let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular...

In scientiic studies objects are often very rough. Mathematically these rough objects are modeled by fractal functions, and fractal dimension is usually used to measure their roughness. The present paper investigates fractal function estimation by wavelet shrinkage. It is shown that wavelet shrinkage can estimate fractal functions with their fractal dimensions virtually preserved.

In [5], W. Taylor shows that each particular compact polyhedron can be characterized in the class of all metrizable spaces containing an arc by means of first order properties of its clone of continuous operations. We will show that such a characterization is possible in the class of compact spaces and in the class of Hausdorff spaces containing an arc. Moreover, our characterization uses only ...

By Gelfand-Neumark duality, the category C∗Alg of commutative C∗algebras is dually equivalent to the category of compact Hausdorff spaces, which by Stone duality, is also dually equivalent to the category uba` of uniformly complete bounded Archimedean `-algebras. Consequently, C∗Alg is equivalent to uba`, and this equivalence can be described through complexification. In this article we study u...

Box-counting dimension is one of the most widely used fractal dimensions, because it is relatively easy for empirical estimation. Unfortunately, the task is simple only if one operates on oneor twodimensional data. Otherwise, the amount of computation grows exponentially with the number of space coordinates.A newmethod of estimation of the box-counting dimension of multivariate objects using sp...

BACKGROUND There is little robust evidence relating to changes in health related quality of life (HRQL) in morbidly obese patients following a multidisciplinary non-surgical weight loss program or laparoscopic Roux-en-Y Gastric Bypass (RYGB). The aim of the present study was to describe and compare changes in five dimensions of HRQL in morbidly obese subjects. In addition, we wanted to assess t...

OBJECTIVES To assess the relationship between social integration and physical and mental health among humanitarian migrants (HMs) in Australia. DESIGN, SETTING AND PARTICIPANTS We used the recently released first wave of data from the 2013 'Building a New Life in Australia' survey, which is an ongoing nationwide longitudinal study. A total of 2399 HMs participated in the survey. MAIN OUTCOM...

The concepts of entropy and dimension as applied to dynamical systems are reviewed from a physical point of view. The information dimension, which measures the rate at which the information contained in a probability density scales with resolution, fills a logical gap in the classification of attractors in terms of metric entropy, fractal dimension, and topological entropy. Several examples are...

abstract aim and background: multiple sclerosis is a chronic neurological disorder which is more prevalent in women than men. therefore, the aim of present study was to evaluate the relationship physical functioning impairment (as criterion variable) with fatigue, psychological symptoms and body mass index (as predictive variables) in the women suffering from this disease. methods and materials...