On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions

The purpose of the paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ-convergence of sequences of fuzzy numbers. We establish some connections between these concepts. It is also shown that if a sequence of fuzzy numbers is strongly almost λ-convergent with respect to a sequence of Orlicz funtions then it is almost λ-statistical convergent.     

Sur les solutions extrêmales d'un système incompatible d'équations

Sans résumé     

A linear filtering problem in complete correlated actions

In the last paper, the geometry of the Sz.-Nagy-Foia model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foia theory, is now recognized as the most adequate operatorial form of the deep classical results of the extrapolation theory. The labeling of the exact intertwining dilations given by [1]Acta Sci. Math. (Szeged) 40 9–32] and the recursive methods used there open a broad perspective for using the Sz.-Nagy-Foia model in multivariate filtering theory. In this paper, using the notion of correlated action (see [5 and 6] Rev. Roumaine Math. Pures Appl. 23, No. 9 1393–1423]) as a time domain, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients of an analytic function which describes the cross correlations is given. In some special cases it is shown that the filter coefficients can be determined using recursive methods from the intertwining dilation theory, of the autocorrelation function of the known data and an intertwining operator, interpreted as the initial estimator given by the prior statistics.     

Charge-dependent three-nucleon potential

The charge-dependent three-nucleon potential due to simultaneous photon and pion exchange was derived. The intermediate state of the three-nucleon system was considered to consist of a Δ (1236) resonance. The contribution of this charge-dependent three-nucleon potential to the charge asymmetric energy of ³He−³H is then evaluated using a reasonable trial wave function for a three-nucleon bound system. This contribution turns out to be small but makes the charge asymmetric energy of ³He−³H slightly larger.     

The language of Einstein spoken by optical instruments

The mathematics of Lorentz transformations, called the Lorentz group, continues to play an important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics are largely based on two-by-two matrices or ABCD matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincaré sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations that correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.     

Retention of configuration in the nucleophilic substitution reactions of some nine-membered ansa derivatives of cyclotriphosphazatriene

X-ray crystallographic evidence shows that nucleophilic substitution reactions of two different types of cyclophosphazene derivatives with relatively rigid nine-membered ansa rings leads to the first demonstration of retention of configuration in these molecular systems.     

Photodissociation of CCH: classical trajectory calculations involving seven electronic states

The photodissociation dynamics of ethynyl radical, C(2)H, involving seven electronic states is studied by classical trajectory calculations. Initial values of the trajectories are selected based on relative absorption intensities calculated by Mebel et al. The energies and the derivatives are interpolated by three-dimensional cubic spline interpolator using an extended data pool. Mean square errors and standard deviations in interpolation of energies for 450 data points are found to be in the range 3.1 x 10(-6)-1.4 x 10(-5) and 1.7 x 10(-3)-3.8 x 10(-3) hartrees, respectively. The photofragments of C(2) and H are produced mainly in the X (1)Sigma(g) (+), a (3)Pi(u), b (3)Sigma(g) (-), c (3)Sigma(u) (+), A (1)Pi(u), B (1)Delta(g) electronic states of C(2) as product. The avoided crossings do not appear to be in the main dissociation pathways. The internal distributions are in good accord with the experimental results where comparison is possible, suggesting that the fragmentation mechanism of C(2)H(2) into C(2) and H is a two step process involving C(2)H radical as an intermediate with a life time long enough to allow complete collection of the phase space in the experiments.