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|  | | 为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法,我们为您准备了出自英文原文的大量英语例句,供您参考。 | |
We study certain naturally-defined analytic domains in the complexified groupHC which are invariant under left and right translation byH?.
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Xi defined a partition ofWf into canonical right cells and the right order ≤R on the set of cells.
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The bases are necessarily generalized Haar functions and the partial sums are a martingale closed on the right by f.
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More precisely, we study the existence of \varepsilon } {f(y)} K(x,y)\left( {1 - \frac{\varepsilon }{{\left| {x - y} \right|}}} \right)^\alpha dy a.e.$$
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The Ces\'aro operator $\mathcal{C}_{\alpha}$ is defined by \begin{equation*} (\mathcal{C}_{\alpha}f)(x) = \int_{0}^{1}t^{-1}f\left( t^{-1}x \right)\alpha (1-t)^{\alpha -1}\,dt~, \end{equation*} where $f$ denotes a function on $\mathbb{R}$.
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Cones of highest weight vectors, weight polytopes, and Lusztig's q-analog
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We relate the invariant theory of cones of highest weight vectors to weight multiplicities and theirq-analogs.
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Whenever the action of a maximal torus on the coneCλ* has some nice properties, we obtain simple closed formulas for all weight multiplicities and theirq-analogs in the representationsVnλ,n∈?.
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We find a connection between the character ofVnλ and the respective weight polytopes.
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A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
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Demands for medicines to treat existing, reemerging and new diseases will escalate and intellectual property rights and patent protection will be increasingly challenged.
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Sexual violence needs to be acknowledged in all parts of the Ukrainian society as a serious threat that requires urgent attention for the improvement of women's reproductive and general health and human rights.
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Conditional access system (CAS) is a key technical component in digital TV broadcasting through which TV operators manage the appropriate rights of different subscribers in order to protect their commercial benefits.
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These areas include the rights of the individual minor herself, the rights of her infant, the rights of her parents or parent, the rights of society, and the rights of the unborn fetus.
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The doctrine specifies the rights of patients to receive information about medical treatment prior to making a decision to consent to or refuse a procedure.
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If is a ?2-grading of a simple Lie algebra, we explicitly describe a-module Spin0 () such that the exterior algebra of is the tensor square of this module times some power of 2.
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The operation adj on matrices arises from the (n - 1)st exterior power functor on modules; the analogous factorization question for matrix constructions arising from other functors is raised, as are several other questions.
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Let q be a power of p and let G(q) be the finite group of Fq-rational points of G.
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We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth.
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A new C*-algebra of strong limit power functions is proposed.
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