Determining Whether a Multivariate Hyperexponential Function is Algebraic

Determining Whether a Multivariate Hyperexponential Function is Algebraic

Let F = C(x1, . . . , x`, x`+1, . . . , xm), where x1, . . . , x` are continuous variables, and x`+1, . . . , xm are discrete variables. We show that a hyperexponential function, which is algebraic over F , is of form g(x1, . . . , xm)q(x1, . . . , x`) 1 t ω x`+1 j+1 · · ·ωxm m where g ∈ F , q ∈ C(x1, . . . , x`), t ∈ Z and ω`+1, . . . , ωm are roots of unity. Furthermore, we present an algorit...

Determining Whether V(A) Has a Model Companion is Undecidable

Using techniques pioneered by R. McKenzie, we prove that there is no algorithm which, given a finite algebra in a finite language, determines whether the variety (equational class) generated by the algebra has a model companion. In particular, there exists a finite algebra such that the variety it generates has no model companion; this answers a question of Burris and Werner from 1979.

Determining whether curcumin degradation/condensation is actually bioactivation (Review).

Curcumin has been shown to exert therapeutic or protective effects against a variety of diseases, such as cancer, pulmonary diseases, neurological, liver, metabolic, autoimmune, cardiovascular diseases and numerous other chronic ailments. Over 116 clinical studies on curcumin in humans were registered with the US National Institutes of Health in 2015. However, it is mystifying how curcumin can ...

Method for Determining Whether a Gene Of

An Algorithm for Determining Whether a given Binary Matroid Is Graphic

1. Introduction. In a recent series of papers [l-4] on graphs and matroids I used definitions equivalent to the following. A binary chain-group N on a. finite set M is a class of subsets of M forming a group under mod 2 addition. These subsets are the chains of N. A chain of N is elementary if it is non-null and has no other non-null chain of AT as a subset. A binary matroid is the class of ele...