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At least 37 records · Page 2Linked to original sources

PubMed2000

A structural model for predicting mathematics achievement: its relation with anxiety and self-concept in mathematics.

This study proposed and tested a model of mathematics achievement and its relations to antecedent and subsequent factors using structural equations modeling. A sample of elementary school students in Al-Ain school district (n = 394) completed an Arabic version of the Self-description Questionnaire as well as a questionnaire measuring their perception of the importance of mathematics, anxiety about it, and the amount of effort they exerted in studying. Mathematics grades were obtained from the official school records. Importance and effort were positively related to achievement which in turn had a positive path coefficient to self-concept and a negative path to anxiety. The hypothesized model explained 40%, 64%, and 73% of the variance in achievement, self-concept, and anxiety, respectively. The results can be interpreted as indicating that achievement is an important outcome and antecedent construct within the proposed model.

Achievement↗

PubMed1977

Cyclic kinetics and mathematical expression of the primary immune response to soluble antigen. VII. The conveyer hypothesis and its mathematical expression.

The conveyer hypothesis is based on the fact that because of clone predetermination, antibody production takes place in an organism without the presence of antigen as a result of natural cell differentiation. Soluble antigen is an analogue of a specific mitogen which gives rise to reproduction mainly of cells carrying on their surface the immunoglobulin receptors to the given antigen. The mathematical model of the conveyer hypothesis takes into account the initial conditions, among them the background level of antibody-producing cells before injection of a soluble antigen, migration of precursor cells in the draining lymphoid organ, and the rate of precursor differentiation, including the rate of the change of the immunoglobulin receptor number on the cell surface. Changes of antigen concentration in blood determine the intensity of precursor proliferation. Comparison of real experiments (intraperitoneal injections of capsular antigen of Pasteurella pestis into inbred mice) with calculations done on the basis of the developed mathematical model shows a definite qualitative resemblance with the kinetics of antibody-producing cells and free antibodies as well as with the decrease of free antigen concentration in blood. In spite of some differences between model experiments and real experiments the conveyer hypothesis and its mathematical model appear suitable for describing the primary immune response of mice immunized with low doses of capsular antigen of Pasteurella pestis.

Animals↗

PubMed1991

Mathematical model of antiviral immune response regulation. II. Mathematical formalization of the modelled processes. Imitation of acute course of hepatitis B.

The mathematical formalization of the conceptual model for antiviral immune response regulation described in the preceding report was carried out. The mathematical model is presented as a system of 30 ordinary nonlinear differential equations with delays. The algorithm for numerical integration of the mathematical model is based on Gear's methods of variable step and variable order. Initial conditions and parameters, as well as intervals of plausible values for them, were chosen for adaptation of the model for description of acute hepatitis B.

Acute Disease↗

PubMed1983

Mathematical immunogenetics I. Mathematics as language.

This paper summarizes approaches to developing mathematics that can act as a language for immunogenetics. The need for this has been documented by showing inadequacies of the standard symbolism. Apparent distinctions in symbolizing and conceptualizing factors involved in immunogenetics are seen to disappear in the mathematical models presented here. One model, a three-fold Boolean matrix factorization, subsumes all approaches to the idea of specificity and yet is general enough to incorporate data beyond that found only in a reaction matrix.

Antibody Specificity↗

PubMed2002

A preliminary study of achievement, attitudes toward success in mathematics, and mathematics anxiety with technology-based instruction in brief calculus.

This study was designed to compare achievement, attitudes toward success in mathematics, and mathematics anxiety of college students taught brief calculus using a graphic calculator, with the achievement and attitudes and anxiety of students taught using the computer algebra system Maple, using a technology based text book. 50 men and 50 women, students in three classes at a large public university in the southwestern United States, participated. Students' achievement in brief calculus was measured by performance on a teacher-made achievement test given at the end of the study. Analysis of variance showed no significant difference in achievement between the groups. To measure change in attitudes and anxiety, responses to paper-and-pencil inventories indicated significant differences in favor of students using the computer.

