204,032 research outputs found
The Cauchy Operator for Basic Hypergeometric Series
We introduce the Cauchy augmentation operator for basic hypergeometric
series. Heine's transformation formula and Sears'
transformation formula can be easily obtained by the symmetric property of some
parameters in operator identities. The Cauchy operator involves two parameters,
and it can be considered as a generalization of the operator . Using
this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy
integral, Sears' two-term summation formula, as well as the -analogues of
Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for
the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big
-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic
Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory
We consider a simple, physical approach to the problem of marginally trapped
surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach
to a particular spherically symmetric, Wyman sector gravitational field,
consisting of a pulse in the antisymmetric field variable. We demonstrate that
marginally trapped surfaces do exist for this choice of initial data.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 3 pages, 1 figur
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Laser-assisted photothermal imprinting of nanocomposite
We report on a laser-assisted photothermal imprinting method for directly patterning carbon
nanofiber-reinforced polyethylene nanocomposite. A single laser pulse from a solid state
Nd:YAG laser (10 ns pulse, 532 nm and 355 nm wavelengths) is used to melt/soften a thin skin
layer of the polymer nanocomposite. Meanwhile, a fused quartz mold with micro-sized surface
relief structures is pressed against the surface of the composite. Successful pattern transfer is
realized upon releasing the quartz mold. Although polyethylene is transparent to the laser beam,
the carbon nanofibers in the high density polyethylene (HDPE) matrix absorb the laser energy
and convert it into heat. Numerical heat conduction simulation shows the HDPE matrix is
partially melted or softened, allowing for easier imprinting of the relief pattern of the quartz
mold.Mechanical Engineerin
Classification of spacelike surfaces in spacetime
A classification of 2-dimensional surfaces imbedded in spacetime is
presented, according to the algebraic properties of their shape tensor. The
classification has five levels, and provides among other things a refinement of
the concepts of trapped, umbilical and extremal surfaces, which split into
several different classes. The classification raises new important questions
and opens many possible new lines of research. These, together with some
applications and examples, are briefly considered.Comment: 42 pages, 10 tables, many diagram
The short-time critical behaviour of the Ginzburg-Landau model with long-range interaction
The renormalisation group approach is applied to the study of the short-time
critical behaviour of the -dimensional Ginzburg-Landau model with long-range
interaction of the form in momentum space. Firstly the
system is quenched from a high temperature to the critical temperature and then
relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws
and the initial slip exponents and of the order
parameter and the response function respectively, are calculated to the second
order in .Comment: 18 pages, 4 figures, 1 tabl
Anomalous microwave response of high-temperature superconducting thin-film microstrip resonator in weak dc magnetic fields
We have studied an anomalous microwave (mw) response of superconducting
YBa_{2}Cu_{3}O_{7-delta} (YBCO) microstrip resonators in the presence of a weak
dc magnetic field, H_{dc}. The surface resistance (R_{s}) and reactance (X_{s})
show a correlated non-monotonic behaviour as a function of H_{dc}. R_{s} and
X_{s} were found to initially decrease with elevated H_{dc} and then increase
after H_{dc} reaches a crossover field, H_{c}, which is independent of the
amplitude and frequency of the input mw signal within the measurements. The
frequency dependence of R_{s} is almost linear at fixed H_{dc} with different
magnitudes (H_{c}). The impedance plane analysis
demonstrates that r_{H}, which is defined as the ratio of the change in
R_{s}(H_{dc}) and that in X_{s}(H_{dc}), is about 0.6 at H_{dc}<H_{c} and 0.1
at H_{dc}>H_{c}. The H_{dc} dependence of the surface impedance is
qualitatively independent of the orientation of H_{dc}.Comment: REVTex 3.1, 5 pages, 6 EPS figures, submitted to Physica
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