The Hamilton-Jacobi equation revisited

A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

Phase space methods and the Hamilton-Jacobi form of dynamics

A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.

Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

Diurnal variation of atmospheric CO2 concentration and delta C-13 in an urban atmosphere during winter-role of the Nocturnal Boundary Layer

The paper presents the importance of the Nocturnal Boundary Layer in driving the diurnal variability of the atmospheric CO2 mixing ratio and the carbon isotope ratio at ground level from an urban station in India. Our observations are the first of their kind from this region. The atmospheric CO2 mixing ratio and the carbon isotopic ratio were measured for both the morning (05:30-07:30 IST) and afternoon time (16:00-18:00 IST) air samples at 5 m above ground level in Bangalore city, Karnataka State (12 degrees 58' N, 77 degrees 38' E, masl = 920 m) for a 10 day period during the winter of 2008. We observed a change of similar to 7% the in CO2 mixing ratio between the morning and afternoon time air samples. A stable isotope analysis of CO2 from morning samples showed a depletion in the carbon isotope ratio by similar to 2 parts per thousand compared to the afternoon samples. Along with the ground-based measurement of air samples, data of radiosonde measurements were also obtained from the Indian Meteorological Department to identify the vertical atmospheric structure at different time in a day. We proposed the presence or absence of the NBL as a controlling factor for the observed variability in the mixing ratio as well as its isotopic composition. Here we used the Keeling model approach to find out the carbon isotope ratio for the local sources. The local sources have further been characterized as anthropogenic and biological respiration (in %) using a two-component mixing model. We also used a vertical mixing model based on the concept of the mixing of isotopically depleted (carbon isotope) ``polluted air'' (PA) with isotopically enriched ``free atmospheric air'' (FA) above. Using this modeling approach, the contribution of FA at ground level is being estimated for both the morning and afternoon time air samples.

Ontheproof of the Poincare´ conjecture

In 2002, Perelman proved the Poincare conjecture, building on the work of Richard Hamilton on the Ricci flow. In this article, we sketch some of the arguments and attempt to place them in a broader dynamical context.

On the proof of the Poincare´ conjecture

In 2002, Perelman proved the Poincare conjecture, building on the work of Richard Hamilton on the Ricci flow. In this article, we sketch some of the arguments and attempt to place them in a broader dynamical context.