Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra

   Abstract. Let g : E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x, ε)) ⊂ E, the image under g of the closed ball about x∈ E with radius ε . When g(x) expresses the solution of an equation depending on x , then the elements of g(B(x,ε )) are ε -pseudosolutions. Our aim is to investigate the size of the set g(B(x,ε )) . We derive upper and lower bounds of the following form: g(x) + Dg (x) ( B(0, c ₁ ε N))

On simple double zeros and badly conditioned zeros of analytic functions of variables

We give a numerical criterion for a badly conditioned zero of a system of analytic equations to be part of a cluster of two zeros.

     

Comment on: On the irreducibility of the Severi variety of nodal curves in a smooth surface,by E. Ballico

Archiv der Mathematik - In this short note, I point out that results of Ballico and Kool–Shende–Thomas together imply that on K3, Enriques, and Abelian surfaces, if L is a very ample...     

On universal Severi varieties of low genus K3 surfaces

We prove the irreducibility of universal Severi varieties parametrizing irreducible, reduced, nodal hyperplane sections of primitive K3 surfaces of genus g, with 3?≤ g≤11, g?≠ 10.     

Identification of uranyl binding proteins from human kidney-2 cell extracts by immobilized uranyl affinity chromatography and mass spectrometry

To improve our knowledge on protein targets of uranyl ion (UO₂²⁺), we set up a proteomic strategy based on immobilized metal-affinity chromatography (IMAC). The successful enrichment of UO₂²⁺-interacting proteins from human kidney-2 (HK-2) soluble cell extracts was obtained using an ion-exchange chromatography followed by a dedicated IMAC process previously described and designed for the uranyl ion. By mass spectrometry analysis we identified 64 proteins displaying varied functions. The use of a computational screening algorithm along with the particular ligand-based properties of the UO₂²⁺ ion allowed the analysis and categorization of the protein collection. This profitable approach demonstrated that most of these proteins fulfill criteria which could rationalize their binding to the UO₂²⁺-loaded phase. The obtained results enable us to focus on some targets for more in-depth studies and open new insights on its toxicity mechanisms at molecular level.     

A note about the average number of real roots of a Bernstein polynomial system

We prove that the real roots of normal random homogeneous polynomial systems with n+1$n+1$ variables and given degrees are, in some sense, equidistributed in the projective space P(Rⁿ⁺¹)$\mathbb{P}\left({\mathbb{R}}^{n+1}\right)$. From this fact we compute the average number of real roots of normal random polynomial systems given in the Bernstein basis.     

State correlation diagrams for the photochemical reactions of organometallics

State correlation diagrams are proposed for a number of photochemical reactions of organometallics. Spin-orbit coupling is found important to understand the reactivity of these organometallics.     

Magnetic resonance imaging contrast-enhanced relaxometry of breast tumors: an MRI multicenter investigation concerning 100 patients

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) using extracellular contrast agents has proved to be useful for the characterization of breast tumors. DCE-MRI has demonstrated a high sensitivity (around 95%) but a rather poor and controversial specificity, varying, according to the different studies, from 45% to 90%. In order to increase (a) the specificity and (b) the robustness of this quantitative approach in multicenter evaluation (five MRI units), a quantitative approach called dynamic relaxometry has been developed. According to the proposed method, the time-dependent longitudinal relaxation rate measured on region of interest of the lesion was calculated during the contrast uptake, after intravenous bolus injection of contrast agent. A specifically developed method was used for fast R(1) measurements. Relaxometry time curves are fitted to the Tofts model allowing the measurement of the parameters describing the enhancement curve (maximum relation rate enhancement, initial, 30-s and 60-s slopes) and the tissue parameters [transfer constant (K(trans) min(-1)) and extracellular extravascular space fraction (v(e))]. Correspondence factorial analysis followed by hierarchical ascendant classification are then performed on the different parameters. Higher K(trans) values were observed in infiltrative ductal carcinomas than in infiltrative lobular carcinomas, in agreement with data published by other groups. Specificity of DCE-MRI has been increased up to 85%, with a sensitivity of 95% with K(trans)/v(e) and enhancement index I (ratio of initial slope by maximum relaxation rate enhancement). A multiparametric data analysis of the calculated parameters opens the way to include quantitative image-based information in new nosologic approaches to breast tumors.     

Cyclocarbopalladation involving an unusual 1,5-palladium vinyl to aryl shift as termination step: theoretical study of the mechanism

A DFT/B3LYP model study has been carried out on the cyclocarbopalladation and on an unusual 1,5 vinyl to aryl palladium shift which are the two first steps of a cyclocarbopalladation-Stille coupling tandem reaction of various gamma-bromopropargylic-1,2 diols with alkenyls or alkynyl stannanes catalyzed by Pd(PPh(3))(4). From the calculations, the active intermediates in the catalytic process appear to bear a single phosphine ligand, the palladium(II) center keeping in all cases a square-planar coordination pattern either through intramolecular binding of the triple bond or via an intramolecular Pd...C(phenyl) interaction. The computation of the various transition states and intermediates for the 1,5 vinyl to aryl palladium shift reveals that the intimate mechanism of this pathway corresponds to a one-step hydrogen transfer between the two negatively charged carbon atoms of the vinyl and phenyl groups. A two-step pathway involving a Pd(IV) intermediate is not likely to occur. This conclusion may apply to other 1,n-palladium shifts which have been experimentally observed in various organometallic transformations.