The sphere, because of its high symmetry, is what might be called a perfect shape. Unfortunately nature is imperfect and many apparently spherical bodies are better represented by an ellipsoid. Consequently in calculations about gravitational potential, for example, spherical harmonics have to be replaced by the much more complex ellipsoidal harmonics. Their theory, which was originated in the ...

Civil war is the most important and troubling problem in international life today. Aside from the tragic killing and injury of innocent civilians, violent civil conflicts inspire lingering, seemingly intractable ills such as state collapse, corruption, dire poverty, rampant injustice, dislocation, environmental degradation, and disease, all of which may in turn instigate renewed and spreading c...

The only fully intact textual evidence from fifth-century and (very) early fourth-century comedy are the eleven completely preserved comedies by Aristophanes, who was born, in all likelihood, shortly after 450 bce and died after 388 bce.1 This is, in fact, not as thin a basis as one might initially think. For not only is the number of completely preserved Aristophanic comedies actually quite hi...

ion, 338 animal visual system, 314 aromatic rings, 340 asymptotic behavior, 85–86, 213 attractor, 147, 236, 314, 317 avalanche process, 324 Avogadro number, 16 Axelrod model, 307 backbone, 60–61 backdoor, 61–64 batch setting, 94 Bayes’ decision rule, 95 Bayes error, 95 Bethe lattice, 39 bifurcations, 317 blind spot, 231, 329, 333 Boltzman constant, 19 boolean algebra, 169 attribute, 169 express...

Since antiquity humans have been fascinated by whales and dolphins. They were attracted by the social behaviour and apparent curiosity of dolphins, which resulted in frequent interaction with humans. Myths were generated, especially around large whales, which behaved differently from other sea fauna. Even if early research on whales may have been driven by the economic interests of the whaling ...

The internuclear potential V(r) of a diatomic molecule is spherically symmetric. It depends only on r, the internuclear separation. The internuclear potential v(r) can be determined using the Born-Oppenheimer approximation, where we assume that the motion of the nuclei is very slow compared to that of the electrons. We solve for the energy of ground electronic state as a function of the internu...

These are lecture notes from a graduate course for Computer Science graduate students at Princeton University in Fall 2013 and Fall 2014. (The course also attracts undergrads and non-CS grads and total enrollment in 2014 was 35.) The course assumes prior knowledge of algorithms at the undergraduate level. This new course arose out of thinking about the right algorithms training for CS grads tod...

The general rationale of analytic number theory is to derive statistical information about a sequence {an} from the analytic behaviour of an appropriate generating function, such as a power series ∑ anz or a Dirichlet series ∑ ann−s . The type of generating function employed depends on the problem being investigated. There are no rigid rules governing the kind of generating function that is app...

Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to students interested in the application of algebra to geometrical problems, specifically the study of surfaces (such as sphere, torus, Möbius band, Klein bottle). In this introduction to simplicial homology – the most easily digested ver...