On extensions of representations for compact Lie groups

Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every complex $G$-vector bundle over the homogeneous space $G/H$ to be trivial. In particular, we show that the condition holds when the fundamental group of $G/H$ is torsion free.Comment: 10 pages, AMS-LaTeX v1.

Log-concavity of complexity one Hamiltonian torus actions

Let $(M,\omega)$ be a closed $2n$-dimensional symplectic manifold equipped with a Hamiltonian $T^{n-1}$-action. Then Atiyah-Guillemin-Sternberg convexity theorem implies that the image of the moment map is an $(n-1)$-dimensional convex polytope. In this paper, we show that the density function of the Duistermaat-Heckman measure is log-concave on the image of the moment map.Comment: 5 pages, 1 figur

Optimalne potrebe juvenilnih morskih grgeča sebastes schlegeli u proteinima i lipidima

U ovom istraživanju su analizirane optimalne potrebe juvenilnih morskih grgeča Sebastes schlegeli u proteinima i lipidima. 810 juvenilnih riba je izabrano po principu slučajnosti i distribuirano u 27 tankova od po 50 L sa protočnih sistemom. Pripremljeno je 9 eksperimentalnih smeša u vidu 3x3 faktorijalne eksperimentalne postavke: tri nivoa proteina (45, 50 i 55%) x tri nivoa lipida (11, 15 i 19%). Nivo proteina je imao uticaj na prirast riba, dok nivo lipida nije. Prirast riba hranjenih smešom u odnosu 50P-15L (50% proteina i 15% lipida) je bio veći nego prirast riba hranjenih smešama sa 45% proteina, bez obzira na nivo lipida, ali je bio isti kao kod riba hranjenih sa smešama 50P-11L, 50P-19L, 55P-11L, 55P-15L i 55P-19L. Stopa efikasnosti hrane (FER) riba je bila pod uticajem proteina u hrani ali ne i nivoa lipida. Stopa efikasnosti proteina (PER) riba je takođe bila pod uticajem proteina u hrani ali ne i nivoa lipida. Može se zaključiti da je za juvenilne Sebastes schlegeli optimalan nivo proteina i lipida za dobar prirast i iskoristljivost hrane (PER and NRE) 50% i 15% odnosno 45% i 19%, dok je optimalan odnos proteina i energije 27.4 i 23.9 mg protein/kJ

Soil-Pile Interaction Analysis using FE-BE Coupling in Frequency Domain

In this study, a numerical method for soil-pile interaction problems in multi-layered half-plane is developed in frequency domain using FE-BE coupling technique. The soil-pile interaction system is divided into two parts, so-called near field and far field. In the near field, beam elements are used for modeling pile and plane-strain finite elements for surrounding soil media. Also, a superstructure is considered as a lumped mass on a pile. In the far field, layered soil media is modeled by boundary element formulation using the dynamic fundamental solution. Then, these two fields are assembled using FE-BE coupling technique. This coupled numerical method automatically satisfies the radiation conditions because the far field boundary element formulation can handle the radiation conditions in a half plane. Additionally, the difference of relative displacement at the interface between soil and pile is considered by applying interface spring elements. In order to verify the proposed method for soil-pile interaction system, the dynamic responses of a pile in a multi-layered half-plane are performed and the numerical results are compared with the measured values from experiments. It is shown that the developed method can be an efficient numerical tool to solve the dynamic response of a pile buried in a multi-layered half plane

Efficient electron dynamics with the planewave-based real-time time-dependent density functional theory: Absorption spectra, vibronic electronic spectra, and coupled electron-nucleus dynamics

The electron dynamics with complex third-order Suzuki-Trotter propagator (ST(3)) has been implemented into a planewave (PW) based density functional theory program, and several applications including linear absorption spectra and coupled electron-nucleus dynamics have been calculated. Since the ST(3) reduces the number of Fourier transforms to less than half compared to the fourth-order Suzuki-Trotter propagator (ST(4)), more than twice faster calculations are possible by exploiting the ST(3). We analyzed numerical errors of both the ST(3) and the ST(4) in the presence/absence of an external field for several molecules such as Al(2), N(2), and C(2)H(4). We obtained that the ST(3) gives the same order of numerical errors (10(-5) Ry after 100 fs) as the ST(4). Also, the time evolution of dipole moments, hence the absorption spectrum, is equivalent for both ST(3) and ST(4). As applications, the linear absorption spectrum for an ethylene molecule was studied. From the density difference analysis, we showed that the absorption peaks at 6.10 eV and 7.65 eV correspond to the pi -> 4a(g) and pi -> pi* excitation bands, respectively. We also investigated the molecular vibrational effect to the absorption spectra of an ethylene molecule and the dynamics of a hydrogen molecule after the sigma -> sigma* transition by formulating coupled electron-nucleus dynamics within the Ehrenfest regime. The trajectory of nuclei follows the excited state potential energy curve exactly. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3671952close