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 For non-spherically complete fields the classical techniques are no longer valid in the p-adic context, which forces us to seek a completely different way to attack the problem.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.     

Direct observation of the preference of hole transfer over electron transfer for radical ion pair recombination in donor-bridge-acceptor molecules

Understanding how the electronic structures of electron donor-bridge-acceptor (D-B-A) molecules influence the lifetimes of radical ion pairs (RPs) photogenerated within them (D+*-B-A-*) is critical to designing and developing molecular systems for solar energy conversion. A general question that often arises is whether the HOMOs or LUMOs of D, B, and A within D+*-B-A-* are primarily involved in charge recombination. We have developed a new series of D-B-A molecules consisting of a 3,5-dimethyl-4-(9-anthracenyl)julolidine (DMJ-An) electron donor linked to a naphthalene-1,8:4,5-bis(dicarboximide) (NI) acceptor via a series of Phn oligomers, where n = 1-4, to give DMJ-An-Phn-NI. The photoexcited charge transfer state of DMJ-An acts as a high-potential photoreductant to rapidly and nearly quantitatively transfer an electron across the Phn bridge to produce a spin-coherent singlet RP 1(DMJ+*-An-Phn-NI-*). Subsequent radical pair intersystem crossing yields 3(DMJ+*-An-Phn-NI-*). Charge recombination within the triplet RP then gives the neutral triplet state. Time-resolved EPR spectroscopy shows directly that charge recombination of the RP initially produces a spin-polarized triplet state, DMJ-An-Phn-3*NI, that can only be produced by hole transfer involving the HOMOs of D, B, and A within the D-B-A system. After the initial formation of DMJ-An-Phn-3*NI, triplet-triplet energy transfer occurs to produce DMJ-3*An-Phn-NI with rate constants that show a distance dependence consistent with those determined for charge separation and recombination.