Let E be a vector space endowed with two norms ∥·∥ 1 , ∥·∥ 2 . A third norm on E can be defined by ∥·∥ 3 =∥(∥·∥ 1 ,∥·∥ 2 )∥ where ∥·∥ is a norm on 2 . We prove: a) The topology defined by ∥·∥ 3 is the supremum of the topologies defined by...
I am trying to solve one equation: Ax=b where A is a 4*3 non-rectangular matrix, x is the 3*1 unknown vector and b is the 3*1 vector. I know if the minimum two norm sum of x, i.e. sqrt(x(1)^2+x(2)^2+x(3)^2), is wanted, then the solution is x=pinv(A)*b, w...
TWO-WEIGHT NORM INEQUALITIES FOR VECTOR-VALUED OPERATORS We study two-weight norm inequalities for a vector-valued operator from a weighted L-P (sigma)-space to mixed norm L-ls(q) (mu) spaces, 1 < p < infinity, 0 < q < p. We apply these results to the boundedness of Wolff's pote...
showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify algorithm is optimal (PSPACE), but only if the input vectors are given in...
A universal construction for moduli spaces of decorated vector bundles over curves Let $X$ be a smooth projective curve over the complex numbers. To everyrepresentation $ho\\colon \\GL(r)\\lra \\GL(V)$ of the complex general lineargroup o... A Schmitt - 《Transformation Groups》 被引量...
(optional) $sDratios shear distances from iNode as a fraction of the element length, size of ratio vector is 1 for 2D-case and 2 for 3D-case (entries: [dy_iNode, dz_iNode] (optional, default = [0.5 0.5]) -doRayleigh to include Rayleigh damping from the element (optional, default =...
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() Citation Context ...lly, DE adds the weighted differencesbetween two population vectors to a third vector. This way no separate probability distribution... Xie, Xiao-Feng,Zhang, Wen-Jun,Bi, De-Chun - IEEE 被引量: 34发表: 2005年 Integrating the heterogeneous control properties of software...
Let R be the vector of Riesz transforms on Rn, and let {\mu}, {\lambda} {\in} {A_p} be two weights on {R_n}, {1 < p < \infty}. The two-weight norm inequality for the commutator {[b, R] : Lp(\mu) ightarrow Lp(\lambda)} is shown to be equivalent to the function ...
In the case of the LL, the vector solitons are stable almost in their entire existence domain, while the NL can only stabilize the solitons in which the component affected by the lattice carries the norm which is comparable to, or larger than the norm of the component in the uniform ...