Stability of the nonlinear filter for slowly switching Markov chains

Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to an incorrect initial condition is derived in the case of a slowly switching signal.     

Relative reactivities of halogen-substituted substrates (R-Br,R-C1) toward the halophilic attack by a carbanion

Relative reactivities of bromine-substituted substrates (R-Br) or chlorine-substituted substrates (R-CI) toward bromophilic or chlorophilic attack by a carbanion have been evaluated by the intermolecular competition kinetics. Relative reactivity orders are CF3CFBr2 >CF3CBr3≥CBr4 > CHBr3 > CF3CFBrCF2Br > CF2Br2 > BrCF2CF2Br > BrCH2CO2Et≥ BrCF2CFHBr > CH2Br2 > BrCH2CH2Br, and CI3CNO2 > CI3CCN > CI3CCOPh > cyclo-C5CI6> CI3CCOCI > CCI3CF2CI > CCI3CF3 ≥ CCI4 > CCI3CCI3 ≥ CCI3(CF2)2CI > CI3CCOCCI3 > CCI3(CF2)6CI > CI3CCO2Et > CI3CF > CI3CPh>CI3CCH2O2CCH3.     

Random Fractal Time Series and the Teen-Birth Phenomenon

The number of babies born to teenagers ranging in ages from 10 to 19 in the state of Texas during the years 1964 to 1990 is not strictly regular, but has both a systematic and random component. Herein we use the relative dispersion, the ratio of the standard deviation to the mean of a time series, to show by systematically aggregating the teen-birth data, that the correlation in the number of teen births is a modulated inverse power law. This scaling of the aggregated relative dispersion indicates the existence of long-time memory in the underlying control process and that the social process leading to teen pregnancy and having a baby are random, fractal and nonlinear. It is shown that this statistical behavior is the same as that observed in other sexual partner selection processes. We discuss the possible allometric nature of time series having such an inverse power-law character, and the implications of such memory for the properties of social control systems.     

Capillary Adhesion Between Elastically Hard Rough Surfaces

The adhesion versus vapor pressure (p/p _s) trend between two elastically hard rough surfaces is modeled and compared with experimental results. The experimental samples were hydrophilic surface-micromachined cantilevers, in which the nanometer-scale surface roughness is on the order of the Kelvin radius. The experimental results indicated that adhesion increases exponentially from p/p _s=0.3 to 0.95, with values from 1 mJ/m² to 50 mJ/m². Using the Kelvin equation to determine the force-displacement curves, the mechanics of a wetted rough interface are treated in two ways. First, the characteristics of a surface with rigid asperities of uniform height are derived. At low p/p _s, menisci surrounding individual asperities do not interact. Beyond a transition value, [p/p _s]_tr, a given meniscus grows beyond the asperity it is associated with, and liquid fills the interface. Capillary adhesion in each realm is found according to the integrated work of adhesion. Second, a more general approach allowing an arbitrary height distribution of Hertzian asperities subject to capillary forces is justified and developed. To compare with experimental results, a Gaussian height distribution is first assumed but significantly underestimates the measured adhesion. This is because equilibrium is found far into the Gaussian tail, where asperities likely do not exist. It is shown that by bounding the tail to more likely limits, the measured adhesion trend is more closely followed but is still not satisfactorily matched by the model. The uniform summit height model fits the data very well with a single free parameter. These results can be rationalized if the upper and lower surfaces are geometrically correlated.     

A Shrinkage Estimator for Combination of Bioassays

A shrinkage estimator and a maximum likelihood estimator are proposed in this paper for combination of bioassays. The shrinkage estimator is obtained in closed form which incorporates prior information just on the common log relative potency after the homogeneity test for combination of bioassays is accepted. It is a practical improvement over other estimators which require iterative procedure to obtain the estimator for the relative potency. A real data is also used to show the superiorities for the newly-proposed procedures.     

Deliquescence Relative Humidity Measurements Using an Electrical Conductivity Method

Several methods used in the published literature for determining the deliquescence relative humidity (DRH) of salts and the mutual deliquescence relative humidity (MDRH) of salt mixtures were reviewed. Experiments were conducted to evaluate an electrical conductivity method for determining the DRH of salts and the MDRH of salt mixtures. The electrical impedance of a conductivity cell containing Na₂SO₄, CaCl₂ and NaCl+NaNO₃+KNO₃ was measured as a function of relative humidity at temperatures up to 70 ^∘C. To provide a basis for interpreting the results of the impedance measurements, computer modeling of the specific electrical conductivity of single salts and salt mixtures at 25 ^∘C also was performed. The results of the study demonstrated that the electrical conductivity method provides a convenient and accurate method for determining the DRH of single salts and the MDRH of salt mixtures. The derived DRH and MDRH values were in good agreement with those determined using a hygrometer method. The conductivity method, however, is a more reliable technique than the hygrometer method for determining the MDRH of salt mixtures because the conductivity method is insensitive to slight deviations of mixture composition from the eutonic value.     

On Resolvable Difference Families

A Steiner 2-design is said to be G-invariantly resolvable if admits an automorphism group G and a resolution invariant under G. Introducing and studying resolvable difference families, we characterize the class of G-invariantly resolvable Steiner 2-designs arising from relative difference families over G. Such designs have been already studied by Genma, Jimbo, and Mishima [13] in the case in which G is cyclic. Developping their results, we prove that any (p, k, 1)-DF (p prime) whose base blocks exactly cover p–1/k(k–1) distinct cosets of the k-th roots of unity (mod p), leads to a Ckp-invariantly resolvable cyclic (kp,k,1)-BBD. This induced us to propose several constructions for DF's having this property. In such a way we prove, in particular, the existence of a C5p-invariantly resolvable cyclic (5p, 5, 1)-BBD for each prime p = 20n + 1 < 1.000.     

关于算符i (α/αt)性质研究的若干评注

从时间平移的角度证明了算符ｉ（／ｔ）的厄米性，讨论了该算符的厄米性与态函数内积之间的关系，指出了Ｃａｐｒｉ在证明时间和能量对易关系不成立的过程中的错误，最后讨论了算符ｉ（／ｔ）和任一量子系统的Ｈａｍｉｌｔｏｎ算符之间的关系．     

The state of the carbon vapour in the regenerative sooting discharge

Formation of the regenerative soot is the process of recycling and introduction of the cathode deposited carbon clusters into the discharge. The agglomerates of carbon clusters on the cathode release their constituents into the plasma that goes from the pure sputtering mode to the sooting one. The process of the regeneration of the soot that emits large carbon clusters is discussed by evaluating the state of the carbon vapour by using the characteristic line emissions from the discharge. Received 17 April 2001 and Received in final form 13 June 2001     

On Relative Difference Sets in Dihedral Groups

In this paper, we study extensions of trivial difference sets in dihedral groups. Such relative difference sets have parameters of the form (uλ,u,uλ, λ) or (uλ+2,u, uλ+1, λ) and are called semiregular or affine type, respectively. We show that there exists no nontrivial relative difference set of affine type in any dihedral group. We also show a connection between semiregular relative difference sets in dihedral groups and Menon–Hadamard difference sets. In the last section of the paper, we consider (m, u, k, λ) difference sets of general type in a dihedral group relative to a non-normal subgroup. In particular, we show that if a dihedral group contains such a difference set, then m is neither a prime power nor product of two distinct primes.