A q-congruence for a truncated 4φ3 series

Czechoslovak Mathematical Journal - Let $${\Phi _n}(q)$$ denote the nth cyclotomic polynomial in q. Recently, Guo, Schlosser and Zudilin proved that for any integer n > 1 with n ≡ 1...     

Study of the reactions of OH with HCl,HBr, and HI between 298 K and 460 K

The reactions between OH radicals and hydrogen halides (HCl, HBr, HI) have been studied between 298 and 460 K by using a discharge flow-electron paramagnetic resonance technique. The rate constants were found to be k_HCl(298 K) = (7.9 ± 1.3) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹ with a weak positive temperature dependence, k_HBr (298-460 K) = (1.04 ± 0.2) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, and k_HI(298 K) = (3.0 ± 0.3) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, respectively. The homogeneous nature of these reactions has been experimentally tested.     

Influence of light on the magnetoelectric effect in Fe-doped Bi<Subscript>12</Subscript>SiO<Subscript>20</Subscript>

We report an extraordinary oxidation state of iron in the Fe-doped Bi₁₂SiO₂₀ single crystal. Magnetoelectric effect and changes of this effect under illumination of the sample were investigated in magnetic fields up to 32 T. Moreover, an absorption line and its shift to higher energy caused by magnetic field (the Zeeman effect) were seen in the optical measurements. Obtained results show that the iron dopant is in unexpected, +4 oxidation state and it changes to +5 after illumination with blue light.     

Use of triarylstibines in C-arylation reactions

A new catalytic system based on triarylstibines for C-arylation of unsaturated compounds is proposed. It was found for a model reaction, the C-arylation of methyl acrylate, that in the presence of equimolar amounts of peroxide and catalytic amounts of a palladium compound (4 mol%), triarylstibines can act as mild efficient arylating agents.     

(±)-Nuevamine,an isoindoloisoquinoline alkaloid,and (±)-lennoxamine,an isoindolobenzazepine

$\text{Berberis darwinii}$ Hook (Berberidaceae) has yielded the lactams (±)-nuevamine (7) and (±)-lennoxamine (8). Nuevamine is the first known isoindoloisoquinoline alkaloid, while lennoxamine is an isoindolobenzazepine structurally related to (±)-chilenine (3).     

Bounds on the sizes of constant weight covering codes

Motivated by applications in universal data compression algorithms we study the problem of bounds on the sizes of constant weight covering codes. We are concerned with the minimal sizes of codes of lengthn and constant weightu such that every word of lengthn and weightv is within Hamming distanced from a codeword. In addition to a brief summary of part of the relevant literature, we also give new results on upper and lower bounds to these sizes. We pay particular attention to the asymptotic covering density of these codes. We include tables of the bounds on the sizes of these codes both for small values ofn and for the asymptotic behavior. A comparison with techniques for attaining bounds for packing codes is also given. Some new combinatorial questions are also arising from the techniques.Part of this work was done while the first and third authors were visiting Bellcore. The third author was supported in part by National Science Foundation under grant NCR-8905052. Part of this work was presented in the Coding and Quantization Workshop at Rutgers University, NJ, October 1992.     

Quantum Reduction for Affine Superalgebras

We extend the homological method of quantization of generalized Drinfeld–Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.     

A connection between a convex programming problem and the LYM property on perfect graphs

We derive three equivalent conditions on a perfect graph concerning the optimal solution of a convex programming problem, the length-width inequality, and the simultaneous vertex covering by cliques and anticliques. By combining proof techniques including Lagrangian dual, Dilworth's Theorem, and Kuhn-Tucker Theorem, we establish a strong connection between the three topics. This provides new insights into the structure of perfect graphs. The famous Lubell-Yamamoto-Meschalkin (LYM) Property or Sperner Property for partially ordered sets is a specialization of our results to a subclass of perfect graphs.