Touchard like polynomials and generalized Stirling numbers

The theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift operator. The proposed technique, along with the use of the relevant operational formalism, allows the straightforward derivation of properties of this family of polynomials and their relationship to different forms of Stirling numbers.     

Mixing Times of Monotone Surfaces and SOS Interfaces: A Mean Curvature Approach

We consider stochastic spin-flip dynamics for: (i) monotone discrete surfaces in \({\mathbb {Z}^3}\) with planar boundary height and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model confined to a box. In both cases we show almost optimal bounds O(L ²polylog(L)) for the mixing time of the chain, where L is the natural size of the system. The dynamics at a macroscopic scale should be described by a deterministic mean curvature motion such that each point of the surface feels a drift which tends to minimize the local surface tension (Spohn in J Stat Phys 71:1081–1132, 1993). Inspired by this heuristics, our approach consists in bounding the dynamics with an auxiliary one which, with very high probability, follows quite closely the deterministic mean curvature evolution. Key technical ingredients are monotonicity, coupling and an argument due to Wilson (Ann Appl Probab 14:274–325, 2004) in the framework of lozenge tiling Markov Chains. Our approach works equally well for both models despite the fact that their equilibrium maximal height fluctuations occur on very different scales (log L for monotone surfaces and \({\sqrt L}\) for the SOS model). Finally, combining techniques from kinetically constrained spin systems (Cancrini et al. in Probab Th Rel Fields 140:459–504, 2008) together with the above mixing time result, we prove an almost diffusive lower bound of order 1/L ²polylog(L) for the spectral gap of the SOS model with horizontal size L and unbounded heights.     

Polymer dynamics in the depinned phase: metastability with logarithmic barriers

We consider the stochastic evolution of a (1?+?1)-dimensional polymer in the depinned regime. At equilibrium the system exhibits a double well structure: the polymer lies (essentially) either above or below the repulsive line. As a consequence, one expects a metastable behavior with rare jumps between the two phases combined with a fast thermalization inside each phase. However, the energy barrier between these two phases is only logarithmic in the system size L and therefore the two relevant time scales are only polynomial in L with no clear-cut separation between them. The whole evolution is governed by a subtle competition between the diffusive behavior inside one phase and the jumps across the energy barriers. Our main results are: (i) a proof that the mixing time of the system lies between ${L^{\frac 5 2}}$ and ${L^{\frac 5 2 +2}}$ ; (ii) the identification of two regions associated with the positive and negative phase of the polymer together with the proof of the asymptotic exponentiality of the tunneling time between them with rate equal to a half of the spectral gap.     

Path integral for equities: Dynamic correlation and empirical analysis

This paper develops a model to describe the unequal time correlation between rate of returns of different stocks. A non-trivial fourth order derivative Lagrangian is defined to provide an unequal time propagator, which can be fitted to the market data. A calibration algorithm is designed to find the empirical parameters for this model and different de-noising methods are used to capture the signals concealed in the rate of return. The detailed results of this Gaussian model show that the different stocks can have strong correlation and the empirical unequal time correlator can be described by the model’s propagator. This preliminary study provides a novel model for the correlator of different instruments at different times.     

Electronic tongue based on an array of metallic potentiometric sensors

An electronic tongue system based on the array of six metallic potentiometric sensors (metallic wires) was developed and utilized for discrimination of foodstuffs: several types of vinegar and fruit juices. Copper, tin, iron, aluminum, brass and stainless steel wires were included in the array and supplemented by pH glass electrode. The response of potentiometric metallic sensors towards various organic acids has been studied and possible sensitivity mechanisms were discussed. Overall potential changes of metallic sensors were exanimate as complex mixed signals influenced by several components presenting in analyte employing chemometric approach. The multisensor array of such a type can be useful for several applications since of simplicity in handling, low cost of sensors and easy measure procedure.     

On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to ?). For β large enough we show that for any ${\varepsilon >0 }We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to −). For β large enough we show that for any ${\varepsilon >0 }${\varepsilon >0 } there exists c=c(b,e){c=c(\beta,\varepsilon)} such that the corresponding mixing time T _mix satisfies lim_L?￥ P(T_mix 3 exp(cL^e)) = 0{{\rm lim}_{L\to\infty}\,{\bf P}\left(T_{\rm mix}\ge {\rm exp}({cL^\varepsilon})\right) =0}. In the non-random case τ ≡ +  (or τ ≡ −), this implies that T_mix ￡ exp(cL^e){T_{\rm mix}\le {\rm exp}({cL^\varepsilon})}. The same bound holds when the boundary conditions are all +  on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior T _mix = O(L ²), considerably improves upon the previous known estimates of the form T_mix ￡ exp(c L^{\frac 12 + e}){T_{\rm mix}\le {\rm exp}({c L^{\frac 12 + \varepsilon}})}. The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.     

Transition Metal Carbides. Dependence of some thermochemical quantities on the chemical nature of reactants and stoichiometry of the product

Linear relationship were found among the plots of ΔH _{T ad} and ΔG ⁰ _{T ad} vs. the adiabatic reaction temperature (T _ad) for transition metals carbides and silicides characterised by the same stoichiometry. The slope of the straight line depends on the product stoichiometry. This revised version was published online in July 2006 with corrections to the Cover Date.     

Homo‐ and copolymerization of methyl methacrylate with ethylene by novel Ziegler‐Natta‐Type nickel catalysts based on N,O‐nitro‐substituted chelate ligands

New Nickel (II) catalytic systems based on N,O chelate ligands, activated by methylaluminoxane, have been checked in the homopolymerization of methyl methacrylate (MMA) and its copolymerization with ethylene. In particular, the bis(8‐hydroxy‐5‐nitro‐quinolate)nickel(II)/methylaluminoxane system as well as the catalysts obtained by oxidative addition of either 8‐hydroxy‐5‐nitro‐quinoline or 8‐hydroxy‐5,7‐dinitro‐quinoline or 4‐nitro‐2‐(p‐nitrobenzylideneamino)‐phenol to Ni(cod)₂, subsequently activated by methylaluminoxane, have been employed. The influence of the reaction parameters on the catalytic activity and the characteristics of the resulting polymers has been investigated. All the obtained poly(methyl methacrylate) samples display a largely prevailing syndiotacticity degree, high molecular weights and a rather large polydispersity. The catalytic systems obtained through the oxidative procedure are able also to give copolymers of MMA with ethylene producing highly linear polyethylenes containing a low amount (1.5–2 mol %) of MMA counits, thus affording materials with improved surface properties. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 620–633, 2006