32,098 research outputs found
Stable subnorms revisited
Let A be a finite-dimensional, power-associative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 not equal a is an element of S, and f(alpha a) = |alpha| f(a) for all a is an element of S and alpha is an element of F. If in addition, S is closed under raising to powers, then a subnorm f shall be called stable if there exists a constant sigma > 0 so that f(a(m)) less than or equal to sigma f(a)(m) for all a is an element of S and m = 1, 2, 3....
The purpose of this paper is to provide an updated account of our study of stable subnorms on subsets of finite-dimensional, power-associative algebras over F. Our goal is to review and extend several of our results in two previous papers, dealing mostly with continuous subnorms on closed sets
Exact Nonperturbative Unitary Amplitudes for 1->N Transitions
I present an extension to arbitrary N of a previously proposed field
theoretic model, in which unitary amplitudes for processes were
obtained. The Born amplitude in this extension has the behavior
expected in a bosonic field theory. Unitarity
is violated when , or when Numerical
solutions of the coupled Schr\"odinger equations shows that for weak coupling
and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit
by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}.
The very small size of the coefficient 1/\g2 , indicative of a very weak
exponential suppression, is not in accord with standard discussions based on
saddle point analysis, which give a coefficient The weak dependence
on could have experimental implications in theories where the exponential
suppression is weak (as in this model). Non-perturbative contributions to
few-point correlation functions in this theory would arise at order $K\ \simeq\
\left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}\g2.$Comment: 11 pages, 3 figures (not included
Initiation of non-tropical thunderstorms by solar activity
Correlative evidence accumulating since 1926 suggests that there must be some physical coupling mechanism between solar activity and thunderstorm occurrence in middle to high latitudes. Such a link may be provided by alteration of atmospheric electric parameters through the combined influence of high-energy solar protons and decreased cosmic ray intensities, both of which are associated with active solar events. The protons produce excess ionization near and above 20km, while the Forbush decreases a lowered conductivity and enhanced fair-weather atmospheric electric field below that altitude. Consequent effects ultimately lead to a charge distribution similar to that found in thunderclouds, and then other cloud physics processes take over to generate the intense electric fields required for lightning discharge
An optimal system design process for a Mars roving vehicle
The problem of determining the optimal design for a Mars roving vehicle is considered. A system model is generated by consideration of the physical constraints on the design parameters and the requirement that the system be deliverable to the Mars surface. An expression which evaluates system performance relative to mission goals as a function of the design parameters only is developed. The use of nonlinear programming techniques to optimize the design is proposed and an example considering only two of the vehicle subsystems is formulated and solved
Weyl-type Fields with Geodesic Lines of Force
The static electrogravitational equations are studied and it is shown that an
aligned type D metric which has a Weyl-type relationship between the
gravitational and electric potential has shearfree geodesic lines of force. All
such fields are then found and turn out to be the fields of a charged sphere,
charged infinite rod and charged infinite plate. A further solution is also
found with shearing geodesic lines of force. This new solution can have
or , but cannot be in the Majumdar-Papapetrou class (in which ). It is algebraically general and has flat equipotential surfaces.Comment: 13 pages, RevTe
General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
The Hamiltonian formulation of general relativity on a null surface is
established in the teleparallel geometry. No particular gauge conditons on the
tetrads are imposed, such as the time gauge condition. By means of a 3+1
decomposition the resulting Hamiltonian arises as a completely constrained
system. However, it is structurally different from the the standard
Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the
basic field quantities are tetrads that transform under the global SO(3,1) and
the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra
Techniques for the realization of ultrareliable spaceborne computers Interim scientific report
Reliability tests on spaceborne digital computer
Completeness of Wilson loop functionals on the moduli space of and -connections
The structure of the moduli spaces \M := \A/\G of (all, not just flat)
and connections on a n-manifold is analysed. For any
topology on the corresponding spaces \A of all connections which satisfies
the weak requirement of compatibility with the affine structure of \A, the
moduli space \M is shown to be non-Hausdorff. It is then shown that the
Wilson loop functionals --i.e., the traces of holonomies of connections around
closed loops-- are complete in the sense that they suffice to separate all
separable points of \M. The methods are general enough to allow the
underlying n-manifold to be topologically non-trivial and for connections to be
defined on non-trivial bundles. The results have implications for canonical
quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-
Hall effect encoding of brushless dc motors
Encoding mechanism integral to the motor and using the permanent magnets embedded in the rotor eliminates the need for external devices to encode information relating the position and velocity of the rotating member
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