Quadratische Räume unendlicher Dimension und partielle Isomorphismen.
Quadratische Semi-Ordnungen und Quadratische Formen.
Quantum permutations, Hadamard matrices, and the search for matrix models
This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements about matrix models.
Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices
This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K. Kurdyka and L. Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic setting.
Quelques généralisations du 17e problème de Hilbert.
Quelques remarques sur les résultats de Tutte concernant le problème de Ulam
Quelques résultats de finitude en théorie des invariants
Quotient Module of Z-module
In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattices [14]. Some theorems in this article are described by translating theorems in [20] and [19] into theorems of Z-module....
Raffinement de la borne spectrale d'un faisceau de matrices
Random matrices and permutations, matrix integrals and integrable systems
Random matrices, magic squares and matching polynomials.
Random matrices, non-colliding processes and queues
Random walk centrality and a partition of Kemeny's constant
We consider an accessibility index for the states of a discrete-time, ergodic, homogeneous Markov chain on a finite state space; this index is naturally associated with the random walk centrality introduced by Noh and Reiger (2004) for a random walk on a connected graph. We observe that the vector of accessibility indices provides a partition of Kemeny's constant for the Markov chain. We provide three characterizations of this accessibility index: one in terms of the first return time to the state...
Range symmetric matrices in Minkowski space.
Ranges of Sylvester maps and a minimal rank problem.
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix.
Rank and perimeter preserver of rank-1 matrices over max algebra
For a rank-1 matrix over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or with some monomial matrices U and V.
Rank decomposition in zero pattern matrix algebras
For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H. Bart, A. P. M. Wagelmans (2000). The proof involves elements from integer programming and employs Farkas' lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred...
Rank of matrices and the Pexider equation.
Rank of tensors of -out-of- functions: An application in probabilistic inference
Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy -out-of- functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank...