Spectral properties of Schrödinger operators on compact manifolds: Rigidity,flows, interpolation and spectral estimates

This note is devoted to optimal spectral estimates for Schrödinger operators on compact connected Riemannian manifolds without boundary. These estimates are based on the use of appropriate interpolation inequalities and on some recent rigidity results for nonlinear elliptic equations on those manifolds.     

Numerical Representation of Semiorders

We introduce a codomain to represent semiorders, total preorders and interval orders by means of a single map. We characterize the semiorders that are representable in the extended real line.     

Positive Projective Space of a <Emphasis Type="Italic">C</Emphasis>*-Algebra with a Tracial Conditional Expectation

Let be a C*-algebra, a subalgebra of its center and Φ: → a tracial faithful conditional expectation. We define the positive projective space as the quotient where G⁺ is the space of positive invertible elements of , and if there exists g invertible in such that a′ = |g|²a. When is abelian, this space is a set of representatives for probability densities equivalent to a given one. The aim of this paper is to endow ℙ⁺ with differentiable structure, a linear connection and a Finsler metric. This is done in a way that given any pair of elements in ℙ⁺, there is a unique geodesic of this connection, which is the shortest curve joining such endpoints for the given metric. The metric space ℙ⁺ with the given geodesic distance is non positively curved.     

Hunting a light CP-odd non-standard Higgs boson through its tauonic decay at a (Super) B factory

Several scenarios beyond the minimal extension of the Standard Model still allow light non-standard Higgs bosons evading LEP bounds. We examine the mixing between a light CP-odd Higgs boson and ηb${\eta }_b$ states and its implications on a slight (but observable) lepton universality breaking in Upsilon decays to be measured at the percent level at a (Super) B factory.     

Photocatalytic Efficiency Tuning by the Surface Roughness of TiO2 Coatings on Glass Prepared by the Doctor Blade Method

A set of opaque films were prepared with Degussa P25^® or Hombikat UV100^® TiO₂ powders by the doctor blade method on glass slides with different compositions of polyethylene glycol of 20 kDa (PEG20), and they were characterized by spectroscopy, microscopy and photochemical kinetics measurements. After annealing treatment at 450 °C, about 5–7% C atom was incorporated into the films, as a consequence of the degradation of the organic complexing agents, inducing a small reduction of the energy band gap of TiO₂ (i.e. 3.02 ≤ E_g (eV) ≤ 3.08). All films were about 15 ± 2 μm thick but their micro‐morphological characteristics depended on the content of PEG20, showing different patterns of cracks and aggregates that produce intense light scattering and retransmission phenomena with the result of a three‐dimensional excitation of the TiO₂ particles in the thick film. Back‐face excitation with UVA light (365 ± 42 nm) of the opaque films in contact with an aqueous solution produced both surface‐bound and free hydroxyl radicals (HO^?), as detected using a coumarin solution as a radical dosimeter. The photogeneration efficiency of HO^? decreased with the surface roughness of the films, which varied between 135 and 439 nm depending on the film's composition.     

Selective cyclopalladation of R3P=NCH2Aryl iminophosphoranes. Experimental and computational study

The orientation of the orthopalladation of iminophosphoranes R3P=NCH2Aryl (R=Ph, Aryl=Ph (1a), C6H(4)-2-Br (1b), C6H4-Me-2 (1e), C6H3-(Me)(2)-2,5 (1f); R=p-tolyl, Aryl=Ph (1c); R=m-tolyl, Aryl=Ph (1d); R3P=MePh2P, and Aryl=Ph (1g)) has been studied. 1a reacts with Pd(OAc)2 (OAc=acetate) giving endo-[Pd(micro-Cl){C,N-C6H4(PPh2=NCH2Ph)-2}]2 (3a), while exo-[Pd(micro-Br){C,N-C6H4(CH2N=PPh3)-2}]2 (3b) could only be obtained by the oxidative addition of 1b to Pd2(dba)3. The endo form of the metalated ligand is favored kinetically and thermodynamically, as shown by the conversion of exo-[Pd(micro-OAc){C,N-C6H4(CH2N=PPh3)-2}]2 (2b) into endo-[Pd(micro-OAc){C,N-C6H4(PPh2=NCH2Ph)-2}]2 (2a) in refluxing toluene. The orientation of the reaction is not affected by the introduction of electron-releasing substituents at the Ph rings of the PR3 (1c and 1d) or the benzyl units (1e and 1f), and endo complexes (3c-3f) were obtained in all cases. The palladation of MePh2P=NCH2Ph (1g) can be regioselectively oriented as a function of the solvent. The exo isomer [Pd(micro-Cl){C6H4(CH2N=PPh2Me)-2}]2 (exo-3g) is obtained in refluxing CH2Cl2, while endo-[Pd(micro-Cl){C,N-C6H4(PPh(Me)=NCH2Ph)-2}]2 (endo-3g) can be isolated as a single isomer in refluxing toluene. In this case, the exo metalation is kinetically favored while an endo process occurs under thermodynamic control, as shown through the rearrangement of [Pd(micro-OAc){C6H4(CH2N=PPh2Me)-2}]2 (exo-2g) into [Pd(micro-OAc){C,N-C6H4(P(Ph)Me=NCH2Ph)-2}]2 (endo-2g) in refluxing toluene. The preference for the endo palladation of 1a and the kinetic versus thermodynamic control in 1g has been explained through DFT studies of the reaction mechanism.     

