Use Of Pascal Research Articles

Cardinal and anti-cardinal points, equalities and chromatic dependence.

Cardinal points are used for ray tracing through Gaussian systems. Anti-principal and anti-nodal points (which we shall refer to as the anti-cardinal points), along with the six familiar cardinal points, belong to a much larger set of special points. The purpose of this paper is to obtain a set of relationships and resulting equalities among the cardinal and anti-cardinal points and to illustrate them using Pascal's ring. The methodology used relies on Gaussian optics and the transference T. We make use of two equations, obtained via the transference, which give the locations of the six cardinal and four anti-cardinal points with respect to the system. We obtain equalities among the cardinal and anti-cardinal points. We utilise Pascal's ring to illustrate which points depend on frequency and their displacement with change in frequency. Pascal described a memory schema in the shape of a hexagon for remembering equalities among the points and illustrating shifts in these points when an aspect of the system changes. We modify and extend Pascal's ring to include the anti-cardinal points. We make use of Pascal's ring extended to illustrate which points are dependent on the frequency of light and the direction of shift of the equalities with change in frequency. For the reduced eye the principal and nodal points are independent of frequency, but the focal points and the anti-cardinal points depend on frequency. For Le Grand's four-surface model eye all six cardinal and four anti-cardinal points depend on frequency. This has implications for definitions, particularly of chromatic aberrations of the eye, that make use of cardinal points and that themselves depend on frequency. Pascal's ring and Pascal's ring extended are novel memory schema for remembering the equalities among the cardinal and anti-cardinal points. The rings are useful for illustrating changes among the equalities and direction of shift of points when an aspect of a system changes. Care should be taken when defining concepts that rely on cardinal points that depend on frequency.

With reasons of the heart before God. On religious experience from an evolutionary-theological perspective

What does the affective-cognitive dimension of being human entails? Many contemporary scholars from theological (especially religious experience) perspectives as well as from evolutionary biological (especially neuroscientific) perspectives have made exciting inroads in the on-going anthropological discourses on this very dimension of being human. My article partially makes work of their respective contributions. For the former theological perspective I will utilize Pascal and Stoker. For the latter neuroscientific perspective I will concentrate on LeDoux and Damasio. I call my contribution an evolutionary-theological re-conceptualisation of religious experience for which I make use of Pascal’s famous words from his Pensees (1670) “The heart has its reasons which reason does not know” and “(i)t is the heart which experiences God and not the reason”. Therefore the title: With reasons of the heart before God. Such a formulation however immediately raises the question: Does such an emphasis on the “heart” re-introduce irrationality into the scientific scholarly dialogue? The answer is clear: Yes, it does. It is argued that it should be re-introduced constructively into contemporary science-theology discourses in order – on the one hand – to critically address the very accusation, and – on the other hand – to present us with a far richer, deeper understanding of personhood. From the constructive integration of the two perspectives, namely the theological and neuroscientific the words of Pascal is finally re-formulated from an evolutionary-theological perspective and qualified in which emotion is presented as the embodiment of the logic of survival.

Deciphering the hidden Pascal code of Guggenheims quasichemical model. Overcoming computational limitations by use of Pascal’s triangle

A general description is given of the mathematical modelling of physical properties of liquid mixtures, with an emphasis on the early progress in mathematical representation of mixtures’ thermodynamics. The core issue is employing long polynomials to represent mixing data accurately, without having to optimise a large number of independent parameters. This is for instance done by deriving the long polynomials from explicit (analytical) models with few independent parameters. It is shown that this field evolved not by gradual changes in model complexity and accuracy, but rather in bursts, followed by pausing for several years or decades whenever researchers hit computational or conceptual limitations. One such limitation that still exists is the Taylor expansion of the above mentioned analytical models. This article presents a novel use of Pascal’s triangle that turns this computationally “hard” problem into a trivial iterative procedure, suitable for standard office spreadsheets. The process of transforming this hard problem into a soft problem may be described as deciphering. The present author conjectures that for every parametric function for which a polynomial expansion can be made, there is a corresponding coefficient pattern involving Pascal’s triangle and/or other binomial sequences and matrices.

