Gross–Pitaevskii dynamics of Bose–Einstein condensates and superfluid turbulence

The Gross–Pitaevskii equation, also called the nonlinear Schrödinger equation (NLSE), describes the dynamics of low-temperature superflows and Bose–Einstein Condensates (BEC). We review some of our recent NLSE-based numerical studies of superfluid turbulence and BEC stability. The relations with experiments are discussed.     

明目科研成果应用及其多元统计分析

本文简介了明目科研成果《易效明目功》的应用，并重点对易效明目功防治青少年近视的效用进行了多元统计分析，Ｐ＜０．０５，效果显著。     

Long-term results of recurrent laryngeal nerve resection for adductor spasmodic dysphonia

From a total of 43 adductor spasmodic patients over a 10-year period, 11 underwent resection of a portion of the recurrent laryngeal nerve on one side. The initial results were excellent but a varying degree of recurrence took place in 8 patients. In 4, a reoperation was done. At the final follow-up, 2–8 years after the primary operation, 4 patients were no longer suffering from spasmodic dysphonia, another 5 were better off than before surgery, and 1 remained unchanged. Only 1 was worse off. Electromyographic findings indicated that the recurrence of symptoms was due to regeneration of the nerve fibers.     

A heuristic technique for the transient behavior of Markovian queueing systems

Through an examination of numerical solutions to Markovian queueing systems, it has been shown that the expected queue length eventually approaches its equilibrium value in an approximately exponential manner. Based on this observation a heuristic is proposed for approximating the transient expected queue length for Markovian systems by scaling the numerical solution of an M/M/1 system.     

Existence theorems in optimal control problems without convexity assumptions

A correction in the statement of Proposition 4.1 of Ref. 1 is given.     

Systematic and statistical errors in quantitative evaluation in TLC and HPTLC. 1. Evaluation by graphic methods

The paper discusses errors and error propagation in respect of graphic methods in quantitative in situ measurements in TLC. An error of 0.3% is possible by measuring only peak height if optimal conditions are chosen. This is in good agreement with analysis done practically which gives errors in the order of 0.3–0.6%. If the peak area is evaluated using the approximation peak height × half width, the error is in the order of 0.6%, but in real experiments only 1.5% had been found. Systematic errors in determining peak heights are introduced by the time constant of the amplifiers and the recorder.     

On large minimal blocking sets in PG(2,q)

The size of large minimal blocking sets is bounded by the Bruen–Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non‐square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non‐prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q^4/3 + 1 or q^4/3 + 2. Density results for the spectrum of minimal blocking sets in Galois planes of non‐prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval . © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 25–41, 2005.     

A version of Sharkovskii's theorem for differential equations

We present a version of the Sharkovskii cycle coexistence theorem for differential equations. Our earlier applicable version is extended here to hold with the exception of at most two orbits. This result, which (because of counter-examples) cannot be improved, is then applied to ordinary differential equations and inclusions. In particular, if a time-periodic differential equation has -periodic solutions with , for all , then infinitely many subharmonics coexist.