The transient blended queue

This study aims to determine the transient behavior of the blended queue. Priority customers arrive over time and benefit from a threshold reservation policy, while non-priority ones can be contacted at any time. We show how to compute the Laplace transforms of the transient probabilities. Using the uniformization technique, we prove some monotonicty properties of the expected number of customers in the queue, explaining why the optimal transient reservation threshold should be lower than the stationary one.     

N叉树上的离散时间量子随机行走

通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走,该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换.作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.     

Cramér theorem on symmetric spaces of noncompact type

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant.     

Characterization of measures by potentials

Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f _E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l _∞ ⁿ and wheref(t)=|t| ^p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ _∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ _∞) is positive definite only iff is a constant function.     

Characterizations of generalized Hermite and sieved ultraspherical polynomials

A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.

     

On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

In situ FTIR diagnostics of the radio-frequency plasma decomposition of N2O

The decomposition of N₂O in a 13.56-MHz parallel-plate system was studied usingin situ Fourier transform infrared (FTIR) spectroscopy. Areas of two infrared absorption bands of N₂O recorded at 8 cm^–1 resolution were used to estimate relative gas-phase dissociation as a function of rf power and flow rate at 500 mT. Flow rate was found to strongly affect band areas over the range of powers investigated (10–90 W). The effect of rf power on band areas diminished above 40 W, probably due to poor plasma confinement. Distortion of the band shapes by the plasma permitted rotational temperatures to be estimated. Rotational temperature increased essentially linearly with power at constant flow rate, reaching 450 K at 80 W, but was independent of flow rate at constant power. Rotational temperatures were also found to depend on the temperature of the electrodes, which were heated by plasma exposure. No infrared-active product species were observed even under batch conditions where all N₂O was irreversibly dissociated. This lack of detectable products and a 50% pressure rise observed in a batch study suggest that N₂ and O₂ are the primary stable discharge products.     

A new algorithm to evaluate bielectronic integrals with 1s Slater‐type orbitals obtained by the integral transforms

This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12|34), with 1s Slater‐type orbitals. It is proved that it is possible to define, out of the expression of (12|34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) = (12|34). Therefore, F(q) may be used to calculate (12|34). It is shown that the evaluation of F(Q) turns out to be simpler than the three‐dimensional integral involved in the calculation of (12|34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10^?3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

傅里叶变换红外光谱和傅里叶变换拉曼光谱法无损鉴别药材的真伪

利用傅里叶变换红外（FT-IR）和近红外傅里叶变换拉曼（NIR FT-aman）光谱法对大黄（西宁大黄）与伪品大黄（华北大黄、山大黄、水根大黄）进行了无损快速的鉴别。结果表明：尽管正品大黄与伪品大黄差别较小，有大部分的化学成分有很大的相同之处，但在红外、拉曼谱图中各自的特征峰较突出，根据谱峰的强度和位置可容易地将它们区别开来。红外和拉曼光谱法相互印证，相互补充，具有快速、准确、操作简单、重复性好、不需对样品进行分离提取，可直接鉴别等特点。