On a geometrical method of construction of maximal t-linearly independent sets

The problem of constructing a maximal t-linearly independent set in V(r; s) (called a maximal L_t(r, s)-set in this paper) is a very important one (called a packing problem) concerning a fractional factorial design and an error correcting code where V(r; s) is an r-dimensional vector space over a Galois field GF(s) and s is a prime or a prime power. But it is very difficult to solve it and attempts made by several research workers have been successful only in special cases.In this paper, we introduce the concept of a {Σ_α=1^kw_α, m; t, s}-min · hyper with weight (w₁, w₂,…, w_k) and using this concept and the structure of a finite projective geometry PG(n ? 1, s), we shall give a geometrical method of constructing a maximal L_t(t + r, s)-set with length t + r + n for any integers r, n, and s such that n ? 3, n ? 1 ? r₀ ? n + s ? 2 and r₁ ? 1, where r = (r₁ + 1)v_n?1 ? r₀ and $\text{v}{}_{\mathrm{n}}\text{=}\text{(s}{}^{\mathrm{n}}\text{? 1)}\text{(s ? 1)}$.     

Acyclic stereocontrol via asymmetric [2,3]-Wittig rearrangement with high enantio- and erythro-selectivity and its use in the chiral synthesis of insect pheromones

Such an asymmetric [2,3]-Wittig variant that is both highly enantio- and erythro-selective is described within the context of the chiral synthesis of the insect pheromones, (3$\text{S}$, 4$\text{S}$)-4-methyl-3-heptanol and ($\text{S}$)-4-methyl-3-heptanone.     

The Nonexistence of Ternary [38, 6, 23] Codes

It has been shown by Bogdanova and Boukliev [1] that there exist a ternary [38,5,24] code and a ternary [37,5,23] code. But it is unknown whether or not there exist a ternary [39,6,24] code and a ternary [38,6,23] code. The purpose of this paper is to prove that (1) there is no ternary [39,6,24] code and (2) there is no ternary [38,6,23] code using the nonexistence of ternary [39,6,24] codes. Since it is known (cf. Brouwer and Sloane [2] and Hamada and Watamori [14]) that (i) n₃(6,23) = 38> or 39 and d₃(38,6) = 22 or 23 and (ii) n₃(6,24) = 39 or 40 and d₃(39,6) = 23 or 24, this implies that n₃(6,23) = 39, d₃(38,6) = 22, n₃(6,24) = 40 and d₃(39,6) = 23, where n3<>(k,d) and d<>3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3).     

Time-resolved total internal reflection fluorescence spectroscopy of polymer films

Using total internal reflection, the possibility of a subnanosecond fluorescence spectroscopy for elucidating photophysical and photochemical processes of polymer surface is demonstrated. The thickness which can be studied under the present experimental conditions is of the order of 0.01 μm.     

Selective INEPT,a new technique for the 13C NMR assignment of methylene carbons with non-equivalent protons,and its application to the analysis of the 13C NMR spectrum of monensin

A new method based on the combination of selective proton decoupling and INEPT is explained in detail. This technique, named selective INEPT (SEL-INEPT), is a useful and sensitive method for the ¹³C NMR assignment of methylene carbons with non-equivalent protons. The ¹³C NMR spectrum of monensin has been analysed by the application of this technique.