Certificateless cryptography eliminates the need of certificates in the Public Key Infrastructure and solves the inherent key escrow problem in the identity-based cryptography. Recently, Huang et al. proposed two certificateless signature schemes from pairings. They claimed that their first short certificateless signature scheme is provably secure against a normal type I adversary and a super type II adversary. In this paper, we show that their short certificateless signature scheme is broken by a type I adversary who can replace users’ public keys and access to the signing oracle under the replaced public keys.

In this note we give a new proof of Witt's formula for Euler numbers, which are related to some known or new identities involving the Euler numbers. We also obtain a brief proof of a classical result on Euler numbers modulo of two due to M.A. Stern using the approach of p-adic integration, which was recently proved by G. Liu, and Z.-W. Sun. Finally some explicit formulas for Genocchi numbers are proved and applications are given.

For an infinite family of modular forms constructed from Klein forms we provide certain explicit formulas for their Fourier coefficients by using the theory of basic hypergeometric series (Theorem 2). By making use of these modular forms we investigate the bases of the vector spaces of modular forms of some levels (Theorem 5) and find its application.

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.