322,673 research outputs found
Calderon-Type Uniqueness Theorem for Stochastic Partial Differential Equations
In this Note, we present a Calder\'on-type uniqueness theorem on the Cauchy
problem of stochastic partial differential equations. To this aim, we introduce
the concept of stochastic pseudo-differential operators, and establish their
boundedness and other fundamental properties. The proof of our uniqueness
theorem is based on a new Carleman-type estimate.Comment:
Extended phase space thermodynamics for third order Lovelock black holes in diverse dimensions
Treating the cosmological constant as thermodynamic pressure and its
conjugate as thermodynamic volume, we investigate the critical behavior of the
third order Lovelock black holes in diverse dimensions. For black hole horizons
with different normalized sectional curvature , the corresponding
critical behaviors differ drastically. For , there is no critical point in
the extended thermodynamic phase space. For , there is a single critical
point in any dimension , and for , there is a single critical
point in dimension and two critical points in dimensions. We
studied the corresponding phase structures in all possible cases.Comment: pdflatex, 22 pages, 36 eps figures included. V2: minor corrections
and new reference
Coupling tunable D-band directional coupler for millimeter-wave applications
A coupling tunable D-band directional coupler is designed based on a novel
coupling grid structure proposed in this letter. The designed directional
coupler has excellent performance with ultra-wideband. The coupling can be
tuned from -28.2 dB to -33.2 dB at 140 GHz by changing the angle of the
coupling grid, and the dynamic range of the coupling is about 5 dB. The return
loss is smaller than -15 dB in the whole D-band from 110 GHz to 170 GHz. A 3-dB
coupler use the similar coupling structure is also designed. The coupling is
3.3144 dB at the center frequency of 140 GHz.Comment: 2 pages, 6figure
Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality
The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is
extended, taking the inverse of the GB coupling constant as a new thermodynamic
pressure . We studied the critical behavior associated with
in the extended thermodynamic phase space at fixed
cosmological constant and electric charge. The result shows that when the black
holes are neutral, the associated critical points can only exist in five
dimensional GB-AdS black holes with spherical topology, and the corresponding
critical exponents are identical to those for Van der Waals system. For charged
GB-AdS black holes, it is shown that there can be only one critical point in
five dimensions (for black holes with either spherical or hyperbolic
topologies), which also requires the electric charge to be bounded within some
appropriate range; while in dimensions, there can be up to two different
critical points at the same electric charge, and the phase transition can occur
only at temperatures which are not in between the two critical values.Comment: 23 pages. V2: modified all P_{GB}-r_+ plots using dimensionless
variables, added comments on the relationship to Einstein limi
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