Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property

We give an explicit formula for the solution to the initial value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szeg\"{o}, and is also interpreted as a consequence of the QR factorization method of Symes \cite{symes}. The sorting property of the dynamics is also proved for the case of a generic symmetric matrix in the sense described in the text, and generalizations of tridiagonal formulae are given for the case of matrices with $2M+1$ nonzero diagonals.Comment: 13 pages, Latex

Iso-spectral deformations of general matrix and their reductions on Lie algebras

We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we consider several reductions of the hierarchy. These include not only the integrable systems studied by Bogoyavlensky and Kostant, but also their generalizations which were not known to be integrable before. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time.Comment: 25 pages, AMSLaTe

Lymphocyte reactivity in patients with carcinoma of the breast and large bowel.

The reactivity of lymphocytes from patients with either carcinoma of the breast or large bowel has been studied using the human to mouse normal lymphocyte transfer (NLT) reaction. It was found that, in the case of breast cancer, there was a direct correlation between the clinical stage and a reduced NLT reaction. Only patients with regional lymph node or generalized metastases showed significantly reduced lymphocyte reactivity. However, in the case of large bowel cancer there was a generalized reduction in NLT reactivity which was independent of the clinical stage. Incubation of lymphocytes from individuals without neoplastic disease in serum or plasma from breast cancer patients, showing reduced NLT reactivity, resulted in a reduced NLT reaction. This appears to be indicative of the presence of circulating "blocking factor" in such patients

A new parenting-based group intervention for young anxious children: results of a randomized controlled trial

Objective Despite recent advances, there are still no interventions that have been developed for the specific treatment of young children who have anxiety disorders. This study examined the impact of a new, cognitive–behaviorally based parenting intervention on anxiety symptoms. Method Families of 74 anxious children (aged 9 years or less) took part in a randomized controlled trial, which compared the new 10-session, group-format intervention with a wait-list control condition. Outcome measures included blinded diagnostic interview and self-reports from parents and children. Results Intention-to-treat analyses indicated that children whose parent(s) received the intervention were significantly less anxious at the end of the study than those in the control condition. Specifically, 57% of those receiving the new intervention were free of their primary disorder, compared with 15% in the control condition. Moreover, 32% of treated children were free of any anxiety diagnosis at the end of the treatment period, compared with 6% of those in the control group. Treatment gains were maintained at 12-month follow-up. Conclusions This new parenting-based intervention may represent an advance in the treatment of this previously neglected group. Clinical trial registration information: Anxiety in Young Children: A Randomized Controlled Trial of a New Cognitive-Behaviourally Based Parenting Intervention; http://www.isrctn.org/; ISRCTN12166762