On two geometric problems related to the travelling salesman problem

The degree-K Minimum Spanning Tree (MST) problem asks for the minimum length spanning tree that has no vertex of degree greater than K. The Euclidean degree-K MST problem is known to be tractable for K ? 5; the degree-2 MST is simply the Euclidean path-TSP, which is NP-complete. It is proved that the Euclidean degree-3 MST problem is also NP-complete, thus leaving open only the case for K = 4. Among the most illustrious approximation algorithms is the heuristic for the Euclidean TSP due to Christofides. It is proved that implementing the “shortcutting phase” of Christofides' algorithm optimally is NP-hard (even so, Christofides' algorithm guarantees a tour which is no more than 50% longer than the optimal one).     

Äther- und Pyridinaddukte von komplexen Halogeno-quecksilbersäuren

The preparation of the ether adducts of simple and mixed halogen acids of mercury(II) is reported and some physical and chemical properties are described. The preparation of salts of the above-mentioned acids with pyridine is also described, and the physical and chemical properties, IR- and UV-spectra, and X-ray diffraction patterns are discussed.     

Adsorption of Cr(VI) from aqueous solutions by HNO3-purified and chemically activated pyrolytic tire char

Pyrolytic tire char adsorbents either demineralized by nitric acid (purified char, PC) or activated with KOH-calcination (activated char, AC) were used for Cr(VI) removal from aquatic solutions and studied by adsorption kinetics, isotherms, and thermodynamics. Adsorbent’s physicochemical characteristics were studied by several techniques such as X-ray diffraction, porosimetry, scanning electron microscopy, elemental analysis, and Boehm titration. For PC, acid treatment leads partially to a mesoporous structure while for AC, KOH activation creates also a microporosity enhancing the specific surface area at 443 m²g^?1. Cr(VI) adsorption onto both adsorbents followed better second-order kinetics and Langmuir isotherm models and it was exothermic (ΔH < 0) and spontaneous (ΔG < 0). The maximum Cr(VI) adsorption capacity for AC and PC was 114 and 79.47 mg g^?1, respectively, at pH = 4. The present work reveals that AC and PC can be efficient sorbents for the removal of heavy metal ions, contributing both positively to wastewater treatment and waste tire pyrolysis plants.     

Kinetic study of the reactions of Cl atoms with CF3CH2CH2OH, CF3CF2CH2OH, CHF2CF2CH2OH, and CF3CHFCF2CH2OH

The reaction kinetics of chlorine atoms with a series of partially fluorinated straight-chain alcohols, CF(3)CH(2)CH(2)OH (1), CF(3)CF(2)CH(2)OH (2), CHF(2)CF(2)CH(2)OH (3), and CF(3)CHFCF(2)CH(2)OH (4), were studied in the gas phase over the temperature range of 273-363 K by using very low-pressure reactor mass spectrometry. The absolute rate coefficients were given by the expressions (in cm(3) molecule(-1) s(-1)): k(1) = (4.42 +/- 0.48) x 10(-11) exp(-255 +/- 20/T); k(1)(303) = (1.90 +/- 0.17) x 10(-11), k(2) = (2.23 +/- 0.31) x 10(-11) exp(-1065 +/- 106/ T); k(2)(303) = (6.78 +/- 0.63) x 10(-13), k(3) = (8.51 +/- 0.62) x 10(-12) exp(-681 +/- 72/T); k(3)(303) = (9.00 +/- 0.82) x 10(-13) and k(4) = (6.18 +/- 0.84) x 10(-12) exp(-736 +/- 42/T); k(4)(303) = (5.36 +/- 0.51) x 10(-13). The quoted 2sigma uncertainties include the systematic errors. All title reactions proceed via a hydrogen atom metathesis mechanism leading to HCl. Moreover, the oxidation of the primarily produced radicals was investigated, and the end products were the corresponding aldehydes (R(F)-CHO; R(F) = -CH(2)CF(3), -CF(2)CF(3), -CF(2)CHF(2), and -CF(2)CHFCF(3)), providing a strong experimental indication that the primary reactions proceed mainly via the abstraction of a methylenic hydrogen adjacent to a hydroxyl group. Finally, the bond strengths and ionization potentials for the title compounds were determined by density functional theory calculations, which also suggest that the alpha-methylenic hydrogen is mainly under abstraction by Cl atoms. The correlation of room-temperature rate coefficients with ionization potentials for a set of 27 molecules, comprising fluorinated C2-C5 ethers and C2-C4 alcohols, is good with an average deviation of a factor of 2, and is given by the expression log(k) (in cm(3) molecule(-1) s(-1)) = (5.8 +/- 1.4) - (1.56 +/- 0.13) x (ionization potential (in eV)).     

