We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. 1. Background on counting zeros of solutions of linear ordinary differential equations 1.1. De la Valée Poussin theorem and Novikov’s counterexample. A linear...

Naphtho[2,1-b]thiophene (NTH) is an asymmetric structural isomer of dibenzothiophene (DBT), and in addition to DBT derivatives, NTH derivatives can also be detected in diesel oil following hydrodesulfurization treatment. Rhodococcus sp. strain WU-K2R was newly isolated from soil for its ability to grow in a medium with NTH as the sole source of sulfur, and growing cells of WU-K2R degraded 0.27 ...

The current emphasis on increasing aeronautical efficiency is leading the way to a new class of lighter more flexible airplane materials and structures, which unfortunately can result in aeroelastic instabilities. To effectively control the wings deformation and shape, appropriate modeling is necessary. Wings are often modeled as cantilever beams using finite element analysis. The drawback of t...

The subsumption theorem is an important theorem concerning resolution. Essentially, it says that a set of clauses logically implies a clause C, ii C is a tautology, or a clause D which subsumes C can be derived from with resolution. It was originally proved in 1967 by Lee in Lee67]. In Inductive Logic Programming, interest in this theorem is increasing since its independent rediscovery by Bain ...

This article discusses some introductory ideas associated with complex numbers, their algebra and geometry. This includes a look at their importance in solving polynomial equations, how complex numbers add and multiply, and how they can be represented. Finally we look at the nth roots of unity, that is, the solutions of the equations z = 1. 1 The Need For Complex Numbers The shortest path betwe...

The subsumption theorem is an important theorem concerning resolution. Essentially, it says that if a set of clauses logically implies a clause C, then either C is a tautology, or a clause D which subsumes C can be derived from with resolution. It was originally proved in 1967 by Lee. In Inductive Logic Programming, interest in this theorem is increasing since its independent rediscovery by Bai...

The subsumption theorem is an important theorem concerning resolution. Essentially , it says that if a set of clauses logically implies a clause C, then either C is a tautology, or a clause D which subsumes C can be derived from with resolution. It was originally proved in 1967 by Lee in Lee67]. In Inductive Logic Programming, interest in this theorem is increasing since its rediscovery by Bain...

In this paper, we consider the generalized Fibonacci and Pell Sequences and then show the relationships between the generalized Fibonacci and Pell sequences, and the Hessenberg permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Pell Sequence, fPng ; is de…ned by the recurrence...