Nanostructures of Si/SiO<Subscript>2</Subscript>/metal systems with tracks of fast heavy ions

Structures based on the SiO₂/n-Si and SiO₂/p-Si systems, with nanopores in silicon dioxide layers filled with Cu and Ni nanoparticles, have been prepared and investigated using the fast heavy ion technology, which includes irradiation with ¹⁹⁷Au²⁶⁺ ions, chemical etching of ion tracks, and subpotential electrochemical deposition. The selectivity of filling nanopores with metals and cluster character of their formation in tracks is shown.     

Zeros in Tables of Characters for the Groups <Emphasis Type="Italic">S</Emphasis><Subscript>n</Subscript> and <Emphasis Type="Italic">A</Emphasis><Subscript>n</Subscript>. II

Let P(n) be the set of all partitions of a natural number n. In the representation theory of symmetric groups, for every partition α ∈ P(n), the partition h(α) ∈ P(n) is defined so as to produce a certain set of zeros in the character table for S_n. Previously, the analog f(α) of h(α) was obtained pointing out an extra set of zeros in the table mentioned. Namely, h(α) is greatest (under the lexicographic ordering ≤) of the partitions β of n such that χ^α(g_β) ≠ 0, and f(α) is greatest of the partitions γ of n that are opposite in sign to h(α) and are such that χ^α(g_γ) ≠ 0, where χ^α is an irreducible character of S_n, indexed by α, and g_β is an element in the conjugacy class of S_n, indexed by β. For α ∈ P(n), under some natural restrictions, here, we construct new partitions h′(α) and f′(α) of n possessing the following properties. (A) Let α ∈ P(n) and n ⩾ 3. Then h′(α) is identical is sign to h(α), χ^α(g_h′(α)) ≠ 0, but χ^α(g_γ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of h(α), and h′(α) < γ < h(α). (B) Let α ∈ P(n), α ≠ α′, and n ⩾ 4. Then f′(α) is identical in sign to f(α), χ^α(g_f′(α)) ≠ 0, but χ^α(g_γ) = 0 for all γ ∈ P(n) such that the sign of γ coincides with one of f(α), and f′(α) < γ < f(α). The results obtained are then applied to study pairs of semiproportional irreducible characters in A_n. Supported by RFBR grant No. 04-01-00463. __________ Translated from Algebra i Logika, Vol. 44, No. 6, pp. 643–663, November–December, 2005.     

Laser Probe Investigations of the Initial Stage of Spark Discharge in Air in the Tip (Cathode)–Plane Gap

Technical Physics - A spark discharge in a 1.5-mm-long tip (cathode)-plane gap in the time interval from the breakdown onset to 200 ns has been studied. Тhe discharge has been found to arise...     

Microstructure of a Spark Discharge in Air in a Point–Plane Gap

A microchannel structure of a spark discharge initiated in atmospheric-pressure air in a point–plane gap has been discovered by shadow photography. The structure has been observed since the onset of the discharge glow. The evolution of the microstructure over times from several nanoseconds to several tens of nanoseconds has been traced. Specifically, the development of microchannels from the point into the discharge gap, expansion of the microchannels, and their interaction have been observed. A correlation has been found between the microstructure of the spark channel in the discharge gap and its autograph on the surface of the plane electrode.     

On Some Classes of Inverse Problems of Recovering the Heat Transfer Coefficient in Stratified Media

Siberian Mathematical Journal - We consider the well-posedness, in Sobolev spaces, of the inverse problem of recovering the heat transfer coefficient at the interface in the transmission condition...     

On the semiproportional character conjecture in groups Sp<Subscript>4</Subscript>(<Emphasis Type="Italic">q</Emphasis>)

Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters φ and ψ, then φ(1) = ψ(1). In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for symplectic groups Sp₄(q) and PSp₄(q).