he matrix functions can be defined by Cauchy's integral formula and approximated the linear combination of inverses shifted matrices using a quadrature formula. In this paper, we propose quantum algorithm for based on procedure to implement computers. Compared with previous study [S. Takahira, A. Ohashi, T. Sogabe, T.S. Usuda, Quant. Inf. Comput., \textbf{20}, 1\&2, 14--36, (Feb. 2020)] tha...

A perturbation method is used to solve eddycurrent testing problems for a flaw of arbitrary shape situated in a conducting half-space when the electric conductivities of the flaw and the surrounding medium are nearly the same. A general formula for the change in impedance is obtained. Examples of cylindrical flaws of finite length and spherical flaws are given. Detailed numerical results are gi...

We introduce a new operation on skew diagrams called composition of transpositions, and use it and a Jacobi-Trudi style formula to derive equalities on skew Schur Q-functions whose indexing shifted skew diagram is an ordinary skew diagram. When this skew diagram is a ribbon, we conjecture necessary and sufficient conditions for equality of ribbon Schur Q-functions. Moreover, we determine all re...

Let s,t be two given real numbers, s = t and m ∈ N . We determine the coefficients aj(s,t) in the asymptotic expansion of integral (or differential) mean of polygamma functions ψ (m)(x) : 1 t− s ∫ t s ψ (m)(x+u)du ∼ ψ (m) ( x ∞ ∑ j=0 aj(s,t) x j ) , x → ∞. We derive the recursive relations for polynomials aj(t,s) , and also as polynomials in intrinsic variables α = 2 (s + t − 1) , β = 4 [1− (t ...

A fourth-order compact difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grunwald formulae combining the compact technique. The properties of proposed fractional difference quotient operator are presented and proved. Then the new approximation formula is applied to solving the space fractional diffusion equations. By the energy...