Sets with two associative operations

In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.     

Investigation of anode and cathode jets influence on electric arc properties with current up to 500 kA

A number of phenomena connected with the formation of electrode jets in discharges in hydrogen at a current of 10/sup 5/-10/sup 6/ A, a current growth rate of 10/sup 10/ A/s, an initial pressure 0.1-4.0 MPa, and a discharge gap length of 5-40 mm were studied. After the secondary breakdown, the jets are observed through a discharge semitransparent channel, widening with velocity (4-7) /spl middot/ 10/sup 2/ m/s. Shockwave formation was detected at the interaction of jets with the surrounding gas and the opposite electrode. Plasma vapor pressure of metal near the end of the tungsten cathode 70 /spl mu/s after initiation of a discharge was 180 MPa. Thus, magnitude of brightness temperature was 59 /spl middot/ 10/sup 3/ K, with an average charge of ions-m~=3.1, and a concentration of metal vapors n=5.3/spl middot/10/sup 19/ cm/sup -3/. While those at the end of the anode 90 /spl mu/s after initiation of discharge: m~=2.6, n=7.4/spl middot/10/sup 19/ cm/sup -3/. Probable reasons of high-voltage drops near the electrodes (the summarized magnitude of which is /spl sim/1 kV) are discussed on the basis of experimental data. For the first time, the shadow method registered symmetric ejection of material from the all-cathode surface the maximum discharge current was observed.     

On the rigidity of sphericalt-designs that are orbits of finite reflection groups

The concept of rigid sphericalt-designs was introduced by Bannai. He conjectured that there is a functionf(t, d) such that ifX is a sphericalt design in thed-dimensional Euclidean space so that |X|>f(t, d), theX is non-rigid. Furthermore, he asked to find examples of rigid but not tight sperical designs. In the present article we shall investigate the case whenX is an orbit of a finite reflection group and prove thatX is rigid iff tight for the groupsA _n ,B _n ,C _n ,D _n ,E ₆,E ₇,F ₄,I ₃.Research was partially supported by Hungarian National Research fund Grant No. 4267.     

Kaon production from 1 to 40 AGeV

Kaon production is studied within the Giessen Boltzmann–Uehling–Uhlenbeck (GiBUU) model. Results are compared with experiment and with other models. The influence of the kaon potential on the kaon azimuthal distributions at SIS energies is considered. We also discuss the role of the many-body collisions at high-density phase of reaction.     

High pressure mössbauer studies of magnetic actinide systems

Due to the wider radial extent of 5f electrons when compared to their 4f counterparts, intermetallics of the light actinides show a broad spectrum of magnetic properties ranging from the localized magnetism of the lanthanides to the itinerant magnetism often found in transition metal compounds. One parameter which strongly influences the magnetic character of the compound is the actinide-actinide separation which can experimentally be varied by the application of high pressure. The question of 5f electron delocalization will be reviewed with respect to Moesshauer high pressure data on NpCo₂si₂, NpAl₂, NpOs₂ and new results will be presented of NpAs. The connection of hyperfine parameters with results of X-ray diffraction studies will be discussed.Work supported by the Bundesministerium für Forschung und Technologie, Federal Republic of Germany     

Fejér means of functions on noncommutative Vilenkin groups with respect to the character system

Summary It is known that the Fejér means - with respect to the character system of the Walsh, and bounded Vilenkin groups - of an integrable function converge to the function a.e. In this work we discuss analogous problems on the complete product of finite, not necessarily Abelian groups with respect to the character system for functions that are constant on the conjugacy classes. We find that the nonabelian case differs from the commutative case. We prove the a.e. convergence of the (C,1) means of the Fourier series of square integrable functions. We also prove the existence of a function f∊L^q for some q >1 such that sup |σ_n f | = + ∞ a.e. This is a sharp contrast between the Abelian and the nonabelian cases.     

Cardy's formula for some dependent percolation models

We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice  (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice 𝕋 with flips when a site disagrees with six, five and sometimes four of its six neighbors. Received: 24 December 2001     

Stirling渐进公式的一个新的构造证明

本文用简易的分析工具，对ｎ！给出了一个精确等式，从而导出Ｓｔｉｒｌｉｎｇ渐近公式（２）的一个新的简短证明.     

关于无环Euler平面地图数目的注记

本文提供了组合上不等价的有根无环Euler平面地图以边数为参数的的数目,同时对于几乎无环的情形也给出了一个计数显式.     

Vacuum discharge effects in the diodes of high-current electronaccelerators

The processes occurring in the diodes of high-current electron accelerators which affect the electron beam structure are discussed. Two types of diodes are analyzed: planar diodes producing large cross-section beams, and magnetically insulated diodes producing cylindrical beams. The effects considered are: the screening effect, the effect of touches, the relay effect, the ring effect, etc. They are entirely associated with the explosive electron emission occurring on the cathode of a high-current diode. Methods which can be employed to eliminate or control some of these effects are described-namely, the application of an additional magnetic field, artificial initiation of emission centers, and employment of metal-dielectric cathodes. Examples of several types of cathode are given