Determination of equilibrium constants and computational interaction energies for adducts of [Rh2(RCO2)(4-n)(PC)n] (n = 0-2) with Lewis bases

Properties of dirhodium catalysts with cyclometalated aryl phosphine ligands have been studied. We report here the study of the acid-base reaction of Rh2(RCO2)2(PC)2(H2O)2 catalysts (PC = cyclometalated aryl phosphine) with different Lewis bases. The determination of the equilibrium constants of these reactions can be used to study to which extent the properties of the axial coordination site of the catalyst, considered the active site, are affected by modification of the metalated phosphines, the carboxylate ligands, or the incoming axial ligand. The trends in the computational density functional theory interaction energies show good agreement with the major trends in the equilibrium constants, thus enabling a further study of the influence of the modification of the ligand core.     

Entropy-driven population distributions in a prototypical molecule with two flexible side chains: O-(2-acetamidoethyl)-N-acetyltyramine

Resonant two-photon ionization (R2PI), resonant ion-dip infrared (RIDIR), and UV-UV hole-burning spectroscopies have been employed to obtain conformation-specific infrared and ultraviolet spectra under supersonic expansion conditions for O-(2-acetamidoethyl)-N-acetyltyramine (OANAT), a doubly substituted aromatic in which amide-containing alkyl and alkoxy side chains are located in para positions on a phenyl ring. For comparison, three single-chain analogs were also studied: (i) N-phenethyl-acetamide (NPEA), (ii) N-(p-methoxyphenethyl-acetamide) (NMPEA), and (iii) N-(2-phenoxyethyl)-acetamide (NPOEA). Six conformations of OANAT have been resolved, with S(0)-S(1) origins ranging from 34,536 to 35,711 cm(-1), denoted A-F, respectively. RIDIR spectra show that conformers A-C each possess an intense, broadened amide NH stretch fundamental shifted below 3400 cm(-1), indicative of the presence of an interchain H bond, while conformers D-F have both amide NH stretch fundamentals in the 3480-3495 cm(-1) region, consistent with independent-chain structures with two free NH groups. NPEA has a single conformer with S(0)-S(1) origin at 37,618 cm(-1). NMPEA has three conformers, two that dominate the R2P1 spectrum, with origin transitions between 35,580 and 35,632 cm(-1). Four conformations, one dominate and three minor, of NPOEA have been resolved with origins between 35,654 and 36,423 cm(-1). To aid the making of conformational assignments, the geometries of low-lying structures of all four molecules have been optimized and the associated harmonic vibrational frequencies calculated using density functional theory (DFT) and RIMP2 methods. The S(0)-S(1) adiabatic excitation energies have been calculated using the RICC2 method and vertical excitation energies using single-point time-dependent DFT. The sensitivity of the S(0)-S(1) energy separation in OANAT and NPOEA primarily arises from different orientations of the chain attached to the phenoxy group. Using the results of the single-chain analogs, tentative assignments have been made for the observed conformers of OANAT. The RIMP2 calculations predict that interchain H-bonded conformers of OANAT are 25-30 kJ/mol more stable than the extended-chain structures. However, the free energies of the interchain H-bonded and extended structures calculated at the preexpansion temperature (450 K) differ by less than 10 kJ/mol, and the number of extended structures far outweighs the number of H-bonded conformers. This entropy-driven effect explains the presence of the independent-chain conformers in the expansion, and cautions future studies that rely solely on relative energies of conformers in considering possible assignments.     

Metric geodesics of isometries in a Hilbert space and the extension problem

We consider the problem of finding short smooth curves of isometries in a Hilbert space . The length of a smooth curve , , is measured by means of , where denotes the usual norm of operators. The initial value problem is solved: for any isometry and each tangent vector at (which is an operator of the form with ) with norm less than or equal to , there exist curves of the form , with initial velocity , which are short along their path. These curves, which we call metric geodesics, need not be unique, and correspond to the so called extension problem considered by M.G. Krein and others: in our context, given a symmetric operator

find all possible extending to all , with . We also consider the problem of finding metric geodesics joining two given isometries and . It is well known that if there exists a continuous path joining and , then both ranges have the same codimension. We show that if this number is finite, then there exist metric geodesics joining and .

     

Adsorption of fluorinated ethers and alcohols on fresh and oxidized carbon overcoats for magnetic data storage

Temperature programmed desorption has been used to study the desorption kinetics and desorption energies of perfluorodiethylether, (CF3CF2)2O, and 2,2,2-trifluoroethanol, CF3CH2OH, adsorbed on fresh and oxidized hydrogenated amorphous carbon (a-CHx) films. (CF3CF2)2O and CF3CH2OH serve as models for the ether backbone and hydroxyl end-groups of Fomblin Zdol, the lubricant most commonly used to lubricate the surfaces of amorphous carbon overcoats on magnetic data storage hard disks. Our measurements clearly reveal, for the first time, the effects of surface oxidation on the adsorption of fluorocarbon lubricants such as Fomblin Zdol on a-CHx films. Oxidation of the a-CHx surface increases the desorption energy of CF3CH2OH but has no observable impact on the desorption energy of (CF3CF2)2O. These results support the suggestion that the alcohols interact with the surface via hydrogen bonding. From a practical perspective, these results imply that the oxidation of the fresh a-CHx film may serve as a means to control or tailor the a-CHx surface to optimize the properties of the lubricant-overcoat interface in hard disks.