Bounds on c 3$ for threefolds

We bound the third Chern number of a minimal smooth threefold with ample canonical bundle by quadratic functions in the first two Chern numbers. Received: 5 December 1997 / Revised version: 9 June 1998     

Yamabe Invariants and $ Spin^c $ Structures

The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that of the 4-sphere. This is done by using Dirac operators to control the lowest eigenvalue of a perturbation of the Yamabe Laplacian. These results dovetail perfectly with those derived from the perturbed Seiberg–Witten equations [Le3], but the present method is much more elementary in spirit. Submitted: October 1997     

A character formula for a family of simple modular representations of $ GL_n $

Let K be an algebraically closed field of finite characteristic p, and let be an integer. In the paper, we give a character formula for all simple rational representations of with highest weight any multiple of any fundamental weight. Our formula is slightly more general: say that a dominant weight λ is special if there are integers such that and . Indeed, we compute the character of any simple module whose highest weight λ can be written as with all are special. By stabilization, we get a character formula for a family of irreducible rational -modules. Received: June 30, 1997.     

Approximations of stable actions on $ \Bbb {R} $-trees

This article shows how to approximate a stable action of a finitely presented group on an -tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an -tree can be approximated by a small action of the same group on a simplicial tree. The techniques we use highly rely on Rips's study of stable actions on -trees and on the dynamical study of exotic components by D. Gaboriau. Received: 22 October, 1997     

On the minimal extension of the sequence $ \langle 0,1,1,7 \rangle $

This note shows that the p _n -sequence has the minimal extension property in the class of algebras with a nonassociative binary operation. This generalizes the result of J. Galuszka and gives a partial solution of problem 18 raised by G. Gr?tzer and A. Kisielewicz of whether has the minimal extension property. This result reduces the problem to the class of algebras with a semilattice operation. Received July 16, 1996; accepted in final form February 28, 1997.     

The $\mu$-measure as a tool for classifying computational complexity

Two simply typed term systems and are considered, both for representing algorithms computing primitive recursive functions. is based on primitive recursion, on recursion on notation. A purely syntactical method of determining the computational complexity of algorithms in , called $\mu$ -measure, is employed to uniformly integrate traditional results in subrecursion theory with resource-free characterisations of sub-elementary complexity classes. Extending the Schwichtenberg and Müller characterisation of the Grzegorczyk classes for , it is shown $\mathcal{E}_{n+1} = \mathcal{R}^n_1n\ge 1\mathcal{R}^n_i$ denotes the \emph{th modified Heinermann class} based on . The proof does not refer to any machine-based computation model, unlike the Schwichtenberg and Müller proofs. This is due to the notion of modified recursion lying on top of each other provided by . By Ritchie's result, characterises the linear-space computable functions. Using the same method, a short and straightforward proof is presented, showing that characterises the polynomial time computable functions. Furthermore, the classes and coincide at and above level 2. Received: 22 September 1997 / Revised version: 12 May 1999     

Evolution of hypersurfaces in $ {\Bbb R}^N$ by Gaussian curvature

In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by Gaussian curvature of a strictly convex hypersurface in . Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized motion existing for each time. Received November 24, 1997     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

Wave Invariants for Non-degenerate Closed Geodesics

((Without abstract)) Submitted: January 1997, Revised version: May 1997, Final version: September 1997     

Lipschitz maps and nets in Euclidean space

((Without abstract)) Submitted: April 1997, Final version: July 1997     

Anti-self-dual Equation on 4-manifolds with Degenerate Metric

((Without abstract)) Submitted: July 1997, Revised version: November 1997     

Complex projective surfaces and infinite groups

((Without abstract)) Submitted: March 1997, Final version: September 1997     

A New Characterization of Finite $ \sigma $ -Soluble $ P\sigma T $ -Groups

Siberian Mathematical Journal - We prove that  $ G $ is a finite $ \sigma $ -soluble group with transitive $ \sigma $ -permutability if and only if the following hold: (i) $ G $ possesses...     

A Geometric Inequality with Applications to the Kakeya Problem in Three Dimensions

((Without abstract)) Submitted: May 1997, Revised version: August 1997     

Bounded and L2 harmonic forms on universal covers

((Without abstract)) Submitted: April 1997, Revision: October 1997     

Frobenius $ \mathbb Q $ -groups

A finite group whose irreducible complex characters are rational is called a -group. In this paper we will find the structure of Frobenius -groups.Received: 14 April 2003     

Multipliers between $ BMO $ Spaces on Open Unit Ball

and spaces consist of all those locally integrable functions on the open unit ball such that their mean oscillations on any Bergman ball are, respectively, bounded and vanishing to zero as the Bergman ball approaches the boundary of the unit ball. The harmonic (or analytic) versions of the and spaces are the Bloch space and the little Bloch space, respectively. The study of these spaces plays an important role in modern analysis, especially in the the area of operator theory and holomorphic spaces. In this paper, we characterize systematically the multipliers of and spaces. Submitted: January 9, 2001?Revised: October 16, 2002     

Recurrence Formula for Polynomials of Two Variables, Orthogonal with Respect to Rotation Invariant Measures

We give the recurrence formula satisfied by polynomials of two variables, orthogonal with respect to a rotation invariant measure. Moreover, we show that for polynomials satisfying such a recurrence formula, there exists an orthogonality measure which is rotation invariant. We also compute explicitly the recurrence coefficients for the disk polynomials. January 4, 1997. Date revised: October 15, 1997. Date accepted: October 21, 1997.     

Blossoming: A Geometrical Approach

A geometrical approach of a notion of blossom for piecewise smooth Chebyshev functions is developed by considering convenient intersections of osculating flats. A subblossoming principle allows us to obtain all the expected properties and leads to the notion of blossom for splines based on a given piecewise smooth Chebyshev function. January 7, 1997. Date revised: October 1, 1997. Date accepted: December 22, 1997.