Symbolic Computation via Program Transformation

AbstractFortran is still widely used in scientific computing, and a very large corpus of legacy as well as new code is written in FORTRAN 77. In general this code is not type safe, so that incorrect programs can compile without errors. In this paper, we present a formal approach to ensure type safety of legacy Fortran code through automated program transformation. The objective of this work is to reduce programming errors by guaranteeing type safety. We present the first rigorous analysis of the type safety of FORTRAN 77 and the novel program transformation and type checking algorithms required to convert FORTRAN 77 subroutines and functions into pure, side-effect free subroutines and functions in Fortran 90. We have implemented these algorithms in a source-to-source compiler which type checks and automatically transforms the legacy code. We show that the resulting code is type safe and that the pure, side-effect free and referentially transparent subroutines can readily be offloaded to accelerators.

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Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽

10.1515/phys-2020-0163 ◽

2020 ◽

Vol 18 (1) ◽

pp. 545-554

Author(s):

Asghar Ali ◽

Aly R. Seadawy ◽

Dumitru Baleanu

Keyword(s):

Wave Propagation ◽

Partial Differential Equations ◽

Differential Equations ◽

Longitudinal Wave ◽

Symbolic Computation ◽

Boussinesq Equation ◽

Nonlinear Partial Differential Equations ◽

Wave Model ◽

Simple Equation ◽

Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

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QCD corrections to heavy quark decays

Canadian Journal of Physics ◽

10.1139/p07-054 ◽

2007 ◽

Vol 85 (6) ◽

pp. 613-617

Author(s):

I Blokland

Keyword(s):

Heavy Quark ◽

Symbolic Computation ◽

Decay Rates ◽

Special Cases ◽

Quark Decays ◽

Quark Decay

The calculation of QCD corrections to heavy quark decay rates has progressed steadily in recent years. With the help of specialized techniques, symbolic computation, and a growing base of experience, a wide variety of special cases have been evaluated. These results have been applied to decays such as t → bW, b → s γ, b → u[Formula: see text]ν, and b → c[Formula: see text]ν. PACS Nos.: 12.38.Bx, 13.30.Ce

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