Mathematical Considerations Research Articles

Mathematics in sport: II

Newton's laws and coded sequences are used to explore sport mathematically. Track and field athletics, American, association, Gaelic and rugby football, golf, rowing, skating, snooker and hockey, among others, provide illustrations. Mathematical considerations include classical mechanics; linear and angular momentum, work, impulse, kinetic and gravitational energy, simple harmonic motion, friction, rolling, rotating frames, Euler angles and projectiles. Some mathematical tools used are differential and integral calculus, vectors and vector spaces, dot and cross products, multiple integrals, orthogonal coordinate systems, fluid mechanics, invariance principles, non‐Abelian algebra, matrices, variational principles, optimization, trigonometry, coordinate geometry, modelling, set theory, transverse and longitudinal waves, elementary statistics, dimensional analysis, combinatorics, partitions and prime numbers, parity, encryption and codes. It is concluded that at all levels of education, primary, secondary and tertiary, sport and games may be used to illustrate and motivate mathematics and for that matter, physics. In paper II, we concentrate on mathematical and physical constants, analysis of performance and codes and encryption.

Mathematics in sport I

Newton's laws and coded sequences are used to explore sport mathematically. Track and field athletics, American, association, Gaelic and rugby football, golf, rowing, skating, snooker and hockey, among others, provide illustrations. Mathematical considerations include classical mechanics; linear and angular momentum, work, impulse, kinetic and gravitational energy, simple harmonic motion, friction, rolling, rotating frames, Euler angles and projectiles. Some mathematical tools used are differential and integral calculus, vectors and vector spaces, dot and cross products, multiple integrals, orthogonal coordinate systems, fluid mechanics, invariance principles, non‐Abelian algebra, matrices, variational principles, optimization, trigonometry, coordinate geometry, modelling, set theory, transverse and longitudinal waves, elementary statistics, dimensional analysis, combinatorics, partitions and prime numbers, parity, encryption and codes. It is concluded that at all levels of education, primary, secondary and tertiary, sport and games may be used to illustrate and motivate mathematics and for that matter, physics. In paper I, we concentrate on natural impulse and spin.

The solution of adsorption integral equations by means of the regularization method

AbstractAn overall adsorption quantity for a heterogeneous solid is usually expressed by an integral equation, which contains a distribution function that describes heterogeneous properties of this solid. The calculation of this distribution function is an ill‐posed problem. The current article shows that the difficulties arising from the ill‐posed nature of an adsorption equation can be overcome with the regularization method. This work presents general principles of regularization for solving the ill‐posed problems without detailed mathematical considerations. The application of the regularization method to calculate a distribution function from any overall adsorption functions is illustrated with both simulated and experimental adsorption isotherms.

On the TEHL Theory. Part I: Dimensionless Problem Formulation

Since the thermoelastohydrodynamic and elastohydrodynamic lubrication (TEHL and EHL) problems are predominantly heat transfer (HT) and/or fluid mechanics (FM) problems, it is proposed that the pertinent dimensionless quantities defined, in some instances tabulated, and commonly used in these branches of engineering science (HT and FM) should be used consistently and uniformly throughout for TEHL and EHL studies. In support of this, it is shown by some mathematical considerations that the published dimensionless quantities (in the TEHL and the EHL problems) can be converted into HT and FM parameters—such as the Reynolds number, Euler number, Eckert number, Prandtl number or Fourier modulus. It is indicated that such parameters have an immediately recognizable physical meaning.

Chapter 3 Reflection and communication: Cognitive considerations in school mathematics reform

The mathematics education reform efforts in the United States are shaped partially by our understanding of how students learn mathematics. Two traditions in psychology influence our current thinking most forcefully — cognitive psychology with its emphasis on individual mental operations and social cognition with its emphasis on context and group interaction. Reflection and communication, as cognitive processes and as representatives of these respective traditions, are used to establish the cognitive-based rationale for the reform and to analyze the nature of recommended changes. Issues addressed include the interdependence of reflection and communication and the way in which these processes can be used to analyze aspects of the school mathematics program, such as the way textbooks ordinarily treat written symbols. Although the theoretical arguments for reflection and communication are being increasingly well-articulated, the empirical data that address the claims are comparatively sparse. Future research efforts should aim to test theoretical claims for reflection and communication and to increase our understanding of the relationships between these cognitive processes and learning mathematics.

