Group theoretic properties of Rijndael-like ciphers

We provide conditions for which the round functions of an ?-bit Rijndael-like block cipher generate the alternating group on the set {0,1}^?. These conditions show that the class of Rijndael-like ciphers whose round functions generate the alternating group on their message space is large, and includes both the actual Rijndael and the block cipher used by the compression function of the Whirlpool hash function. The result indicates that there is no trapdoor design for a Rijndael-like cipher based on the imprimitivity of the group action of its proper round functions which is difficult to detect.     

Structural elucidation of new ferulic acid-containing phenolic dimers and trimers isolated from maize bran

Four new phenolic dimers and trimers that contain ferulic acid moieties were isolated from the alkaline hydrolyzate of insoluble maize bran fiber and their structures were established by 1D/2D NMR and mass spectrometry. The biological role of one dimer remains unclear whereas the dimeric vanillin-ferulic acid-cross-product probably represents an oxidative degradation product from the corresponding diferulate. Both ferulic acid dehydrotrimers are able to cross-link polysaccharide chains. However, the 5-5/8-O-4(H₂O)-triferulic acid may be a cross-link in its identified structure whereas we assume that the identified 8-O-4/8-5(non-cyclic)-triferulic acid arose from a natural 8-O-4/8-5(cyclic)-triferulate analog during the saponification process.     

Convex bodies of constant width and constant brightness

In 1926 Nakajima (= Matsumura) showed that any convex body in R³ with constant width, constant brightness, and boundary of class C² is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness.     

Dual-Sampling-Rate Moving-Horizon Control of a Class of Linear Systems with Input Saturation and Plant Uncertainty

Moving-horizon control is a type of sampled-data feedback control in which the control over each sampling interval is determined by the solution of an open-loop optimal control problem. We develop a dual-sampling-rate moving-horizon control scheme for a class of linear, continuous-time plants with strict input saturation constraints in the presence of plant uncertainty and input disturbances. Our control scheme has two components: a slow-sampling moving-horizon controller for a nominal plant and a fast-sampling state-feedback controller whose function is to force the actual plant to emulate the nominal plant. The design of the moving-horizon controller takes into account the nonnegligible computation time required to compute the optimal control trajectory.We prove the local stability of the resulting feedback system and illustrate its performance with simulations. In these simulations, our dual-sampling-rate controller exhibits performance that is considerably superior to its single-sampling-rate moving-horizon controller counterpart.     

The Zig-Zag Property and Exponential Cancellation of Ordered Sets

This paper outlines a chapter in the theory of ordered sets that concerns decompositions of ordered sets using various natural operations introduced by Garrett Birkhoff in 1940 – chiefly, the operations of sum (disjoint union), Cartesian product, and exponentiation. This area has seen two brief, four-year flowerings of research activity during the past sixty-four years. Ivan Rival, working with several collaborators around 1978, obtained beautiful results on exponentiation which attracted other researchers to this topic. Altogether, about a dozen people contributed a chain of significant new results between 1978–1982. The subject then lay dormant until a major contribution by Jonathan D. Farley appeared in 1996. This pre-figured the solution, four years later, of a central problem about exponentiation of finite ordered sets that Birkhoff had formulated in 1942. The theory of operations on ordered sets is a beautiful chapter of mathematics. We concentrate on those portions that are most relevant for the solution of the Birkhoff problem, offering (hopefully) accessible proofs of many results, including some new results. We would like to see a new renaissance of activity in this area, which continues to offer many attractive open problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

UV light‐mediated alkylation of inorganic selenium

In the presence of low molecular weight organic acids (formic, acetic, propionic and malonic), inorganic selenium(IV) is converted by UV irradiation to volatile selenium carbonyl, dimethylselenide and diethylselenide, depending on the acid used. Gas chromatography–mass spectrometry analysis of the volatile products shows that, in 0.7 M formic acid solution, approximately 60–70% (v/v) SeH₂ and 30–40% (v/v) SeCO are formed. The presence of nitrate ion appears to increase threefold the formation of SeCO while completely suppressing formation of SeH₂. Copyright © 2003 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.     

