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.     

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.     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Characterization of Metallo Bis(terpyridine) Diblock Polymers by Nonaqueous Capillary Zone Electrophoresis

A method of nonaqueous capillary zone electrophoresis (CZE) has been developed to characterize block (co)polymers of poly(ethylene oxide) and poly(styrene) containing metallo bis(terpyridine) complexes as bridging units. Specific CZE separation conditions had to be applied, with barium perchlorate dissolved in N-methylformamide (NMF) as background electrolyte and OV-1701-OH deactivated capillaries. For detection UV absorption was measured at a wavelength of 316 nm. Metallo diblock polymers with molecular weights up to 30,000 Da could be analyzed by the proposed nonaqueous CZE method. Experiments performed with polymeric compounds containing Fe, Ni or Ru as central metal ions showed that their electrophoretic mobilities were independent of the type of metal ion. Therefore, the data on the size of the polymeric compounds could be obtained using just one set of calibration standards. Polydispersities of the samples calculated from the experimental results were in correlation with the polydispersities of the polymers used in the synthesis of the metallo diblock polymers. Several polymeric samples contained metallo mono(terpyridine) complexes as impurities. These by-products could be separated from the main product. With symmetrical diblock polymers only one by-product was detected, while with an asymmetric diblock polymer two types of mono-complexes were found. The amount of the mono-complexes present as impurities was dependent on the type of central metal ion (Ni > Fe >> Ru).     

Discrete global descent method for discrete global optimization and nonlinear integer programming

A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10¹⁰⁴ feasible points have demonstrated the applicability and efficiency of the proposed method.     

Some aerodynamic and acoustic characteristicsof acute laryngitis

The purpose of the present study was to describe the effects ofacute laryngitis on some aerodynamic, acoustic, and perceptual measures. Eleven subjects with diagnosed acute laryngitis due to upper respiratory infection were recorded during a laryngitic episode and 1 week to 10 days after amelioration of the laryngitic condition. Fundamental frequency values, collapsed across the five vowels, were significantly reduced in the laryngitic compared with the normal speaking condition. The decrease in fundamental frequency associated with acute laryngitis suggests an increase in the mass of the vocal folds. In addition, aerodynamic values differed significantly for the laryngitic condition compared with the normal speaking condition, suggesting the presence of laryngeal hypofunction. Perceptual data indicated that speakers in the laryngitic condition were judged to have a hoarse voice when compared with the normal speaking condition.     

Correlation of Plasma Sprayed Coating Deposition Efficiency with Volume Flux Measurements by Phase Doppler Anemometry (PDA)

The use of phase-Doppler anemometry (PDA) to characterize the detail in-flight plasma sprayed particle behavior has been demonstrated previously [Ma et al. Plasma Chem Plasma Process 24(1):85; 25(1):56] The present articles shows further that a direct relationship may exist between the PDA measured particle volume flux and the coating microstructure and deposition efficiency (DE). In the situation when the precise particle temperature information is not available, the PDA measured particle volume flux may provide an alternative to predict quantitatively the variation of the coating microstructure and the DE. By monitoring the in-flight particle volume flux variations, instead of the particle velocity, size and temperature individually and simultaneously, the optimal settings of the plasma spraying parameters may also be determined conveniently. However, it is noted that the effective applications of such approach depend largely on the particle surface morphology and the pre-determination of the particle size range.     

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.     

A note on acyclic domination number in graphs of diameter two

A subset S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γ_a(G), is called the acyclic domination number of G. Hedetniemi et al. [Acyclic domination, Discrete Math. 222 (2000) 151-165] introduced the concept of acyclic domination and posed the following open problem: if δ(G) is the minimum degree of G, is γ_a(G)?δ(G) for any graph whose diameter is two? In this paper, we provide a negative answer to this question by showing that for any positive k, there is a graph G with diameter two such that γ_a(G)-δ(G)?k.