Topologische Affine Ebenen Mit Nichtstetigem Parallelismus

In this paper, we present a general method of constructing topological affine planes having non-continuous parallelism. We prove that a topological affine plane E with point set L ^k ×L ^k , and with a special K-algebraic slope has a topological affine subplane with non-continuous parallelism (Satz 4.6). Here, K is a real-closed subfield of a real-closed field L. The crucial tools needed to make our method work are the notion of a slope and the notion of K-algebraicity, a concept which is introduced and intensively studied here. As an application of our general method, we obtain in Section 5 affine Salzmann planes with lines being bent countably infinitely often admitting a subplane with non-continuous parallelism. This provides a negative answer to a question posed by H. Salzmann [13, p. 52].     

О Тригонометрическом (0, 2)-Интерполировании

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There are uncountably many universal topological planes

We prove the existence of uncountably many nonisomorphic topological projective planes, each universal in the sense that it contains an isomorphic copy of every pseudoline arrangement.     

A new approach to the single point catalytic super-Brownian motion

Summary A new approach is provided to the super-Brownian motionX with a single point-catalyst _c as branching rate. We start from a superprocessU with constant branching rate and spatial motion given by the 1/2-stable subordinator. We prove that the occupation density measure ^c ofX at the catalystc is distributed as the total occupation time measure ofU. Furthermore, we show thatX _t is determined from ^c by an explicit representation formula. Heuristically, a mass ^c (ds) of particles leaves the catalyst at times and then evolves according to Itô's Brownian excursion measure. As a consequence of our representation formula, the density fieldx ofX satisfies the heat equation outside ofc, with a noisy boundary condition atc given by the singularly continuous random measure ^c . In particular,x isC outside the catalyst. We also provide a new derivation of the singularity of the measure ^c .     

On the Rate of Local Convergence of High-Order-Infeasible-Path-Following Algorithms for P*-Linear Complementarity Problems

A simple and unified analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P_*-linear complementarity problem (P_*-LCP). It is shown that the rate of local convergence of a -order algorithm with a centering step is + 1 if there is a strictly complementary solution and ( + 1)/2 otherwise. For the -order algorithm without the centering step the corresponding rates are and /2, respectively. The algorithm without a centering step does not follow the fixed traditional central path. Instead, at each iteration, it follows a new analytic path connecting the current iterate with an optimal solution to generate the next iterate. An advantage of this algorithm is that it does not restrict iterates in a sequence of contracting neighborhoods of the central path.     

Random time change and an integral representation for marked stopping times

Summary Consider the set of all possible distributions of triples (, , ), such that is a finite stopping time with associated mark in some fixed Polish space, while is the compensator random measure of (, ). We prove that is convex, and that the extreme points of are the distributions obtained when the underlying filtration is the one induced by (, ). Moreover, every element of has a corresponding unique integral representation. The proof is based on the peculiar fact that EV _, =0 for every predictable processV which satisfies a certain moment condition. From this it also follows thatT _, isU(0, 1) wheneverT is a predictable mapping into [0, 1] such that the image of , a suitably discounted version of , is a.s. bounded by Lebesgue measure. Iterating this, one gets a time change reduction of any simple point process to Poisson, without the usual condition of quasileftcontinuity. The paper also contains a very general version of the Knight-Meyer multivariate time change theorem.Research supported by NSF grant DMS-8703804     

The transposition of locally compact,connected translation planes

This note deals with the transposition of translation planes in the topological context. We show that a topological congruenceC of the real vector space ²ⁿ has the property that every hyperplane of ²ⁿ contains a component ofC. This makes it possible to define the transposeP of the topological translation planeP associated withC; it is proved that the translation planeP is topological also. The relationship between collineation groups and the relationship between coordinatizing quasifields ofP andP are also discussed.     

