A Novel Approximate Divider using Binomial Expansion

A general solution is presented for a thin, curved circular tube under in-plane bending. It includes the solution given by Clark and Reissner as a particular case in which the ratio of the radius of the tube to the radius of its center line is very small. The series expansions satisfy the equilibrium equation for any radius ratio while the compatibility condition is guaranteed by minimizing the complementary energy. The minimization is achieved in the manner of Raileigh-Ritz whereas the evaluation of integrals are facilitated by the use of binomial expansion. Numerical results correlate well with the experimental data. The solution is more rapidly convergent as compared to the existing analytical methods.

Download Full-text

A characterization of subnormal operators

Glasgow Mathematical Journal ◽

10.1017/s0017089500005474 ◽

1984 ◽

Vol 25 (1) ◽

pp. 99-101 ◽

Cited By ~ 1

Author(s):

Alan Lambert

Keyword(s):

Hilbert Space ◽

Hilbert Spaces ◽

Commutative Algebras ◽

Binomial Expansion ◽

Subnormal Operators

In this note a characterization of subnormality of operators on Hilbert space is given. The characterization is in terms of a sequence of polynomials in the operator and its adjoint reminiscent of the binomial expansion in commutative algebras. As such no external Hilbert spaces are needed, nor is it necessary to introduce forms dependent on arbitrary sequences of vectors from the Hilbert space.

Download Full-text

A serendipitous path to a famous inequality

The Mathematical Gazette ◽

10.1017/s0025557200182518 ◽

2008 ◽

Vol 92 (523) ◽

pp. 50-54

Author(s):

Robert M. Young

Keyword(s):

Real Number ◽

Geometric Means ◽

Algebraic Identity ◽

Binomial Expansion

The mysterious path of discovery – the tireless experimentation in search of patterns, the veiled connections that suddenly unfold, serendipity – all these elements combine to make mathematics so magical. The purpose of this note is to show how a routine algebraic identity, the binomial expansion of (x- 1)2, can be used to give a new proof of the fundamental inequality between the arithmetic and geometric means. The proof will provide further evidence that a great deal of useful mathematics can be derived from the obvious assertion that the square of a real number is never negative.

Download Full-text