We characterize the approximate monomial complexity, sign monomial complexity, and the approximate L1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L1 norm solves the main conjecture in [AFH12]. As an application of the characterization of the sign monomial complexity, we prove a conjecture in [ZS09] and provide a...

We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for ...

One of the most important primitive data types in modern data processing is text. Text data are known to have a variety of inconsistencies (e.g., spelling mistakes and representational variations). For that reason, there exists a large body of literature related to approximate processing of text. This monograph focuses specifically on the problem of approximate string matching, where, given a s...

In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

in the present paper, a numerical method is considered for solving one-dimensionalheat equation subject to both neumann and dirichlet initial boundaryconditions. this method is a combination of collocation method and radial basis functions (rbfs). the operational matrix of derivative for laguerre-gaussians (lg) radial basis functions is used to reduce the problem to a set of algebraic equations...