Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

The covariance matrix of the Potts model: A random cluster analysis

We consider the covariance matrix,G ^mm =q ²<(_x,m);(_y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point _o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at _o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure.     

Removal of H2S from Exhaust Gas by Use of Alkaline Activated Carbon

The purpose of this research was to select an activated carbon and alkaline solution blend that generated the best H₂S adsorption on alkaline-activated carbon. RB₂ (activated carbon) impregnated with NaOH solution was shown to have the optimum H₂S removal efficiency. The optimum NaOH concentration was 50 mg per gram of carbon. H₂S adsorption via RB₂-NaOH₅₀ was five times that of a corresponding fresh-activated carbon. The adsorption equivalent of H₂S is nearly 1 (mol-H₂S/mol-AOH), therefore, H₂S + AOH AHS + H₂O was the major reaction. The H₂S adsorption isotherm corresponded to the Freundlich isotherm.     

A new approach to the determination of the statistical segment length of wormlike polymers

The Stockmayer-Fixman-Burchard (SFB) and the Dondos-Benoit (DB) equations have been applied to determine the unperturbed dimensions parameterK of wormlike polymers. An empirical relation between the Flory's constant and the Mark-Houwink-Sakurada (MHS) exponenta has been proposed. The values found by this equation are lower than the value 2.5×10²³ used in the case of flexible polymers and this deviation is attributed to the influence of the draining effect. From theK value and the so calculated value of , we calculate the Kuhn statistical segment length of wormlike polymers. The obtained — for a great number of wormlike polymers — statistical segment lengths are almost the same as these calculated by the Yamakawa-Fujii and the Bohdanecky methods. The molecular mass regions in which the SFB, the DB, and the MHS equations are valid are explored. A criterion for the distinction between flexible and wormlike polymers is proposed based on the way of approach to the power law.     

阴离子嵌段共聚的交联聚苯乙烯的网络链长多分散性与网络结构非均一性

用链长分布不同的活性聚苯乙烯子聚物与二乙烯基苯进行阴离子嵌段共聚,合成了一系列两相模型交联网络。以作者等提出的方法测定了所合成网络的结构非均一因子Z。实验测定的网络结构非均一因子Z与交联前聚苯乙烯活性链的分子量分布宽度指数d之间有平行的相应变化规律,表明所给予的非均一因子Z的物理意义是合理的。同时说明,子聚物链长分布较宽时,在网络的高交联区中除了二乙烯基苯外,还有一些对溶胀无贡献的子聚物以悬挂链的形式存在。     

Small angle X-ray scattering investigations of thermodynamic properties of fluid mixtures

Absolute small angle X-ray studies of concentration fluctuations were performed in order to determine thermodynamic properties of a model blend, consisting ofn-hexane and perfluoro-n-hexane. The quantities which we determined were the second derivate of the Gibbs free energy of mixing with respect to the concentration of the components, the location of the spinodal, interaction and solubility parameters, the energy gradient density coefficient as well as the correlation length of the fluctuations at various compositions and temperatures, particularly in the neighbourhood of the spinodal and the critical point. The data obtained were compared with those obtainable from the well known location of the binodal, to test the reliability of the scattering method.     

RELATIONSHIPS BETWEEN X—H STRETCHING OVERTONE FREQUENCIES AND BOND LENGTHS/BOND ANGLES

A relationship between the X-H (X = N, O, C, and so on) equilibrium bond length in a Morse oscillator and the X-H stretching overtone frequency shifts is obtained theoretically. We use the equation to discuss the empirical linear relationships that have been proposed for heterocyclics, alkanes and fluorinated benzenes. On the other hand, a unified relationship between the X-H bond angles and the experimental quantities (ω(?) and the coupling strength λ) is also presented for XH2, XH, and XH4 molecules or molecular fragments. Calculations of X-H bond angles for a number of molecules show that the results from our equations are in excellent agreement with the experimental values. Also we can extract the information of relative magnitude of bond coupling force field.     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Correlation analysis of quantum chemical data and the polarizability effect in H-complexes

The study is concerned with analysis of the energies of formation (E), frequency shifts (Δν) in IR spectra, ionization potentials (IP) of H-complexes, hydrogen bond lengths (r), and spin densities (sd) in H-complexes involving radical cations, obtained from quantum chemical calculations for 20 series of H-complexes. It was for the first time established that the E, IP, r, and sd values and the changes in enthalpy (δH) depend not only on the inductive and resonance effects but also on the polarizability effect of the substituents bound to the donor and acceptor centers in the H-complexes. Interrelations between the polarizability effect and the molecular structure of H-complexes are considered. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 602–608, April, 2006.     

Zur kenntnis ‚Kationen-reicher’︁ Tantalate und Niobate Über Na5TaO5 und Na5NbO5

On Tantalates and Niobates ‘rich in Cations’. On Na₅TaO₅ and Na₅NbO₅ Colourless, transparent single crystals of Na₅TaO₅ [annealed mixtures of Na₂O, Li₂O, and Ta₂O₅, Na : Li : Ta = 6.6 : 1.1 : 1, Ni-cylinder, 1000°C, 75 d] as well as Na₅NbO₅ [annealed mixtures of Na₂O, Li₂O, and Nb₂O₅, Na : Li : Nb = 6.6 : 1.1 : 1, Ni-cylinder, 1000°C, 75 d] have been prepared. Single crystal data show that both isotypic oxides represent a deformed variant of the NaCl-type of structure [Na₅TaO₅: 1154 from 1250 I₀ (hkl), four-cycle diffractometer Philips PW 1100, ω2-θ scan, Ag? Kα , R = 4.88%, space group c2/c with a = 629.3(1) pm, b = 1025.4(2) pm, c = 1004.6(2) pm, b? 106.80(2)°, z = 4 and Na₅NbO₅: 998 from 1247 I₀(hkl), four-cycle diffractometer Philips PW 1100, ω-2θ scan, Ag? Kα , R = 8.58% and R_w = 7.67%, space group C2/2 with a = 629.1(1) pm, b = 1024.4(2) pm, c = 1004.2(2) pm, b? = 106.80(2)°, Z = 4]. The Madelung Part of Lattice Energy, MAPLE, and Effective Coordination Numbers, ECoN, the latter derived from Mean Effective Fictive Ionic Radii, MEFIR, as well as Charge Distribution, CHARDI, are calculated.