Symbolic use of export information:a multidimensional conceptualisation, its' effect on performance and key antecedents

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On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

A quantitative application of symbolic interactionism to advance directive completion by older adults

This study examined contextual and situational influences on older adults' decision to complete advance directives by means of a conceptual framework derived from symbolic interactionist theory and a cross-sectional, correlational research design. It was hypothesized that completion of advance directives among older adults would be associated with visiting or participating in the care of a terminally ill or permanently incompetent individual sustained by technology. Using a 53-item questionnaire, computer assisted telephone interviews (CATI) were conducted with 398 community dwelling adults between September and October 2003. Respondents were contacted using random-select dialing from a listed sample of 99% of household telephone numbers in one South Florida census tract. Over 90% of households in this tract include an individual age 65 or older. ^ The results revealed that contrary to most reports in the literature a substantial proportion of older adults (82%) had completed advance directives and that the link between older adults and document completion was mainly through attorneys and not mandated agents, health care professionals. Further, more than one third of older adults reported that religion/spirituality was not an important part of their life, suggesting that the recommended practice of offering religious/spiritual counseling to all those approaching death be reexamined. The hypothesis was not supported (p > .05) and is explained by the situational emphasis on the variables rather than on structural influences. In logistic regression analysis, only increasing age (p = .001) and higher education (p = < .001) were significant but explained only 10% of the variance in document completion. ^ Based on the findings, increased interdisciplinary collaboration is suggested with regard to the advance directive agenda. Since attorneys play a key role in document completion, other professions should seek their expertise and collaboration. In addition, the inclusion of a religious/spiritual preference section in all living wills should be considered as an essential part of a holistic and individually appropriate document. Implications for social work education, practice, and advocacy are discussed as well as suggestions for further research. ^

A software tool that generates symbolic model verifier (SMV) input language from a predicate transition net

The purpose of this research was to apply model checking by using a symbolic model checker on Predicate Transition Nets (PrT Nets). A PrT Net is a formal model of information flow which allows system properties to be modeled and analyzed. The aim of this thesis was to use the modeling and analysis power of PrT nets to provide a mechanism for the system model to be verified. Symbolic Model Verifier (SMV) was the model checker chosen in this thesis, and in order to verify the PrT net model of a system, it was translated to SMV input language. A software tool was implemented which translates the PrT Net into SMV language, hence enabling the process of model checking. The system includes two parts: the PrT net editor where the representation of a system can be edited, and the translator which converts the PrT net into an SMV program.