Controlled synthesis of gold nanostars by using a zwitterionic surfactant

By replacing cetyltrimethylammonium bromide (CTAB) with the zwitterionic lauryl sulfobetaine (LSB) surfactant in the classical seed-growth synthesis, monocrystalline gold nanostars (m-NS) and pentatwinned gold asymmetric nanostars (a-NS) were obtained instead of nanorods. The main product under all synthetic conditions was a-NS, which have branches with high aspect ratios (AR), thus leading to LSPR absorptions in the 750-1150?nm range. The percentage of m-NS versus a-NS, the aspect ratio of the a-NS branches, and consequently the position of their LSPR absorption can be finely tuned simply by regulating the concentration of reductant, the concentration of surfactant, or the concentration of the "catalytic" Ag(+) cation. The m-NS have instead shorter and larger branches, the AR of which is poorly influenced by synthetic conditions and displays an LSPR positioned around 700?nm. A growth mechanism that involves the direct contact of the sulfate moiety of LSB on the surface of the nano-object is proposed, thereby implying preferential coating of the {111} Au faces with weak interactions. Consistent with this, we also observed the straightforward complete displacement of the LSB surfactant from the surface of the nanostars. This was obtained by the simple addition of thiols in aqueous solution to yield extremely stable coated a-NS and m-NS that are resistant to highly acidic, basic, and in similar to in vivo conditions.     

Limits of Gaudin Algebras,Quantization of Bending Flows,Jucys–Murphy Elements and Gelfand–Tsetlin Bases

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra \({U(\mathfrak {g})}\) of a semisimple Lie algebra \({\mathfrak {g}}\). This family is parameterized by collections of pairwise distinct complex numbers z ₁, . . . , z _n . We obtain some new commutative subalgebras in \({U(\mathfrak {g})^{\otimes n}}\) as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the Hamiltonians of bending flows and to the Gelfand–Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.     

Darboux Coverings and Rational Reductions of the KP Hierarchy

We use the method of Darboux coverings to discuss the invariant submanifolds of the KP equations presented as conservation laws in the space of monic Laurent series in the spectral parameter (the space of the Hamiltonian densities). We identify a special class of these submanifolds with the rational invariant submanifolds entering matrix models of two-dimensional gravity recently characterized by Dickey and Krichever. Four examples of the general procedure are provided.     

Bihamiltonian reductions and ωn-algebras

We discuss the geometry of the Marsden-Ratiu (MR) reduction theorem for a bihamiltonian manifold. We consider the case of the manifolds associated with the Gel'fand-Dickey theory, i.e., loop algebras over. We provide an explicit identification, tailored on the MR reduction, of the Adler-Gel'fand-Dickey brackets (AGD) with the Poisson brackets on the reduced bihamiltonian manifold . Such an identification relies on a suitable immersion of T^*N into the algebra of pseudodifferential operators connected to geometrical features of the theory of (classical) _n-algebras.     

Synthesis of branched Au nanoparticles with tunable near-infrared LSPR using a zwitterionic surfactant

Asymmetric branched gold nanoparticles are obtained using for the first time in the seed-growth approach a zwitterionic surfactant, laurylsulfobetaine, whose concentration in the growth solution allows to control both the length to base-width ratio of the branches and the LSPR position, that can be tuned in the 700-1100 nm near infrared range.     

A cast-mold approach to iron oxide and Pt/iron oxide nanocontainers and nanoparticles with a reactive concave surface

We report the synthesis of various iron oxide nanocontainers and Pt-iron oxide nanoparticles based on a cast-mold approach, starting from nanoparticles having a metal core (either Au or AuPt) and an iron oxide shell. Upon annealing, the particles evolve to asymmetric core-shells and then to heterodimers. If iodine is used to leach Au out of these structures, asymmetric core-shells evolve into "nanocontainers", that is, iron oxide nanoparticles enclosing a cavity accessible through nanometer-sized pores, while heterodimers evolve into particles with a concave region. When starting from a metal domain made of AuPt, selective leaching of the Au atoms yields the same iron oxide nanoparticle morphologies but now encasing Pt domains (in their concave region or in their cavity). We found that the concave nanoparticles are capable of destabilizing Au nanocrystals of sizes matching that of the concave region. In addition, for the nanocontainers, we propose two different applications: (i) we demonstrate loading of the cavity region of the nanocontainers with the antitumoral drug cis-platin; and (ii) we show that nanocontainers encasing Pt domains can act as recoverable photocatalysts for the reduction of a model dye.     

Algebraic properties of Manin matrices 1

We study a class of matrices with noncommutative entries, which were first considered by Yu.I. Manin in 1988 in relation with quantum group theory. They are defined as “noncommutative endomorphisms” of a polynomial algebra. More explicitly their defining conditions read: (1) elements in the same column commute; (2) commutators of the cross terms are equal: [M_ij,M_kl]=[M_kj,M_il] (e.g. [M₁₁,M₂₂]=[M₂₁,M₁₂]). The basic claim is that despite noncommutativity many theorems of linear algebra hold true for Manin matrices in a form identical to that of the commutative case. Moreover in some examples the converse is also true, that is, Manin matrices are the most general class of matrices such that linear algebra holds true for them. The present paper gives a complete list and detailed proofs of algebraic properties of Manin matrices known up to the moment; many of them are new. In particular we provide complete proofs that an inverse to a Manin matrix is again a Manin matrix and for the Schur formula for the determinant of a block matrix; we generalize the noncommutative Cauchy–Binet formulas discovered recently arXiv:0809.3516, which includes the classical Capelli and related identities. We also discuss many other properties, such as the Cramer formula for the inverse matrix, the Cayley–Hamilton theorem, Newton and MacMahon–Wronski identities, Plücker relations, Sylvester's theorem, the Lagrange–Desnanot–Lewis Carroll formula, the Weinstein–Aronszajn formula, some multiplicativity properties for the determinant, relations with quasideterminants, calculation of the determinant via Gauss decomposition, conjugation to the second normal (Frobenius) form, and so on and so forth. Finally several examples and open question are discussed. We refer to [A. Chervov, G. Falqui, Manin matrices and Talalaev's formula, J. Phys. A 41 (2008) 194006; V. Rubtsov, A. Silantiev, D. Talalaev, Manin matrices, elliptic commuting families and characteristic polynomial of quantum gl_n elliptic Gaudin model, in press] for some applications in the realm of quantum integrable systems.