On numerical ranges and roots

Existence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated.     

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.     

Chemical Constituents from the Root of Antidesma Pentandrum var. Barbatum

Investigation of the root extract of Antidesma pentandrum var. barbatum led to the isolation of seven new compounds, antidesmol ( 1 ), antidesmanins E ( 2 ) and F ( 3 ), antidesnone ( 4 ), antidesnol ( 5 ), barbatumols A ( 6 ) and B ( 7 ), together with 14 known compounds including sodium aristolochate‐I ( 10 ) and aristolochic acid‐I methyl ester ( 11 ).     

Tamely Ramified Towers and Discriminant Bounds for Number Fields

The root discriminant of a number field of degree n is the nth root of the absolute value of its discriminant. Let R _2m be the minimal root discriminant for totally complex number fields of degree 2m, and put ₀ = lim inf _m R _2m . One knows that ₀ 4e 22.3, and, assuming the Generalized Riemann Hypothesis, ₀ 8e 44.7. It is of great interest to know if the latter bound is sharp. In 1978, Martinet constructed an infinite unramified tower of totally complex number fields with small constant root discriminant, demonstrating that ₀ < 92.4. For over twenty years, this estimate has not been improved. We introduce two new ideas for bounding asymptotically minimal root discriminants, namely, (1) we allow tame ramification in the tower, and (2) we allow the fields at the bottom of the tower to have large Galois closure. These new ideas allow us to obtain the better estimate ₀ < 83.9.     

火焰原子吸收光谱法测定中药防风中铜、锰、锌和铁的不确定度评定

采用HNO3和HClO4消解防风样品,利用火焰原子吸收光谱法测定其中铜、锰、锌和铁含量.对测量过程中不确定度的产生原因进行了分析,并对防风中4种元素含量测定结果的不确定度进行了评定.     

Surface properties of plasma membrane vesicles isolated from melon (Cucumus melo L.) root cells differing in salinity tolerance

The hypotheses that genotypic differences in salinity tolerance may result from (i) differences in global surface charge density or (ii) from differences in global Ca²⁺ binding were tested. An attempt was made to correlate the differing salinity tolerance of four melon cultivars with surface properties of vesicles extracted from the plasma membrane (PM) of their root cells. Surface characterization involved measurements of electrophoretic mobility and sorption of ⁴⁵Ca²⁺ to the vesicles in the presence of varying concentrations of Ca²⁺, Na⁺ and Mg²⁺. Irrespective of salinity tolerance, vesicles from the four cultivars yielded similar ζ potentials under similar conditions, indicating similar global surface charge densities. Sorption studies with vesicles from two cultivars differing in salinity tolerance predicted independently this result of equal surface charge density. The estimated global binding affinities of Ca²⁺, Na⁺ and Mg²⁺ to the PM of both cultivars were the same with binding coefficients of 50, 0.8 and 9 M⁻¹, respectively. Consequently, the hypotheses enumerated above to interpret genotypic differences in salinity toxicity are rejected. However, vesicles from the salt-resistant strain sorbed 19% more Ca²⁺ per given amount of protein in the membrane, indicating the existence of a larger number of negatively charged surface sites per given amount of protein and a smaller amount of protein per given area of membrane. Genotypic differences in site-specific Ca²⁺-binding affinity (e.g. at ion channels) remain a viable hypothesis for genotypic differences in salinity tolerance.     

荧光分光光度法测定黄芪口服液中黄芪甲甙的研究

利用在硫酸条件下香草醛与黄芪甲甙的荧光反应测定黄芪口服液中的黄芪甲甙，黄芪甲甙与香草醛反应产物的最大激发波长为λｅｘ＝３６８ｎｍ，最大发射波长λｅｍ４３５ｎｍ。黄芪甲甙在０．０－３０．０ｍｇ／Ｌ范围呈良好的线性关系，最低检出限为０．３μｇ／ｍＬ，测定样品的回收率为９６．７２％－１０３．３０％。     

The non-approximability of bicriteria network design problems

Let G be an undirected graph with two edge costs (c-cost and d-cost). We want to minimize the diameter of a spanning subgraph S (under d-cost) subject to the constraint that the total cost of the edges in S (with respect to c) does not exceed a given budget. We prove that this problem is non-approximable, even in some special cases. Similar results are proved if the stretch factor or the root stretch factor is considered instead of the diameter.     

ON SOLVABLE COMPLETE LIE SUPERALGEBRAS

The authors discuss the properties of solvable complete Lie superalgebra, proving that solvable Lie superalgebras of maximal rank are complete.