Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Failure to Achieve PSA Level ≤I ng/ml Following Neo-Adjuvant LHRHa Therapy Predicts for a Lower Biochemical Control Rate and Overall Survival in Localized Prostate Cancer Treated with Radiotherapy

PURPOSE: To investigate whether failure to suppress the prostate-specific antigen (PSA) level to /=2 months of neoadjuvant luteinizing hormone-releasing hormone agonist therapy in patients scheduled to undergo external beam radiotherapy for localized prostate carcinoma is associated with reduced biochemical failure-free survival. METHODS AND MATERIALS: A retrospective case note review of consecutive patients with intermediate- or high-risk localized prostate cancer treated between January 2001 and December 2002 with neoadjuvant hormonal deprivation therapy, followed by concurrent hormonal therapy and radiotherapy was performed. Patient data were divided for analysis according to whether the PSA level in Week 1 of radiotherapy was 1 ng/mL in 52. At a median follow-up of 49 months, the 4-year actuarial biochemical failure-free survival rate was 84% vs. 60% (p = 0.0016) in favor of the patients with a PSA level after neoadjuvant hormonal deprivation therapy of 1 ng/mL at the beginning of external beam radiotherapy after >/=2 months of neoadjuvant luteinizing hormone-releasing hormone agonist therapy have a significantly greater rate of biochemical failure and lower survival rate compared with those with a PSA level of

Maternal mental health and non-organic failure to thrive.

This study reports on the first phase of a large-scale, longitudinal, multidisciplinary community study examining the growth, learning and development of young children with a particular focus on failure to thrive without organic cause. However, the group identified in this study may be better described as weight faltering. This paper examines the psychological data collected using the Parenting Stress Index, Rosenberg Self-Esteem and the General Health Questionnaire in relation to child growth. There were no significant differences between the mothers of the weight faltering and control children in terms of parenting stress, maternal depression, maternal perceptions of their parenting competence or maternal self-esteem. Maternal sensitivity to comments about child size, regardless of direction, had a negative impact on mood.