Products of sets: Ordered and unordered

In this article we study the (Cartesian) Products of sets. As a prelude to it, we examine various definitions offered by different mathematicians to the concept of an ordered pair. The subtle difference between the notions of ordered products of sets and unordered products of sets is highlighted.     

Situation of Divorced Mothers in India: Implications for Counseling

In a culture where high premium is placed on marriage, a divorced mother faces many challenges. Striving for shelter and economic security is harder due to lack of social acceptance, support and inadequate services. For a counsellor the social realities are as important as the psychological ones.This article is based on the observations and experiences of the author who has been a marriage counsellor at the first Family Court in India.     

Lyman Spitzer: Life,times, and science

Lyman Spitzer was one of the major figures of twentieth century theoretical astrophysics. Over more than fifty years, he kept up sustained research of his own, on problems concerning the interstellar medium, star formation, and galaxies. In addition he was a major influence on observational programmes, and created a thriving school of theoretical astrophysics at Princeton University along with a strong plasma physics programme. This article brings out his contributions, placing them in context.     

Distribution of H.pylori antigens in gastric mucosa and its significance

INTRODUCTION Helicobacter pylori (H.pylori) was grouped as a class I carcinogen by the International Agency for Research on Cancer in 1994. A direct relation be-tween H.pylori infection and gastric carcinogenesis was demonstrated in 1998 in an experimental animal model (Watanabe et al., 1998). However, the role of H.pylori in human gastric carcinogenesis is sup-ported almost exclusively by epidemiological data and prospective histopathological studies. So far the mechanism of H.pylor…     

“I have a Preschool Buddy” Exploring the Role of High School Students in Facilitating the Pre-academic Skills and Social Development of Preschool Children

The purpose of this research is to explore the role of a director of a preschool program who mentors and trains high school students to teach and work directly with preschool children in the context of individual lessons, small group activities, and large group instruction. This participant-observer research study also examines how the director assesses the high school students ability to work effectively with the preschoolers they are assigned to teach and addresses the pre-academic and social learner outcomes for these children in this unique preschool program. Parent feedback pertaining to preschool learning outcomes is also examined.     

Intersections of two offset parametric surfaces based on topology analysis

Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the topological relations between different intersection loops and calculates intersection loops with the help of previously calculated intersection loops. It first pre-processes two parametric surfaces to obtain the characteristic points, called topology transition points (TTPs), which can help in the subsequent finding of the topologies of the intersection curves. Then these points are categorized into several distinct groups, and we can determine the calculation strategy for searching initial points by analyzing the properties of these TTPs on the surfaces. Hence, all intersection curves can be marched from initial points by the tracing algorithm. The proposed algorithm could calculate intersection curves robustly and effectively, and has been tested to be capable of overcoming the degenerate conditions such as loop and singularities leaking that occur frequently in conventional algorithms. Project supported by the National Research Foundation for the Doctoral Program (No. 2000033554) of Higher Education of China and the Natural Science Foundation of Zhejiang Province, China (No. 6001107)     

MFV-Class: a multi-faceted visualization tool of object classes

Classes are key software components in an object-oriented software system. In many industrial OO software systems,there are some classes that have complicated structure and relationships. So in the processes of software maintenance,testing,software reengineering,software reuse and software restructure,it is a challenge for software engineers to understand these classes thoroughly. This paper proposes a class comprehension model based on constructivist learning theory,and implements a software visualization tool(MFV-Class)to help in the comprehension of a class. The tool provides multiple views of class to uncover manifold facets of class contents. It enables visualizing three object-oriented metrics of classes to help users focus on the understanding process. A case study was conducted to evaluate our approach and the toolkit.     

Exploring the atmosphere with lidars

In Part 1¹, we described the basic principle of the lidar (Light Detection and Ranging), the different scattering processes in the atmosphere and the Mie and Rayleigh lidars. In this part, we describe three other types of lidars: Raman lidar, differential absorption lidar (DIAL) and doppler lidar. A lidar system consists of a pulsed laser which sends out pulses of laser light and a sensor that senses the scattered light from the different molecules and aerosols in the atmosphere. The characteristics of the scattered light are used to determine the nature and amount of the constituents.     

Simulation of electron motion in fields — An interactive teaching aid

Conclusion Since the input parameters and conditions/situations are defined by students to see the quantitative effects displayed on the screen, this C programme becomes an interesting and interactive teaching aid. The two simulation modules can be used to determine e/m using the principle proposed in Thomson’s method.