In this article, we study Hilbert Series of non-Cohen-Maculay tangent cones for some 4-generated pseudo symmetric monomial curves. We show that the Function is nondecreasing by explicitly computing it. also compute standard bases these toric ideals.

A renewal model in risk theory is considered, where H(u, y) is the tail of the distribution of the deficit at ruin with initial surplus u and F(y) is the tail of the ladder height distribution. Conditions are derived under which the ratio H(u, y)/F(u + y) is nondecreasing in u for any y ≥ 0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then...

The proof of the main result in Reny and Perry (2006) is provided here. We also provide an example in which the best reply to nondecreasing bidding functions fails to be nondecreasing, and we show how to approximate a degenerate density by one that satis…es the assumptions in Reny and Perry (2006). Finally, we establish that Reny and Perry’s (2006) main result continues to hold when the notion ...

This paper is devoted to the study of nonlinear stability steady incompressible Euler flows in two dimensions. We prove that a flow nonlinearly stable L p <mml:annotation encoding="applicati...

Given a barrier 0 ≤ b0 ≤ b1 ≤ · · · , let f(n) be the number of nondecreasing integer sequences 0 ≤ a0 ≤ a1 ≤ · · · ≤ an for which aj ≤ bj for all 0 ≤ j ≤ n. Known formulæ for f(n) include an n × n determinant whose entries are binomial coefficients (Kreweras, 1965) and, in the special case of bj = rj + s, a short explicit formula (Proctor, 1988, p.320). A relatively easy bivariate recursion, d...