at finite temperature, we find the underestimation of finite-temperature-effect in the mean-field approximation method. If we further consider the spin excitations in the insulating states of spin-1 system in external field, distinct spin phases are expected. Therefore, in the Mott lobes with $n=1$ and $n=2$ atoms per site, we give analytical and numerical boundaries of the singlet, nematic, partially magnetic and ferromagnetic phases in the magnetic phase diagrams.Comment: 14 pages, 6 figure

Proposal for measuring new transverse momentum dependent parton distributions g1Tg_{1T} and h1L⊥h_{1L}^\perp through semi-inclusive deep inelastic scattering

We calculate $g_{1T}$ and $h_{1L}^\perp$, two of the eight leading twist transverse momentum dependent parton distributions (TMDs), in the light-cone quark-diquark model. The new TMDs can be measured through semi-inclusive deep inelastic scattering (SIDIS). We present predictions of the single and double spin asymmetries related to $g_{1T}$ and $h_{1L}^\perp$ in SIDIS at HERMES, COMPASS, and JLab kinematics respectively.Comment: 14 latex pages, 7 figures, final version for journal publicatio

Efficiency of GCSC-BtA, as a new type of biocide, on different agricultural arthropod pests and its side-effect on some predators

A new type of biocide GCSC-BtA, named from "Germany-China Scientific Cooperation-Bacillus thuringiensis-Abamectin", was successfully developed by conjugating delta-endotoxin of Bacillus thuringiensis (B.t.) with Abamectin from Streptomyces avermitilis through conjugator EDC for control of different agricultural arthropod pests. The laboratory results of efficiency of biocide GCSC-BtA to four different arthropod pests and its side-effect on two species of predators are presented in this paper. The results showed significant differences in the mortalities of Tetranychus cinnabarinus (BOISD.) (Acari, Tetranychidae), Frankliniella occidentalis PERGANDE (Thys., Thripidae), Aphis fabae SCOPOLI (Hom., Aphididae) and Cameraria ohridella DESCHKA ET DIMI´C (Lep., Gracillariidae) caused by treatment of 0.6250 mg/ml of formulated product of GCSC-BtA, B.t., Abamectin and Cypermethrin. GCSC-BtA treatment caused higher mortalities of 86.37%, 94.82%, 94.15% and 93.23% in T. cinnabarinus, F. occidentalis, A. fabae and C. ohridella, respectively. Mortalities caused by Abamectin treatment were 73.92%, 63.3%, 86.52% and 73.48%, and by Cypermethrin treatment were 44.29%, 57.28%, 97.68% and 51.26%, respectively. B.t. could only kill C. ohridella with 87.62% mortality. Pesticidal treatment gave variations in mortalities of Orius strigicollis POPPIUS (Het., Anthocoridae) and Stethorus cantonensis PANG (Col., Coccinellidae) predators at p < 0.01, where 0.6250 mg/ml GCSC-BtA caused 21.76% and 32.42% mortalities, while the same rate of products of Abamectin with 73.26% and 87.67% as well as Cypermethrin with 86.43% and 93.83% mortalities, respectively. It is concluded that the biocide GCSC-BtA has increased efficacies as well as host ranges of B.t. and Abamectin, but displayed safer to some predators