60,865 research outputs found
A Two-Stage Penalized Least Squares Method for Constructing Large Systems of Structural Equations
We propose a two-stage penalized least squares method to build large systems
of structural equations based on the instrumental variables view of the
classical two-stage least squares method. We show that, with large numbers of
endogenous and exogenous variables, the system can be constructed via
consistent estimation of a set of conditional expectations at the first stage,
and consistent selection of regulatory effects at the second stage. While the
consistent estimation at the first stage can be obtained via the ridge
regression, the adaptive lasso is employed at the second stage to achieve the
consistent selection. The resultant estimates of regulatory effects enjoy the
oracle properties. This method is computationally fast and allows for parallel
implementation. We demonstrate its effectiveness via simulation studies and
real data analysis
Eigenfunctions for quasi-laplacian
To study the regularity of heat flow, Lin-Wang[1] introduced the
quasi-harmonic sphere, which is a harmonic map from
to with finite energy.
Here is Euclidean metric in . Ding-Zhao [2] showed that
if the target is a sphere, any equivariant quasi-harmonic spheres is
discontinuous at infinity. The metric is
quite singular at infinity and it is not complete. In this paper , we mainly
study the eigenfunction of Quasi-Laplacian for . In particular, we show that non-constant
eigenfunctions of must be discontinuous at infinity and non-constant
eigenfunctions of drifted Laplacian is also discontinuous at infinity
Constructing Nonabelian (1,0) Hypermultiplet Theories in Six Dimensions
We construct a class of nonabelian superconformal (1,0) hypermultiplet
theories in six dimensions by introducing an abelian auxiliary field. The gauge
fields of this class of theories are non-dynamical, and this class of theories
can be viewed as Chern-Simons-matter theories in 6D.Comment: 5 pages, minor changes, reference adde
Steady-state bifurcation analysis of a strong nonlinear atmospheric vorticity equation
The quasi-geostrophic equation or the Euler equation with dissipation studied
in the present paper is a simplified form of the atmospheric circulation model
introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205-1216] on the
existence of multiple steady states to the understanding of the persistence of
atmospheric blocking. The fluid motion defined by the equation is driven by a
zonal thermal forcing and an Ekman friction forcing measured by . It
is proved that the steady-state solution is unique for while
multiple steady-state solutions exist for with respect
to critical value .
Without involvement of viscosity, the equation has strong nonlinearity as its
nonlinear part contains the highest order derivative term. Steady-state
bifurcation analysis is essentially based on the compactness, which can be
simply obtained for semi-linear equations such as the Navier-Stokes equations
but is not available for the quasi-geostrophic equation in the Euler
formulation. Therefore the Lagrangian formulation of the equation is employed
to gain the required compactness.Comment: 20 pages, 0 figures, 30 reference
Ill-posedness of waterline integral of time domain free surface Green function for surface piercing body advancing at dynamic speed
In the linear time domain computation of a floating body advancing at a
dynamic speed, the source formulation for the velocity potential of the
hydrodynamic problem is commonly used so that the velocity potential is
expressed as the integral of time domain free surface sources distributed on
the two-dimensional wetted body surface and the one-dimensional waterline,
which is the intersection of the wetted body surface and the mean free water
surface. A time domain free surface source is corresponding to the time domain
free surface Green function associated with a suitable source strength, which
is to be solved from body boundary condition and normal velocity boundary
integral equation of the source formulation.
