Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

The numerical solution of Dirichlet's problem for a second-orderelliptic operator in divergence form with arbitrary nonlinearitiesin the first- and zero-order terms is considered. The mixedfinite-element method is used. Existence and uniqueness of theapproximation are proved and optimal error estimates in L² aredemonstrated for the relevant functions. Error estimates arealso derived in L^q, 2q+     

Pentafluorophenyl Esters as Exchangeable Stoppers for the Construction of Photoactive [2]Rotaxanes

Stable pillar[5]arene-containing [2]rotaxane building blocks with pentafluorophenyl ester stoppers have been efficiently prepared on a multi-gram scale. Reaction of these building blocks with various nucleophiles gave access to a wide range of [2]rotaxanes with amide, ester or thioester stoppers in good to excellent yields. The rotaxane structure is fully preserved during these chemical transformations. Actually, the addition-elimination mechanism at work during these transformations totally prevents the unthreading of the axle moiety of the mechanically interlocked system. The stopper exchange reactions were optimized both in solution and under mechanochemical solvent-free conditions. While amide formation is more efficient in solution, the solvent-free conditions are more powerful for the transesterification reactions. Starting from a fullerene-functionalized pillar[5]arene derivative, this new strategy gave easy access to a photoactive [2]rotaxane incorporating a C₆₀ moiety and two Bodipy stoppers. Despite the absence of covalent connectivity between the Bodipy and the fullerene moieties in this photoactive molecular device, efficient through-space excited state interactions have been evidenced in this rotaxane.     

SUPERPOROUS HYDROGELS: FAST RESPONSIVE HYDROGEL SYSTEMS

ABSTRACT

Superporous hydrogels, hydrogels with pore sizes in the range of 100 μm and larger, were synthesized using N-isopropyl-acrylamide (NIPAM) and acrylamide (AM). The superporous hydrogels were synthesized by crosslinking polymerization of monomers in the presence of gas bubbles. The pores of superporous hydrogels were connected to each other to form open capillary channels, which provided fast response to the changes in the environmental temperature. Upon increase in temperature from 10°C to 65°C, the superporous hydrogel made from a monomer solution of NIPAM:AM = 9:1 shrank from the fully swollen state (volume of 36 cm³) to the fully collapsed state (volume of 6.5 cm³) in 72±14 sec. When the temperature was changed back to 10°C, the superporous hydrogel swelled to 36 cm³ in 78±15 sec. This deswelling-swelling cycle was repeated many times without changes in the thermo-reversible property of the superporous hydrogel. The response time of the superporous hydrogels was thousand times faster than that of conventional hydrogels. The fast response of the superporous hydrogels is due to the rapid uptake or exclusion of water molecules through the extensive capillary channels. Because superporous hydrogels still maintain the open capillary structure even after drying, the dried superporous hydrogels can also swell to the equilibrium swelling state within minutes. These fast responsive hydrogels can find many pharmaceutical and medical applications.     

Precise characterization method of antibody‐conjugated magnetic nanoparticles for pathogen detection using stuffer‐free multiplex ligation‐dependent probe amplification

Antibody‐conjugated magnetic nanoparticles (Ab‐MNPs) have potential in pathogen detection because they allow target cells to be easily separated from complex sample matrices. However, the sensitivity and specificity of pathogen capture by Ab‐MNPs generally vary according to the types of MNPs, antibodies, and sample matrices, as well as preparation methods, including immobilization. Therefore, achieving a reproducible analysis utilizing Ab‐MNPs as a pathogen detection method requires accurate characterization of Ab‐MNP capture ability and standardization of all handling processes. In this study, we used high‐resolution CE‐single strand conformational polymorphism coupled with a stuffer‐free multiplex ligation‐dependent probe amplification system to characterize Ab‐MNPs. The capture ability of Ab‐MNPs targeting Salmonella enteritidis and nine pathogens, including S. enteritidis, was analyzed in phosphate buffer and milk. The effect of storage conditions on the stability of Ab‐MNPs was also assessed. The results showed that the stuffer‐free multiplex ligation‐dependent probe amplification system has the potential to serve as a standard characterization method for Ab‐MNPs. Moreover, the precise characterization of Ab‐MNPs facilitated robust pathogen detection in various applications.     

Rapid and sensitive detection of lower respiratory tract infections by stuffer‐free multiplex ligation‐dependent probe amplification

Lower respiratory tract infection is one of the most common infectious diseases. However, conventional methods for detecting infectious pathogens are time‐consuming, and generally have a limited impact on early therapeutic decisions. We previously reported a rapid and sensitive method for detecting such pathogens using stuffer‐free multiplex ligation‐dependent probe amplification coupled with high‐resolution CE‐SSCP. In this study, we report an application of this method to the detection of respiratory pathogens. As originally configured, this method was capable of simultaneously detecting seven bacterial species responsible for lower respiratory tract infections, but its detection limit and assay time were insufficient to provide useful information for early therapeutic decisions. To improve sensitivity and shorten assay time, we added a target‐specific preamplification step, improving the detection limit from 50 pg of genomic DNA to 500 fg. We further decreased time requirements by optimizing the hybridization step, enabling the entire assay to be completed within 7 h while maintaining the same detection limit. Taken together, these improvements enable the rapid detection of infectious doses of pathogens (i.e. a few dozen cells), establishing the strong potential of the refined method, particularly for aiding early treatment decisions.     

Examples of entropy generating sequence

We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.     

THE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORUSTHE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORU

1. IntroductionGiven a locally compact abelian group G and a multiplier p on G, one can associate tothem the twisted group C*-algebra C*(G, p), which is the universal object for unitary prepresentations of G. C* (Zm, p) is said to be a noncommutative torns of rank m and denotedby A.. The multiplier p determines a subgroup S. of G, called its symmetry group, andthe multiplier p is called totally skew if the symmetry group S. is trivial. And A. is calledcompletely irrational if p is totally…     

Wedge Operations and Doubling Operations of Real Toric Manifolds

This paper deals with two things.First,the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G.Second,the author focuses on a specific canonical extensions called doublings and presents their various properties.They include existence of infinitely many real topological toric manifolds admitting complex structures,and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover,some questions about real topological toric manifolds related to Halperin's toral rank conjecture are presented.