In this paper, a semi-analytical method, i.e. homotopy analysis is used to find the linear and non-linear Klein–Gordon equation solution. The method very effective, easy calculate. solution has faster convergence than traditional Adomian decomposition can be applied other problems. This method’s efficiency with been illustrated via different examples such as homogeneous linear, inhomogeneous no...

We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e. without appealing to the classification of finite Coxeter groups) using basic facts about noncrossing partitions. We solve these recursions for each finite Coxeter group in the classification. Amon...

The paper gives a self-contained survey of fast algorithms for solving linear systems of equations with Toeplitz or Hankel coefficient matrices. It is written in the style of a textbook. Algorithms of Levinson-type and of Schur-type are discussed. Their connections with triangular factorizations, Padè recursions and Lanczos methods are demonstrated. In the case in which the matrices possess add...

We give a construction of the moduli space of stable maps to the classifying stack Bμr of a cyclic group by a sequence of r-th root constructions on M0,n. We prove a closed formula for the total Chern class of μreigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus zero Gromov-Witten theory of stacks of the form [C/μr ]. We deduce linear recursions for all genus-zero ...

TheWigner phase-space distribution function provides the basis for Moyal’s deformation quantization alternative to the more conventional Hilbert space and path integral quantizations. General features of time-independent Wigner functions are explored here, including the functional (“star”) eigenvalue equations they satisfy; their projective orthogonality spectral properties; their Darboux (“sup...

At Crypto 2009 [1], Bernstein initiated an optimization of Karatsuba formula for binary polynomial multiplication by reorganizing the computations in the reconstruction part of two recursions of the formula. This approach was generalized in [10] to an arbitrary number of recursions resulting in the best known bit parallel multiplier based on Karatsuba formula. In this paper we extend this appro...