........................................................................................................................... i Acknowledgments ........................................................................................................... iii

The winding number transition in the Mottola-Wipf model with and without Skyrme term is examined. For the model with Skyrme term the number of discrete modes of the fluctuation operator around sphaleron is shown to be dependent on the value of λm2. Following Gorokhov and Blatter we derive a sufficient condition for the sharp first-order transition, which indicates that first-order transition oc...

a piece of statuary, or in music. But, linked with the stream of heredity, we find also the environment of a "Little Italy," with all its life and color. Little winding streets of shops invite one to roam about. Here one may purchase brown Italian cakes, huge crusty loaves of bread, dried octopi, looking rather forlorn as they hang by one claw. Temptingly spread out on the curb markets are many...

We introduce the notion of the projective linking number LinkP(Γ, Z) of a compact oriented real submanifold Γ of dimension 2p − 1 in complex projective n-space P with an algebraic subvariety Z ⊂ P − Γ of codimension p. This notion is related to projective winding numbers and quasi-plurisubharmonic functions, and it is generalized to any projective manifold X . It is shown that a basic conjectur...

We study the statistics of semi-meanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct enumeration up to n = 29, we perform on the one hand a large n extrapolation and on the other hand we reformulate the available data into a large q expansio...

We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can then be compactified and can be identified topologically (but not metrically!) with a three sphere. Therefore, at fixed time, the winding of the map is define...

Contents Preface v Chapter 1. From i to z: the basics of complex analysis 1 1. The field of complex numbers 1 2. Differentiability and conformality 3 3. Möbius transforms 7 4. Integration 12 5. Harmonic functions 19 6. The winding number 21 7. Problems 24 Chapter 2. From z to the Riemann mapping theorem: some finer points of basic complex analysis 27 1. The winding number version of Cauchy's th...

For transportation of natural gas (NG), pipeline transportation is often used. However, when gas volumes are moderate, and/or transportation distances are large, the capital and operating costs for pipeline transport become prohibitive. In such cases, transport of Liquefied Natural Gas (LNG) in tankers is often the preferred choice for bringing the gas to the market. In the liquefaction process...

A novel method of determining the number of superhelical turns of a covalently-closed plasmid DNA is described. It relies on the determination of the hyperchromicity, and hence the proportion of unstacked basepairs, of a partially heat-denatured sample which co-migrates during electrophoresis with nicked circular duplex DNA. The values obtained for plasmid pBR beta G DNA at 4 degrees C (-29.8 a...

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been ex...