分裂的正则Hom-Leibniz-Rinehart代数

作为Hom-Leibniz代数胚的代数类比, 本文引入Hom-Leibniz-Rinehart代数的概念. 证明了分裂的正则Hom-Leibniz-Rinehart代数$L$写成$L=U+\sum_{\gamma}I_\gamma$, 其中$U$为极大交换子代数$H$的子空间和$I_\gamma$为$L$的理想, 若$[\gamma]\neq[d]$, 满足$[I_\gamma, I_d]=0$. 随后分别发展了分裂Hom-Leibniz-Rinehart代数的根和权的连通技术.最后研究了紧致的正则Hom-Leibniz-Rinehart代数的结构.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Meromorphic singular foliations on complex projective surfaces

Here we show that many numerical computations and bounds on the degrees of the algebraic leaves for singular meromorphic foliations on ² may be extended to large classes of foliations and complex projective surfaces.The author was partially supported by MURST and GNSAGA of CNR (Italy)     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Conversion of sodium lactate to lactic acid with water-splitting electrodialysis

The conversion of sodium lactate to lactic acid with water-splitting electrodialysis was investigated. One way of reducing the power consumption is to add a conductive layer to the acid compartment. Doing this reduced the power consumption by almost 50% in a two-compartment cell, whereas the electric current efficiency was not affected at all. Three different solutions were treated in the electrodialysis unit: a model solution with 70 g/L of sodium lactate and a fermentation broth that had been prefiltered two different ways. The fermentation broth was either filtered in an open ultrafiltration membrane (cut-off of 100,000 Dalton) in order to remove the microorganisms or first filtered in the open ultrafiltration membrane and then in an ultrafiltration membrane with a cut-off of 2000 Dalton to remove most of the proteins. The concentration of sodium lactate in the fermentation broth was 70 g/L, as well. Organic molecules present in the broth (peptides and similar organic material) fouled the membranes and, therefore, increased power consumption. Power consumption increased more when permeate from the more open ultrafiltration membrane was treated in the electrodialysis unit than when permeate from the membrane with the lower cut-off was treated, since there was a higher amount of foulants in the former permeate. However, the electrodialysis membranes could be cleaned efficiently with a 0.1 M sodium hydroxide solution.     

Modeling of the relationship between electroosmotic flow and separation parameters in capillary zone electrophoresis using artificial neural networks and experimental design

The prediction of migration time of electroosmotic flow (EOF) marker was achieved by applying artificial neural networks (ANN) model based on principal component analysis (PCA) and standard normal distribution simulation to the input variables. The voltage of performance, the temperature in the capillary, the pH and the ionic strength of background electrolytes (BGE) were applied as the input variables to ANN. The range of the performance voltage studied was from 15 to 27 kV, and that of the temperature in the capillary was from 20 to 30 °C. For the pH values studied, the range was from 5.15 to 8.04. The range of the ionic strength investigated in this paper was from 0.040 to 0.097. The prediction abilities of ANN with different pre-processing procedure to the input variables were compared. Under the same performance conditions, the average prediction error of the migration time of the EOF marker was 5.46% with RSD = 1.76% according to 10 parallel runs of the optimized ANN structure by the proposed approach, and that of the 10 parallel predictions of the optimal ANN structure for the different performance conditions was 12.95% with RSD = 2.29% according to the proposed approach. The study showed that the proposed method could give better predicted results than other approaches discussed.     

The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G) and nonlinear (N ₁) elastic properties of viscoelastic systems. Like the Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively.This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expression work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse.For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that neither rule is obeyed for any of our systems.     

A graphical method to construct a phylogenetic tree

A 3D graphical representation of DNA sequences, which has no circuit or degeneracy, is derived for mathematical denotation of DNA sequence. Based on this graphical representation, we propose a new sequence distance measure. We make use of the corresponding similarity matrix to construct a phylogenic tree by virtue of the fuzzy theory. The examination of phylogenic tree belong to eight species illustrates the utility of our approach. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Resolution of (+/-)-ibuprofen using (-)-brucine as a chiral selector by thin layer chromatography

The enantiomeric resolution of (+/-)-ibuprofen into its enantiomers was achieved by TLC on silica gel plate using optically pure (-)-brucine as a chiral selector and acetonitrile-methanol (5:1, v/v) as the solvent system. Spots were located in an iodine chamber. The detection limit was 4.9 microg. The effect of concentration of the chiral selector, temperature and pH on resolution has been studied.     

A result on hypothesis testing for a multivariate normal distribution when some observations are missing

Let U_i = (X_i, Y_i), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μ_x, μ_y) and covariance matrix

. Let X_i, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H₀ : μ = 0 vs. H₁ : μ ≠ 0. We prove that Hotelling's T² test, which uses (X_i, Y_i), i = 1, 2,…, n (and discards X_i, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T²-test cannot be beaten. A similar result is also proved for the problem of testing μ_x ? μ_y = 0. A Bayes test and other competitors which are similar tests are discussed.