Metrics of separation performance in chromatography. Part 1. Definitions and application to static analyses

Earlier introduced metrics of separation performance are described in a systematic way. After providing the definitions of the metrics suitable for a broad variety of applications, the study focuses on static analyses (isothermal GC, isocratic LC, etc.) and their general separation performance. Statistically expected number of resolved (adequately separated) single-component peaks is treated as the ultimate metric of general separation performance of chromatographic analysis. That number depends on the peak capacity of the analysis and the number of components in a test mixture. The peak capacity, in turn, depends on the separation capacity of a column and the lowest separation required by the data-analysis system for resolving poorly separated peaks. The separation capacity is a special case of a broader metric of the separation measure which is a function of column efficiency, solute separability, and the level of the solute interaction with a column stationary phase. The formulae for theoretical prediction of all these metrics for arbitrary pairs of peaks in static analyses are derived. To provide a better insight into the basic metrics of the separation performance, additional metrics such as the solute discrimination (relative difference in solute velocities), utilization of separability (solute discrimination per unit of their separability), specific separation (the separation per unit of separability), and others are defined and found for static analyses.     

Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta

We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of such metrics. We show that these metrics have certain useful properties similar to those of Riemannian Liouville metrics, namely:

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they admit geodesically equivalent metrics;     

Comparison of multivariate preprocessing techniques as applied to electronic tongue based pattern classification for black tea

In an electronic tongue, preprocessing on raw data precedes pattern analysis and choice of the appropriate preprocessing technique is crucial for the performance of the pattern classifier. While attempting to classify different grades of black tea using a voltammetric electronic tongue, different preprocessing techniques have been explored and a comparison of their performances is presented in this paper. The preprocessing techniques are compared first by a quantitative measurement of separability followed by principle component analysis; and then two different supervised pattern recognition models based on neural networks are used to evaluate the performance of the preprocessing techniques.     

A consumption model with separability and imperfect decision makers

A consumption model is considered, where agents may have a simplified image of reality and a simplified way of reaching decisions. Some rules of behaviour are assumed, considering, in particular, the decision-theoretic ideas of decentralization and price aggregation. The consumers have a price-independent relative income distribution. The existence and unicity of temporary equilibria are investigated.      

A proof that commutative artinian rings are noetherian

Abstract

Integrals in Hopf algebras are an essential tool in studying finite dimensional Hopf algebras and their action on rings. Over fields it has been shown by Sweedler that the existence of integrals in a Hopf algebra is equivalent to the Hopf algebra being finite dimensional. In this paper we examine how much of this is true Hopf algebras over rings. We show that over any commutative ring R that is not a field there exists a Hopf algebra H over R containing a non-zero integral but not being finitely generated as R-module. On the contrary we show that Sweedler's equivalence is still valid for free Hopf algebras or projective Hopf algebras over integral domains. Analogously for a left H-module algebra A we study the influence of non-zero left A#H-linear maps from A to A#H on H being finitely generated as R-module. Examples and application to separability are given.     

Fuzzy measures and discreteness

The main result is to show that the space of nonmonotonic fuzzy measures on a measurable space (X,X) with total variation norm is separable if and only if the σ-algebra X is a finite set. Our result is related to fuzzy analysis, functional spaces and discrete mathematics.     

Classical mechanics of directly interacting relativistic particles

We discuss the classical mechanics of relativistic systems containing any number of particles with direct interaction. We continue our previous approach of restricting the observables to gauge invariant variables. As a preliminary we show how to constructN-particle mass shell constraints. Physical momentum and position variables are constructed in consonance with nonsuperluminality and relativity and consistent with a slightly weakened separability which allows the position four vector of separated particles to differ from the canonical coordinate four vector by a constant term which depends on its history but does not affect future dynamics. The formalism is mathematically consistent though slightly more complicated than previous attempts in this direction.     

Multivariate analysis of diffusion tensor imaging data improves the detection of microstructural damage in young professional boxers

In this study, we present two different methods of multivariate analysis of voxel-based diffusion tensor imaging (DTI) data, using as an example data derived from 59 professional boxers and 12 age-matched controls. Conventional univariate analysis ignores much of the diffusion information contained in the tensor. Our first multivariate method uses the Hotelling's T² statistic and the second uses linear discriminant analysis to generate the linear discriminant function at each voxel to form a separability metric. Both multivariate methods confirm the findings from the individual metrics of large-scale changes in the bilateral inferior temporal gyri of the boxers, but they also reveal greater sensitivity as well as identifying major subcortical changes that had not been evident in the univariate analyses. Linear discriminant analysis has the added strength of providing a quantitative measure of the relative contribution of each metric to any differences between the two subject groups. This novel adaptation of statistical and mathematical techniques to neuroimaging analysis is important for two reasons. Clinically, it develops the findings of a previous mild head injury study, and, methodologically, it could equally well be applied to multivariate studies of other pathologies.