7,591 research outputs found
Cylindrical Algebraic Sub-Decompositions
Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic
geometry, used primarily for eliminating quantifiers over the reals and
studying semi-algebraic sets. In this paper we introduce cylindrical algebraic
sub-decompositions (sub-CADs), which are subsets of CADs containing all the
information needed to specify a solution for a given problem.
We define two new types of sub-CAD: variety sub-CADs which are those cells in
a CAD lying on a designated variety; and layered sub-CADs which have only those
cells of dimension higher than a specified value. We present algorithms to
produce these and describe how the two approaches may be combined with each
other and the recent theory of truth-table invariant CAD.
We give a complexity analysis showing that these techniques can offer
substantial theoretical savings, which is supported by experimentation using an
implementation in Maple.Comment: 26 page
Diversity in Parametric Families of Number Fields
Let X be a projective curve defined over Q and t a non-constant Q-rational
function on X of degree at least 2. For every integer n pick a point P_n on X
such that t(P_n)=n. A result of Dvornicich and Zannier implies that, for large
N, among the number fields Q(P_1),...,Q(P_N) there are at least cN/\log N
distinct, where c>0. We prove that there are at least N/(\log N)^{1-c} distinct
fields, where c>0.Comment: Minor inaccuracies detected by the referees are correcte
Advanced water iodinating system
Potable water stores aboard manned spacecraft must remain sterile. Suitable sterilization techniques are needed to prevent microbial growth. The development of an advanced water iodinating system for possible application to the shuttle orbiter and other advanced spacecraft, is considered. The AWIS provides a means of automatically dispensing iodine and controlling iodination levels in potable water stores. In a recirculation mode test, simulating application of the AWIS to a water management system of a long term six man capacity space mission, noniodinated feed water flowing at 32.2 cu cm min was iodinated to 5 + or - ppm concentrations after it was mixed with previously iodinated water recirculating through a potable water storage tank. Also, the AWIS was used to successfully demonstrate its capability to maintain potable water at a desired I2 concentration level while circulating through the water storage tank, but without the addition of noniodinated water
Open circular billiards and the Riemann hypothesis
A comparison of escape rates from one and from two holes in an experimental
container (e.g. a laser trap) can be used to obtain information about the
dynamics inside the container. If this dynamics is simple enough one can hope
to obtain exact formulas. Here we obtain exact formulas for escape from a
circular billiard with one and with two holes. The corresponding quantities are
expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate
a direct connection between recent experiments and a major unsolved problem in
mathematics, the Riemann hypothesis.Comment: 5 pages, 4 embedded postscript figures; v2: more explicit on how the
Reimann Hypothesis arises from a comparison of one and two hole escape rate
Composite fermion model for entanglement spectrum of fractional quantum Hall states
We show that the entanglement spectrum associated with a certain class of
strongly correlated many-body states --- the wave functions proposed by
Laughlin and Jain to describe the fractional quantum Hall effect --- can be
very well described in terms of a simple model of non-interacting (or weakly
interacting) composite fermions.Comment: 6 pages, 2 figure
Evaluation and characterization of the methane-carbon dioxide decomposition reaction
A program was conducted to evaluate and characterize the carbon dioxide-methane (CO2-CH4) decomposition reaction, i.e., CO2 + CH4 = 2C + 2H2O. The primary objective was to determine the feasibility of applying this reaction at low temperatures as a technique for recovering the oxygen (O2) remaining in the CO2 which exits mixed with CH4 from a Sabatier CO2 reduction subsystem (as part of an air revitalization system of a manned spacecraft). A test unit was designed, fabricated, and assembled for characterizing the performance of various catalysts for the reaction and ultraviolet activation of the CH4 and CO2. The reactor included in the test unit was designed to have sufficient capacity to evaluate catalyst charges of up to 76 g (0.17 lb). The test stand contained the necessary instrumentation and controls to obtain the data required to characterize the performance of the catalysts and sensitizers tested: flow control and measurement, temperature control and measurement, product and inlet gas analysis, and pressure measurement. A product assurance program was performed implementing the concepts of quality control and safety into the program effort
A nullstellensatz for sequences over F_p
Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in
F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1
x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually
characterizes A up to a nonzero multiplicative constant, which is no longer
true for l < p. The critical case l=p is of particular interest. In this
context, we prove that whenever l=p and A is nonconstant, the above equation
has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The
subcritical case l=p-1 is studied in detail also. Our approach is algebraic in
nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper
type theorem.Comment: 23 page
Non‐Homogeneous Cubic Equations
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135443/1/jlms0657.pd
Spinful Composite Fermions in a Negative Effective Field
In this paper we study fractional quantum Hall composite fermion
wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these
filling fractions, there are several possible wavefunctions with different spin
polarizations, depending on how many spin-up or spin-down composite fermion
Landau levels are occupied. We calculate the energy of the possible composite
fermion wavefunctions and we predict transitions between ground states of
different spin polarizations as the ratio of Zeeman energy to Coulomb energy is
varied. Previously, several experiments have observed such transitions between
states of differing spin polarization and we make direct comparison of our
predictions to these experiments. For more detailed comparison between theory
and experiment, we also include finite-thickness effects in our calculations.
We find reasonable qualitative agreement between the experiments and composite
fermion theory. Finally, we consider composite fermion states at filling
factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be
spin polarized even at zero Zeeman energy.Comment: 17 pages, 5 figures, 4 tables. (revision: incorporated referee
suggestions, note added, updated references
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