On the asymptotic joint distributions of certain functions of the eigenvalues of four random matrices

In this paper, the authors obtained asymptotic expressions for the joint distributions of certain functions of the eigenvalues of the Wishart matrix, correlation matrix, MANOVA matrix and canonical correlation matrix when the population roots have multiplicity.     

On tree census and the giant component in sparse random graphs

For each of the two models of a sparse random graph on n vertices, G(n, # of edges = cn/2) and G(n, Prob (edge) = c/n) define t_n(k) as the total number of tree components of size k (1 ≤ k ≤ n). the random sequence {[t_n(k) - nh(k)]n^?1/2} is shown to be Gaussian in the limit n →∞, with h(k) = k^k?2c^k?1e^?kc/k! and covariance function being dependent upon the model. This general result implies, in particular, that, for c> 1, the size of the giant component is asymptotically Gaussian, with mean nθ(c) and variance n(1 ? T)^?2(1 ? 2Tθ)θ(1 ? θ) for the first model and n(1 ? T)^?2θ(1 ? θ) for the second model. Here Te^?T = ce^?c, T<1, and θ = 1 ? T/c. A close technique allows us to prove that, for c < 1, the independence number of G(n, p = c/n) is asymptotically Gaussian with mean nc^?1(β + β²/2) and variance n[c^?1(β + β²/2) ?c^?2(c + 1)β²], where βe^β = c. It is also proven that almost surely the giant component consists of a giant two-connected core of size about n(1 ? T)β and a “mantle” of trees, and possibly few small unicyclic graphs, each sprouting from its own vertex of the core.     

Improved HPLC of triglycerides by special tempering procedures

Summary Three new methods of improving triglyceride separation by RP-HPLC using propionitrile as eluent and an RI detector are described. First the baseline was stabilized by indirect thermostating of the detector. Relatively high sensitivity adjustments (4×10^–5 RI units full scale deflection) were possible allowing small fat samples to be injected (down to 200 g). Second the increase of selectivity with decreasing temperature and the increasing sharpness of peaks at higher temperatures are shown. A high temperature is indispensible for saturated long chain compounds which tend to crystallize on the column. To fulfill this requirement and avoid loss of selectivity temperature programming has been investigated. Third at higher temperatures an additional axial temperature gradient up to 0.05 K/cm was applied to enhance peak symmetry. All chromatograms achieved by those temperature gradients show higher resolution than those obtained at constant temperatures. Butterfat could be separated into more peaks than has previously been possible. The chromatogram of soybean oil, besides showing excellent selectivity for more polar components shows a series of ten long chain compounds following POP.     

Elemental fingerprint analysis of barley (<Emphasis Type="Italic">Hordeum vulgare</Emphasis>) using inductively coupled plasma mass spectrometry,isotope-ratio mass spectrometry,and multivariate statistics

