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.     

Polymer-assisted complexing controlled orientation growth of ZnO nanorods

The growth of the oriented zinc oxide (ZnO) nanorods on silicon substrates based on a simple novel chemical transformation and thermal hydrolysis by using polyvinyl alcohol (PVA) as self-assembling complex polymer was introduced in this paper. All the polymers were removed after chemical oxidation and only the carbonized grid backbones remained that confines the ZnO nanorod’s diameter and enhance the absorption and diffusion of ZnO at the tips of the nanorods during growth. The ZnO nanorods are investigated by FTIR, XRD and FE-SEM. The results indicated that these nanorods have fine hexagonal wurtzite crystal structure and their diameter varies from 20 to 90 nm and the length up to about 1 μm. A polymer-localized ZnO growth model is proposed, which well explains the growth behavior of ZnO nanorods.This revised version was published online in August 2005 with a corrected issue number.     

Search for lepton flavor violation in the decay tau+/- --> mu+ gamma

A search for the nonconservation of lepton flavor number in the decay tau(+/-) --> mu(+/-) has been performed using 2.07 x 10(8) e(+ )e(-) tau(+) tau(-) events produced at a center-of-mass energy near 10.58 GeV with the BABAR detector at the PEP-II storage ring. We find no evidence for a signal and set an upper limit on the branching ratio of Beta(tau(+/-) --> mu(+/-) gamma) < 6.8 x 10(-8) at 90% confidence level.     

Limit on the B0-->rho0rho0 branching fraction and implications for the Cabibbo-Kobayashi-Maskawa angle alpha

We search for the decay B0-->rho(0)rho(0) in a data sample of about 227x10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at SLAC. We find no significant signal and set an upper limit of 1.1x10(-6) at 90% C.L. on the branching fraction. As a result, the uncertainty due to penguin contributions on the Cabibbo-Kobayashi-Maskawa unitarity angle alpha measured in B-->rhorho decays is decreased to 11 degrees at 68% C.L.     

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.     

Direct numerical simulation of passive scalar in decaying compressible turbulence

1IntroductionDirectnumericalsimulation(DNS)becomesanimportanttoolinrecentresearchofturbulence[1].DNSofcompressibleturbulenceismoredifficultthanthatoftheincompressibleturbulence.WhentheturbulentMachnumberisgreaterthan0.3theshockletsmayappearinthecompressibleturbulentflowfields.Thereasonandmechanismofshockletsexistencearenotclearyet.TheturbulentMachnumberinDNScannotbeveryhighwiththepresentexistingnumericalmethodsandcomputerresource.Fortheproblemofcompressibleisotropicturbulencewiththeinitia…     

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.     

⊕-Cofinitely Supplemented Modules

Let R be a ring and M a right R-module. M is called -cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is -cofinitely supplemented. In addition, if M has the summand sum property, then M is -cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M.