We introduce 3N × 3N Lax pair with spectral parameter for Calogero-Inozemtsev model. The one degree of freedom case appears to have 2 × 2 Lax representation. We derive it from the elliptic Gaudin model via some reduction procedure and prove algebraic integrability. This Lax pair provides elliptic linear problem for the Painlevé VI equation in elliptic form.

The effects of dietary 18:3n 3 on the fatty acid composition of plasma, red blood cells, aorta, platelets, plasma cholesterol, triglycerides, and platelet response to collagen-induced aggregation in swine was investigated. Pigs (n ) 25) were fed diets containing 18:3n 3 at 0% (control), 1.5% (LNA1), 2.5% (LNA2), and 3.6% (LNA3). Dietary 18:3n 3 resulted in a significant (P < 0.05) enrichment of...

We previously reported the tumor-suppressive activity of insulin-like growth factor binding protein-related protein 1 (IGFBP-rP1) through induction of apoptosis in human prostate cancer cells. The aim of this study was to investigate the effects of IGFBP-rP1 for radiosensitivity and chemosensitivity in hormone-refractory human prostate PC-3 cancer cells. Five assays were performed using PC-3 ce...

The desaturation of [1-(14)C] 18:3n-3 to docosahexaenoic acid (DHA; 22:6n-3) is enhanced in an essential fatty acid deficient cell line (EPC-EFAD) in comparison with the parent cell line (EPC) from carp. In the present study, the effects of DHA on lipid and fatty acid compositions, and the metabolism of [1-(14)C]18:3n-3 were investigated in EPC-EFAD cells in comparison with EPC cells. DHA suppl...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

The complete tripartite graph Kn,n,n has 3n 2 edges. For any collection of positive integers x1, x2, . . . , xm with m ∑ i=1 xi = 3n 2 and xi > 3 for 1 6 i 6 m, we exhibit an edge-disjoint decomposition of Kn,n,n into closed trails (circuits) of lengths x1, x2, . . . , xm.

We show that there is n0 such that if H is a 3-uniform hypergraph on n ∈ 4Z, n ≥ n0, vertices such that δ1(H) ≥ ( n−1 2 ) − ( 3n/4 2 ) + 3n 8 + 1 2 , then H can be tiled with copies of C4, the unique 3-uniform hypergraph on four vertices with two edges. The degree condition is tight when 8|n.

We will introduce a generalization of the concept of cooperative game. First, we consider the set 3N of all the ordered pairs of disjoint coalitions. Next, we de...ne bicooperative games b : 3N ! R and we study the class of bisubmodular (bisupermodular) games. Journal of Economic Literature Classi...cation Number: C71.

The graph (non-)planarity game is played on the complete graph Kn between an Enforcer and an Avoider, each of whom take one edge per round. The game ends when the edges chosen by Avoider form a non-planar subgraph. We show that Avoider can play for 3n− 26 turns, improving the previous bound of 3n− 28 √ n.