The Milnor–Totaro Theorem for Space Polygons

If denotes the curvature and the torsion of a closed, generic, and oriented polygonal space curve X in , then we show that _X (² + ²) ds = _X ds + _X | | ds > 4 if is positive. We also show that _X (² + ²) ds 2n if no four consecutive vertices lie in a plane and X has linking number n with a straight line. These extend theorems of Milnor and Totaro.     

Coproducts in the Category <Emphasis Type="Bold">M</Emphasis>κ<Emphasis Type="Bold">Frm</Emphasis>

The purpose of this paper is to study coproducts in the category MFrm (resp. M_cFrm), of metric -frames and uniform (resp. contractive) -frame maps. First, by applying the same technic that was used to find coproducts in Frm, we construct coproducts in the category Frm of -frames and -frame maps. Then, we define a metric diameter on the coproduct in Frm of a family of metric -frames and show that coproduct in Frm preserves metrizability.Mathematics Subject Classifications (2000) 06B23, 06D22, 18A30.     

Nice separation axioms

The epi-reflective hull B of an objectB in the category of locales is called anice separation axiom provided it enjoys certain properties which are natural generalizations of properties satisfied by the categories of completely regular locales and zero dimensional locales. Invariably, a family ofStone-like duality theorems ensues, distinguishing (for each large enough regular cardinal ) the full subcategory of all -LindelöfB-objects. Some corollaries for topological spaces arise, as well as some open problems, upon taking of spatial parts.This paper, consisting primarily of excerpts from the author's Ph.D. thesis, Wesleyan University, Middletown, Connecticut (1992), also represents, in part, the results of research engaged in at Charles University, Prague, during the 1992–1993 academic year, with the support of the United States Information Agency and the Fulbright Program.     

On graphs that can be oriented as diagrams of ordered sets

We study some equivalent and necessary conditions for a finite graph to be the covering graph of a (partially) ordered set. For each 1, M. Aigner and G. Prins have introduced a notion of a vertex colouring, here called -good colouring, such that a 1-good colouring is the usual concept and graphs that have a 2-good colouring are precisely covering graphs. We present some inequalities for the corresponding chromatic numbers , especially for x ₂. There exist graphs that satisfy these inequalities for =2 but are not covering graphs. We show also that x ₂ cannot be bounded by a function of x=x ₁. A construction of Neetil and Rödl is used to show that x ₂ is not bounded by a function of the girth.     

On the free subset property at singular cardinals

We give a proof ofTheorem 1. Let be the smallest cardinal such that the free subset property Fr (, ₁)holds. Assume is singular. Then there is an inner model with ₁ measurable cardinals.     

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

On ηα-groups and fields

Let :=. The following are known: two -sets of power are isomorphic. Let >0. Two ordered divisible Abelian groups that are -sets of power are isomorphic, two real closed fields that are -sets of power are isomorphic. The following is shown: (1) there exist 2 nonisomorphic ordered Abelian groups (respectively ordered fields) that are -sets of power ; (2) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) of power all having the same order type; (3) there exist 2 nonisomorphic ordered divisible Abelian groups (respectively real closed fields) that are -sets having the same order type.     

Das 0-1-Gesetz der terminalen σ-Algebra bei Harrisirrfahrten

Für homogene M.K., bestehend aus einer aperiodischen rekurrenten Klasse, ist bekannt, da\ die terminale -Algebra das 0–1-Gesetz erfüllt. Der erste Teil dieser Arbeit behandelt die Gültigkeit des 0–1-Gesetzes für transiente Ketten, für die eine Folge ₀, ₁, ₂, ₃,... von ZustÄnden existiert mit P(nX_n= _l+1¦X₀= _l) = 1, N. Das herzuleitende Kriterium wird nur von dieser Folge und den Stoppzeiten, von _l nach _l+1 zu gelangen, abhÄngen. Eine Anwendung auf Harrisirrfahrten wird uns dort konkrete Aussagen liefern.     

On the Densities of Certain Lattice Packings by Parallelepipeds

Given any (non-degenerate) n-dimensional lattice L, let (L) denote the supremum of the numbers such that there exists a lattice packing Q + L of density where Q is some o-symmetric parallelepiped with faces parallel to the coordinate axes. Many efforts have been made to determine or estimate the minimal such density _n taken over all n-dimensional lattices. It is known that 0$$ " align="middle" border="0"> . Here we investigate a sequence of lattices L _n which are known to minimize the function (L) in dimensions n 3 and are likely to provide the minima _n = (L _n ) in certain higher dimensions. We establish the inequality (L _n ) n ^–n/2 which supports the conjecture that lim sup _n ( _n )^{1/(n log n)} is positive.     

