Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Bcl-X-L translocation in renal tubular epithelial cells in vitro protects distal cells from oxidative stress

Background. The molecular pathogenesis of different sensitivities of the renal proximal and distal tubular cell populations to ischemic injury, including ischemia-reperfusion (IR)-induced oxidative stress, is not well-defined. An in vitro model of oxidative stress was used to compare the survival of distal [Madin-Darby canine kidney (MDCK)] and proximal [human kidney-2 (HK-2)] renal tubular epithelial cells, and to analyze for links between induced cell death and expression and localization of selected members of the Bcl-2 gene family (anti-apoptotic Bcl-2 and Bcl-X-L, pro-apoptotic Bax and Bad), Methods. Cells were treated with 1 mmol/L hydrogen peroxide (H2O2) Or were grown in control medium for 24 hours. Cell death (apoptosis) was quantitated using defined morphological criteria. DNA gel electrophoresis was used for biochemical identification. Protein expression levels and cellular localization of the selected Bcl-2 family proteins were analyzed (West ern immunoblots, densitometry, immunoelectron microscopy). Results. Apoptosis was minimal in control cultures and was greatest in treated proximal cell cultures (16.93 +/- 4.18% apoptosis) compared with treated distal cell cultures (2.28 +/- 0.85% apoptosis, P < 0.001). Endogenous expression of Bcl-X-L and Bax, but not Bcl-2 or Bad, was identified in control distal cells, Bcl-X-L and Bax had nonsignificant increases (P > 0.05) in these cells. Bcl-2, Bax, and Bcl-X-L, but not Bad, were endogenously expressed in control proximal cells. Bcl-X-L was significantly decreased in treated proximal cultures (P < 0.05), with Bas and Bcl-2 having nonsignificant increases (P > 0.05). Immunoelectron microscopy localization indicated that control and treated hut surviving proximal cells had similar cytosolic and membrane localization of the Bcl-2 proteins. In comparison, surviving cells in the treated distal cultures showed translocation of Bcl-X-L from cytosol to the mitochondria after treatment with H2O2, a result that was confirmed using cell fractionation and analysis of Bcl-XL expression levels of the membrane and cytosol proteins. Bax remained distributed evenly throughout the surviving distal cells, without particular attachment to any cellular organelle. Conclusion. The results indicate that in this in vitro model, the increased survival of distal compared with proximal tubular cells after oxidative stress is best explained by the decreased expression of anti-apoptotic Bcl-X-L in proximal cells, as well as translocation of Bcl-X-L protein to mitochondria within the surviving distal cells.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Back, chest and abdominal pain: How good are spinal signs at identifying musculoskeletal causes of back, chest or abdominal pain?

Background: Spinal signs found in association with atypical chest and abdominal pain may suggest the pain is referred from the thoracic spine. However, the prevalence of such signs in these conditions has rarely been compared with that in those without pain. In this study, the prevalence of spinal signs and dysfunction in patients with back, chest and abdominal pain is compared with that in pain free controls. The aim of the study is to determine the significance of spinal findings in patients with such pain. Methods: A general practitioner blinded to the patients' histories performed a cervical and thoracic spinal examination on general practice patients with back, chest and/or abdominal pain and on controls without pain. Thoracic intervertebral dysfunction was diagnosed on the basis of movement and palpation findings. Results: Seventy three study patients plus 24 controls, were examined. For cervical spinal signs, pain in the back, chest and/or abdomen was associated with pain with active movements and overpressure at end range and with loss of movement range. For thoracic spinal signs, this association held for pain with active movements and overpressure, but not with loss of movement range. The prevalence of thoracic intervertebral dysfunction was 25.0% in controls, 65.5% with chest/abdominal pain, 72.0% with back pain and 79.0% with back pain with chest/abdominal pain. This prevalence was higher with chest pain than with abdominal pain. Conclusions: The results show an association, but not a causal link between thoracic intervertebral dysfunction and atypical chest/abdominal pain. A spinal examination should be performed routinely assessing these conditions. The minimum examination for the detection of intervertebral dysfunction is testing for pain with spinal movements and palpation for tenderness. The interpretation of positive signs requires knowledge of their prevalence in pain free controls and in patients with visceral disease

The validity of self-reported energy intake as determined using the doubly labelled water technique

In the 1980s the development of the doubly labelled water (DLW) technique made it possible to determine the validity of dietary assessment methods using external, independent markers of intake in free-living populations. Since then, the accuracy of self-reported energy intake (EI) has been questioned on a number of occasions as under-reporting has been found to be prevalent in many different populations. This paper is a review of investigations using the DLW technique in conjunction with self-reported EI measures in groups including adults, children and adolescents, obese persons, athletes, military personnel and trekking explorers. In studies where a person other than the subject is responsible for recording dietary intake, such as parents of young children, EI generally corresponds to DLW determined energy expenditure. However, in instances where the subjects themselves report their intake, EI is generally under-reported when compared with energy expenditure. It was originally believed that this phenomenon of under-reporting was linked to increased adiposity and body size, however, it is now apparent that other factors, such as dietary restraint and socio-economic status, are also involved. This paper therefore aims to present a more comprehensive picture of under-reporting by tying in the findings of many DLW studies with other studies focusing particularly on the characteristics and mechanisms for under-reporting. Awareness of these characteristics and mechanisms will enable researchers to obtain more accurate self-reports of EI using all dietary recording techniques.

The radical homopolymerization of N-phenylmaleimide, N-n-hexylmaleimide and N-cyclohexylmaleimide in tetrahydrofuran

The kinetics and mechanisms of thermally initiated (using 2,2'-azobisisoburyronitrile (AIBN) as initiator) radical homopolymerizations of a series of maleimides, including N-phenymaleimide (PHMI) [l-phenyl-1H-pyrrole-2,5-dione]; N-n-hexylmaleimide (nHMI) [l-(n-hexyI)-1H-pyrrole-2,5-dione]; and N-cyclohexylmaIeimide (CHMI) [l-cyclohexyl- 1H-pyrrole-2,5-dione] have been investigated in THF solution by an on-line FT-NIR technique. It was found that the order of the activation energies for the three N-sub-MIs is: E-a PHMI < E-a (PHMI) < E-a (CHMI). The overall polymerization rate parameter k and the pre-exponential factor A were calculated. The kinetic order with respect to the N-sub-MIs was in the range of 0.71 < m < 0.75 for the initiator and n = 1.0 for the monomer. Radical transfer to solvent was found to be the key factor in determining the apparent order with respect to the initiator. All of the homopolymers had a relatively low molecular weight. The end groups of the polymer chains were characterized by MALDI-TOF, GPC and NMR methods and the results clearly indicate that the polymerization was initiated by THF radicals, and that the termination reaction is mainly controlled by chain transfer to solvent through an hydrogen abstraction mechanism. (C) 2001 Elsevier Science Ltd. All rights reserved.