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Search: All articles in the CMB digital archive with keyword embedding

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1. CMB 2011 (vol 56 pp. 265)

Chen, Yichao; Mansour, Toufik; Zou, Qian
Embedding Distributions of Generalized Fan Graphs
Total embedding distributions have been known for a few classes of graphs. Chen, Gross, and Rieper computed it for necklaces, close-end ladders and cobblestone paths. Kwak and Shim computed it for bouquets of circles and dipoles. In this paper, a splitting theorem is generalized and the embedding distributions of generalized fan graphs are obtained.

Keywords:total embedding distribution, splitting theorem, generalized fan graphs
Category:05C10

2. CMB 2008 (vol 51 pp. 140)

Rossi, Julio D.
First Variations of the Best Sobolev Trace Constant with Respect to the Domain
In this paper we study the best constant of the Sobolev trace embedding $H^{1}(\Omega)\to L^{2}(\partial\Omega)$, where $\Omega$ is a bounded smooth domain in $\RR^N$. We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we consider deformations that preserve volume.

Keywords:nonlinear boundary conditions, Sobolev trace embedding
Categories:35J65, 35B33

3. CMB 2006 (vol 49 pp. 82)

Gogatishvili, Amiran; Pick, Luboš
Embeddings and Duality Theorem for Weak Classical Lorentz Spaces
We characterize the weight functions $u,v,w$ on $(0,\infty)$ such that $$ \left(\int_0^\infty f^{*}(t)^ qw(t)\,dt\right)^{1/q} \leq C \sup_{t\in(0,\infty)}f^{**}_u(t)v(t), $$ where $$ f^{**}_u(t):=\left(\int_{0}^{t}u(s)\,ds\right)^{-1} \int_{0}^{t}f^*(s)u(s)\,ds. $$ As an application we present a~new simple characterization of the associate space to the space $\Gamma^ \infty(v)$, determined by the norm $$ \|f\|_{\Gamma^ \infty(v)}=\sup_{t\in(0,\infty)}f^{**}(t)v(t), $$ where $$ f^{**}(t):=\frac1t\int_{0}^{t}f^*(s)\,ds. $$

Keywords:Discretizing sequence, antidiscretization, classical Lorentz spaces, weak Lorentz spaces, embeddings, duality, Hardy's inequality
Categories:26D10, 46E20

4. CMB 2005 (vol 48 pp. 622)

Vénéreau, Stéphane
Hyperplanes of the Form ${f_1(x,y)z_1+\dots+f_k(x,y)z_k+g(x,y)}$ Are Variables
The Abhyankar--Sathaye Embedded Hyperplane Problem asks whe\-ther any hypersurface of $\C^n$ isomorphic to $\C^{n-1}$ is rectifiable, {\em i.e.,} equivalent to a linear hyperplane up to an automorphism of $\C^n$. Generalizing the approach adopted by Kaliman, V\'en\'ereau, and Zaidenberg which consists in using almost nothing but the acyclicity of $\C^{n-1}$, we solve this problem for hypersurfaces given by polynomials of $\C[x,y,z_1,\dots, z_k]$ as in the title.

Keywords:variables, Abhyankar--Sathaye Embedding Problem
Categories:14R10, 14R25

5. CMB 2002 (vol 45 pp. 349)

Coppens, Marc
Very Ample Linear Systems on Blowings-Up at General Points of Projective Spaces
Let $\mathbf{P}^n$ be the $n$-dimensional projective space over some algebraically closed field $k$ of characteristic $0$. For an integer $t\geq 3$ consider the invertible sheaf $O(t)$ on $\mathbf{P}^n$ (Serre twist of the structure sheaf). Let $N = \binom{t+n}{n}$, the dimension of the space of global sections of $O(t)$, and let $k$ be an integer satisfying $0\leq k\leq N - (2n+2)$. Let $P_1,\dots,P_k$ be general points on $\mathbf{P}^n$ and let $\pi \colon X \to \mathbf{P}^n$ be the blowing-up of $\mathbf{P}^n$ at those points. Let $E_i = \pi^{-1} (P_i)$ with $1\leq i\leq k$ be the exceptional divisor. Then $M = \pi^* \bigl( O(t) \bigr) \otimes O_X (-E_1 - \cdots -E_k)$ is a very ample invertible sheaf on $X$.

Keywords:blowing-up, projective space, very ample linear system, embeddings, Veronese map
Categories:14E25, 14N05, 14N15

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