Application of binomial coefficients in representing central difference solution to a class of PDE arising in chemistry

The use of differential equations for modeling chemical systems and solving by numerical approaches (e.g. finite difference methods) are prevalent in chemistry-related problems. As an extension to the direct use of Pascal’s Triangle to obtain the forward and backward difference equations to partial differentials by Lim [Mathematical Medley 31 (2004) 2], this paper proposes the use of binomial coefficient to generate central difference equations to odd-ordered partial differentials in a single-step operation. All finite difference equations to partial differentials shown herein display finite series of palindromic coefficients with alternating signs

On DR/BEM for eigenvalue analysis of 2-D acoustics

This paper discusses the efficiency of several DR/BEM formulations and other boundary techniques for the eigenvalue extraction of two-dimensional acoustic cavities. First, the paper shows that the well-known conical radial basis functions lead to extremely ill conditioning results in cases that the height of the cone is not properly chosen. Moreover, the accuracy of other known high-degree basis functions is tested. Second, the use of Pascal’s triangle is proposed as a better approximation of the inertial forces at least for the case of rectangular domains. Using Gordon’s blending-function formula, a systematic procedure is proposed for the selection of the proper monomials. Third, it is shown that the aforementioned functional set can be also used to establish an alternative boundary-type method where both inertial and static terms are treated in a consistent manner. The solution quality of these formulations is investigated by calculating the eigenvalues of a rectangular and a circular acoustic cavity where analytical solutions are known.

Programming language impacts on learning

What programming language should be taught in an introductory computer science course? Studies and experiences at West Point provide some insight into these questions. This paper reports the statistical results obtained from a side-by-side comparison of Pascal and Ada. The unique nature of our institution provided the opportunity to isolate and study causal factors, and allowed us to follow the experimental and control groups through graduation.We conducted a side by side comparison of the use of Pascal, which was specifically designed for instructional purposes, and Ada in an introductory course. The experiment demonstrated that students were much more successful in Ada than in Pascal, and led to the revision of the Academy core curriculum to use Ada 95 in our introductory computer science class. This paper discusses the details of our comparison, citing specific examples to illustrate a rational basis for evaluating programming language features.

Recommendations for changes in advanced placement computer science (panel session)

In 1981 the APCS Development Committee recommended the use of Pascal in an AP course whose first exam was given in 1984. This decision was controversial; BASIC was in widespread use and serious consideration was given to a language-neutral exam and course. In 1985 an ad-hoc committee made recommendations on changing the exam format, essentially creating two courses that correspond roughly to CS1 and CS2. In 1995 an ad-hoc committee was convened to make recommendations on how best to incorporate C++ into the AP course and exam. The decision to adopt C++, made in 1994, was decidedly controversial. The ad-hoc committee made recommendations on a subset of C++ and on classes similar to those in the standard library, but which were safe for novice programmers to use.

A comparison of Ada and Pascal in an introductory computer science course

Pascal’s long and successful run at West Point illustrated Winston Churchill’s dictum that, “The absence of alternatives clears the mind wonderfully.” However, by the mid-90s, the United States Military Academy was finding that Pascal, long the educational workhorse, was no longer the clear choice for serious computer science education. The decision was taken to evaluate alternatives to Pascal. The criteria selected for programming language evaluation were student learning outcomes based on course goals and objectives. The controlled educational environment of a service academy provides an excellent opportunity to conduct research using control groups and experimental groups. We conducted a side by side comparison of the use of Pascal, which was specifically designed for instructional purposes, and Ada in an introductory course. The experiment demonstrated that students were much more successful in Ada than in Pascal, and led to the revision of the Academy core curriculum to use Ada 95 in our introductory computer science class. This paper discusses the details of our comparison, citing specific examples to illustrate a rational basis for evaluating programming language features against course objectives.

Tritangent centres, Pascal's theorem and Thebault's problem

Thebault's problem was posed in 1938, but a solution did not appear until 1983. Since then other solutions of the original problem and of various generalisations have been given. In this paper we discuss the generalisations (including some new results) and various background theorems on tritangent centres, making extensive use of Pascal's theorem.

