Permutation functions and (n,m)-commutativity of semigroups

By [4], a semigroupS is called an (n, m)-commutative semigroup (n, m ∈ ?⁺, the set of all positive integers) if $$x_1 x_2 \cdot \cdot \cdot x_n y_1 y_2 \cdot \cdot \cdot y_m = y_1 y_2 \cdot \cdot \cdot y_m x_1 x_2 \cdot \cdot \cdot x_n $$ holds for allx ₁,...,x _n ,y ₁,...,y _m ∈S It is evident that ifS is an (n, m)-commutative semigroup then it is (n′,m′)-commutative for alln′≥n andm′≥m. In this paper, for an arbitrary semigroupS, we determine all pairs (n, m) of positive integersn andm for which the semigroupS is (n, m)-commutative. In our investigation a special type of function mapping ?⁺ into itself plays an important role. These functions which are defined and discussed here will be called permutation functions.     

On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.     

Resistant starches and health

It was initially hypothesized that resistant starches, i.e., starch that enters the colon, would have protective effects on chronic colonic diseases, including reduction of colon cancer risk and in the treatment of ulcerative colitis. Recent studies have confirmed the ability of resistant starch to increase fecal bulk, increase the molar ratio of butyrate in relation to other short-chain fatty acids, and dilute fecal bile acids. However the ability of resistant starch to reduce luminal concentrations of compounds that are damaging to the colonic mucosa, including fecal ammonia, phenols, and N-nitroso compounds, still requires clear demonstration. As such, the effectiveness of resistant starch in preventing or treating colonic diseases remains to be assessed. Nevertheless, there is a fraction of what has been termed resistant (RS1) starch, which enters the colon and acts as slowly digested or lente carbohydrate in the small intestine. Foods in this class are low glycemic index and have been shown to reduce the risk of chronic disease. They have been associated with systemic physiological effects such as reduced postprandial insulin levels and higher HDL cholesterol levels. Consumption of low glycemic index foods has been shown to be related to reductions in risk of coronary heart disease and Type 2 diabetes. Type 2 diabetes has in turn been related to a higher risk of colon cancer. If carbohydrates have a protective role in colon cancer prevention this may lie partly in the systemic effects of low glycemic index foods. The colonic advantages of different carbohydrates, varying in their glycemic index and resistant starch content, therefore, remain to be determined. However, as recent positive research findings continue to mount, there is reason for optimism over the possible health advantages of those resistant starches, which are slowly digested in the small intestine.     

Elaboration of a programmed,semi-automated radiochemical processing system for neutron activation analysis of some volatile elements

Based on the method of SAMSAHL a programmed, semi-automated processing system has been developed and tested for the neutron activation analysis of the following elements: As, Se, Sb, Br, Sn and Te. The main characteristics of the procedure are the following: wet ashing of the sample (by means of digestion in a mixture of concentrated sulphuric acid and hydrogen peroxide), bromination, and chlorination. The procedure is controlled via the appropriate dosage of the reagents and a carefully managed thermal balance. The chemical yield and its reproducibility were determined by tracer techniques using exactly the same parameters as for the active runs. According to the results the method can be used for the routine determination of the given elements except antimony. Presented at the 4th Symposium on the Recent Developments in Neutron Activation Analysis, 1975, Cambridge.     

Molecular orbital study of molecular nitrogen fixation

The model systems of molecular nitrogen fixation [N₂ + H]?, [N₂ + H]⁺, [N₂ + H]^?, [N₂ + H₂], [N₂ + H₂]⁺, and [N₂ + H₂]^? were studied by the semiempirical INDO method. The study was based on the formal analogy between the catalytic reactions and the photochemical, radical, and ionic reactions on the other side. Symmetrical and donor-acceptor properties of necessary catalytic systems were proposed using the dependence of energy characteristics and electron structure on reaction coordinate. On the basis of this MO study we have proposed the appropriate symmetry types of catalysts for each of acceptable models of nitrogen fixation. For one of the proposed systems there was realised a model MO computation with explicit inclusion of atoms of transition metals (Fe, V).     

Molecular structure of ethynylbenzene from electron diffraction and ab initio molecular orbital calculations

The molecular structure and benzene ring distortions of ethynylbenzene have been investigated by gas-phase electron diffraction and ab initio MO calculations at the HF/6-31G^* and 6-3G^** levels. Least-squares refinement of a model withC _2v, symmetry, with constraints from the MO calculations, yielded the following important bond distances and angles:r _g(C _i -C _o )=1.407±0.003 Å,r _g(C _o -C _m )=1.397±0.003 Å,r _g(C _m -C _p )=1.400±0.003 Å,r _g(Cr _i -CCH)=1.436 ±0.004 Å,r _g(C=C)=1.205±0.005 Å, C _o -C _i -C _o =119.8±0.4°. The deformation of the benzene ring of ethynylbenzene given by the MO calculations, including o-C_i-C_o=119.4°, is insensitive to the basis set used and agrees with that obtained by low-temperature X-ray crystallography for the phenylethynyl fragment, C₆H₅-CC-, in two different crystal environments. The partial substitution structure of ethynylbenzene from microwave spectroscopy is shown to be inaccurate in the ipso region of the benzene ring.     

Mössbauer studies in thermally treated iron-samarium mixed oxide system

Mössbauer spectroscopy and X-ray diffractometry have been used to study Sm–Fe mixed oxides (with different SmFe atomic ratios) annealed at 550, 850, 1000 and 1250 °C. The room temperature Mössbauer spectra can be interpreted in terms of one, two or three sextets and in some cases by an additional doublet depending on the composition and the heat treatment. The sextets have been associated with SmFeO₃ perovskite, Sm₃Fe₅O₁₂ garnet and -Fe₂O₃ hematite. These results are in agreement with those of X-ray diffractometric measurements, which give a clear, evidence of the presence of these phases.