Ultrathin silver‐coated gold nanoparticles as suitable substrate for surface‐enhanced Raman scattering

Surface‐enhanced Raman scattering (SERS) is an extremely powerful tool for the analysis of the composition of bimetallic nanoparticle (BNP) surfaces because of the different adsorption schemes adopted by several molecules on different metals, such as Au and Ag. The preparation of BNPs normally implies a change in the plasmonic properties of the core metal. However, for technological applications it could be interesting to synthesize core–shell structures preserving these original plasmonic properties. In this work, we present a facile method for coating colloidal gold nanoparticles (NPs) in solution with a very thin shell of silver. The resulting bimetallic Au@Ag system maintains the optical properties of gold but shows the chemical surface affinity of silver. The effectiveness of the coating method, as well as the progressive silver enrichment of the outermost part of the Au NPs, has been monitored through the SERS spectra of several species (chloride, luteolin, thiophenol and lucigenin), which show different behaviors on gold and silver surfaces. A growth mechanism of the Ag shell is proposed on the basis of the spectroscopic and microscopic data consisting in the formation and deposit of Ag clusters on the Au NP surface. Copyright © 2009 John Wiley & Sons, Ltd.     

Coherence and the statistics of the phase difference between partially polarized electromagnetic waves

Coherence between two vectorial harmonic light vibrations is analyzed in terms of the statistics of their phase difference. This provides a natural and simple extension of second-order coherence to cover more complicate situations. In particular this assigns large coherence to quantum light states providing the most accurate interferometric measurements allowed by the quantum theory, even if they are incoherent according to the standard second-order approach.     

Search for f(J)(2220) in radiative J/ψ decays

We present a search for f(J)(2220) production in radiative J/ψ→γf(J)(2220) decays using 460 fb?1 of data collected with the BABAR detector at the SLAC PEP-II e(+)e? collider. The f(J)(2220) is searched for in the decays to K(+)K? and K(S)?K(S)?. No evidence of this resonance is observed, and 90% confidence level upper limits on the product of the branching fractions for J/ψ→γf(J)(2220) and f(J)(2220)→K(+)K?(K(S)?K(S)?) as a function of spin and helicity are set at the level of 10??, below the central values reported by the Mark III experiment.     

Recursions associated to trapezoid,symmetric and rotation symmetric functions over Galois fields

Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of ${\mathbb{F}}_2$, an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field ${\mathbb{F}}_q$. Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences.     

Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

Rugged modules: The opposite of flatness

Relative notions of flatness are introduced as a mean to gauge the extent of the flatness of any given module. Every module is thus endowed with a flatness domain and, for every ring, the collection of flatness domains of all of its modules is a lattice with respect to class inclusion. This lattice, the flatness profile of the ring, allows us, in particular, to focus on modules which have a smallest flatness domain (namely, one consisting of all regular modules.) We establish that such modules exist over arbitrary rings and we call them Rugged Modules. Rings all of whose (cyclic) modules are rugged are shown to be precisely the von Neumann regular rings. We consider rings without a flatness middle class (i.e., rings for which modules must be either flat or rugged.) We obtain that, over a right Noetherian ring every left module is rugged or flat if and only if every right module is poor or injective if and only if R = S×T, where S is semisimple Artinian and T is either Morita equivalent to a right PCI-domain, or T is right Artinian whose Jacobson radical properly contains no nonzero ideals. Character modules serve to bridge results about flatness and injectivity profiles; in particular, connections between rugged and poor modules are explored. If R is a ring whose regular left modules are semisimple, then a right module M is rugged if and only if its character left module M⁺ is poor. Rugged Abelian groups are fully characterized and shown to coincide precisely with injectively poor and projectively poor Abelian groups. Also, in order to get a feel for the class of rugged modules over an arbitrary ring, we consider the homological ubiquity of rugged modules in the category of all modules in terms of the feasibility of rugged precovers and covers for arbitrary modules.