We investigate, in this article, a generalization of the Riemann–Roch theorem for graphs of Baker and Norine, with a view toward identifying new objects for which a two-variable zeta-function can be defined. To a lattice Λ of rank n − 1 in Z n and perpendicular to a positive integer vector R, we define the notions of g-number and of canonical vector , in analogy with the notions of genus and ca...

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed an...

This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description [Formula: see text] with [Formula: see text] a tall constant matrix of full column rank and with the determinantal zeros of [Formula: see text] all stable, i.e. in [Formula: see text]. To obtain a parsimonious AR model, ...

The electronic partition function for the hydrogen atom was recently derived by integration over the Coulomb propagator. A much simpler derivation is given here, based on Schrfdinger's exact solution for a hydrogenic atom in a Riemannian space of positive curvature. The energy spectrum is entirely discrete, including states which correspond to the ionized atom. The curvature in Riemannian space...

A new kind of ambiguity function (AF) associated with the linearcanonical transform (LCT) is proposed in this article, this new AF is defined based on the LCT and the classical AF. Firstly, the main properties and physical meanings of the newly defined AF are investigated, the results show that this kind of AF can be seen as one generalization of the classical AF. Then, the newly defined AF is ...

In a well-known result on graph property testing, [GT03] showed that every testable graph property has a “canonical” testing algorithm in which a set of vertices is selected uniformly at random and the edges queried are the complete graph over the selected vertices. In this paper we define a similar-in-spirit canonical form for Boolean function testing algorithms, and show that under some mild ...

To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an environment of functions on an input space X induc...

The Canonical Function Method (CFM) is a powerful method that solves the radial Schrödinger equation for the eigenvalues directly without having to evaluate the eigenfunctions. It is applied to various quantum mechanical problems in Atomic and Molecular physics with presence of regular or singular potentials. It has also been developed to handle single and multiple channel scattering problems w...

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness.