Sensitive chemically amplified electrochemical detection of ruthenium tris-(2,2′-bipyridine) on tin-doped indium oxide electrode

Optimized combination of chemical agents was selected for sensitive electrochemical detection of dissolved ruthenium tris-(2,2′-bipyridine) (Ru-bipy). The detection was based on the chemical amplification mechanism, in which the anodic current of a redox-active analyte was amplified by a sacrificial electron donor in solution. On indium-doped tin oxide (ITO) electrodes, electrochemical reaction of the analyte was reversible, but that of the electron donor was greatly suppressed. Several transition metal complexes, such as ferrocene and tris-(2,2′-bipyridine) complexes of osmium, iron and ruthenium, were evaluated as model analyte. A correlation between the amplified current and the standard potential of the complex was observed, and Ru-bipy generated the largest current. A variety of organic bases, acids and zwitterions were assessed as potential electron donor. Sodium oxalate was found to produce the largest amplification factor. With Ru-bipy as the model analyte and oxalate as the electron donor, the analyte concentration curve was linear up to 50 μM, with a lower detection limit of approximately 50 nM. Preliminary work was presented in which a Ru-bipy derivative was attached to bovine serum albumin and detected electrochemically. Although the combination of Ru-bipy, oxalate and ITO electrode has been used before for electrochemiluminescent detection of Ru-bipy and oxalate, as well as electrochemical detection of oxalate, its utility in amplified voltammetric detection of Ru-bipy as a potential electrochemical label has not been reported previously.     

On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Interlaboratory comparisons and improvements of methods for acid number determination in used motor oils

The results of two interlaboratory comparisons of acid number determinations in used motor oils are discussed. It is shown that the comparability of the measurement results is not as good as that required by known standards for petroleum products. The problem is motor oil contaminants which accumulated during use, and which are the source of a matrix effect in the acid number determination. The standard methods’ drawbacks are analyzed and some improvements are proposed. Repeatability and accuracy of the improved methods are evaluated. Received: 11 December 2001 Accepted: 15 February 2002     

Some formulae for the q-Bernoulli and Euler polynomials of higher order

The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570).     

Interference of probabilities and number field structure of quantum models

We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p‐adic representations.     

INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

The aim of this paper is to study the conditions by which a P-prime submodule can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions

This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size.

     

There are infinitely many limit points of the fractional parts of powers

Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα ⁿ , n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational non-integer number, this result was proved by Vijayaraghavan.