Form Of Mathematical Equations Research Articles

A comparative evaluation of analytical methods to allocate individual marks from a team mark

This study presents a comparative evaluation of analytical methods to allocate individual marks from a team mark. Only the methods that use or can be converted into some form of mathematical equations are analysed. Some of these methods focus primarily on the assessment of the quality of teamwork product (product assessment) while the others put greater emphasis on the assessment of teamwork performance (process assessment). The remaining methods try to strike a balance between product assessment and process assessment. To discuss the characteristics of these methods, graphical plots generated by the mathematical equations that collectively cover all possible team learning scenarios are discussed. Finally, a typical teamwork example is used to simplify the discussions. Although each of the methods discussed has its own merits for a particular application scenario, recent methods are relatively better in terms of a number of evaluation criteria.

Derivation of Material Constants in Non-Linear Electro-Magneto-Thermo-Elasticity

All the investigations on the mechanics and physics of electro-magneto-thermo-elastic materials are based on the set of constitutive equations in which the strain, electric displacement, and magnetic induction and entropy are expressed in terms of the stress, electric field, magnetic field and temperature. A concise formulation of relevant non-linear constitutive relations is presented in this paper. The electro-magneto-thermo-elastic materials show significant interaction among the elastic, electric, magnetic and thermal fields due to the coupled nature of constitutive equations. The thermodynamic Gibbs function of state describes stress, strain, internal energy, electric field, electric displacement, magnetic field, magnetic induction, temperature and entropy. The anisotropic non-linear problem of electro-magneto-thermo-elasticity has been derived on the basis of thermodynamic principle. The Gibbs function is expanded into Taylor series. Material constants have been analyzed from strain, electric displacement, magnetic induction and entropy which are in Gibbs function. In the form of mathematical equations, relationships of material constants have been shown. The derived coefficients (tensor components) of non-linear electro-magneto-thermo-elasticity are presented in tabular forms.

Bicriteria optimal design of open cross sections of cold-formed thin-walled beams

This paper presents a analysis of the problem of optimal design of the beams with two I-type cross section shapes. These types of beams are simply supported and subject to pure bending. The strength and stability conditions were formulated and analytically solved in the form of mathematical equations. Both global and selected types of local stability forms were taken into account. The optimization problem was defined as bicriteria. The cross section area of the beam is the first objective function, while the deflection of the beam is the second. The geometric parameters of cross section were selected as the design variables. The set of constraints includes global and local stability conditions, the strength condition, and technological and constructional requirements in the form of geometric relations. The optimization problem was formulated and solved with the help of the Pareto concept of optimality. During the numerical calculations a set of optimal compromise solutions was generated. The numerical procedures include discrete and continuous sets of the design variables. Results of numerical analysis are presented in the form of tables, cross section outlines and diagrams. Results are discussed at the end of the work. These results may be useful for designers in optimal designing of thin-walled beams, increasing information required in the decision-making procedure.

Trip generation rates and land use-transport planning in urban environment

In order to assess the land use policy implications, trip generation rates are essential knowledge for both planners and engineers working in the field. Within the framework of this paper trip generation rates are presented for the Thessaloniki Metropolitan Area (T.M.A.). The structure of the land use system in T.M.A. produces numerous problems the transportation system. The results of research activities of the Laboratory of Transportation Engineering of A.U.Th concerning trip generation rates regarding different land uses (education, administration, banks, cultural, hotel industry, hospitals) in T.M.A. are presented. These results are in the form of mathematical equations that have been derived with regression analysis and take into account data resulting from properly designed questionnaire surveys.

First material-adapted force hypothesis for calculating equivalent stress in human femurs

Strength hypotheses are assumptions, usually in the form of mathematical equations, which are applied in material science to convert multiaxial stress states in a material to a uniaxial stress state. Of particular interest regarding this conversion is the fact that the calculated uniaxial stress value in the material produces the same stress as the respective individual multiaxial stress. The "fictional" uniaxial stress determined in this way is also referred to as equivalent stress. Owing to the lack of experimental material data, many researchers and practitioners have in the past applied only the equivalent stress calculation based on the equations developed by von Mises under the assumption that the "material", bone, possesses isotropic properties. The present experimental work on selected human femora has been able for the first time, to quantify the anisotropy of these bones. At the same time a strength hypothesis has been formulated that can be used to convert multiaxial stress states for the material femoral bone to a uniaxial stress state (determination of equivalent stress).

Qualitative Simulation in Physiology with Bond Graphs

The simulation of a physiological system involves the construction of a model. generally in the form of mathematical equations. the manipulation of this model to obtain the solution of the equations, and finally the interpretation of the result. In a qualitative simulation, in a certain sense, we go directly from the real system to the interpretation without use of the mathematical model. This approach was introduced using artificial intelligence techniques, where we try to reproduce a human reasoning explaining the behavior of the physical system. The qualitative model is constituted by facts and functioning rules. However it is not easy to chose the cause and effect of a functioning rule well suited in each case. The main goal of the work is to present a methodology, based on bond graphs, and the causal stroke algorithm (CASA for short), to obtain the antecedent and consequent of rules, model that explains the functioning of a physiological system. To illustrate the methodology, it is discussed a qualitative dynamic compliance model of a ventricle.

A new look at chimney design

AbstractMaximum concentration formulas make it possible to limit ground‐level concentrations of pollutants.

APL continuous system modelling program: an interactive simulation language

APL continuous system modelling program (APL-CSMP) is an APL based compiler and simulator system that enables the user to define and execute mathematical equations which may contain certain predefined mathematical functions and special operation blocks, supplied by APL-CSMP. Facilities allowing definition and changing of parametric data, end conditions, error bounds for computations, selection of the integration method, and control of the display of the results produced by the simulation run can also be included within the model. The source language has a syntax very similar to that of CSMP-III. Models are directly entered via the APL terminal in the form of mathematical equations and analysed by a compiler. The result of the compilation is a set of automatically generated APL functions incorporating an APL program equivalent to the model.