Simply terminating rewrite systems with long derivations

A term rewrite system is called simply terminating if its termination can be shown by means of a simplification ordering. According to a result of Weiermann, the derivation length function of any simply terminating finite rewrite system is eventually dominated by a Hardy function of ordinal less than the small Veblen ordinal. This bound had appeared to be of rather theoretical nature, because all known examples had had multiple recursive complexities, until recently Touzet constructed simply (and even totally) terminating examples with complexities beyond multiple recursion. This was established by simulating the Hydra battle for all ordinal segments below the proof-theoretic ordinal of Peano arithmetic. By extending this result to the small Veblen ordinal we prove the huge bound of Weiermann to be sharp. As a spin-off we can show that total termination allows for complexities as high as those of simple termination. This paper is part of the authors doctoral dissertation project (under the supervision of Professor A. Weiermann at the University of Münster).The work on this paper was supported by DFG grant WE 2178/2–1 Mathematics Subject Classification (2000): 03D20, 68Q15, 68Q42     

On criteria for extremality of Teichmüller mappings

Let be a Teichmüller self-mapping of the unit disk corresponding to a holomorphic quadratic differential . If satisfies the growth condition (as ), for any given 0$">, then is extremal, and for any given , there exists a subsequence of such that

is a Hamilton sequence. In addition, it is shown that there exists with bounded Bers norm such that the corresponding Teichmüller mapping is not extremal, which gives a negative answer to a conjecture by Huang in 1995.

     

Infinite systems of linear equations for real analytic functions

We study the problem when an infinite system of linear functional equations

has a real analytic solution on for every right-hand side and give a complete characterization of such sequences of analytic functionals . We also show that every open set has a complex neighbourhood such that the positive answer is equivalent to the positive answer for the analogous question with solutions holomorphic on .

     

Weak and Strong Convergence for Fixed Points of Asymptotically Non-expansive Mappings

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and hniagbosor (2000), Rhoades (1994) and Schu (1991).     

On images of Borel measures under Borel mappings

Let and be metric spaces. We show that the tight images of a (fixed) tight Borel probability measure on , under all Borel mappings , form a closed set in the space of tight Borel probability measures on with the weak-topology. In contrast, the set of images of under all continuous mappings from to may not be closed. We also characterize completely the set of tight images of under Borel mappings. For example, if is non-atomic, then all tight Borel probability measures on can be obtained as images of , and as a matter of fact, one can always choose the corresponding Borel mapping to be of Baire class 2.

     

New Families in the Stable Homotopy of Spheres Revisited

This paper constructs a new family in the stable homotopy of spheres π _{t −6} S represented by h _n g ₀γ₃∈E ^{6 t} ₂ in the Adams spectral sequence which revisits the b _{n −1} g ₀γ₃-elements ∈π _{t −7} S constructed in [3], where t = 2p ⁿ (p− 1) + 6(p ² + p + 1)(p− 1) and p≥ 7 is a prime, n≥ 4. Received October 7, 1998, Revised May 8, 2000, Accepted August 8, 2000.     

Some Classes of L 1-Convergence of Fourier Series

In this paper equivalent classes of the classes M and S _pr , p > 1, > 0. r { 0,1,2, ... ,[]} defined by Shuyun [3] are obtained. Then, it is shown that the class S _pr , 1 > p 2, 0, r {0,1,2,...,[]} is a subclass of BVC _r , where S _pr is the equivalent class of the Shuyun's class S _pr , BV is the class of null sequences of bounded variation and C _r is the extension of the Garrett--Stanojevic class. As a corollary of this result, we have obtained the theorem, proved in [7].     

Folding of lattice protein chains with modified Gō potential

We propose a modified Gō model in which the pairwise interaction energies vary as local environment changes. The stability difference between the surface and the core is also well considered in this model. Thermodynamic and kinetic studies suggest that this model has improved folding cooperativity and foldability in contrast with the Gō model. The free energy landscape of this model has broad barriers and narrow denatured states, which is consistent with that of the two-state folding proteins and is lacked for the Gō model. The role of non-native interactions in protein folding is also studied. We find that appropriate consideration of the contribution of the non-native interactions may increase the folding rate around the transition temperature. Our results show that conformation-dependent interaction between the residues is a realistic representation of potential functions in protein folding. Received 10 April 2002 / Received in final form 20 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wangwei@nju.edu.cn     

Unconditional structures of weakly null sequences

The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of , or there exists a subsequence which is boundedly convexly complete.