Programmable Pocket Calculator Research Articles

Phenetic and phylogenetic studies based on measurements of Plantago ser. Brasilienses

Numerical taxonomic methods for a programmable pocket calculator are proposed. Operational taxonomic units (OTU's) may be either accepted taxa or single specimens, or a mixture of both. All types of characters are employable. A calculated or estimated common standard deviation and the mean (or reading) define the normal distribution curve for each measurement variable. Similarity between two OTU's is calculated as the overlapping area below their distribution curves. Ninety specimens of Plantago ser. Brasilienses are used as examples. The clusters are finally grouped using both phenetic and several cladistic methods. Results from phylogenetic sys–tematics cannot be used directly in taxonomy because the basic principles are discordant with those in the botanical code.

Strain field analysis with the X‐ray integration method

The so‐called X‐ray sin2 method for measuring internal stresses is not always acceptable, because it postulates a constant orthogonal stress distribution in the layer passed by the beam. It is demonstrated that the often measured non‐linear distribution of deformations is numerically connected with stress distributions, which are variable and inclined against the surface. The calculation of the internal stresses and their parameters is based on the solution of trigonometric polynoms of the variable with integrals. The penetration depth of the X‐ray beam must be known. For general numeric solutions a computer program can be given. Solutions step by step can be carried out with a programmable pocket calculator. The ‘sin2 method’ is a special case of the integration method, which is still developing.

Area approximations in the mathematical laboratory

The article discusses the educational potential and special advantages of a mathematical laboratory in the teaching of mathematics at the pre‐calculus level. The laboratory envisaged is equipped with a set of microcomputers or programmable pocket calculators, which play a central role in the teaching process, with particular emphasis on algorithmization. As a typical laboratory subject we concentrate on the approximation of areas to a prescribed accuracy, including the appropriate error analysis. Different types of approximations, with progressively increasing efficiency, are examined and their laboratory implementation discussed. Extensions and generalizations are indicated for more advanced mathematical education.

Computation of the Electromagnetic Response of a Layered Earth to a Vertical Coaxial Loop System

The electromagnetic (EM) mutual coupling ratio for a vertical coaxial loop system over a layered earth is expressed as a Hankel transformable integral. This expression facili- tates the computation, using an available digital linear filter, for the response of either a perpendicular or a vertical coplanar loop configuration, or a Schlumberger electrode configuration. Such computations may be carried out on a programmable pocket calculator.

A simple method for calculating diffusional recombination probabilities

We present a numerical method for calculating the diffusion-controlled recombination probability of a pair of interacting particles in an isotropic medium with scavengers. The method is finite and has a controllable accuracy. The algorithm is remarkably simple and can be implemented on a programmable pocket calculator.

Calculating atmospheric humidity

Abstract Derivations are given for the functional relationships between psychrometric and barometric observations, and the commonly encountered atmospheric humidity parameters. The use of a programmable pocket calculator is recommended for the practical application of the material.

A pocket calculator program for the solution of pH problems via the method of successive approximations

37. Bits and pieces, 14. A description of a pocket calculator program for the solution of pH problems via the method of successive approximations .

Exact Buckling and Frequency Calculations Surveyed

The usefulness and simplicity of an existing stiffness matrix method is emphasized by presenting it without its relatively complex proofs, and with simple examples. The method ensures that no natural frequencies are missed in undamped free vibration problems, and that no critical load factors are missed in buckling problems. This is maintained even when using the ‘exact’ member equations obtained by solving the appropriate differential equations. The method applies to all structures for which ‘exact’ member equations exist. The published applications are surveyed. They include rigidly jointed plane frames, space frames, and prismatic assemblies of flat or curved plates which are isotropic or anisotropic, and subjected to in‐plane normal or shear stresses. They also cover efficient multi‐level substructuring, design instead of analysis, damping, forced vibrations, elastic‐plastic collapse and programs for large computers, small computers, and programmable pocket calculators.

An efficient algorithm for discrete modelling of tracer kinetics

Effective study of certain health care problems and biomedical systems requires development and utilization of duly validated models for characterization of tracer kinetics in compartmental systems. This report presents an efficient algorithm for evaluation of discrete-time models in this context, starting from real patient data. The procedure evolved is systematic and involves parameter identification, model order determination and ascertaining the validity of the model: mathematical techniques proposed for this three-tier approach are robust as well as simple. A method for deriving state-space representations for multicompartmental systems directly from observations vector is also outlined. An illustrative example is given which demonstrates the effectiveness of the algorithm when applied to tracer analysis of the hepatobiliary system. The methodology proposed is recursive in nature such that it can be implemented very conveniently utilizing a microcomputer or even a programmable pocket calculator.

Densimetric detection in gel permeation chromatography : VII. Calculation of molecular weight distributions using a programmable pocket calculator

It is shown that the measurement of density (mass per unit volume) according to the mechanical oscillator method can be used with advantage for detection in high-performance gel chromatography. The digital signals obtained from such an instrument are inherently integrated over each measuring interval, hence calculation of molecular weight averages from the raw data can be done very easily by means of a programmable pocket calculator. The program described in this paper has been written for the HP 34C; it includes compensation for flow-rate changes and baseline drift and accepts a sufficiently large number of data points. The performance of the method was tested by arranging a photometer and the density detector in series in the eluent stream from a gel permeation chromatographic column.

