Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz functions

We describe the possible restrictions of the cotangent bundle to an elliptic curve . We apply this in positive characteristic to the computation of the Hilbert-Kunz function of a homogeneous R₊-primary ideal in the graded section ring .     

Polarization switching properties of spray deposited CsNO3: PVA composite films

The ferroelectric and switching properties of spray deposited cesium nitrate: poly (vinyl alcohol) composite films at different substrate temperatures (T _s ) have been studied. The optimum value of remanent polarization was obtained in the film deposited at T _s =200°C, which may be due to larger structural distortion (c/a ratio) and less porosity as revealed by x-ray diffraction and field emission scanning electron microscope (FESEM) analysis. The switching current transients have been analyzed by nucleation limited switching model (NLS) with the Lorentzian distribution function. This model gives excellent agreement with the experimental polarization current throughout the whole time range. The switching parameters were determined in the composite films deposited at different T _s and found to be optimum at T _s =200°C. The effect of pulse amplitude on the domain switching properties has also been studied and analyzed. The peak value of polarization current exhibits an exponential dependence on the external applied field.     

The inverse inertia problem for the complements of partial k-trees

Let F$\mathbb{F}$ be an infinite field with characteristic not equal to two. For a graph G=(V,E)$G=(V,E)$ with V={1,…,n}$V=\{1,\dots ,n\}$, let S(G;F)$S(G;\mathbb{F})$ be the set of all symmetric n×n$n\times n$ matrices A=[_ai,j]$A=[a_{i,j}]$ over F$\mathbb{F}$ with _ai,j≠0$a_{i,j}\ne 0$, i≠j$i\ne j$ if and only if ij∈E$ij\in E$. We show that if G is the complement of a partial k  -tree and m?k+2$m?k+2$, then for all nonsingular symmetric m×m$m\times m$ matrices K   over F$\mathbb{F}$, there exists an m×n$m\times n$ matrix U   such that U^TKU∈S(G;F)$U^{T}KU\in S(G;\mathbb{F})$. As a corollary we obtain that, if k+2?m?n$k+2?m?n$ and G is the complement of a partial k-tree, then for any two nonnegative integers p and q   with p+q=m$p+q=m$, there exists a matrix in S(G;R)$S(G;\mathbb{R})$ with p positive and q negative eigenvalues.     

Über eine neue Methode zur Darstellung von Chromoxydhydrat-Gallerten

Zusammenfassung Die w?sserigen L?sungen der Ammoniakate von Dihalogenchromalkylaten CrX₂. OR. 3 NH₃, die leicht durch Ammoniak aus den Reaktionsl?sungen von Chrom(2)haloiden mit geeigneten ?thern gef?llt werden k?nnen, gelatinieren bei passender Konzentration zu Chromoxydhydrat-Gallerten. Die zugrunde liegenden hydrolytischen Vorg?nge, die sich schon in einem vorangehenden Farbwechsel andeuten, offenbaren sich auch in der Leitf?higkeits- und vor allem in der für Kolloidbildungen typischen Viskosit?tszunahme der L?sungen.     

Selective and diagnostic labelling of serine hydrolases with reactive phosphonate inhibitors

Reactive phosphonates are important probes to target the active site of serine hydrolases, one of the largest and most diverse family of enzymes. Developing such inhibitory probes is of special importance in activity based protein profiling, a strategy that is increasingly used to gain information about a certain class of enzymes in complex proteosomes. Therefore, gaining detailed information about these inhibition events on the individual protein level is important since it affords information that can be used to fine-tune the probe for a specific task. Here, we report a novel and versatile synthesis protocol to access a variety of functionalised p-nitrophenyl phosphonate (PNPP) inhibitors from a common azide functionalised precursor using click chemistry. The obtained PNPPs were successfully used to covalently label serine hydrolases in their active sites with molecular tags. Furthermore, a model study is described in which we developed straightforward protocols that can be used to study protein inhibition events. Kinetic studies using UV-Vis and fluorescence spectroscopy techniques revealed that these PNPPs possess different inhibition rates for various proteins and were shown to be suitable probes to discriminate between various lipases. Additionally, we demonstrate that PNPPs are highly selective for serine hydrolases, making these probes very interesting as diagnostic or affinity probes for studying proteins in complex proteosomes.     

Synthesis of 6H-indolo[2,3-b]quinoxaline-N-glycosides and their cytotoxic activity against human ceratinocytes (HaCaT)

N-glycosides of 6H-indolo[2,3-b]quinoxalines were prepared and structurally characterized. The synthesis relies on the cyclocondensation of isatine-N-glycosides with 1,2-diaminobenzenes. Some products exhibit weak cytotoxic activity against human ceratinocytes (HaCaT).     

Stable aqueous film coating dispersion of zein

The effects of plasticizers, pH, and electrolytes on film formation and physical stability of aqueous film coating dispersions (pseudolatexes) of zein were evaluated. The influence of plasticizer on film formation mechanism and minimum film-formation temperature (MFT) were monitored by means of hot stage microscopy (HSM). Furthermore, the effects of pH and electrolytes on the short-term physical stability of pseudolatexes were investigated by measuring relative absorbance, zeta potential, and particle size of the dispersions. With aqueous coating dispersions of zein, stages of film formation were identified. The dispersions plasticized with 20% (w/w) PEG 400 or glycerol formed mechanically strong and flexible films with the lowest glass transition temperature (T(g)). Physical stability of the aqueous zein dispersions was dependent on both pH and electrolyte content. At a pH ranging from 3 to 4, the aqueous dispersions of zein were stable for at least 2 months exhibiting the highest values for zeta potential, the smallest particle size, and a low volume of aggregates. The stable dispersion could be obtained containing a lower concentration of electrolytes (e.g., 10(-5) M). The physical stability of aqueous zein dispersions can be determined by the combined measurements of relative absorbance, zeta potential, and particle size.