Abelianization of the <Emphasis Type="Italic">F</Emphasis>-divided fundamental group scheme

Let (X , x ₀) be a pointed smooth proper variety defined over an algebraically closed field. The Albanese morphism for (X , x ₀) produces a homomorphism from the abelianization of the F-divided fundamental group scheme of X to the F-divided fundamental group of the Albanese variety of X. We prove that this homomorphism is surjective with finite kernel. The kernel is also described.     

Quasidiagonality and the hyperinvariant subspace problem

In a sequence of recent papers, [11], [13], [9] and [5], the authors (together with H. Bercovici and C. Foias) reduced the hyperinvariant subspace problem for operators on Hilbert space to the question whether every C ₀₀-(BCP)-contraction that is quasidiagonal and has spectrum the unit disc has a nontrivial hyperinvariant subspace (n.h.s.). An essential ingredient in this reduction was the introduction of two new equivalence relations, ampliation quasisimilarity and hyperquasisimilarity, defined below. This note discusses the question whether, by use of these relations, a further reduction of the hyperinvariant subspace problem to the much-studied class (N + K) (defined below) might be possible.     

On quasinilpotent operators

In this note we modify a new technique of Enflo for producing hyperinvariant subspaces to obtain a much improved version of his ``two sequences' theorem with a somewhat simpler proof. As a corollary we get a proof of the ``best' theorem (due to V. Lomonosov) known about hyperinvariant subspaces for quasinilpotent operators that uses neither the Schauder-Tychonoff fixed point theorem nor the more recent techniques of Lomonosov.

     

Spectral pictures of Aluthge transforms of operators

In this paper we continue our study, begun in [12], of the relationships between an arbitrary operatorT on Hilbert space and its Aluthge transform . In particular, we show that in most cases the spectral picture ofT coincides with that of , and we obtain some interesting connections betweenT and as a consequence.     

The Iterated Aluthge Transform of an Operator

The Aluthge transform (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated , and this study was continued in [7], in which relations between the spectral pictures of T and were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates { ⁽ⁿ⁾} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence { ⁽ⁿ⁾} converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6). Submitted: December 5, 2000? Revised: August 30, 2001.     

Almost commuting matrices

It is shown that if A and B are n × n complex matrices with $\text{A = A}{}^1\text{and}\text{∥AB ? BA∥</}\text{2?}{}^2\text{(n ? 1)}$, then there exist n × n matrices A′ and B′ with $\text{A′ = A′}{}^1\text{such that}\text{A′B′ = B′A′}\text{and}\text{∥A ? A′∥? ?, ∥B ? B′∥? ?}$.     

FEATURES AND APPLICATIONS OF BERTALANFFY-RICHARDS‘ AND SCHNUTE'S GROWTH EQUATIONS

ABSTRACT. Based on various ranges of the parameter m (or b), the paper analyzes the features and the integral forms of the Schnute and the Bertalanffy-Richards growth equations as well as the two aspects of their special cases (such as Gompertz, logistic and monomolecular models). It is a first attempt to investigate all the corresponding relationships among parameters of the models derived from the Schnute and the Bertalanffy-Richards growth equations. All the models from the two are empirically fitted by different data sets for eucalypt plantations. Unlike earlier papers, the results of this paper show that either of the two growth equations can be considered as a model for estimating forest growth given a parameter range, and both can produce similar growth performances. Some other aspects of the two growth equations are discussed so that the two can be used correctly.     

Glass Formation Ability and Kinetics of the Gd55A120Ni25 Bulk Metallic Glass

We report a new bulk glass-forming alloy GdssA12oNi25. The bulk sample of the alloy is prepared in the shape of rods in diameter 2ram by suction casting. The rod exhibits typical amorphous characteristics in the x-ray diffraction pattern, paramagnetic property at 30OK, distinct glass transition and multi-step crystallization behaviour in differential scanning calorimetry traces. The gJass formation ability of the alloy is investigated by using the reduced glass transition temperature Trg and the parameter γ- Kinetics of glass transition and primary crystallization is also studied. The fragility parameter m obtained from the Vogel-Fulcher-Tammann dependence of glass transition temperature Tg on In φ （φ is the heating rate） classifies the bulk metallic glasses into the intermediate category according to Angell＇s classification.     

MoWeD, a computer program to rapidly deconvolute low resolution electrospray liquid chromatography/mass spectrometry runs to determine component molecular weights

A computer program is described that can rapidly process low-resolution electrospray liquid chromatography/mass spectrometry (LC/MS) for peptides and proteins and assign molecular weights for observed components. The program first analyzes individual scans using a deconvolution algorithm similar to that previously described by Zhang and Marshall. Results for the entire run are then sorted by mass and those values found in adjacent scans are grouped together. The list of found components can also be compared to a user defined list of target molecular weight values making it easy to compare the results from different analyses. The program also has the capability to process a rolling average of scans that improves the performance when analyzing high molecular weight components. Other program features facilitate closer examination of selected spectra or regions of the chromatogram to check the MoWeD mass assignments. The utility of the program was demonstrated by the analysis of LC/MS data derived from a complex mixture of proteins derived from a bacterial whole cell lysate that had previously been analyzed manually. The MoWeD analysis was 30 times faster and provided a more comprehensive list of the components present.