Lu, Nancy C.

National Taiwan University, Taiwan, BS, 1963 University of Wyoming, Laramie, Wyoming, MS, 1964 University of California, Berkeley, PhD, 1973 University of California, Berkeley, Post-doctoral Fellowship 1974https://scholarworks.sjsu.edu/erfa_bios/1355/thumbnail.jp

Social and Political Dimensions of Identity

We study the interior regularity of solutions to the Dirichlet problem Lu = g in Omega, u = 0 in R-nOmega, for anisotropic operators of fractional type Lu(x) = integral(+infinity)(0) dp integral(Sn-1) da(w) 2u(x) - u(x + rho w) - u(x - rho w)/rho(1+2s). Here, a is any measure on Sn-1 (a prototype example for L is given by the sum of one-dimensional fractional Laplacians in fixed, given directions). When a is an element of C-infinity(Sn-1) and g is c(infinity)(Omega), solutions are known to be C-infinity inside Omega (but not up to the boundary). However, when a is a general measure, or even when a is L-infinity(s(n-1)), solutions are only known to be C-3s inside Omega. We prove here that, for general measures a, solutions are C1+3s-epsilon inside Omega for all epsilon > 0 whenever Omega is convex. When a is an element of L-infinity(Sn-1), we show that the same holds in all C-1,C-1 domains. In particular, solutions always possess a classical first derivative. The assumptions on the domain are sharp, since if the domain is not convex and the measure a is singular, we construct an explicit counterexample for which u is not C3s+epsilon for any epsilon > 0 - even if g and Omega are C-infinity

Petrophysical Evaluation and Reservoir Characterization of the Zubair Formation in the Luhais and Rachi oil fields, Southern Iraq

The Barremian succession in the present study is represented by the Zubair Formation which the most significant sandstone reservoir in Iraq.The area of study is located in the Southern part of Iraq at the Luhaisand Rachi oil fields, within the Mesopotamian basin. The thickness of the Zubair Formation is about 450 m in the studied area. It is divided into three lithofacies:- The upper unit is composed mostly of shale layers, the middle unit is consists of thick layers of sandstone rocks and the lower ones is consists mainly of Shale with less sandstone layers. These units are characterized by three types of petrophysical features according to total porosity/effective porosity: - High-moderate effective porosity rocks (type I), moderate effective porosity rocks (type II) and low-non pores rocks (type III). The upper unit of theZubair Formation at the Luhais oil field is characterized by two horizons. The first is showing high resistivity-high gamma ray which represents the upper part; while the lower ones is shown low resistivity-low gamma ray. There are two good reservoir horizones with high oil saturation (low water saturation) in this unit at the Rachi oil field and Lu-3 borehole, while at the Lu-12 is appeared as one uncontaneoushorizon. The middle is characterized by two subzones in the southwestern part of Luhais oil field (Lu-12). The upper one characterized by high- moderate effective porosity while the lower one characterized by moderate effective porosity because of presence a low volume of shale. This unit is dominated by low resistivity-low gamma ray with three susbended bands of high resistivity-low gamma ray, these appeared in both studied oil fields. The high percentage of water saturation in this unit caused the lack of clarity of the oil saturation, which appears in narrow bands The lower unit is represented the shale – dominated member of Zubair Formation, with low to non-pores rocks. This appeared in all studied wells. There are limit presences for the high- moderate effective porosity of rock within the sand bands lithofacies appears in these wells. This unit is characterized by alternative the high resistivity-high gamma ray horizon with the low resistivity-low gamma ray horizon as four cycles. There are two good reservoir horizons with high oil saturation (low water saturation) in this unit with a distribution similar to that found in the upper part. From the reservoir geology which represent by property modelling, preparing data, construction of three-dimension clump and scale up for the studied oil fields. The Rachi oil field is appeared the better hydrocarbon saturation compared to Luhais oil field, although the Luhais oil field (Lu-3 and Lu-12) is the best of pertophysicalproperties. This indicates that the Rachi oil field was affected by the structural position as indicated by the model, while the model did not show any structural properties in the field of Lahis. Therefore, the structural and/or stratigraphic positions have the greatest influence on the hydrocarbon accumulation, regardless of petrophysical properties

A Scalable Null Model for Directed Graphs Matching All Degree Distributions: In, Out, and Reciprocal

Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null model to compare algorithms or perform experimental studies. Furthermore, there are scalable algorithms that implement these models and they are invaluable in the study of graphs. However, networks in the real-world are often directed, and have a significant proportion of reciprocal edges. A stronger relation exists between two nodes when they each point to one another (reciprocal edge) as compared to when only one points to the other (one-way edge). Despite their importance, reciprocal edges have been disregarded by most directed graph models. We propose a null model for directed graphs inspired by the Chung-Lu model that matches the in-, out-, and reciprocal-degree distributions of the real graphs. Our algorithm is scalable and requires $O(m)$ random numbers to generate a graph with $m$ edges. We perform a series of experiments on real datasets and compare with existing graph models.Comment: Camera ready version for IEEE Workshop on Network Science; fixed some typos in tabl