A new, modified acid phosphatase assay for determining the extent of heat treatment in canned hams

A modified acid phosphatase assay is presented in this paper for indication of heat treatment in canned hams. Adequate blending of the sample, increased substrate concentration and working at the pH optimum in the reaction mixture considerably improved the sensitivity of the method. Difficulties arose with the use of concentrated meat slurries: high rate of adsorption of released phenol from phenyl phosphate and reduced activities for the high level of endogenous competitive inhibitors (phosphates). Taking the thermal processing curve of Lind as reference, a heat treatment equivalent F c{70°C} = 80 min value is provisionally proposed (at Z = 6.94°C) for the central area of the cans instead of the not unambiguous end-point temperature regulation ( 69° C 156° F ). This F c value assures the destruction of heat resistant Streptococci in the product. However, at present, such F c and Z values are not available for the FMD virus. An adequate inspection system, based on mathematical statistical considerations is also briefly discussed here. In conclusion, results of this study indicate that the new, modified method has potential for the successful and rather simple measurement of the extent of heating in canned hams.

Some mathematical considerations on two-mode searching II

Along the lines of a previous paper (Seno [2]), making use of an intuitive model, we consider mathematically the relation between the efficiency of searcher’s two-mode searching behavior and the target’s patchy distribution, and discuss the strategic adaptability of two-mode searching. In this paper, the model is constructed by a time-discrete stochastic process on S1, that is, on a circle. It can be regarded as a modification of Model 2 analyzed in Seno [2]. Differently from Model 2, the searcher’s present location is assumed to be influenced by the past passage configuration. This modification yields some particular results for the present model. Also in the present model, if the patch size becomes sufficiently small, a two-mode searching behavior is strategically adaptable for the searcher. In this model, two-mode searching behavior has high strategic adaptability. Moreover, two-mode searching with an outstanding behavior change is strategically rather adaptable. As for the target’s distribution, it appears that a particular patchy distribution is likely to be adopted, depending on the searcher’s searching strategy. This result obviously indicates that the target’s distribution may be adopted as its evolutionary strategy against the searcher, like a relation between a patchy distributed prey and its predator.

Use of model solutions in random sequential adsorption on a lattice.

We consider random sequential adsorption on a lattice. We use analytical results on the Bethe lattice and cactus as references to develop systematic perturbationlike expansions which are very rapidly convergent. The latter produces the jamming density of a square lattice with an accuracy within 10{sup {minus}5}. This expansion is based on both physical and mathematical considerations and is not restricted to random sequential adsorption.

Mechano-mathematical model of cardiac fibre length-pressure pulsations

On the basis of mechanical and mathematical considerations a nonlinear autonomic dynamic model, describing the left ventricle pulsations in terms of contractile length and internal ventrical pressure is deduced. It is shown under defined conditions the model behaves as a relaxant system, which is investigated quantitatively and qualitatively by asymptotic and phase analysis respectively. Bifurcation analysis of the model transitions from relaxant behavior to another ones is presented. Haemodynamic interpretation of the obtained results, orientated to propose a hypothesis for arterial hypertension and hypotension genesis is made.

Alternative specifications of state variables in stochastic-dynamic-programming models of reservoir operation

Stochastic dynamic programming (SDP) has been one of the techniques most commonly used in the solution of the strategic (long-range) problem of reservoir operation. This technique requires the definition of a state vector, which commonly defines two variables: the amount of water in storage in the reservoir at the beginning of a time period and the total inflow of water. Two versions of this formulation are commonly used: one considers the total inflow in the past period of time; the other uses the inflow forecast for the current period. As a result of using SDP and under Markovian assumptions, a steady-state policy for the operation of the reservoir is always obtained. Nevertheless, and because the differences involved in the definition of the state vector on the abovementioned versions, their steady-state policies are not always the same. Looking at the definition of the state vector of those versions, the former has the advantage of not dealing with forecasted information. However, some mathematical considerations indicating that the latter could be more desirable than the former under condition of reliable forecasts are presented in this paper.

