Formula Manipulation Research Articles

Young Tableaux, Gelfand Patterns, and Branching Rules for Classical Groups

Young tableaux and Gelfand patterns which combinatorially describe characters of irreducible finite dimensional representations of complex classical Lie groups are presented. Some branching rules and/or character recursions are given explicit combinatorial descriptions. These recursions are derived from manipulations of determinantal character formulas.

Automated formula manipulation supports object-oriented continuous-system modeling

Digital continuous-system simulation languages are discussed. It is demonstrated how sophisticated automated formula manipulation can be used to automatically generate state-space models from an object-oriented description of a physical system. The two major complications, algebraic loops and structural singularities, occur frequently as a consequence of couplings between submodels (objects), and these difficulties can often be dealt with by automated formula manipulation. A software tool, Dymola, in which the various formula manipulation techniques have been implemented, is presented. Dymola is an object-oriented continuous-system modeling language and a model manipulator that can be used to generate models in several simulation languages. >

The beginning and development of FORMAC (FORmula MAnipulation Compiler)

The first widely available programming language for symbolic mathematical computation to have significant practical usage was FORMAC (FORmula MAnipulation Compiler). This paper discusses the earliest conceptual work in detail, and then provides information about later developments of the language. Other languages and systems of the early and mid-1960s are described briefly, with emphasis on their relation to FORMAC. There are also a few glimpses into the software management process at IBM. Finally there is an evaluation of FORMAC and its influence.

The need for high-level programming support in scientific computing applied to mechanical analysis

We describe the current state of the art in computerized support of mathematical and numerical modelling for mechanical analysis. An overview of relevant high-level languages, computer algebra systems, and hybrid symbolic-numerical systems is also given. Several problems with current tools are identified, and a high-level programming environment is proposed as a solution. Such an environment should include object oriented model description, symbolic formula manipulation, generation of numeric code, automatic use of equation solvers and optimization techniques, in addition to graphical presentation of model and simulation data.

Software tools for micro‐analysis of programs

AbstractThe paper proposes and describes several tools enabling their user to estimate the efficiency of Pascal or C‐like programs. The approach consists of generating symbolic formulas expressing the efficiency of the programs being analyzed. The formulas are applicable to a variety of compiler‐machine configurations. The actual numeric values of the variables in the symbolic formula are determined using linear programming techniques. The proposed approach reduces considerably the amount of benchmarking needed to analyze programs. Several examples are presented showing the applicability of the tools. The effort necessary to implement them is considerably reduced by the combined usage of Prolog and a symbolic formula manipulation package (Maple).

“Twirling an Edge”: Occupational Rituals, Verbal Art and the English Market Trader

The ritualistic nature of communication and work techniques in many occupational settings is often overlooked. The art of “pitching” is a distinctive, traditional approach to merchandising employed by English market traders that has gone largely unnoticed in folkloristic literature. The stable, recurrent and recognizable component of this occupational ritual and verbal art is the consistent use by its practitioners of a unique marketing strategy. The manipulation of verbal formulas, gesture, costume and merchandise in performance constitute elements of variability within the tradition. This paper examines the principal features of a neglected ritual of English folklore.

The Joule-Thomson expansion coefficient by formula manipulation [Erratum to document cited in CA113(6):42946v

The Joule-Thomson expansion coefficient by formula manipulation [Erratum to document cited in CA113(6):42946v

The Joule-Thomson expansion coefficient by formula manipulation

By use of formula manipulation, practical programs used to estimate the Joule-Thomson coefficients are presented in this paper. The available equations of state used include the following: van der Waals, Virial, BWR, RK, and SRK. The Joule-Thomson coefficients for nitrogen and ethane are estimated by the proposed programs, and their ability to reproduce experimental values is tested. It is found that the RK equation yields the best results for nitrogen and ethane despite its simplicity.

Structural Analysis Consultation System Developed by Use of Knowledge Bases and Symbolic Manipulation

An attempt is made to constitute an integrated consultation system for structural analysis. The objective at present is to furnish a prototype consultation system with the ability to recognize a structure and its properties in terms of the physical model and to predict the model response qualitatively. Elastic beams and plates are taken as the physical model. The system consists of the analysis knowledge base and structure-domain base of the physical model linked mutually by message communication and supported by the inference engine. The knowledge is stated in the form of the frame model. A symbolic processor is provided for the manipulation of equations and formulae. The inference engine is described in Prolog language. The system is implemented on a personal computer PC 9801 VX 2. The case studies of beam problems confirm the potential of the prototype system to evolve into sophisticated consultation systems for large computers in the future.

Formula manipulation in statistics on the computer: Evaluating the expectation of higher-degree functions of normally distributed matrices

Symbolic manipulation on the computer is a field whose potential for computational statistics has up till now been only barely explored. The present paper intends to contribute in this field by considering the case of higher degree functions of normally distributed random matrices, an area where there is a certain amount of recent literature. We show that the expectation of such functions can simply be evaluated algebraically by a method that we call repeated conditioning. We next show that this method is well-suited for being performed on a computer, and give examples of its outcome. Moreover, such symbolic manipulation leads to formulas that can be transformed straightforwardly (again by the computer) into a source text in a programming language like Pascal.

The specific heat puzzle in black-body radiation

Discusses some misconceptions concerning the status and significance of specific heat in black-body radiation in equilibrium. An extension list of references is provided to indicate the various positions adopted by different authors on this issue. The way in which simple mathematical manipulation of thermodynamic formulae may lead to unphysical results for radiation in equilibrium is indicated and a consistent derivation and interpretation of the specific heat for black-body radiation is presented.