A note on extensions of infinitary logic

We show that a strong form of the so called Lindströms Theorem [4] fails to generalize to extensions of L and L : For weakly compact there is no strongest extension of L with the (,)-compactness property and the Löwenheim-Skolem theorem down to . With an additional set-theoretic assumption, there is no strongest extension of L with the (,)-compactness property and the Löwenheim-Skolem theorem down to <.We are indebted to Lauri Hella, Tapani Hyttinen and Kerkko Luosto for useful suggestions.Research partially supported by the United States-Israel Binational Science Foundation. Publication number [ShVa:726]Research partially supported by grant 40734 of the Academy of Finland.     

On certain indestructibility of strong cardinals and a question of Hajnal

A model in which strongness of is indestructible under ⁺ -weakly closed forcing notions satisfying the Prikry condition is constructed. This is applied to solve a question of Hajnal on the number of elements of { |2 <}.     

Über das Modell einer Nicht-Newtonschen Flüssigkeit mit Relaxationseigenschaften

This paper deals with the equations ·u=o,u – u – u+u · u+p=f, describing a Non-Newtonian liquid with velocityu, pressure p under the external forcef. The difference to the Navier-Stokes equations consists in the fact that it is assumed here that the external forcef only has an effect on the volume-element of the liquid after the relaxation-time /.     

Products of chains with monochromatic maximal chains and antichains

There is a product of two linear orders of size with the property that every subset or complement thereof contains a maximal chain. Furthermore, for regular , there is a product of two linear orders of size ₊₂ that when colored with fewer than colors always has a monochromatic maximal chain. As a corollary, for every uncountable strong limit cardinal , there is an ordered set of cardinality that must be colored with at least colors before no monochromatic maximal chains are present. Duals of these results show that at least as much is true for maximal antichains.Research supported in part by ONR Grant N00014-91-J-1150.     

The Busy Period of the M/GI/∞ Queue

An equation for the distribution Z() of the duration T of the busy period in a stationary M/GI/ service system is constructed from first principles. Two scenarios are examined, being distinguished by the half-plane Re()>₀ for some ₀0 in which the generic service time random variable S, always assumed to have a finite mean E(S), has an analytic Laplace–Stieltjes transform E(e^–S ). If ₀<0 then E(e^–T ) is analytic in a half-plane (₁,), where ₀₁<0 and ₁ is determined by the distribution of S; then for any 0<s<|₁|.When ₀=0, E(e^–T ) is analytic in (0,), and now more is known about T. Inequalities on the tail () are used to show that for any 1, E(T ) is finite if and only if E(S ) is finite. It follows that the point process consisting of the starting epochs of busy periods is long range dependent if and only if E(S ²)=, in which case it has Hurst index equal to [frac12](3–), where is the moment index of S.If also the tail (x)=Pr{Sx} of the service time distribution satisfies the subexponential density condition ₀ ^x (x–u) (u)du/ (x)2E(S) as x, then (x)/ (x)e^E(S), where is the arrival rate.     

A certain class of functions that are univalent in an annulus

In the class F₁ of functions f(), regular and univalent in the annulus ={<||<1} and satisfying the conditions ¦f()¦ < 1 and f() 0 for , ¦f()¦=1 ¦¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f for an arbitrary fixed point A. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985.     

On the distribution of points of maximal deviation in complex Čebyšev approximation

f — , . p _n (f) f . , n+2 , f–p _n (f) . , n . , .

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On the distribution of points of maximal deviation in complex ebyev approximation

     

On the existence of strongly normal ideals overP κ λ

For every uncountable regular cardinal and any cardinal,P denotes the set . Furthermore, < denotes=" the=" binary=" operation=" defined=">P byx<> iffxy¦x<>.By anideal over P we mean a proper, non-principal,-complete ideal overP extending the ideal dual to the filter generated by . For any idealI overP ,I ⁺ denotes the setP –I, andI ^* the filter dual toI.     

Interpolation of monotone functions in lattices

We show that for every latticeL ₀ and for every cardinal there is a lattice on which every monotone function can be interpolated by a polynomial on any set of size .Presented by G. Grätzer.Dedicated to '"N     

Probabilities of large deviations in a certain scheme of summation of dependent random variables

In the paper one investigates questions regarding the CLT for an Ising scheme. If , where S _n = ₌₁ ⁿ X _n, while (X_nk) is a triangular array of random variables, constituting an Ising scheme, then in the zone one proves the equalities lim(1 — F_n(x))(1 — (x))^–1=1, lim F_n(–x)(–1))^–1=1.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 138–144, 1989.     

Stochastic Loewner evolution in doubly connected domains

This paper introduces the annulus SLE processes in doubly connected domains. Annulus SLE₆ has the same law as stopped radial SLE₆, up to a time-change. For 6, some weak equivalence relation exists between annulus SLE and radial SLE. Annulus SLE₂ is the scaling limit of the corresponding loop-erased conditional random walk, which implies that a certain form of SLE₂ satisfies the reversibility property. We also consider the disc SLE process defined as a limiting case of the annulus SLEs. Disc SLE₆ has the same law as stopped full plane SLE₆, up to a time-change. Disc SLE₂ is the scaling limit of loop-erased random walk, and is the reversal of radial SLE₂.