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.     

Tripeptides adopt stable structures in water. A combined polarized visible Raman,FTIR, and VCD spectroscopy study

We have measured the band profile of amide I in the infrared, isotropic, and anisotropic Raman spectra of L-alanyl-D-alanyl-L-alanine, acetyl-L-alanyl-L-alanine, L-vanyl-L-vanyl-L-valine, L-seryl-L-seryl-L-serine, and L-lysyl-L-lysyl-L-lysine at acid, neutral, and alkaline pD. The respective intensity ratios of the two amide I bands depend on the excitonic coupling between the amide I modes of the peptide group. These intensity ratios were obtained from a self-consistent spectral decomposition and then were used to determine the dihedral angles between the two peptide groups by means of a recently developed algorithm (Schweitzer-Stenner, R. Biophys. J. 2002, 83, 523-532). The validity of the obtained structures were checked by measuring and analyzing the vibrational circular dichroism of the two amide I bands. Thus, we found two solutions for all protonation states of trialanine. Assuming a single conformer, one obtains a very extended beta-helix-like structure. Alternatively, the data can be explained by the coexistence of a 3(1)(PII) and a beta-sheet-like structure. Acetyl-L-alanyl-L-alanine exhibits a structure which is very similar to that obtained for trialanine. The tripeptide with the central D-alanine adopts an extended structure with a negative psi and a positive phi angle. Trivaline and triserine adopt single beta(2)-like structures such as that identified in the energy landscape of the alanine dipeptide. Trilysine appears different from the other investigated homopeptides in that it adopts a left-handed helix which at acid pD is in part stabilized by hydrogen bonding between the protonated carboxylate (donor) and the N-terminal peptide carbonyl. Our result provides compelling evidence for the capability of short peptides to adopt stable structures in an aqueous solution, which at least to some extent reflect the intrinsic structural propensity of the respective amino acids in proteins. Furthermore, this paper convincingly demonstrates that the combination of different vibrational spectroscopies provides a powerful tool for the determination of the secondary structure of peptides in solution.     

Giant improvement of time-delayed feedback control by spatio-temporal filtering

Control of spatio-temporal chaos by the time-delay autosynchronization method is improved by several orders of magnitude. Unstable time periodic patterns are efficiently stabilized if one employs filters and couplings which originate from the Floquet eigenvalue problem of the unstable orbit. We illustrate our scheme by an application to a globally coupled reaction-diffusion model which describes charge transport in semiconductor devices.     

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.