An oscillating Universe from the linearized R 2 theory of gravity

An oscillating Universe which arises from the linearized R ² theory of gravity is discussed, showing that some observative evidences like the cosmological redshift and the Hubble law are in agreement with the model. In this context Dark Energy is seen like a pure curvature effect arising by the Ricci scalar.     

Ueber eine mit den Bessel'schen Functionen verwandte Function

Ohne Zusammenfassung     

Flächen vom Grad 8 imP 4

Ohne Zusammenfassung     

A study of frost growth and densification on flat surfaces

The present study advances a theoretical and experimental investigation of the frost growth and densification on flat surfaces. This study focuses on the most important factors affecting the frost formation process, i.e. the surrounding air temperature, humidity and velocity, and the surface temperature. The processes of frost growth and densification were investigated experimentally in order to provide a physical basis for the development of a theoretical model to predict the variation of the frost layer thickness and mass with time. The mathematical model was based on mass and energy balances within the frost layer, assuming the frost as a porous medium and accounting for the supersaturation of the moist air on the frost surface. The governing equations for mass and heat diffusion were integrated analytically, giving rise to a semi-algebraic formulation which requires numerical integration of only one time dependent ordinary differential equation. When compared with experimental data, the model predictions of the frost thickness as a function of time agreed to within ±10% error bands. The experimentally-validated model was then used to predict the frost layer growth and densification with respect to the operation conditions such as plate surface temperature, air stream temperature, humidity and velocity.     

Liouville numbers, Rajchman measures, and small Cantor sets

We show that the set of Liouville numbers carries a positive measure whose Fourier transform vanishes at infinity. The proof is based on a new construction of a Cantor set of Hausdorff dimension zero supporting such a measure.

     

Synthesis of dendritic macromolecules through divergent iterative thio‐bromo “Click” chemistry and SET‐LRP

The development of a novel nucleophilic thio‐bromo “Click” reaction, specifically base‐mediated thioetherification of thioglycerol with α‐bromoesters was reported in an earlier article. The combination of this thio‐bromo click reaction with subsequent acylation with 2‐bromopropionyl bromide provides an iterative two‐step divergent growth approach to the synthesis of a new class of poly(thioglycerol‐2‐ propionate) (PTP) dendrimers. In this article, the addition of a third step, the single‐electron transfer living radical polymerization (SET‐LRP) of methyl acrylate (MA), was shown to provides access to a three‐step “branch” and “grow” divergent approach to dendritic macromolecules wherein poly(methyl acrylate) (PMA) connects the branching subunits. This facile methodology can provide a diversity of dendritic macromolecular topologies and will ultimately provide the means to the development of self‐organizable dendritic macromolecules. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3940–3948, 2009     

Universal Extension and Excision for Topological Algebras

We construct a topology on the tensor algebra that makes the multiplication jointly continuous and is universal for algebras with jointly continuous multiplication. This result, together with the methods developed by Cuntz for m-algebras are used to prove the excision theorem of Cuntz and Quillen in the more general case of c-algebras.