The inner ear as an electrosensory sense organ

A model for cochlear perception is introduced based on the consideration that the organ of Corti is an electrosensory organ like that found in fish physiology during phylogenetic development. The inner hair cells work as electroreceptors, the outer hair cells as electrocytes. A layer of potassium ions on the lower surface of the tectorial membrane causes the excitation of the inner hair cells as soon as contact with a stereocilium occurs. A model for the basilar membrane motion, based on mathematical considerations and in accordance with the typical tuning curves of single auditory nerve fibres can serve as basis to explain the results of frequency and intensity analyses if we assume an electric excitation of the inner hair cells.

Some mathematical considerations on two-mode searching I

Some mathematical considerations on two-mode searching I

Approximate inertial manifolds and effective viscosity in turbulent flows

The recently formulated concept of approximate inertial manifolds is exploited as a means for eliminating systematically the fine structure of the velocity field in two-dimensional flows. The resulting iterative procedure does not invoke any statistical properties of the solutions of Navier–Stokes equations. It leads to a modification of those equations, such that effective viscosity-like terms arise in a natural way. The rigorous mathematical considerations can be related to the corresponding physical concepts and intuition. The result leading to a numerical algorithm, essentially a nonlinear Galerkin method, provides a basis for large eddy simulation in which the subgrid model is derived from the properties of the Navier–Stokes equations, rather than from more or less justifiable ad hoc arguments. Some limited speculations concerning the expected results in three dimensions are also offered.

Further aspects of the kinetic compensation effect

Mathematical considerations are used to show that the existence of an isokinetic point does not always indicate the kinetic compensation effect as a result of physicochemical reasons. The correlation of the Arrhenius parameters is given for both the inappropriate kinetic model function and the working temperature interval.

On some morphological principles in botany arising from mathematical considerations

On etudie dans cet article l'apparence morphologique des plantes a travers des modeles geometriques et statiques puis on examine quelques caracteres-cles des processus de croissance a la lumiere des proprietes de certains systemes differentiels.

Estimating N2 fixation by Sesbania rostrata and S. cannabina (syn. S. aculeata) in lowland rice soil by the 15N dilution method

A field experiment in concrete-based plots was conducted to estimate the contribution of N derived from air (Ndfa) or biological N2 fixation in Sesbania rostrata and S. cannabina (syn. S. aculeata), using various references, by the 15N dilution method. The two Sesbania species as N2-fixing reference plants and four aquatic weed species as non-N2-fixing references were grown for 65 days after sowing in two consecutive crops, in the dry and the wet seasons, under flooded conditions. Soil previously labeled with 15N at 0.26 atom % 15N excess in mineralizable N was further labeled by ammonium sulfate with 3 and 6 atom % 15N excess. The results showed that 15N enrichment of soil NH 4 + -N dropped exponentially in the first crop to half the original level in 50 days while in the second crop, it declined gradually to half the level in 130 days. The decline in 15N enrichment, in both N2-fixing and non-fixing species, was also steeper in the first crop than in the second crop. Variations in 15N enrichment among non-fixing species were smaller in the second crop. The ratio of the uptake of soil N to that of fertilizer N in N2-fixing and non-fixing species was estimated by the technique of varying the 15N level. In the second crop, this ratio in non-fixing species was higher than that in N2-fixing species. Comparable estimates of % Ndfa were obtained by using 15N enrichment of various non-fixing species. There was also good agreement between the estimates obtained by using 15N enrichment of non-fixing species and those by using soil NH 4 + -N, particularly in the second crop. By 25 days after sowing, the first crop of both Sesbania spp. had obtained 50% of total N from the atmosphere and the second crop had obtained 75%. The contribution from air increased with the age of the plant and ranged from 70% to 95% in 45–55 days. S. rostrata fixed substantially higher amounts of N2 due to its higher biomass production compared with S. cannabina. Mathematical considerations in applying the 15N dilution method are discussed with reference to these results.

