109,171 research outputs found
The enumeration of fully commutative affine permutations
We give a generating function for the fully commutative affine permutations
enumerated by rank and Coxeter length, extending formulas due to Stembridge and
Barcucci--Del Lungo--Pergola--Pinzani. For fixed rank, the length generating
functions have coefficients that are periodic with period dividing the rank. In
the course of proving these formulas, we obtain results that elucidate the
structure of the fully commutative affine permutations.Comment: 18 pages; final versio
Benchmark ultra-cool dwarfs in widely separated binary systems
Ultra-cool dwarfs as wide companions to subgiants, giants, white dwarfs and
main sequence stars can be very good benchmark objects, for which we can infer
physical properties with minimal reference to theoretical models, through
association with the primary stars. We have searched for benchmark ultra-cool
dwarfs in widely separated binary systems using SDSS, UKIDSS, and 2MASS. We
then estimate spectral types using SDSS spectroscopy and multi-band colors,
place constraints on distance, and perform proper motions calculations for all
candidates which have sufficient epoch baseline coverage. Analysis of the
proper motion and distance constraints show that eight of our ultra-cool dwarfs
are members of widely separated binary systems. Another L3.5 dwarf, SDSS 0832,
is shown to be a companion to the bright K3 giant Eta Cancri. Such primaries
can provide age and metallicity constraints for any companion objects, yielding
excellent benchmark objects. This is the first wide ultra-cool dwarf + giant
binary system identified.Comment: 4 pages, 3 figures, conference, "New Technologies for Probing the
Diversity of Brown Dwarfs and Exoplanets", oral tal
Time-Scale and Noise Optimality in Self-Organized Critical Adaptive Networks
Recent studies have shown that adaptive networks driven by simple local rules
can organize into "critical" global steady states, providing another framework
for self-organized criticality (SOC). We focus on the important convergence to
criticality and show that noise and time-scale optimality are reached at finite
values. This is in sharp contrast to the previously believed optimal zero noise
and infinite time scale separation case. Furthermore, we discover a noise
induced phase transition for the breakdown of SOC. We also investigate each of
the three new effects separately by developing models. These models reveal
three generically low-dimensional dynamical behaviors: time-scale resonance
(TR), a new simplified version of stochastic resonance - which we call steady
state stochastic resonance (SSR) - as well as noise-induced phase transitions.Comment: 4 pages, 6 figures; several changes in exposition and focus on
applications in revised versio
Biodetection grinder
Work on a biodetection grinder is summarized. It includes development of the prototype grinder, second generation grinder, and the production version of the grinder. Tests showed the particle size distribution was satisfactory and biological evaluation confirmed the tests
Irrigation market for solar thermal parabolic dish systems
The potential size of the onfarm-pumped irrigation market for solar thermal parabolic dish systems in seven high-insolation states is estimated. The study is restricted to the displacement of three specific fuels: gasoline, diesel and natural gas. The model was developed to estimate the optimal number of parabolic dish modules per farm based on the minimum cost mix of conventional and solar thermal energy required to meet irrigation needs. The study concludes that the potential market size for onfarm-pumped irrigation applications ranges from 101,000 modules when a 14 percent real discount rate is assumed to 220,000 modules when the real discount rate drops to 8 percent. Arizona, Kansas, Nebraska, New Mexico and Texas account for 98 percent of the total demand for this application, with the natural gas replacement market accounting for the largest segment (71 percent) of the total market
Two techniques for digital filter design
Digital controllers, one using a special-purpose computer and the other using a combination of digital and analog techniques, are designed around /1/ computers that simulate the transfer function and interface with the system, and /2/ analog and digital circuits, converters, amplifiers, constant multipliers, and delay lines that form a digital filter
Results and conjectures on simultaneous core partitions
An n-core partition is an integer partition whose Young diagram contains no
hook lengths equal to n. We consider partitions that are simultaneously a-core
and b-core for two relatively prime integers a and b. These are related to
abacus diagrams and the combinatorics of the affine symmetric group (type A).
We observe that self-conjugate simultaneous core partitions correspond to the
combinatorics of type C, and use abacus diagrams to unite the discussion of
these two sets of objects.
In particular, we prove that (2n)- and (2mn+1)-core partitions correspond
naturally to dominant alcoves in the m-Shi arrangement of type C_n,
generalizing a result of Fishel--Vazirani for type A. We also introduce a major
statistic on simultaneous n- and (n+1)-core partitions and on self-conjugate
simultaneous (2n)- and (2n+1)-core partitions that yield q-analogues of the
Coxeter-Catalan numbers of type A and type C.
We present related conjectures and open questions on the average size of a
simultaneous core partition, q-analogs of generalized Catalan numbers, and
generalizations to other Coxeter groups. We also discuss connections with the
cyclic sieving phenomenon and q,t-Catalan numbers.Comment: 17 pages; to appear in the European Journal of Combinatoric
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