Pattern recognition display methods for the analysis of computed molecular properties

Summary Pattern recognition methods, particularly the unsupervised learning techniques, are well suited for the preliminary analysis of the large data sets produced by computer chemistry. The use of linear and non-linear display methods for such exploratory analysis are exemplified with the aid of two data sets of biologically active molecules. Advantages and disadvantages of these techniques are discussed.     

Point processes and multivariate extreme values

A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models.     

EOL and ETOL array languages

In this paper we study the families of ETOL and EOL array languages. Standard forms for ETOL and EOL array systems are defined and closure properties of the families are studied. Relations of these families with other developmental array languages and other array languages are studied.     

A note on asymptotic inference in a class of non-stationary processes

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.     

Conditions for the convergence in distribution of maxima of stationary normal processes

The asymptotic distribution of the maximum M_n=max_1?t?nξ_t in a stationary normal sequence ξ₁,ξ,… depends on the correlation r_t between ξ₀ and ξ_t. It is well known that if r_t log t → 0 as t → ∞ or if Σr²_t<∞, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time.     

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

Electronic and vibrational properties of fluorenone in the channels of zeolite L

Fluorenone (C13H8O) was inserted into the channels of zeolite L by using gas-phase adsorption. The size, structure, and stability of fluorenone are well suited for studying host-guest interactions. The Fourier transform IR, Raman, luminescence, and excitation spectra, in addition to thermal analysis data, of fluorenone in solution and fluorenone/zeolite L are reported. Normal coordinate analysis of fluorenone was performed, based on which IR and Raman bands were assigned, and an experimental force field was determined. The vibrational spectra can be used for nondestructive quantitative analysis by comparing a characteristic dye band with a zeolite band that has been chosen as the internal standard. Molecular orbital calculations were performed to gain a better understanding of the electronic structure of the system and to support the interpretation of the electronic absorption and luminescence spectra. Fluorenone shows unusual luminescence behavior in that it emits from two states. The relative intensity of these two bands depends strongly on the environment and changes unexpectedly in response to temperature. In fluorenone/zeolite L, the intensity of the 300 nm band (lifetime 9 micros) increases with decreasing temperature, while the opposite is true for the 400 nm band (lifetime 115 micros). A model of the host-guest interaction is derived from the experimental results and calculations: the dye molecule sits close to the channel walls with the carbonyl group pointing to an Al3+ site of the zeolite framework. A secondary interaction was observed between the fluorenone's aromatic ring and the zeolite's charge-compensating cations.     

An Analog for the Frattini Factorization of Finite Groups

Using the classification of finite simple groups, we prove that if H is an insoluble normal subgroup of a finite group G, then H contains a maximal soluble subgroup S such that G=HN_G(S). Thereby Problem 14.62 in the Kourovka Notebook is given a positive solution. As a consequence, it is proved that in every finite group, there exists a subgroup that is simultaneously a -projector and a -injector in the class, , of all soluble groups.     

Completeness theorem for propositional probabilistic models whose measures have only finite ranges

A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P_s (with the intended meaning the probability is at least s). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.This research was supported by Ministarstvo za nauku, tehnologije i razvoj Republike Srbije, through Matematiki institut, under grant 1379Mathematics Subject Classification (2000): 03C70, 03B48     

On a Theorem of Høegh-Krohn

A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products , where \mathfraka _t , t are time automorphisms and F _j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F _j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.