Elementary constructions of locally compact affine planes

In this paper we describe several elementary constructions of 4-, 8- and 16-dimensional locally compact affine planes. The new planes share many properties with the classical ones and are very easy to handle. Among the new planes we find translation planes, planes that are constructed by gluing together two halves of different translation planes, 4-dimensional shift planes, etc. We discuss various applications of our constructions, e.g. the construction of 8- and 16-dimensional affine planes with a point-transitive collineation group which are neither translation planes nor dual translation planes, the proof that a 2-dimensional affine plane that can be coordinatized by a linear ternary field with continuous ternary operation can be embedded in 4-, 8- and 16-dimensional planes, the construction of 4-dimensional non-classical planes that admit at the same time orthogonal and non-orthogonal polarities. We also consider which of our planes have tangent translation planes in all their points. In a final section we generalize the Knarr-Weigand criterion for topological ternary fields.This research was supported by a Feodor Lynen fellowship.     

Estimation of the Intensity of the Flow of Nonmonotone Refusals in the Queuing System (≤ λ)/G/m

We consider a queuing system ()/G/m, where the symbol () means that, independently of prehistory, the probability of arrival of a call during the time interval dtdoes not exceed dt. The case where the queue length first attains the level r m+ 1 during a busy period is called the refusal of the system. We determine a bound for the intensity ₁(t) of the flow of homogeneous events associated with the monotone refusals of the system, namely, ₁(t) = O( ^{r+ 1}₁ ^{m– 1} _{r– m+ 1}), where _k is the kth moment of the service-time distribution.     

On 4-dimensional Minkowski planes with 7-dimensional automorphism groups

This paper concerns 4-dimensional (topological locally compact connected) Minkowski planes that admit a 7-dimensional automorphism group . It is shown that such a plane is either classical or has a distinguished point that is fixed by the connected component of and that the derived affine plane at this point is a 4-dimensional translation plane with a 7-dimensional collineation group.This research was supported by a Feodor Lynen Fellowship.     

Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator

We obtain asymptotic bounds for the perturbed eigenvalues and eigenvectors of a perturbed linear bounded operator A(), in a Hilbert space under the assumption that A() is holomorphic at the point =₀ and the eigenvalue ₀= gl(₀) of the operator A(₀) is isolated and of finite multiplicity. We study certain cases of high degeneracy in the limiting problem, i.e., the case when there are generalized associated vectors.Translated from Matematicheskie Zametki, Vol. 12, No. 4, pp. 403–412, October, 1972.The author wishes to express his sincere gratitude to his scientific director T. Sabirov for valuable observations and advice.     

General Topology — the Monadic Case, Examples, Applications

The paper deals with monadic as well as monadic-free topological notions. For defining these monadic-free notions the notion of basic triple is introduced. A lot of monadic-free topological notions are presented, for instance that of -convergence structure, -hull operator and -uniform structure. By means of a generalized metric, e.g. a probabilistic metric, and the general notion of -zero approach introduced in this paper, a -uniform structure is generated. In case of a fuzzy metric the related -uniform structure defines in a canonic way a fuzzy topology which is used for developing a fuzzy analysis and fuzzy calculus.     

Sur la convergence presque sure,au sens de Cesaro d'ordre α, 0<α<1, de variables aléatoires indepéndantes et identiquement distribuées

Summary We prove the following theorem: «Given 0<1, the (C, )-means of a sequence of i.i.d. random variables X _n converge a.s. iff E|X _n|^1/<.» For 1/2<1 and 0<<1/2 this result is essentially known. We give here a proof of the case =1/2; an important tool is a theorem of Hsu and Robbins [5].     

Über lokalarchimedische Anordnungen projektiver Ebenen

The question, whether the Archimedean ordering of only one of the ternary rings of a projective plane implies that is Archimedean, i.e. that every ternary ring of is Archimedean, is answered in the negative by the construction of local-Archimedean orderings of free planes. There exists even Archimedean affine planes with non-Archimedean associated projective planes.     

