Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space

Liko and Wesson have recently introduced a new 5-dimensional induced matter solution of the Einstein equations, a negative curvature Robertson-Walker space embedded in a Riemann flat 5-dimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain N+1-dimensional Riemann flat spaces which are all solutions of the Einstein equations. These solutions encapsulate N-dimensional curved manifolds. Such spaces are said to "induce matter" in the sub-manifolds by virtue of their geometric structure alone. We prove that the N-manifold can be any maximally symmetric space.Comment: 3 page

BRAVO economic study of LANDSAT follow-on

The LANDSAT Follow-On satellite consists of two major systems: the instrument module and the Multi-Mission Modular Spacecraft (MMS). The instrument module contains the thematic mapper and the five-band multispectral scanner instruments. The instrument module also includes the solar array, the tracking and data relay satellite (TDRS) antenna, and the wideband data module. The MMS contains the modularized and standardized power, propulsion, attitude control, and command and data handling subsystems. The Shuttle will be supporting the LANDSAT Follow-On system. The LANDSAT Follow-On Project plans two Delta 3910 launches. The first is scheduled for 1981; the second Delta launch will occur as needed to keep one satellite operational on orbit. The second satellite will be ready six months after the first. It could be launched any time after that. Shuttle support of the system could begin in early 1983 but would be scheduled to start after the second Delta launch

The chemical composition of food preservatives. Solutions for testing cream and milk.

There are many substances which are found on the market at the present time intended for preserving food products under various brands and names. The claims made for these substances by the manufacturers would lead one to believe that the brand of substance for which the claim is made possessed a wonderful power for preserving food products. When these mixtures are examined it is found that they are composed of common substances and such that any one could readily prepare for a small part of the price charged for them. In the development of the dairy industry from the farm dairy to the creamery, it has been found that the processes connected with the industry must be controlled in an intelligent manner in order that success may resul

Explorations, Vol. 1, No. 2

The cover print is a multi-plate colored etching entitled Skull and Sun Dial, by Susan Groce, Associate Professor of Art at the University of Maine at Orono, where she teaches Printmaking and Drawing. Articles include: The Quaternary Ice Age Plants and Animals: Secrets of the Colorado Plateau, by Jim I. Mead and Emilee M. Mead Finding the Facts: Pieces of the Puzzle On Location: In Search of the First Americans A Temporal Vegetational Continuum: From Tundra to Forest, by Carole J. Bombard for Ronald B. Davis Anatomy of an Excavation, by Robson Bonnichsen What the Bones Tell Us, by Marcella H. Sorg People of the Americas Publication Program, by Emilee M. Mea

Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(nn)

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.Comment: Minor changes, journal reference adde

Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

The Quantum Adiabatic Approximation and the Geometric Phase

A precise definition of an adiabaticity parameter $\nu$ of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator $U(\tau)=\sum_\ell U^{(\ell)}(\tau)$ with $U^{(\ell)}(\tau)$ being at least of the order $\nu^\ell$. In particular $U^{(0)}(\tau)$ corresponds to the adiabatic approximation and yields Berry's adiabatic phase. It is shown that this series expansion has nothing to do with the $1/\tau$-expansion of $U(\tau)$. It is also shown that the non-adiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. Some related issues concerning the geometric phase are also discussed.Comment: uuencoded LaTeX file, 19 page

Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo