Quantum measurement II

Some of the basic results of the quantum theory of measurement are reviewed and an application of the theory of sequential measurements to a determination of a geometric phase in a measurement cycle is discussed.     

An evaluation of some sodium ion-selective glass electrodes in aqueous solution: Part I. Electrode calibration characteristics and selectivity with respect to hydrogen ions

Some properties of a series of commercial sodium ion-selective electrodes have been investigated and the results compared. In general the potential response of the electrodes was found to approach Nernstian with aging.An improved method for investigating the selectivity of ion-selective electrodes with respect to hydrogen ions is based on the mixed solution method utilizing tris buffers. The selectivity of the sodium ion electrodes with respect to hydrogen ions was also found to depend on the ratio of the primary to interfering ion activity. Some other improvements in technique are also reported.     

Synthesis and characterization of core-shell europium(III)-silica nanoparticles

Luminescent core-shell europium(III)-silica nanoparticles were prepared using europium(III) chelate core structure and polyvinylpyrrolidone synthesis strategy for silica shell. Europium(III):naphtoyltrifluoroacetone:trioctylphosphineoxide complex was spontaneously agglomerated from organic solvent to water. Polyvinylpyrrolidone was adsorbed onto the core structure and stable silica shell was synthesized using tetraethylorthosilicate. Nanosized particles with a diameter of 71 ± 5 nm and 11 nm shell thickness were obtained with fluorescence decay rate of 517 μs and excitation and emission wavelengths of 334 and 614 nm, respectively.     

Magnetic-field-induced quadrupole splitting in gaseous and liquid 131Xe NMR: quadratic and quartic field dependence

A theory for the magnetic-field-dependent quadrupole splitting in the 131Xe NMR spectra in isotropic media is presented and tested by ab initio electronic structure calculations. Evidence exists only for even-power magnetic field dependence. The dominant mechanism is verified to be the electric field gradient caused by the diamagnetic distortion of the atomic electron cloud, quadratic in the magnetic field. The computed results are in excellent agreement with the recent experiment by Meersmann and Haake.     

Heisenberg's uncertainty principle

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.     

A Multiobjective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, nonlinearities, and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this article introduces the multiobjective genetic algorithm for variable selection (MOGA-VS) that provides the user with an optimal set of regression models for a given dataset. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision-making process is executed which allows the user to choose the most preferred model using visualizations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime Within the United States.