Planning for the utilization of the PCDS in studying the interaction of clouds (ISCCP-C data) and the Earth radiation budget (ERBE data)

The Pilot Climate Data System (PCDS) affords an opportunity to analyze data from different but highly complementary data sets. Two of these highly complementary data sets supported by the PCDS are the International Satellite Cloud Climatology Project (ISCCP) and the Earth Radiation Budget Experiment (ERBE). Both data set sponsors are aware of the utility of one data set to the other, and both projects utilize gridded data on a 2.5 deg by 2.5 deg grid. The ISCCP data have been collected since July 1983, and the NOAA-9 data for ERBE have been collected for more than a year. Therefore, there is a good chance to use these temporally overlapping data sets to investigate hypothesized relationships. Changes in cloudiness affect both cloud albedo feedback (shortwave) and the greenhouse effect (longwave). The relative importance of the effects of clouds on albedo versus outgoing longwave radiation (OLR) in determining the radiation balance has long been a matter of controversy. Now, however, changes in cloud amount as observed by the ISCCPO can be correlated to corresponding changes in the albedo and changes in the OLR from ERBE. Monthly means can be utilized in all instances

Mathematical Support to Braneworld Theory

The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold in a space of high dimension, the bulk, solution of Einstein's equations in high dimension. In this paper we approach the mathematical consistency of this theory with a new proof of the fundamental theorem of submanifolds for case of semi-Riemannian manifolds. This theorem consist an essential mathematical support for this new theory. We find the integrability conditions for the existence of space-time submanifolds in a pseudo-Euclidean space. Keywords: Submanifolds, Braneworld, Pseudo-Riemannian geometryComment: 10 page

A cloud physics investigation utilizing Skylab data

There are no author-identified significant results in this report

Solar variability indications from Nimbus 7 satellite data

The cavity pyrheliometer sensor of the Nimbus 7 Earth Radiation Experiment indicated low-level variability of the total solar irradiance. The variability appears to be inversely correlated with common solar activity indicators in an event sense. the limitations of the measuring system and available data sets are described

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of such null vectors provide a very useful tool. A work of Hill, Lewandowski and Nurowski has given a good foundation for this, reducing the field equations to a set of differential equations for two functions, one real, one complex, of three variables. Under the assumption of the existence of one Killing vector, the (infinite-dimensional) classical symmetries of those equations are determined and group-invariant solutions are considered. This results in a single ODE of the third order which may easily be reduced to one of the second order. A one-parameter class of power series solutions, g(w), of this second-order equation is realized, holomorphic in a neighborhood of the origin and behaving asymptotically as a simple quadratic function plus lower-order terms for large values of w, which constitutes new solutions of the twisting type N problem. The solution found by Leroy, and also by Nurowski, is shown to be a special case in this class. Cartan's method for determining equivalence of CR manifolds is used to show that this class is indeed much more general. In addition, for a special choice of a parameter, this ODE may be integrated once, to provide a first-order Abel equation. It can also determine new solutions to the field equations although no general solution has yet been found for it.Comment: 28 page

The asymptotic expansion of a CR invariant and Grauert tubes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46246/1/208_2005_Article_BF01446285.pd

The masterpieces of John Forbes Nash Jr.

In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader

Molecular Mechanism of the Constitutive Activation of the L250Q Human Melanocortin-4 Receptor Polymorphism †

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65471/1/j.1747-0285.2006.00362.x.pd