Physical Sciences and Mathematics Commons^™

Classes Of Commutative Clean Rings, Wolf Iberkleid, Warren William Mcgovern

Mathematics Faculty Articles

Let A be a commutative ring with identity and I an ideal of A. A is said to be I-clean if for every element α∈A there is an idempotent e = e²∈A such that α−e is a unit and αe belongs to I. A filter of ideals, say F, of A is Noetherian if for each I∈F there is a finitely generated ideal J∈F such that J⊆I. We characterize I-clean rings for the ideals 0, n(A), J( …

Chebyshev Optimized Approximate Deconvolution Models Of Turbulence, Iuliana Stanculescu, William Layton

Mathematics Faculty Articles

If the Navier–Stokes equations are averaged with a local, spacial convolution type filter,ϕ¯¯¯=gδ∗ϕ, the resulting system is not closed due to the filtered nonlinear termuu¯¯¯¯. An approximate deconvolution operator DD is a bounded linear operator which satisfies

u=D(u¯¯)+O(δα), Turn MathJaxon

where δδ is the filter width and α⩾2α⩾2. Using a deconvolution operator as an approximate filter inverse, yields the closure

uu¯¯¯¯=D(u¯¯)D(u¯¯)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+O(δα). Turn MathJaxon

The residual stress of this model (and related models) depends directly on the deconvolution error,u−D(u¯¯). This report derives deconvolution operators yielding an effective turbulence model, which minimize the deconvolution error for velocity fields with finite kinetic energy. …

Characterization Of Partial Derivatives With Respect To Boundary Conditions For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Jeffrey W. Lyons, Johnny Henderson

Mathematics Faculty Articles

Under certain conditions, solutions of the nonlocal boundary value problem, y⁽ⁿ⁾ = f(x, y, y', ... , y^{(n- 1)}), y(x_i) = Y_i for 1 £ i £ n- 1, and y(x_n) - Σ^m_k=1 Υ_iy (n_i) = y _n, are differentiated with respect to boundary conditions, where a < X₁ < X₂ < · · · < X_n-1 < n₁ < · · · < n_m < X_n < b, r₁, ... , r_m, Y1, ... , Y_n ∈ R .