Uncovering subtypes of microarray

We derive the time evolution of the two-mode amplitude probability density function. Using this
equation, we derive conditions for the existence of a zero flux steady-state solution. We also derive the
equation for a vortex solution and show that the product of two one-mode steady-state solutions can be a
two-mode steady-state solution only when an extra condition is satisfied. With this extra condition
assumed, we plot the flux of probability vector on two mode’s plane. It is shown that this flux lines
circulate around the center (n_a, n_b), which are the mean values of the two mode’s amplitude square.

We provide an observation suggesting a strong correlation between helicity and enstrophy in fluid turbulence.
Helicity statistics were obtained in a direct numerical simulation of forced isotropic turbulence. An
investigation of coherent structures revealed that intermittently large local helicity was found in the core region
of the coherent rotational structures, thus showing a strong correlation with local enstrophy, not dissipation.
Statistics regarding the relative helicity and the correlation between velocity and vorticity conditioned on
different levels of enstrophy clearly suggest that velocity and vorticity tend to be aligned in the core of the
coherent structures.？

In this paper we give a non-existence theorem for Hopf hypersurfaces in complex two-plane Grassmannians
satisfying the condition that the structure Jacobi operator commutes with the 3-structure tensors.

The absorption cross section is studied in the low-frequency region for a propagating
scalar field under the warped AdS3 black hole background in the cosmological
topologically massive gravity. It can be shown that the absorption cross section is unexpectedly
deformed by the gravitational Chern-Simons term, which is proportional to the
scattering area of black hole with an additional contribution depending on the combinations
of left-moving and right-moving temperatures. It means that the cross section is larger than
the area in spite of the s-wave limit. Finally, we discuss the left-right quasinormal modes
for the scalar perturbation in this black hole.

Partial Differential Equation(PDE) based methods in image processing
have been actively studied in the past few years. One of the
effective methods is the method based on a total variation
introduced by Rudin, Oshera and Fatemi (ROF) \cite{ROF}. This method
is a well known edge preserving model and an useful tool for image
removals and decompositions..........？

Main Purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to
elliptic analogue of the Hardy sums, are given

We study the gravitational collapse problem of rotating shells in three-dimensional Einstein gravity
with and without a cosmological constant. Taking the exterior and interior metrics to be those of
stationary metrics with asymptotically constant curvature, we solve the equations of motion for the
shells from the Darmois-Israel junction conditions in the co-rotating frame. We study various
collapse scenarios with arbitrary angular momentum for a variety of geometric configurations,
including anti-de Sitter, de Sitter, and flat spaces. We find that the collapsing shells can form
a BTZ black hole, a three-dimensional Kerr-dS spacetime, and an horizonless geometry of
point masses under certain initial conditions. For pressureless dust shells, the curvature
singularity is not formed due to the angular momentum barrier near the origin. However
when the shell pressure is nonvanishing, we find that for all types of shells with polytropic-type
equations of state (including the perfect fluid and the generalized Chaplygin gas), collapse to
a naked singularity is possible under generic initial conditions. We conclude that in three
dimensions angular momentum does not in general guard against violation of cosmic censorship.

The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schrödinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δ_{c, q}. Our development is employed for two special cases, namely, the Caldirola–Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.

A new method based on the Clenshaw-Curtis quadrature for the numerical solution of the integro-differential Schrodinger equation is investigated. The method shows that it converges quickly and the truncation errors decrease faster than any power of the inverse number of the Chebyshev support points. Discretization technique is presented in detail. Accompanying C^+^+ code for the Fredholm type method is available upon request.