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At least 19 recordsLinked to original sources
PubMed1999

Graph-set analysis of hydrogen-bond patterns: some mathematical concepts.

To provide a foundation for further theoretical and software development of the application of graph sets to patterns of hydrogen bonding and other intermolecular interactions a number of mathematical concepts and tools are defined, developed and demonstrated. Following a review of the basic definitions and uses of graph sets, the directional properties of hydrogen bonds are now included in the treatment. The concepts of a constructor graph and covalent distance matrix have been developed to aid in the generation of a qualitative descriptor for the straightforward, consistent and ultimately automatic (with appropriate software) definition of patterns. An additional mathematical tool, the arrowed T-labeling, has been developed to deal with situations in which pattern-forming moieties are located on crystallographic special positions. To demonstrate the utility and various features of these concepts they are applied in detail to two particular structures, polymorphic iminodiacetic acid [N-(carboxymethyl)glycine] and trans-tetraamminedinitrocobalt(III) acetate. To facilitate the application and use of graph sets many of these developments have already been incorporated into the software of the Cambridge Structural Database, as described in the accompanying paper.

Journal Article↗
PubMed2000

Graph-set analysis of hydrogen-bond patterns: some mathematical concepts

To provide a foundation for further theoretical and software development of the application of graph sets to patterns of hydrogen bonding and other intermolecular interactions a number of mathematical concepts and tools are defined, developed and demonstrated. Following a review of the basic definitions and uses of graph sets, the directional properties of hydrogen bonds are now included in the treatment. The concepts of a constructor graph and covalent distance matrix have been developed to aid in the generation of a qualitative descriptor for the straightforward, consistent and ultimately automatic (with appropriate software) definition of patterns. An additional mathematical tool, the arrowed T-labeling, has been developed to deal with situations in which pattern-forming moieties are located on crystallographic special positions. To demonstrate the utility and various features of these concepts they are applied in detail to two particular structures, polymorphic iminodiacetic acid [N-(carboxymethyl)glycine] and trans-tetraamminedinitrocobalt(III) acetate. To facilitate the application and use of graph sets many of these developments have already been incorporated into the software of the Cambridge Structural Database, as described in the accompanying paper.

Journal Article↗
PubMed1979

Role of mathematical concepts in cancer research.

The role of mathematics in cancer research is not confined to epidemiology (population level). The expected contribution of it in various levels is exemplified stepwise. At the individual level, prediction of life expectancy of a cancer case or psychological analysis of life-threatened patient; at the tissue level, stochastic estimation of future metastases; at the cellular level, model contruction for abnormal metabolic processes in malignant cell; at the molecular level, elucidation of carcinogenetic mechanism from a thermodynamic standpoint of view.

Forecasting↗
PubMed1994

What do we mean by normal? The mathematical concept and social dimension of normality.

1. Normality has a mathematical definition as well as a social dimension. 2. It is essential to consider the social dimension when formulating care. 3. Concepts of normality differ according to an individual's life experiences, which are shaped by age, sex, gender, race, culture and social class. 4. Concepts of normality also vary in accordance with the group defining it--for example, the developers of social policy, the recipients of that policy and the rest of the society concerned.

Age Factors↗
PubMed1989

[Medicine and symmetry. On the use of a mathematical concept in the early writings of the Corpus Hippocraticum].

The conception of symmetry in medical texts of the 5th century has never been connected with the development of the mathematical theory of proportions. However, we can find in Alcmaion and the hippocratic writings de vetere medicina, de natura hominis and de victu the differentiation between an arithmetical determinable measure and a qualitative determinable measure which is defined by a common lógos for incommensurable sizes. In de vetere medicina and de victu we see a conception of proportion and symmetry/commensurability, which requires the discovery of incommensurability. This discovery can be connected with the greek mathematician Hippocrates of Chios and his theorems of doubling the cube. We can detect an answer to this revolutionary development in mathematics in the methodological ideas of medical writers, who wanted to turn away medicine from the anti-descriptive and anti-empirical attitude in mathematics and philosophy.

Greece, Ancient↗
PubMed2005

Nigerian undergraduate education majors' conceptions of mathematics.

The Conceptions of Mathematics Questionnaire by Crawford, et al. was administered to 130 southwest Nigerian undergraduate education majors who took mathematics. Coefficient alphas of .86 and .84 for the Fragmented and Cohesive subscales were similar to prior values. There were no statistically significant mean differences between men and women or between undergraduates taking mathematics with science and nonscience topics.

Adolescent↗