Duality for Stochastic Models of Transport

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particle densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites. The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.     

A generalized notion of compliance

It is a known fact in structural optimization that for structures subject to prescribed non-zero displacements the work done by the loads is not a good measure of compliance, neither is the stored elastic energy. We briefly discuss a possible alternative measure of compliance, valid for general boundary conditions. We also present the adjoint states (necessary for the computation of the structural derivative) for the three functionals under consideration.     

On non-solvable Camina pairs

In this paper we study non-solvable and non-Frobenius Camina pairs (G,N). It is known [D. Chillag, A. Mann, C. Scoppola, Generalized Frobenius groups II, Israel J. Math. 62 (1988) 269–282] that in this case N is a p-group. Our first result (Theorem 1.3) shows that the solvable residual of G/O_p(G) is isomorphic either to SL(2,p^e),p is a prime or to SL(2,5), SL(2,13) with p=3, or to SL(2,5) with p7.Our second result provides an example of a non-solvable and non-Frobenius Camina pair (G,N) with |O_p(G)|=5⁵ and G/O_p(G)SL(2,5). Note that G has a character which is zero everywhere except on two conjugacy classes. Groups of this type were studies by S.M. Gagola [S.M. Gagola, Characters vanishing on all but two conjugacy classes, Pacific J. Math. 109 (1983) 363–385]. To our knowledge this group is the first example of a Gagola group which is non-solvable and non-Frobenius.     

Nonpositive curvature in p-Schatten class

We study the geometry of the set Δp, with 1<p<∞, which consists of perturbations of the identity operator by p-Schatten class operators, which are positive and invertible as elements of B(H). These manifolds have natural and invariant Finsler structures. In [C. Conde, Geometric interpolation in p-Schatten class, J. Math. Anal. Appl. 340 (2008) 920-931], we introduced the metric dp and exposed several results about this metric space. The aim of this work is to prove that the space (Δp,dp) behaves in many senses like a nonpositive curvature metric space.     

Potential modularity for elliptic curves and some applications

In this paper we prove the simultaneous potential modularity for a finite number of elliptic curves defined over a totally real field. As an application we prove the meromorphic continuation of some L-functions associated to elliptic curves and Tate conjecture for a product of 2 or 4 elliptic curves defined over a totally real field.     

Organoselenium(II) complexes containing organophosphorus ligands. Crystal and molecular structure of PhSeSP(S)Ph2, [2-{MeN(CH2CH2)2NCH2}C6H4]SeSP(S)R′2 (R′ = Ph,OPri) and [2-{O(CH2CH2)2NCH2}C6H4]SeSP(S)(OPri)2

Arylselenium(II) derivatives of dithiophosphorus ligands of type ArSeSP(S)R₂ [Ar = Ph, R = Ph (1), OPrⁱ (2); 2-[MeN(CH₂CH₂)₂NCH₂]C₆H₄, R = Ph (3), OPrⁱ (4); 2-[O(CH₂CH₂)₂NCH₂]C₆H₄, R = OPrⁱ (6)] were prepared by redistribution reactions between Ar₂Se₂ and [R₂P(S)S]₂. The derivative [2-{O(CH₂CH₂)₂NCH₂}C₆H₄]SeSP(S)Ph₂ (5) was obtained by the salt metathesis reaction between [2-{O(CH₂CH₂)₂NCH₂}C₆H₄]SeCl and NH₄S₂PPh₂. The compounds were investigated by multinuclear (¹H, ¹³C, ³¹P, ⁷⁷Se) NMR and infrared spectroscopy. The crystal and molecular structures of 1, 3, 4 and 6 were determined by single-crystal X-ray diffraction. In compounds 3, 4 and 6 the N(1) atom is intramolecularly coordinated to the selenium center, resulting in a T-shaped geometry (hypervalent 10-Se-3 species). The dithiophosphorus ligands act as anisobidentate in 1 and monodentate in 3, 4 and 6. Supramolecular architectures based on intermolecular S?H and N?H contacts between molecular units are formed in the hypervalent derivatives 3 and 4, while in the compounds 1 and 6 the molecules are associated into polymeric chains through either Se?S or O?H contacts, with no further inter-chain interactions.     

Diorganotin(IV) compounds containing 2-(Et2NCH2)C6H4 moieties: Configurational stability in solution and solid state structures

Hypercoordinated diorganotin(IV) dichloride, [2-(Et₂NCH₂)C₆H₄]₂SnCl₂ (1), was prepared by reacting [2-(Et₂NCH₂)C₆H₄]Li with SnCl₄. Halide-exchange reactions between 1 and the appropriate potassium halides gave [2-(Et₂NCH₂)C₆H₄]₂SnX₂ [X = F (2), Br (3), I (4)]. Reaction of 1 with excess of Na₂S gave the cyclo-[{2-(Et₂NCH₂)C₆H₄}₂SnS]₂ (5). The solution behavior of the title compounds in solution was investigated by multinuclear (¹H, ¹³C, ¹⁹F and ¹¹⁹Sn) NMR spectroscopy, including variable temperature studies. Single-crystal X-ray diffraction analysis revealed for all compounds intramolecular N → Sn coordination thus resulting in distorted octahedral (C,N)₂SnX₂ configurations. Planar chirality is observed as result of the non-planarity of the SnC₃N rings; all compounds, however, crystallizing as racemates. The isomers are linked by extensive hydrogen bonds to give different supramolecular architectures in the crystals of compounds 1, 3 and 4.     

Reactions of M3Te7 (M = Mo, W) clusters with electrophilic reagents: Chalcogen exchange in the Te2 ligand and the first complexes of (TeS)

Reactions of triangular telluride-bridged Mo and W clusters [M₃(μ₃-Te)(μ₂-Te₂)₃(dtp)₃]⁺ (M = Mo, W; dtp = (EtO)₂PS₂) with S₂Cl₂ or Br₂ lead to Te/S exchange in the Te₂ ligands, with the formation of complexes with a novel TeS²⁻ ligand. Reaction of [W₃(μ₃-Te)(μ₂-Te₂)₃(dtp)₃]⁺ with Br₂ or S₂Cl₂ gives a mixture of complexes formulated as [W₃Te_4.25S_2.75(dtp)₃]⁺ and [W₃Te_4.30S_2.70(dtp)₃]⁺, respectively, on the basis of X-ray structural analysis. Reaction of the Mo homolog, namely [Mo₃(μ₃-Te)(μ₂-Te₂)₃(dtp)₃]⁺, with S₂Cl₂ gives rise to [Мо₃Te_4.74S_2.26((EtO)₂PS₂)₃]⁺. Electrospray ionization mass spectrometry (ESI-MS) complements the information gathered from X-ray analysis regarding the degree of Te by S substitution; moreover, detailed insights on the regioselectivity of such replacement are also obtained from ESI-MS analysis. These experimental evidences indicate that Te by S replacement in W complexes display high regioselectivity (as evidenced by the exclusive formation of a W₃Te₄S₃⁴⁺ core), the equatorial Te ligands being preferentially replaced over the Te_ax and μ₃-Te ligands. Conversely, for the Mo homologs, a broad distribution of Mo₃Te_7−xS_x⁴⁺ cluster species ranging from x = 0 to 6 is observed. Bond distance analysis as well as crystal packing trends as a function of the cluster core M₃Te_7−xS_x⁴⁺ (M = Mo, W; x = 0–6) composition are also reported.