Bishop provides excellent guide

A Bishop surface with a vanishing Bishop invariant

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant s < ∞ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real...

The Mergelyan-Bishop Theorem

We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

New Government Accountability Office Report on Regenerative Medicine Provides an Excellent Assessment of the Field

The Aspergillus nidulans bimC4 mutation provides an excellent tool for identification of kinesin-14 inhibitors.

Centrosome amplification is a hallmark of many types of cancer cells, and clustering of multiple centrosomes is critical for cancer cell survival and proliferation. Human kinesin-14 HSET/KFIC1 is essential for centrosome clustering, and its inhibition leads to the specific killing of cancer cells with extra centrosomes. Since kinesin-14 motor domains are conserved evolutionarily, we conceived a...

Coating Thickness Measurement with SIDSP®- Technology Digital technology provides excellent Interference Immunity

Intelligent sensors with integrated digital signal processing are becoming the trend in an increasing number of applications. There are considerable valuable advantages do to the interference immunity resulting in higher repeatability, durability and reliability. And because this technology does not involve higher manufacturing costs, it’s merely a matter of time before “digital” will also domi...