Noise effect on Grover algorithm

The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is directly related to the quantum network construction. The numerical simulation concludes an exponential damping law for the successive probability of the maxima as time increases. We have obtained an allowed-error law for the algorithm: the error threshold for the allowed noise behaves as ε_th(N) ∼1/N^1.1 (N being the size of the data set). As the power of N is almost one, we consider the Grover algorithm as robust to a certain extent against decoherence. This law also provides an absolute threshold: if the free evolution error is greater than 0.043, Grover algorithm does not work for any number of qubits affected by the present error model. The improvement in the probability of success, in the case of two qubits has been illustrated by using a fault-tolerant encoding of the initial state by means of the [[7,1,3]] quantum code.     

Exact Potts Model Partition Functions for Strips of the Square Lattice

We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex square-lattice strip graphs G for a variety of transverse widths L _t and for arbitrarily great length L , with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form Z(G, q, v)= . We give general formulas for N _{Z, G, j} and its specialization to v=–1 for arbitrary L _t for both types of boundary conditions, as well as other general structural results on Z. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite square lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus , arising as the accumulation set of partition function zeros as L , in the q plane for fixed v and in the v plane for fixed q.     

Development of a capillary zone electrophoretic method to determine six antidepressants in their pharmaceutical preparations. Experimental design for evaluating the ruggedness of method

A capillary zone electrophoresis method is proposed for the separation of six of the antidepressants most used for the treatment of mental illness (clomipramine, paroxetine, fluoxetine, citalopram, fluvoxamine, and trazodone). Optimum conditions for their separation were investigated. A background electrolyte solution consisting of 50 mM phosphate buffer adjusted to pH 2.0, hydrodynamic injection, and 25 kV as separation voltage were used. Relative standard deviations (RSD) were <0.38% and <2.93% for migration time and corrected peak area (n = 24), respectively. Detection limits obtained for the six antidepressants ranged from 0.03 to 0.11 mg L(-1). Stability of the solutions, linear concentration range, accuracy, and precision were examined during validation of the method. A ruggedness test of this method was performed using the fractional factorial model of Plackett-Burman, requiring in our case design of a matrix of 15 experiments, in which the influence of seven factors at three different levels was tested on different electrophoretic results: efficiency; resolution; and corrected peak area. Statistical evaluation of electrophoretic results was achieved by Youden and Steiner's method. The described method is rapid, sensitive, and rugged and it was tested for the pharmaceutical formulation analysis, giving recoveries between 95.6 and 99.1% with respect to the nominal content.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. II. Extended Results for Square-Lattice Chromatic Polynomial

We study the chromatic polynomials for m×n square-lattice strips, of width 9m13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.     

Synthesis and characterization of new complexes of the type [Ru(CO)2Cl2 (2‐phenyl‐1,8‐naphthyridine‐kN) (2‐phenyl‐1,8‐naphthyridine‐kN′)]. Preliminary applications in homogeneous catalysis

Novel ruthenium (II) complexes were prepared containing 2‐phenyl‐1,8‐naphthyridine derivatives. The coordination modes of these ligands were modified by addition of coordinating solvents such as water into the ethanolic reaction media. Under these conditions 1,8‐naphthyridine (napy) moieties act as monodentade ligands forming unusual [Ru(CO)₂Cl₂(η¹‐2‐phenyl‐1,8‐naphthyridine‐ kN )(η¹‐2‐phenyl‐1,8‐naphthyridine‐kN′)] complexes. The reaction was reproducible when different 2‐phenyl‐1,8‐naphthyridine derivatives were used. On the other hand, when dry ethanol was used as the solvent we obtained complexes with napy moieties acting as a chelating ligand. The structures proposed for these complexes were supported by NMR spectra, and the presence of two ligands in the [Ru(CO)₂Cl₂(η¹‐2‐phenyl‐1,8‐naphthyridine‐ kN )(η¹‐2‐phenyl‐1,8‐naphthyridine‐kN′)] type complexes was confirmed using elemental analysis. All complexes were tested as catalysts in the hydroformylation of styrene showing moderate activity in N,N′‐dimethylformamide. Copyright © 2008 John Wiley & Sons, Ltd.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

Microbial transformation of marine halogenated sesquiterpenes

The sesquiterpene pacifenol is one of the main constituents of the red alga Laurencia claviformis. Earlier work on the semisynthetic derivatives of pacifenol afforded a series of halogenated sesquiterpenes. The aim of the present work was to obtain new hydroxylated derivatives of halogenated sesquiterpenes by means of microbial transformation using Aspergillus niger, Gibberella fujikuroi and Mucor plumbeus. The best results were obtained with M. plumbeus. The microbiological transformation by M. plumbeus of pacifenol, and two semisynthetic derivatives, is described. The structures of the new compounds obtained were determined by spectroscopic means.     

Finite-temperature phase transition in a class of four-state Potts antiferromagnets

We argue that the four-state Potts antiferromagnet has a finite-temperature phase transition on any Eulerian plane triangulation in which one sublattice consists of vertices of degree 4. We furthermore predict the universality class of this transition. We then present transfer-matrix and Monte?Carlo data confirming these predictions for the cases of the Union Jack and bisected hexagonal lattices.