(1) Background: Panax ginseng root is one of the most important herbal products, and the profiling of ginsenosides is critical for the quality control of ginseng roots at different ages in the herbal markets. Furthermore, interest in assessing the contents as well as the localization of biological compounds has been growing. The objective of this study is to carry out the mass spectrometry (MS)...

In recent works, we have studied linear predictive models constrained by time-domain filters. In the present study, we will study the one-dimensional case in more detail. Firstly, we obtain root-exchange properties between the roots of an all-pole model and corresponding constraints. Secondly, using the root-exchange property we can construct a novel matrix decomposition A RA = I, where R is a ...

The eigenvalues of a matrix polynomial can be determined classically by solving a generalized eigenproblem for a linearized matrix pencil, for instance by writing the matrix polynomial in companion form. We introduce a general scaling technique, based on tropical algebra, which applies in particular to this companion form. This scaling, which is inspired by an earlier work of Akian, Bapat, and ...

Necessary conditions, under which the maximal-rank minors of a (possibly singular) Macaulay matrix of a polynomial system vanish, are analyzed. It is shown that the vanishing of the maximal-rank minors of the Macaulay matrix of a system of parametric polynomials under specialization is a necessary condition for the specialized polynomials to have an additional common root even when the parametr...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

We give an algorithm for constructing the algebraic hull of a given matrix Lie algebra. It is based on an algorithm for finding integral linear dependencies of the roots of a polynomial, that is probably of independent interest.

We derive bounds on the variance of a finite universe. Some related inequalities for the roots of the polynomial equations and bounds for the largest and smallest eigenvalues of a square matrix with real spectrum are obtained.

There are several methods to count the number of real roots of an univariate polynomial p(x) ∈ R[x] of degree n (for details we refer to [BPR]). Among them, the Sturm algorithm says that the number of real roots of p(x) is equal to the number of Permanence minus the number of variations of signs which appears in the leading coefficients of the signed remainders sequence of p(x) and p(x). Anothe...