A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49

Existing bounds on the minimum weight d ^⊥ of the dual 7-ary code of a projective plane of order 49 show that this must be in the range 76 ≤ d ^⊥ ≤ 98. We use combinatorial arguments to improve this range to 88 ≤ d ^⊥ ≤ 98, noting that the upper bound can be taken to be 91 if the plane has a Baer subplane, as in the desarguesian case. A brief survey of known results for the minimum weight of the dual codes of finite projective planes is also included. Dedicated to Dan Hughes on the occasion of his 80th birthday.     

双波长分光光度法同时测定环境水样中钙和镁

本文采用双波长分光度法使钙、镁不经掩蔽而同时测定，方法简单、准确。利用该方法对环境水样中的钙、镁进行了测定,结果令人满意。     

Focused,Nanoscale Electron-Beam-Induced Deposition and Etching

Focused electron-beam-induced (FEB-induced) deposition and etching are versatile, direct-write nanofabrication schemes that allow for selective deposition or removal of a variety of materials. Fundamentally, these processes are governed by an electron-induced reaction with a precursor vapor, which may either result in decomposition to a solid deposit or formation of a volatile etch by-product. The ability to induce such localized reactions by placement of a nanometer-sized focused electron probe has recently drawn considerable attention. In response, we have reviewed much of the relevant literature pertaining to both focused electron-beam-induced etching and deposition. Because these nanoscale processing techniques are still in their relative infancy, a significant amount of scientific research is being conducted to understand, and hence improve, the processes. This article summarizes the associated physics of electron-solid-vapor interactions, discusses related physical processes, and provides an introduction to electron-beam-induced etching (EBIE) and electron-beam-induced deposition (EBID). Additionally, specific applications of FEB-induced processes are discussed and several FEB computer model and simulation results are reviewed.     

Minimal full polarized embeddings of dual polar spaces

Let Δ be a thick dual polar space of rank n ≥ 2 admitting a full polarized embedding e in a finite-dimensional projective space Σ, i.e., for every point x of Δ, e maps the set of points of Δ at non-maximal distance from x into a hyperplane e∗(x) of Σ. Using a result of Kasikova and Shult [11], we are able the show that there exists up to isomorphisms a unique full polarized embedding of Δ of minimal dimension. We also show that e∗ realizes a full polarized embedding of Δ into a subspace of the dual of Σ, and that e∗ is isomorphic to the minimal full polarized embedding of Δ. In the final section, we will determine the minimal full polarized embeddings of the finite dual polar spaces DQ(2n,q), DQ ⁻(2n+1,q), DH(2n−1,q ²) and DW(2n−1,q) (q odd), but the latter only for n≤ 5. We shall prove that the minimal full polarized embeddings of DQ(2n,q), DQ ⁻(2n+1,q) and DH(2n−1,q ²) are the `natural' ones, whereas this is not always the case for DW(2n−1, q).B. De Bruyn: Postdoctoral Fellow of the Research Foundation - Flanders.     

On Small and Large Hyperplanes of DW(5, q)

We determine lower and upper bounds for the size of a hyperplane of the dual polar space DW(5, q). In some cases, we also determine all hyperplanes attaining these bounds.     

Dual mixed volumes and the slicing problem

We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and quotients of Lp and related spaces. An extension of these results to negative values of p is also obtained, using generalized intersection-bodies. In particular, we show that the isotropic constant of a convex body which is contained in an intersection-body is bounded (up to a constant) by the ratio between the latter's mean-radius and the former's volume-radius. We also show how type or cotype 2 may be used to easily prove inequalities on any isotropic measure.     

The synthesis and electronic absorption spectra of 3-phenyl-3(4-pyrrolidino-2-substituted phenyl)-3H-naphtho[2,1-b]pyrans: further exploration of the ortho substituent effect

Introduction of a substituent into a sterically demanding 2-position of a 3-(4-pyrrolidinophenyl) ring of a 3,3-diaryl-3H-naphtho[2,1-b]pyran results in the generation of an additional short wavelength absorption band leading to organic photochromes that appear as dull shades of orange and red.     

Singularities of Dual Varieties in Characteristic 3

We investigate singularities of a general plane section of the dual variety of a smooth projective variety, or more generally, the discriminant variety associated with a linear system of divisors on a smooth projective variety. We show that, in characteristic 3, singular points of E ₆-type take the place of ordinary cusps in characteristic 0.     

罗丹明B同步荧光猝灭法测微量磷的条件研究

本文研究了罗庆明Ｂ－磷钼杂多酸离子缔合物体系的荧光特性及测定方法，对实验条件进行了优化选择，并引入非离子表面活性剂ＯＰ对体系增敏，增稳。本法用于黑色食品中磷的测定，结果满意。