LOCAL POLYNOMIAL DOUBLE-SMOOTHING ESTIMATION OF A CONDITIONAL DISTRIBUTION FUNCTION WITH DEPENDENT

Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

Calculation of the Hardness Space Distribution in the As Quenched Condition of a Medium Hardening Tool Steel

The calculation of the hardness profile is a powerful tool for the selection of the right steel for a given purpose. Computer programs INC-PHATRAN and INDUCTER-B were formerly developed by the authors for the calculation of hardness profiles after heat treatment processes of low alloy and carbon steels. The first one simulates quenching as well as through hardening operations, and the second one models electromagnetic induction heat treatments processes. These codes make use of the SAE Standard 3406 in order to obtain the hardness profile, with enhanced regression coefficients recently obtained by the authors. The present work broadens the field of application of this method, allowing to apply it for low hardenability tool steels such as the ASTM O1 Tool Steel. The method used for the calculation of the hardness profile is here summarized, and an example of application is described, which shows good correspondence between the calculated and measured values.

A closed-form pricing formula for European options in an illiquid asset market

This article addresses the problem of pricing European options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stochastic process and the sensitivity of the underlying price to market-wide liquidity is firstly introduced,so that the impact of liquidity on the underlying asset can be captured by the option pricing model.The characteristic function is analytically worked out using the Feynman–Kac theorem and a closed-form pricing formula for European options is successfully derived thereafter.Through numerical experiments,the accuracy of the newly derived formula is verified,and the significance of incorporating liquidity risk into option pricing is demonstrated.

Sequential city growth： Theory and evidence from the US

City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical model under new economic geography framework and the empirical evidence from the US. The results show that cities grow in a sequential pattern. Cities with the best economic conditions are the first to grow fastest until they reach a critical size, then their growth rates slow down and the smaller cities farther down in the urban hierarchy become the fastest-growing ones in sequence. This paper also reveals three related features of urban system. First, the city size distribution evolves from low-level balanced to primate and finally high-level balanced pattern in an inverted U-shaped path. Second, there exist persistent discontinuities, or gaps, between city size classes. Third, city size in the upper tail exhibits conditional convergence characteristics. This paper could not only contribute to enhancing the understanding of urbanization process and city size distribution dynamics, but also be widely used in making effective policies and scientific urban planning.

Influence of haze pollution on water-soluble chemical species in PM2.5 and size-resolved particles at an urban site during fall

To investigate the influence of haze on the chemical composition and formation processes of ambient aerosol particles,PM_（2.5） and size-segregated aerosol particles were collected daily during fall at an urban site of Gwangju,Korea.During the study period,the total concentration of secondary ionic species（SIS） contributed an average of 43.9% to the PM_（2.5） ,whereas the contribution of SIS to the PM_（2.5） during the haze period was 62.3%.The NO_3 and SO^（2-）_4 concentrations in PM_（2.5） during the haze period were highly elevated,being 13.4 and 5.0 times higher than those during non-haze period,respectively.The PM,NO^-_3,SO^（2-）_4,oxalate,water-soluble organic carbon（WSOC）,and humic-like substances（HULIS） had tri-modal size distributions peaks at 0.32,1.0,and 5.2 μm during the non-haze and haze periods.However,during the non-haze period they exhibited dominant size distributions at the condensation mode peaking at 0.32 μm,while on October 21 when the heaviest haze event occurred,they had predominant droplet mode size distributions peaking at 1.00 μm.Moreover,strong correlations of WSOC and HULIS with SO^（2-）_4,oxalate,and K＋at particle sizes of 〈 1.8 μm indicate that secondary processes and emissions from biomass burning could be responsible for WSOC and HULIS formations.It was found that the factors affecting haze formation could be the local stable synoptic conditions,including the weak surface winds and high surface pressures,the long-range transportation of haze from eastern China and upwind regions of the Korean peninsula,as well as the locally emitted and produced aerosol particles.

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.