2-Normalization of lattices

Let τ be a type of algebras. A valuation of terms of type τ is a function v assigning to each term t of type τ a value v(t) ⩾ 0. For k ⩾ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to valuation v) if either s = t or both s and t have value ⩾ k. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called k-normal (with respect to the valuation v) if all its identities are k-normal. For any variety V, there is a least k-normal variety N _k (V) containing V, namely the variety determined by the set of all k-normal identities of V. The concept of k-normalization was introduced by K. Denecke and S. L. Wismath in their paper (Algebra Univers., 50, 2003, pp.107–128) and an algebraic characterization of the elements of N _k (V) in terms of the algebras in V was given in (Algebra Univers., 51, 2004, pp. 395–409). In this paper we study the algebras of the variety N ₂(V) where V is the type (2, 2) variety L of lattices and our valuation is the usual depth valuation of terms. We introduce a construction called the 3-level inflation of a lattice, and use the order-theoretic properties of lattices to show that the variety N ₂(L) is precisely the class of all 3-level inflations of lattices. We also produce a finite equational basis for the variety N ₂(L). This research was supported by Research Project MSM6198959214 of the Czech Government and by NSERC of Canada.     

Enhanced broadband optical transmission in metallized woodpiles

We present an optimized isotropic metal deposition technique used for covering three-dimensional polymer structures with a 50 nm smooth silver layer. The technology allows fast and isotropic coating of complex 3D dielectric structures with thin silver layers. Transmission measurements of 3D metallized woodpiles reveal a new phenomenon of enhanced optical transmission in broadband range (up to 300 nm) in the near IR.     

Electrochemical Characteristics of Poly(<Emphasis Type="Italic">o</Emphasis>-Aminobenzoic Acid) Modified Glassy-Carbon Electrode and Its Electrocatalytic Activity towards Oxidation of Epinephrine

Poly(o-aminobenzoic acid) (o-ABA) film is deposited on glassy-carbon electrode (GCE) by electropolymerization in pH 7.0 phosphate buffer solution (PBS). Electrochemical behavior of modified electrode is investigated by electrochemical impedance spectroscopy (EIS), different pulse voltammetry (DPV), and cyclic voltammetry (CV). The results indicate that there is a greater resistance during the electron transfer process in poly(o-ABA) film than in bare GCE for the redox of [Fe(CN)₆]³⁻/[Fe(CN)₆]⁴⁻. Further research indicates that epinephrine (EP) can be strongly absorbed on the surface of the poly(o-ABA) film-modified electrode. The modified electrode shows an excellent electrocatalytical activity on EP oxidation. The EP cathodic peak potential shifts negatively with a slope of −53.5 mV/pH, indicating that equal amounts of proton and electron are involved in the electrode reaction process. In pH 7.0 PBS, the peak current of EP and the concentration has a linear relationship from 0 to 65 μM by amperometric current-time curve. __________ From Elektrokhimiya, Vol. 41, No. 9, 2005, pp. 1059–1065. Original English Text Copyright ? 2005 by Cheng, Jin, Zhang. The text was submitted by the authors in English.