Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock Hypothesis and using these solutions, we are able to describe the space-time transformations between two uniformly accelerated and rotating systems.Comment: 15 pages 1 figur

A new view on relativity: Part 2. Relativistic dynamics

The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by introducing a new principle which is analogous to the Einstein's Equivalence Principle, but can be applied for any force. By this principle, the relativistic dynamic equation is defined by an element of the Lie algebra of the above representation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By the above principle, we show that the relativistic dynamic equation for the four-velocity leads to an analog of the electromagnetic tensor. This indicates that force in special relativity is described by a differential two-form

Wildlife and Human Diseases: Symptoms of Endangered Marine Ecosystems & Climate Change

The Center for Health and the Global Environment, Harvard Medical School; Wildlife Trust; the Consortium for Conservation Medicine; and the Environmental and Energy Study Institute hosted a Congressional briefing entitled "Wildlife and Human Diseases: Symptoms of Endangered Marine Ecosystems and Climate Change." The marine coastal environment is being subjected to increased pressure from residential, recreational, and commercial development. The combined effects of spills, leaks and accidents associated with oil extraction and transport further weakens coastal ecosystems leaving them vulnerable to injury. These disturbances, in conjunction with new stresses posed by climate change, is adversely affecting the health of marine life. An increase in disease among marine species raises significant concern on the part of scientists, environmental researchers, and policymakers who believe such events herald heightened risk to wildlife and humans

Neutron skins of 208^{208}Pb and 48^{48}Ca from pionic probes

The neutron skin of $^{208}$Pb has received considerable attention in recent years. A variety of strongly-interacting probes depict a rather consistent picture but pionic probes have not been referred to in this context. We present here neutron-skin values from pionic atoms and from total reaction cross sections of $\pi ^+$ between 0.7 and 2 GeV/c which fit well into the picture. In addition we show that a neutron skin for $^{48}$Ca can be obtained from existing data on pionic atoms and the result agrees with pion scattering experiments and with the scattering of $\alpha$ particles.Comment: 9 pages, 3 figures, to be published in Nuclear Physics

The wave-function description of the electromagnetic field

For an arbitrary electromagnetic field, we define a prepotential $S$, which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential is Lorentz covariant under a spin half representation. For a moving charge and any observer, we obtain a complex dimensionless scalar. The prepotential is a function of this dimensionless scalar. The prepotential $S$ of an arbitrary electromagnetic field is described as an integral over the charges generating the field. The Faraday vector at each point may be derived from $S$ by a convolution of the differential operator with the alpha matrices of Dirac. Some explicit examples will be calculated. We also present the Maxwell equations for the prepotential

Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity

This paper is motivated by questions such as P vs. NP and other questions in Boolean complexity theory. We describe an approach to attacking such questions with cohomology, and we show that using Grothendieck topologies and other ideas from the Grothendieck school gives new hope for such an attack. We focus on circuit depth complexity, and consider only finite topological spaces or Grothendieck topologies based on finite categories; as such, we do not use algebraic geometry or manifolds. Given two sheaves on a Grothendieck topology, their "cohomological complexity" is the sum of the dimensions of their Ext groups. We seek to model the depth complexity of Boolean functions by the cohomological complexity of sheaves on a Grothendieck topology. We propose that the logical AND of two Boolean functions will have its corresponding cohomological complexity bounded in terms of those of the two functions using ``virtual zero extensions.'' We propose that the logical negation of a function will have its corresponding cohomological complexity equal to that of the original function using duality theory. We explain these approaches and show that they are stable under pullbacks and base change. It is the subject of ongoing work to achieve AND and negation bounds simultaneously in a way that yields an interesting depth lower bound.Comment: 70 pages, abstract corrected and modifie