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991.
Hamiache axiomatized the Shapley value as the unique solution verifying the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values. In this paper, we introduce the notion of row (resp. column)-coalitional matrix in the framework of cooperative game theory. The Shapley value as well as the associated game are represented algebraically by their coalitional matrices called the Shapley standard matrix MSh and the associated transformation matrix Mλ, respectively. We develop a matrix approach for Hamiache’s axiomatization of the Shapley value. The associated consistency for the Shapley value is formulated as the matrix equality MSh = MSh · Mλ. The diagonalization procedure of Mλ and the inessential property for coalitional matrices are fundamental tools to prove the convergence of the sequence of repeated associated games as well as its limit game to be inessential. In addition, a similar matrix approach is applicable to study Driessen’s axiomatization of a certain class of linear values. In summary, it is illustrated that matrix analysis is a new and powerful technique for research in the field of cooperative game theory. 相似文献
992.
We study the question: For which (r,n) can a linear r-field on the (n-1)-sphere in an n-dimensional real linear space be deformed through a continuous path of linear r-fields into an orthonormal r-field. We provide complete answers for the cases: (r,n)=(2,4),(3,4), and provide several partial results for the cases (r,n)=(2,2m), where m is an even integer satisfying m4. Characterizations of linear r-fields are pivotal in the investigation. 相似文献
993.
994.
Roman Werpachowski 《Linear algebra and its applications》2008,428(1):316-323
We describe a method to approximate the matrix elements of a real power α of a positive-definite (for α∈R) or positive-semidefinite (for α?0), infinite, bounded, sparse and Hermitian matrix W. The approximation uses only a finite part of the matrix W. 相似文献
995.
We consider matrix and vector models in the large-N limit: we study N × N matrices and vectors with N2 components. In the case of a zero-dimensional model (D = 0), we prove that in the strong coupling limit (g → ∞), the partition
functions of the two models coincide up to a coefficient. This also holds for D = 1.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 236–243, May, 2008. 相似文献
996.
In this paper we propose a reduced vertex result for the robust solution of uncertain semidefinite optimization problems subject
to interval uncertainty. If the number of decision variables is m and the size of the coefficient matrices in the linear matrix inequality constraints is n×n, a direct vertex approach would require satisfaction of 2
n(m+1)(n+1)/2 vertex constraints: a huge number, even for small values of n and m. The conditions derived here are instead based on the introduction of m slack variables and a subset of vertex coefficient matrices of cardinality 2
n−1, thus reducing the problem to a practically manageable size, at least for small n. A similar size reduction is also obtained for a class of problems with affinely dependent interval uncertainty.
This work is supported by MIUR under the FIRB project “Learning, Randomization and Guaranteed Predictive Inference for Complex
Uncertain Systems,” and by CNR RSTL funds. 相似文献
997.
Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. H-matrices such that their comparison matrices are nonsingular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or nonsingular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance property are used in the characterizations. Finally, a classification of the set of general H-matrices is obtained. 相似文献
998.
It is shown that in a closed equispaced three-level ladder system, by controlling the relative phase of two applied coherent fields, the conversion from absorption with inversion to lasing without inversion (LWI) can be realized; a large index of the refraction with zero absorption can be gotten; considerable increasing of the spectrum region and value of the LWI gain can be achieved. Our study also reveals that the incoherent pumping will produce a remarkable effect on the phase-dependent properties of the system. Modifying value of the incoherent pumping can change the property of the system from absorption to amplification and enhance significantly LWI gain. If the incoherent pumping is absent, we cannot get any gain for any value of the relative phase. 相似文献
999.
In this paper, we study the Farkas alternative over indefinite inner product spaces using the recently proposed indefinite
matrix product. 相似文献
1000.
Abbas Heydari 《Linear algebra and its applications》2008,429(7):1744-1757
Let H be a simple graph with n vertices and G be a sequence of n rooted graphs G1,G2,…,Gn. Godsil and McKay [C.D. Godsil, B.D. McKay, A new graph product and its spectrum, Bull. Austral. Math. Soc. 18 (1978) 21-28] defined the rooted product H(G), of H by G by identifying the root vertex of Gi with the ith vertex of H, and determined the characteristic polynomial of H(G). In this paper we prove a general result on the determinants of some special matrices and, as a corollary, determine the characteristic polynomials of adjacency and Laplacian matrices of H(G).Rojo and Soto [O. Rojo, R. Soto, The spectra of the adjacency matrix and Laplacian matrix for some balanced trees, Linear Algebra Appl. 403 (2005) 97-117] computed the characteristic polynomials and the spectrum of adjacency and Laplacian matrices of a class of balanced trees. As an application of our results, we obtain their conclusions by a simple method. 相似文献