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Algebraic Geometry over the Complex Numbers

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

From now on, we are going to work almost exclusively with complex-valued
functions and forms. So we revise our notation accordingly. Given a C∞ manifold
X, let C∞X (respectivelyE kX) now denote the space of complex-valuedC∞ ...

Potential Theory in the Complex Plane

Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.

The choice lay between several excellent but encyclopaedic treatises on the
subject, from which it was hard work to extract what was needed, and several
equally excellent books on complex variable, each containing a useful chapter
on ...

Evaluating the Complex

Attribution, Contribution, and Beyond

In the economic atmosphere following the crisis of 2008, not only have governments reacted by creating more complex policy initiatives, but they have also promised that all of these initiatives will be evaluated. Due to the complexity of many of the initiatives, the ways of evaluating are becoming equally complex. The book begins with a theoretical and conceptual explanation of the process and shows how this translates into the practice of evaluation. The chapters cover a wide variety of subjects, such as poverty, homelessness, smoking prevention, HIV/AIDS, and child labor. The use of case studies sheds light on the conceptual ideas at work in organizations addressing some of the world’s largest and most varied problems. The evaluation process seeks a balance between order and chaos. The interaction of four elements—simplicity, inventiveness, flexibility, and specificity—allows complex patterns to emerge. The case studies illustrate this framework and provide a number of examples of practical management of complexity, in light of contingency theories of the evaluation process itself. These theories in turn match the complexity of evaluated policies, strategies, and programs. The evaluation process is examined for its impact on policy outcomes and choices.

Implications of Complicated and Complex Characteristics for Key Tasks in
Evaluation Patricia J. Rogers “Complex problems have simple, easy to
understand, wrong answers.” Henry Louis Mencken “Life is really simple, but we
insist on ...

The Complex Variable Boundary Element Method

The Complex Variable Boundary Element Method or CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method or BIEM. This generalization allows an immediate and extremely valuable transfer of the modeling techniques used in real variable boundary integral equation methods (or boundary element methods) to the CVBEM. Consequently, modeling techniques for dissimilar materials, anisotropic materials, and time advancement, can be directly applied without modification to the CVBEM. An extremely useful feature offered by the CVBEM is that the pro duced approximation functions are analytic within the domain enclosed by the problem boundary and, therefore, exactly satisfy the two-dimensional Laplace equation throughout the problem domain. Another feature of the CVBEM is the integrations of the boundary integrals along each boundary element are solved exactly without the need for numerical integration. Additionally, the error analysis of the CVBEM approximation functions is workable by the easy-to-understand concept of relative error. A sophistication of the relative error analysis is the generation of an approximative boundary upon which the CVBEM approximation function exactly solves the boundary conditions of the boundary value problem' (of the Laplace equation), and the goodness of approximation is easily seen as a closeness-of-fit between the approximative and true problem boundaries.

CHAPTER 2 A REVIEW OF COMPLEX WARIABLE THEORY 2.0
INTRODUCTION Before developing the mathematical foundations of the
Complex Variable Boundary Element Method (CWBEM), the basic tools needed
for the method's ...

The Complex Infrastructure Known as the Female Mind

According to Relient K

In The Complex Infrastructure Known as the Female Mind, Relient K expounds on their experiences observing the opposite sex. Detailing some of the "girl types" they've encountered--like the Homecoming Queen, The Athlete, and The Overachiever--they share personal stories and biblical advice for girls of any type to become women of God. The band's fun attitude is present throughout the book in quizzes, lists, personal stories, and more!

If we were to take an educated guess, it would break out like this: Blonde HQ = 60
%, Brunette HQ = 35%, Black haired HQ = 5%. Blondes would definitely win out
with an almost 2-to-1 margin. Statistically speaking, redheads 28 The Complex ...

The Complex Reality of Religious Peacebuilding

Conceptual Contributions and Critical Analysis

This insightful book focuses on the multifaceted subject of sustainable religious peacebuilding. Katrien Hertog discusses the ways in which religious actors can utilize resources to prevent violent conflict from occurring, reduce conflict when it does happen, and rebuild bridges between sides in after conflict has ceased.

—Madeleine Albright, The Mighty and the Almighty: Reflections on America, God
and World Affairs (New York: HarperCollins, 2006), 77 THE COMPLEX REALITY
OF RELIGION AND PEACEBUILDING ctober 2007. The nonviolent protest ...