ROBUST MATHEMATICAL PROGRAMMING FOR NATURAL RESOURCE MODELING UNDER PARAMETRIC UNCERTAINTY

Abstract Inaccurate specification of model coefficients can lead to false or distorted findings in modeling investigations of natural resource management. Hence, this paper outlines a decision framework for optimization problems in which only the bounded set of outcomes for uncertain parameters is known. These models can be solved with standard mathematical programming software and are no larger than their deterministic equivalent. The robust approach is contrasted against deterministic analysis and is demonstrated for two applications regarding the management of natural resources. Deterministic plans are infeasible in at least 40% of cases when parameters vary from their point estimates. Inclusion of robust constraints immunizes against this infeasibility, thereby removing errors arising from false certainty. Additionally, incorporation of bounded parameters in the objective function yields interval‐valued sets containing potential outcomes. However, this increase in the general relevance of model output introduces some degree of suboptimality as deterministic plans are buffered to proactively account for potential variability. The cost of robustness increases with the simulated spread of uncertain coefficients but may be reduced through accounting for the uncertainty aversion of decision makers.     

超越整函数半群的游荡域

设G是由一族超越整函数生成的半群,其中半群运算是函数的复合.在满足某些假设下,文中得到G在其游荡域内的极限函数要么是∞,要么属于G中某个函数φ的奇异值集合singφ~(-1)的导集.     

Total Fractionation and Analysis of Polysaccharides from Leaves of Panax ginseng C. A. Meyer

The water-soluble polysaccharides isolated from the leaves of Panax ginseng C.A.Meyer were totally fractionated into one neutral fraction(GLPN-1),six acidic fractions(GLPN-2,GLPA-1a,GLPA-1b,GLPA-1c,GLPA-2 and GLPA-3) by a combination of ethanol precipitation,ion-exchange and gel permeation chromatography.All the fractions were analyzed by determining monosaccharide composition,molecular weight distribution.The results show that GLPN-1 was mainly composed of Gal(38.1%) and Ara(33.6%) and presumed to be an ar...     

A Cauchy integral method of the solution of the 2D Dirichlet problem for simply or doubly connected domains

In this paper we propose a new method for solving the 2D Laplace equation with Dirichlet boundary conditions in simply and doubly connected domains. Here, we apply the numerical algorithm based on truncated Fourier series and reduce the corresponding Fredholm integral equation to a finite system of linear equations.     

Composite finite element approximation for nonlinear parabolic problems in nonconvex polygonal domains

We study a new class of finite elements so‐called composite finite elements (CFEs), introduced earlier by Hackbusch and Sauter, Numer. Math., 1997; 75:447‐472, for the approximation of nonlinear parabolic equation in a nonconvex polygonal domain. A two‐scale CFE discretization is used for the space discretizations, where the coarse‐scale grid discretized the domain at an appropriate distance from the boundary and the fine‐scale grid is used to resolve the boundary. A continuous, piecewise linear CFE space is employed for the spatially semidiscrete finite element approximation and the temporal discretizations is based on modified linearized backward Euler scheme. We derive almost optimal‐order convergence in space and optimal order in time for the CFE method in the L^∞(L²) norm. Numerical experiment is carried out for an L‐shaped domain to illustrate our theoretical findings.     

Spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in circular domain

In this paper, we present spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in a circular domain. First of all, we use the polar coordinate transformation and technique of separation of variables to reduce the problem to a sequence of equivalent 1‐dimensional eigenvalue problems that can be solved individually in parallel. Then, we derive the pole conditions and introduce weighted Sobolev space according to pole conditions. Together with the approximate properties of orthogonal polynomials, we prove the error estimates of approximate eigenvalues for each 1‐dimensional eigenvalue problem. Finally, we provide some numerical experiments to validate the theoretical results and algorithms.     

Non-isotropic weighted L~p estimates for the -equation on piecewise smooth strictly pseudoconvex domains

In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.     

A novel integrated method realizing iteratively optimized modeling for proximity field patterning nanolithography

Processing methods used in photonics and nanotechnology have many limitations hindering the ability to realize devices and restricting the actual number of applications. An ideal processing method should require low-cost equipment, be able to produce very fine details, and be scalable to process large area specimens in an acceptable amount of time. Proximity field nanopatterning (PnP) is a lithography method possessing these features. By using interference patterns produced by a two-dimensional phase mask, the technique is able to generate a submicron detailed exposure on a millimeter-size slab of light sensitive photopolymer, which is then developed like a photographic plate to reveal three-dimensional interference patterns from the phase mask. While it is possible to use computer aided simulations to obtain the interference patterns produced by a mask with a certain pattern, the inverse problem of producing a mask for a desired interference pattern cannot be solved in the same way due to the intricacies of light interactions involved in producing the final interference pattern. An alternative method is to iteratively optimize the phase mask so that the interference patterns obtained converge to the desired pattern. The method is elaborated in this article.