低能N离子注入对蚕豆根尖细胞的诱变效应

为了研究低能N离子束的细胞遗传学效应, 以不同剂量的N离子束对蚕豆种子的种胚进行辐照, 观察分析根尖细胞的微核率、 有丝分裂指数和染色体畸变效应。 研究发现, 离子束的注入抑制了根尖细胞的有丝分裂, 干扰了正常的有丝分裂过程, 引发了染色体的结构、 行为和数目畸变; 随着离子注入剂量的增加, 微核率增加、 有丝分裂指数降低、 染色体畸变率增加。 In order to study the cytogenetic effects of low energy nitrogen ion irradiation, broad bean seed embryo was irradiated by different doses of nitrogen ions. Micronucleus rate, mitotic index and chromosome aberration in root tip cells were analyzed. The results showed that the injection of ions inhibited mitosis of root tip cells, interfered the normal process of mitosis, caused aberrations of chromosome structure, behavior and number. The frequency of micronucleus and chromosomal aberrations increased with the increasing radiation dosage, while mitotic index decreased.     

无衍射光的干涉实验与理论分析

分析了两束无衍射光的干涉场分布形式和干涉条纹轨迹。将一束单色光入射两小孔产生的两束相干光照射轴锥镜,在轴锥镜后将产生两束无衍射光。根据单束倾斜光入射轴锥镜的无衍射理论,分析出这两束无衍射光产生的干涉场为每束无衍射光的无衍射场的线性叠加。利用零阶贝塞尔函数的零点公式,推导出两束无衍射光的干涉条纹的轨迹为双曲线。计算结果表明,干涉场中两中心的间距与两孔实际的间距和干涉场距轴锥镜的距离成正比。实验结果与理论仿真相一致。     

Two novel abietane dimers from transformed root cultures of Salvia broussonetii

Broussonetone A (1) and broussonetone B (2), two novel dimeric abietane diterpenes, have been isolated from Salvia broussonetii root cultures transformed by Agrobacterium rhizogenes. The structure of broussonetone A was determined from spectroscopic data and confirmed by X-ray analysis. This dimer can be formed by a [4+2]-cycloaddition of two molecules of 13β-hydroxyabieta-8(14),9(11)-dien-12-one. NMR data of broussonetone B indicated that the C-20 methyl in part B of the broussonetone A molecule had been substituted by an aldehyde group. Thus, broussonetone B could be formed by an analogous Diels Alder reaction between 13β-hydroxyabieta-8(14),9(11)-dien-12-one as the dienophile and its 20-oxo derivative as the electrophile.     

Evaluation of Vetiver Volatile Compound Production under Aeroponic-Grown Conditions for the Perfume Industry

Vetiver (Chrysopogon zizanioides (L.) Roberty) is a major tropical perfume crop. Access to its essential oil (EO)-filled roots is nevertheless cumbersome and land-damaging. This study, therefore, evaluated the potential of vetiver cultivation under soilless high-pressure aeroponics (HPA) for volatile organic compound (VOC) production. The VOC accumulation in the roots was investigated by transmission electron microscopy, and the composition of these VOCs was analyzed by gas chromatography coupled with mass spectrometry (GC/MS) after sampling by headspace solid-phase microextraction (HS-SPME). The HPA-grown plants were compared to plants that had been grown in potting soil and under axenic conditions. The HPA-grown plants were stunted, demonstrating less root biomass than the plants that had been grown in potting soil. The roots were slender, thinner, more tapered, and lacked the typical vetiver fragrance. HPA cultivation massively impaired the accumulation of the less-volatile hydrocarbon and oxygenated sesquiterpenes that normally form most of the VOCs. The axenic, tissue-cultured plants followed a similar and more exacerbated trend. Ultrastructural analyses revealed that the HPA conditions altered root ontogeny, whereby the roots contained fewer EO-accumulating cells and hosted fewer and more immature intracellular EO droplets. These preliminary results allowed to conclude that HPA-cultivated vetiver suffers from altered development and root ontology disorders that prevent EO accumulation.     

On the imaginary parts of chromatic roots

While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order $n$ (ie, with $n$ vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed $\text{◂+▸}p\in \left(0,1\right)$, almost every random graph $G$ in the Erdös-Rényi model has a nonreal root.     

Computing the real roots of a polynomial by the exclusion algorithm

We describe a new algorithm for localizing the real roots of a polynomialP(x). This algorithm determines intervals on whichP(x) does not possess any root. The remainder set contains the real roots ofP(x) and can be arbitrarily small.     

Finding the Minimal Root of an Equation with the Multiextremal and Nondifferentiable Left-Hand Part

A problem very often arising in applications is presented: finding the minimal root of an equation with the objective function being multiextremal and nondifferentiable. Applications from the field of electronic measurements are given. Three methods based on global optimization ideas are introduced for solving this problem. The first one uses an a priori estimate of the global Lipschitz constant. The second method adaptively estimates the global Lipschitz constant. The third algorithm adaptively estimates local Lipschitz constants during the search. All the methods either find the minimal root or determine the global minimizers (in the case when the equation under consideration has no roots). Sufficient convergence conditions of the new methods to the desired solution are established. Numerical results including wide experiments with test functions, stability study, and a real-life applied problem are also presented.     

Multiplicative Invariants and Semigroup Algebras

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.     

An iterative method for solving the stable subspace of a matrix pencil and its application

This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a semigroup property depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order.