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71.
Andr�� Uschmajew 《Constructive Approximation》2011,34(3):371-391
We investigate first-order conditions for canonical and optimal subspace (Tucker format) tensor product approximations to
square integrable functions. They reveal that the best approximation and all of its factors have the same smoothness as the
approximated function itself. This is not obvious, since the approximation is performed in L
2. 相似文献
72.
Eugenio Hern��ndez Jos�� Mar��a Martell Maria de Natividade 《Constructive Approximation》2011,33(1):1-14
We study the efficiency of the greedy algorithm for wavelet bases in Lorentz spaces in order to give the near best approximation.
The result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces. 相似文献
73.
Let X be a real linear space and $D\subseteq X$ be a nonempty convex subset. Given an error function E:[0,1]×(D?D)?????{+??} and an element $t\in\left]0,1\right[$ , a function f:D??? is called (E,t)-convex if $$f(tx+(1-t)y)\le tf(x)+(1-t)f(y)+E(t,x-y)$$ for all x,y??D. The main result of this paper states that, for all a,b??(???{0})+{0,t,1?t} such that {a,b,a+b}??????, every (E,t)-convex function is also $\big(F,\frac{a}{a+b}\big)$ -convex, where $$F(s,u):=\frac{{(a+b)}^2s(1-s)}{t(1-t)}E\left(t,\frac{u}{a+b}\right),\qquad (u\in (D-D), \, s\in\left]0,1\right[).$$ As a consequence, under further assumptions on E, the strong and approximate convexity properties of (E,t)-convex functions can be strengthened. 相似文献
74.
Friedrich Philipp Andr�� C. M. Ran Micha? Wojtylak 《Integral Equations and Operator Theory》2011,71(4):491-508
The spectral properties of two products AB and BA of possibly unbounded operators A and B in a Banach space are considered. The results are applied in the comparison of local spectral properties of the operators ${T^{[\ast]} T}$ and ${TT^{[\ast]}}$ in a Krein space. It is shown that under the assumption that both operators ${T^{[\ast]} T}$ and ${TT^{[\ast]}}$ have non-empty resolvent sets, the operator ${T^{[\ast]} T}$ is locally definitizable if and only if ${TT^{[\ast]}}$ is. In this context the critical points of both operators are compared. 相似文献
75.
Erik D. Demaine Martin L. Demaine Vi Hart John Iacono Stefan Langerman Joseph O��Rourke 《Graphs and Combinatorics》2011,27(3):363-376
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming. 相似文献
76.
A proper vertex colouring of a graph G is 2-frugal (resp. linear) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths). A graph
G is 2-frugally (resp. linearly) L-colourable if for a given list assignment
L:V(G)? 2\mathbb N{L:V(G)\mapsto 2^{\mathbb N}} , there exists a 2-frugal (resp. linear) colouring c of G such that c(v) ? L(v){c(v) \in L(v)} for all v ? V(G){v\in V(G)} . If G is 2-frugally (resp. linearly) L-list colourable for any list assignment such that |L(v)| ≥ k for all v ? V(G){v\in V(G)}, then G is 2-frugally (resp. linearly) k-choosable. In this paper, we improve some bounds on the 2-frugal choosability and linear choosability of graphs with small maximum
average degree. 相似文献
77.
Zachary Abel Brad Ballinger Prosenjit Bose S��bastien Collette Vida Dujmovi? Ferran Hurtado Scott Duke Kominers Stefan Langerman Attila P��r David R. Wood 《Graphs and Combinatorics》2011,27(1):47-60
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture
of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005]. 相似文献
78.
Va?ek Chv��tal 《Graphs and Combinatorics》2011,27(2):171-175
We show that the method of counting closed walks in strongly regular graphs rules out no parameter sets other than those ruled
out by the method of counting eigenvalue multiplicities. 相似文献
79.
M��rio J. Edmundo Gareth O. Jones Nicholas J. Peatfield 《Archive for Mathematical Logic》2011,50(1-2):19-31
We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers. 相似文献
80.
We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all ${\square}$ -free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula ${\phi}$ and a sublanguage L of the language of the formula, we can decide whether ${\phi}$ has a uniform interpolant with respect to L in K4. The ${\square}$ -free case is proved using a reduction to the G?del L?b Logic GL, while in the general case we prove that the question of whether a modal formula has uniform interpolants over transitive frames can be reduced to a decidable expressivity problem on the???-calculus. 相似文献