Geometry of Critical Loci

Let :(Z,z)(U,0) be the germ of a finite (that is, proper with finite fibres)complex analytic morphism from a complex analytic normal surfaceonto an open neighbourhood U of the origin 0 in the complexplane C². Let u and v be coordinates of C² defined on U. Weshall call the triple (, u, v) the initial data. Let stand for the discriminant locus of the germ , that is,the image by of the critical locus of . Let ()_A be the branches of the discriminant locus at O whichare not the coordinate axes. For each A, we define a rational number d by where I(–, –) denotes the intersection number at0 of complex analytic curves in C². The set of rational numbersd, for A, is a finite subset D of the set of rational numbersQ. We shall call D the set of discriminantal ratios of the initialdata (, u, v). The interesting situation is when one of thetwo coordinates (u, v) is tangent to some branch of , otherwiseD = {1}. The definition of D depends not only on the choiceof the two coordinates, but also on their ordering. In this paper we prove that the set D is a topological invariantof the initial data (, u, v) (in a sense that we shall definebelow) and we give several ways to compute it. These resultsare first steps in the understanding of the geometry of thediscriminant locus. We shall also see the relation with thegeometry of the critical locus.     

Regularized Brownian Motion on the Siegel Disk of Infinite Dimension

We construct a process of Brownian motion on the Siegel disk of infinite dimension.     

Determination of Polychlorinated Biphenyls and Chlorinated Pesticides in Environmental Biological Samples Using Focused Microwave-assisted Extraction

Abstract

Organochlorine compounds such as polychlorinated biphenyls (PCBs) and chlorinated pesticides have been analysed in environmental biological samples using focused microwave-assisted extraction (FMW). The analytical procedure is presented and the results for two Standard Reference Materials, a cod liver oil and a freeze-dried mussel tissue, are reported. The average recoveries for the sum of the PCBs are between 93% and 106%, and for the sum of the chlorinated pesticides are between 109 to 115% for all the certified compounds analysed. The developped analytical procedure is highly reproducible with an average standard deviation of 8% for the sum of the PCBs and 9.7% for the sum of the chlorinated pesticides in the two matrices.     

Biginelli Reaction Synthesis of Novel Multitarget-Directed Ligands with Ca2+ Channel Blocking Ability,Cholinesterase Inhibition,Antioxidant Capacity,and Nrf2 Activation

Novel multitarget-directed ligands BIGI 4a-d and BIGI 5a-d were designed and synthesized with a simple and cost-efficient procedure via a one-pot three-component Biginelli reaction targeting acetyl-/butyrylcholinesterases inhibition, calcium channel antagonism, and antioxidant ability. Among these multitarget-directed ligands, BIGI 4b, BIGI 4d, and BIGI 5b were identified as promising new hit compounds showing in vitro balanced activities toward the recognized AD targets. In addition, these compounds showed suitable physicochemical properties and a good druglikeness score predicted by Data Warrior software.     

Lichtabsorption der Gelatine-Farbstoffphosphore und das Beersche Gesetz

Zusammenfassung Es wurde das Beer'sche Gesetz in bezug auf feste Gelatine-Farbstoffphosphore untersucht. Der untersuchte Farbstoff war Rhodulin Orange N, dessen Phosphoreszenzemission sehr bedeutend ist. Die Absorption wurde in einem Konzentrationsbereiche von 10⁻²−10^−3,5 g Farbstoff per ccm Gelatine im sichtbaren und ultravioletten Spektrum bestimmt. Bei gewissen gro\en Konzentrationen folgt der Gelatinephosphor dem Beer'schen Gesetze, bei kleineren Konzentrationen aber ist die Extinktion nicht konstant, sondern sie w?chst arithmetisch, wenn die Konzentration nach einer geometrischen Reihe sinkt. Die Resultate sind mit den von anderen Autoren über flüssige Farbstoffl?sungen gefundenen im Einklang. Es liegt nahe anzunehmen, da\ derjenige Anteil der Absorption, welcher die Abweichung vom Beer'schen Gesetz verursacht, zur Fluoreszenzerregung verbraucht wird. Vorstehende Arbeit wurde mit den Mitteln der Rockefeller Foundation im Institut für Experimentalphysik der Kgl. ungarischen Horthy Miklos Universit?t vollendet. Herrn Prof. Dr. Paul Fr?hlich bin ich für seine Unterstützung und st?ndiges Interesse zu gr?\tem Danke verpflichtet.     

Decay scheme of92m Nb

The beta decay of the 2^{+ 92m} Nb was reinvestigated via⁹³Nb(γ, n) reaction. The feeding of the 2⁺ 2,067 keV level of⁹²Zr was determined measuring the intensity of the 1,132 keV gamma-ray transition.     

Beta decay of57Ni

The decay of⁵⁷Ni was studied using both single and coincidence gamma-ray spectroscopy. Four new low-intensity transitions were observed in the single spectra. The energies and intensities of these transitions related to the 1378 keV transition were determined as 304.1 keV, 0.002%; 696.0 keV, 0.001%, 1350.5 keV, 0.002% and 1603.3 keV, 0.005%. Weak transitions at 541.9, 755.3 and 1279.9 keV were confirmed in agreement to earlier works, and their intensities related to 1378 keV were determined as 0.005%, 0.007% and 0.0012%, respectively.     

Admissible sequences and the preprojective component of a quiver

This paper concerns indecomposable preprojective modules over the path algebra of a finite connected quiver without oriented cycles. For each such module, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the module. An efficient way to compute the module is to recover it from its shortest (+)-admissible sequence. The set of equivalence classes of the above sequences has a natural structure of a partially ordered set. For a large class of quivers, the Hasse diagram of the partially ordered set is isomorphic to the preprojective component of the Auslander-Reiten quiver. The techniques of (+)-admissible sequences yield a new result about slices in the preprojective component.     

3D Bioprinting of Tissue/Organ Models

In vitro tissue/organ models are useful platforms that can facilitate systematic, repetitive, and quantitative investigations of drugs/chemicals. The primary objective when developing tissue/organ models is to reproduce physiologically relevant functions that typically require complex culture systems. Bioprinting offers exciting prospects for constructing 3D tissue/organ models, as it enables the reproducible, automated production of complex living tissues. Bioprinted tissues/organs may prove useful for screening novel compounds or predicting toxicity, as the spatial and chemical complexity inherent to native tissues/organs can be recreated. In this Review, we highlight the importance of developing 3D in vitro tissue/organ models by 3D bioprinting techniques, characterization of these models for evaluating their resemblance to native tissue, and their application in the prioritization of lead candidates, toxicity testing, and as disease/tumor models.