A Note on Ostrowski's Inequality

This paper deals with the problem of estimating the deviation of the values of a function from its mean value. We consider the following special cases: i) the case of random variables (attached to arbitrary probability fields); ii) the comparison is performed additively or multiplicatively; iii) the mean value is attached to a multiplicative averaging process

Wonders of Technology-Teaching Physics to Non-Scientists

Wonders of Technology is a conceptual physics course developed for non—science majors. The approach taken here in the introduction of the physical concepts is to depict their role in today’s technology, specifically the technology familiar to the students, and also to emphasize the connection between technology, art, and culture from the historical perspective. Why this approach? The traditional method of teaching physics is perceived by many students as user-unfriendly — they think physics is difficult, abstract, and, in fact, of little or no relevance to everyday life. The course Wonders of Technology alleviates this perception by placing the students on familiar ground that provides a fertile environment for an easier assimilation of knowledge. By examining the technology students use on a daily basis to demonstrate how physics makes things work, students are motivated to seek understanding of the principles underlying their operation. The course was developed within the guidelines of the new general education requirements at Virginia Commonwealth University. This presentation highlights some of the highly successful features of the newly developed course, with emphasis on responses from the education majors who are enrolled in the course

Attitudes in Physics Education: An Alternative Approach to Teaching Physics to Non-Science College Students

In this article, we present an alternative way of teaching conceptual physics for non-science majors by depicting the role of physics in today\u27s technology. The goal of this approach is to increase in the minds of non-science students the acceptance of physics as a useful component in general education, and as a major tool in comprehending the present-day technological world experienced by students outside the classroom

A NEW LOOK AT THE LYAPUNOV INEQUALITY

Given a Banach space E, it is proved that any function u in C2([a; b];E) verifies a Lyapunov inequality. The provided constant is sharp. Several applications are included

Controlling the Precision-Recall Tradeoff in Differential Dependency Network Analysis

Graphical models have gained a lot of attention recently as a tool for learning and representing dependencies among variables in multivariate data. Often, domain scientists are looking specifically for differences among the dependency networks of different conditions or populations (e.g. differences between regulatory networks of different species, or differences between dependency networks of diseased versus healthy populations). The standard method for finding these differences is to learn the dependency networks for each condition independently and compare them. We show that this approach is prone to high false discovery rates (low precision) that can render the analysis useless. We then show that by imposing a bias towards learning similar dependency networks for each condition the false discovery rates can be reduced to acceptable levels, at the cost of finding a reduced number of differences. Algorithms developed in the transfer learning literature can be used to vary the strength of the imposed similarity bias and provide a natural mechanism to smoothly adjust this differential precision-recall tradeoff to cater to the requirements of the analysis conducted. We present real case studies (oncological and neurological) where domain experts use the proposed technique to extract useful differential networks that shed light on the biological processes involved in cancer and brain function

The Hornich-Hlawka functional inequality for functions with positive differences

We analyze the role played by $n$-convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\left( x\right) +f\left( y\right) +f\left( z\right) +f\left( x+y+z\right) \geq f\left( x+y\right) +f\left( y+z\right)+f\left( z+x\right) +f(0),$ including extensions to the case of positive operators.Comment: 20 page