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1,709
An equilibrium characterization of the term structure.
 J. Financial Econometrics
, 1977
"... The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.l) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. ..."
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Cited by 1041 (0 self)
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. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation
Modeling and simulation of genetic regulatory systems: A literature review
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
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Cited by 738 (14 self)
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, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rulebased formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.
PETSc users manual
 ANL95/11  Revision 2.1.0, Argonne National Laboratory
, 2001
"... tract W31109Eng38. 2 This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on highperformance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provid ..."
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Cited by 282 (20 self)
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tract W31109Eng38. 2 This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on highperformance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines
Symbolic software for the study of nonlinear partial differential equations
 IN: ADVANCES IN COMPUTER METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS VII, EDS
, 1993
"... Three entirely symbolic MACSYMA programs are presented. The first one carries out the Painleve integrability test, the second computes solitons and the third program aids in finding the Lie symmetry group for systems of differential equations. ..."
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Cited by 1 (1 self)
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Three entirely symbolic MACSYMA programs are presented. The first one carries out the Painleve integrability test, the second computes solitons and the third program aids in finding the Lie symmetry group for systems of differential equations.
Solutions Of Partial Differential Equations Using Symmetry And Symbolic Computation
, 2000
"... Contents Glossary of key symbols iv Summary vi Statement of authorship vii Acknowledgements viii 1 Introduction 1 2 Preliminary material 11 2.1 Basicdiff.c! tial geometry . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 Manifolds and submanifolds . . . . . . . . . . . . . . . . . . . 11 2.1 ..."
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Cited by 1 (0 self)
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Contents Glossary of key symbols iv Summary vi Statement of authorship vii Acknowledgements viii 1 Introduction 1 2 Preliminary material 11 2.1 Basicdiff.c! tial geometry . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 Manifolds and submanifolds . . . . . . . . . . . . . . . . . . . 11 2
The Symbolic Integration of Exact PDEs,
 J. Symb. Comp.
, 2000
"... Abstract An algorithm is described which decides if a given polynomial differential expression ∆ of multivariate functions is exact, i.e. whether there exists a first integral P such that D x P = ∆ for any one x of a set of n variables and to provide the integral P . A generalization is given to al ..."
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Cited by 10 (6 self)
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to allow integration in the case that the exactness is prevented by terms which contain only functions of less than n independent variables. Motivation The common way to deal with problems that involve the solution of nonlinear differential equations is to try different ansätze which are either
Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations
, 1998
"... Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that ..."
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Cited by 85 (12 self)
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Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis
Analytical Solving of Partial Differential Equations using Symbolic Computing
, 1995
"... This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as a implementation of part of this plan as the PDEtools softwarepackage of commands. To be published in the Proceedings of ..."
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This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as a implementation of part of this plan as the PDEtools softwarepackage of commands. To be published in the Proceedings of
Symbolic Computation of Local Symmetries of Nonlinear and Linear Partial and Ordinary Differential Equations
, 2011
"... The paper illustrates the use of a symbolic software package GeM for Maple to compute local symmetries of nonlinear and linear differential equations (DE). In the cases when a given DE system contains arbitrary functions or parameters, symbolic symmetry classification is performed. Special attenti ..."
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The paper illustrates the use of a symbolic software package GeM for Maple to compute local symmetries of nonlinear and linear differential equations (DE). In the cases when a given DE system contains arbitrary functions or parameters, symbolic symmetry classification is performed. Special
Results 1  10
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1,709