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 fixed The paper studies generic commutative and anticommutative algebras of a fixed dimension, their invariants, covariants and algebraic properties (e.g., the structure of subalgebras). 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. Rational smoothness and fixed points of torus actions The symmetric varieties considered in this paper are the quotientsG/H, whereG is an adjoint semi-simple group over a fieldk of characteristic ≠ 2, andH is the fixed point group of an involutorial automorphism ofG which is defined overk. LetMm be a closed smooth manifold with an involution having fixed set of the form (point)?Fn, 0>amp;lt;n>amp;lt;m. Erratum to "Rational Smoothness and Fixed Points of Torus Actions" It is injective and its image coincides with the set ofEx-fixed points inI. Erratum to "rational smoothness and fixed points of torus actions" The identity component G acts on a fixed exterior component Gτ, id ≠ τ ∈ Γ by conjugation. This map corresponds geometrically to restriction to the fixed point set of an action of a one-dimensional torus on the flag variety of a semisimple group G. The set ${\mathcal A}$ of all non-associative algebra structures on a fixed 2-dimensional real vector space $A$ is naturally a ${\mbox{\rm GL}}(2,{\mbox{\bf R}})$-module. This paper studies intersection theory on the compactified moduli space ${\mbox{$\cal M$}} (n,d)$ of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface $\Sigma$ of genus $g \geq 2$ where n and d may have common factors. Let Θ denote an involution for a simply connected compact Lie group U, let K denote the fixed point set, and let μ denote the U-invariant probability measure on U/K. For quantized enveloping algebras with fixed deformation parameter $q\in {\Bbb C}\backslash\{0\}$ exactness is proven for all q which are not a root of unity. Assume that the associated Bochner-Riesz kernel sRδ satisfies the estimate, |sRδ(x, y)| ≤ C Rn/d(1+R1/d|x - y|-αδ+β)for some fixed constants a>amp;gt;0 and β. A Weyl-Heisenberg frame (WH frame) for L2(?) allows every square integrable function on the line to be decomposed into the infinite sum of linear combination of translated and modulated versions of a fixed function. In this article, we deal with the case of $\mathcal{D}F$ restricted to all lines passing through a fixed smooth curve. By means of somea priori estimates of the solution and the Leray-Schauder's fixed point theorem, we prove the existence and the uniqueness theorems of the generalized global solution of the mentioned problem. These characterizations are based on the joint conditional probability distribution of arrival times given that the number of arrivals occuring up to any fixed time is known. Recognizing essentially disconnected benzenoids with fixed double bonds

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