Adolescent↗

PubMedDate not supplied

[Interactive determination of the parameters of mathematical models for planning radiotherapy of malignant tumors. I. Mathematical models for calculating dose tolerance, adequate doses and the likelihood of development of radiation complications in normal organs and tissues].

Mathematical models for calculating tolerance doses, adequate doses and the likelihood of radiation complications in the body's normal tissues are considered. To determine the parameters of these models that describe the outcomes of radiation exposure of complicated biological systems, a method of local adjustment of the parameters of the models has been developed, which will be described in parts 2 and 3 of the proposed paper. In part 1 (the present paper), particular emphasis is laid on the inclusion of an important parameter, such as a volume, into Ellis and LQ models. A mathematical model is presented for calculating the likelihood of a radiation complication in the tissue, which is the basis for deriving a formula to calculate an adequate uniform tissue radiation dose that is equivalent to the nonuniform tissue distribution of a dose in terms of the likelihood of radiation complications.

Humans↗

PubMed1989

Quantitative and morphological studies of the bones by mathematical morphology--theory and practice of mathematical morphology.

To quantitatively analyze internal bone structures, trabecular bones were quantitatively studied through the application of mathematical morphology. Mathematical morphology considers the shape of the analyze objects and utilizes image processing theory in an approach that is extremely effective on for studying the complex shapes of trabecular bones. This paper describes quantitative studies made of trabecular bone density and width, trabecular specific length per unit area, and trabecular bone orientation.

Bone Density↗

PubMed1985

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells.

A mathematical model of glycolysis in human erythrocytes is proposed to study the influence of a pyruvate kinase deficiency on the energy metabolism. The model takes into account the main regulatory properties of the non-equilibrium enzymes and the magnesium-complex formation by the adenine nucleotides and by 2,3-bisphosphoglycerate. In the normal case (no enzyme defect) the calculated flux rates and metabolite concentrations are in a good agreement with experimental data. It is shown that a severe pyruvate kinase deficiency manifested in a tenfold diminished activity of that enzyme leads to a remarkable decrease of the glycolytic flux and the ATP concentration of about 50% of the normal values. On the other hand a lowering of the pyruvate kinase activity to half of the normal value, characteristic for the heterozygotes, gives no significant alterations of the metabolite concentrations and the flux rates compared with the normal case which is in accordance with the lack of clinical symptoms for a metabolic disease of these probands. For three patients with known alterations of their pyruvate kinase mutants the calculated metabolite concentrations and the control characteristics permit estimation of the degree of disorder of the glycolytic pathway. The resulting classification corresponds well to other independent experimental and clinical findings. In particular, the calculation demonstrates that there is no simple correlation between the lowered enzyme activity and the reduced flux rate through the affected pathway.

Adenosine Triphosphate↗

PubMed1981

A mathematical model for the analysis of the turnover of protein mixtures I. General mathematical formalism.

In tracer experiments which are mostly performed to determine the rate of protein turnover the treatment of protein degradation as a first-order reaction leads to a monoexponential function as a representation of the decrease of the initial labelling. In a protein mixture, however, the assumption of a single turnover constant is no more admissible. The analysis of curves by a sum of exponential functions is only a makeshift and is level less appropriate if protein degradation is only a partial process in a complex model. -- As in the cell (or, more generally, in a biological object) a multitude of proteins with very different turnover constants is present, continuous distributions of protein synthesis rates and turnover constants are proposed. The hypothesis is made that the distributions of the two quantities are independent of each other. A number of arguments lead to a gamma distribution for the turnover constants. On this basis a model for protein turnover consisting of a homogeneous pool (soluble amino acid) and an inhomogeneous one (proteins) is proposed and mathematically described by a system of integro-differential equations which is not analytically solvable in the general case. The distribution of the relative protein amount in dependence on the turnover constant as well as quantities characterizing the inhomogeneous protein pool are discussed. The analysis of a case of full dependence between synthesis and degradation rates shows the usefulness of the model also beyond its original range of validity.

Kinetics↗

PubMed2003