Flag transitive planes of orderq n with a long cyclel ∞ as a collineation

Baker and Ebert [1] presented a method for constructing all flag transitive affine planes of orderq ² havingGF(q) in their kernels for any odd prime powerq. Kantor [6; 7; 8] constructed many classes of nondesarguesian flag transitive affine planes of even order, each admitting a collineation, transitively permuting the points at infinity. In this paper, two classes of non-desarguesian flag transitive affine planes of odd order are constructed. One is a class of planes of orderq ⁿ , whereq is an odd prime power andn 3 such thatq ⁿ 1 (mod 4), havingGF(q) in their kernels. The other is a class of planes of orderq ⁿ , whereq is an odd prime power andn 2 such thatq ⁿ 1 (mod 4), havingGF(q) in their kernels. Since each plane of the former class is of odd dimension over its kernel, it is not isomorphic to any plane constructed by Baker and Ebert [1]. The former class contains a flag transitive affine plane of order 27 constructed by Kuppuswamy Rao and Narayana Rao [9]. Any plane of the latter class of orderq ⁿ such thatn 1 (mod 2), is not isomorphic to any plane constructed by Baker ad Ebert [1].The author is grateful to the referee for many helpful comments.     

Special Fibres and Critical Locus for a Pencil of Plane Curve Singularities

We will analyze the relationships between the special fibres of a pencil of plane curve singularities and the Jacobian curve J of (defined by the zero locus of the Jacobian determinant for any fixed basis ). From the results, we find decompositions of J (and of any special fibre of the pencil) in terms of the minimal resolution of . Using these decompositions and the topological type of any generic pair of curves of , we obtain some topological information about J. More precise decompositions for J can be deduced from the minimal embedded resolution of any pair of fibres (not necessarily generic) or from the minimal embedded resolution of all the special fibres.     

The Moduli of Flat U(p, 1) Structures on Riemann Surfaces

For X a smooth projective curve over of genus g>1, Hom⁺(₁(X), U(p, 1))/U(p, 1) is the moduli space of flat semi-simple U(p, 1)-connections on X. There is an integer invariant, , the Toledo invariant associated with each element in Hom⁺(₁(X), U(p, 1))/U(p, 1). This paper shows that Hom⁺(₁(X), U(p, 1))/U(p, 1) has one connected component corresponding to each & in 2 with –2(g–1) 2(g–1). Therefore the total number of connected components is 2(g–1)+1.     

On Simulated Annealing and Nested Annealing

Simulated Annealing is a family of randomized algorithms used to solve many combinatorial optimization problems. In practice they have been applied to solve some presumably hard (e.g., NP-complete) problems. The level of performance obtained has been promising [2,5,6,14]. The success of this heuristic technique has motivated analysis of this algorithm from a theoretical point of view. In particular, people have looked at the convergence of this algorithm. They have shown (see e.g., [10]) that this algorithm converges in the limit to a globally optimal solution with probability 1. However few of these convergence results specify a time limit within which the algorithm is guaranteed to converge (with some high probability, say). We present, for the first time, a simple analysis of SA that will provide a time bound for convergence with overwhelming probability. The analysis will hold no matter what annealing schedule is used. Convergence of Simulated Annealing in the limit will follow as a corollary to our time convergence proof. In this paper we also look at optimization problems for which the cost function has some special properties. We prove that for these problems the convergence is much faster. In particular, we give a simpler and more general proof of convergence for Nested Annealing, a heuristic algorithm developed in [12]. Nested Annealing is based on defining a graph corresponding to the given optimization problem. If this graph is small separable, they [12] show that Nested Annealing will converge faster. For an arbitrary optimization problem, we may not have any knowledge about the separability of its graph. In this paper we give tight bounds for the separability of a random graph. We then use these bounds to analyze the expected behavior of Nested Annealing on an arbitrary optimization problem. The separability bounds we derive in this paper are of independent interest and have the potential of finding other applications.     

On Ω-closed sets and Ωs-closed sets in topological spaces

Summary New classes of sets called -closed sets and s-closed sets are introduced and studied. Also, we introduce and study -continuous functions and s-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces -T_1/2 and -T_s.     

Склярные дифференциалвные инварианты третвего порядка риамнового простанства трех измерений

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