Investigation of the single crystal growing process of neodymium-doped YAG garnets using radiotracers

Radioisotopic methods of investigation of Nd behaviour during pulling of single crystals of YAG-type garnets were applied. For the investigation of homogeneity of Nd distribution an autoradiographic method was used, and for the determination of Nd contents in single crystals and Nd effective partition ratios — techniques of radiotracers and gamma spectrometry. The conclusions from this work can find technological application.     

On the conformation of the propranolol molecule

The structure of the propranolol molecule has been optimized within the AM1 and PM3 semiempirical framework followed by ab initio HF/6-31G^* refinement. On each calculation level the conformational space was sampled to search for the lowest-energy conformer(s) from among a few hundreds of conformers at the semiempirical step and next from among a few dozens of conformers at the ab initio level. Finally, five stable conformers were found; each stabilized by one or two of the three possible hydrogen bonds. The geometrical and electronic parameters were established and found to differ only slightly in the structures with the hydrogen bond either present or not.     

Background elimination in three-dimensional spectroscopy using the intensian method

The method to eliminate background in the case of quantitative multidimensional spectroscopy, chromatography or any analytical 3-dimensional technique is shown. The 3-dimensional signal is required to be proportional to the concentration of determined substance and the additivity of signals should be obeyed. Eliminated background is assumed to be a low-order polynomial of two variables. The intensian method [1] is a generalization of the Beer-Lambert law, where a certain determinant called intensian replaces absorption and absorptivity. In practice there will be no need to use determinants, since usually they are replaced by expressions of few terms. Some details on the practical use of the method are given.Index of used symbols x, y UV, IR, GC, NMR or other scale. - A (x, y) intensity (absorption) of the 3-dimensional band of interest. - a (x, y) standard intensity (absorption) of the 3-dimensional band of interest. - B(x, y) intensity (absorption) of 3-dimensional background. - S(tx, y) intensity (absorption) of 3-dimensional multicomponent spectrum. - f (x, y) auxiliary function:f (x, y) =A (x, y), B(x, y), a(x, y), S(x, y). - (x _i, Yi) selected point,i positive integer number. - f(xi, yi) value off (x, y) in point (xi, yi). - S _i value ofS(x, y) in point (x _i, y_i). - b pathlength, measurement coefficient,c concentration. - , , , real numbers. - ij, _ij real coefficients of power expansions. - x ⁱy^j monomial of degree (i +j). - F(·) linear functional acting on 3-dimensional spectral functions. - J^3-dim(·) 3-dimensional intensian acting on 3-dimensional spectral functions. - J _n ^3-dim (·) 3-dimensionaln-points intensian. - d _i ith intensian coefficient, cofactor of expansion of J _n ^3-dim (f(x, y)) according to its first row (eq. (10)). - (.) absolute error. - r _i,, R random variables: eqs. (13) and (14). - G(.) (normal) distribution function. - z ordinate axis. - a - f , h abreviations for some arguments. - d _ijk,D _mnp abreviations defined in eq. (22).     

Large Sets of Lattices without Order Embeddings

Let I and μ be an infinite index set and a cardinal, respectively, such that |I| ≤ μ and, starting from ?₀, μ can be constructed in countably many steps by passing from a cardinal λ to 2^λ at successor ordinals and forming suprema at limit ordinals. We prove that there exists a system X = {L_i: i ∈ I} of complemented lattices of cardinalities less than |I| such that if i, j ∈ I and φ: L_i → L_j is an order embedding, then i = j and φ is the identity map of L_i. If |I| is countable, then, in addition, X consists of finite lattices of length 10. Stating the main result in other words, we prove that the category of (complemented) lattices with order embeddings has a discrete full subcategory with |I| many objects. Still in other words, the class of these lattices has large antichains (that is, antichains of size |I|) with respect to the quasiorder “embeddability.” As corollaries, we trivially obtain analogous statements for partially ordered sets and semilattices.     

Two Notes on the Variety Generated by Planar Modular Lattices

Let Var(M _plan) denote the variety generated by the class M _plan of planar modular lattices. In 1977, based on his structural investigations, R. Freese proved that Var(M _plan) has continuumly many subvarieties. The present paper provides a new approach to this result utilizing lattice identities. We also show that each subvariety of Var(M _plan) is generated by its planar (subdirectly irreducible) members. Dedicated to the memory of András P. Huhn This research was partially supported by the NFSR of Hungary (OTKA), grant no. T 049433, T 48809 and K 60148.     

The Jordan-H?lder theorem with uniqueness for groups and semimodular lattices

For subnormal subgroups ${A{\vartriangleleft}B}$ and ${C{\vartriangleleft}D}$ of a given group G, the factor B/A will be called subnormally down-and-up projective to D/C if there are subnormal subgroups ${X{\vartriangleleft}Y}$ such that ${AY = B, A \cap Y = X, CY = D}$ , and ${C \cap Y = X}$ . Clearly, ${B/A \cong D/C}$ in this case. As G. Gr?tzer and J. B. Nation have recently pointed out, the standard proof of the classical Jordan-H?lder theorem yields somewhat more than is widely known; namely, the factors of any two given composition series are the same up to subnormal down-and-up projectivity and a permutation. We prove the uniqueness of this permutation. The main result is the analogous statement for semimodular lattices. Most of the paper belongs to pure lattice theory; the group theoretical part is only a simple reference to a classical theorem of H. Wielandt.     

Chirality measures of α-amino acids

To measure molecular chirality, the molecule is treated as a finite set of points in the Euclidean R(3) space supplemented by k properties, p(1)((i)), p(2)((i)), ..., p(k)((i)) assigned to the ith atom, which constitute a point in the Property P(k) space. Chirality measures are described as the distance between a molecule and its mirror image minimized over all its arbitrary orientation-preserving isometries in the R(3) × P(k) Cartesian product space. Following this formalism, different chirality measures can be estimated by taking into consideration different sets of atomic properties. Here, for α-amino acid zwitterionic structures taken from the Cambridge Structural Database and for all 1684 neutral conformers of 19 biogenic α-amino acid molecules, except glycine and cystine, found at the B3LYP/6-31G** level, chirality measures have been calculated by a CHIMEA program written in this project. It is demonstrated that there is a significant correlation between the measures determined for the α-amino acid zwitterions in crystals and the neutral forms in the gas phase. Performance of the studied chirality measures with changes of the basis set and computation method was also checked. An exemplary quantitative structure–activity relationship (QSAR) application of the chirality measures was presented by an introductory model for the benchmark Cramer data set of steroidal ligands of the sex-hormone binding globulin.