Determination of Thiols and Disulfides in Whole Blood and Its Fractions by Anodic Stripping Voltammetry and Anodic Stripping Voltammetric Titration

SH‐ and SS‐groups content and their ratio is one of the most important factors of organism antioxidant system. Change in ratio of thiols to disulfides can serve as an indicator of oxidative stress. Anodic stripping voltammetry and anodic stripping voltammetric titration (direct and reverse variants) methods are proposed for determination of thiols and disulfides concentration. Disulfides are preliminary reduced with sodium sulfite. Ag⁺+RSH→AgSR+H⁺ reaction is used to provide the information. Unreacted silver ions concentration is determined by anodic stripping voltammetry method using platinum working electrode. Calibration free method is suggested. The possibilities of express analysis of blood and its fractions are described. Reliability of results and accuracy are confirmed by model solutions analysis and recovery study of whole blood and its fractions. Results of whole blood, erythrocyte mass, plasma and serum taken from different groups of patients' investigations are given, that demonstrate perspectives of the application methods in clinical practice.     

Prediction for Z-mass is a crucial test of the standard model

In schemes with oneW boson and twoZ-bosons (mediating the charged and neutral current interactions involving ordinary fermions) based on the direct product and simple groups, SU(2) × U(1) ×u′(1) andG × U(1) (G is a simple group of rank two), the following two questions are discussed. (1) What are the necessary and sufficient conditions for minimal reducibility of the effective four-fermion neutral current interaction (involving ν_μ-hadron, electron-hadron and ν_μ-electron sectors) to the corresponding prediction of the standard model? (2) In what way are the masses of the twoZ-bosons constrained relative to the mass of the neutral boson of standard model? The answers to these questions are given first by keeping the underlying Higgs structure, responsible for gauge-boson (and fermion) mass generation, completely arbitrary (called Higgs-independent case) and then by making a specific choice for the Higgs structure resulting in a natural mass relation for theW andZ-bosons that is an exact counterpart toM _W ^(S)/2 =M _Z ^(S)/2 sec² ? _W for the standard model (called Higgs-dependent case). The distinction between these two cases is brought out clearly as also that between the direct product and simple groups. Whether or not any assumption is made about the Higgs structure, with either the direct product or the simple group, it is concluded that in general there is aZ-boson lighter than the neutral boson of the standard model.     

标准加入火焰原子吸收法测定钨及钨化合物中的钾、钠

在以钨为基体的溶液中,利用柠檬酸为掩蔽剂,氯化铯为消电离剂,应用火焰原子吸收法进行钨及钨化合物中钾、钠的测定,5次测定结果的极差值在0．0002％-0．0004％之间,K、Na的加标准回收率分别为98．0％-104．0％及96．4％-102．6％。本方法已应用于钨及钨化合物中钾、钠的测定。     

On open questions in the geometric approach to structural learning Bayesian nets

The basic idea of an algebraic approach to learning Bayesian network (BN) structures is to represent every BN structure by a certain uniquely determined vector, called the standard imset. In a recent paper [18], it was shown that the set S of standard imsets is the set of vertices (=extreme points) of a certain polytope P and natural geometric neighborhood for standard imsets, and, consequently, for BN structures, was introduced.The new geometric view led to a series of open mathematical questions. In this paper, we try to answer some of them. First, we introduce a class of necessary linear constraints on standard imsets and formulate a conjecture that these constraints characterize the polytope P. The conjecture has been confirmed in the case of (at most) 4 variables. Second, we confirm a former hypothesis by Raymond Hemmecke that the only lattice points (=vectors having integers as components) within P are standard imsets. Third, we give a partial analysis of the geometric neighborhood in the case of 4 variables.     

Elementary operators on self-adjoint operators

Let H be a Hilbert space and let A and B be standard ∗-operator algebras on H. Denote by As and Bs the set of all self-adjoint operators in A and B, respectively. Assume that and are surjective maps such that M(AM^∗(B)A)=M(A)BM(A) and M^∗(BM(A)B)=M^∗(B)AM^∗(B) for every pair A∈As, B∈Bs. Then there exist an invertible bounded linear or conjugate-linear operator and a constant c∈{−1,1} such that M(A)=cTAT^∗, A∈As, and M^∗(B)=cT^∗BT, B∈Bs.     

Selecting two different defective coins

In this paper, given a balance scale and the information that there are exactly two different defective coins present, the authors consider the problem of ascertaining the minimum number of testing which suffice to determine the two different defective coins in a set of λ coins in same appearance, and here λ  3. A testing algorithm for all the possible values of λ is constructed, and the testing algorithm needs at most one testing step more than the optimal testing algorithm.     

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order α(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order β(0,1) and of order α(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.     

On Copositive Programming and Standard Quadratic Optimization Problems

A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FF ^T where F is some non-negative matrix). The dual of this cone is the cone of copositive matrices (i.e., those matrices which yield a non-negative quadratic form on the positive orthant). This conic formulation allows us to employ primal-dual affine-scaling directions. Furthermore, these approaches are combined with an evolutionary dynamics algorithm which generates primal-feasible paths along which the objective is monotonically improved until a local solution is reached. In particular, the primal-dual affine scaling directions are used to escape from local maxima encountered during the evolutionary dynamics phase.     

Standard triangularization of semigroups of non-negative operators

We show that, under mild conditions, a semigroup of non-negative operators on L^p(X,μ) (for 1?p<∞) of the form scalar plus compact is triangularizable via standard subspaces if and only if each operator in the semigroup is individually triangularizable via standard subspaces. Also, in the case of operators of the form identity plus trace class we show that triangularizability via standard subspaces is equivalent to the submultiplicativity of a certain function on the semigroup.     

Bounds for symmetric elliptic integrals

Lower and upper bounds for the four standard incomplete symmetric elliptic integrals are obtained. The bounding functions are expressed in terms of the elementary transcendental functions. Sharp bounds for the ratio of the complete elliptic integrals of the second kind and the first kind are also derived. These results can be used to obtain bounds for the product of these integrals. It is shown that an iterative numerical algorithm for computing the ratios and products of complete integrals has the second order of convergence.