Mahler’s measure is generalized to create the class of multiplicative distance functions. These functions measure the complexity of polynomials based on the location of their zeros in the complex plane. Several examples of multiplicative distance functions are given including those formed from equilibrium potentials of compact connected subsets of C. To each multiplicative distance function we ...

Mahler’s measure is generalized to create the class of multiplicative distance functions. These functions measure the complexity of polynomials based on the location of their zeros in the complex plane. Following work of S.-J. Chern and J. Vaaler in [1], we associate to each multiplicative distance function two families of analytic functions which encode information about its range on C[x] and ...

We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. Namely, we introduce the class of Krein–Langer strings and show that there is a bijective correspondence between moment sequences and this class of generalized indefinite strings. This result can be viewed as a complement to the classical results of M. G. Krein on the co...

It is a challenging task to design orthogonal filter banks, especially multidimensional (MD) ones. In the onedimensional (1D) two-channel finite impulse response (FIR) filter bank case, several design methods exist. Among them, designs based on spectral factorizations (by Smith and Barnwell) and designs based on lattice factorizations (by Vaidyanathan and Hoang) are the most effective and widel...

given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...

which is clearly angle-dependent. If all orientations of L with respect to B were allowed, then a continuous range of E would occur and an atomic transition would show a spectral line broadened by an amount proportional to the field strength. Instead such spectral lines are observed to split into several discrete lines, indicating that only certain values of L · B are allowed; this implies spat...

Some partition theorems similar to the Rogers-Ramanujan theorems are proved. We shall prove the following partition theorems, namely THEOREM 1. The number of partitions of k, k = a 1 + a 2 + a 3 + · · · with a 1 > a 2 ≥ a 3 > a 4 ≥ · · ·

The modified LF voice source model of KLSYN88 was investigated through spectral and glottal waveform analysis of synthesized vowels, where each of the four parameters of the model was systematically varied; open quotient (OQ), speed quotient (SQ), spectral tilt (TL), and the amplitude of voicing (AV). There was particular emphasis on comparison with the original LF model. The spectral analysis ...

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse ske...

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...