ON THE LATTICE PATH METHOD IN CONVOLUTION-TYPE COMBINATORIAL IDENTITIES(Ⅱ)—THE WEIGHTED COUNTING FUNCTION METHOD ON LATTICE PATHS

An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.

Limiting stand density and basal area projection models for even-aged Tecomella undulata plantations in a hot arid region of India

This paper presents equations for estimating limiting stand density for Z undulata plantations grown in hot desert areas of Raj asthan State in India. Five different stand level basal area projection models, belonging to the path invariant algebraic difference form of a non-linear growth function, were also tested and compared. These models can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are necessary for reviewing different silvicultural treatment options. Data from 22 sample plots were used for modelling. An all possible growth intervals data structure was used. Both, qualitative and quantitative criteria were used to compare alternative models. The Akaike＇s information criteria differ- ence statistic was used to analyze the predictive ability of the models. Results show that the model proposed by Hui and Gadow performed best and hence this model is recommended for use in predicting basal area development in 12 undulata plantations in the study area. The data used were not from thinned stands, and hence the models may be less accurate when used for predictions when natural mortality is very significant.

Pathwise no-arbitrage in a class of Delta hedging strategies

We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.

Accuracy analysis of PPDF-based method to parameterize aerosol scattering effect

We introduce the path length probability density function(PPDF) method, which is based on an equivalence theorem and parameterizes the aerosol scattering effect by adding four factors to the atmospheric transmittance model. Using simulated observations in the O2-A band, we examined the utility of the PPDF-based method to account for the aerosol scattering effect. First, observations were simulated using a forward model under different aerosol conditions; PPDF factors were then retrieved using an optimal estimation method; PPDF factors were used to reconstruct the observations; and finally, simulated true observations and reconstructions were compared. Analysis of the difference between the true observations and reconstructions confirmed the utility of the PPDF-based method. Additionally, the O2 band was demonstrated to be an efficient observing band for assisting the remote sensing of atmospheric trace gases in the near-infrared band.