Normalizable operators

AbstractAs a common generalization of normal operators and strictly dissipative operators, the class of normalizable operators is introduced and studied in the finite-dimensional case. Results on simultaneous normalizability are also included

Inequalities for proper contractions and strictly dissipative operators

AbstractSome inequalities for proper contractions and strictly dissipative operators on a Hilbert space are proved. These inequalities for operators are related to the classical Harnack's inequalities for analytic functions with a positive real part

Temporal lobe resection for intractable epilepsy: review of 11 cases

OBJECTIVE. To review the management of medically intractable epilepsy by performing temporal lobe resection. DESIGN. Retrospective study. SETTING. University teaching hospital, Hong Kong. PATIENTS. Eleven patients: seven women and four men (mean age, 28 years; range, 19-49 years) who underwent temporal lobe resection for intractable epilepsy from 1994 through 1998. MAIN OUTCOME MEASURES. Preoperative and operative aspects of treatment, postoperative complications, mortality, and seizure control before and after surgery. RESULTS. All but one patient had long-standing medically intractable temporal lobe epilepsy; the duration between the onset of seizure and surgery ranged from 12 to 27 years (mean, 17.2 years). A total of 12 resections were performed without any mortalities or major postoperative complications. After surgery, two patients became seizure-free without the need for antiepileptic medication; six patients were seizure-free but required medication; and two patients showed >90% of improvement in seizure control, whereas one patient showed between 50% and 90% of improvement. Nine (81%) of the 11 patients reported significant improvement in their social life and performance of daily activities. Two (18%) patients, including one with improved seizure control, reported no improvement in their performance of daily functions. CONCLUSIONS. Temporal lobe resection can produce significant improvements in patients who have medically intractable epilepsy. The risks of surgery are relatively small and justifiable.published_or_final_versio

Effective modulus of polycrystalline aggregates in different geometrical configurations

In the present study, a finite element scheme with random distribution strategy is employed to systematically investigate the modulus difference of polycrystalline copper aggregates in different geometrical configurations (three-dimensional bulk and thin film configurations). Firstly, the finite element simulation is performed to estimate the effective elastic constants in three-dimensional bulk configuration. The numerical estimations are in good agreement with the existing analytical solutions and experimental measurements. Secondly, the proven finite element scheme is extended to the prediction of the effective moduli of the free-standing and substrate-attached thin films. For the free-standing thin film, the effective Young's modulus decreases with reducing the film thickness. For the substrate-attached thin film, its effective modulus is affected by the relative stiffness between the substrate and the film. The spread of the effective moduli in different configurations could be as large as 20%. © 2010 Elsevier B.V.postprin

Four- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problem

In this paper, four- and eight-node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane Helmholtz problems. In these models, frame (boundary) and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from Trefftz solution sets. The equality of the two approximations are enforced along the element boundary. Both the Bessel and plane wave solutions are employed to construct the domain approximation. For full rankness, a minimal of four and eight domain modes are required for the four- and eight-node elements, respectively. By using local coordinates and directions, rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised. In most tests, the proposed hybrid-Trefftz elements with the same number of nodes yield close solutions. In absolute majority of the tests, the proposed elements are considerably more accurate than their single-field counterparts. © 2009 Elsevier B.V. All rights reserved.postprin

Electric assumptions for piezoelectric laminate analysis

In computational analysis of piezoelectric laminates which may comprise piezoelectric and non-piezoelectric plies, the transverse electric field is often assumed to be piecewise constant along the transverse direction. This conventional assumption may lead to significant errors unless the piezoelectric ply is considerably thinner than the overall thickness of the laminate. To this end, two alternate assumptions termed EL and DC on the spatial distributions of the electric variables are proposed. In EL, the transverse electric field is taken to be piecewise linear along the transverse direction. In the DC assumption, the transverse electric displacement is taken to be piecewise constant along the transverse direction. The rationales leading to the proposed assumptions are discussed. Numerical examples indicate that the proposed assumptions are markedly more accurate than the conventional one. However, EL becomes inaccurate when its piecewise function spans more than one ply. In this light, DC often consumes less electric potential d.o.f.s and is more efficient than EL. © 2003 Elsevier Ltd. All rights reserved.postprin