Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unity

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using Schilling's bijection between ribbon tableaux and ribbon rigged configurations.     

On a new interpretation of the classical Maxwell model

Recently, [Rao, I.J., Rajagopal, K.R., 2007. Status of the K-BKZ model within the framework of materials with multiple natural configurations. Journal of Non-Newtonian Fluid Mechanics, 141, 79–84] showed that the K-BKZ Model is a special sub-class of models based on a thermodynamic framework that takes into account the fact that bodies are capable of existing stress free in multiple configurations with special choices being made for the way in which the body stores energy and the way it dissipates energy. They also showed that several generalizations of the K-BKZ model are possible. In this short note we show that two distinct methods of storing energy and dissipating energy lead to the classical Maxwell model. That is, in addition to the classical choice for the storage of energy and rate of dissipation (the usual spring dashpot analogy) a more complicated choice also leads to the same model. This result is rather important as it shows that a variety of means for storing and dissipating energy can lead to the same mechanical response, when one restricts oneself to purely mechanical considerations.     

Optical Mobius Cubes: Integrated Packaging Configurations

Two integrated packaging configurations of optical Mobius cubes are demonstrated. One is based on space division multiplex technique, the other is based on wavelength djvision multiplex technique. The physical constraints from the effect of diffraction on the optical Mdbius cubes are also discussed which defines the upper bound of the space-bandwidth product.     

快速推求等效组态的原子谱项

本文根据置换群方法，运用Ｃ语言编制了计算程序，可快速、准确地推求等效组态ｓ＾Ｎ、ｐ＾Ｎ、ｄ＾Ｎ、ｆ＾Ｎ、…ｘ＾Ｎ、ｙ＾Ｎ、ｚ＾Ｎ的原子谱项。     

A note on maximally repeated sub-patterns of a point set

We answer a question raised by Brass on the number of maximally repeated sub-patterns in a set of n points in R^d. We show that this number, which was conjectured to be polynomial, is in fact Θ(2^n/2) in the worst case, regardless of the dimension d.     

Evidence for multiple band terminations in Pd

The level structure of ¹⁰²Pd has been investigated using data collected with the Eurogam 2 array. Several cascades of γ-rays have been established up to high spins. Termination of rotational bands has been observed at I^π = 28⁻ and 32⁺, and tentatively at I^π = 38⁺ and 42⁺. The nucleus ¹⁰²Pd is the first case where rotational bands built on valence space configurations are followed from spin close to zero up to termination and, at higher spins, a smooth rotational band which appears to terminate is built on core excited configurations.     

dN离子在三角场中的基矢及有关矩阵元

通过选用合适的单电子基矢, 使按群链[(O?D_3?C_3)×SU(2)]~N构成的多电子基矢, 成为dN体系D_3?C_3旋量群不可约表示的基矢或其两个一维不可约表示直和的基矢。讨论了有关矩阵元和顺磁参数的计算。     

Interaction configurations of H2O molecules in a protein (Stratum Corneum) by infrared spectrometry

The procedure previously used to determine the interaction configurations of H₂O molecules in various polysaccharides is applied to a protein: Stratum Corneum (SC). It consists of following by infrared (IR) spectrometry the evaporation, heating and addition of water to a SC membrane. Analyses of the spectra corresponding to these experiments show that even H₂O molecules in equilibrium with the atmosphere are inserted in the protein itself and are held by one hydrogen bond which they accept from an N---H group of the protein and at least one hydrogen bond which they establish (donate) on a C=O group of the protein. At higher concentrations of water, H₂O molecules aggregate and form microdroplets embedded in the protein. Addition of water followed by evaporation of the added H₂O molecules results in an enhancement of the number of hydrogen bonds of type N---HO=C inside the protein. It makes water molecules appear as catalysts to rebuild hydrogen bonds in the protein.     

Probing actinide electronic structure through pu cluster calculations

Calculations of the electronic structure of clusters of plutonium have been performed, within the framework of the relativistic discrete‐variational method. These theoretical results and those calculated earlier for related systems have been compared to spectroscopic data produced in the experimental investigations of bulk systems, including photoelectron spectroscopy. Observation of the changes in the Pu electronic structure as a function of size provides powerful insight for aspects of bulk Pu electronic structure. © 2013 Wiley Periodicals, Inc.     

Exceptional points for Lebesgue's density theorem on the real line

For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither 0 nor 1. We quantify this statement, following work by V. Kolyada, and obtain the unexpected result that there is always a point where the upper and the lower densities are closer to 1/2 than to zero or one. The method of proof uses a discretized restatement of the problem, and a self-similar construction.