Recent developments in computer design and error analysis have made feasible the use of variable precision arithmetic and the preparation of programs that automatically determine their own precision requirements. Such...
Recent developments in computer design and error analysis have made feasible the use of variable precision arithmetic and the preparation of programs that automatically determine their own precision requirements. Such programs enable the user to specify the accuracy he wants, and yield answers guaranteed to lie within the bounds prescribed. A class of such programs, called “contracting error programs,” is defined in which the precision is determined by prescribing error bounds on the data. A variant of interval arithmetic is defined which enables a limited class of algorithms to be programmed as contracting error programs. A contracting error program for the solution of simultaneous linear equations is described, demonstrating the application of the idea to a wider class of problems.
A common approximation for deriving solutions to the Lamm equation is to neglect diffusion. This paper presents a singular perturbation technique that allows one to estimate the band spreading due to nonzero diffusion...
A common approximation for deriving solutions to the Lamm equation is to neglect diffusion. This paper presents a singular perturbation technique that allows one to estimate the band spreading due to nonzero diffusion coefficient. We illustrate the general mathematical technique by its application to sedimentation when pressure effects are important. Comparison of the approximate solution with accurate numerical solutions shows that the relative errors are of the order of 1% both for concentration and concentration gradient for parameters of chemical interest.
A theory is developed for sedimentation velocity experiments when the sedimentation coefficient s p depends on pressure P as s p / s o = (1 + γ P ) −1 , where γ is a constant. In contrast to the more usually analyze...
A theory is developed for sedimentation velocity experiments when the sedimentation coefficient s p depends on pressure P as s p / s o = (1 + γ P ) −1 , where γ is a constant. In contrast to the more usually analyzed from s p / s o = 1 − γ P , this model does not lead, in extreme cases, to a negative sedimentation rate. A theory is presented for homogeneous macromolecules sedimenting with no diffusion. It leads to estimations of s o and γ from a knowledge of the point of maximum concentration gradient as a function of time. Results of these calculations are compared with accurate numerical solutions of the Lamm equation with diffusion included.
Solutions for the normal displacement w and tangential displacements ux and uy for a shallow cylindrical shell subjected to concentrated forces are obtained in this paper. The normal force and the two tangential for...
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Solutions for the normal displacement w and tangential displacements ux and uy for a shallow cylindrical shell subjected to concentrated forces are obtained in this paper. The normal force and the two tangential force cases are treated. The results for the displacements in all cases are expressible in terms of elementary functions, modified Bessel functions, and one new function of two variables. A reasonably complete investigation of this function is included.
The study reported in this paper is an ongoing effort. We reported a preliminary analysis of the data in the paper. The current experiments varied the subjects to c- duct online group learning activities by the commun...
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ISBN:
(数字)9783540304814
ISBN:
(纸本)9783540238928
The study reported in this paper is an ongoing effort. We reported a preliminary analysis of the data in the paper. The current experiments varied the subjects to c- duct online group learning activities by the communication media such as email and threaded discussion. Although, we could have easily learned the impact of mobile devices in learning if we divided the subjects to use different hardware such as p- sonal computers, personal digital assistant, or mobile phones, we believe our findings will still be able to provide useful insights on the difficulties that the mobile learners will face in solving problems as a group. Our analysis result will also provide ba- line information on whether the traits of the successful or failed online groups are applicable to the mobile learners. For example, we expect the SMS will be a better medium to overcome the major problem of instant communication or the rapid propagation of the information as the mobile phones have built-in mechanism to remind the users of the incoming new messages and also the mobile phone users are expected to be interrupted for the incoming messages. However, we need further investigation of other problems, which hinder the optimum online group work. For example, ‘accuracy of the transferred information’ was identified as one of the pr- lems of using emails as the communication medium. Personal Digital Assistant (PDA) or SMS are more apt to deliver shorter messages than the typical emails.
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