Formula Manipulation and Its Application to System and Control Engineering

Formula Manipulation and Its Application to System and Control Engineering

Structural analysis consultation system developed by the use of knowledge bases and symbolic manipulation.

An attempt is made to constitute an integrated consultation system for structural analysis. The objective at present is to afford a prototype consultation system the ability to recognize a structure and its properties in terms of the physical model and to predict the model response qualitatively. Elastic beams and plates are taken for the physical model. The system consists of the analysis knowledge base and structure-domain base of the physical model linked mutually by message communication and supported by the inference engine. The knowledge is stated in the form of the frame model. A symbolic processor is provided for the manipulation of equations and formulae. The inference engine is described in Prolog language. The system is implemented on a personal computer PC 9801 VX 2. The case studies of beam problems assure the potential of the prototype system to evolve into sophisticated consultation systems by large computers in the future.

Seventh RIMS Conference on FORMULA MANIPULATION AND ITS APPLICATION TO MATHEMATICAL STUDY

The Conference of the above title was held on November 12 to 14 in Kyoto. The Conference chairman is Prof. Sin Hitotumatu, RIMS, Kyoto University, and the conference organizer is Dr. Tateaki Sasaki, The Institute of Physical and Chemical Research. Presented were fourteen papers on algorithm study, application to pure and applied mathematics, etc., and system implementation. The number of attendees is 46, from the fields of pure mathematics, applied mathematics, physics, and computer science. The papers presented and their abstracts are given below.

ABSTRACTS: Sixth RIMS Conference on FORMULA MANIPULATION AND ITS APPLICATION TO MATHEMATICAL STUDY

The conference of the above title was held on November 13 to 15 in Kyoto. The conference chairman is Dr. Tateaki Sasaki, The Institute of Physical & Chemical Research, and the conference organizer is Prof. Hidetsune Kobayashi, Nihon University. Presented were fourteen papers on algorithm study, system implementation, and application to mathematics and physics. The number of attendants is about 60, from the fields of pure and applied mathematics, computer science, physics, and engineering. The papers presented and their abstracts are given below.

Computer-algebra methods for investigation of hereditary operators of higher order soliton equations

The hereditariness of recursion operators is discussed for some 5th order nonlinear partial differential equations as well as for several coupled systems. Consequences of the hereditary property are surveyed. An outline of the corresponding computer algebra proofs (based on the formula manipulation systems MAPLE and MACSYMA) is given. Several new hierarchies of completely integrable systems are presented.

Location of the travelling wave for the Kolmogorov equation

Under appropriate initial data, solutions of the Kolmogorov equation \(u_{t = } \tfrac{1}{2}u_{xx} + f(u)\) converge to travelling waves wλ(x), λ≧21/2, as t→∞. In the case λ>21/2, a general formula for the asymptotic position of the wave is known, as are formulas for certain cases of λ=21/2. The general formula for the case λ=21/2 given in [4] involves the behavior of the solution at earlier times and is typically not explicit enough for computation. Here, we give an improvement of this formula not requiring such information. The methodology involves use of sample path estimates for Brownian bridge and manipulation of certain formulas from [4].

Decision tables and logic in decision analysis.

Unmanageable bushy decision trees result when a decision analysis involves several investigations. They can be simplified for riskless tests by deriving the maximum expected utility decision table for the problem as an intermediate step. This table can be logically summarized as Boolean expressions involving the tests. A minimum-cost testing sequence may then be found by manipulation of the Boolean formulas. The relationship between the resulting decision criteria and the receiver operating characteristic is shown.

Automatic GKS Stability Analysis

A new algorithm is presented for automatic stability investigation according to the theory of Gustafsson, Kreiss and Sundstrom. It is more efficient than approaches tried earlier, by taking advantage of the special structure of the system of algebraic equations whose solutions govern stability.The software system IBSTAB implements this algorithm, as well as procedures for checking von Neumann- and P-stability. IBSTAB combines symbolic formula manipulation and numerical routines. Furthermore, a user oriented problem description language is included. The software system is entirely FORTRAN based, the symbol manipulation parts being written in LISP, using the FORTRAN coded LISP-F3 interpreter.Results are presented from tests, in which IBSTAB was addressed to problems with known results. Also, a study is presented, in which IBSTAB was used as a tool in the development of stable numerical boundary conditions for a problem in fluid dynamics.

Prolonged Use of Modular Enteral Hyperalimentation

A 55‐year‐old male with squamous cell carcinoma of the left mandible, who was treated with chemotherapy, surgery, and radiation, received enteral hyperalimentation for 83 of his 102‐day hospital stay. The hospital course was complicated by fluid and electrolyte imbalance, sepsis, gastric outlet obstruction, and ileus. A modular system of individual nutrient components was used to prepare enteral formulations during 62 of the 83 days of enteral hyperalimentation. The 10 enteral prescription modifications involved both macro‐ and micronutrients, and could not easily have been prepared using standard enteral products. Enteral formula modifications resulted in extended use of the gastrointestinal tract for nutritional support. Continued use of the gastrointestinal tract instead of the intravenous route resulted in a net savings of $4380. The use of modular enteral hyperalimentation may be indicated when the gastrointestinal tract is functional, but when frequent formula manipulation is desired. Modular enteral hyperalimentation can be adapted easily for use by nutrition support teams in acute care settings.