Multiplet Decomposition Research Articles

Fitting Blazhko light curves

The correct amplitude and phase modulation formalism of the Blazhko modulation is given. The harmonic order dependent amplitude and phase modulation form is equivalent with the Fourier decomposition of multiplets. The amplitude and phase modulation formalism used in electronic transmission technique as introduced by Benk\H{o}, Szab\'o and Papar\'o (2011, MNRAS 417, 974) for Blazhko stars oversimplifies the amplitude and phase modulation functions thus it does not describe the light variation in full detail. The results of the different formalisms are compared and documented by fitting the light curve of a real Blazhko star, CM UMa.

On superconformal characters and partition functions in three dimensions

Possible short and semishort positive energy, unitary representations of the Osp(2N|4) superconformal group in three dimensions are discussed. Corresponding character formulas are obtained, consistent with character formulas for the SO(3,2) conformal group, revealing long multiplet decomposition at unitarity bounds in a simple way. Limits, corresponding to reduction to various Osp(2N|4) subalgebras, are taken in the characters that isolate contributions from fewer states, at a given unitarity threshold, leading to considerably simpler formula. Via these limits, applied to partition functions, closed formula for the generating functions for numbers of BPS operators in the free field limit of superconformal U(n)×U(n) N=6 Chern–Simons theory and its supergravity dual are obtained in the large n limit. Partial counting of semishort operators is performed and consistency between operator counting for the free field and supergravity limits with long multiplet decomposition rules is explicitly demonstrated. Partition functions counting certain protected scalar primary semishort operators, and their superconformal descendants, are proposed and computed for large n. Certain chiral ring partition functions are discussed from a combinatorial perspective.

N-impurity superstring spectra near the pp-wave limit

The complicated non-linear sigma model that characterizes the first finite-radius curvature correction to the pp-wave limit of IIB superstring theory on AdS 5 × S 5 has been shown to generate energy spectra that perfectly match, to two loops in the modified 't Hooft parameter λ ′ , finite R-charge corrections to anomalous dimension spectra of large- R N = 4 super-Yang–Mills theory in the planar limit. This test of the AdS/CFT correspondence has been carried out for the specific cases of two and three string excitations, which are dual to gauge theory R-charge impurities. We generalize this analysis on the string side by directly computing string energy eigenvalues in certain protected sectors of the theory for an arbitrary number of worldsheet excitations with arbitrary mode-number assignments. While our results match all existing gauge theory predictions to two-loop order in λ ′ , we again observe a mismatch at three loops between string and gauge theory. We find remarkable agreement to all loops in λ ′ , however, with the near pp-wave limit of a recently proposed Bethe ansatz for the quantized string Hamiltonian in the su ( 2 ) sector. Based on earlier two- and three-impurity results, we also infer the full multiplet decomposition of the N-impurity superstring theory with distinct mode excitations to two loops in λ ′ .

THE HIGGS SECTOR IN THE MINIMAL 3-3-1 MODEL WITH THE MOST GENERAL LEPTON-NUMBER CONSERVING POTENTIAL

The Higgs sector of the minimal 3-3-1 model with three triplets and one sextet is investigated in detail under the most general lepton-number conserving potential. The mass spectra and multiplet decomposition structure are explicitly given in a systematic order and a transparent way allowing them to be easily checked and used in further investigations. A previous problem that arose from the inconsistent signs of f2is also automatically solved.

Element analysis of radiation from natural objects in the presence of asymmetric spectral line shapes

Mathematical models of radiation spectra are considered. The tasks and algorithms for the main data processing stages are described: decomposition of multiplets into singlets, approximation and precision correction of the calibration coefficients, determination of element (nuclide) content, estimation of the linear and nonlinear parameters of the apparatus weighting function. Analysis of alpha-radiation spectra is used as an example to illustrate the various analytical issues in the presence of strong asymmetry of the apparatus weighting function. The solution of element analysis problems exploits the bilinear relationship of the linear parameters in the approximating model and the quasi=exponential dependence on the nonlinear parameters. The procedure successively applies groups of computer algorithms combined with simulation using empirical databases.

A tangent formula derived from Patterson-function arguments. VI. structure solution from powder patterns with systematic overlap

Besides accidental peak overlap, systematic overlap constitutes one of the principal limitations for the solution of crystal structures from powder diffraction data. Unlike accidental overlap which affects all types of structures, systematic overlap is restricted to high-symmetry structures (e.g.65% of the space groups compatible with a hexagonal lattice). In this work, the direct-methods sum function is adapted to cope with data extracted from patterns containing systematic overlap. Preliminary results indicate that at least for moderate-size inorganic structures, systematic overlap should not represent a serious drawback for the application of direct methods. In contrast to the usual two-stage procedures employed for solving structures with accidental overlap, here both multiplet decomposition and phase refinement are carried out simultaneously. This procedure is illustrated using two examples: the dominant crystalline phase of a hydrated high-alumina cement and the fibrous alumino-silicate `aerinite'.