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.     

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.     

On orthogonal arrays of strength 3 and 5 achieving Rao's bound

It is shown that ifA is an orthogonal array (N, n, q, 3) achieving Rao's bound, thenA is either

1. an orthogonal array (2n, n, 2, 3) withn ≡ 0 (mod 4), or
2. an orthogonal array (q ³,q + 2,q, 3) withq even.

This result should be compared with a theorem of P.J. Cameron on extendable symmetric designs. It is also shown that ifA is an orthogonal array (N, n, q, 5) achieving Rao's bound, thenA is either the orthogonal array (32, 6, 2, 5) or the orthogonal array (3⁶, 12, 3, 5).     

A Chiral Coordination Polymer of Silver(I) with Saccharinate and Pyridine: Synthesis,Spectral, Thermal,and Structural Characterization of [Ag(sac)(py)]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The first silver(I) complex of saccharinate (sac) with pyridine (py), [Ag(sac)(py)]_n has been synthesized and characterized by elemental analysis, IR spectroscopy and single crystal X-ray diffractometry. The complex crystallizes in chiral, trigonal space group P3₁21 (No. 152) with unit cell parameters of a = 11.2605(2) Å, c = 17.3300(4) Å, V = 1903.02(6) ų and Z = 6. [Ag(sac)(py)]_n contains monomeric [Ag(sac)(py)] units linked into infinite helices by way of Ag⋅sAg interactions [d(Ag⋅sAg) = 2.909(2) and 2.985(1) Å]. The distorted square-planar environment of Ag is completed by an N-bonded sac [Ag—N = 2.084(2) Å] and a py molecule [Ag—N = 2.116(2) Å]. The N_sac—Ag—N_py angle is 173.85(10)^∘. The one-dimensional chains are crosslinked by C—H⋅sO interactions involving the carbonyl and sulfonyl O atoms of sac and aromatic-ring hydrogen atoms of both sac and py. The thermal stability of the title complex was investigated using thermogravimetry and differential thermal analysis in a static atmosphere of air. The first decomposition stage between 90 and 160^∘C corresponds to removal of the py molecule in a single stage, while the degradation of the sac moiety occurs at two stages in the temperature range 370–515^∘C, giving an end product of metallic Ag.     

Synthesis of new polymetallic carbene complexes: Uracil analogs

The easy cycloaddition of ureas with alkynyl alkoxy biscarbene complexes afforded, in fairly good yields, new biscarbene uracil analogs. X-ray structural data is reported for the dimethyluracil biscarbene complex. By changing the reaction conditions, a new non symmetric complex was obtained whose reaction with ethylenediamine afforded a new tetrakis amino carbene complex.     

The Conductance- and Capacitance-Frequency Characteristics of the Rectifying Junctions Formed by Sublimation of Organic Pyronine-B on p-Type Silicon

The rectifying junction characteristics of the organic compound pyronine-B film on a p-type Si substrate has been studied. The pyronine-B has been sublimed on the top of p-Si surface. The barrier height and ideality factor values of 0.79±0.04 and 1.13±0.06 eV for this structure have been obtained from the forward bias current-voltage (I-V) characteristics. From the low capacitance-frequency (C-f) characteristics as well as conductance-frequency (G-f) characteristics, the energy distribution of the interface states and their relaxation time have been determined in the energy range of (0.53−E_v)-(0.79−E_v) eV taking into account the forward bias I-V data. The interface state density N_ss ranges from 4.93×10¹⁰ cm⁻² eV⁻¹ in (0.79−E_v) eV to 3.67×10¹³ cm⁻² eV⁻¹ in (0.53−E_v) eV. Furthermore, the relaxation ranges from 3.80×10⁻³ s in (0.53−E_v) eV to 4.21×10⁻⁴ s in (0.79−E_v) eV. It has been seen that the interface state density has an exponential rise with bias from the midgap towards the top of the valence band. The relaxation time shows a slow exponential rise with bias from the top of the valence band towards the midgap.     

Oxygen/nitrogen ordering in lanthanum new phase (La3Si8N11O4)

High-resolution ¹⁷O NMR spectra have been collected for crystalline samples of lanthanum new phase, La₃Si₈N₁₁O₄. In conjunction with previously published ²⁹Si and ¹⁵N spectra obtained for this phase, and in the light of the high-quality crystal structure data reported recently, a more detailed interpretation of the NMR spectra is presented than was possible in previous studies. The non-bridging oxygens in the structure are responsible for the single sharp peak seen in the ¹⁷O spectrum at 188 ppm; the remaining oxygens, occupying bridging sites shared with nitrogen, show up only weakly on the ¹⁷O spectrum as a broad diffuse band centered around zero ppm. The peak at −57.3 ppm on the ²⁹Si spectrum is believed to correspond to an overlap of [SiN₄] and [SiON₃] environments, with the −68.2 ppm peak corresponding to an [SiO₂N₂] environment.