Second virial coefficient for the exponent--spline-Morse-spline-van der Waals potential and its application

An analytical expression for the second virial coefficient based on an exponent-spline-Morse-spline-van der Waals (ESMSV) potential is presented here for use in defining the thermodynamic properties of rare gases. Our method is established based on a series expansion of the exponential function, Meijer function, gamma function, binomial function, and hypergeometric function. Numerical approaches have commonly been used for the evaluation of the second virial coefficient with the ESMSV potential in the literature. The general formula obtained here can be applied to estimate the thermal properties of rare gases. Our results for the second virial coefficient based on the ESMSV potential of He-He, He-Ne, He-Ar, and He-Xe rare gases are compared with numerical calculations and experimental data, and it is shown that our analytical expression can be successfully used for other gases.

A new Alzer type Inequality Related to Binomial Function

In this paper, we establish a new Alzer type inequality related to binomial function by using Sitnik methods.

Radial basis function and its application in tourism management

In this work, several applications and the performances of the radial basis function (RBF) are briefly reviewed at first. After that, the binomial function combined with three different RBFs including the multiquadric (MQ), inverse quadric (IQ) and inverse multiquadric (IMQ) distributions are adopted to model the tourism data of Huangshan in China. Simulation results showed that all the models match very well with the sample data. It is found that among the three models, the IMQ-RBF model is more suitable for forecasting the tourist flow.

Modeling probability of additional cases of natalizumab-associated JCV sero-negative progressive multifocal leukoencephalopathy

JCV serologic status is used to determine PML risk in natalizumab-treated patients. Given two cases of natalizumab-associated PML in JCV sero-negative patients and two publications that question the false negative rate of the JCV serologic test, clinicians may question whether our understanding of PML risk is adequate. Given that there is no gold standard for diagnosing previous JCV exposure, the test characteristics of the JCV serologic test are unknowable. We propose a model of PML risk in JCV sero-negative natalizumab patients. Using the numbers of JCV sero-positive and -negative patients from a study of PML risk by JCV serologic status (sero-positive: 13,950 and sero-negative: 11,414), we apply a range of sensitivities and specificities in order calculate the number of JCV-exposed but JCV sero-negative patients (false negatives). We then apply a range of rates of developing PML in sero-negative patients to calculate the expected number of PML cases. By using the binomial function, we calculate the probability of a given number of JCV sero-negative PML cases. With this model, one has a means to establish a threshold number of JCV sero-negative natalizumab-associated PML cases at which it is improbable that our understanding of PML risk in JCV sero-negative patients is adequate.

On the bias of recombination fractions, Kosambi's and Haldane's distances based on frequencies of gametes

The estimation of recombination frequencies is a crucial step in genetic mapping. For the construction of linkage maps, nonadditive recombination fractions must be transformed into additive map distances. Two of the most commonly used transformations are Kosambi’s and Haldane’s mapping functions. This paper reports on the calculation of the bias associated with estimation of recombination fractions, Kosambi’s distances, and Haldane’s distances. I calculated absolute and relative biases numerically for a wide range of recombination fractions and sample sizes. I assumed that the ratio of recombinant gametes to the total number of gametes can be adequately represented by a binomial function. I found that the bias in recombination fraction estimates is negative, i.e., the estimator is an underestimate. However, significant values were only obtained when recombination fractions were large and sample sizes were small. The relevant estimates of recombination fractions were, therefore, nearly unbiased. Haldane’s and Kosambi’s distances were found to be strongly biased, with positive bias for the most interesting values of recombination fractions and sample sizes. The bias of Kosambi’s distance was considerably smaller than the bias of Haldane’s distance.

Parasite aggregations in host populations using a reformulated negative binomial model

The negative binomial distribution model is reformulated and used to demarcate a host population at a specific level of infection by defining an attribute spanning a range of parasite aggregations. The upper limit of the range specifies the boundary for the classification of the host population and provides a technique to determine the cumulative probability at any level of parasite infection to a high degree of accuracy. This approach also leads to the evaluation of thekparameter, i.e. an inverse measure of dispersion of parasite aggregation, for each fraction of the host population with a discrete level of infection. The basic mathematical premise of the negative binomial function is unaltered in developing this reformulation which was applied to data on the distribution of the trichostrongylid nematodeHeligmosomoides polygyrusin populations of the field mouse,Apodemus sylvaticus.

Impurity Effects on the Local Structure in the Mixed Hexachlorometallate (A2BCl6 : A = K, Rb, B = Sn, Re, and Pb) Studied by the Chlorine NQR

Chlorine NQR was studied for the isostructural hexachlorometallate mixed system. The study shows that Isomorphic hexachlorometallate solid solutions exhibit often impurity induced local structural order because of their relatively clear local site symmetry. This is manifested in the formation of a few satellite lines near the original resonance line and results from the random distribution of impurities on the lattice sites of the corresponding counterpart ions. Using the point charge model and a simple binomial function for the occupation probability of the guest ions on the host lattice sites, the position and the line intensity could be determined, the results of which are in good agreement with the NQR-observation. The temperature region of lattice dynamics in the crystal seems to shift in proportion to the impurity content. This fact explains the gradual change of the transition temperature in the mixed crystal between two starting materials.

An Integral Representation for the Generalized Binomial Function

The generalized binomial function can be obtained as the solution of the equation y = 1 +zyα which satisfies y(0) = 1 where α ≠ 1 is assumed to be real and positive. The technique of Lagrange inversion can be used to express as a series which converges for |z| < α-α|a — l|α-1. We obtain a representation of the function as a contour integral and show that if α > 1 it is an analytic function in the complex z plane cut along the nonnegative real axis. For 0 < α < 1 the region of analyticity is the sector |arg(—z)| < απ. In either case defined by the series can be continued beyond the circle of convergenece of the series through a functional equation which can be derived from the integral representation.

Predicting the Distribution of Aflatoxin Test Results from Farmers’ Stock Peanuts

Suitability of the negative binomial function for use in estimating the distribution of sample aflatoxin test results associated with testing farmers1 stock peanuts for aflatoxin was studied. A 900 kg portion of peanut pods was removed from each of 40 contaminated farmers1 stock lots. The lots averaged about 4100 kg. Each 900 kg portion was divided into fifty 2.26 kg samples, fifty 4.21 kg samples, and fifty 6.91 kg samples. The aflatoxin in each sample was quantified by liquid chromatography. An observed distribution of sample aflatoxin test results consisted of 50 aflatoxin test results for each lot and each sample size. The mean aflatoxin concentration, m; the variance, s2xamong the 50 sample aflatoxin test results; and the shape parameter, k, for the negative binomial function were determined for each of the 120 observed distributions (40 lots times 3 sample sizes). Regression analysis indicated the functional relationship between k and m to be k = 0.000006425m0.8047. The 120 observed distributions of sample aflatoxin test results were compared to the negative binomial function by using the Kolmogorov–Smirnov (KS) test. The null hypothesis that the true unknown distribution function was negative binomial was not rejected at the 5% significance level for 114 of the 120 distributions. The negative binomial function failed the KS test at a sample concentration of 0 ng/g in all 6 of the distributions where the negative binomial function was rejected. The negative binomial function always predicted a smaller percentage of samples testing 0 ng/g than was actually observed. However, the negative binomial function did fit the observed distribution for sample test results at a concentration greater than 0 in 4 of the 6 cases. As a result, the negative binomial function provides an accurate estimate of the acceptance probabilities associated with accepting contaminated lots of farmers' stock peanuts for various sample sizes and various sample acceptance levels greater than 0 ng/g.