Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Usage of supplementary cementitious materials: advantages and limitations

Journal of Thermal Analysis and Calorimetry - It is well known that cement production is not neutral for natural environment among others due to high CO2 emission. Different strategies of...     

Synthesis and Biological Evaluation of RGD Peptidomimetic–Paclitaxel Conjugates Bearing Lysosomally Cleavable Linkers

Two small‐molecule–drug conjugates (SMDCs, 6 and 7 ) featuring lysosomally cleavable linkers (namely the Val–Ala and Phe–Lys peptide sequences) were synthesized by conjugation of the α_vβ₃‐integrin ligand cyclo[DKP–RGD]‐CH₂NH₂ ( 2 ) to the anticancer drug paclitaxel (PTX). A third cyclo[DKP–RGD]–PTX conjugate with a nonpeptide “uncleavable” linker ( 8 ) was also synthesized to be tested as a negative control. These three SMDCs were able to inhibit biotinylated vitronectin binding to the purified α_Vβ₃‐integrin receptor at nanomolar concentrations and showed good stability at pH 7.4 and pH 5.5. Cleavage of the two peptide linkers was observed in the presence of lysosomal enzymes, whereas conjugate 8 , which possesses a nonpeptide “uncleavable” linker, remained intact under these conditions. The antiproliferative activities of the conjugates were evaluated against two isogenic cell lines expressing the integrin receptor at different levels: the acute lymphoblastic leukemia cell line CCRF‐CEM (α_Vβ₃?) and its subclone CCRF‐CEM α_Vβ₃ (α_Vβ₃+). Fairly effective integrin targeting was displayed by the cyclo[DKP–RGD]–Val–Ala–PTX conjugate ( 6 ), which was found to differentially inhibit proliferation in antigen‐positive CCRF‐CEM α_Vβ₃ versus antigen‐negative isogenic CCRF‐CEM cells. The total lack of activity displayed by the “uncleavable” cyclo[DKP–RGD]–PTX conjugate ( 8 ) clearly demonstrates the importance of the peptide linker for achieving the selective release of the cytotoxic payload.     

Expedient and Diastereodivergent Assembly of Terpenoid Decalin Subunits having Quaternary Stereocenters through Organocatalytic Robinson Annulation of Nazarov Reagent

We report an expedient approach to highly functionalized cis‐ and trans‐decalines that could function as key structural subunits toward the synthesis of various classes of terpenoids. Key to the strategy is an organocatalyzed Robinson annulation reaction of the Nazarov reagent that affords chiral enone building blocks with high enantioselectivities. The quaternary carbon stereogenic center can direct the subsequent reactions and allow the rapid and diastereoconvergent assembly of complex decalines with contiguous stereocenters.     

Viscoelastic type magnetic effects and self-gravity on the propagation of MHD waves

Meccanica - We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional...     

Ammonia Synthesis at Room Temperature and Atmospheric Pressure from N2: A Boron-Radical Approach

Ammonia, NH₃, is an essential molecule, being part of fertilizers. It is currently synthesized via the Haber–Bosch process, from the very stable dinitrogen molecule, N₂ and dihydrogen, H₂. This process requires high temperatures and pressures, thereby generating ca 1.6 % of the global CO₂ emissions. Alternative strategies are needed to realize the functionalization of N₂ to NH₃ under mild conditions. Here, we show that boron-centered radicals provide a means of activating N₂ at room temperature and atmospheric pressure whilst allowing a radical process to occur, leading to the production of borylamines. Subsequent hydrolysis released NH₄⁺, the acidic form of NH₃. EPR spectroscopy supported the intermediacy of radicals in the process, corroborated by DFT calculations, which rationalized the mechanism of the N₂ functionalization by R₂B radicals.