Inductively coupled plasma mass spectrometry (ICP–MS) and isotope-ratio mass spectrometry (IR-MS) have been used to examine the multi-elemental composition and ¹⁵N/¹⁴N and ¹³C/¹²C isotope ratios of three spring barley (Hordeum vulgare) genotypes (Orthega, Barke, and Bartok) grown in three typical Danish agricultural soils (North Jutland, West Jutland, and East Zealand) differing in soil fertility. The aim of the study was to examine whether it was possible to generate a unique elemental fingerprint of individual barley genotypes irrespective of the elemental imprint plants had received from soils differing in fertility and agricultural practice. Multivariate statistics were used to analyze the elemental fingerprints of the barley genotypes at different times during a full growing season from early tillering to full maturity of the barley grains. Initially, 36 elements were analyzed in the plant samples but this number was subsequently reduced to 15 elements: B, Ba, C, Ca, Cu, Fe, K, Mg, Mn, N, Na, P, S, Sr, and Zn. These elements exceeded the limit of detection (LOD) for all genotypes, soil types, and plant growth stages and for these elements the accuracy was better than 90% compared with apple leaf certified reference material (CRM). Principal component analysis (PCA) separated multi-elemental data in accordance with soil type when plants of similar physiological age were compared, whereas this separation disappeared if plants of all ages were compared simultaneously. Isotope ratios (¹⁵N) of plants also proved to be a highly accurate property for classification of samples according to soil type. In contrast, the differences in ¹³C were too small to enable such classification. The differences in ¹⁵N among soils were so pronounced that separation of samples according to the physiological age of plants became redundant. However, ¹⁵N and the multi-elemental analysis revealed no differences between the three barley genotypes, indicating that the influence of soil chemistry and possibly also climate and agricultural practice was too large to allow an unique elemental fingerprint for the genotypes. This finding was substantiated by analyzing the multi-elemental composition of grain from two additional genotypes (Otira and Barthos) grown at the north and east locations, respectively. PCA showed not only that the elemental fingerprints of these two genotypes were similar to those of the others, but also that the soil in which the plant had been growing could be accurately predicted on the basis of the PCA scores from the genotypes Orthega, Barke, and Bartok. Similar conclusions could be drawn using ¹⁵N data.     

On the comparison of the spaces

The notion of -variation and the space arise in the study of regularity properties of solutions to perturbed conservation laws. In this article we show that this notion is equivalent to variation in the regular sense, and therefore the space is the same as the space in the sense of Cesari-Tonelli. We also point out some connection between the space and the Favard classes for translation semigroups.

     

On the location of the essential spectrum of Schrödinger operators

We give estimates on the bottom of the essential spectrum of Schrödinger operators in .

     

On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds

For any hyperbolic 3-manifold with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of is bounded from above.

     

Thermal Decomposition of Medicinal Plant Raw Materials Based on Principal Component Analysis

Studies on the thermal decomposition of commercial raw plant materials used in medicine were performed. 144 independent samples of plant materials — herbs, leaves,flowers, inflorescences, fruits, roots, rhizomes and barks, collected by Medicinal Plant Works‘Herbapol’, were analyzed. Thermal decomposition was performed using OD-103 Derivatograph. As a result of analysis, it was established, that thermal decomposition of majority of samples proceeds through three stages. The analysis of fruits revealed, that their thermal decomposition proceeds in four stages. In order to obtain a more clear classification of the analyzed plant materials principal component analysis (PCA) was applied. Interpretation of the PCA results allows to state, that samples of raw materials from the same plant species in majority of cases are characterized by similar course of thermal decomposition due to similar chemical composition. In this way the differences in general chemical composition of medicinal plants raw materials can be determined. This revised version was published online in August 2006 with corrections to the Cover Date.     

Maximum Monoreflections and Essential Extensions

An extension operator c in a category is an assignment, to each object A a monomorphism c _A : AcA. Seeking to approximate such a c by a functor, in our earlier paper Maximum monoreflections, we showed that with some hypotheses on the category, and on c, there is a monoreflection (c) maximum beneath c. Thus, in a suitable category of rings, using the complete ring of quotients operator Q, each object A has a maximum functorial ring of quotients (Q)A. But the proof gave no hint of how to calculate the general (c)A's, nor the particular (Q)A's. In the present paper, we give an explicit formula (and separate proof of existence) for the (c)A's, under more complicated hypotheses on the category and assuming the c _A 's are essential monomorphisms. We discuss briefly how the formula proves adequate to calculate the (Q)A's in Archimedean f-rings, and some related and necessary constructs in Archimedean l-groups.     

柚子果皮油挥发性成分的气相色谱-质谱分析

采用溶剂萃取提取柚子果皮的精油,经气相色谱和质谱联机分析,同时依据各成分的保留指数,鉴定出71种挥发性物质,其中有21种碳氢化合物,50种含氧化合物。在碳氢化合物中以柠烯、γ－萜品烯为主要成分;而在含氧化合物中主要是沉香醇、α－萜品醇、百里酚以及一些脂肪族醛。