Large Lattices Over Orders

Let K be the quotient field of a Dedekind domain R. We characterizethe R-orders in a separable K-algebra for which every R-projective-module decomposes into -lattices. Butler, Campbell and Kovácshave recently shown that the latter holds for the integral groupring of a cyclic group of prime order, as well as for lattice-finiteorders over a complete discrete valuation domain. 2000 MathematicsSubject Classification 16H05, 16G30 (primary), 05C65 (secondary).     

Formation of hafnium carbide thin films by plasma enhanced chemical vapor deposition from bis(η-cyclopentadienyl)dimethylhafnium as precursor

Thin films of hafnium carbide have been deposited by plasma-enhanced chemical vapor deposition using bis(-cyclopentadienyl)dimethylhafnium, Cp₂ Hf(CH₃)₂, as precursor in 13.56 MHz planar reactor. The influence of the various experimental parameters on film properties has been studied. The carbon content ranged from 11 to 40 weight % and increased with the deposition rate. The film hardness varied between 1300 and 2000 HK. Depending on the carbon content and power delivered in the discharge, the film resistivity and film density ranged from 271 to 10⁵ ·cm and from 3.4 to 10.4 g/cm³, respectively, and the film composition varied from HfC to hafnium containing a-C: H films.     

Targeted Synthesis of Two Super‐Complex Zeolites with Embedded Isoreticular Structures

A novel structural coding approach combining structure solution, prediction, and the targeted synthesis of new zeolites with expanding complexity and embedded isoreticular structures was recently proposed. Using this approach, the structures of two new zeolites in the RHO family, PST‐20 and PST‐25, were predicted and synthesized. Herein, by extending this approach, the next two higher generation members of this family, PST‐26 and PST‐28, have been predicted and synthesized. These two zeolites have much larger unit cell volumes (422 655 ų and 614 912 ų, respectively) than those of the lower generations. Their crystallization was confirmed by a combination of both powder X‐ray and electron diffraction techniques. Aluminate and water concentrations in the synthetic mixture were found to be the two most critical factors influencing the structural expansion of embedded isoreticular zeolites under the synthetic conditions studied herein.     

Fast and Parallel Interval Arithmetic

Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Moreover, we describe an implementation of midpoint-radius interval arithmetic entirely using BLAS. Therefore, in particular, matrix operations are very fast on almost any computer, with minimal effort for the implementation. Especially, with the new definition it is seemingly the first time that full advantage can be taken of the speed of vector and parallel architectures. The algorithms have been implemented in the Matlab interval toolbox INTLAB.     

Ill-Conditionedness Need not be Componentwise Near to Ill-Posedness for Least Squares Problems

The condition number of a problem measures the sensitivity of the answer to small changes in the input, where small refers to some distance measure. A problem is called ill-conditioned if the condition number is large, and it is called ill-posed if the condition number is infinity. It is known that for many problems the (normwise) distance to the nearest ill-posed problem is proportional to the reciprocal of the condition number. Recently it has been shown that for linear systems and matrix inversion this is also true for componentwise distances. In this note we show that this is no longer true for least squares problems and other problems involving rectangular matrices. Problems are identified which are arbitrarily ill-conditioned (in a componentwise sense) whereas any componentwise relative perturbation less than 1 cannot produce an ill-posed problem. Bounds are given using additional information on the matrix.     

Wireless Packet Scheduling Algorithm for OFDMA System Based on Time‐Utility and Channel State

In this paper, we propose an urgency‐ and efficiencybased wireless packet scheduling (UEPS) algorithm that is able to schedule real‐time (RT) and non‐real‐time (NRT) traffics at the same time while supporting multiple users simultaneously at any given scheduling time instant. The UEPS algorithm is designed to support wireless downlink packet scheduling in an orthogonal frequency division multiple access (OFDMA) system, which is a strong candidate as a wireless access method for the next generation of wireless communications. The UEPS algorithm uses the time‐utility function as a scheduling urgency factor and the relative status of the current channel to the average channel status as an efficiency indicator of radio resource usage. The design goal of the UEPS algorithm is to maximize throughput of NRT traffics while satisfying quality‐of‐service (QoS) requirements of RT traffics. The simulation study shows that the UEPS algorithm is able to give better throughput performance than existing wireless packet scheduling algorithms such as proportional fair (PF) and modifiedlargest weighted delay first (M‐LWDF), while satisfying the QoS requirements of RT traffics such as average delay and packet loss rate under various traffic loads.     

PAQM: an adaptive and proactive queue management for end‐to‐end TCP congestion control

Two functions, the congestion indicator (i.e. how to detect congestion) and the congestion control function (i.e. how to avoid and control congestion), are used at a router to support end‐to‐end congestion control in the Internet. Random early detection (RED) (IEEE/ACM Trans. Networking 1993; 1 (4):397–413) enhanced the two functions by introducing queue length averaging and probabilistic early packet dropping. In particular, RED uses an exponentially weighted moving average (EWMA) queue length not only to detect incipient congestion but also to smooth the bursty incoming traffic and its resulting transient congestion. Following RED, many active queue management (AQM)‐based extensions have been proposed. However, many AQM proposals have shown severe problems with detection and control of the incipient congestion adaptively to the dynamically changing network situations. In this paper, we introduce and analyse a feedback control model of TCP/AQM dynamics. Then, we propose the Pro‐active Queue Management (PAQM) mechanism, which is able to provide proactive congestion avoidance and control using an adaptive congestion indicator and a control function under a wide range of traffic environments. The PAQM stabilizes the queue length around the desired level while giving smooth and low packet loss rates and high network resource utilization. Copyright © 2004 John Wiley & Sons, Ltd.     

Schurian vector space categories, hereditary algebras and Roiter's norm

We associate a positive real number to any vector space K-category over a field K. Generalizing a result of Nazarova and Roiter, we show that a schurian vector space K-category is representation-finite if and only if is finite and . Such vector space categories are quasilinear, i.e. its indecomposables are simple modules over their endomorphism ring. Recently, Nazarova and Roiter introduced the concept of -faithful poset in order to clarify the structure of critical posets. Their conjecture on the precise form of -faithful posets was established by Zeldich. We generalize these results and characterize -faithful quasilinear vector space K-categories in terms of a class of hereditary algebras H_ρ(D) parametrized by a skew-field D and a rational number ρ1.     

Verified error bounds for multiple roots of systems of nonlinear equations

It is well known that it is an ill-posed problem to decide whether a function has a multiple root. Even for a univariate polynomial an arbitrary small perturbation of a polynomial coefficient may change the answer from yes to no. Let a system of nonlinear equations be given. In this paper we describe an algorithm for computing verified and narrow error bounds with the property that a slightly perturbed system is proved to have a double root within the computed bounds. For a univariate nonlinear function f we give a similar method also for a multiple root. A narrow error bound for the perturbation is computed as well. Computational results for systems with up to 1000 unknowns demonstrate the performance of the methods.