四次函数实零点的完全判据和正定条件

本文给出了四次函数实零点的完全判据和正定条件,这一结果在研究多项式系统的奇点分析和分支问题时给出了可以实用的判据．     

New light on Hensel''s lemma

The historical development of Hensel's lemma is briefly discussed (Section 1). Using Newton polygons, a simple proof of a general Hensel's lemma for separable polynomials over Henselian fields is given (Section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots (Section 4) and continuity of factors (Section 6) are demonstrated. Using this and a general Krasner's lemma (Section 7), we give a short proof of a general Hensel's lemma and show that it is, in a certain sense, best possible (Section 8). All valuations here are non-Archimedean and of arbitrary rank. The article is practically self-contained.     

Studies on mass production of transformed Panax ginseng hairy roots in bioreactor

The growth properties of Panax ginseng hairy roots transformed by Agrobacterium rhizogenes were compared between flask and aerated column or stirred bioreactor. In flask cultures, sucrose, initially 30 g/L, was nearly exhausted after 45 d of culture. The pH of the medium dropped from 5.5 to 4.96 after 10 d, but afterward it gradually increased to 6.4. After 45 d, hairy roots grew about 16-folds. The growth rate of hairy roots in air-bubble column or stirred bioreactor cultures was 1.13 (1.11) to 1.23 (1.20) g fresh wt (dry wt)/(g of cells·d), respectively. For both bioreactors, growth was about three times as high as in the flask cultivation.     

16-Demethoxymethyllycaconitine,a new norditerpenoid alkaloid from Delphinium cuneatum

A new norditerpenoid alkaloid has been isolated from the roots of Delphinium cuneatum. On the basis of ¹H, ¹³C NMR, IR, and mass spectra, the structure of the alkaloid was established as 1,6,14-trimethoxy-7,8-dihydroxy-18-(2-methyl)succinylanthranoyloxyaconane (16-demethoxymethyllycaconitine). The roots of Delphinium cuneatum also contain the known alkaloid methyllycaconitine and N,N"-di(methoxycarbonyl)-3,4-diaminotoluene.     

Datura stramonium hairy roots tropane alkaloid content as a response to changes in Gamborg’s B5 medium

Hairy roots are less susceptible to manipulation by changes in medium composition than callus and cell suspension cultures. However, when the individual components of the Gamborg’s B₅ medium were modified one by one, several of them modified the yield of root cultures. Nitrogen (N) source changes, the absence of phosphorus (P), calcium (Ca), and cobalt (Co), and the increase in the sucrose content of the medium increased the level of alkaloids inDatura stramonium hairy root cultures. The use of ammoniun as N source provoked the alkaloid excretion into the medium. The addition of different auxins inhibited the alkaloid accumulation, but the addition of abscisic acid (ABA) did not change the alkaloid content of the cultures. The use of MeJa increased the content of hyoscyamine to 100%.     

Friction coefficients of spheres having sticky or hairy surfaces

The theoretical equations for friction coefficients of spheres having sticky or hairy surfaces are presented. In the present treatment, the sticky surface is represented by a higher viscosity of fluid in the surface layer and the hairy surface is assumed to have a porous structure. The friction coefficients are given as functions of the thickness of the surface layer, the fluid viscosity in the surface layer and the segmental density of hairy chains.     

Binary hairy nanoparticles: Recent progress in theory and simulations

Binary polymer brushes, including mixed homopolymer brushes and diblock copolymer brushes, are an attractive class of environmentally responsive nanostructured materials. Owing to microphase separation of the two chemically distinct components in the brush, multifaceted nanomaterials with functionalized and patterned surfaces can be obtained. This review summarizes recent progress on the theory and simulations related to binary polymer brushes grafted to flat, spherical, and cylindrical substrates, with a focus on patterned morphologies of multifaceted hairy nanoparticles, an intriguing class of hybrid nanostructured particles (e.g., nanospheres and nanorods). In particular, powerful field theory and particle-based simulations suitable for revealing novel structures on these patterned surfaces, including self-consistent field theory and dissipative particle dynamics simulations, are emphasized. The unsolved yet critical issues in this research field, such as dynamic response of binary polymer brushes to environmental stimuli and the hierarchical self-assembly of binary hairy nanoparticles, are briefly discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1583–1599     

A Note on twin primes and the modular ring Z 6

The modular ring ?₆ defines integers via (6r _i + (i ? 3)) where i is the class and r _i the row when tabulated in an array. Since only Classes 2₆ and 4₆ contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.