Certain pairs of irreducible characters of the groups <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The investigation of the pairs of irreducible characters of the symmetric group S _n that have the same set of roots in one of the sets A _n and S _n ? A _n is continued. All such pairs of irreducible characters of the group S _n are found in the case when the least of the main diagonal’s lengths of the Young diagrams corresponding to these characters does not exceed 2. Some arguments are obtained for the conjecture that alternating groups A _n have no pairs of semiproportional irreducible characters.     

A property of the character table for a finite group

A character table X of a finite group is broken up into four squares: A, B, C, and D. We establish relations via which ranks of the matrices inX are connected. In particular, ifX is an l × l-matrix, A is an s × t-matrix, and, moreover, the squares A and C are opposite, thenr(A)=r(C) + s + t − l; here.r(M) is the rank of a matrix M. Associated with such each block ofX is some integral nonnegative parameter m, and we have m=0 iff A, B, C, and D are active fragments ofX. Supported by RFFR grant No. 96-01-00488. Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 273–279, May–June, 2000.     

Dynamics of Gliding Arc Climbing in a Unipolar Jacob’s Ladder

Technical Physics - We have designed a device with a gliding unipolar arc of the Jacob’s ladder type. The dynamics of arc rising has been investigated. It is found that the arc climbs at a...     

Investigation of the foil destruction dynamics in an explosively formed fuse opening switch by proton radiography

The dynamics of mechanical destruction of a conductor in an explosively formed fuse opening switch on a finned obstacle under the action of detonation products is studied in the injection channel of the U-70 proton synchrotron. Protonograms are recorded with digital multiframe electron-optic cameras. The exposure time per frame, about 30 ns, is determined by the duration of a proton bunch. The time from the beginning of motion of the conductor to its destruction is about 3 ??s. It is shown that the switch with typical sizes of the obstacle (the thickness of the fin is 1.5 mm, and the width and depth of the groove are 1.5 and 4.5 mm, respectively) provides operation with satisfactory gasdynamic parameters.     

Recovering an Erased Row or Column in a Table of Characters for a Finite Group

We argue that an erased row or column in a table of characters of a finite group can be constructively recovered from retained data.