完备格上基于Sup-T合成算子的矩阵的平方根

对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S⊙S=R,则称S为R的平方根,其中I表示指标集|I|的基数,⊙在本文中指的是sup-T合成算子并且T是无限∨分配的保序的算子。本文给出了完备格上基于sup-T合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根。     

Carrageenan as an elicitor of induced secondary metabolites and its effects on various growth characters of chickpea and maize plants

The effects of polysaccharide elicitor k-carrageenan obtained from Hypnea musciformis, red algae on the production of Induced Secondary Metabolites, ISMs (the disease resistance compounds) and on various growth characters of chickpea and maize plants were studied. Experiments were conducted in the field of PCSIR Laboratories Complex Karachi during December 2008–April 2009 in randomized complete block design with three replications. Three elicitor treatments were used, a solid preparation in which the elicitor was mixed with soil (T₂ 1 mg/g) and applied around the seeds in the soil. The two other preparations were liquid, T₁ and T₃ at a concentration of 100 μg glc eq ml⁻¹ and were applied around the sowing seeds and as a foliar spray on the plants, respectively. Statistical analysis of the data revealed that these treatments significantly enhanced all the growth characters of chickpea except T₂ that gave the nonsignificant difference in the plant height. Maximum plant height (80.3 cm), number of pods plant⁻¹ (76.2), number of branches plant⁻¹ (25.0), number of leaves plant⁻¹ (125.6), earlier flowering and high ISMs contents in leaves, stem and grains of chickpea were recorded in T₁ treated chickpea plants. In maize plants only T₁ and T₃ treatments (with minor exceptions) had significant effects on few characters like plant height, stem diameter, number of leaves plant⁻¹ and on ISMs contents in leaves while number of cobs plant⁻¹ and flowering time were nonsignificantly affected by these treatments. These results suggested that k-carrageenan elicitor can be used as a potent plant protectant as well as growth promoting agent especially for chickpea plants.     

First findings of monocrystalline aragonite inclusions in garnet from diamond-grade UHPM rocks (Kokchetav Massif, Northern Kazakhstan)

The crystal field effect and microscopic origins of the Zeeman g-factors g(//) and g(⊥) for (6)S(3d(5)) state ions at tetragonal symmetry crystal filed, taking into account the spin-spin (SS), the spin-other-orbit (SOO), and the orbit-orbit (OO) magnetic interactions besides the well-known spin-orbit (SO) magnetic interaction, have been investigated using the microscopic spin Hamiltonian theory and the complete diagonalization method (CDM). It is found that the g(//)(±1/2)≠g(//)(±5/2) and g(⊥)(±1/2)≠g(⊥)(±5/2), where the g-factors g(//)(±1/2) and g(⊥)(±1/2) express the g-factors of the ground state |M?(s)=±1/2), whereas the g-factors g(//)(±5/2) and g(⊥)(±5/2) express the g-factors of the ground state |M?(s)=±5/2). It is shown that although the SO magnetic interaction is the most important one, the contributions to the shifts of g-factors Δg(//)(=2.0023-g(//)) and Δg(⊥)(=2.0023-g(⊥)) from other three magnetic interactions including the SS, SOO, and OO magnetic interactions are appreciable and should not be omitted, especially for the shifts of g-factors Δg(//)(±5/2) and Δg(⊥)(±5/2). The individual contributions to the shifts of g-factors arising from the spin quartet states and spin doublet states have been studied. The investigations show that the Δg(//)(±1/2) and Δg(⊥)(±1/2) primarily result from the spin quartet states, whereas Δg(//)(±5/2) and Δg(⊥)(±5/2) from the spin quartet states as well as the combined effects between the spin quartet states and the spin doublet states. The contribution to the shifts of g-factors from the net spin doublet states is zero.     

Micromechanical analysis of the behavior of stiff clay

Cementations formed in geological timescale are observed in various stiff clays.A micromechanical stress strain model is developed for modeling the effect of cementation on the deformation behavior of stiff clay.The proposed approach considers explicitly cementations at intercluster contacts,which is different from conventional model.The concept of inter-cluster bonding is introduced to account for an additional cohesion in shear sliding and a higher yield stress in normal compression.A damage law for inter-cluster bonding is proposed at cluster contacts for the debonding process during mechanical loading.The model is used to simulate numerous stress-path tests on Vallericca stiff clay.The applicability of the present model is evaluated through comparisons between the predicted and the measured results.In order to explain the stress-induced anisotropy arising from externally applied load,the evolution of local stresses and local strains at inter-cluster planes are discussed.     

