65,476 research outputs found
A dichotomy result for prime algebras of Gelfand-Kirillov dimension two
Let be an uncountable field. We show that a finitely generated prime
Goldie -algebra of quadratic growth is either primitive or satisfies a
polynomial identity, answering a question of Small in the affirmative.Comment: 10 page
Noetherian algebras over algebraically closed fields
Let be an uncountable algebraically closed field and let be a
countably generated left Noetherian -algebra. Then we show that is left Noetherian for any field extension of . We conclude that all
subfields of the quotient division algebra of a countably generated left
Noetherian domain over are finitely generated extensions of . We give
examples which show that need not remain left Noetherian if the
hypotheses are weakened.Comment: 10 page
Submerged dunes and breakwater embayments mapped using wave inversions of shore-mounted marine X-Band radar data
Surveying very shallow coastal areas, particularly around
coastal defences, can be a logistically difficult and time
consuming process. A marine-radar based bathymetry mapping technique has been used to remotely map the embayments around a series of shore-parallel breakwaters at Sea Palling on the south east coast of England during the
LEACOAST2 project. The duration of the deployment spanned over 2 years, with the aim of observing any evolution of bathymetric features over that timescale while providing a clear indication of the spatial variability of wave and current patterns contributing to such evolution. The embayments generated by the shore parallel breakwaters at that site are resolved and a field of subtidal dunes with a wavelength of the order of 200m and amplitude around 1m located in approximately 6-10m of water were within the radar field of view and are evident in the remotely sensed bathymetry. Comparisons between bathymetric data obtained using conventional survey techniques and the radar based technique are presented together with measurements of tidal currents mapped using the same remote sensing method and compared with ADCP data during a storm even
On Spontaneous Wave Function Collapse and Quantum Field Theory
One way of obtaining a version of quantum mechanics without observers, and
thus of solving the paradoxes of quantum mechanics, is to modify the
Schroedinger evolution by implementing spontaneous collapses of the wave
function. An explicit model of this kind was proposed in 1986 by Ghirardi,
Rimini, and Weber (GRW), involving a nonlinear, stochastic evolution of the
wave function. We point out how, by focussing on the essential mathematical
structure of the GRW model and a clear ontology, it can be generalized to
(regularized) quantum field theories in a simple and natural way.Comment: 14 pages LaTeX, no figures; v2 minor improvement
The Identity Correspondence Problem and its Applications
In this paper we study several closely related fundamental problems for words
and matrices. First, we introduce the Identity Correspondence Problem (ICP):
whether a finite set of pairs of words (over a group alphabet) can generate an
identity pair by a sequence of concatenations. We prove that ICP is undecidable
by a reduction of Post's Correspondence Problem via several new encoding
techniques.
In the second part of the paper we use ICP to answer a long standing open
problem concerning matrix semigroups: "Is it decidable for a finitely generated
semigroup S of square integral matrices whether or not the identity matrix
belongs to S?". We show that the problem is undecidable starting from dimension
four even when the number of matrices in the generator is 48. From this fact,
we can immediately derive that the fundamental problem of whether a finite set
of matrices generates a group is also undecidable. We also answer several
question for matrices over different number fields. Apart from the application
to matrix problems, we believe that the Identity Correspondence Problem will
also be useful in identifying new areas of undecidable problems in abstract
algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the
published journal version of this article, see footnote 3 on page 1
Process for preparing higher oxides of the alkali and alkaline earth metals
High purity inorganic higher oxides of the alkali and alkaline earth metals are prepared by subjecting the hydroxide of the alkali and alkaline earth metal to a radio frequency discharge sustained in oxygen. The process is particulary adaptable to the production of high purity potassium superoxide by subjecting potassium hydroxide to glow discharge sustained in oxygen under the pressure of about 0.75 to 1.00 torr
The combined solar and tidal influence in climate
To provide an early warning indication of the CO2 warning signal, we are searching for periodic or projectable trends in climate. The strong 20.5 year oscillation in Eastern North American January temperature found by Mock and Hibler shows evidence of a beat between waves with periods of 22.36 (22.21 to 22.55) years and 18.64 (18.45 to 18.79) years with an opposition at about 1880. These are interpreted to be the 22.279 year solar Hale magnetic cycle and the 18.61 year lunar nodal tidal cycle. The lunar nodal cycle is known to produce changes in the sea surface temperature through increased mixing of the mixed layer of the ocean. This beat note is shown to be evident in the Western High Plains drought record of Mitchell, Stockton and Meko and to provide a better bit to the drought series, especially at the beat oppositions in 1880 and 1770
Predominant periods in the time series of drought area index for the Western High Plains AD 1700 to 1962
The detection of the combined presence of the Hale magnetic sunspot cycle (22.28 years) and the lunar nodal tidal cycle (18.61 years) in both the Eastern North American January air temperatures and the Western U.S. High Plains drought series led to an extended analysis of the Drought Area Index time series. This analysis indicated that the mean dominant period of the drought series should be 20.0 to 20.5 years and that the principal period should be resolvable into two components of about 22.28 and 18.61 years. This note details the successful accomplishment of this task
Growth of surface and corner cracks in beta-processed and mill-annealed Ti-6Al-4V
Empirical stress-intensity expressions were developed to relate the growth of cracks from corner flaws to the growth of cracks from surface flaws. An experimental program using beta-processed Ti-6Al-4V verified these expressions for stress ratios, R greater than or equal to 0. An empirical crack growth-rate expression which included stress-ratio and stress-level effects was also developed. Cracks grew approximately 10 percent faster in transverse-grain material than in longitudinal-grain material and at approximately the same rate in longitudinal-grain mill-annealed Ti-6Al-4V. Specimens having surface and corner cracks and made of longitudinal-grain, beta-processed material were tested with block loads, and increasing the stresses in a block did not significantly change the crack growth rates. Truncation of the basic ascending stress sequence within a block caused more rapid crack growth, whereas both the descending and low-to-high stress sequences slowed crack growth
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