Optical experiments beyond the quantum limit: Squeezing,entanglement, and teleportation

Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.     

Infrared studies of the effect of acetylene, hydrogen, and oxygen on CO adsorption on platinum hydrosols

Infrared spectra of CO-treated platinum hydrosols subsequently treated with acetylene, hydrogen, and oxygen reveal that v(CO)_ads decreases from 2070 cm⁻¹ with increasing gas-treatment time. This has been attributed to a reduction in the coverage of adsorbed CO. In Pt sol/CO/C₂H₂ systems, v(CO)_ads decreases to a limiting value of ca. 2060 cm⁻¹ after exposure to acetylene. In the Pt sol/CO/H₂ systems, v(CO)_ads decreases to ca. 2050 cm⁻¹ after exposure to hydrogen gas. The lower frequency in the Pt sol/CO/H₂ system has been attributed to CO adsorption on more active metal sites formed from the reduction of surface platinum oxides. Exposure of the CO-treated platinum hydrosols to O₂ gas was found to cause the eventual disappearance of the v(CO)_ads band in infrared spectra, which was attributed to oxidation of adsorbed CO to CO₂ by weakly bound surface layers of platinum oxides formed by the oxygen treatment.     

Synthesis and structural characterization of five new coordination polymer chain structures using a new,Z-shaped ligand, 2,2′-bis-(4-pyridylethynyl)tolane

Using the new ligand, 2,2-bis-(4-pyridylethynyl)tolane we have synthesized five new coordination polymers: HgBr₂[2,2-bis-(4-pyridylethynyl)tolane] (1), HgI₂[2,2-bis-(4-pyridylethynyl)tolane] (2), Ni(acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane] (3), Zn(acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane] (4), and Cu(hexafluoro acetylacetonate)₂[2,2-bis-(4-pyridylethynyl)tolane]CHCl₃ (5). 2,2-Bis-(4-pyridyl ethynyl)tolane is a rigid ligand with a Z-shape that promotes the formation of zig-zag chains. Compounds 1– 5 were characterized by single crystal X-ray diffraction; and compounds 1– 3 were additionally characterized by IR, elemental analysis, and thermogravimetric analysis. Compound 1 crystallizes in the monoclinic space group C2/c with a = 29.761(3) Å, b = 5.0531(5) Å, c = 16.7823(15) Å, = 104.090(2), V = 2447.9(4) ų, Z = 4. Each mercury is bound to two tolane ligands and two bromine anions, resulting in a tetrahedral coordination environment. Compound 2 crystallizes in the monoclinic space group P2/c, with a = 20.3061(17) Å, b = 5.6303(5) Å, c = 24.5459(19) Å, = 110.338(2), V = 2631.4(4) ų, Z = 4. Here also, each mercury is bound to two tolane ligands and two iodine anions in a tetrahedral coordination environment. The ligand orientation differs in compounds 1 and 2 being trans oriented in 1 and cis oriented in 2. Compound 3 crystallizes in the monoclinic space group P2₁/c with a = 14.5947(14) Å, b = 6.3082(6) Å, c = 18.3939(18) Å, = 112.112(2), V = 1568.9(3) ų, Z = 2. Each nickel is bound to two tolane ligands and two bidentate AcAc anions, resulting in an octahedral coordination environment. Compound 4, which is isostructural with 3, also crystallizes in the monoclinic space group P2₁/c with a = 14.6990(9) Å, b = 6.2724(4) Å, c = 18.6433(11) Å, = 112.8610(10), V = 1583.86(17) ų, Z = 2. Compound 5 crystallizes in the triclinic space group P-1 with a = 6.5487(4) Å, b = 11.6471(7) Å, c = 14.3225(9) Å, = 70.1360(10), = 89.3990(10), = 88.7680(10), V = 1027.18(11) ų, Z = 1. Each copper in 5 is bound to two tolane ligands and two bidentate hfAcAc anions, resulting in an octahedral coordination environment identical to that found in 3 and 4.     

Congruence modularity implies the Arguesian identity

It is shown that if is any variety of algebras all of whose congruence lattices are modular, then the congruence lattice of every algebra in satisfies the Arguesian law.