2,600 research outputs found
AK-cut crystal resonators
Calculations have predicted the existence of crystallographically doubly rotated quartz orientations with turnover temperatures which are considerably less sensitive to angular misorientation then comparable AT- or BT-cuts. These crystals are arbitrarily designated as the AK-cut. Experimental data is given for seven orientations, phi-angle variations between 30-46 deg and theta-angle variations between 21-28 deg measured on 3.3-3.4 MHz fundamental mode resonators vibrating in the thickness shear c-mode. The experimental turnover temperatures of these resonators are between 80 C and 150 C, in general agreement with calculated values. The normalized frequency change as a function of temperature has been fitted with a cubic equation
A Nonliearly Dispersive Fifth Order Integrable Equation and its Hierarchy
In this paper, we study the properties of a nonlinearly dispersive integrable
system of fifth order and its associated hierarchy. We describe a Lax
representation for such a system which leads to two infinite series of
conserved charges and two hierarchies of equations that share the same
conserved charges. We construct two compatible Hamiltonian structures as well
as their Casimir functionals. One of the structures has a single Casimir
functional while the other has two. This allows us to extend the flows into
negative order and clarifies the meaning of two different hierarchies of
positive flows. We study the behavior of these systems under a hodograph
transformation and show that they are related to the Kaup-Kupershmidt and the
Sawada-Kotera equations under appropriate Miura transformations. We also
discuss briefly some properties associated with the generalization of second,
third and fourth order Lax operators.Comment: 11 pages, LaTex, version to be published in Journal of Nonlinear
Mathematical Physics, has expanded discussio
A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres
Pizzas, pizzen, pizze: frequency, iconicity, cue validity, and productivity in the plural acquisition of German preschoolers
Some factors which influence the choice of plural markers in German are discussed: frequency of nouns and plural allomorphs, iconicity, cue validity, productivity, and gender specific distribution of plural allomorphs. The evidence comes from studies on a language screening conducted in the state of Hesse in Germany in 2007-2010 with three-, four-, and five-year-old monolingual and multilingual children.Some factors which influence the choice of plural markers in German are discussed: frequency of nouns and plural allomorphs, iconicity, cue validity, productivity, and gender specific distribution of plural allomorphs. The evidence comes from studies on a language screening conducted in the state of Hesse in Germany in 2007-2010 with three-, four-, and five-year-old monolingual and multilingual children
Euler configurations and quasi-polynomial systems
In the Newtonian 3-body problem, for any choice of the three masses, there
are exactly three Euler configurations (also known as the three Euler points).
In Helmholtz' problem of 3 point vortices in the plane, there are at most three
collinear relative equilibria. The "at most three" part is common to both
statements, but the respective arguments for it are usually so different that
one could think of a casual coincidence. By proving a statement on a
quasi-polynomial system, we show that the "at most three" holds in a general
context which includes both cases. We indicate some hard conjectures about the
configurations of relative equilibrium and suggest they could be attacked
within the quasi-polynomial framework.Comment: 21 pages, 6 figure
Reconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants
We apply the technique of self-similar exponential approximants based on
successive truncations of continued exponentials to reconstruct functional laws
of the quasi-exponential class from the knowledge of only a few terms of their
power series. Comparison with the standard Pad\'e approximants shows that, in
general, the self-similar exponential approximants provide significantly better
reconstructions.Comment: Revtex file, 21 pages, 21 figure
Viking navigation
A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented
Grandparental Child Care in Europe : Evidence for Preferential Investment in More Certain Kin
Peer reviewe
Radiative Corrections to the Casimir Energy
The lowest radiative correction to the Casimir energy density between two
parallel plates is calculated using effective field theory. Since the
correlators of the electromagnetic field diverge near the plates, the
regularized energy density is also divergent. However, the regularized integral
of the energy density is finite and varies with the plate separation L as
1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but
more transparent theory of a massless scalar field in 1+1 dimensions confined
to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late
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