Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide numerical examples to verify the theoretical results

Links of complex analytic singularities

This is a part survey part research paper studying the local topology of complex analytic spaces. We review and strengthen the results of Kapovich--Koll\'ar "Fundamental groups of links of isolated singularities" (1109.4047) and incorporate the paper "Dual graphs of exceptional divisors" (1203.2640) into the current one. A new result is the characterization of the fundamental group of links of Cohen-Macaulay singularities. The last section lists numerous open problems and conjectures. Version 2: Questions 62--65 revised following comments of Shaneson and Maxim. Version 3: Many small changes, especially in section about Questions and Problems.Comment: arXiv admin note: substantial text overlap with arXiv:1203.264

Planar splines on a triangulation with a single totally interior edge

We derive an explicit formula, valid for all integers $r,d\ge 0$, for the dimension of the vector space $C^r_d(\Delta)$ of piecewise polynomial functions continuously differentiable to order $r$ and whose constituents have degree at most $d$, where $\Delta$ is a planar triangulation that has a single totally interior edge. This extends previous results of Toh\v{a}neanu, Min\'{a}\v{c}, and Sorokina. Our result is a natural successor of Schumaker's 1979 dimension formula for splines on a planar vertex star. Indeed, there has not been a dimension formula in this level of generality (valid for all integers $d,r\ge 0$ and any vertex coordinates) since Schumaker's result. We derive our results using commutative algebra.Comment: 20 pages, 3 figure

Using mixed methods in monitoring and evaluation : experiences from international development

This paper provides an overview of the various ways in which mixing qualitative and quantitative methods could add value to monitoring and evaluating development projects. In particular it examines how qualitative methods could address some of the limitations of randomized trials and other quantitative impact evaluation methods; it also explores the importance of examining"process"in addition to"impact", distinguishing design from implementation failures, and the value of mixed methods in the real-time monitoring of projects. It concludes by suggesting topics for future research -- including the use of mixed methods in constructing counterfactuals, and in conducting reasonable evaluations within severe time and budget constraints.Poverty Monitoring&Analysis,Scientific Research&Science Parks,Science Education,Poverty Impact Evaluation,Statistical&Mathematical Sciences