Debris Flow Hazard Assessment Using Set Pair Analysis Models:Take Beichuan County as an Example

Assessment of debris flow hazards is important for developing measures to mitigate the loss of life and property and to minimize environmental damage. Two modified uncertainty models, Set Pair Analysis （SPA） and modified Set Pair Analysis （mSPA）, were suggested to assess the regional debris flow hazard. A ease study was conducted in seven towns of the Beichuan county, Sichuan Province, China, to test and compare the application of these two models in debris flow hazard assessment. The results showed that mSPA only can fit for value-variables, but not for non value-variable assessment indexes, Furthermore, as for a given assessment index xi, mSPA only considers two cases, namely, when grade value increases with xi and when grade value decreases with xi. Thus, mSPA can not be used for debris flow hazard assessment but SPA is credible for the assessment because there are no limitations when using SPA model to assess the debris flow hazard. Therefore, in this study SPA is proposed for assessing debris flow hazard.

A New Proposal to Adjust a Straight Line to a Normal Q-Q Plot

In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile Plot, or normal Q-Q plot, is presented. This probability plot allows us to determine whether a set of sample observations is distributed according to a normal distribution. For this, the sample quantiles are represented against the quantiles of a theoretical probability model, which in this case is the normal distribution. If the data set follows the above mentioned distribution, the plotted points will have a rectilinear configuration. To verify this, there are different alternatives for fitting a straight line to the plotted points. Among the straight lines which can be fitted to a Q-Q plot, in this paper, besides the proposed straight line, the following straight lines are considered： straight line that passes through the first and third quartiles, straight line that passes through the 10th and 90th percentiles, straight line fitted by the method of least squares, straight line with slope s and constant the average of the data set, Theil＇s line and Tukey＇s line. In addition, an example, in which there are represented the different straight lines considered and the proposed straight line on a normal Q-Q plot obtained for the same set of observations, is developed. In this example the existing differences among the straight lines are observed.

Spatial Probabilistic Model of Block Failure Capacity of Piles in Clay

A probability based model of block failure capacity of pile foundation in clay soil under axial load is developed. The model was based on the first order second moment method. Instead of using point variability, the soil inherent variability is modelled as random field model. Based on this model, a reliability based factor of safety for designing pile group foundation, taking into account bock failure mechanism, is proposed. Furthermore, using simplified lognormal model, the relationship between the factor of safety used in design practice and target reliability may be derived explicitly.

Gillnet Selectivity and Length at Maturity of Nile Tilapia （Oreochromis niloticus L.） in a Tropical Reservoir （Amerti： Ethiopia）

The selectivity of gillnets for Oreochromis niloticus in Amerti reservoir （9°63′ N, 37°23′ E） was determined from gillnets with four mesh sizes （60, 80, 100 and 120 mm）. Four selectivity models （a normal model assuming fixed spread, a normal model assuming that spread is proportional to mesh size, a lognormal model and a gamma model） were fitted to the data by using the share each length＇s catch total （SELECT） method. A total of 657 specimens of Oreochromis niloticus were caught （12.0-35.5 cm total length, TD. The sizes at first sexual maturity were 21.5 cm TL and 18.9 cm TL, respectively, for male and female Oreochromis niloticus. The lognormal selectivity curve provided the best fit to the data according to model deviance estimates with optimum selectivity of 16.66, 22.26, 27.78 and 33.38 cm TL for the 60, 80, 100 and 120 mm mesh sizes, respectively.

A generalized sinusoidal model and its applications

A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.

Late Quaternary Activity and Strong Earthquake Recurrence Interval along the North Segment of the Longling-Ruili Fault

According to field investigation and interpretation of remote sensing images,the north segment of the Longling-Ruili fault is a Holocene dextral strike-slip fault with a small amount of normal faulting.Based on large-scale geological mapping at some typical locations and quantitative geomorphologic deformation measurement and dating analysis,this fault is a Holocene active fault.The strike-slip rate of the Longling-Ruili fault is 2.2 ~2.5mm / a and vertical slip rate is 0.6mm /a since the late Pleistocene epoch.The strike-slip rate of the Longling-Ruili fault is 1.8~3.0mm /a and vertical slip rate is 0.5mm /a since the Holocene epoch.Based on the Poisson model,lognormal model and BPT model,the occurrence probability of strong earthquakes in 50 years is estimated to be 6.32%,0.08%and 0.05%,respectively.Then,a 1.82% probability of occurrence of characteristic earthquake for the north segment of the Longling-Ruili fault is obtained by setting a weight of 0.28,0.36 and 0.36 to the Poisson model,lognormal model and BPT model,respectively.

