In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman estimate proved in our previous work [5]. We then apply the three-region inequality to study the size estimate problem with one boundary measurement.

â â â â  â  abstract â  most debates about the role of tariff cuts on the level of employment and rate of wages in labor market have come out of well-known hecscher – ohlin and stopler – samuelson (hos) theorems. considering the fact that we have divided the workforce into skilled and unskilled labors the present paper assesses the impacts of tariff cuts on labor market indicators in iran. ...

This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations. 1. Introduction. It is well known that integral inequalities play a very crucial role in the stud...

Let eij be the number of edges in a convex 3–polytope joining the vertices of degree i with the vertices of degree j. We prove that for every convex 3-polytope there is 20e3,3 +25e3,4 +16e3,5 +10e3,6 + 6 2 3 e3,7+5e3,8+2 1 2 e3,9+2e3,10+16 2 3 e4,4+11e4,5+5e4,6+1 2 3 e4,7+5 1 3 e5,5+ 2e5,6 ≥ 120; moreover, each coefficient is the best possible. This result brings a final answer to the conjectur...

Solution to the optimal stopping problem V (x) = sup E(x + X) + is given, where X = fXtg t0 is a L evy process, and the supremum is taken over the class of stopping times. Results are expressed in terms of the distribution of the random variable M = sup t Xt, under the hypothesis E(M) < +1, and simple conditions for this hypothesis to hold are given. Based on this, the prophet inequality V (x) ...

In this paper, we prove that the inequality [Γ(x + y + 1)/Γ(y + 1)]1/x [Γ(x + y + 2)/Γ(y + 1)]1/(x+1) < s x + y x + y + 1 is valid if and only if x+ y > y +1 > 0 and reversed if and only if 0 < x+ y < y + 1, where Γ(x) is the Euler gamma function. This completely extends the result in [Y. Yu, An inequality for ratios of gamma functions, J. Math. Anal. Appl. 352 (2009), no. 2, 967–970.] and thor...

0.2. Remarks. The proof, which was included in the author’s thesis [א], follows closely a suggestion of N. Elkies. In the exposition here many details were added to the argument in [א]. We utilize the work [L-Y] of P. Li and S. T. Yau on conformal volumes, as well as the known bound on the leading nontrivial eigenvalue of the non-euclidean Laplacian λ1 ≥ 21 100 [L-R-S]. If Selberg’s eigenvalue ...

1.9 Decide for which n the inequality 2 > n holds true, and prove it by mathematical induction. The inequality is false n = 2, 3, 4, and holds true for all other n ∈ N. Namely, it is true by inspection for n = 1, and the equality 2 = 4 holds true for n = 4. Thus, to prove the inequality for all n ≥ 5, it suffices to prove the following inductive step: For any n ≥ 4, if 2 ≥ n, then 2 > (n+ 1). T...