Model updating of the non-linear vibrating structures through Volterra series and proper orthogonal decomposition

Classical procedures for model updating in non-linear mechanical systems based on vibration data can fail because the common linear metrics are not sensitive for non-linear behavior caused by gaps, backlash, bolts, joints, materials, etc. Several strategies were proposed in the literature in order to allow a correct representative model of non-linear structures. The present paper evaluates the performance of two approaches based on different objective functions. The first one is a time domain methodology based on the proper orthogonal decomposition constructed from the output time histories. The second approach uses objective functions with multiples convolutions described by the first and second order discrete-time Volterra kernels. In order to discuss the results, a benchmark of a clamped-clamped beam with an pre-applied static load is simulated and updated using proper orthogonal decomposition and Volterra Series. The comparisons and discussions of the results show the practical applicability and drawbacks of both approaches.

The laurent series for the quaternionic case

The present work has the scope to show the Laurent Series for quaternionic functions. It will be shown that the Laurent Series for the Quaternionic Case is analogous to the textbook case of Complex Analysis [1]-[2] already well established.

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Square of the Error Octonionic Theorem and Hypercomplex Fourier Series

The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.

Do anticoagulant and antiplatelet agents prevent acute graft thrombosis in renal transplantation? A meta-analysis of case series studies

Introduction & Objectives: Thrombosis of the renal allograft is expected to occur in 1–6% of kidney transplants, and graft loss is expected in almost all cases. Anticoagulant and anti-platelet agents could serve as an adjunctive preventive measure, but sound evidence of benefits are still lacking, in this setting. We therefore assessed the efficacy and safety of anticoagulant and anti-platelet agents, in reducing the rate of renal allograft thrombosis. Methods: A review of the literature was carried out in major databases (MEDLINE, EMBASE and LILACS), with a comprehensive search strategy, to locate all available case series studies of anticoagulant and/or anti-platelet prophylaxis of thrombosis in renal transplantation. The date of the last search was 11 August 2014. We pooled all case series in a proportional meta-analysis. Statistical significance was achieved if the 95% confidence intervals obtained for each intervention did not overlap. Results: Our search strategy retrieved 7160 titles, from which 21 case series were chosen for analysis. A total of 3246 patients were identified (1718 treated with antiplatelet and/or anticoagulant agents, and 1528 non-treated control subjects). Allograft thrombosis occurred in 7.24% (95% CI 3.45 to 12.27%) of the patients receiving no intervention, compared to 3.38% (95% CI 1.45 to 6.1%), 1.2% (95% CI 0.6 to 2.1%) and 0.47% (95% CI 0.001 to 1.79%), in the anticoagulant, aspirin, and aspirin + anticoagulant groups, respectively. Bleeding complication rates were 28.0% (95% CI 15.4 to 42.7%) for anticoagulants, compared to 12.13% (95% CI 0.8 to 33.93%) for aspirin + anticoagulant, 0.31% (95% CI 0.0001 to 1.32%) for aspirin, and 6.1% (95% CI 2.2 to 11.7%) for the control group. Conclusions: Aspirin is more effective in reducing allograft thrombosis, after kidney transplantation, whether alone or in association with an anticoagulant, when compared to no drug prophylaxis, and without higher haemorrhagic complication rates. Anticoagulants, when used alone, do not show a beneficial effect on thrombosis rates, additionally yielding higher bleeding rates.