7,947 research outputs found
Dynamics and the Godbillon-Vey Class of C^1 Foliations
Let F be a codimension-one, C^2-foliation on a manifold M without boundary.
In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is
non-zero, then F has a hyperbolic resilient leaf. Our approach is based on
methods of C^1-dynamical systems, and does not use the classification theory of
C^2-foliations. We first prove that for a codimension--one C^1-foliation with
non-trivial Godbillon measure, the set of infinitesimally expanding points E(F)
has positive Lebesgue measure. We then prove that if E(F) has positive measure
for a C^1-foliation F, then F must have a hyperbolic resilient leaf, and hence
its geometric entropy must be positive. The proof of this uses a pseudogroup
version of the Pliss Lemma. The theorem then follows, as a C^2-foliation with
non-zero Godbillon-Vey class has non-trivial Godbillon measure. These results
apply for both the case when M is compact, and when M is an open manifold.Comment: This manuscript is a revision of the section 3 material from the
previous version, and includes edits to the pictures in the tex
On a conjecture of Helleseth
We are concern about a conjecture proposed in the middle of the seventies by
Hellesseth in the framework of maximal sequences and theirs cross-correlations.
The conjecture claims the existence of a zero outphase Fourier coefficient. We
give some divisibility properties in this direction
Assessing the time-sensitive impacts of energy efficiency and flexibility in the US building sector
The building sector consumes 75% of US electricity, offering substantial energy, cost, and CO2 emissions savings potential. New technologies enable buildings to flexibly manage electric loads across different times of day and season in support of a low-cost, low-carbon electric grid. Assessing the value of such technologies requires an understanding of building electric load variability at a higher temporal resolution than is demonstrated in previous studies of US building efficiency potential. We adapt Scout, an open-access model of US building energy use, to characterize sub-annual variations in baseline building electricity use, costs, and emissions at the national scale. We apply this baseline in time-sensitive analyses of the energy, cost, and CO2 emissions savings potential of various degrees of energy efficiency and flexibility, finding that efficiency continues to have strong value in a time-sensitive assessment framework while the value of flexibility depends on assumed electricity rates, measure magnitude and duration, and the amount of savings already captured by efficiency
Proof of a Conjectured Three-Valued Family of Weil Sums of Binomials
We consider Weil sums of binomials of the form , where is a finite field, is
the canonical additive character, , and .
If we fix and and examine the values of as runs
through , we always obtain at least three distinct values unless
is degenerate (a power of the characteristic of modulo ).
Choices of and for which we obtain only three values are quite rare and
desirable in a wide variety of applications. We show that if is a field of
order with odd, and with , then
assumes only the three values and . This
proves the 2001 conjecture of Dobbertin, Helleseth, Kumar, and Martinsen. The
proof employs diverse methods involving trilinear forms, counting points on
curves via multiplicative character sums, divisibility properties of Gauss
sums, and graph theory.Comment: 19 page
Dynamic Surface Tension of Aqueous Solutions of Ionic Surfactants: Role of Electrostatics
The adsorption kinetics of the cationic surfactant dodecyltrimethylammonium
bromide at the air-water interface has been studied by the maximum bubble
pressure method at concentrations below the critical micellar concentration. At
short times, the adsorption is diffusion-limited. At longer times, the surface
tension shows an intermediate plateau and can no longer be accounted for by a
diffusion limited process. Instead, adsorption appears kinetically controlled
and slowed down by an adsorption barrier. A Poisson-Boltzmann theory for the
electrostatic repulsion from the surface does not fully account for the
observed potential barrier. The possibility of a surface phase transition is
expected from the fitted isotherms but has not been observed by Brewster angle
microscopy.Comment: 13 pages, 5 figure
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