On（N,U）-Coherence of Modules and Rings

Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U.     

Supersymmetry at Dø and other new phenomena searches in Run II

The RunII of the Dø experiment was started in March 2001. The first preliminary results on searches for new physics are presented, with a luminosity of ～ 10 pb^?1 from the data collected in 2001-2002. We report results in mSUGRA (jets + missingEt channel), GMSB (diphotons), RPV (trileptons and like sign dileptons) and large extra dimensions (dielectrons and diphotons).     

MULTIFRACTAL FORMALISMS：BOXED VERSUS CENTERED INTERVALS

There are mainly two approaches to the multifractal analysis of measures. The first one, which is used in applications and in studying problems arising from dynamical systems, uses a hierarchy of boxes. The second one, which is more satisfactory from the viewpoint of geometric measure theory, uses more intrinsicconcepts. This article is an account of a work by J. Barral, F. Ben Nasr, and J. Peyriere [3] which pro-vides a bridge between these two theories.     

DIMENSIONS FORRANDOM SELF——CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets.     

DMRG studies on interchain coupling model for quasi-one-dimensional organic magnet

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦. Received 14 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

Proper actions on cohomology manifolds

Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.

     

Convex Drawings of Planar Graphs and the Order Dimension of 3-Polytopes

We define an analogue of Schnyder's tree decompositions for 3-connected planar graphs. Based on this structure we obtain: Let G be a 3-connected planar graph with f faces, then G has a convex drawing with its vertices embedded on the (f–1)×(f–1) grid. Let G be a 3-connected planar graph. The dimension of the incidence order of vertices, edges and bounded faces of G is at most 3.The second result is originally due to Brightwell and Trotter. Here we give a substantially simpler proof.     

螺线的Steinhaus维数

Ｄｕｐａｉｎ Ｙ,Ｆｒａｎｃｅ Ｍ．Ｍ．和 Ｔｒｉｃｏｔ Ｃ．［１］利用积分几何中的经典的Ｓｔｅｉｎｈａｕｓ定理,引入 Ｓｔｅｉｎｈａｕｓ维数,并研究了螺线的 Ｓｔｅｉｎｈａｕｓ维数与盒维数的关系．本文深入这一研究,对Ｓｔｅｉｎｈａｕｓ维数的值域,单调性等基本性质作了进一步的考察．     

Homological Dimension of Coalgebras and Crossed Coproducts

Let H be a Hopf k-algebra. We study the global homological dimension of the underlying coalgebra structure of H. We show that gl.dim(H) is equal to the injective dimension of the trivial right H-comodule k. We also prove that if D = C H is a crossed coproduct with invertible , then gl.dim(D) gl.dim(C) + gl.dim(H). Some applications of this result are obtained. Moreover, if C is a cocommutative coalgebra such that C ^* is noetherian, then the global dimension of the coalgebra C coincides with the global dimension of the algebra C ^*.