Linear and nonlinear heat equations in $L^q_\delta$ spaces and universal bounds for global solutions

We develop a theory of both linear and nonlinear heat equations in the weighted Lebesgue spaces , where is the distance to the boundary. In particular, we prove an optimal estimate for the heat semigroup, and we establish sharp results on local existence-uniqueness and local nonexistence of solutions for semilinear heat equations with initial values in those spaces. This theory enables us to obtain new types of results concerning positive global solutions of superlinear parabolic problems. Namely, under certain assumptions, we prove that any global solution is uniformly bounded for by a universal constant, independent of the initial data. In all previous results, the bounds for global solutions were depending on the initial data. Received March 15, 2000 / Accepted October 18, 2000 / Published online February 5, 2001     

Espaces Homogenes Principaux et Points de 2-Division de Courbes Elliptiques

Dans cet article, nous nous intéressons aux problèmesde structure galoisienne associés aux couples (E/L, a),où E désigne une courbe elliptique définiesur le corps de nombres L et a un endomorphisme de E. Si E està multiplication complexe, nous notons k le corps quadratiqueimaginaire dont l'anneau des entiers décrit End(E) etL une extension de k. Ainsi a est-il selon les cas un entieralgébrique de k ou un élément de Z.     

On a class of degenerate elliptic operators arising from Fleming-Viot processes

We are dealing with the solvability of an elliptic problem related to a class of degenerate second order operators which arise from the theory of Fleming-Viot processes in population genetics. In the one dimensional case the problem is solved in the space of continuous functions. In higher dimension we study the problem in spaces with respect to an explicit measure which, under suitable assumptions, can be taken invariant and symmetrizing for the operators. We prove the existence and uniqueness of weak solutions and we show that the closure of the operator in such spaces generates an analytic -semigroup. Received December 4, 2000; accepted December 9, 2000.     

Periodic Mesoporous Organosilica Nanoparticles for CO2 Adsorption at Standard Temperature and Pressure

(1) Background: Due to human activities, greenhouse gas (GHG) concentrations in the atmosphere are constantly rising, causing the greenhouse effect. Among GHGs, carbon dioxide (CO₂) is responsible for about two-thirds of the total energy imbalance which is the origin of the increase in the Earth’s temperature. (2) Methods: In this field, we describe the development of periodic mesoporous organosilica nanoparticles (PMO NPs) used to capture and store CO₂ present in the atmosphere. Several types of PMO NP (bis(triethoxysilyl)ethane (BTEE) as matrix, co-condensed with trialkoxysilylated aminopyridine (py) and trialkoxysilylated bipyridine (Etbipy and iPrbipy)) were synthesized by means of the sol-gel procedure, then characterized with different techniques (DLS, TEM, FTIR, BET). A systematic evaluation of CO₂ adsorption was carried out at 298 K and 273 K, at low pressure. (3) Results: The best values of CO₂ adsorption were obtained with 6% bipyridine: 1.045 mmol·g⁻¹ at 298 K and 2.26 mmol·g⁻¹ at 273 K. (4) Conclusions: The synthetized BTEE/aminopyridine or bipyridine PMO NPs showed significant results and could be promising for carbon capture and storage (CCS) application.     

Improving the picture of atomic structure in nonoriented polymer domains using the pair distribution function: A study of polyamide 6

Investigations of the atomic structures within polyamides started over 80 years ago and continue today. These weakly ordered materials diffract X-rays poorly and typically require postprocessing to obtain idealized samples for structural studies. An important goal remains to develop techniques to study the local structure in its natural state, with atomic resolution, and with sensitivity to subtle changes due to synthesis conditions or other technologically relevant processing procedures. Here, we compare the structures of as-produced, nonoriented polyamide 6 ([C₆H₁₁NO] _n) from both hydrolytic and anionic processes. A total scattering pair distribution function approach is used to elucidate information about the atomic bonding, molecular conformation, chain packing, crystallite size, and ratio of ordered to disordered domain content. The results are compared with those from standard analytical methods.     

