Pullback Attractors for Stochastic Young Differential Delay Equations

We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term which has no delay factor and has eigenvalues of negative real parts, then the generated random dynamical system possesses a random pullback attractor provided that the Lipschitz coefficients of the remaining parts are small.

     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Evidence of lanthanum–chromium mixed oxides formed in CrOx/La2O3 model catalysts

CrO_x/La₂O₃ mixed oxides, prepared by impregnating La₂O₃ with appropriate aqueous solutions of (NH₄)₂CrO₄ and calcining at 600 °C for 4 h, have been investigated by means of XRD, TPR, XPS, DRIFTS, and Raman spectroscopy (RS). The formation of the compounds La₂CrO₆, La(OH)CrO₄ and LaCrO₄ under these conditions was evidenced. Strong peaks at 864, 884, 913, and 921 cm⁻¹, as well as weak peaks at 136, 180, 354, 370, and 388 cm⁻¹ in the RS spectrum of CrO_x/La₂O₃ have been assigned to La₂CrO₆.     

Optical modes in nanoscale one-dimensional spin chains

The spin chain systems with one-dimensional magnetic ordering are promising candidates for quantum optical devices. This paper shows how the optical excitation can induce various phonon modes in an ideal Cu-O chain at various lengths. The calculation was carried out at different level theories including configuration interaction singles for excited states, density functional theory and second-order Möller-Plesset perturbation. In general, the number of modes increases with chain length due to growing asymmetry of atomic positions when chain exceeds 5 nm. There were, however, only two basic modes: one is associated with the symmetric oscillation of oxygen and another with the asymmetric motion of the same along the chain. At the length below 4.3 nm, the Raman activity of the symmetric mode (440 cm⁻¹) dominates. From analysis of density of states, this mode may be associated with the excitation across the lowest LUMO bands with changing in spin state.     

Combinatorial study of colored Hurwitz polyzêtas

A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyzêtas. The combinatorial aspects of the products and co-products involved in these algebras will be examined.     

Dalitz analysis of D0-->K(0)(S)pi(+)pi(-)

In e(+)e(-) collisions using the CLEO detector, we have studied the decay of the D0 to the final state K(0)(S)pi(+)pi(-) with the initial flavor of the D0 tagged by the decay D(*+)-->D0pi(+). We use the Dalitz technique to measure the resonant substructure in this final state and clearly observe ten different contributions by fitting for their amplitudes and relative phases. We observe a K(*)(892)(+)pi(-) component which arises from doubly Cabibbo suppressed decays or D0-D0; mixing.     

Observation of B-->K(0)(S)pi(+)pi(-) and Evidence for B-->K(*+/-)pi(-/+)

We report on a search for charmless hadronic B decays to the three-body final states K(0)(S)h(+)pi(-), K(+)h(-)pi(0), K(0)(S)h(+)pi(0) (h(+/-) denotes a charged pion or kaon), and their charge conjugates, using 13.5 fb(-1) of integrated luminosity produced near sqrt[s]=10.6 GeV, and collected with the CLEO detector. We observe the decay B-->K0pi(+)pi(-) with a branching fraction (50(+10)(-9)(stat.)+/-7(syst.))x10(-6) and the decay B-->K(*+)(892)pi(-) with a branching fraction (16(+6)(-5)(stat.)+/-2(syst.))x10(-6).     

Synthesis of 5-aroylamino-3H-1,3,4-thiadiazole-2-thiones and their tautomerism

5-Aroylamino-3H-1,3,4-thiadiazole-2-thiones 2 have been synthesized by acylation of 5-amino-3H-1,3,4-thiadiazole-2-thione 1 . 5-Aroylamino-3H-1,3,4-thiadiazole-2-thiones can exist in two tautomeric forms — a thiol form and a thione form. On the basis of the ¹³C nmr spectra and additional experimental information, it has been established that the thione form is the stable form in which these compounds exist.     

Decoherence in josephson phase qubits from junction resonators

Although Josephson junction qubits show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. Improving the operation of a Josephson junction based phase qubit has revealed microscopic two-level systems or resonators within the tunnel barrier that cause decoherence. We report spectroscopic data that show a level splitting characteristic of coupling between a two-state qubit and a two-level system. Furthermore, we show Rabi oscillations whose "coherence amplitude" is significantly degraded by the presence of these spurious microwave resonators. The discovery of these resonators impacts the future of Josephson qubits as well as existing Josephson technologies.