Upper Bounds for the Betti Numbers of a given Hilbert Function

From a Macaulay's paper it follows that a lex-segment ideal has the greatest number of generators (the 0-th Betti number \b_0) among all the homogeneous ideals with the same Hilbert function. In this paper we prove that this fact extends to every Betti number, in the sense that all the Betti numbers of a minimal free resolution of a lex segment ideal are bigger than or equal to the ones of any homogeneous ideal with the same Hilbert function.Comment: 18 pages, plain te

Non commutative geometry and super Yang-Mills theory

We aim to connect the non commutative geometry ``quotient space'' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size \Sigma / N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification.Comment: 11 pages, LaTeX, two .gif files of (hand sketched) figures; a misprint corrected and some references adde

A note on discrete light cone quantization

In this brief note we would like to discuss, in a simple model system, the conditions under which the discrete light cone quantization framework should be trusted as an approximation scheme, with regard, in particular, to the size and mass of the system. Specifically, we are going to discuss ``quark-antiquark'' bound states in 1+1 dim., for which a natural size is provided by analogy with a ``two points and a spring'' system, and show that the condition for obtaining a reliable estimate is the same as the one derived in a recent paper for black holes in matrix theory.Comment: 4 pages, LaTeX; two misprints and a reference correcte

A Comparison of Quality of Life Measures in Husbands of Women with Breast Cancer

The Quality of Well-Being Scale (QWB-SA) and Medical Outcome Study SF-36 short form (SF-36) are popular health-related quality of life (HRQOL) assessment tools; however, it is unclear whether these measures overlap enough to be interchangeable, and if not, which might be a better choice. This study examined conceptual overlap, validity, and relation with psychosocial functioning of the QWB-SA and SF-36 in a sample of partners of women undergoing adjuvant treatment for breast cancer. Partners (n = 79) of breast cancer patients, recruited in a chemotherapy infusion clinic, completed the QWB-SA and SF-36 and additional psychosocial measures. Descriptive content review shows that both instruments provide a breadth of HRQOL coverage including physical health, mental health, social functioning, role functioning and general health perceptions; however, more QWB-SA scales suffered floor effects. Subscales correlated, with the strongest correlations between the QWB-SA total score and the mental health scales of the SF-36. The QWB-SA and the SF-36 Mental Health Component Summary score, but not the SF-36 Physical Component Summary score were strongly correlated to measures of mood, satisfaction with life, burden, and social support. The QWB-SA and SF-36 measure distinct aspects of HRQOL. Each instrument presents distinct advantages and disadvantages in coverage of particular domains. Labels assigned to SF-36 scales more accurately reflect what they measure. The SF-36 appeared more sensitive to the impact that psychological health played on overall assessment of HRQOL in these partners