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1.
M Pavan 《Analytica chimica acta》2004,515(1):167-181
Interest is growing in decision making strategies and several techniques are now available. The assessment of priorities is a typical premise before final decisions are taken. Total and partial order ranking (POR) strategies, which from a mathematical point of view are based on elementary methods of discrete mathematics, appear as an attractive and simple tool to asses priorities. Despite the well-known total ranking strategies, which are scalar methods combining the different criteria values into a global index which always ranks elements in an ordered sequence, the partial order ranking is a vectorial approach which recognises that not all the elements can be directly compared with all the others. In fact when many criteria are considered, contradictions in the ranking are bound to exist and the higher the number of criteria, the higher the probability that contradictions in the ranking occur. The Hasse diagram technique (HDT) is a very useful tool to perform partial order ranking. The results of the partial order ranking are visualised in a diagram, called Hasse diagram. Incomparable elements are located at the same geometrical height and as high as possible in the diagram, thus incomparable elements are arranged in levels. The quality of a ranking procedure has to be evaluated by a deep analysis and by several indices, i.e. scalar functions that describe features of an ordered set and allow comparison among different rankings. For this purpose, new indices for ranking analysis are proposed here, compared with the ones found in literature and tested on theoretical examples and on real data. 相似文献
2.
Karin Erdmann 《Linear algebra and its applications》2011,434(12):2475-2496
In this paper we evaluate Chebyshev polynomials of the second kind on a class of symmetric integer matrices, namely on adjacency matrices of simply laced Dynkin and extended Dynkin diagrams. As an application of these results we explicitly calculate minimal projective resolutions of simple modules of symmetric algebras with radical cube zero that are of finite and tame representation type. 相似文献
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5.
Andreas Schweizer 《Transactions of the American Mathematical Society》2005,357(3):1047-1059
We study the extension generated by the -coordinates of the -torsion points of an elliptic curve over a function field of characteristic . If is a non-isotrivial elliptic surface in characteristic with a -torsion section, then for 11$"> our results imply restrictions on the genus, the gonality, and the -rank of the base curve , whereas for such a surface can be constructed over any base curve . We also describe explicitly all occurring in the cases where the surface is rational or or the base curve is rational, elliptic or hyperelliptic.
6.
Takao Yamazaki 《Mathematische Zeitschrift》2009,261(1):109-121
We prove that the kernel of the reciprocity map for a product of curves over a p-adic field with split semi-stable reduction is divisible. We also consider the K
1 of a product of curves over a number field.
相似文献
7.
研究有限域 上一类方程 , , 的解数. 在保持方程系数不变的前提下, 通过对其次数矩阵进行有效降次, 可以改进对原方程解数的各种估计. 若对方程未知变量和系数进行适当限定, 则可将其化为椭圆曲线方程, 从而利用Hasse定理得到原方程解数的一个精确界. 相似文献
8.
Let be the finite field with q elements and let . It was conjectured that for integers and , the polynomial is a permutation polynomial of if and only if (i) and , or (ii) and . In the present paper we confirm this conjecture. 相似文献
9.
J. F. Jardine 《K-Theory》2006,37(3):291-309
Suppose that A is a presheaf of categories enriched in simplicial sets on a small Grothendieck site. It is shown that the
homotopy theory of enriched A-diagrams of equivalences taking values in simplicial sets can be identified with the homotopy
theory of simplicial presheaves fibred over the diagonalized nerve dBA of A. The set [*,dBA] of morphisms in the simplicial
presheaf homotopy category is identified with the set of path components of a category of A-torsors, for a suitable definition
of A-torsor. These statements are special cases of localized results which hold when the corresponding localized model structures
are proper. Examples of the latter include the motivic homotopy category, and so these results lead to a theory of motivic
A-torsors which is classifiable up to equivalence by a family of morphisms in the motivic homotopy category.
This research was supported by NSERC.
Received: March 2006 相似文献
10.
We give a short combinatorial proof of the generic invertibility of the Hasse–Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse–Witt matrix and certain A-hypergeometric series, which is what motivated the proof. 相似文献