Surfaces of order three with a peak! I

A surfaceF of order three in the real projective three space is met by every line, not inF, in at most three points. We present a synthetic theory of these surfaces based upon a concept of differentiability. A pointv inF is a peak ifF has a unique tangent atvs and it does not lie inF. We classify theF with a peak by determining the number of lines inF and their configuration. We describe each surface by determining the tangent plane sections ofF at the differentiable points.     

Imbedding problem with a noncommutative kernel of order p4. II

The problem of imbedding number fields is investigated for p-groups, where the kernel is a non-Abelian group of order p⁴ with two generators , and relationsIt is shown that the solvability of this problem is equivalent to the simultaneous solvability of all the collateral local problems and the collateral Abelian problem obtained by the factorization of the kernel by the derived group.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 101–113, 1991.     

On a Steffensen-Hermite method of order three

In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the Hermite inverse interpolation polynomial of degree 2. We study the convergence of the iterative method and we provide new convergence conditions which lead to bilateral approximations for the solution; it is known that the bilateral approximations have the advantage of offering a posteriori bounds of the errors. The numerical examples confirm the advantage of considering these error bounds.     

On construction of a fourth order rotatable design with three factors

The necessary and sufficient conditions for a set of points to form a rotatable design of order four have been given by Patel and Arap Koske [1], In this paper, a set of 98 points for three factors which satisfies these conditions is given.     

Generalized quadrangles of order 4. II

There is a unique generalized quadrangle of order 4.     

Groups with handles of order different from three

We obtain a test for the unsimplicity of an infinite group.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1030–1042, August, 2004.     

Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. II

We study the inhomogeneous Riemann boundary problem with infinite index of logarithmic order on an open rectifiable spiral-form Jordan contour where the influence of the contour on the solvability of the problem is comparable with the influence of the argument of its coefficient. A solution of the problem is constructed explicitly in the class of functions admitting weak power singularities at the ends of a line of conjugacy.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1672–1681, December, 1990.     

Embeddedsdirk-methods of basic order three

The purpose of this report is to construct 3-stage SDIRK-methods (Singly Diagonally Implicit Runge-Kutta) to be used for the code SIMPLE. The local error control is performed by embedding techniques. Pairs with and without extrapolation are given.Dedicated to Germund Dahlquist, on the occasion of his 60'th birthday.This work was supported by NATO, grant 96.80/D1.     

Large minimal realizers of a partial order II

The rank (resp. dimension) of a poset P is the cardinality of a largest (resp. smallest) set of linear orders such that its intersection is P and no proper subset has intersection P. Dimension has been studied extensively. Rank was introduced recently by Maurer and Rabinovitch in [4], where the rank of antichains was determined. In this paper we develop a general theory of rank. The main result, loosely stated, is that to each poset P there corresponds a class of graphs with easily described properties, and that the rank of P is the maximum number of edges in a graph in this class.     

Ergodicity of mapping class group actions on representation varieties,II. Surfaces with boundary

The mapping class group of a compact oriented surface of genus greater than one with boundary acts ergodically on connected components of the representation moduli corresponding to a connected compact Lie group, for every choice of conjugacy class boundary condition.     

一类三次系统的极限环

主要研究一类三次系统的极限环存在性问题,推广了C.Chicone[2]的结果,给出此类系统极限环存在定理.     

Prime divisors of second order linear recurrences. II

It is shown that, on average but independent of any hypothesis, the density of prime divisors of an infinite set of second order linear recurrences is greater than 0. It is also proved that the rough estimate, suggested by R. R. Laxton, for calculating this density is true on average.