3,789 research outputs found
Permutation of elements in double semigroups
Double semigroups have two associative operations related by
the interchange relation: . Kock \cite{Kock2007} (2007) discovered a
commutativity property in degree 16 for double semigroups: associativity and
the interchange relation combine to produce permutations of elements. We show
that such properties can be expressed in terms of cycles in directed graphs
with edges labelled by permutations. We use computer algebra to show that 9 is
the lowest degree for which commutativity occurs, and we give self-contained
proofs of the commutativity properties in degree 9.Comment: 24 pages, 11 figures, 4 tables. Final version accepted by Semigroup
Forum on 12 March 201
VALUE OF IRRIGATION WATER IN THE MIDDLE ATLANTIC STATES: AN ECONOMETRIC APPROACH
Estimation of the economic value of irrigation water is complicated by a lack of data on the price or marginal cost of water. Through econometric estimation of an aggregate total value product function, this paper obtains marginal irrigation water value estimates for the Middle Atlantic region. Additionally, the impact of temperature and soil conditions on aggregate production within the region is estimated. Ridge regression and covariance analysis are employed to deal with problems of multicollinearity and simultaneous equation bias, respectively. Estimates indicate a substantial and growing return to irrigation within the region.Resource /Energy Economics and Policy,
Seismic Radiation From Simple Models of Earthquakes
We review some basic features of shear wave generation and energy balance for a
2D anti plane rupture. We first study the energy balance for a flat fault, and for a fault
that contains a single localized kink. We determine an exact expression for the partition
between strain energy flow released from the elastic medium surrounding the
fault, radiated energy flow and energy release rate. This balance depends only on the
rupture speed and the residual stress intensity factor. When the fault contains a kink,
the energy available for fracture is reduced so that the rupture speed is reduced. When
rupture speed changes abruptly, the radiated energy flow also changes abruptly. As
rupture propagates across the kink, a shear wave is emitted that has a displacement
spectral content that decreases like ω^(-2) at high frequencies. We then use spectral elements
to model the propagation of an antiplane crack with a slip-weakening friction
law. Since the rupture front in this case has a finite length scale, the wave emitted by
the kink is smoothed at very high frequencies but its general behavior is similar to
that predicted by the simple sharp crack model. A model of a crack that has several kinks and wanders around a mean rupture directions, shows that kinks reduce the rupture speed along the average rupture direction of the fault. Contrary to flat fault models, a fault with kinks produces high frequency waves that are emitted every time the rupture front turns at a kink. Finally, we discuss the applicability of the present results to a 3D rupture model
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