Bin packing can be solved within 1 + ε in linear time

For any listL ofn numbers in (0, 1) letL* denote the minimum number of unit capacity bins needed to pack the elements ofL. We prove that, for every positive ε, there exists anO(n)-time algorithmS such that, ifS(L) denotes the number of bins used byS forL, thenS(L)/L*≦1+ε for anyL providedL* is sufficiently large. The work of this author was supported by NSF Grant MCS 70-04997.     

Exact solution of the Zn+1 × Zn+1 symmetric generalization of the XXZ model

We give a generalization of the XXZ model where the spin takes n + 1 values, and the hamiltonian is not parity invariant. The diagonalization problem is solved exactly by the use of the n nested Bethe ansatz. We compute the ground-state energy in both the ferromagnetic and the antiferromagnetic case.     

Tunneling in the proton transfer between two water molecules

SCF CNDO calculations were performed for the species H₅O⁺₂ at several positions of the intervening proton and at interoxygen distances of 2.65, 2.70 and 2.75 Å. The energy profile was fitted to a potential energy function containing a quadratic term plus a gaussian. The eigenvalues and eigenvectors were obtained by using the variational method with the eigenfunctions of the parabolic potential as basis set. The results indicate that at 2.65 Å the top of the barrier is below the first energy level and that at 2.75 Å the first two energy levels are below the top of the barrier with the splitting of the symmetric-antisymmetric pair of 0.00132 au indicating that tunneling occurs at a frequency of 10¹⁴ reciprocal seconds.     

Solid-state characterization of spray-dried ice cream mixes

The main physicochemical properties of spray-dried ice cream mixes (i.e. surface composition, wettability, flowability and microstructure) were analyzed. Emulsions contained 19-44% milk fat on a dry basis and included mixes with no added emulsifier and/or sucrose. The time necessary for complete wetting of the powders correlated with the amount of surface free-fat measured by means of solvent extraction. Non-micellar casein (sodium caseinate) showed to be a better co-encapsulant than micellar casein (skim milk) as demonstrated by surface fat coverage measured by electron spectroscopy for chemical analysis (ESCA). Emulsifiers influenced the fat surface composition of the powders by reducing the amount of surface protein due to their lower interfacial tension. Surface fat caused an initial overestimation of the particle size of the powders due to fat-related caking. Powders showed no flow before and after surface fat extraction which was attributed to fat-related caking and very small particle size (<80 microm), respectively.     

Travelling wavefronts of reaction-diffusion equations in cylindrical domains

Abstract

Function spaces with asymptotics is a usual tool in the analysis on manifolds with singularities. The asymptotics are singular ingredients of the kernels of pseudodifferential operators in the calculus. They correspond to potentials supported by the singularities of the manifold, and in this form asymptotics can be treated already on smooth configurations. This article is aimed at describing refined asymtotics in the Dirichlet problem in a ball. The beauty of explicit formulas actually highlights the structure of asymptotic expansions in the calculi on singular varieties.     

Persistent Organic High‐Spin Trinitrenes

The septet ground state trinitrenes 1,3,5‐trichloro‐2,4,6‐trinitrenobenzene and 1,3,5‐tribromo‐2,4,6‐trinitrenobenzene were isolated in inert (Ar, Ne, and Xe) as well as reactive matrices (H₂, O₂, and H₂O) at cryogenic temperatures. These trinitrenes were obtained in high yields by UV photolysis of the corresponding triazides and characterized by IR and UV/Vis spectroscopy. The trinitrenes, despite bearing six unpaired electrons, are remarkably unreactive towards molecular oxygen and hydrogen and are persistent in water ice up to 160 K where the water matrix starts to sublime off.     

Determination of natural uranium by various analytical techniques in soils of Zacatecas State (Mexico)

Journal of Radioanalytical and Nuclear Chemistry - 238U is a radionuclide present in the earth’s crust that provides 65.9% of annual average radiation dose and represents 99.27% of total...     

New palladium (II) complexes containing phosphine‐nitrogen ligands and their use as catalysts in aminocarbonylation reaction

Aminocarbonylation of aryl halides, homogeneously catalysed by palladium, is an efficient method that can be employed for obtaining amides for pharmaceutical and synthetic applications. In this work, palladium (II) complexes containing P^N ligands were studied as catalysts in the aminocarbonylation of iodobenzene in the presence of diethylamine. Two types of systems were used: a palladium (II) complex formed in situ; and one prepared prior to the catalytic reaction. In general, the palladium complexes studied achieved high conversions in an average reaction time of less than 2 hr, which is less than that for the standard system (Pd (II)/PPh₃) used. The pre‐synthesized complexes were faster than their in situ counterparts, as the latter require an induction time to form the Pd/P^N species. The structure and electronic properties of the ligand P^N can influence both the activity and the selectivity of the reaction, stabilizing the acyl‐palladium intermediates formed in a better manner.