Functions are exhibited which interpolate the magnitude of a solution y of a linear, homogeneous, second-order differential equation at its critical points, \y'\ at the zeros of y, and \fi0y(t)Kt) àt\ at the zeros of y. Except for a normalization condition, the interpolating functions are independent of the specific solution v. A theorem similar in its conclusions to the Sonin-Pólya-Butlewski t...

This paper describes the interpolation of head related transfer functions (HRTFs) for all direction in the median plane. The interpolation of HRTFs enables us to reduce the number of measurements for new user’s HRTFs, and also reduce the data of HRTFs in auditory virtual systems. In this paper, a simple linear interpolation method and the spline interpolation method are evaluated and it is clar...

The computation of functions of matrices is a classical topic in numerical linear algebra. In the recent years research in this area has received new impulse due to the introduction of Krylov subspace techniques for the treatment of functions of large and sparse matrices, in particular in the context of the solution of di erential problems. Such techniques are projective in nature, since they r...

A multiattribute utility function can be represented by a function of single-attribute utility functions if the decision maker’s preference satisfies additive independence or mutually utility independence. Additive independence is a preference condition stronger than mutually utility independence, and the multiattribute utility function is in the additive form if the former condition is satisfi...

Abstract We prove that smooth Wigner–Weyl spectral sums at an energy level E exhibit Airy scaling asymptotics across the classical surface Σ . This was proved earlier by authors for isotropic harmonic oscillator and proof is extended in this article to all quantum Hamiltonians − ℏ 2 Δ + V where a confining potential with most quadratic growth infinity. The main tools are Herman–Kluk initial val...