C++QED: an object-oriented framework for wave-function simulations of cavity QED systems

We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting qua ntum dynamics in general. The user is provided with a number of “elements”, e.g. pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulations on such systems. A number of tools are provided to facilitate the implementation of new elements.     

Determination of 3-Chloro-4-(Dichloromethyl)-5-Hydroxy-2(5H)-Furanone (Toxicant MX) in Drinking Water by Chromatography–Tandem Mass Spectrometry

It is shown that toxicant MX can be reliably identified and determined quantitatively by ion-trap tandem mass spectrometry with an accuracy as high as that for high-resolution mass spectrometry.     

Application of time-variable feedback to the input amplifier of pulse magnetic resonance spectrometers: Experimental studies

Experimental research on the improvement of the sensitivity and time resolution of pulsed magnetic resonance spectrometers is discussed. It is shown that application of a time-variable feedback of a signal to the input of the receiver amplifier can decouple, the “fixed” relationship between the quality factorQ and the ringdown time of the resonance system. Experiments were performed with low-frequency, radio-frequency and microwave pulse-type magnetic resonance receivers. Modifications of an S/C-band electron spin echo modulation spectrometer carried out to check the “time-variable feedback” performance are described. It is demonstrated that the application of a time-variable feedback can significantly reduce the ringdown time and improve the recovery properties of the magnetic resonance receiver system. It is also demonstrated that the time-variable feedback can improve the overall receiver sensitivity due to the fact that the working bandwidth of the resonance system can be optimized separately for the transmitting and the receiving mode. Signal values could be increased at least three times and the signal-to-noise ratio about 1.5–2 times. The largest improvement is achieved with the initially overcoupled resonator. Experimental spectra of test samples for different settings of the time-variable feedback are shown.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Remark on minimization of depth of Boolean circuits

It is shown that Lozhkin’s method (1981) for minimization of the depth of formulas with a bounded number of changing types of elements in paths from input to output and Hoover-Klawe-Pippenger’s method (technical report in 1981, journal publication in 1984) for minimization of the depth of circuits with unbounded branching by insertion of trees from buffers with bounded branching of outputs for each buffer are dual to each other and can be proved by one and the same method.     

Complex projections of completely positive quaternionic maps

We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007.     

Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions

In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions lying in planes at integer distances 2, 3, 4, …  to the origin. The faces are considered up to the action of the group of integer-linear transformations.