A Ramsey‐type result for the hypercube

We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Q_n with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Q_n contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006     

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.     

A remark on convergence in the limit theorem for the distribution of random functionals

Estimates are established which characterize the rate of convergence in a global limit theorem for random functionals.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 197–206, 1979.The author is grateful to L. N. Dovbysh for assistance and to I. A. Ibragimov for valuable consultations.     

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.     

Equivalence and Singularity of Gaussian Measures on the Conic Sigma-Field

The alternative: equivalence-singularity on the conic sigma-field is established for a pair of centered Gaussian distributions and a corresponding criterion is given. The behavior of the logarithmic variation is established for the Radon–Nikodym derivative on the conic sigma-subfield. Bibliography: 6 titles.     

Sparse pseudo‐random graphs are Hamiltonian

In this article we study Hamilton cycles in sparse pseudo‐random graphs. We prove that if the second largest absolute value λ of an eigenvalue of a d‐regular graph G on n vertices satisfies and n is large enough, then G is Hamiltonian. We also show how our main result can be used to prove that for every c >0 and large enough n a Cayley graph X (G,S), formed by choosing a set S of c log⁵ n random generators in a group G of order n, is almost surely Hamiltonian. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 17–33, 2003     

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.     

Pairwise Interactions of Fe3+ Ions in InBO3 Crystals

Measurements of the electron paramagnetic resonance (EPR) of Fe³⁺ ion pairs in InBO₃ crystals are conducted. Some parts of the procedure of spectrum identification without measuring the temperature dependence of the resonant line intensities have been developed. Experimental curves of the second- and fourth-order axial Hamiltonian constants D _S and (a – F)_S, respectively, of the total spin number S are constructed. The single-ion second-order axial constant D _c is well described by a linear dependence on S. The constant (a – F)_S has a quadratic dependence.