Related papers: Symbolic Computation of Equivalence Transformation…
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
The complete optimal systems of subalgebras of all nonisomorphic three- and four-dimensional real Lie algebras are analyzed by the program \symbolie running in the computer algebra system \emph{Wolfram Mathematica}\texttrademark. The…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of…
In this paper, we study estimation of nonlinear models with cross sectional data using two-step generalized estimating equations (GEE) in the quasi-maximum likelihood estimation (QMLE) framework. In the interest of improving efficiency, we…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many non-equilibrium processes can be described by suitable subsets of the equilibrium…
We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra,…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the…
A Maple package for computing Groebner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for…
A class of partial differential equations (a conservation law and four balance laws), with four independent variables and involving sixteen arbitrary continuously differentiable functions, is considered in the framework of equivalence…
In this article, we discuss how a kind of hybrid computation, which employs symbolic, numeric, classic, and quantum algorithms, allows us to conduct Hartree-Fock electronic structure computation of molecules. In the proposed algorithm, we…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…