Perturbation theory of p-adic Fredholm and semi-Fredholm operators

The main goal of this paper is to prove that Fredholm and semi-Fredholm operators between p-adic (or non-archimedean) Banach spaces, as well as the index of those that are Fredholm, are preserved when they are perturbed by a small operator. In this way we obtain the non-archimedean counterparts of some well-known results of classical Operator Theory. For non-spherically complete fields the classical techniques are no longer valid in the p-adic context, which forces us to seek a completely different way to attack the problem. The p-adic concept of orthogonality will be one of the key tools to get our purpose.     

Enrichment of biologically active U1 small nuclear RNAs by ion-exchange high-performance liquid chromatography

The use of ion-exchange high-performance liquid chromatography in conjunction with preparative electrophoresis to facilitate the purification of biologically active snRNAs is described. Separation of total nuclear RNA from a Bombyx mori cell line was done with a Bio-Rad MA7 plasmid column in a HRLC 500 system. Individual fractions were subjected to electrophoresis through 14% polyacrylamide gels for identification. High levels of U1 RNA were confirmed by Northern analysis with a human U1 probe. Biological activity of RNAs from the column was demonstrated by their ability to incorporate 32P-AMP at the 3' end. Ion-exchange chromatography provides a rapid, automated method for purifying large amounts of RNAs that can then be utilized in further studies.     

Families of commuting transfer matrices and integrable models with disorder

A family of commuting transfer matrices is shown to be associated to each symmetry transformation of a given Yang-Baxter algebra. This applies in lattices models and field theory.The Yang-Baxter algebra remains unchanged when an arbitrary parameter μ_l is associated to each lattice site. We generate in this way integrable one-dimensional hamiltonians with long-range couplings and disorder given by the <{;μ₁<};. These operators are lattice versions of the non-local charges in sigma models. As a simple example we get a Dzialozhinski-Moriya interaction with an arbitrary coupling per site from the six-vertex model. A similar model with a disordered magnetic field follows too. Their exact solution by an algebraic Bethe ansatz is presented. We derive the excitations spectrum in terms of the density of parameters (μ).As another application, the total spin S² is computed for a XXZ Heisenberg chain (μ_l ≡ 0) as a function of the anisotropy Δ (− ∞ < Δ < + ∞).     

Diamagnetic susceptibility effects in NMR measurements of the properties of water in polymeric membranes

The NMR spectra of water adsorbed at various relative humidities on various cellulose ester membranes have been studied. Membranes of cellulose acetate (CA), cellulose triacetate (CTA), and cellulose acetate butyrate (CAB) were investigated. It was found that the resonance peak of a liquid imbibed in or adsorbed on membranes from high relative humidity is very sensitive to the angle between the membrane plane and the direction of the magnetic field, shifting 5–7 ppm to higher fields as the membrane plane is rotated from a perpendicular to a parallel position with respect to the direction of the external magnetic field. This phenomenon was found to be independent of the nature of the polymeric material (namely CA, CTA, or CAB), porosity of the membrane (varying from an “all bulk” dense sheet to an 80% porosity and 0.2 μm average pore size membrane), nature of the magnetic nuclei (H₂O or D₂O), intensity of the external magnetic field (60 Mcps or 100 Mcps), and nature of the liquid in the membrane (water, methanol, or n-hexane). It is therefore concluded that the dependence of the position of the resonance peak on the position of the membrane plane with respect to the external magnetic field, is a geometrical phenomenon due to the magnetic “bulk susceptibility” of the medium. Quantitative estimations of the magnitude of the diamagnetic susceptibility effect in a cylindrically rolled sheet are given. These estimates agree well with the experimentally observed “splittings.”     

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.     

Highly sensitive differential pulse amperometric detection of second generation anti-tumor platinum compounds in HPLC effluents

Summary A highly sensitive on-line amperometric detection of platinum compounds in HPLC effluents was possible with the use of a polarographic detector. For TNO-1 (=cis-1,1-di(aminomethyl)-cyclohexane Pt(II)chloride) a linear dynamic range of at least three decades could be obtained (0.034–108g TNO-1/ml) with a detection limit of three times the noise signal at 0.7 ng TNO-1 (20ng Pt/ml). The sensitivity was 0.1 nA/ng TNO-1 (0.2nA/ng Pt). The within-day presicion was 1.1% at a concentration of 10.8g TNO-1/ml (n=10). With this system the compatibility was measured of TNO-6 with infusion fluids. In 0.15 M NaCl, TNO-6 (=cis-1,1-di(aminomethyl)-cyclohexanePt(II)sulphate) was converted into TNO-1 within 40 minutes. Molecular changes of TNO-6 were also observed in a 5% aqueous glucose solution.     

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.