On k-planar crossing numbers

The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number of K_2k+1,q, for k?2. We prove tight bounds for complete graphs. We also study the rectilinear k-planar crossing number.     

Filling analytic sets by the derivatives of -smooth bumps

If is an infinite-dimensional Banach space, with separable dual, and is an analytic set such that any point can be reached from  by a continuous path contained (except for the point ) in the interior of , then is the range of the derivative of a -smooth function on  with bounded nonempty support.

     

2‐Triazolylpyrimido[1,2,3‐cd]purine‐8,10‐diones via 1,3‐dipolar cycloadditions to 2‐ethynylpyrimido[1,2,3‐cd]purine‐8,10‐dione

This paper presents the synthesis of a series of 5,6‐dihydro‐4H,8H‐pyrimido[1,2,3‐cd]purine‐8,10(9H)‐dione ring system derivatives with a [1,2,3]triazole ring bonded in position 2. The procedure is based on cycloaddition of substituted alkyl azides to the terminal triple bond of 5,6‐dihydro‐2‐ethynyl‐9‐methyl‐4H,8H‐pyrimido[1,2,3‐cd]purine‐8,10(9H)‐dione ( 4 ). This cycloaddition produced two regioisomers ?5,6‐dihydro‐9‐methyl‐2‐(1‐substituted‐1H‐[1,2,3]triazol‐5‐yl)‐4H,8H‐pyrimido[1,2,3‐cd]purine‐8,10(9H)‐dione ( 7 ) and 2‐(1‐substituted‐1H‐[1,2,3]triazol‐4‐yl) derivative 8 . The required 2‐ethynyl deriva tive 4 was obtained from the starting 2‐unsubstituted compound 1 by bromination to yield the 2‐bromo derivative 2 , which was converted by Sonogashira reaction to trimethylsilylethyne 3 and finally, the protective trimethylsilyl group was removed by hydrolysis.     

Ternary Hybrid γ‐Fe2O3/CrVI/Amine Oxidase Nanostructure for Electrochemical Sensing: Application for Polyamine Detection in Tumor Tissue

Dichromate binds to surface‐active maghemite nanoparticles (SAMNs) to form a stable core–shell nanostructures (SAMN@Cr^VI). The hybrid was characterized by Mössbauer spectroscopy, high‐angle annular dark‐field imaging, electron energy‐loss spectroscopy, and electrochemical techniques, which revealed a strong interaction of dichromate with the nanoparticle surface. Electrochemical characterization showed lower charge‐transfer resistance, better electrochemical performance, and more reversible electrochemical behavior with respect to naked SAMNs. Moreover, SAMN@Cr^VI is an excellent electrocatalyst for hydrogen peroxide reduction. Furthermore, an enzyme, namely, bovine serum amine oxidase (BSAO: EC 1.4.3.6), was immobilized on SAMN@Cr^VI by self‐assembly to give a ternary hybrid nanostructured catalyst for polyamine oxidation (SAMN@Cr^VI‐BSAO). SAMN@Cr^VI‐BSAO was applied for the development of a reagentless, fast, inexpensive, and interference‐free polyamine biosensor, which was successfully exploited for the discrimination of tumorous tissue from healthy tissue in human crude liver extracts.     

An oscillation criterion for discrete trigonometric systems

In this paper, we investigate oscillation properties of discrete trigonometric systems whose coefficients matrices are simultaneously symplectic and orthogonal. The main result generalizes a necessary and sufficient condition of non-oscillation of trigonometric systems proved by M. Bohner and O. Do?lý (J. Differential Equations 163 (2000), pp. 113–129) in the case when the block in the upper right corner of the coefficient matrix is symmetric and positive definite. Now, we present this oscillation criterion for an arbitrary trigonometric system. The obtained results are applied to formulate a necessary and sufficient condition for non-oscillation of even-order Sturm–Liouville difference equations.     

Synthesis and Extended Activity of Triazole‐Containing Macrocyclic Protease Inhibitors

Peptide‐derived protease inhibitors are an important class of compounds with the potential to treat a wide range of diseases. Herein, we describe the synthesis of a series of triazole‐containing macrocyclic protease inhibitors pre‐organized into a β‐strand conformation and an evaluation of their activity against a panel of proteases. Acyclic azido–alkyne‐based aldehydes are also evaluated for comparison. The macrocyclic peptidomimetics showed considerable activity towards calpain II, cathepsin L and S, and the 20S proteasome chymotrypsin‐like activity. Some of the first examples of highly potent macrocyclic inhibitors of cathepsin S were identified. These adopt a well‐defined β‐strand geometry as shown by NMR spectroscopy, X‐ray analysis, and molecular docking studies.     

Doxorubicin Encapsulation Investigated by Capillary Electrophoresis with Laser-Induced Fluorescence Detection

Doxorubicin (DOX) belongs to the group of anthracycline antibiotics with very effective anticancer properties. On the other hand, the cardiotoxic effects limit its application over the maximum cumulative dose. To overcome this obstacle, encapsulation of this drug into the protective nanotransporter such as apoferritin is beneficial. In this study, fluorescent behavior of DOX in various solvents was determined by fluorescence spectrometry, demonstrating the fluorescence quenching effect of water, which is often used as a solvent. It was found that by increasing the amount of the organic phase in the DOX solvent the dynamic quenching is significantly suppressed. Ethanol, acetonitrile and dimethyl sulfoxide were tested and the best linearity of the calibration curve was obtained when above 50 % of the solvent was present in the binary mixture with water. Moreover, pH influence on the DOX fluorescence was also observed within the range of 4–10. Two times higher fluorescence intensity was observed at pH 4 compared to pH 10. Further, the DOX behavior in capillary electrophoresis (CE) was investigated. Electrophoretic mobilities (CE) in various pH of the background electrolyte were determined within the range from 16.3 to −13.3 × 10 ⁻⁹ m⁻² V⁻¹ s⁻¹. Finally, CE was also used to monitor the encapsulation of DOX into the cavity of apoferritin as well as the pH-triggered release.

     

Metabolic fingerprinting based on high-resolution tandem mass spectrometry: a reliable tool for wine authentication?

Ultra-high-performance liquid chromatography coupled with quadrupole time-of-flight mass spectrometry (MS) and an alternative technology represented by direct analysis in real time coupled with quadrupole time-of-flight MS were investigated for metabolic fingerprinting of 343 red and white wine samples. Direct injection of pure wine and an extraction procedure optimized for isolation of polyphenols were used to compare different analytical and data handling strategies. After data processing and data pretreatment, principal component analysis was initially used to explore the data structure. Initially, the unsupervised models revealed a notable clustering according to the grape varieties, and therefore supervised orthogonal partial least squares discriminant analysis models were created and validated for separation of red and white wines according to the grape variety. The validated orthogonal partial least squares discriminant analysis models based on data (ions) recorded in positive ionization mode were able to classify correctly 95 % of samples. In parallel, authentication parameters, such as origin and vintage, were evaluated, and they are discussed. A tentative identification of markers was performed using accurate mass measurement of MS and MS/MS spectra, different software packages and different online libraries. In this way, different flavonol glucosides and polyphenols were identified as wine markers according to the grape varieties.