The normal velocity boundary integral equation contains an integral of the
normal derivative of the time domain free surface Green function on the
waterline. It is shown that the waterline integral is ill-posed. Thus the
source strength of velocity potential is not obtainable
OSp(4|4) superconformal currents in three-dimensional N=4 Chern-Simons quiver gauge theories
We prove explicitly that the general D=3, N=4 Chern-Simons-matter (CSM)
theory has a complete OSp(4|4) superconformal symmetry, and construct the
corresponding conserved currents. We re-derive the OSp(5|4) superconformal
currents in the general N=5 theory as special cases of the OSp(4|4) currents by
enhancing the supersymmetry from N=4 to N=5. The closure of the full OSp(4|4)
superconformal algebra is verified explicitly.Comment: 23 pages, published in PR
OSp(5|4) Superconformal Symmetry of N=5 Chern-Simons Theory
We demonstrate that the general D=3, N=5 Chern-Simons matter theory possesses
a full OSp(5|4) superconformal symmetry, and construct the corresponding
superconformal currents. The closure of the superconformal algebra is verified
in detail. We also show that the conserved OSp(6|4) superconformal currents in
the general N=6 theory can be obtained as special cases of the OSp(5|4)
currents by enhancing the R-symmetry of the N=5 theory from USp(4) to SU(4).Comment: 24 pages, minor changes, version published in Nucl.Phys.
Symplectic Three-Algebra Unifying N=5,6 Superconformal Chern-Simons-Matter Theories
We define a 3-algebra with structure constants being symmetric in the first
two indices. We also introduce an invariant anti-symmetric tensor into this
3-algebra and call it a symplectic 3-algebra. The general N=5 superconformal
Chern-Simons-matter (CSM) theory with SO(5) R-symmetry in three dimensions is
constructed by using this algebraic structure. We demonstrate that the
supersymmetry can be enhanced to N=6 if the sympelctic 3-algebra and the fields
are decomposed in a proper fashion. By specifying the 3-brackets, some
presently known N=5, 6 superconformal theories are described in terms of this
unified 3-algebraic framework. These include the N=5, Sp(2N) X O(M) CSM theory
with SO(5) R-symmetry , the N=6, Sp(2N) X U(1) CSM theory with SU(4)
R-symmetry, as well as the ABJM theory as a special case of U(M) X U(N) theory
with SU(4) R-symmetry.Comment: 31 pages, minor changes, final results remain the sam
New formulation of the finite depth free surface Green function
For a pulsating free surface source in a three-dimensional finite depth fluid
domain, the Green function of the source presented by John [F. John, On the
motion of floating bodies II. Simple harmonic motions, Communs. Pure Appl.
Math. 3 (1950) 45-101] is superposed as the Rankine source potential, an image
source potential and a wave integral in the infinite domain . When
the source point together with a field point is on the free surface, John's
integral and its gradient are not convergent since the integration
of the corresponding integrands does not tend to zero in a
uniform manner as tends to . Thus evaluation of the Green
function is not based on direct integration of the wave integral but is
obtained by approximation expansions in earlier investigations. In the present
study, five images of the source with respect to the free surface mirror and
the water bed mirror in relation to the image method are employed to
reformulate the wave integral. Therefore the free surface Green function of the
source is decomposed into the Rankine potential, the five image source
potentials and a new wave integral, of which the integrand is approximated by a
smooth and rapidly decaying function. The gradient of the Green function is
further formulated so that the same integration stability with the wave
integral is demonstrated. The significance of the present research is that the
improved wave integration of the Green function and its gradient becomes
convergent. Therefore evaluation of the Green function is obtained through the
integration of the integrand in a straightforward manner. The application of
the scheme to a floating body or a submerged body motion in regular waves shows
that the approximation is sufficiently accurate to compute linear wave loads in
practice.Comment: 24 pages, 7 figure
Instability of the Kolmogorov flow in a wall-bounded domain
In the magnetohydrodynamics (MHD) experiment performed by Bondarenko and his
co-workers in 1979, the Kolmogorov flow loses stability and transits into a
secondary steady state flow at the Reynolds number . This problem is
modelled as a MHD flow bounded between lateral walls under slip wall boundary
condition. The existence of the secondary steady state flow is now proved. The
theoretical solution has a very good agreement with the flow measured in
laboratory experiment at . Further transition of the secondary flow
is observed numerically. Especially, well developed turbulence arises at
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