The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).     

Fluctuating hydrodynamics and principal oscillation pattern analysis

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x_i(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t) _j (t*Q _ij (t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection.     

Plasma-driven inflation

The possibility of inflation without any genuine scalar is discussed. It is suggested that drops of primordial plasma may drive inflation. The model, although naive, is consistent with observational data.     

Sufficiency and fuzziness in random experiments

In previous papers, the consequences of the “presence of fuzziness” in the experimental information on which statistical inferences are based were discussed. Thus, the intuitive assertion «fuzziness entails a loss of information» was formalized, by comparing the information in the “exact case” with that in the “fuzzy case”. This comparison was carried out through different criteria to compare experiments (in particular, that based on the “pattern” one, Blackwell's sufficiency criterion). Our purpose now is slightly different, in the sense that we try to compare two “fuzzy cases”. More precisely, the question we are interested in is the following: how will different “degrees of fuzziness” in the experimental information affect the sufficiency? In this paper, a study of this question is carried out by constructing an alternative criterion (equivalent to sufficiency under comparability conditions), but whose interpretation is more intuitive in the fuzzy case. The study is first developed for Bernoulli experiments, and the coherence with the axiomatic requirements for measures of fuzziness is also analyzed in such a situation. Then it is generalized to other random experiments and a simple example is examined.     

Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

Discontinuities in the specific heat of magnesium and associated latent heat at pressure-induced structural phase transitions using a local first principles pseudopotential

After a successful application of a local first principles pseudopotential to the study of the structural pressure-induced phase transition for magnesium, I now use the same local first principles type of pseudopotential, to study the specific heat as function of the pressure, at 300 K, in the region around the predicted phase transitions. I found that the specific presents two discontinuities, one for each transition of phase. These discontinuities are associated to the existence of latent heat at each transition, which has not been yet reported experimentally.     

Trading by Quantum Rules: Quantum Anthropic Principle

This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is discussed and Quantum Anthropic Principle is put forward. The review is addressed to nonspecialists.     

Pulsed-field gradient nuclear magnetic resonance study of transport properties of fluid catalytic cracking catalysts

Pulsed-field gradient nuclear magnetic resonance (PFG NMR) has been applied to study molecular diffusion in industrial fluid catalytic cracking (FCC) catalysts and in USY zeolite for a broad range of molecular displacements and temperatures. The results of this study have been used to elucidate the relevance of molecular transport on various displacements for the rate of molecular exchange between catalyst particles and their surroundings. It turned out that this rate, which may determine the overall rate and selectivity of FCC process, is primarily related to the diffusion mode associated with displacements larger than the size of zeolite crystals located in the particles but smaller than the size of the particles. This conclusion has been confirmed by comparative studies of the catalytic performance of different FCC catalysts.     

A reanalysis of branching fractions of charmed mesonsD 0,D + andD s +

We combine highly complementary information on branching fractions of charmed mesonsD ⁰,D ⁺ andD _s ⁺ coming from two experiments both yielding doublecharm samples. The NA 32 experiment provided exclusive branching fractions for channels with at least two charged decay products while a recent Mark III paper provides results on inclusive charm decay properties. The knowledge of channels withK ⁰'s in the former is used to recalculate the charged multiplicity distribution in the latter. We obtain 〈n _ch〉=2.25±0.08 forD ⁰, 〈n _ch〉=1.96±0.08 forD ⁺ and 〈n _ch〉=2.41±0.38 forD _s ⁺ . In turn the knowledge of the charged multiplicity improves the overall normalization of exclusive branching fractions. This reanalysis yields model-independent results for charmed mesons. In particular we obtain branching fractions for 16D _s ⁺ decay channels including $$BF(D_s^ + \to \phi \pi ^ + ) = \left( {4.4\begin{array}{*{20}c} { + 2.3} \\ { - 1.8} \\ \end{array} } \right)\% .$$ .     

The new method of fabrication of submicron structures by optical lithography with mask shifting and mask rotation

This paper presents the methods of fabricating narrow parallel submicrometric stripes in silicon dioxide and a resist layer. The experiments were conducted by two techniques: double patterning lithography and double exposure lithography. In addition to the above mentioned processes, mask translation was applied. For all conducted experiments, chrome masks and a 405 nm line of the high pressure mercury lamp of an MA-56 Mask Aligner System were used. The main aim of the performed tests was to establish the utility and the possible applications of the methods used.