On the orthogonality of natural modes of vibration

The natural modes of a discrete linear system are orthogonal with respect to the mass and stiffness matrices in a generalized sense. However, these modes are usually not orthogonal to each other in the ordinary sense. The purpose of this paper is to document a number of conditions under which the modes are also orthogonal in an ordinary fashion.     

Synthesis and characterization of oxidized cellulose

Samples of oxidized cellulose (OC) with various carboxyl contents and degrees of crystallinity were obtained by the oxidation of native and mercerized cellulose with a solution of nitrogen(IV) oxide in CCl₄. A detailed characterization of these OC samples was performed. The effect of oxidation conditions (concentration of N₂O₄ in the solution and oxidation time) and starting cellulose material on OC characteristics (carboxyl, carbonyl and nitrogen content, degree of crystallinity and polymerization, surface area and swelling, and acidic properties) was investigated. Reactivity in the oxidation process was higher in mercerized cellulose than in native cellulose. The action of dilute solutions (10–15%) of N₂O₄ did not affect the degree of crystallinity of cellulose samples. Under these conditions, the oxidation took place mainly in amorphous regions and on the surface of crystallites. Oxidation in a concentrated (40%) N₂O₄ solution led to the destruction of crystallites, which increased the surface area and swelling of cellulose in water. The surface area and the swelling of OC samples increased with a decrease in the index of crystallinity. The acidic properties of OC were shown to increase with an increase of swelling in water. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4785–4791, 2004     

Desorption behavior of a surfactant in a linear low‐density polyethylene blend at elevated temperatures

The desorption behavior of a surfactant in a linear low‐density polyethylene (LLDPE) blend at elevated temperatures of 50, 70, and 80 °C was studied with Fourier transform infrared spectroscopy. The composition of the LLDPE blend was 70:30 LLDPE/low‐density polyethylene. Three different specimens (II, III, and IV) were prepared with various compositions of a small molecular penetrant, sorbitan palmitate (SPAN‐40), and a migration controller, poly(ethylene acrylic acid) (EAA), in the LLDPE blend. The calculated diffusion coefficient (D) of SPAN‐40 in specimens II, III, and IV, between 50 and 80 °C, varied from 1.74 × 10^?11 to 6.79 × 10^?11 cm²/s, from 1.10 × 10^?11 to 5.75 × 10^?11 cm²/s, and from 0.58 × 10^?11 to 4.75 × 10^?11 cm²/s, respectively. In addition, the calculated activation energies (E_D) of specimens II, III, and IV, from the plotting of ln D versus 1/T between 50 and 80 °C, were 42.9, 52.7, and 65.6 kJ/mol, respectively. These values were different from those obtained between 25 and 50 °C and were believed to have been influenced by the interference of Tinuvin (a UV stabilizer) at elevated temperatures higher than 50 °C. Although the desorption rate of SPAN‐40 increased with the temperature and decreased with the EAA content, the observed spectral behavior did not depend on the temperature and time. For all specimens stored over 50 °C, the peak at 1739 cm^?1 decreased in a few days and subsequently increased with a peak shift toward 1730 cm^?1. This arose from the carbonyl stretching vibration of Tinuvin, possibly because of oxidation or degradation at elevated temperatures. In addition, the incorporation of EAA into the LLDPE blend suppressed the desorption rate of SPAN‐40 and retarded the appearance of the 1730 cm^?1 peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1114–1126, 2004     

Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms

We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6].     

A Characterisation of Posets that Are nearly Antichains

We present a characterisation of posets of size n with linear discrepancy n − 2. These are the posets that are “furthest” from a linear order without being an antichain. This revised version was published online in September 2006 with corrections to the Cover Date.     

Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Boundary position feedback control of Kirchhoff's non‐linear strings

This paper is concerned with global stabilization of an undamped non‐linear string in the case where any velocity feedback is not available. The linearized system has an infinite number of poles and zeros on the imaginary axis. In the case where any velocity feedback is not available, a parallel compensator is effective. The stabilizer is constructed for the augmented system which consists of the controlled system and a parallel compensator. It is proved that the string can be stabilized by linear boundary control. Copyright © 2003 John Wiley & Sons, Ltd.     

Delta and singular delta locus for one‐dimensional systems of conservation laws

This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left‐hand side value of Riemann data, the condition obtained in the paper describes a set of possible right‐hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau‐type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd.     

Pointwise stabilization of strings with non‐linear feedback

We consider an initial and boundary value problem for a homogenous string subject to an internal pointwise control. The solution resulting from a non‐linear feedback is studied. We give various explicit decay estimates depending on the control position and the feedback non‐linearity. Copyright © 2004 John Wiley & Sons, Ltd.