On Weyl modules over affine Lie algebras in prime characteristic

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.Comment: 30 pages, 1 figure, 3 tables; v4: clarifying the statement of Conjecture 6.1 regarding the strong linkage principl

Neural Network Based Microgrid Voltage Control

The primary purpose of this study is to improve the voltage profile of Microgrid using the neural network algorithm. Neural networks have been successfully used for character recognition, image compression, and stock market prediction, but there is no directly application related to controlling distributed generations of Microgrid. For this reason the author decided to investigate further applications, with the aim of controlling diesel generator outputs. Firstly, this thesis examines the neural network algorithm that can be utilized for alleviating voltage issues of Microgrid and presents the results. MATLAT and PSCAD are used for training neural network and simulating the Microgrid model respectively. The Feedforward Back-propagation algorithm is used in this study and the Microgrid consists of wind, solar, and diesel power generations, and battery storage. Neural network will indicate how much real and reactive power is needed from each generator. In the second stage, several scenarios are proposed to verify that the monitoring points are very important for training neural networks. Finally, the comparison of results is shown for further discussion of critical points. In conclusion, the results of the study show that neural network algorithm is well suited for the application, and it was effectively certified for the purpose of improving the voltage profile of Microgrid

Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures.

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures

THE U.S. FOOD DEMAND FOR WHEAT BY CLASS

This study investigates the nature of demand peculiar to each class and quantify the economic and physical interrelationships existing among the five major classes of wheat produced in the United States.Crop Production/Industries, Demand and Price Analysis,