Nonmechanical image rotation with an acousto-optic dove prism

We report what we believe to be the first method for nonmechanical and programmable image rotation. The method uses a pair of crossed acousto-optic beam deflectors and a polygon mirror to emulate the mechanical dove prism. It is capable of fast (of the order of microseconds) image rotation to an arbitrary angle in a programmable manner. An experimental result that proves the concept is provided.     

Pressure representation and boundary regularity of the Navier-Stokes equations with slip boundary condition

We first represent the pressure in terms of the velocity in . Using this representation we prove that a solution to the Navier-Stokes equations is in under the critical assumption that , with r?3, while for r=3 the smallness is required. In [H.J. Choe, Boundary regularity of weak solutions of the Navier-Stokes equations, J. Differential Equations 149 (2) (1998) 211-247], a boundary L^∞ estimate for the solution is derived if the pressure on the boundary is bounded. In our work, we remove the boundedness assumption of the pressure. Here, our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate for L^∞-norm of u.     

Reaction and stabilizing mechanism of the cross-type macromonomers in the dispersion polymerization of styrene

The cross-type (C-VUM) and linear-type (L-VUM) bifunctional vinyl urethane macromonomers and polystyrene (PS) using these macromonomers were synthesized in the dispersion polymerization in ethanol, and the reaction and stabilizing mechanism of the macromonomers was proposed. The structural verification of the macromonomers and PS was studied using (1)H NMR. The weight-average particle size of C-PS (PS prepared with C-VUM) and L-PS (PS prepared with L-VUM) decreased from 4.41 to 1.36 microm and from 3.56 to 1.52 microm, whereas the average-molecular weight of those increased from 34,100 to 100,500 g/mol and from 32,200 to 71,800 g/mol, respectively. The XPS result showed that the C-PS was anchored with a larger amount of PEG than that of the L-PS on the particle surface. Thus, the reaction and stabilizing mechanism of the macromonomers for the formation of PS particles is proposed as the following. The particle surface of the C-PS is surrounded by a large amount of tail shaped macromonomers leading to higher molecular weights and smaller particle sizes. On the other hand, the particle surface of the L-PS is comprised of relatively small amounts of loop shaped macromonomers inducing lower molecular weights and larger particles of L-PS than C-PS.     

Dictyostelium cells bind a secreted autocrine factor that represses cell proliferation

Background  

Dictyostelium cells secrete the proteins AprA and CfaD. Cells lacking either AprA or CfaD proliferate faster than wild type, while AprA or CfaD overexpressor cells proliferate slowly, indicating that AprA and CfaD are autocrine factors that repress proliferation. CfaD interacts with AprA and requires the presence of AprA to slow proliferation. To determine if CfaD is necessary for the ability of AprA to slow proliferation, whether AprA binds to cells, and if so whether the binding requires the presence of CfaD, we examined the binding and effect on proliferation of recombinant AprA.     

Multiple Existence Results for the Self-Dual Chern–Simons–Higgs Vortex Equation

We study the asymptotic behavior for the condensate solutions of the self-dual Chern–Simons–Higgs equation as the Chern–Simons parameter tends to zero. By using these estimates, we establish existence results for solutions of non-topological type.