Recently, a previous contributor showed how the delta-wye conversion may be applied to find the equivalent capacitance of five capacitors arranged in a bridge configuration. In fact, that contributor gave an algorithm for this purpose which showed that the equivalent capacitance depends upon all five capacitors. However, in this paper, we point out that there is a special case where the equival...

Analytic curves are classified w.r.t. their symmetry under a given regular and separately analytic Lie group action G×M→M on an manifold. We show that non-constant curve γ:D→M is either free or exponential – i.e., up to reparametrization of the form t↦exp⁡(t⋅g→)⋅x. The vector g→∈g additionally proven be unique (non-zero scalation and) addition elements in algebra stabilizer Gγ≡{g∈G|g⋅γ=γ} γ. fu...

We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycl...

The convergence rate of a Krylov method such as the Generalized Conjugate Resid10 ual (GCR) [6] method, to solve a linear system Au = f , A = (ai j) ∈ Rm×m,u ∈ 11 R m, f ∈ Rm, decreases with increasing condition number κ2(A) = ||A||2||A−1||2 12 of the non singular matrix A. Left preconditioning techniques consist of solving 13 M−1Au=M−1 f such that κ2(M−1A)<<κ2(A). The Additive Schwarz (AS) pre...

environmental variables, including soil water content (swc), act as constraints on crop growth and productivity. therefore, open air (e0), perforated (e1) and non-perforated (e2) plastic housings were used with well-watered (w0), moderately-watered (w1) and water-stressed (w2) bush bean plants to explore the relationships between water-use efficiency (wue), carbon isotope discrimination (δ) and...

An independent dominating set of a graph, also known as maximal set, is S pairwise non-adjacent vertices such that every vertex not in adjacent to some S. We prove for Δ=4 or Δ≥6, connected n-vertex graph maximum degree at most Δ has an size (1−Δ⌊Δ2/4⌋+Δ)(n−1)+1. In addition, we characterize all graphs having the equality and show other have (1−Δ⌊Δ2/4⌋+Δ)n.

Peroxisome proliferator-activated receptor β/δ (PPARβ/δ) is a nuclear receptor involved in regulation of lipid and glucose metabolism, wound healing and inflammation. PPARβ/δ has been associated also with cancer. Here we investigated the expression of PPARβ/δ and components of the prostaglandin biosynthetic pathway in non-small cell lung cancer (NSCLC). We found increased expression of PPARβ/δ,...