Search results for "Computational Mathematic"
showing 10 items of 987 documents
New special function recurrences giving new indefinite integrals
2018
ABSTRACTSequences of new recurrence relations are presented for Bessel functions, parabolic cylinder functions and associated Legendre functions. The sequences correspond to values of an integer variable r and are generalizations of each conventional recurrence relation, which correspond to r=1. The sequences can be extended indefinitely, though the relations become progressively more intricate as r increases. These relations all have the form of a first-order linear inhomogeneous differential equation, which can be solved by an integrating factor. This gives a very general indefinite integral for each recurrence. The method can be applied to other special functions which have conventional …
A multiscale approach to liquid flows in pipes I: The single pipe
2012
Abstract In the present paper we study the propagation of pressure waves in a barotropic flow through a pipe, with a possibly varying cross-sectional area. The basic model is the Saint–Venant system. We derive two multiscale models for the cases of weak and strong damping, respectively, which describe the time evolution of the piezometric head and the velocity. If the damping is weak, then the corresponding first-order hyperbolic system is linear but contains an additional integro-differential equation that takes into account the damping. In the case of strong damping, the system is nonlinear. The full and multiscale models are compared numerically; we also discuss results obtained by a lar…
Network structure and optimal technological innovation
2019
The role of networks in the emergence, diffusion and evolution of technological innovations has attracted much theoretical and empirical attention. Yet, much of the work has explored the role of undirected and homogeneous networks. In real cases, many networks are directed. The flow of information, benefits or observations is directed from one node towards another node. Real networks are also heterogeneous, for example, few nodes have a high degree while many others have a low degree. In this article, we report on the results of an evolutionary agent-based model in which a group of agents, in our case firms, collectively search a complex (rugged) technological landscape and observe each oth…
Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III
1980
In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
2009
A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed
DRUDIT: Web-based DRUgs DIscovery Tools to design small molecules as modulators of biological targets
2019
Abstract Motivation New in silico tools to predict biological affinities for input structures are presented. The tools are implemented in the DRUDIT (DRUgs DIscovery Tools) web service. The DRUDIT biological finder module is based on molecular descriptors that are calculated by the MOLDESTO (MOLecular DEScriptors TOol) software module developed by the same authors, which is able to calculate more than one thousand molecular descriptors. At this stage, DRUDIT includes 250 biological targets, but new external targets can be added. This feature extends the application scope of DRUDIT to several fields. Moreover, two more functions are implemented: the multi- and on/off-target tasks. These tool…
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Can aromaticity be connected with molecular polarizability? A theoretical study of benzene isomers and five-membered heterocyclic molecules
2004
Extended calculations of molecular electric dipole polarizability tensor, at Hartree-Fock and correlated level of accuracy (MP2, CCS, CC2, CCSD, and CCSD(T)) have been carried out to investigate whether aromaticity could be related to the electric dipole polarizability of planar ring systems. The calculations prove the exaltation of the average property of conjugated molecules, which is possibly due to their easily polarizable π-electron cloud. On the other hand, theoretical out-of-plane polarizability components are smaller in benzene than in any other C$_6$H$_6$ isomer. The aromatic stabilization energies of monosubstituted five-membered conjugated cyclic molecules increase in the same di…
INCIDENCE CONSTRAINTS: A COMBINATORIAL APPROACH
2006
The simplest geometric constraints are incidences between points and lines in the projective plane. This problem is universal, in the sense that all algebraic systems reduce to such geometric constraints. Detecting incidence dependences between these geometric constraints is NP-complete. New methods to prove incidence theorems are proposed, which use strictly no computer algebra but only combinatorial arguments.
Finite Satisfiability of the Two-Variable Guarded Fragment with Transitive Guards and Related Variants
2018
We consider extensions of the two-variable guarded fragment, GF2, where distinguished binary predicates that occur only in guards are required to be interpreted in a special way (as transitive relations, equivalence relations, pre-orders or partial orders). We prove that the only fragment that retains the finite (exponential) model property is GF2 with equivalence guards without equality. For remaining fragments we show that the size of a minimal finite model is at most doubly exponential. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NExpTime-upper bou…