Diagnosing the status of crop nitrogen (N) helps to optimize crop yield, improve N use efficiency, and reduce the risk of environmental pollution. The objectives of the present study were to develop a critical N (Nc) dilution curve for winter wheat (based on spike dry matter [SDM] during the reproductive growth period), to compare this curve with the existing Nc dilution curve (based on plant d...

Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...

The quotient of the upper half plane by Γ1(N), acting by fractional linear transformations, is the complex manifold associated to an affine algebraic curve Y1(N)/C. This curve has a natural model Y1(N)/Q, which for N > 3 is a fine moduli scheme for elliptic curves with a point of exact order N . We will let X1(N) denote the smooth projective curve which contains Y1(N) as a dense Zariski open su...

Results The mean primary right thoracic curve was 29° uncorrected; the mean secondary curve measured 19°. In the Boston brace group the mean primary right thoracic curve was 22° ; the mean secondary curve measured 16°. The mean corrective force over the lumbar brace pad in standing position was 382 N; over the thoracic brace pad it was 285 N. In the M brace group the mean primary right thoracic...

A geometric interpretation of the diagonal of a tensor-product trivariate Bézier volume using degree elevation of Bézier triangles is given. A brief discussion of the diagonal curve of a tensor-product bivariate Bézier surface will help to motivate our geometric interpretation for the diagonal curve of a Bézier volume. Suppose we have a tensor-product Bézier surface, x(u, v), given by x(u, v) =...