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In this paper, we correct some errors in the extended first and second Gordan's theorems in a recent paper-Information Sciences 504 (2019) 276-292. (C) 2021 Elsevier Inc. All rights reserved.
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In this article, we present a modern viewpoint on the Gordan algorithm for binary forms. The symbolic method is recast in terms of equivariant homomorphisms. A graphical approach is used to define Gordan's ideal, a central tool us...
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In this article, we present a modern viewpoint on the Gordan algorithm for binary forms. The symbolic method is recast in terms of equivariant homomorphisms. A graphical approach is used to define Gordan's ideal, a central tool used to obtain an integrity basis for the covariant algebra of a binary form. To illustrate the power of this method, we compute for the first time a minimal integrity basis for the covariant algebra of , and for the invariant algebra of .
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Every regular map on a closed surface gives rise to generally six regular maps, its Petrie relatives, that are obtained through iteration of the duality and Petrie operations (taking duals and Petrie-duals). It is shown that the s...
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Every regular map on a closed surface gives rise to generally six regular maps, its Petrie relatives, that are obtained through iteration of the duality and Petrie operations (taking duals and Petrie-duals). It is shown that the skeletal polyhedra in Euclidean 3-space which realize a Petrie relative of the classical Gordan regular map and have full icosahedral symmetry, comprise precisely four infinite families of polyhedra, as well as four individual polyhedra.
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We derive from Motzkin's Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker's Theorem of the alternative. A generalisati...
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We derive from Motzkin's Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker's Theorem of the alternative. A generalisation of the residual existence theorem for linear equations which has recently been proved by Rohn [8] is a corollary. We state all the results in the setting of a general vector space over a linearly ordered (possibly skew) field.
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In this paper, we mainly introduced the invexity and generalized invexity of n-dimensional fuzzy number-valued functions based on the new ordering which defined by Gong and Hai in [9]. Simultaneously, we discussed the relationship...
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In this paper, we mainly introduced the invexity and generalized invexity of n-dimensional fuzzy number-valued functions based on the new ordering which defined by Gong and Hai in [9]. Simultaneously, we discussed the relationship between semicontinuous and preinvex fuzzy number-valued functions, and some properties among invexity and generalized invexity of n-dimensional fuzzy number-valued functions. Finally, we studied the necessary and sufficient conditions for weakly efficient point of fuzzy optimization.
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摘要 :
In this paper, we mainly introduced the invexity and generalized invexity of n-dimensional fuzzy number-valued functions based on the new ordering which defined by Gong and Hai in [9]. Simultaneously, we discussed the relationship...
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In this paper, we mainly introduced the invexity and generalized invexity of n-dimensional fuzzy number-valued functions based on the new ordering which defined by Gong and Hai in [9]. Simultaneously, we discussed the relationship between semicontinuous and preinvex fuzzy number-valued functions, and some properties among invexity and generalized invexity of n-dimensional fuzzy number-valued functions. Finally, we studied the necessary and sufficient conditions for weakly efficient point of fuzzy optimization.
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