Weak real integral characterizations for exponential stability of semigroups in reflexive spaces

Let (t _n ) be a sequence of nonnegative real numbers tending to ∞, such that 1≤t _n+1?t _n ≤α for all natural numbers n and some positive α. We prove that a strongly continuous semigroup {T(t)} _t≥0, acting on a Hilbert space H, is uniformly exponentially stable if $$\sum_{n=0}^\infty\varphi\bigl(\bigl|\bigl\langle T(t_n)x, y\bigr\rangle\bigr|\bigr)<\infty, $$ for all unit vectors x, y in H. We obtain the same conclusion under the assumption that the inequality $$\sum_{n=0}^\infty\varphi\bigl(\bigl|\bigl\langle T(t_n)x, x^\ast\bigr\rangle\bigr|\bigr)<\infty, $$ is fulfilled for all unit vectors x∈X and x ^?∈X ^?, X being a reflexive Banach space. These results are stated for functions φ belonging to a special class of functions, such as defined in the second section of this paper. We conclude our paper with a Rolewicz’s type result in the continuous case on Hilbert spaces.     

A characterization theorem for geometric logic

We establish a criterion for deciding whether a class of structures is the class of models of a geometric theory inside Grothendieck toposes; then we specialize this result to obtain a characterization of the infinitary first-order theories which are geometric in terms of their models in Grothendieck toposes, solving a problem posed by Ieke Moerdijk in 1989.     

Synthesis of "two-story" calix[6]aza-cryptands

The first four members of a new family of C(3v)-symmetrical "two-story" calix[6]aza-cryptands have been synthesized. These large funnel shaped aza-ligands are formed through introduction of three aromatic arms as spacers onto the small rim of a calix[6]arene and subsequently capped with the tripodal aza caps tacn [1,3,5-triazacyclononane] or tren [tris(aminoethyl)amine]. A key feature for an efficient final 1:1 macrocyclization appears to be an adequate geometrical fit between the extended calixarene scaffold and the aza caps.     

Biodegradable poly(ethylene carbonate) nanoparticles as a promising drug delivery system with "stealth" potential

The goal of this study was to investigate the suitability of poly(ethylene carbonate) (PEC) nanoparticles as a novel drug delivery system, fulfilling the requirements for a long circulation time. Particles were obtained with a narrow size distribution and nearly neutral zeta potential. Adsorption studies with human plasma proteins revealed that PEC nanoparticles bind much less proteins in comparison to polystyrene (PS) nanoparticles. Cell experiments with fluorescently labeled PEC showed no uptake of the nanoparticles by macrophages. These novel PEC nanospheres with their unique surface properties are a promising candidate for long circulating drug delivery systems in vivo.     

Solvation structure of I- and Na+ on the surface of NaI aqueous solution studied by photodetachment spectroscopy in combination with mass spectrometry

We investigated solvation structures of I(-) and Na(+) on an aqueous solution surface by photodetachment spectroscopy and mass spectrometry. An aqueous solution of NaI was introduced into the vacuum as a continuous liquid flow (liquid beam), and the liquid beam was irradiated with a UV laser pulse. The abundance of electrons emitted by the laser excitation was measured as a function of wavelength (photodetachment spectroscopy). For a concentrated aqueous solution of NaI, we observe an absorption peak at longer wavelengths than the charge-transfer-to-solvent band of I(-) in solution. This feature is assigned to the photoabsorption of I(-) at the surface. This finding indicates that when the concentration of NaI is high (>1.0 M), I(-) exists on the solution surface. The identity of the ion clusters ejected from the liquid beam following selective laser excitation of I(-) on the surface or I(-) inside the solution was revealed by mass spectrometry. The mass spectra show that Na rich clusters are formed when I(-) inside the solution is excited, whereas Na rich clusters are hardly formed by the excitation of surface I(-). These findings lead us to conclude that Na(+) does not exist on the surface of the NaI aqueous solution.     

Some modular relations for the Göllnitz-Gordon functions and Ramanujan’s modular equations

Huang used the methods of Rogers, Watson and Bressoud to derive some new modular relations involving the Göllnitz-Gordon functions. In this paper, using Ramanujan’s modular equations, we present a uniform method to prove these modular relations established by Huang.     

Electrochemically Driven Cup‐and‐Ball CuI and CuII Complexes

The conformation of copper “funnel” complexes that contains a coordinating appended arm can be electrochemically switched between endo, which corresponds to the self‐coordination of the arm through the cavity, and exo positions. This process, which is reminiscent of a cup‐and‐ball device, is activated by an exogenous ligand for complexes that contain a hydroxy‐terminated arm. The exchange is electrochemically triggered and is operated in either Cu^I or Cu^II redox states, depending on the exogenous ligand, that is, CO or n‐butylamine, respectively.     

Proof of a conjecture on a congruence modulo 243 for overpartitions

Periodica Mathematica Hungarica - Let $$\bar{p}(n)$$ denote the number of overpartitions of n. Recently, numerous congruences modulo powers of 2, 3 and 5 were established regarding $$\bar{p}(n)$$ ....     

Heterologous Expression of Transaldolase Gene Tal from Saccharomyces cerevisiae in Fusarium oxysporum for Enhanced Bioethanol Production

The filamentous fungus Fusarium oxysporum is known for its ability to ferment xylose-producing ethanol. However, efficiency of xylose utilization and ethanol yield was low. In this study, the transaldolase gene from Saccharomyces cerevisiae has been successfully expressed in F. oxysporum by an Agrobacterium tumefaciens-mediated transformation method. The enzymatic activity of the recombinant fungus (cs28pCAM-Sctal4) was 0.195 times higher than that of the wild-type strain (cs28). The recombinant strain also exhibited a 28.83% increase in ethanol yield on xylose media compared to the parental strain. Enhanced ethanol production and a reduction in the biomass were observed during xylose fermentation. Ethanol yield from rice straw by simultaneous saccharification and fermentation with cs28pCAM-Sctal4 was 0.25 g?g?1 of rice straw. The transgenic strain of F. oxysporum cs28pCAM-Sctal4 might therefore have potential applications in industrial bioenergy production.     

Druggable hot spots in trypanothione reductase: novel insights and opportunities for drug discovery revealed by DRUGpy

Journal of Computer-Aided Molecular Design - Assessment of target druggability guided by search and characterization of hot spots is a pivotal step in early stages of drug-discovery. The raw output...