Maximal multihomogeneity of algebraic hypersurface singularities

From the degree zero part of the logarithmic vector fields along analgebraic hypersurface singularity we identify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism group. These results are motivated by Kyoji Saito’s characterization of quasihomogeneity for isolated hypersurface singularities [Saito in Invent. Math. 14, 123–142 (1971)] and extend previous work with Granger and Schulze [Compos. Math. 142(3), 765–778 (2006), Theorem 5.4] and of Hauser and Müller [Nagoya Math. J. 113, 181–186 (1989), Theorem 4].     

Spotting and quantification of phosphoproteins purified by gel electrophoresis and laser ablation-element mass spectrometry with phosphorus-31 detection.

Laser ablation inductively coupled plasma-mass spectrometry (ICP-MS) with (31)P detection has been used for spotting of phosphoproteins after one-dimensional polyacrylamide gel electrophoresis (1-D PAGE) and membrane transfer. By analyzing a mixture of myoglobin, alpha-casein and reduced fibrinogen it is demonstrated that phosphoproteins are specifically recognized by this method. A special washing step was found to be necessary to remove phosphate noncovalently bound to proteins. The (31)P signal was found to contain quantitative information both with respect to relative and absolute amounts of phosphorus present in phosphoproteins. Normalizing the (31)P signal from a single laser ablation trace by the total amount of phosphoprotein applied to the gel, a detection limit of 5 pmol of phosphorus is estimated.     

Convergence to equilibrium for the Cahn–Hilliard equation with a logarithmic free energy

In this paper we investigate the asymptotic behavior of the nonlinear Cahn–Hilliard equation with a logarithmic free energy and similar singular free energies. We prove an existence and uniqueness result with the help of monotone operator methods, which differs from the known proofs based on approximation by smooth potentials. Moreover, we apply the Lojasiewicz–Simon inequality to show that each solution converges to a steady state as time tends to infinity.     

A note on the schemes of replacement and collection

We derive the schemes of from certain weak forms of the same.     

(−)‐Englerin A is a Potent and Selective Activator of TRPC4 and TRPC5 Calcium Channels

Current therapies for common types of cancer such as renal cell cancer are often ineffective and unspecific, and novel pharmacological targets and approaches are in high demand. Here we show the unexpected possibility for the rapid and selective killing of renal cancer cells through activation of calcium‐permeable nonselective transient receptor potential canonical (TRPC) calcium channels by the sesquiterpene (?)‐englerin A. This compound was found to be a highly efficient, fast‐acting, potent, selective, and direct stimulator of TRPC4 and TRPC5 channels. TRPC4/5 activation through a high‐affinity extracellular (?)‐englerin A binding site may open up novel opportunities for drug discovery aimed at renal cancer.