Characterization of flavonoid subgroups and hydroxy substitution by HPLC-MS/MS

HPLC-DAD coupled with mass spectrometry in the positive ionization mode was applied to study the fragmentation of twelve selected flavonoids. Compounds belonging to all the major subgroups found in common plants, i.e. flavonols, flavones, dihydroflavonols, flavanones and flavanols were studied. Compound standards were injected into the spectrometer and produced characteristic mass spectra. The fragmentation of each compound was studied and it was shown that the dehydration and carbon monoxide losses from the [M+H]+ ion by the members of each subgroup produced specific fragments, thus allowing the characterization of the flavonoid subgroups. Moreover, fragments resulting from fission of the C-rings are specific of each subgroup and revealed the substitution pattern of A- and B-rings. In order to verify the identifying efficiency of the positive ionization mode through these characteristic fragmentations, the unknown flavonoids of an Origanum vulgare diethyl ether extract were separated with the HPLC system and the major peaks were successfully identified with the mass spectrometer.     

Liposomal drugs dispersed in hydrogels. Effect of liposome, drug and gel properties on drug release kinetics

Release of calcein and griseofulvin (GRF) from control (gels in which solutes are dissolved in) and liposomal gels was studied using agarose-assisted immobilization as a technique to separate gels from drug-receptor compartments. Liposomes composed of phosphatidylcholine (PC) or distearoyl-glycero-PC and cholesterol (DSPC/Chol), and incorporating calcein or GRF were prepared by thin film hydration. After cleaning the liposomes they were dispersed in different hydrogels (carbopol 974 [1, 1.5 or 2% (w/w)], hydroxylethyl-cellulose (HEC) [4% (w/w)], or a mixture of the two), and release of calcein or GRF was followed by fluorescence or photometric technique, respectively. Results show that calcein release from liposomal gels is slower compared to control gels, and can be further retarded by using rigid-membrane liposomes (faster release from PC-liposome compared to DSPC/Chol-liposome gels). Additionally, calcein release is not affected by the lipid amount loaded (in the range from 2 to 8 mg/ml), therefore solute loading can be controlled according to needs.

Oppositely, GRF release from liposomal gels is determined by drug loading. At high drug loading levels (compared to GRF aqueous solubility), GRF is released with constant rate from liposomal gels irrespective of liposome type (PC or DSPC/Chol). Thereby, for amphiphilic/lipophilic drugs, drug properties (solubility, log P) determine the system behavior.

Calcein and GRF release from control carbopol gels is faster compared to HEC and mixture gels. The same is true for calcein in liposomal gels. Carbopol gel rheological properties were found to be significantly different (compared to the other gels), implying that these characteristics are important for drug diffusion from gels.     

Structural Basis of Artemisinin Binding Sites in Serum Albumin with the Combined Use of NMR and Docking Calculations

Artemisinin is known to bind to the main plasma protein carrier serum albumin (SA); however, there are no atomic level structural data regarding its binding mode with serum albumin. Herein, we employed a combined strategy of saturation transfer difference (STD), transfer nuclear Overhauser effect spectroscopy (TR-NOESY), STD–total correlation spectroscopy (STD-TOCSY), and Interligand Noes for PHArmacophore Mapping (INPHARMA) NMR methods and molecular docking calculations to investigate the structural basis of the interaction of artemisinin with human and bovine serum albumin (HSA/BSA). A significant number of inter-ligand NOEs between artemisinin and the drugs warfarin and ibuprofen as well as docking calculations were interpreted in terms of competitive binding modes of artemisinin in the warfarin (FA7) and ibuprofen (FA4) binding sites. STD NMR experiments demonstrate that artemisinin is the main analyte for the interaction of the A. annua extract with BSA. The combined strategy of NMR and docking calculations of the present work could be of general interest in the identification of the molecular basis of the interactions of natural products with their receptors even within a complex crude extract.