Let a ! 0 and T ! 0 first, and then let k ! 1 to obtain lim sup a!0 lim sup

Members of the LIM homeodomain family of transcription factors have been implicated in specifying cell identity in a range of species. In Drosophila three LIM homeobox genes, apterous, lim3 and isl, have been shown to control axon pathfinding of subsets of neurons within the embryo. Here we describe the isolation and characterization of another LIM homeobox gene in Drosophila termed dlim1, a ho...

Nuclear LIM domains interact with a family of coregulators referred to as Clim/Ldb/Nli. Although one family member, Clim-2/Ldb-1/Nli, is highly expressed in epidermal keratinocytes, no nuclear LIM domain factor is known to be expressed in epidermis. Therefore, we used the conserved LIM-interaction domain of Clim coregulators to screen for LIM domain factors in adult and embryonic mouse skin exp...

The LIM-homeodomain (LIM-HD) family of transcription factors is well known for its functions during several developmental processes including cell fate specification, cell migration and axon guidance, and its members play fundamental roles in hippocampal development. The hippocampus is a structure that displays striking activity dependent plasticity. We examined whether LIM-HD genes and their c...

The LIM-homeodomain (LIM-HD) family of transcription factors is well known for its functions during several developmental processes including cell fate specification, cell migration and axon guidance, and its members play fundamental roles in hippocampal development. The hippocampus is a structure that displays striking activity dependent plasticity. We examined whether LIM-HD genes and their c...

The high temperature and high pressure supersonic jet is one of the key problems in the design of solid rocket motors. To reduce the jet temperature and noise, cooling water is typically injected into the exhaust plume. Numerical simulations for the gas-liquid multiphase flow field with mixture multiphase model were developed and a series of experiments were carried out. By introducing the ener...

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equa...

Applying the voltage-mode hysteretic control to multiphase Voltage Regulator Modules (VRMs) can satisfy many of the new and future generation of microprocessors and ICs powering requirements. This is because of the numerous advantages that can be obtained when both techniques are used. However, several challenges arise that include current sharing, multiphase control signals distribution, high-...

We used ultrafast x radiography and developed a novel multiphase numerical simulation to reveal the origin and the unique dynamics of the liquid-jet-generated shock waves and their interactions with the jets. Liquid-jet-generated shock waves are transiently correlated to the structural evolution of the disintegrating jets. The multiphase simulation revealed that the aerodynamic interaction betw...

This important result is listed in the theorem on the next page. Note that the derivative of the vector-valued function is itself a vector-valued function. You can see from Figure 12.8 that is a vector tangent to the curve given by and pointing in the direction of increasing values. tr t r t r f t i g t j lim t→0 f t t f t t i lim t→0 g t t g t t j lim t→0 f t t f t t i g t t g t t j lim t→0 f ...