The rotational spectrum of epifluorohydrin measured by chirped-pulse Fourier transform microwave spectroscopy

The rotational spectrum of epifluorohydrin measured by chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy is presented. A new CP-FTMW spectrometer capable of measuring the entire 7.5-18.5 GHz spectrum with a single polarizing pulse is described briefly. The CP-FTMW spectrometer takes advantage of recent advances in digital electronics by utilizing a 4.2 GS/s arbitrary waveform generator as a frequency source and a 12 GHz digital oscilloscope to digitize the down converted molecular free induction decay (FID). Signal averaging in the time domain is used to increase the signal-to-noise ratio. The rotational constants of three unique conformers of epifluorohydrin were measured, as well as the rotational constants of the three unique ¹³C isotopomers and the ¹⁸O isotopomer (in natural abundance) of the most stable conformer. The rotational constants of the two less stable conformers differ significantly from those previously reported [F.G. Fujiwara, J.L. Painter, H. Kim, J. Mol. Struct. 41 (1977) 169-175]. Ab initio calculations were performed for all three conformations and are compared to experimental values.     

Lowest priority waiting time distribution in an accumulating priority Lévy queue

We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.     

When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

Let _t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when _t is in different states. This new process Z_t is a hidden Markov process. We study the probability distribution of the first passage time for Z_t.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull).     

Distribution of the maxima of random Takagi functions

This paper concerns the maximum value and the set of maximum points of a random version of Takagi’s continuous, nowhere differentiable function. Let F(x):=∑ _n=1^∞ ε _n ϕ(2 ⁿ⁻¹ x), x ∈ R, where ɛ ₁, ɛ ₂, ... are independent, identically distributed random variables taking values in {−1, 1}, and ϕ is the “tent map” defined by ϕ(x) = 2 dist (x, Z). Let p:= P (ɛ ₁ = 1), M:= max {F(x): x ∈ R}, and := {x ∈ [0, 1): F(x) = M}. An explicit expression for M is given in terms of the sequence {ɛ _n }, and it is shown that the probability distribution μ of M is purely atomic if p < , and is singular continuous if p ≧ . In the latter case, the Hausdorff dimension and the multifractal spectrum of μ are determined. It is shown further that the set is finite almost surely if p < , and is topologically equivalent to a Cantor set almost surely if p ≧ . The distribution of the cardinality of is determined in the first case, and the almost-sure Hausdorff dimension of is shown to be (2p − 1)/2p in the second case. The distribution of the leftmost point of is also given. Finally, some of the results are extended to the more general functions Σa ^{n − 1} ɛ _n ϕ(2 ^{n − 1} x), where 0 < a < 1.      

Two-worker blocking congestion model with walk speed m in a no-passing circular passage system

This paper introduces a blocking model and closed-form expression of two workers traveling with walk speed m (m = integer) in a no-passing circular-passage system of n stations and assuming n = m + 2, 2m + 2, …. We develop a Discrete-Timed Markov Chain (DTMC) model to capture the workers’ changes of walk, pick, and blocked states, and quantify the throughput loss from blocking congestion by deriving a steady state probability in a closed-form expression. We validate the model with a simulation study. Additional simulation comparisons show that the proposed throughput model gives a good approximation of a general-sized system of n stations (i.e., n > 2), a practical walk speed system of real number m (i.e., m ? 1), and a bucket brigade order picking application.     

Entrance laws for Feller diffusions on (0, ∞) and Doob's h-path transformation

We consider the problem of constructing entrance laws for Feller diffusions on the state space (0, ∞). Our method, based on Feller-McKean theory of one-dimensional diffusions, gives an analytic expression for the entrance density in terms of transition density. Moreover, the entrance density is the density of the first passage time to the left boundary {0}. Also, the entrance density is related to the transition density via Doob's h-path transformation.     

工程施工中运输网络优化方案

施工工地运输方案的优化设计可以归结为 :按施工期要求设计运输线路或验证已有线路通行能力 ,计算总线路中影响提高流量的关键路段 ,取得最小费用最大流 .本文运用图论理论这一数学工具把实际问题抽象为有向网络 ,进而建立数学模型 .此方法理论上严密 ,解题步聚直观清晰 ,对水利、公路、水路、铁路等其它运输系统有普遍意义 .     

On first passage time structure of random walks

For continuous time birth-death processes on {0,1,2,…}, the first passage time T⁺_n from n to n + 1 is always a mixture of (n + 1) independent exponential random variables. Furthermore, the first passage time T_0,n+1 from 0 to (n + 1) is always a sum of (n + 1) independent exponential random variables. The discrete time analogue, however, does not necessarily hold in spite of structural similarities. In this paper, some necessary and sufficient conditions are established under which T⁺_n and T_0,n+1 for discrete time birth-death chains become a mixture and a sum, respectively, of (n + 1) independent geometric random variables on {1,2,…};. The results are further extended to conditional first passage times.