Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone

We consider a particle moving on a cone and bound to its tip by 1/r or harmonic oscillator potentials. When the deficit angle of the cone divided by 2π is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional “spin” and unusual degeneracies.     

Short and Long SU(2, 2/4) Multiplets in the AdS/CFT Correspondence

We analyze short and long multiplets which appear in the OPE expansion of chiral primary operators in N=4 Super Yang–Mills theory. Among them, higher spin long and new short multiplets appear having the interpretation in the AdS/CFT correspondence of string states and supergravity multiparticle states, respectively. We also analyze the decomposition of long multiplets under N=1 supersymmetry as a possible tool exploring other supersymmetric deformations of IIB string on AdS₅×S₅.     

A Generalization of the Bott–Borel–Weil Theorem and Euler Number Multiplets of Representations

The Bott–Borel–Weil theorem (BBW) is a statement about a complex homogeneous space X=G/R where G is a compact semisimple Lie group and R is the centralizer of a torus in G. One knows that BBW is equivalent to the determination of how R operates on the cohomology of a certain nilpotent Lie algebra of antiholomorphic tangent vectors operating on an arbitrary irreducible G-module. Upon replacing the complex structure with a space S of spinors BBW is equivalent to a statement about the eigenvalues of the Casimir operator of R in the module S V where V is the irreducible G-module with highest weight . But then the complex structure is eliminated and the problem makes sense for any compact subgroup R G. We solve the problem in the case where R and G have the same rank. The very special case where R is the centralizer of a torus then yields BBW. Involved in the general case (i.e. arbitrary R) is a new (at least to mathematicians) Dirac operator with a cubic term whose square is expressed in terms of the Casimir operator. Actually the spectral resolution of the Dirac operator is determined in the general case. The kernel of the Dirac operator is only given in the equal rank case. A key feature in that case is that, associated to , there is a multiplet of representations of R, having rather striking properties, and cardinality equal to the Euler number of G/R.     

Selective excitation of overlapping multiplets; the application of doubly selective and chemical shift filter experiments to complex NMR spectra

Standard 1D TOCSY and NOE experiments have limitations where signals are severely overlapped. Here, two recently published selective excitation methods are evaluated, the first of which uses a chemical shift selective filter to select a single resonance based on its chemical shift, and the second of which is a doubly selective experiment comprising a 1D TOCSY preparation step and subsequent 1D NOE. We also demonstrate the improvement in spectral quality obtained by the use of the zero quantum filter, which is incorporated into both of these experiments. The application of these different methods of selectively exciting overlapped multiplets, to different types of samples is considered.     

Baryon Ratios in Quark-Gluon Plasma

A way to calculate ratios of baryon produced from quark gluon plasma in relativistic heavyion collisionsis presented. It is assumed that at the beginning of the hadronization there are diquarks and anti-diquarks in the quarkmatter. The number of three-quark states is distributed between the corresponding multiplets, and hadronic decays aretaken into account. The results are shown at last.     

Short Representations of SU(2,2/N) and Harmonic Superspace Analyticity

We consider the harmonic superspaces associated with SU(2,2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] elementary ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k=1...[N/2]) with top spin J _top=(N/2–k/2,0). For N=2n, we analyze UIR's obtained by tensoring the self-conjugate ultrashort multiplet J _top=(n/2,0) and show that N–1 different basic products give rise to all possible UIR's with residual shortening.     

连续搅拌反应器中产物─底物非竞争性抑制动力学的无因次分析

本文研究在ＣＳＴＲ反应器中进行非竞争性和抑制微生物反应动力学行为,将产物－底物非竞争性抑制动力学模型无因次处理后,分析可能出现的解的多重态现象,表明在多解操作区内的稳态解是具有高产量、高底物利用率的最优操作态,指出从发酵液中不断移去产物能有效地缓和产物抑制,增大多解操作区的范围。     

Nuclear spin species,spin statistical weights and rovibronic tunnelling splittings of non-rigid water hexamer

Powerful multinomial generating functions together with the character table of the six-dimensional hyperoctahedral wreath product group S₆[S₂] of the non-rigid water hexamer are employed to obtain the nuclear spin species, nuclear spin multiplets and the total nuclear spin statistical weights of the rovibronic-tunnelling levels for both deuterated and regular forms. The methods are composed of algebraic generating functions involving 531,441 nuclear spin functions for (D₂O)₆ in a group of 46,080 operations and 65 irreducible representations of the S₆[S₂] group. Although the deuterated form of the non-rigid water hexamer possesses nuclear spin populations in 58 of the 65 possible symmetries of tunnelling levels, for the regular water hexamer only 23 of the 65 symmetries are populated with nuclear spin functions. The tunnelling splitting correlations of rovibronic levels of the water hexamer have been obtained from the Saykally's semi-rigid (G₄) model to the fully non-rigid limit (G₄₆₀₈₀). The computed nuclear spin statistical weights for protonated form of (H₂O)₆ call for a reinterpretation of the previous assignment of the observed spectra. The results can also be applied to enumerate the hyperfine patterns using the nuclear spin multiplets and intensities in semi-rigid to fully non-rigid limits.     

Baryon Ratios in Quark-Gluon Plasma

A way to calculate ratios of baryon produced from quark gluon plasma in relativistic heavy ion collisions is presented. It is assumed that at the beginning of the hadronlzation there are diquarks and anti-diquarks in the quark matter. The number of three-quark states is distributed between the corresponding multiplets, and hadronic decays are taken into account. The results are shown at last.     

密度泛函理论处理激发态与多重态结构研究进展

用密度泛函理论处理分子激发态和电子多重态结构是密度泛函理论发展的重要方面, 研究工作一直很活跃。本文对近年来在这一领域取得的重要进展作简要的综述。