Performance of Kohonen Self-organising Map in Statistical Analysis of Hydrologic Data

The statistical characteristics of a hydrological data for the purposes of decision making in water resource planning and management is only justifiable if the data has the right attributes. This requires that the data being analysed are consistent, free of trend and being part of a stochastic process whose random characteristics is described by an appropriate distribution hypothesis. The data available for statistical analysis had a lot of missing values which could not be ordinarily filled but required a more comprehensive approach to fill these missing values. The KSOM （Kohonen Self-organising Map） was used to fill the missing runoff data from the Jidere-Bonde, Lokoja and Makundi river sites in the Niger basin. Results from the studies have shown that KSOM is the best tool for filling hydrological data with high number of missing values. After the data had been processed, some statistical applications were used to establish the runoff time-series characteristics of the three river sites of the Niger River basin. The results showed good attributes for all three river sites, except that Jidere River＇s data exhibited inconsistency. The presence of trend was also established for all three river sites; Jidere River was modelled based on 3-pararneter lognormal, the other two river sites were modelled based on normal distribution probability. The presence of trend and other attributes require that a more stochastic modelling process be carried out. However, the results established give reference for water resource planning and management.

Lee discrepancy on asymmetrical factorials with two-and three-levels

Lee discrepancy has been employed to measure the uniformity of fractional factorials.In this paper,we further study the statistical justification of Lee discrepancy on asymmetrical factorials.We will give an expression of the Lee discrepancy of asymmetrical factorials with two-and three-levels in terms of quadric form,present a connection between Lee discrepancy,orthogonality and minimum moment aberration,and obtain a lower bound of Lee discrepancy of asymmetrical factorials with two-and three-levels.

Working characteristics of a new ventilator with automatic secretion clearance function

Secretions in the airways of ventilated patients must be cleared efficiently and timely. A novel ventilator(SC ventilator) is proposed with an automatic secretion clearance function in order to provide a new approach. A mathematical model of a ventilation system with the SC ventilator is set up to optimize the SC ventilator. Based on the research, conclusion can be reached as follows. First, the experimental results and the mathematical model are proved to be authentic and reliable. Second, the secretion clearance efficiency of the SC ventilator may be higher than that of IL-IE device. Finally, increasing the inspiratory positive airway pressure or decreasing the expiatory positive airway pressure of the SC ventilator can improve the efficiency of the secretion clearance. This paper lays a foundation for the secretion clearance improvement of the SC ventilator.

ESTIMATION IN A SEMI-VARYING COEFFICIENT MODEL FOR PANEL DATA WITH FIXED EFFECTS

This paper considers a semi-varying coefficient model for panel data with fixed effects,proposes the profile-likelihood-based estimators for the parametric and nonparametric components,and establishes convergence rates and asymptotic normality properties for both estimators.Simulation results show that the proposed estimators behave well in finite sample cases.

A moving average Cholesky factor model in joint mean-covariance modeling for longitudinal data

Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using generalized estimation equation techniques, we propose a new kind of regression models for parameterizing covariance structures. Using a novel Cholesky factor, the entries in this decomposition have moving average and log innovation interpretation and are modeled as the regression coefficients in both the mean and the linear functions of covariates. The resulting estimators for eovarianee are shown to be consistent and asymptotically normally distributed. Simulation studies and a real data analysis show that the proposed approach yields highly efficient estimators for the parameters in the mean, and provides parsimonious estimation for the covariance structure.

Exact Solitary Wave Solutions of Nonlinear Evolution Equations with a Positive Fractional Power Term

The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.

Tail asymptotic expansions for L-statistics

We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures, stop-loss premium and excess return on capital, respectively. Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital