Young diagrams without hooks of length 4 and characters of the group <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

All finite Young diagrams not containing hooks of length 4 are found. Self-associated diagrams possessing this property are subdivided into three series. Sets of all hook lengths are determined for diagrams contained in each series. The research conducted has proven necessary for the study of certain pairs of irreducible characters of symmetric and alternating groups.     

Zeros in tables of characters for the groups Sn and An

In the representation theory of symmetric groups, for each partition of a natural number n, the partition h() of n is defined so as to obtain a certain set of zeros in the table of characters for S_n. Namely, h() is the greatest (under the lexicographic ordering ) partition among P(n) such that (g) 0. Here, is an irreducible character of S_n, indexed by a partition , and g is a conjugacy class of elements in S_n, indexed by a partition . We point out an extra set of zeros in the table that we are dealing with. For every non self-associated partition P(n), the partition f() of n is defined so that f() is greatest among the partitions of n which are opposite in sign to h() and are such that (g) 0 (Thm. 1). Also, for any self-associated partition of n > 1, we construct a partition () P(n) such that () is greatest among the partitions of n which are distinct from h() and are such that (g) 0 (Thm. 2).Supported by RFBR grant No. 04-01-00463 and by RFBR-BRFBR grant No. 04-01-81001.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 24–43, January–February, 2005.     

Substructure and orientation of Pd-Cu solid solution thin films

The phase and elemental composition, substructure, orientation, and relief of Pd-Cu thin films produced by magnetron sputtering have been investigated using the techniques of TEM, HEED, and AFM. Three-orientation epitaxial β-phase structures (CsCl-type lattice) have been obtained by plasma-ion sputtering a Pd-Cu target on (001) fluorphlogopite (F) cleavages in the substrate temperature range of 550–800 K. The β-phase crystallites in the two-phase epitaxial solid solution films were oriented, with respect to the α-phase, according to Nishiyama—Wassermann and Kurdyumov—Sachs relations. Single-crystal films of α-and β-phase solid solutions have been grown on fluorphlogopite. The effect of the second component appeared as the formation of (001)[110] β_CuAu ∥ (001)[100]_F-type orientations.     

Dynamics of the Spatial Structure of a Microsecond Pulsed Barrier Discharge Initiated in Atmospheric Pressure Air in the Point–Plane Geometry at Different Polarities of Feed Voltage

Technical Physics - The evolution of a microsecond pulsed barrier discharge initiated in atmospheric pressure air in the point–plane electrode geometry has been investigated using streak...     

Effective Charge in LiNbO3 Films Fabricated by Radio-Frequency Magnetron Sputtering Method

Physics of the Solid State - Amorphous Li–Nb–O films were deposited onto Si substrates by radio-frequency magnetron sputtering method. The fabricated heterostructures demonstrated the...     

Dynamics of the Initial Stage of the Spark and Diffuse Discharges in Air in a Point–Plane Gap at Different Parameters of the Tip Electrode

Technical Physics - Dynamics of the initial stage of discharge in air is studied at atmospheric pressure in a point–plane gap at different parameters of the tip electrode and lengths of the...     

Finite simple groups in which all maximal subgroups are π-closed. I

Finite simple nonabelian groups G that are not π-closed for some set of primes π but have π-closed maximal subgroups (property (*) for (G, π)) are studied. We give a list L of finite simple groups that contains any group G with the above property (for some π). It is proved that 2 ? π for any pair (G, π) with property (*) (Theorem 1). In addition, we specify for any sporadic simple group G from L all sets of primes π such that the pair (G, π) has property (*) (Theorem 2). The proof uses the author’s results on the control of prime spectra of finite simple groups.