Limit distribution “in the large” of linear functionals over a random process of the second order

An infinite-dimensional analogue of the theorem on the existence of an -typical distribution of linear functionals in a vector space of high dimension does not exist. There are given some additional conditions ensuring, nevertheless, the existence of a typical distribution of linear functionals in the infinite-dimensional case.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 199–202, 1980.The author is grateful to S. B. Makarov for pointing out and corresponding these errors.     

Decomposition of vector-valued additive functions

From the additive nonnegative fonctions, defined on a - algebra of subsets, the property of countable additivity separates a class of regular objects, namely measures. Among additive Banach-valued functions, countable additivity is already not necessary for non-pathology. In the paper one isolates a class of regular vector-valued additive functions (measures) and one proves a theorem on the decomposition of a vector-valued additive function into the sum of a regular component (measure) and a purely pathological additive function, similar to a purely finitely additive measure.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 148–156, 1989.     

Optically induced rotation of an exciton spin in a semiconductor quantum dot

We demonstrate control over the spin state of a semiconductor quantum dot exciton using a polarized picosecond laser pulse slightly detuned from a biexciton resonance. The control pulse follows an earlier pulse, which generates an exciton and initializes its spin state as a coherent superposition of its two nondegenerate eigenstates. The control pulse preferentially couples one component of the exciton state to the biexciton state, thereby rotating the exciton's spin direction. We detect the rotation by measuring the polarization of the exciton spectral line as a function of the time difference between the two pulses. We show experimentally and theoretically how the angle of rotation depends on the detuning of the second pulse from the biexciton resonance.     

High-resolution in vivo imaging of blood vessels without labeling

We demonstrate that both oxyhemoglobin and deoxyhemoglobin have sequential two-color, two-photon absorption properties that can serve as endogenous contrasts in microvasculature imaging. Using a sensitive modulation transfer technique, we are able to image hemoglobin in red blood cells with micrometer resolution, both in vitro and in vivo. We show that excellent contrast from hemoglobin without any labeling can be obtained in tissue.     

Electrosprayed NiCo<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles for long cycle life and high-power Li-ion battery anode

Electrospraying-based synthesis of NiCo₂O₄ (NCO-ES) nanoparticles that exhibit long cycle life and high rate capability is reported. The results are compared with a conventionally prepared NiCo₂O₄ sample by direct annealing (NCO-DA). The structure and morphology of NCO-ES and NCO-DA nanoparticles have been characterized by X-ray diffraction, transmission electron microscopy, and X-ray photoelectron spectroscopy to confirm the size, morphology, structure, and surface chemistry of the as-prepared samples. Electrochemical testing established that the NCO-ES sample displayed enhanced Li-ion storage performance. The NCO-ES delivered a discharge capacity of almost 370 mAh/g at the end of 50 cycles at 1C rate (890 mA/g) while only 180 mAh/g was retained for the NCO-DA sample at the same condition. At a high rate of 5C (4450 mA/g), NCO-ES electrodes delivered a stabilized specific capacity of 225 mAh/g with almost 100% Coulombic efficiency over 1000 cycles. Its rate capability and cycle life were found to be superior to NCO-DA electrodes. The nanoscale grain boundaries in the NCO-ES sample enhanced the lithium-ion diffusion and enabled high rate capability. The impedance analysis at different stages of lithiation/delithiation indicates a lower impedance and better kinetics as one of the reasons for better performance of the NCO-ES sample.     

Oral malodor,assessed by closed-loop,gas chromatography,and ion-trap technology

A method is described for the analysis of volatile organic compounds in saliva and tongue coating samples. The techniue is based on an off-line preconcentration step by means of a closed-loop trapping system followed by gas chromatography-ion trap detection. With the closed-loop technique, the volatile organic compounds(VOCs) are released from the matrix and trapped on an adsorbent without interference of water. The VOCs are released from the adsorbent into the gas chromatograph by thermdesorption. After separation, identification of the compounds is performed by ion trap technology. By this technique 82 compounds could be demonstrated in saliva and tongue coating samples. The technique is also used to demonstrate the formation of volatile bacterial fermentation compounds when a protein substrate is added to tongue coating samples. It is considered a very promising tool in further research on oral malodor.