Vertex coloring complete multipartite graphs from random lists of size 2

Let K_s×m be the complete multipartite graph with s parts and m vertices in each part. Assign to each vertex v of K_s×m a list L(v) of colors, by choosing each list uniformly at random from all 2-subsets of a color set C of size σ(m). In this paper we determine, for all fixed s and growing m, the asymptotic probability of the existence of a proper coloring φ, such that φ(v)∈L(v) for all v∈V(K_s×m). We show that this property exhibits a sharp threshold at σ(m)=2(s−1)m.     

Lambda-fold 2-perfect 6-cycle systems in equipartite graphs

A 6-cycle system of a graph G is an edge-disjoint decomposition of G into 6-cycles. Graphs G, for which necessary and sufficient conditions for existence of a 6-cycle system have been found, include complete graphs and complete equipartite graphs. A 6-cycle system of G is said to be 2-perfect if the graph formed by joining all vertices distance 2 apart in the 6-cycles is again an edge-disjoint decomposition of G, this time into 3-cycles, since the distance 2 graph in any 6-cycle is a pair of disjoint 3-cycles.Necessary and sufficient conditions for existence of 2-perfect 6-cycle systems of both complete graphs and complete equipartite graphs are known, and also of λ-fold complete graphs. In this paper, we complete the problem, giving necessary and sufficient conditions for existence of λ-fold 2-perfect 6-cycle systems of complete equipartite graphs.     

Complete photonic band gaps in one-dimensional ternary photonic crystals containing single negative materials

Complete photonic band gaps (PBGs) are found in one-dimensional ternary photonic crystals (1D TPCs) composed of an ordinary dielectric and single negative metamaterials. The proposed TPC gives omni directional PBG completely independent of polarizations dependent weekly on angle of incidence. Here the choice of different parameters of TPC is done in such a way so that it eliminates the Brewster's-angle transmission resonance, thus allowing a complete 3D PBG. It exhibits a photonic band or gap near frequencies where either the magnetic permeability or the electric permittivity of the metamaterial changes sign, whose width increases with the increasing angle of incidence. These result from the dispersive properties of the metamaterials and disappear for the particular case of propagation along the stratification direction. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material for TE and TM polarizations.     

Complete ( q 2?+ q +?8)/2-caps in the spaces PG (3, q ), q ≡ 2 (mod 3) an odd prime, and a complete 20-cap in PG (3, 5)

An infinite family of complete (q ² + q + 8)/2-caps is constructed in PG(3, q) where q is an odd prime ≡ 2 (mod 3), q ≥ 11. This yields a new lower bound on the second largest size of complete caps. A variant of our construction also produces one of the two previously known complete 20-caps in PG(3, 5). The associated code weight distribution and other combinatorial properties of the new (q ² + q + 8)/2-caps and the 20-cap in PG(3, 5) are investigated. The updated table of the known sizes of the complete caps in PG(3, q) is given. As a byproduct, we have found that the unique complete 14-arc in PG(2, 17) contains 10 points on a conic. Actually, this shows that an earlier general result dating back to the Seventies fails for q = 17.      

有机污染物的生物富集因子与拓扑指数的数学模型

依据价连接性指数(xi)、电性拓扑态指数(ej)及电性距离矢量(mk)构建239种有机污染物生物富集因子(FBC)的6参数QSFR(定量结构-生物富集因子相关性)模型, 不仅相关程度高, 而且所用自变量数少. 该模型的传统相关系数(R2)为0.821, LOO(levae-one-out)交互验证系数(Q2)为0.809, 证明具有良好的稳健性及预测能力. 根据进入该模型的6个参数可知, 影响有机污染物FBC的主要结构基团是: —C—、>C—、—O—、—X、—NH2以及分子的柔韧性、折叠程度等空间因素. 可以认为在生物富集过程中,“诱导契合机理”也发挥一定作用. 对自变量集进行正交变换, 既不影响模型的相关性, 又能降低其自相关性.     

可加广义代数格上的 Tietze 扩张定理

可加的广义代数格范畴与 T₀ 拓扑空间范畴相等价, 从这个观点出发, 作者把可加广义代数格作为一个闭集格, 在其上建立 Urysohn 引理和 Tietze 扩张定理. 这是拓扑理论在格上的一种新推广, 有助于格上拓扑理论的研究和广义连续格理论的应用.