Decidability of finite quasivarieties generated by certain transformation semigroups

No Abstract. Received January 2, 2000; accepted in final form August 28, 2000.     

On the scarcity of contravariant left adjunctions

It is shown that any pair of contravariant mutually left adjoint functors between varieties of algebrasC andD factors through the retractions of these categories onto the complete lattices of epimorphs of their respective initial objects, and is thus fairly degenerate. However, some interesting contravariant left adjoint functors do exist between categories of finitely generated (or otherwise restricted) algebras.This work was done while the author was partly supported by NSF contract DMS 85-02330.Presented by F. E. J. Linton.     

Existence of the non-primitive Weierstrass gap sequences on curves of genus 8

We show that for any possible Weierstrass gap sequence L on a non-singular curve of genus 8 with twice the smallest positive non-gap is less than the largest gap there exists a pointed non-singular curve (C, P) over an algebraically closed field of characteristic 0 such that the Weierstrass gap sequence at P is L. Combining this with the result in [6] we see that every possible Weierstrass gap sequence of genus 8 is attained by some pointed non-singular curve. *Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science. **Partially supported by Grant-in-Aid for Scientific Research (17540030), Japan Society for the Promotion of Science.     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.     

Riesz transforms for a non-symmetric Ornstein-Uhlenbeck semigroup

Let (ℋ _t ) _t≥0 be the Ornstein-Uhlenbeck semigroup on ℝ ^d with covariance matrix I and drift matrix −λ(I+R), where λ>0 and R is a skew-adjoint matrix and denote by γ _∞ the invariant measure for (ℋ _t ) _t≥0. Semigroups of this form are the basic building blocks of Ornstein-Uhlenbeck semigroups which are normal on L ²(γ _∞). We investigate the weak type 1 estimate of the Riesz transforms for (ℋ _t ) _t≥0. We prove that if the matrix R generates a one-parameter group of periodic rotations then the first order Riesz transforms are of weak type 1 with respect to the invariant measure γ _∞. We also prove that the Riesz transforms of any order associated to a general Ornstein-Uhlenbeck semigroup are bounded on L ^p (γ _∞) if 1<p<∞. The authors have received support by the Italian MIUR-PRIN 2005 project “Harmonic Analysis” and by the EU IHP 2002-2006 project “HARP”.     

Modified quasi-reversibility method for final value problems in Banach spaces

This paper is concerned with the final value problem associated with a linear operator A in a Banach space, where −A is the generator of a uniformly bounded analytic semigroup. Based on the deLaubenfels' functional calculus, we use new quasi-reversibility method, introduced by Boussetila and Rebbani recently, to form an approximate problem. We obtain some results in a Banach space similar to those in a Hilbert space.     

Cayley color graphs of inverse semigroups and groupoids

The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.     

Sub-semigroups determined by the zero-divisor graph

In this paper we study sub-semigroups of a finite or an infinite zero-divisor semigroup S determined by properties of the zero-divisor graph Γ(S). We use these sub-semigroups to study the correspondence between zero-divisor semigroups and zero-divisor graphs. In particular, we discover a class of sub-semigroups of reduced semigroups and we study properties of sub-semigroups of finite or infinite semilattices with the least element. As an application, we provide a characterization of the graphs which are zero-divisor graphs of Boolean rings. We also study how local property of Γ(S) affects global property of the semigroup S, and we discover some interesting applications. In particular, we find that no finite or infinite two-star graph has a corresponding nil semigroup.     

Slowly changing vectors and the asymptotic finite-dimensionality of an operator semigroup

Siberian Mathematical Journal - Let X be a Banach space and let T: X → X be a linear power bounded operator. Put X 0 = {x ∈ X | T n x → 0}. We prove that if X 0 ≠ X then...     

The existence of global attractors for 2D Navier-Stokes equations in <Emphasis Type="Italic">H</Emphasis><Superscript><Emphasis Type="Italic">k</Emphasis></Superscript> spaces

In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.