Frontispiece: From Phosphidic to Phosphonium? Umpolung of the P4-Bonding Situation in [CpFe(CO)(L)(η1-P4)]+ Cations (L=CO or PPh3)

Upon coordinating P₄ to electron poor cyclopentadienyl-iron cations, the average P−P bond distances shrink and the respective P₄ breathing mode in the Raman spectra (600 cm⁻¹, P_{4, free}) is blueshifted by >40 cm⁻¹ in [CpFe(CO)(L)(η¹-P₄)]⁺ cations (L=CO or PPh₃). Analysis suggests that this corresponds to an umpolung of the bonding from more phosphidic in the known, electron-rich systems to more phosphonium-like in the reported electron-poor versions. This may open new functionalization pathways for white phosphorus P₄.     

The Taming of Redox-Labile Phosphidotitanocene Cations

Tame d⁰ phosphidotitanocene cations stabilized with a pendant tertiary phosphane arm are reported. These compounds were obtained by one-electron oxidation of d¹ precursors with [Cp₂Fe][BPh₄]. The electronic structure of these compounds was studied experimentally (EPR, UV/Vis, and NMR spectroscopy, X-ray diffraction analysis) and through DFT calculations. The theoretical analysis of the bonding situation by using the electron localization function (ELF) shows the presence of π-interactions between the phosphido ligand and Ti in the d⁰ complexes, whereas dπ–pπ repulsion prevents such interactions in the d¹ complexes. In addition, CH–π interactions were observed in several complexes, both in solution and in the solid state, between the phosphido ligand and the phosphane arm. The d⁰ complexes were found to be light sensitive, and decompose through Ti−P bond homolysis to give Ti^III species. A naked d⁰ phosphidotitanocene cation has been trapped by reaction with diphenylacetylene, yielding a Ti/P frustrated Lewis pair (FLP), which was found to be less reactive than a previously reported Zr analog.     

Insights into the Two-Electron Reductive Process of [FeFe]H2ase Biomimetics: Cyclic Voltammetry and DFT Investigation on Chelate Control of Redox Properties of [Fe2(CO)4(κ2-Chelate)(μ-Dithiolate)]

The electrochemical reduction of complexes [Fe₂(CO)₄(κ²-phen)(μ-xdt)] (phen=1,10-phenanthroline; xdt=pdt ( 1 ), adt^iPr ( 2 )) in MeCN-[Bu₄N][PF₆] 0.2 m is described as a two-reduction process. DFT calculations show that 1 and its monoreduced form 1⁻ display metal- and phenanthroline-centered frontier orbitals (LUMO and SOMO) indicating the non-innocence of the phenanthroline ligand. Two energetically close geometries were found for the doubly reduced species suggesting an intriguing influence of the phenanthroline ligand leading to the cleavage of a Fe−S bond as proposed generally for this type of complex or retaining the electron density and avoiding Fe−S cleavage. Extension of calculations to other complexes with edt, adt^iPr bridge and even virtual species [Fe₂(CO)₄(κ²-phen)(μ-adt^R)] (R=CH(CF₃)₂, H) or [Fe₂(CO)₄(κ²-phen)(μ-pdt^R)] (R=CH(CF₃)₂, iPr) showed that the relative stability between both two-electron-reduced isomers depends on the nature of the bridge and the possibility to establish a remote anagostic interaction between the iron center {Fe(CO)₃} and the group carried by the bridged-head atom of the dithiolate group.     

Real-Time Analysis of Polyphenol–Protein Interactions by Surface Plasmon Resonance Using Surface-Bound Polyphenols

A selection of bioactive polyphenols of different structural classes, such as the ellagitannins vescalagin and vescalin, the flavanoids catechin, epicatechin, epigallocatechin gallate (EGCG), and procyanidin B2, and the stilbenoids resveratrol and piceatannol, were chemically modified to bear a biotin unit for enabling their immobilization on streptavidin-coated sensor chips. These sensor chips were used to evaluate in real time by surface plasmon resonance (SPR) the interactions of three different surface-bound polyphenolic ligands per sensor chip with various protein analytes, including human DNA topoisomerase IIα, flavonoid leucoanthocyanidin dioxygenase, B-cell lymphoma 2 apoptosis regulator protein, and bovine serum albumin. The types and levels of SPR responses unveiled major differences in the association, or lack thereof, and dissociation between a given protein analyte and different polyphenolic ligands. Thus, this multi-analysis SPR technique is a valuable methodology to rapidly screen and qualitatively compare various polyphenol–protein interactions.