Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

Changing DNA grooves--a 1,4,5,8-naphthalene tetracarboxylic diimide bis-intercalator with the linker (beta-Ala)(3)-Lys in the minor groove

We have been investigating a modular, threading DNA polyintercalator design based upon the 1,4,5,8-naphthalene tetracarboxylic diimide (NDI) intercalating unit. Previously, we have reported the NMR analysis of a bis-intercalator-DNA complex in which the peptide linker between NDI units was found to occupy the DNA major groove (Guelev, Lee, Sorey, Hoffman, Iverson, Chem. Biol. 2001, 8, 415-425). Here we describe the NMR analysis of a complex between a related bis-intercalator known to display altered DNA sequence specificity. In this case, the linker resides in the DNA minor groove. We have thus shown that within this set of sequence specific bis-intercalators, both DNA grooves can be accessed, setting the stage for longer threading polyintercalators designed to have linkers occupying both grooves in an alternating fashion.     

Mechanism studies of the conversion of 13C-labeled n-butane on zeolite H-ZSM-5 by using 13C magic angle spinning NMR spectroscopy and GC-MS analysis

By using 13C MAS NMR spectroscopy (MAS = magic angle spinning), the conversion of selectively 13C-labeled n-butane on zeolite H-ZSM-5 at 430-470 K has been demonstrated to proceed through two pathways: 1) scrambling of the selective 13C-label in the n-butane molecule, and 2) oligomerization-cracking and conjunct polymerization. The latter processes (2) produce isobutane and propane simultaneously with alkyl-substituted cyclopentenyl cations and condensed aromatic compounds. In situ 13C MAS NMR and complementary ex situ GC-MS data provided evidence for a monomolecular mechanism of the 13C-label scrambling, whereas both isobutane and propane are formed through intermolecular pathways. According to 13C MAS NMR kinetic measurements, both pathways proceed with nearly the same activation energies (E(a) = 75 kJ mol(-1) for the scrambling and 71 kJ mol(-1) for isobutane and propane formation). This can be rationalized by considering the intermolecular hydride transfer between a primarily initiated carbenium ion and n-butane as being the rate-determining stage of the n-butane conversion on zeolite H-ZSM-5.     

Amphiphilic treelike rods at interfaces: layered stems and circular aggregation

Amphiphilic dendron-rod molecules with three hydrophilic poly(ethylene oxide) (PEO) branches attached to a hydrophobic octa-p-phenylene rod stem were investigated for their ability to form two-dimensional micellar structures on a solid surface. A treelike shape of the molecules was reported to be a major factor in the formation of nonplanar micellar structures in solution and in the bulk state (cylindrical and spherical). We observed that in these treelike amphiphilic molecules the hydrophilic terminated dendron branches assemble themselves in surface monolayers with the formation of two-dimensional layered or circular micellar structures. We suggested the formation of the planar ribbon-like structures with interdigitated layering within the loosely packed monolayers and circular, ringlike structures (2D circular aggregates) in the precollapsed state.     

A role of non-hydrogen framework vibrational modes in formation of ferroelectric properties of H-bonded K3H(SO4)2-like materials

An effect of molecular vibrational modes within the dimers [O₃AO–(H/D)OAO₃]³⁻ on behavior of H-bond protons or deuterons is studied theoretically for H-bonded antiferroelectrics and quantum paraelectrics of the M₃(H/D)(AO₄)₂ family (M=alkali metal, A=S, Se). The ‘heavy’ reorganization modes in D-species of this family and both reorganization and promoting modes in corresponding H-analogues are examined. It is shown that the analysis with due regard for the reorganization modes results in insignificant decreasing of the effective tunneling frequency of light nuclei. Hence the reasonable estimations of the critical temperature of the low-temperature phase transition in M₃D(AO₄)₂ materials are available only with additional corrections related to potential profiles of a deuteron. It is noted that in the limits of the proposed model the promoting mode in the case of H-species can favor, in principle, the increasing as well as the decreasing of effective proton level splitting.     

Effect of cholesterol on the properties of phospholipid membranes. 4. Interatomic voids

The properties of the interatomic voids present in fully hydrated dimyristoylphosphatidylcholine (DMPC)-cholesterol mixed membranes of different compositions are analyzed in detail using a generalized variant of the Voronoi-Delaunay method on the basis of computer simulation results. The systems investigated are chosen from both sides of the DMPC-cholesterol miscibility gap; the pure DMPC bilayer has also been included in the analysis as a reference system. The results obtained show that the empty space is organized in a more compact way, forming larger voids in the presence than in the absence of cholesterol. The voids located in the region of the rigid cholesterol rings become, on average, less spherical, oriented more parallel with the membrane normal axis with increasing cholesterol concentration, whereas an opposite effect of cholesterol is observed in the middle of the membrane among the chain terminal methyl groups. In general, the preferential orientation of the voids is found to strongly correlate with that of the molecules in the hydrocarbon phase of the membranes. The membranes are found to contain rather large voids, the volume of which can be an order of magnitude larger than the largest spherical cavities present in the systems. These voids are elongated or branching channels rather than big empty holes. The voids located among the DMPC and cholesterol molecules are lying preferably parallel with the membrane normal axis. The existence of such empty channels can be of great importance in the cross-membrane permeation of small, uncharged penetrants, in particular, of polar molecules.     

Field operators and their spectral properties in finite-dimensional quantum field theory

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C ^r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L ²(R^r,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We shall show that the isomorphism between the exponential ofV andL ²(R^r,dx) can be understood as the decomposition by generalized eigenvectors of field operators (Fourier transform).