Classification of auxin plant hormones by interaction property similarity indices

Although auxins were the first type of plant hormone to be identified, little is known about the molecular mechanism of this important class of plant hormones. We present a classification of a set of about 50 compounds with measured auxin activities, according to their interaction properties. Four classes of compounds were defined: strongly active, weakly active with weak antiauxin behaviour, inactive and inhibitory. All compounds were modeled in two low-energy conformations, P and T, so as to obtain the best match to the planar and tilted conformations, respectively, of indole 3-acetic acid. Each set of conformers was superimposed separately using several different alignment schemes. Molecular interaction energy fields were computed for each molecule with five different chemical probes and then compared by computing similarity indices. Similarity analysis showed that the classes are on average distinguishable, with better differentiation achieved for the T conformers than the P conformers. This indicates that the T conformation might be the active one. Further, a screening was developed which could distinguish compounds with auxin activity from inactive compounds and most antiauxins using the T conformers. The classifications rationalize ambiguities in activity data found in the literature and should be of value in predicting the activities of new plant growth substances and herbicides.     

Uniqueness of large radial solutions and existence of nonradial solutions for a superlinear Dirichlet problem in annulii

Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichlet problem in annulii. Our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions. We prove that, for k>0 large, there exist exactly two radial solutions with k nodal regions (connected components of ). The problem need not be homogeneous.     

The Hosoya polynomial decomposition for catacondensed benzenoid graphs

For a graph G with the vertex set V(G), we denote by d(u,v) the distance between vertices u and v in G, by d(u) the degree of vertex u. The Hosoya polynomial of G is H(G)=∑_{u,v}⊆V(G)x^d(u,v). The partial Hosoya polynomials of G are for positive integer numbers m and n. It is shown that H(G₁)−H(G₂)=x²(x+1)²(H₃₃(G₁)−H₃₃(G₂)),H₂₂(G₁)−H₂₂(G₂)=(x²+x−1)²(H₃₃(G₁)−H₃₃(G₂)) and H₂₃(G₁)−H₂₃(G₂)=2(x²+x−1)(H₃₃(G₁)−H₃₃(G₂)) for arbitrary catacondensed benzenoid graphs G₁ and G₂ with equal number of hexagons. As an application, we give an affine relationship between H(G) with two other distance-based polynomials constructed by Gutman [I. Gutman, Some relations between distance-based polynomials of trees, Bulletin de l’Académie Serbe des Sciences et des Arts (Cl. Math. Natur.) 131 (2005) 1-7].     

A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.     

Normality and modulability indices. Part II: Convex cones in Hilbert spaces

Let K be a closed convex cone in a Hilbert space X. Let BX be the closed unit ball of X and K_•=(BX+K)∩(BX−K). The normality index

     

Characterization of oxidation progress by chemiluminescence: A study of polyethylene with pro-oxidant additives

Non-isothermal chemiluminescence measurements in nitrogen and isothermal measurements in oxygen were used for the evaluation of degradation in pre-oxidized polyethylene either pure or containing Mn-based pro-oxidant additives. The results were compared with infrared spectroscopy data. Chemiluminescence measurements of pure polyethylene and polyethylene with additive made it possible to calculate the set of rate constants, based on the Bolland-Gee oxidation scheme. The oxidation rate constants of polyethylene with additive were significantly higher, while the activation energy of the process appeared lower (65 kJ mol⁻¹), than those of pure polyethylene. The method provides an access to study oxidation processes during the induction period of oxidation when infrared spectroscopy cannot provide sufficient information.     

一个环硫乙烷中间体的合成

为了获得制备超高折光树脂的单体, 合成了一个能够有效制备环高折光树脂的硫乙烷中间体——(甲氧基羰基二硫化)-环硫乙烷. 该中间体可以和硫醇在温和的条件下生成环硫单体. 和二巯基甲烷反应能生成2,2’-(亚甲基双二硫化)-双环硫乙烷单体, 聚合后得到了折光指数和阿贝数高达nD/νD＝1.79/28的热固性光学树脂.     

T型微混合器混合特性的浓度分布评价法

提出一种微混合器混合性能的评价方法.在样品盒中注入不同浓度罗丹明B溶液并用体视显微镜观察捕获图像,通过Image J软件读取图像灰度值,建立不同深度下溶液的浓度-灰度值函数关系,运用此关系式将T型微混合器3种不同深度(0.1、 0.2和0.4 mm,质量浓度0.05 %的罗丹明B溶液和去离子水作为配对流体)混合实验中捕获的图像中各像素点上的灰度值转换为浓度值,绘制浓度等高线图及浓度频数分布图,分析各自混合情况,最后引入浓度混合指数概念及计算公式,分析3种深度混合器内不同截面上的混合程度.此方法从定性和定量两方面分析了微尺度下混合腔深度对微混合的影响程度,具有一定的应用价值.     

The smallest Hosoya index in (<Emphasis Type="Italic">n</Emphasis>, <Emphasis Type="Italic">n</Emphasis> + 1)-graphs

A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. In this paper, we determine the lower bound for the Hosoya index in (n, n + 1)-graphs in terms of the order n, and characterize the (n, n + 1)-graph with the smallest Hosoya index.     

Kekulé structures of hexagonal chains—some unusual connections

It is known since 1977 that the number K of Kekulé structures of a hexagonal chain is equal to the topological Z-index of a pertinently constructed “caterpillar” tree. Based on this relation we now connect K with some of other, seemingly unrelated, concepts: continuants (from number theory) and matchings of the path–graph (further related to Fibonacci numbers). We also arrive at a tridiagonal determinantal expression for K.