Representation of shift-invariant operators onL 2 byH ∞ transfer functions: An elementary proof,a generalization toL p,and a counterexample forL ∞

We give an elementary proof of the well-known fact that shift-invariant operators onL ²[0, ∞) are represented by transfer functions which are bounded and analytic on the right open half-plane. We prove a generalization to Banach space-valuedL ^p -functions, where 1≤p<∞. We show that the result no longer holds forp=∞. This research was supported partially by the Weizmann Fellowship, and partially by the Air Force Office of Scientific Research under Contract F49620-86-C-0111.     

Neuropsychological functioning of girls with attention-deficit/hyperactivity disorder followed prospectively into adolescence: Evidence for continuing deficits?

The current study prospectively followed girls with attention-deficit/hyperactivity disorder (ADHD), along with a matched comparison sample, 5 years after childhood neuropsychological assessments. Follow-up neuropsychological measures emphasized attentional skills, executive functions, and language abilities. Paralleling childhood findings, the childhood-diagnosed ADHD group displayed moderate to large deficits in executive/attentional performance as well as in rapid naming relative to the comparison group at follow up (Mage 14.2 years). ADHD-inattentive versus ADHD-combined contrasts were nonsignificant and of negligible effect size, even when a refined, sluggish cognitive tempo subgroup of the inattentive type was examined. Although ADHD versus comparison group differences largely withstood statistical control of baseline demographics and comorbidities, control of childhood IQ reduced executive function differences to nonsignificance. Yet when the subset of girls meeting diagnostic criteria for ADHD in adolescence was compared with the remainder of the participants, neuropsychological deficits emerged even with full statistical control. Overall, childhood ADHD in girls portends neuropsychological and executive deficits that persist for at least 5 years. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

关于Smarandache可乘函数的均值研究

本文的主要目的是利用初等方法研究Smarandache可乘函数在简单数集中的均值性质,并给出一个有趣的渐近公式。     

Analysis of an algorithm for solution of conditional optimization problems with linear-fractional objective functions over permutations

A method is considered to solve a conditional optimization problem with a linear-fractional objective function over permutations. The performance of sub algorithms to solve this problem is evaluated. The practical efficiency of the algorithm is analyzed by conducting numerical experiments. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 133–146, July–August 2007.     

Measuring consistency in TTL-based caches

We propose a general modeling framework to evaluate the performance of cache consistency algorithms. In addition to the usual hit rate, we introduce the hit^* rate as a consistency measure, which captures the fraction of non-stale downloads from the cache. We apply these ideas to the analysis of the fixed TTL consistency algorithm in the presence of network delays. The hit and hit^* rates are evaluated when requests and updates are modeled by renewal processes. Classical results on the renewal function lead to various bounds.     

A new stereological principle for test lines in three-dimensional space

A new principle is presented to generate isotropic uniform random (IUR) test lines hitting a geometric structure in three-dimensional space (3D). The principle therefore concerns the estimation of surface area, volume, membrane thickness, etc., of arbitrary structures with piecewise smooth boundary. The principle states that a point-sampled test line on an isotropic plane through a fixed point in 3D is effectively an invariant test line in 3D. Particular attention is devoted to the stereology of particles, where an alternative to the surfactor method is obtained to estimate surface area. An interesting case arises when the particle is convex. The methods are illustrated with synthetic examples.     

静态球对称时空中的标量场辐射

采用多项式函数代替乌龟坐标的方法,给出静态球对称时空中黑洞事件视界和宇宙视界区域内标量场方程的解,并对事件视界附近势垒的性质进行了讨论。发现对带电量不同的时空,标量场辐射的形式亦有所不同;势垒随宇宙学常数的减小而变窄、变高。     

Cycle detection using a stack

We present an algorithm for detecting periodicity in sequences produced by repeated application of a given function. Our algorithm uses logarithmic memory with high probability, runs in linear time, and is guaranteed to stop within the second loop through the cycle. We also present a partitioning technique that offers a time/memory tradeoff. Our algorithm is especially well suited for sequences where the cycle length is typically small compared to the length of the acyclic prefix.     

Measurement of the coolant flow rate using correlation of temperature fluctuations

The transit time of the coolant, and thus its velocity, has been measured using the temperature fluctuation at the outlet of a reactor core. An impulse response function estimation is introduced, which substitutes the widely used cross-correlation measurement technique. It is shown in theory and practice that the time delay estimation is improved when using the impulse response function instead of the cross-correlation function in parameter estimation. Extremely low velocities (down to 2 cm/sec) have been measured in a natural circulation regime in a research reactor.