A plane algebraic curve can be represented as the zero-set of a polynomial in two or if one takes homogenous coordinates: three variables. The coefficients of the polynomial determine the curve uniquely. Thus features of the curve, like for instance rotation symmetry, must find their correspondence in the algebraic structure of the coefficients of the polynomial. In this article we will investi...

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension...

In this paper an algorithm that provides an equivalent, but of reduced order, representation for multivariate polynomial matrices is given. It combines ideas from computational symbolic algebra and from established techniques in graph representation and polynomial/matrix algebraic manipulations. The algorithm is applied to the problem of finding minimal linear fractional transformation models. ...

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary r-fold atypical gl m|n-Kac-module and the set of composition factors of some r-fold atypical gl r|r-Kac-module. The result of...

— A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain. Polynomial phase signals are not sparse in commonly used domains such as Fourier or wavelet domain. Therefore, for polynomial phase signals standard CS algo...

In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinations of roots of several univariate polynomial equations. The main advantage of this representation is that the precision of the roots can be easily controlled. In fact, based on the linear univari...

Among private set operations, the privacy preserving element reduction of a multiset can be an important tool for privacy enhancing technology as itself or in the combination with other private set operations. Recently, a protocol, over-threshold-set-union-protocol, for a privacy preserving element reduction method of a multiset was proposed by Kissner and Song in Crypto 2005. In this paper, we...

The aim of this paper is to study and investigate some new properties of the beta polynomials. Taking derivative of the generating functions for beta type polynomials, we give two partial differential equations (PDEs). By using these PDEs, we derive derivative formulas of the beta type polynomials. In order to construct a matrix representation for the beta polynomials, we firstly show that the ...

We focus on how the choice of input-output representation has a crucial impact on the expressiveness of so-called “logics of polynomial time.” Our analysis illustrates this dependence in the context of Light Affine Logic (LAL), which is both a restricted version of Linear Logic, and a primitive functional programming language with restricted sharing of arguments. By slightly relaxing representa...