A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Experimental investigation of liquid flow shift due to gas cross flow in non-wetted packed beds

An experimental study has been carried out for the gas-liquid two-phase flow in a packed bed simulating conditions of the gas and liquid flows in the lower part of blast furnace. The localised liquid flow phenomenon in presence of gas cross flow, which usually occurs around the cohesive zone and raceway in blast furnace, was investigated in detail. Such liquid flow is characterised in terms of liquid shift distance or liquid shift angle that can effectively be measured by the experiments involved in the current study. It is found that liquid shift angle does not significantly increase or decrease with different packing depth. This finding supports the hypothesis of the force balance model where a vectorial relationship among acting forces, i.e. gas drag force, gravitational force and solid-liquid friction force, and liquid shift angle does exist. Liquid shift angle is inversely proportional to particle size and liquid density, and proportional to square of gas superficial velocity, but is almost independent on liquid flowrate and liquid viscosity. The gas-liquid drag coefficient, an important aspect for quantifying the interaction between gas and liquid flows, was conceptually modified based on the discrete feature of liquid flow through a packed bed and evaluated by the combined theoretical and experimental investigation. Experimental measurements suggest that the gas-liquid drag coefficient is approximately a constant (C-DG(')=5.4+/-1.0) and is independent on liquid properties, gas velocity and packing structure. The result shows a good agreement with previous experimental data and prediction of the existing liquid flow model.

Using postoperative cardiac troponin-I (cTi) levels to detect myocardial ischaemia in patients undergoing vascular surgery

Background, Cardiac complications occur commonly in vascular surgery patients. Diagnosis of cardiac complications is difficult because of the inaccuracies associated with traditional cardiac enzyme measurements. CTi, a highly sensitive and specific marker of myocardial injury, may be able to detect cardiac complications with greater ease and accuracy. Methods. The study prospectively examined 100 consecutive patients who underwent major vascular surgery between 6/7/98 and 31/12/98 at the Royal Brisbane Hospital. Daily measurements of cTi, creatine kinase (CK), creatine kinase MB (CKMB), CKMB index, renal function and haemoglobin were taken for three postoperative days. One postoperative electrocardiograph (ECC) was taken. An extensive cardiac history was taken. Intraoperative and postoperative events were recorded. Findings. There were 100 patients, 18 patients (18%) had a cTi elevation. On the basis of classical diagnostic criteria, 15 patients (15%) suffered one or more cardiac complication (either myocardial infarction, congestive cardiac failure, unstable angina or atrial fibrillation), One patient (1%) who had a cTi elevation died. CTI elevation occurred in five patients (5%) who were not diagnosed with cardiac complications based on traditional criteria. Despite not meeting specific diagnostic criteria for cardiac complications, all patients showed signs and symptoms that could be attributed to myocardial ischaemia, Every patient who developed congestive cardiac failure or atrial fibrillation had a cTi elevation. A Chi-square analysis revealed a significant association between cTi elevation and postoperative cardiac complications. Four variables contributed small but significant amounts of unique variance to the prediction of peak cTi on linear regression analysis. These were peak CKMB index, postoperative congestive cardiac failure, postoperative chest pain and postoperative cardiac complications. Conclusions. Routine cTi monitoring of postoperative vascular patients would be an effective and inexpensive way to detect patients with cardiac complications. The relationship between postoperative cTi elevation and significant coronary artery disease remains to be shown, (C) 2001 The international Society for Cardiovascular Surgery. Published by Elsevier Science Ltd. All rights reserved.

Effect of leucaena supplementation level, and provision of urea, on utilisation by sheep of Rhodes grass hay

Tarramba leucaena (Leucaena leucocephala cv. Tarramba) foliage had per kilogram dry matter, 169 g protein and 29.8 g condensed tannins. Its value as a supplement, given either with or without urea, to sheep given a low-quality Callide Rhodes grass (Chloris gayana cv. Callide) hay was studied. Six rumen fistulated sheep (mean +/- s.d. liveweight, 34 +/- 1.4 kg) were used to compare 6 dietary treatments in an incomplete latin square design. Rhodes grass hay was given ad libitum either alone, or with urea 7 g/day (U), or with leucaena 150 g/day (L150), or leucaena with urea (L150U), or leucaena 300 g/day (L300), or leucaena with urea (L300U). Digestible organic matter intake was increased significantly by leucaena supplementation although digestibility of the whole diet did not alter. Rumen fluid ammonia-N was not altered by leucaena supplementation, but was increased by urea. This suggests that Tarramba foliage protein has some resistance to ruminal degradation. Liquid and solids passage rates were not affected by the treatments. Microbial nitrogen supply to the intestine (g/day), and the efficiency of microbial nitrogen synthesis (g/kg organic matter apparently digested in the rumen), were increased by leucaena supplementation (P

Thue's theorem and the diophantine equation x2 - Dy2 = ±N

A constructive version of a theorem of Thue is used to provide representations of certain integers as x(2) - Dy-2, where D = 2, 3, 5, 6, 7.

On the Hamilton-Waterloo problem

The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling

We study, with exact diagonalization, the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V, to the bandwidth drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is in agreement with the observed optical conductivity of several layered molecular crystals with the theta and beta crystal structures.

The metamorphosis of lambda-fold K-3,K-3-designs into lambda-fold 6-cycle systems

In this paper necessary and sufficient conditions are given for the metamorphosis of a lambda-fold K-3,K-3-design of order n into a lambda-fold 6-cycle system of order n, by retaining one 6-cycle subgraph from each copy of K-3,K-3, and then rearranging the set of all the remaining edges, three from each K-3,K-3, into further 6-cycles so that the result is a lambda-fold 6-cycle system.

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.