Bracing rhombic structure by one-dimensional tensegrities

Certain behaviors of some material are characterized by the periodic bar and joint elements. We present a kinematic, geometric and graph theoretic connected model that describes the stability, rigidity property of these rhombic tiling materials in two dimensions. Cables, struts or rods are placed as bracing elements between opposite pairs of diagonal joints, to prevent the rhombic tiling from the rotation of the bars around their common joint. We characterize the rigidity of the finite parts of the rhombic bracing structure in the plane. The results of this paper are based on the theorem of the rigidity of one-dimensional tensegrity framework from Recski and Shai. We have applied our results to describe some auxetic type structures that were mentioned earlier in the scientific literature. We also introduce the model as a possible candidate for the mechanical information processing system in a repetitive bar and joint structure.     

Reduction of Capsorubin and Cryptocapsin

(6′S)‐ and (6′R)‐‘Capsorubol‐6‐one' (=(3S,3′S,5R,5′R,6′S)‐ and (3S,3′S,5R,5′R,6′R)‐3,3′,6′‐trihydroxy‐κ,κ‐caroten‐6‐one; 8 and 9 , resp.), (6S,6′R)‐ and (6R,6′R)‐capsorubol (=3S,3′S,5R,5′R,6S,6′R)‐ and (3S,3′S,5R,5′R,6R,6′R)‐κ,κ‐carotene‐3,3′,6,6′‐tetrol; 11 and 12 , resp.) and (6′S)‐ and (6′R)‐cryptocapsol (=(3′S,5′R,6′S)‐ and (3′S,5′R,6′R)‐β,κ‐carotene‐3′,6′‐diol; 5 and 6 , resp.) were prepared in crystalline from by the reduction of capsorubin (=(3S,3′S,5R,5′R)‐3,3′‐dihydroxy‐κ,κ‐carotene‐6,6′‐dione; 7 ) and cryptocapsin (=(3′S,5′R)‐3′‐hydroxy‐β,κ‐caroten‐6′‐one; 4 ) and characterized by their UV/VIS, CD, ¹H‐NMR, and mass spectra.     

Hamiltonian chains in hypergraphs

A cyclic ordering of the vertices of a k‐uniform hypergraph is called a hamiltonian chain if any k consecutive vertices in the ordering form an edge. For k = 2 this is the same as a hamiltonian cycle. We consider several natural questions about the new notion. The main result is a Dirac‐type theorem that provides a sufficient condition for finding hamiltonian chains in k‐uniform hypergraphs with large (k − 1)‐minimal degree. If it is more than than the hypergraph contains a hamiltonian chain. © 1999 Wiley & Sons, Inc. J Graph Theory 30: 205–212, 1999     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Fourier transform of symmetric gauss measures on the Heisenberg group

An explicit form is derived for the Fourier transform of symmetric Gauss measures on the Heisenberg group at the Schrödinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two symmetric Gauss measures to be a symmetric Gauss measure and for commutability of two symmetric Gauss measures. Moreover, necessary and sufficient conditions are presented for the convolution of two symmetric Gauss convolution semigroups to be a convolution semigroup.     

Conditional Lagrange derivative and its application

Our paper aims to show what to do in material modeling for an inelastic body. The method we use is based on the virtual work σ ′δε and on the variation of some function W with respect to the strain tensor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of polyelectrolytes applied in drinking water treatment

The applicability of an inorganic, polyaluminium-type flocculent was tested comparing to polyacrylamides — an organic-type flocculent — used in the drinking water treatment process. The efficiency of this inorganic flocculent in the removal of suspended solids and also in minimizing the residual concentrations of the dissolved organic and inorganic micro-pollutants was checked in the case of purifying filter backwash water. Experimental data showed the advantage of the inorganic flocculent applying procedure as a part of recent water treatment technology. The applied polyaluminium-salt was economically competitive, improved the process stability and also ensured good water quality parameters.     

Determination of trace elements in Antarctic krill samples by inductively coupled atomic emission and graphite furnace atomic absorption spectrometry

Analytical methods were developed for the determination of trace elements in Antarctic krill samples applying inductively coupled plasma atomic emission spectrometry (ICP-AES) and graphite furnace atomic absorption spectrometry (GF-AAS). Cu, Fe, Mn and Zn were determined by ICP-AES, while Cd and Pb by GF-AAS technique. Two microwave assisted digestion procedures were elaborated for the preparation of 0.5-g krill samples using open and closed vessel systems. The efficiency of the digestion processes was checked by measurements of the total organic carbon content of the solutions obtained. The deviations of the analytical data from the certified values and the relative standard deviations of the concentration measurements were lower for all six elements investigated applying the closed vessel digestion system.