Ein etwas modificirtes Calcimeter

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On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

Necessary stationary condition for polarized radiation in scattering media

The stationary condition is derived taking into account the polarization of radiation in the general case of a scattering inhomogeneous medium in an arbitrary-shape emitter. The necessary stationary condition for an emitter in which radiation is emitted and extinguished simultaneously is complete extinction of the entire emitted radiation. Radiation extinction as a result of absorption by the medium and the emergence of radiation from the emitter is analyzed. The stationary condition is an analytical form of writing that extinction of radiation is a sure event whose probability is equal to unity. The passage of radiation through the medium is described on the basis of the linear transport theory with the help of the matrices of the Green functions. The stationary condition includes the characteristics of polarized radiation extinction of which is analyzed, the absorption coefficients of the medium, and the elements of the matrices of the Green functions, which are determined by optical and geometrical parameters of the emitter. The stationary condition obtained is used for deriving the relations between the components of scalar intensity observed in an arbitrary region of the emitter. These relations include, in addition to the absorption coefficients and the matrix elements of the Green functions, the powers of the primary radiation. Possible applications of the stationary condition and the relations between intensity components in computations and experimental studies are considered.     

ON THE ACOUSTIC ABSORPTION OF MULTI-LAYER ABSORBERS WITH DIFFERENT INNER STRUCTURES

A rigorous finite element analysis procedure is developed to study the effect of the inner structures on the acoustic absorption of multi-layer absorbers. To do this, four types of basic inner structure compartments adopted in the multi-layer absorbers are selected for analysis. These compartments are composed of porous materials inlaid with perforated plates of various shapes, say, triangle, semicircle, convex rectangle and plate shapes. As it is different from the conventional finite element analysis for the acoustic system in the literature, the perforated plates are simulated by appropriate equivalent boundary conditions, depending on their thickness, hole radius, hole pitch and porosity and the air contained in the holes. A large number of total degrees of freedom generated from meshing the air in the holes of perforated plates are thus avoided. The results reveal that the inner structures of the multi-layer absorbers will influence the acoustic absorption at some frequency bands significantly. Based on those features, the multi-layer absorber with a novel inner structure is then designed and manufactured. Both the finite element and experimental results show that its acoustic absorption would be distinctly promoted.     

Entangled Bell states of two electrons in coupled quantum dots—phonon decoherence

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned self assembled quantum dots by studying the dynamics of two interacting electrons driven by external electric field. The present entanglement involves the spatial degree of freedom for the two electrons system. We show that system of two interacting electrons initially delocalized (localized each in one dot) oscillate slowly in response to electric field, since the strong Coulomb repulsion makes them behaving so. We use an explicit formula for the entanglement of formation of two qubit in terms of the concurrence of the density operator. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, real quantum systems will inevitably be influenced by surrounding environments. We discuss the degree of entanglement of this system in which we introduce the decoherence effect caused by the acoustic phonon. In this entangled states proposal, the decohering time depends on the external parameters.     

Sulphide based anode material for lithium rechargeable battery

In this study, lead sulphide (PbS) was prepared by the chemical bath deposition technique. The sample was characterized by X-ray diffraction (XRD), Energy Dispersive Analysis of X-rays (EDAX) and cyclic voltammetry. EDAX spectrum shows peaks attributable to lead and sulphur. The EDAX analysis also shows that the prepared sample is stoichiometric. Cyclic voltammetry experiments were recorded at 100 mV·s⁻¹ and 400 mV·s⁻¹ scan rates. Results show that the rate controlling electrochemical reaction is electron transfer. The presence of redox waves shows that the lithium intercalation and deintercalation can occur as a result of lattice expansion in PbS. There were no differences in the PbS XRD data before and after the cyclic voltammetry experiments indicating that the PbS structure is not modified upon lithium ion intercalation and deintercalation in PbS. The discharge characteristics for 35 cycles of the cell using the LiCoO₂/PbS couple is presented indicating the possible development of such materials as anode in lithium ion cells.     

Long-wavelength optical phonons in the ZnTe/Zn<Subscript>0.8</Subscript>Cd<Subscript>0.2</Subscript>Te superlattice

The lattice IR reflection spectra of a ZnTe/Zn_0.8Cd_0.2Te superlattice measured at temperatures of 300 and 10 K are analyzed. The ZnTe/Zn_0.8Cd_0.2Te superlattice is grown by molecular-beam epitaxy on a GaAs substrate with a ZnTe buffer layer. It is found that the lattice IR reflection spectra of the studied structure exhibit only one reflection band. Dispersion analysis of the experimental spectrum has revealed the presence of one lattice TO mode close in frequency to the mode of pure ZnTe. This result is explained by a shift in the frequency of the lattice modes of the ZnTe and Zn_0.8Cd_0.2Te layers of the superlattice toward each other. In turn, this shift is caused by internal elastic stresses in the superlattice due to a mismatch between the lattice parameters of the materials of these layers.     

Waves in multilayer ferrite-dielectric transversely magnetized waveguides with an electrically controlled slowing factor

Multilayer wave-guiding structures comprising transversely magnetized ferrites are studied. A numerical theoretical model is constructed with the Galerkin method. An experimental investigation technique is developed. Theoretical and experimental results are found to be in good agreement. Such structures offer a high phase activity and may provide a basis for small-size millimeter-wave phase shifters and a new class of antenna systems, namely, integrated phased arrays.     

Grain-boundary diffusion in nanocrystals with a time-dependent diffusion coefficient

A solution to the equation of grain-boundary diffusion is obtained under conditions where migration of the diffusant from the boundaries into the grains is absent and the diffusion coefficient decreases with time from an increased value to a value characteristic of equilibrium grain boundaries. The specific features of the grain-boundary diffusion in nanocrystals are qualitatively analyzed in terms of this solution.     

Beryllium (boron) clustering quest in relativistic multifragmentation (BECQUEREL Project)

A physical program of irradiation of emulsions in beams of relativistic nuclei named the BECQUEREL Project is reviewed. It is destined to study in detail the processes of relativistic fragmentation of light radioactive and stable nuclei. The expected results would make it possible to answer some topical questions concerning the cluster structure of light nuclei. Owing to the best spatial resolution, the nuclear emulsions would enable one to obtain unique and evident results. The most important irradiations will be performed in the secondary beams of He, Be, B, C, and N radioactive nuclei formed on the basis of JINR Nuclotron beams of stable nuclei. We present results on the charged state topology of relativistic fragmentation of the ¹⁰B nucleus at low energy-momentum transfers as the first step of the research.