(3) The Extension Theorem (Theorem 7.6) describes the extension of a fundamental derivation of ak-domainBtoB[t] by an invariant function. The Classification Theorem is used to describe three-dimensional UFDs which admit a certain kind ofSL2(k) action (Theorem 6.2). This description is used ...
Let k be an algebraically closed field of characteristic zero and B a factorial affine k -domain equipped with a locally nilpotent derivation δ . We investigate B when there exists an element z ∈ B such that δ (z) = α p for p ≥ 1 and a prime element α of A = Ker δ . ...
We derive and discuss a set of parametric equations which, when given a convex 3D feature domain, K, will generate affine invariants with the property that the invariants' values are uniformly distributed in the region [0,1]×[0,1]×[0,1]. Once the shape of the feature domain K is de...
On the Structure of Maximal Cohen–Macaulay Modules over the Ring K[[x, y]]/(xn)\\boldsymbol{K[[x, y]]/(x^n)} We study maximal Cohen–Macaulay modules over the hypersurface ring K[[x, y]]/(xn), n ³ 3,K[[x, y]]/(x^n),\\ n\\geq 3, K being a field. Infinite ...
The imageaffine of Image for PHP return an image containing the affine transformed src image, using an optional clipping area. Syntax imageaffine( GdImage $image, array $affine, ?array $clip = null ): GdImage|false Parameters image
As an application of the aane resultant, we give an explicit formula for the degree of a zero-dimensional intersection of n algebraic hypersurfaces in K n , for any algebraically closed eld K. The latter formula reenes and generalizes the celebrated mixed volume formula of David N. Bernshtein...
\begin{aligned} {[}a,b,c] = v \circ c \qquad \text {and} \qquad \Lambda (k,a,b) = kv \circ a, \end{aligned} where v\in V is the unique vector such that v \circ a = b. It is clear that \begin{aligned} \Lambda (1,a,b) = v\circ a = b \qquad \text {and} ...
Instead of analyzing the geometry of matched feature points, the problem is recast in the frequency domain through the use of Integral Projection, showing how this is a reasonable model for orthographic cameras. The problem now reduces to one of identifying matching lines in the frequency domain ...
Using a previous method on cyclotomic walled Brauer algebras, we prove that $BC_{k, r, t}$ is free over $R$ with super rank $(k^{r+t}2^{r+t-1} (r+t)!, k^{r+t}2^{r+t-1} (r+t)!)$ if and only if it is admissible. Finally, we give a proof of Comes-Kujawa's ...
A bipartite graph Gn = (U, V, E) is said an (n, k, &dgr;) expander if |U| = |V| = n, |E| ≤ kn, and for any X ⫅ U, |&Ggr;Gn(X)| ≥ (1+&dgr;(1-|X|/n)) ... S Jimbo,A Maruoka - Springer-Verlag New York, Inc. 被引量: 167发表: 1985年 Properly Discon...