Flexible Deburring of Castings per Skilfully Used Telerobot

The idea of using industrial robots partially as hand-guided manipulators is derived from problems of inefficiency when trying to automate coarse grinding and milling processes. A spherical force-torque sensor is used as a transducer of intuitive commands and some efforts are made to attach temporal signal sequences to intentions regarding the robot movements. In order to avoid extremely long and expensive optimizations of programmed robot trajectories and to cope with irregular object geometries and orientations a rather elastic robot is used, the trajectories of which obey more the ballistic laws rather than following the preprogrammed paths. A quick estimation of necessary impulses got along short acceleration paths is exspected from the unconscious experience of a metal worker more easily than from mathematical considerations of an engineer. This justifies the attempt to start some short automatically driven trajectories in relation to manually defined tool positions and orientations. The workers qualification must be concentrated on own decisions when choosing tools and mounting configurations as well as organizing the manual and the automated parts of the work process. It remains as a challenge to the creative engineer, to adapt the robot guidance and control to the workers requirements and to support a variety of simple observation facilities. Some examples of this task are shown when reporting on a cooperative project, in which some unemployed metal workers attending qualification courses are involved.

Averaged damping in random vibrations of the Baltic drilling platform

Some findings of an investigation into the stochastic and dynamic response of steel jack-up platforms under wave excitation are discussed. Since the submerged elements of these structures are usually sufficiently slender, one can use a modified Morison equation for evaluation of the in-line component of wave force. Transverse forces and the influence of vortex shedding are ignored in this study. The modified form of the Morison equation under the relative velocity assumption contains a non-linear function of the Gaussian wave particle kinematics and a non-linear term in the structural response velocity. The mathematical considerations of the problem formulated are based on the stochastic averaging method. The response is approximated by a diffusive Markov vector process analyzed by using Itô's stochastic differential equations. From the stationary solution of these equations, statistics of second order are derived. The stability conditions or stochastic averaging used for the dissipative energy of the vibrating system gives an expression for the equivalent damping ratio. Illustrative analyses of a one-degree-of-freedom system and a numerical example referred to engineering problems of a Baltic drilling platform are presented. The sea surface is described by the one-dimensional wave spectrum proposed by Striekalov and Massel for the Baltic Sea.

Generalized Slice Method for Slope Stability Analysis

ABSTRACT Many slice methods already proposed for slope stability analysis have two weak points, assumption on interslice forces and complicated calculation technique. In this paper, an extended wedge method in which equilibrium equations of forces acting on slices are directly presented and safety factors on interslice planes are defined, is proposed. Followings are clarified after mathematical consideration. If the problem to obtain safety factor along main slip surface is considered as optimization problem with constraints, the solution can be obtained even if the number of variables exceeds the number of equations. This means that the safety factor can be optimized not only by geometry of slip surface but also by assumption on interslice forces. The equilibrium equations of forces are sufficient to obtain and minimize safety factor without equilibrium equations of moment. Safety factor, Fsmin, which assumes no tangential force on interslice planes, and safety factor Fsmax, which assumes that interslice planes are just failing, are minimum and maximum limit of safety factors, respectively. Together with Fsmed which assumes that safety factor along main slip surface is equal to ones along interslice planes, Fsmin and Fsmax are the standard for evaluation of other slice methods from the state of forces acting on interslice planes. Then, some comparisons suggest that Fellenius method and simplified Janbu method give the lowest safety factors which are nealy equal to Fsmin and that Morgenstern-Price method gives the safety factor higher than Fsmed.

Two‐Event Model for Carcinogenesis: Biological, Mathematical, and Statistical Considerations

A two-mutation model for carcinogenesis is reviewed. General principles in fitting the model to epidemiologic and experimental data are discussed, and some examples are given. A general solution to the model with time-dependent parameters is developed, and its use is illustrated by application to data from an experiment in which rats exposed to radon developed lung tumors.