Optimal partitioning of a measurable space into countably many sets

Summary A notion of an optimal partition of a measurable space into countably many sets according to given nonatomic probability measures is defined. It is shown that the set of optimal partitions is nonempty. Bounds for the optimal value are given and the set of optimal partitions is characterized. Finally, an example related to statistical decision theory is presented.     

Scattering matrix in conformal geometry

Inventiones mathematicae -     

Harmonic functions of polynomial growth on certain complete manifolds

Given a complete manifold with a particular structure at infinity, we give the dimension of the space of harmonic functions with prescribed polynomial growth.     

Metal nanowires fabricated by means of magnetostrictive actuator

A new method of fabricating nanowires for electric conductance quantization studies is proposed as an alternative to the method based on converse piezoelectric effect. Commonly used for nanowire fabrication, piezoelectric actuators are expensive and require high-level voltage control signal. The method presented in this paper is based on the use of magnetostrictive actuator. Both the actuator structure and the method of the conversion factor measurement are discussed. The results of the tests of the magnetostrictive actuator are also reported. The parameters of the proposed actuator are compared with those of its piezoelectric counterpart used to date. The results of measurement confirm that the proposed actuator can be used for studying electric conductance quantization in nanowires. Presented at the X-th Symposium on Surface Physics, Prague, Czech Republic, July 11–15, 2005     

Differential equation for the generalized Bell function

The generalized Bell function is introduced and an ordinary differential equation which it obeys is derived.     

Degradation of the Giant Magnetoresistance in Fe/Cr Multilayers Due to Ar-Ion Beam Mixing

The influence of 200 keV Ar-ion irradiation on the interlayer coupling in the Fe/Cr multilayer system exhibiting the giant magnetoresistance effect (GMR) is studied by conversion electron Mössbauer spectroscopy (CEMS), VSM hysteresis loops, magnetoresistivity and electric resistivity measurements and supplemented by the small-angle X-ray diffraction (SAXRD). The increase of Ar ion dose causes an increase of interface roughness, as evidenced by the increase of the Fe step-sites detected by CEMS as a result of which the GMR gradually decreases and vanishes at doses exceeding 1×10¹⁴ Ar/cm². A degradation of GMR with increasing Ar-ion dose is related to the formation of pinholes between Fe layers and the decrease of the antiferromagnetically coupled fraction.

     

Shift of the shadow boundary in high frequency scattering

The microlocal theory of diffraction is used to establish the conjecture of Keller and Rubinow relating the shift of the shadow boundary in high frequency scattering to the directional curvatures of a strictly convex obstacle.     

Trapped ion chain as a neural network: error resistant quantum computation

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such a network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems.     

Bulk derivatization and cation exchange restricted access media-based trap-and-elute liquid chromatography–mass spectrometry method for determination of trace estrogens in serum

Estrone (E1), estradiols (α/β-E2), and estriol (E3) are four major metabolically active estrogens exerting strong biological activities at very low circulating concentrations. This paper reports a sensitive and efficient method with automated, on-line clean-up and detection to determine trace estrogens in a small volume of serum samples using liquid chromatography–electrospray ionization–tandem mass spectrometry directly, without off-line liquid–liquid or solid-phase extraction pretreatments. Serum aliquots (charcoal stripped fetal bovine serum, 100 μL) were spiked with four estrogen standards and their corresponding isotope-labeled internal standards, then bulk derivatized with 2-fluoro-1-methyl-pyridium p-toluenesulfonate (2-FMP) to establish the calibration curves and perform method validation. Calibration was established in the concentration ranges of 5–1000 pg mL⁻¹, and demonstrated good linearity of R² from 0.9944 to 0.9997 for the four derivatized estrogens. The lower detection limits obtained were 3–7 pg mL⁻¹. Good accuracy and precision in the range of 86–112% and 2.3–11.9%, respectively, were observed for the quality control (QC) samples at low, medium, and high concentration levels. The stability tests showed that the derivatized serum samples were stable 8 h after derivatization at room temperature and at least to 48 h if stored at −20 °C. The method was applied to measure trace estrogens in real human and bovine serum samples, and three of four estrogen compounds studied were observed and quantified.