Limited-trial Chase decoding

Chase decoders permit flexible use of reliability information in algebraic decoding algorithms for error-correcting block codes of Hamming distance d. The least complex version of the original Chase algorithms uses roughly d/2 trials of a conventional binary decoder, after which the best decoding result is selected as the final output. On certain channels, this approach achieves asymptotically the same performance as maximum-likelihood (ML) decoding. In this correspondence, the performance of Chase-like decoders with even less trials is studied. Most strikingly, it turns out that asymptotically optimal performance can be achieved by a version which uses only about d/4 trials.     

Pion correlations and resonance effects in \bar{p}p annihilation to 4\pi^0 at rest

We study correlations in the exclusive reaction at rest with complete reconstruction of the kinematics for each event. The inclusive distribution is fairly flat at small invariant mass of the pion pair while a small enhancement in the double differential distribution is observed for small invariant masses of both pion pairs. Dynamical models with resonances in the final state are shown to be consistent with the data while the stochastic HBT mechanism is not supported by the present findings. Received: 26 February 2002 / Revised version: 22 July 2002 / Published online: 30 August 2002     

Herstellung von substituierten 2-Aminooxazol-4-carbonitrilen

Preparation of Substituted 2-Aminooxazole-4-carbonitriles During our synthetic programme to convert 4-isoxazolylthioureas 3 into the corresponding carbodiimides 5 , a side reaction leading to the hitherto unknown 2-aminooxazole-4-carbonitriles 6 was observed. By selecting appropriate reaction conditions, it was possible to improve the yields of the carbodiimides 5 as well as of the novel oxazole-carbonitriles 6 at will, thus allowing the synthesis of 6 to be conducted in very good yields. To overcome the difficulty of isolating unstable carbodiimides, the synthesis of 6 is best carried out in a one-pot procedure. A limited mechanistic study showed that the formation of 6 proceeds via 5 as the only intermediate. The stability of the N?C?N bonds against base attack (depending strongly on both sterical hindrance and electronic-density factors) forms the only limitation of this new synthetic pathway to oxazole-4-carbonitriles.     

A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

Limits of the output power in Er3+:ZBLAN singlemodefibre lasers

The saturation of the 2.71 μm laser output has been measured in erbium-doped ZBLAN singlemode fibres with Er³⁺ concentrations of 1000, 5000 and 10000 ppm mol. Limits of the single-mode-laser output are discussed     

Dynamic effects in hot-carrier degradation relevant for CMOS operation

We describe different dynamic degradation effects in n- and p-MOSFETs as they are clearly proven and generally accepted to date. It turns out that they are connected with time constants in the oxide and at the interface and that time constants related to the device operation are too short to be relevant in this context. The effects are detrapping of fixed charges, the slow movement of holes in the oxide, an enhanced-degradation effect caused by alternating voltage conditions, during dynamic stress, and a post-stress interface state formation effect in nitride passivated n-MOSFETs. Furthermore, we discuss the relevance of those effects, under different operation conditions, finding that the fast non-stationary effects are of little significance. Only the “slow” effects, with time constants of seconds and above, play a role in reliability issues of MOSFETs.     

Elektrische Charakterisierung von Hochfrequenz-Niederdruck-Gasentladungen

In recent years there has emerged significant interest in low pressure radio frequency (rf) glow discharges which are used widely particulary in IC fabrication. Various parameters of the rf glow discharge have been found to be useful for its electrical characterization; however, there is no uniformity and agreement. Extensive experimental investigations on various discharge systems have shown, that the self-bias on the rf driven electrode, the complex conductivity and the breakdown characteristic are preferable parameters of rf discharges. Advantageously the self-bias and the complex conductivity should be presented in dependence on the pressure and the applied rf voltage. The discharge current cannot be measured quite accurately due to currents via leaky capacitors and the deviations from a sinusoidal form of the current due to nonlinearities.     

On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.     

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

Some examples of application of the metric entropy method

We show how the metric entropy method can be substituted for the dyadic chaining, to prove in a unified setting several classical results. Among them are Stechkin's theorem, Gál--Koksma theorems and quantitative Borel--Cantelli lemmas. We give simpler proofs and improve some of these results. Two classes of examples are given: firstly stationary Gaussian sequences with applications to upper and lower classes and the law of the iterated logarithm for subsequences, and secondly in Diophantine approximation relatively to Gál and Schmidt's theorems.