A note on δ-I-sets

We characterize δ-I-sets, discuss the relation between δ-sets, δ-I-sets and I _δ-sets and generalize some of the results.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.     

A generalization of the katona theorem for crosst-intersecting families

LetX be ann-element set and letA and? be families of subsets ofX. We say thatA and? are crosst-intersecting if |A ∩ B| ≥ t holds for all A ∈A and for allB ∈ ?. Suppose thatA and ? are crosst-intersecting. This paper first proves a crosst-intersecting version of Harper's Theorem:

1. There are two crosst-intersecting Hamming spheresA ₀,? ₀ with centerX such that |A| ≤ |A ₀| and|?| ≤ |? ₀| hold.
2. Suppose thatt ≥ 2 and that the pair of integers (|A) is maximal with respect to direct product ordering among pairs of crosst-intersecting families. Then,A and? are Hamming spheres with centerX.

Using these claims, the following conjecture of Frankl is proven:

1. Ifn + t = 2k ? 1 then |A| |?| ≤ max \(\left\{ {\left( {K_k^n + \left( {_{k - 1}^{n - 1} } \right)} \right)^2 ,K_k^n K_{k - 1}^n } \right\}\) holds, whereK _l ⁿ is defined as \(\left( {_n^n } \right)\left( {_{n - 1}^n } \right) + \cdots + \left( {_l^n } \right).\)
2. Ifn + t = 2k then |A| |? ≤ (K _k ⁿ )² holds.

The extremal configurations are also determined.     

61Ni Mössbauer study of the surface hyperfine magnetic field in nickel

⁶¹Ni Mössbauer measurements have been performed at 4.2 K on spherical Ni particles with an average diameter of 100 and 30 Å, covered with a protective layer of SiO. Their spectra contain a surface component with a significantly reduced hyperfine magnetic field as compared with the field in the bulk. This result confirms recent theoretical predictions.     

Synthesis, spectroscopic and thermal studies of the copper(II) aspartame chloride complex

Aspartame adduct of copper(II) chloride Cu(Asp)₂Cl₂·2H₂O (Asp=aspartame) is synthesized and characterized by elemental analysis, FT IR, UV/vis, ESR spectroscopies, TG, DTG, DTA measurements and molecular mechanics calculations. Aqueous solution of the green solid absorbs strongly at 774 and 367 nm. According to the FT IR spectra, the aspartame moiety coordinates to the copper(II) ion via its carboxylate ends, whereas the ammonium terminal groups give rise to hydrogen bonding network with the water, the chloride ions or neighboring carboxylate groups. The results suggest tetragonally distorted octahedral environment of the copper ions.     

Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.     

流动注射化学发光法测定自来水中二氧化氯

在pH12．5的NaOH—KCl缓冲介质中，ClO2直接氧化Luminol能产生很强的化学发光，而且发光强度在一定的范围内与ClO2的浓度呈线性关系，据此建立了流动注射化学发光测定ClO2的新方法。探讨了最佳的发光条件，测定ClO2的线性范围为0．5—200μg／L，检出限为0．3μg／L。本法简便、怏速、灵敏，选择性和重复性较好，应用于自来水中剩余ClO2的测定，结果满意。     

A short synthesis of 4-amino-3-hydroxybutyric acid (GABOB) via allyl cyanide

4-Amino-3-hydroxybutyric acid was synthesized from allyl cyanide in four steps in an overall yield of 38%. Ultrasonically promoted epoxidation of allyl cyanide with m-chloroperoxybenzoic acid giving oxiranylacetonitrile was used as a key step.     

NMR studies of chiral recognition mechanisms: interaction of enantiomers of N-imidazole derivatives with cyclodextrin hosts. Correlation with the CD-EKC studies

The inclusion complexes formed between two chiral N-imidazole derivatives and four cyclodextrins (α-, β-, γ-, and highly sulfated-β-CDs) were investigated by one- and two-dimensional ¹H NMR. With the additional results of an ESI-MS study, a 1:1 stoichiometry was proven for all the complexes studied. The complexes were also characterized in terms of binding constants and the results were compared to those obtained by CD-EKC. An identical affinity order for the various CDs was obtained with both techniques. Furthermore, the affinity order for both enantiomers determined by their binding constants values is confirmed by the enantiomer migration orders previously determined by CD-EKC. The structural data obtained by the 2D-ROESY experiments allowed us to understand the interaction mechanisms and to propose, for different analyte structures, theoretical models of inclusion orientation in the CD cavity. These models are in accordance with our previous hypothesis based on the analyte structure–enantioseparation relationships and the thermodynamic parameters determined by CD-EKC.