The ability to make inductive inferences is crucial for humans, and it has long been demonstrated that labels play an important role in induction. However, the mechanism by which labels contribute to induction remained unclear. According to one theoretical position, often referred to as the naïve theory, even for young children labels presented as count nouns are special properties: even young ...

The fully Sinc-Galerkin method is developed for a family of complex-valued partial differential equations with time-dependent boundary conditions. The Sinc-Galerkin discrete system is formulated and represented by a Kronecker product form of those equations. The numerical solution is efficiently calculated and the method exhibits an exponential convergence rate. Several examples, some with a re...

In our recent publications we have introduced the incomplete cosine expansion of the sinc function for efficient application in sampling [Abrarov & Quine, Appl. Math. Comput., 258 (2015) 425-435; Abrarov & Quine, J. Math. Research, 7 (2) (2015) 163-174]. Here we show that it can also be utilized as a flexible and efficient tool in mathematical analysis. In particular, an application of the inco...

The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation still works accurately when combined with a proper variable transformation. The convergence rate has been analyzed for typical cases including finite, semi-infinite, and infinite intervals....

The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation. Their convergence rates have been analyzed for typical cases including finite, semi-infinite, and infinite intervals. In addition, for verified automatic integra...

in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

A fast multilevel algorithm (MuST) for evaluating an n-sample sinc interpolant at mn points is presented. For uniform grids, its complexity is 25mn log(1/δ) flops for the sinc kernel and 75mn log(1/δ) for the sincd kernel, where δ is the target evaluation accuracy. MuST is faster than FFTand FMM-based evaluations for large n and/or for large δ. It is also applicable to non-uniform grids and to ...