Improvement of “A BASIC Program to Construct Evolutionary Trees from Restriction Endonuclease Data” with the Use of PASCAL

Improvement of “A BASIC Program to Construct Evolutionary Trees from Restriction Endonuclease Data” with the Use of PASCAL

On the use of Pascal for power flow programming

The suitability of Pascal for power-flow programming applications is demonstrated. The implementation of a fast decoupled algorithm on a personal computer using the MS-DOS operating system is documented. The program includes MW and MVAr dispatch with power limits. The relevant advantages of Pascal as used in the program are discussed. The algorithm has been tested using the IEEE 14-bus test system. A 20-bus 24-line sample system has been used for instructional purposes. >

The Construction and Description of Algorithms

Notes on the form to be taken by contributions to the Algorithms Section of Applied Statistics have appeared previously under this title (Working Party on Statistical Computing, 1968, 1975, 1979) and in Chapter 2 of Griffiths and Hill (1985). This revision follows closely the recommendations issued in 1979, but reflects the experience gained and the changes in computing practice which have taken place in the intervening years. It also contains a shift of emphasis from Fortran 66 to Fortran 77 and for the first time authorises and discusses the use of Pascal.

Random Dot E Stereogram-Reply

In Reply. —We quite agree with Dr Schecter's observation on the matter of statistically significant end points. The use of Pascal's triangle or the formula (p + q) n brought us to the same conclusion— perhaps five correct answers out of six is too charitable. 1 Selection of pass/fail criteria when trying to establish an efficient, effective screening procedure for use on large populations while simultaneously minimizing false-positives and false-negatives is a process of balancing. As stated in our article, a disproportionate number of false-positives or false-negatives is undesirable and often decreases the effectiveness of the procedure. 2 However, increasing the number of trials in a procedure increases the time required to carry out the screening process. If time constraints are present, time also limits the number of individuals it is possible to screen. Increasing from six to eight trials is a 33% increase in time, or a 33% decrease in

Pascal circuit compiler for UK5000

A Pascal compiler is described which can parse a limited subset of Pascal, and generates a circuit description in a format which can then be input to the UK5000 gate array software. A set of Pascal utilities completes this package by allowing the Pascal circuit description to be compiled by a standard Pascal system. This complete package allows the development of systems containing single or multiple UK5000 chips. More-over this can be performed on any software development system. The use of Pascal as a hardware description language is not new, but this system promotes good top-down hierarchical design of UK5000 chips and also allows quick and efficient verification of the system, prior to the automatic generation of data for entry into the UK5000 system.

Pascal circuit compiler for UK5000

A Pascal compiler is described which can parse a limited subset of Pascal, and generates a circuit description in a format which can then be input to the UK5000 gate array software. A set of Pascal utilities completes this package by allowing the Pascal circuit description to be compiled by a standard Pascal system. This complete package allows the development of systems containing single or multiple UK5000 chips. More-over this can be performed on any software development system. The use of Pascal as a hardware description language is not new, but this system promotes good top-down hierarchical design of UK5000 chips and also allows quick and efficient verification of the system, prior to the automatic generation of data for entry into the UK5000 system.

Pascal's Triangle— a Serendipitous Source for Programming Activities

Pascal's triangle is an elegant array of numbers that has fascinated mathematicians since its invention. Its applications in algebra, number theory, and probability are well known. The use of Pascal's triangle in the classroom need not be restricted to these conventionally accepted applications. Explorations of Pascal's triangle through the use of computer programming create situations that are incredibly rich in their mathematical yield.

Simulation in Microcomputers Revisited

This note discusses experiences in running discrete-events simulation models on an Apple II microcomputer. The use of PASCAL as a simulation language is commented on. To give an indication of the type of simulations that can be run on a micro, a fairly complex model relating to icebreaking operations is discussed. Run times for this model are mentioned. It is indicated how those run times can be reduced by programming part of the random number generation in assembly language. The conclusion is that significant simulation work can be done on a small micro like the Apple II.

Drawing bridges by computer

The graphical technique presented in this paper allows the user to draw almost any type of bridge. Bridges are created as graphical variables and can be easily manipulated. Different kinds of bridges are classified and specified according to the characteristics of the road, the piers, the superstructure and the parapets. Several examples are presented. The terminology used stems from the use of Pascal.

The use of PASCAL as a teaching tool in introductory, intermediate and advanced computer science courses

The use of PASCAL as a teaching tool in introductory, intermediate and advanced computer science courses