Differentiation between two diseases using a programmable hand-held calculator and Bayes' theorem: Application to Crohn's disease and ulcerative colitis

A short general program is presented for the Hewlett-Packard HP-41C programmable pocket calculator that calculates posterior probabilities of two diseases on the basis of frequencies of nosographic characteristics using Bayes' theorem. Extended memory and functions modules allow the storage of many data in an ASCII file.

A course for secondary school teachers concerning the use of programmable pocket calculators

This paper describes the development of a course concerning the use of programmable pocket calculators given by the author to upper secondary school mathematics teachers. The search for the approximated solutions of equations is used as an example. This problem illustrates many important aspects of computer use, such as algorithm construction and the need for precise numerical considerations. The possibility that computers offer to examine some traditional mathematical subjects in more depth is also discussed.

A pocket calculator program to sort data

A program is presented for use with a TI59 calculator in sorting up to 98 data.

Experiences with calculating intraocular lenses

The necessity of calculating the refractive power of intraocular lenses in advance is emphasized and the authors' procedure described: Measurement of corneal radii with the Zeiss ophthalmometer, measurement of the bulb length with the A-Scan method, calculation of refractive power and the desired dioptric aniseikonia with the authors' own pocket calculator program using the formulas cited by Gernet. In 74% of the cases the postoperative difference from the pre-calculated refractions is less than 1 D, in 22% up to 2 D and in 4% up to 3 D.

Determination of Gear Ratios

Finding the number of teeth for each gear in a gear train required to provide a specified noninteger ratio (or its inverse) of angular velocity between input and output shafts has been a troublesome problem throughout the history of gearing. A direct method for finding the required number of teeth is presented, along with a program for its implementation on a programmable pocket calculator.

Simple Formula for the Ionization Rate of Rydberg States in Static Electric Fields

With use of a full three-turning-point WKB analysis, a simple formula is obtained for the ionization rate of hydrogenic atoms. Contrary to current belief, WKB ionization rates are found to be excellent approximations to exact numerical calculations. In addition, the symmetries of the WKB solution are explored and it is shown that the resonance parameters can all be written as simple functions of three objects, ${{I}_{\ensuremath{\xi}}}^{(j)}$, ${{I}_{\ensuremath{\eta}}}^{(j)}$, and ${\ensuremath{\theta}}^{(j)}$, which can easily be calculated on programmable pocket calculators.

Glucose control in mobile type 1 (insulin-dependent) diabetic patients by means of a semi-automatic feedback controlled insulin infusion system.

A portable insulin dosing device (Siemens) was used together with a programmable pocket calculator and a glucose analyzer for short-term adaptation of continuous intravenous insulin infusion to blood glucose alterations. A special algorithm was developed which utilizes a given blood glucose value and the glucose rate of change obtained from two to four consecutive samples as input variables. In contrast to current techniques of feedback-regulation, which require continuous glucose monitoring, intermittent blood sampling allows greater mobility of patients. With the semi-automatic feedback system, euglycaemic control was obtained for 12-h periods in ten Type 1 (insulin-dependent) diabetic patients (maximum value 9.50 mmol/l, minimum value 2.83 mmol/l). Severe hypoglycaemia occurred in no case and additional control by glucose infusion appeared to be unnecessary. Light exercise after termination of insulin dose for standard meals led to glycaemic excursions with a rapid decrease (mean 1.08 +/- 0.09 mmol/l), followed by a rebound (0.59 +/- 0.07 mmol/l) in each patient. The amplitude of these excursions decreased with increasing distance from the peak of the meal dose. Comparison of feedback-control alone with feedback by glucose plus preprogrammed dose (4 U/h) at the onset of the test meal revealed lower post-prandial glucose levels (post-prandial maximum +/- SEM: 6.49 +/- 0.18 versus 7.71 +/- 0.79 mmol/l) and a lower infusion rate of insulin for the combined regimen (mean post-prandial maximum +/- SEM: 8.4 +/- 1.2 versus 12.0 +/- 0 IU/h). The system is useful for programming of portable infusion devices and studies based on euglycaemic control in unrestrained patients.

Approximating the Normal Tail

It is very useful to have simple approximations to the cumulative normal distribution. About every statistician carries a pocket calculator, but how many of us carry a book of tables everywhere we go? When working 'with a desk-top microcomputer it would be inefficient to have to stop to look up tables frequently. One could store a look-up table, but this would use up a lot of storage and the accuracy of interpolation in the table may not be good. The approximation does not have to be all that simple for the micro or programmable calculator but clearly it should be very simple for manual operation of a calculator, and simplicity would also help you to remember the formula. All of the formulae used in this paper were calculated very easily on a Casio 502-P programmable pocket calculator.

Computer assisted planning of parenteral hyperalimentation therapy.

A computer program has been written to assist the physician in the planning of nutritional support. The program is divided into individual segments dealing with nutritional assessment, caloric requirements, hyperalimentation planning, and evaluation of nutritional therapy. Tables of anthropometric data have been fitted to exponential and polynomial equations in order to minimize data storage requirements and eliminate the need for interpolation schemes. Operation of the program does not require any form of reference material and prior computer training is not a prerequisite for program users. The program may be run on either a large desktop computer or a hand-held programmable pocket calculator with continuous memory and optional printer.

A NOTE ON THE STATUS OF SELF-REDUCING TACHEOMETERS

Abstract Although it appears that sales and usage of self-reducing tacheometers remain at signfiicant levels, their continued purchase and use is largely unjustified. The combination of scale reading theodolites (of comparable accuracy) with inexpensive continuous memory programmable electronic pocket calculators provides a cheaper and generally more satisfactory solution.