Asymptotic behaviour of Gaussian random fields

Summary Let X={X(t), t ^N} be a centred Gaussian random field with covariance X(t)X(s)=r(t–s) continuous on ^N×^N and r(0)=1. Let (t,s)=((X(t)–X(s)) ²)^1/2; (t,s) is a pseudometric on ^N. Assume X is -separable. Let D ₁ be the unit cube in ^N and for 0<k, D _k= {x^N: k ^–1 xD₁}, Z(k)=sup{X(t),tD _k}. If X is sample continuous and ¦r(t)¦ =o(1/log¦t¦) as ¦t¦8 then Z(k)-(2Nlogk) ^1/20 as k a.s.     

Knoevenagel Condensation Catalyzed by a Mexican Bentonite Using Infrared Irradiation

Diethyl malonate undergoes condensation with aromatic aldehydes without solvents. in the presence of a Mexican bentonite using infrared irradiation as the energy source, to give the benzylidenemalonate compounds in fair yield.     

Bis­(diethyl­enetri­amine-κ3N)­nickel(II) 5-amino-1,3,4-thia­diazo­le-2-sulfonamidate chloride monohydrate

In the X-ray crystal structure of the title complex, [Ni(C₄H₁₃N₃)₂](C₂H₃N₄O₂S₂)Cl·H₂O, the coordination polyhedron is composed of non-centrosymmetric [Ni(diethyl­enetri­amine)₂]²⁺ cations in which the tri­amine ligands coordinate to the metal centre as tridentate ligands in a facial position. The Ni^II ions are linked to six N atoms in an octahedral arrangement, slightly compressed in one extreme. The sulfon­amide behaves as a counter-ion instead of as a ligand. Important information about the deprotonated sulfon­amide group conformation has been obtained.     

Kinetics and dynamics of the NH3 + H → NH2 + H2 reaction using transition state methods, quasi-classical trajectories, and quantum-mechanical scattering

On a recent analytical potential energy surface developed by two of the authors, an exhaustive kinetics study, using variational transition state theory with multidimensional tunneling effect, and dynamics study, using both quasi-classical trajectory and full-dimensional quantum scattering methods, was carried out to understand the reactivity of the NH(3) + H → NH(2) + H(2) gas-phase reaction. Initial state-selected time-dependent wave packet calculations using a full-dimensional model were performed, where the total reaction probabilities were calculated for the initial ground vibrational state and for four excited vibrational states of ammonia. Thermal rate constants were calculated for the temperature range 200-2000 K using the three methods and compared with available experimental data. We found that (a) the total reaction probabilities are very small, (b) the symmetric and asymmetric N-H stretch excitations enhance the reactivity, (c) the quantum-mechanical calculated thermal rate constants are about one order of magnitude smaller than the transition state theory results, which reproduce the experimental evidence, and (d) quasi-classical trajectory calculations, which were performed with the main goal of analyzing the influence of the zero-point energy problem on the final dynamics results, reproduce the quantum scattering calculations on the same surface.     

Cimetidine complexes derived from cobalt(II), nickel(II) and copper(II) salts of polyatomic anions

Summary Cobalt(II), nickel(II) and copper(II) complexes [M(CM)₂]X₂ (X = BF₄ or NO₃) have been prepared with cimetidine (CM). Powder data, molar conductivities, magnetic moments, i.r. and electronic spectra support apseudo-octahedral stereochemistry with MN₂N ₂ S₂ chromophore and tentative structures are proposed for the complexes. Their properties are compared with these of previously prepared complexes.     

Dealing with the inventory risk: a solution to the market making problem

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho and Stoll (J Fin Econ 9(1): 47–73, 1981) and formalized mathematically by Avellaneda and Stoikov (Quant Fin 8(3):217–224, 2008). The market is modeled using a reference price S _t following a Brownian motion with standard deviation σ, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price S _t and a market maker maximizes the expected utility of its P&L over a finite time horizon. We show that the Hamilton–Jacobi–Bellman equations associated to the stochastic optimal control problem can be transformed into a system of linear ordinary differential equations and we solve the market making problem under inventory constraints. We also shed light on the asymptotic behavior of the optimal quotes and propose closed-form approximations based on a spectral characterization of the optimal quotes.