Elasticity of factorizations in integral domains

Integral representations of displacements in linear elasticity

We present some new formulae for the solution of boundary value problems for a two-dimensional isotropic elastic body. In particular, using the so-called Dbar formalism and the method introduced by Fokas (2008) [4], we obtain integral representations of the Fourier type for the displacements appearing in boundary value problems formulated in an arbitrary convex polygon with n sides. © 2011 Else...

Of Integral Domains

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-mult...

Integral Equations Formulation of Classical Elasticity

Factorization in Integral Domains II

Theorem 1.1 (Rational roots test). Let f = anx n + · · · + a0 ∈ Z[x] be a polynomial of degree n ≥ 1 with integer coefficients and nonzero constant term a0, and let p/q ∈ Q be a rational root of f such that the fraction p/q is in lowest terms, i.e. gcd(p, q) = 1. Then p divides the constant term a0 and q divides the leading coefficient an. In particular, if f is monic, then a rational root of f...

Unique Factorization in Integral Domains

Throughout R is an integral domain unless otherwise specified. Let A and B be sets. We use the notation A ⊆ B to indicate that A is a subset of B and we use the notation A ⊂ B to mean that A is a proper subset of B. The group of elements in R which have a multiplicative inverse (the group of units of R) is denoted R×. Since R has no zero divisors cancellation holds. If a, b, c ∈ R and a 6= 0 th...