A theoretical model describing the interaction between crystalline swelling and cation exchange selectivity is proposed for expanding 2:1 phyllosilicates. The model is based on the assumption that changes in basal spacing of a clay are phase changes, and that each phase of a clay has a different selectivity constant for a particular cation exchange reaction. Energy barriers stabilize the various phases over a limited range of interlayer ionic composition. These energy barriers cause hysteresis in crystalline swelling, which in turn causes hysteresis in cation exchange. Results are presented for an experiment involving Ba-Mg exchange on a synthetic fiuoro-hectorite. The results demonstrate key aspects of the proposed model, including a correlation between measured selectivity coefficients and basal spacings (R2 = 0.85), an abrupt change in basal spacing that corresponds with an abrupt change in selectivity and corresponding hysteresis in crystalline swelling and cation exchange selectivity. The results also demonstrate increased selectivity for the preferred cation (Ba) at high solution mole fraction of the preferred cation. This trend is opposite of that observed for heterogeneous natural smectites but consistent with predictions of the model for a homogeneous smectite.

An indirect Fourier transformation applied to small-angle X-ray scattering data has been used to determine the thickness and surface properties of two common clay minerals. For an illite system, the particle density distribution function (PDDF) generated by the analysis gave a correct description of particle geometry, and the calculated electron density profile was in accordance with the theoretical electron density distribution for this mineral. This approach provides the opportunity to determine the thickness of fundamental particles of illite while avoiding the difficulties encountered in other methods. Both the PDDF and the electron density profile accurately predict the thickness of Na-montmorillonite layers, and the results suggest that an electron inhomogeneity exists at the interface of this mineral.

It has been suggested that interstratified illite-smectite (I-S) minerals are composed of aggregates of fundamental particles. Many attempts have been made to measure the thickness of such fundamental particles, but each of the methods used suffers from its own limitations and uncertainties. Small-angle X-ray scattering (SAXS) can be used to measure the thickness of particles that scatter X-rays coherently. We used SAXS to study suspensions of Na-rectorite and other illites with varying proportions of smectite. The scattering intensity (I) was recorded as a function of the scattering vector, q = (4 π/λ) sin(θ/2), where λ is the X-ray wavelength and θ is the scattering angle. The experimental data were treated with a direct Fourier transform to obtain the pair distance distribution function (PDDF) that was then used to determine the thickness of illite particles. The Guinier and Porod extrapolations were used to obtain the scattering intensity beyond the experimental q, and the effects of such extrapolations on the PDDF were examined. The thickness of independent rectorite particles (used as a reference mineral) is 18.3 Å. The SAXS results are compared with those obtained by X-ray diffraction peak broadening methods. It was found that the power-law exponent (α) obtained by fitting the data in the region of q = 0.1–0.6 nm−1 to the power law (I = I0q−α) is a linear function of illite particle thickness. Therefore, illite particle thickness could be predicted by the linear relationship as long as the thickness is within the limit where α <4.0.

We firstly report a 2-μm all-fiber nonlinear pulse compressor based on two pieces of normal dispersion fiber (NDF), which enables a high-power scaling ability of watt-level and a high pulse compression ratio of 13.7. With the NDF-based all-fiber nonlinear pulse compressor, the 450-fs laser pulses with a repetition rate of 101.4 MHz are compressed to 35.1 fs, corresponding to a 5.2 optical oscillation cycle at the 2-μm wavelength region. The output average power reaches 1.28 W, which is believed to be the highest value never achieved from the previous 2-μm all-fiber nonlinear pulse compressors with a high pulse repetition rate above 100 MHz. The dynamic evolution of the ultrafast pulse inside the all-fiber nonlinear pulse compressor is numerically analyzed, matching well with the experimental results.

In this paper, we consider a discrete-time queueing model for a Time Division Multiplexing (TDM) system with integration of voice and data (a model introduced by Li and Mark [16]). The voice traffic is a superposition of N Markov chains, which alternate between two states: the talkspurt state and the silence state. The data traffic is Poisson and independent of the voice sources. We show that the average queue size is increasing in certain correlation coefficients of the voice sources, increasing convex in the proportion of time the voice sources are in talkspurts, increasing convex in the number of voice sources, and increasing convex in the data traffic intensity. However, it is decreasing convex in the number of channels. These structural results yield various bounds. To take video traffic into account as well, we adapt a model of Maglaris et al. [18]. In their model, video traffic is generated by a continuous-state autoregressive Markov process that matches the average rate and the autocovariance of the output of a video coder. We show that if we replace their autoregressive model by a two-state Markov chain model with the same rate and correlation coefficient, we obtain an upper bound for the queue size. This replacement enables us to treat the video traffic as a voice source and use the techniques developed for dealing with voice/data integration to obtain bounds and estimates.

Because the severe acute respiratory syndrome (SARS) outbreak in Taiwan in 2003 was worsened by hospital infections, we analyzed 229 questionnaires (84.8% of 270 sent) completed by surveyed healthcare workers who cared for patients with SARS in 3 types of hospitals, to identify surveillance problems. Atypical clinical presentation was the most often reported problem, regardless of hospital type, which strongly indicates that more timely syndromic surveillance was needed.

We consider scheduling problems with m machines in parallel and n jobs. The machines are subject to breakdown and repair. Jobs have exponentially distributed processing times and possibly random release dates. For cost functions that only depend on the set of uncompleted jobs at time t we provide necessary and sufficient conditions for the LEPT rule to minimize the expected cost at all t within the class of preemptive policies. This encompasses results that are known for makespan, and provides new results for the work remaining at time t. An application is that if the cµ rule has the same priority assignment as the LEPT rule then it minimizes the expected weighted number of jobs in the system for all t. Given appropriate conditions, we also show that the cµ rule minimizes the expected value of other objective functions, such as weighted sum of job completion times, weighted number of late jobs, or weighted sum of job tardinesses, when jobs have a common random due date.

In this paper, we compare queueing systems that differ only in their arrival processes, which are special forms of doubly stochastic Poisson (DSP) processes. We define a special form of stochastic dominance for DSP processes which is based on the well-known variability or convex ordering for random variables. For two DSP processes that satisfy our comparability condition in such a way that the first process is more ‘regular' than the second process, we show the following three results: (i) If the two systems are DSP/GI/1 queues, then for all f increasing convex, with V(i), i = 1 and 2, representing the workload (virtual waiting time) in system. (ii) If the two systems are DSP/M(k)/1→ /M(k)/l ∞ ·· ·∞ /M(k)/1 tandem systems, with M(k) representing an exponential service time distribution with a rate that is increasing concave in the number of customers, k, present at the station, then for all f increasing convex, with Q(i), i = 1 and 2, being the total number of customers in the two systems. (iii) If the two systems are DSP/M(k)/1/N systems, with N being the size of the buffer, then where denotes the blocking (loss) probability of the two systems. A model considered before by Ross (1978) satisfies our comparability condition; a conjecture stated by him is shown to be true.