Majoration de sommes trigonométriques modulo pn

We give a generic estimation of trigonometric sums defined over closed sub-schemes with semi-stable reduction of the standard affine scheme modulo pn(n 2). We use Greenberg realisation to reduce to trigonometric sums defined over smooths sub-schemes of a finite product of Witt vectors over the finite field of p elements. Using the cohomological interpretation of this sums over a finite field, the sum is directly related to the Fourier–Deligne transformation of the dual pairs of Witt vectors. We deduce the estimation from the properties of the Fourier–Deligne transformation on simple perverse sheaves and pure sheaves.     

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation.     

A novel, neutral hydroxylated octadecyl acrylate monolith with fast electroosmotic flow velocity and its application to the separation of various solutes including peptides and proteins in the absence of electrostatic interactions

A neutral hydroxylated octadecyl monolith (ODM-OH) for reversed-phase capillary electrochromatography has been developed. The ODM-OH was prepared by the in situ polymerization of octadecyl acrylate and pentaerythritol triacrylate (PETA) in a ternary porogenic solvent. Pentaerythritol triacrylate possesses a hydroxyl functional group, which imparts the monolith with a hydrophilic group, thus the acronym ODM-OH. The ODM-OH column exhibited cathodal EOF over a wide range of pH and ACN concentration in the mobile phase despite the fact that it was devoid of any fixed charges. This ODM-OH monolith exhibited stronger EOF than its counterpart the ODM made from the in situ polymerization of octadecyl acrylate and trimethylolpropane trimethacrylate. Similar to ODM, it is believed that the EOF was due to the adsorption of ions from the mobile phase onto the surface of the monolith thus imparting the neutral monolithic column the zeta potential necessary to support the EOF. The higher EOF exhibited by ODM-OH was due to the presence of polar OH groups on its surface, which would favor stronger adsorption of ions from the mobile phase. The wide applications of the neutral ODM-OH column were demonstrated in the separation of a wide range of small and large solutes. As a typical result, the ODM-OH was able to separate proteins quite rapidly yielding 200,000 plates/m.     

Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor

We report the implementation of a 3-qubit quantum error-correction code on a quantum information processor realized by the magnetic resonance of carbon nuclei in a single crystal of malonic acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high-fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test bed for the implementation of quantum algorithms.     

Symmetry group analysis and similarity solutions for the (2+1)‐dimensional coupled Burger's system

Symmetry group analysis and similarity reduction of nonlinear system of coupled Burger equations in the form of nonlinear partial differential equation are analyzed via symmetry method. The symmetry method has led to similarity reductions of this equation to solvable form to third‐order partial differential equation. The infinitesimal, similarity variables, dependent variables, and reduction have been tabulated. The search for solutions of these systems by using the improved tanh method has yielded certain exact solutions expressed by rational functions. Some figures are given to show the properties of the solutions. Copyright © 2013 John Wiley & Sons, Ltd.