Solving the knapsack problem via -transform

Given vectors and , we consider the (unbounded) knapsack optimization problem . We compute the minimum value p^* using techniques from complex analysis, namely Cauchy's Residue Theorem to integrate a function in , and the -transform of an appropriate function related to . The computational complexity depends on s ∑_j=1ⁿa_j, not on the magnitude of b as in dynamic programming based approaches. We also completely characterize the number of solutions with value less than p, as a function of p.     

On separation properties of finite dimensional compact convex sets

In a real finite-dimensional vector space, we study families of sets such that every compact convex set in the space is the intersection of all members of the family that contains it.

     

Mass spectra of some 2-(p-R2-phenyl)-indole-3-carboxaldehyde derivatives

The mass spectra of eight new substituted 2-(p-R²-phenyl)-indole-3-carboxyaldehydes which have potentially useful pharmacological properties, are presented.     

Catalytic polarographic wave of cobalt(II) in sodium azide with hydrazoic acid

Extensive catalytic waves of Co(II) are observed in N₃^?/HN₃ buffers, in which hydrogen discharge is not the dominant process, but rather HN₃ reduction to NH₄⁺ and N₂. Cobalt(I) was shown to be the active intermediate of the catalytic process. The rate-determing step was found to be the Co(I) reduction to the metal. Heterogeneous rate constants were calculated and relationships with average ligand number were derived.     

8‐Hydroxy‐1,3,6‐pyrene trisulfonic acid (pyranine) bleaching by 2,2′‐azobis(2‐amidinopropane) derived peroxyl radicals

8‐Hydroxy‐1,3,6‐pyrene trisulfonic acid, trisodium salt (pyranine), readily reacts with peroxyl radicals generated in the aerobic pyrolysis of 2,2′‐azobis(2‐amidinopropane) (AAPH). The process can be followed by monitoring the decrease in pyranine absorbance (460 nm) or fluorescence (excitation: 460 nm; emission: 510 nm). The reaction follows a nearly zero‐order kinetics in pyranine (0.25–30 μM range), suggesting a very efficient trapping of peroxyl radicals. In agreement with this, the process is order one in AAPH. The bleaching process is totally prevented by Trolox (μM range), and partially prevented by Trp (mM range). The protection afforded by Trp is very little dependent upon the pyranine concentration. This result indicates that the main protective pathway is not a competitive scavenging of the peroxyl radicals. The data suggest protection due to repair of the initially produced pyranyl radicals. These radicals are also very efficient in the destruction of C‐phycocyanin bilin groups. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 525–531, 2003     

Determination of pore diameter from rejection measurements with a mixture of oligosaccharides

This paper present a method to determine pore diameters and effective transport through membranes using a mixture of oligosaccharides. The results are compared with the Maxwell–Stefan equations. The partition coefficients of the solutes are a function of the pore diameter according to the Ferry equation. Thus, with the pore diameter as the only unknown parameter, rejection is described and the pore diameter is obtained by a Marquardt–Levenberg optimization procedure.     

A C3′ modified nucleotide. The difluorophosphonate function, a phosphate mimic, governs the conformational behaviour of the ribofuranose

A conformational analysis using the Pseurot 6.3 software package of a modified nucleoside-3′-phosphate is reported and reveals that the phosphate mimic strongly influences the conformational behaviour of the ribose ring and shifts the North/ South equilibrium to a northern position. A rational classification by the group electronegativity of several phosphate analogues is presented. The λ factor of the difluorophosphonate group in water (Diez-Donders generalised Karplus equation) is also determined.     

Integral geometry and geometric inequalities in hyperbolic space

Using results from integral geometry, we find inequalities involving mean curvature integrals of convex hypersurfaces in hyperbolic space. Such inequalities generalize the Minkowski formulas for euclidean convex sets.     

Photometric determination of palladium with the inclusion complex 1,2-Diaminoanthraquinone-β-cyclodextrin as ligand

1,2-Diaminoanthraquinone forms a 11 inclusion complex with-cyclodextrin in aqueous media and at different pH. This can be employed to solubilize the anthraquinone in water for use as a ligand for metal ions. This ligand can be used to determine palladium at trace levels spectrophotometrically. The limit of detection is 11 ng/ml and the R.S.D. is 2.1%. The performance can be improved by using derivative spectrometry.