Control of de-excitation to selected vibrational levels in the ground state of NaH molecule using two broadband ultrashort pulses

We show that the de-excitation to different vibrational levels of the ground state in NaH molecule can be controlled by using two delayed ultrashort pulses (4 fs Gaussian). A vibrational wave packet generated on the excited A¹Σ⁺ state by the first pulse is de-excited back to the ground state by a second pulse after a time delay. The cross-section for de-excitation of the wave packet to different vibrational levels of the ground electronic state can be controlled by controlling the delay time between the two pulses as well as by choosing a pulse duration much shorter than the vibrational period of the molecule, such that the de-excited wave packet remains localized in the Franck–Condon region of a particular vibrational level of the ground state. Hence, the de-excitation to a particular vibrational level can be enhanced by suppressing that in others. In spite of the large bandwidth of the pulse which includes nine vibrational levels of the upper state and five vibrational levels of the ground state, one can selectively de-excite the molecule to any one or two vibrational levels of the ground state by carefully choosing the delay time between the pulses and the pulse duration. We are designing the wave packet in the ground state by two short pulses and selectively distributing the population in one or two levels at various values of the delay time. In light molecules having small vibrational period, this selectivity in de-excitation to one or two vibrational levels in the ground state can be achieved only by using ultrashort (4 fs) pulses in the presence of which the localization of the wave packet in the Franck–Condon region of the vibrational levels are particularly possible. It has been shown that the de-excitation cross-section to a particular vibrational level oscillates with delay between the pulses which can be realized as a time-dependent quantum gate.     

Localization and Screening Enhancement in Asymmetric Binary Ionic Mixtures

The equation of state of binary ionic mixtures of similar ions, such as nitrogen, oxygen and carbon, has been extensively studied. The study of dense asymmetric mixtures, where Z₂ >> Z₁, has primarily focused on mixtures of hydrogen and iron at solar conditions. Using molecular dynamics simulations, we examine the behavior of highly asymmetric binary ionic mixtures, where the coupling of the high‐Z species may be orders of magnitude higher than the coupling of the low‐Z species. For the conditions we have studied, we find that strong correlations and signatures of solidification occur in the high‐Z species, while the low‐Z species exists as a freely flowing fluid within the high‐Z solid matrix. Solidification of the low‐Z species is correlated with the coupling between the two components. Using the Widom expansion method, we compute the plasma screening enhancement of the nuclear reaction rates for Z = 1 in a high‐Z matrix. We also provide some estimates of the coefficient of binary diffusion in the mixture. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.     

New insights on the origins of the stereocontrol of the staudinger reaction: [2 + 2] cycloaddition between ketenes and N-silylimines

Density-functional theory studies on the [2 + 2] reaction between N-silylimines and ketenes to form the corresponding 2-azetidinones (beta-lactams) help to clarify several aspects on the mechanism of the Staudinger reaction. This reaction has been studied experimentally by Panunzio et al. It is shown that the formation of the 2-azetidinone ring takes place via two consecutive reactions. The first reaction consists of the nucleophilic addition of the iminic nitrogen to the sp-hybridized carbon atom of the ketene, with simultaneous migration of the silyl group from the imine to the oxygen atom of the ketene. This leads to silyl enol intermediates, in good agreement with the experimental results. Formation of the N-silylated beta-lactam takes place via a domino reaction consisting of a conrotatory thermal electrocyclization followed by a new silatropic rearrangement. It is also found that isomerization of the starting N-silylimine has a lower activation barrier than that associated with the formation of the C-N bond, which explains the stereochemical outcome experimentally observed. Further considerations on the asymmetric torquoelectronic effects involved in this reaction are also reported.     

Thermoluminescent a-CN thin films properties as a function of plasma parameters

Amorphous carbon nitride (a-CN) thin films show luminescent properties that are of interest for many applications. Particularly interesting are their previously reported thermoluminescent characteristics. In order to optimize these properties, the plasma parameters (ion energy, plasma density and type of excited species) were studied in the present work as a function of the laser fluence and the working pressure. The plasma was produced using the fundamental line of a Nd:YAG laser with 28 ns pulse duration focused on a high purity graphite target. The laser fluences used in this work could be varied between 9 and 40 J/cm². Measurements and deposition of a-CN films were carried out in a nitrogen atmosphere at pressures from 3×10^-3 to 7.5×10^-2 Torr. We observed an optimum value of pressure, close to 7.5×10^-2 Torr, in which the nitrogen incorporation into the film achieved its maximum value close to 29 at.% and the thermoluminescent response of the material, after irradiation with UV becomes evident. PACS 81.15.Fg; 78.60.Kn; 81.05.Uw     

Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations

We prove a local existence and uniqueness theorem for abstract parabolic problems of the type when the nonlinearity satisfies certain critical conditions. We apply this abstract result to the Navier-Stokes and heat equations.

     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Polynomials: a theme which should not be forgotten

There is a definite movement to remove many of the topics concerning polynomials from the school curriculum. The purpose of this paper is to point out why this movement is misguided and should be reversed.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.