A comment on the potential in heavy quarkonium quantum-mechanical systems

I discuss the characteristics of the non-relativistic potential responsible for the ψ and ? systems. In particular a comparison is made between the recently advocated flavour independent power behaved potential and the QCD inspired Coulomb + linear potential. The ratios $\text{ΔM}{}_{\mathrm{?}}\text{ΔM}{}_{\mathrm{\psi }}$ of radical excitation energy level differences are used as sensitive tests to the r dependence of V(r). Deviations of these ratios from a constant value may indicate a gradual increase in the effective power of the potentials as r increases (in agreement with the Coulomb + linear potential). Decisive tests have to come from the not yet discovered toponium family where the ratios $\text{ΔM}{}_{\mathrm{T}}\text{ΔM?}$ should start to become greater than 1 if a singularity of the potential exists at r → 0.     

Conditions for equality of decomposable symmetric tensors. II.

We derive consequences of a condition for the equality of two star products given by the second author. We also study another method for the same problem which consists of comparing the components, in an appropriate basis, of the star products involved.     

Alkaline side-coordination strategy for the design of nickel(II) and nickel(III) bis(1,2-diselenolene) complex based materials

The deprotonated form of the pyrazine-2,3-diselenol (pds) ligand, pds(2-), reacts with Ni(II) inorganic salts to form the nickel compounds [Ni(II)(pds)(2)](nBu(4)N)(2) (1), [Ni(II)(pds)(2)]Na(2).2H(2)O (2), and [Ni(III)(pds)(2)](2)Na(2).4H(2)O (3), depending on the reaction conditions. They are characterized by NMR, EPR, UV-vis, and IR spectroscopies, elemental analysis, cyclic voltammetry, and X-ray crystallography. The crystal structure of compound 3 shows the formation of segregated stacks of Ni(pds)(2-) units, with a strong dimerization along the stacks. The stacked fashion of the crystal packing was expected since the supramolecular forces of the alkaline side coordination to the pyrazine moieties dominate, as happens in the recently reported analogous copper system [Cu(III)(pds)(2)]Na.2H(2)O. The structure of 2 further emphasizes the alkaline coordination as the dominating supramolecular event, and an orthogonal array of 2D layers is observed. The absence of alkaline cations in complex 1 is reflected in a crystal packing with isolated complex Ni(pds)(2)(2-) units. The dimerization found in the paramagnetic Ni(III) complex 3 promotes a very strong antiferromagnetic interaction, leading to a singlet ground state.     

Discrimination among eight modified michaelis-menten kinetics models of cellulose hydrolysis with a large range of substrate/enzyme ratios

The kinetics of exoglucanase (Cel7A) from Trichoderma reesei was investigated in the presence of cellobiose and 24 different enzyme/Avicel ratios for 47 h, in order to establish which of the eight available kinetic models best explained the factors involved. The heterogeneous catalysis was studied and the kinetic parameters were estimated employing integrated forms of Michaelis-Menten equations through the use of nonlinear least squares. It was found that cellulose hydrolysis follows a model that takes into account competitive inhibition by cellobiose (final product) with the following parameters: Km = 3.8 mM, Kic = 0.041 mM, kcat = 2 h-1 (5.6 x 10-4 s-1). Other models, such as mixed type inhibition and those incorporating improvements concerning inhibition by substrate and parabolic inhibition, increased the modulation performance very slightly. The results support the hypothesis that nonproductive enzyme substrate complexes, parabolic inhibition, and enzyme inactivation (Selwyn test) are not the principal constraints in enzymatic cellulose hydrolysis. Under our conditions, the increment in hydrolysis was not significant for substrate/enzyme ratios <6.5.