A basis of the set of sequences satisfying a given m-th order linear recurrence.
A class of Cardinal Lacunary interpolation problems by spline functions.
A comparison of two upper bounds on the permanent of -matrices. (Ein Vergleich zweier oberer Schranken für die Permanente von -Matrizen.)
A conjecture on minimum permanents
We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square -matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.
A Deformed Quon Algebra
The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators , , on an infinite dimensional vector space satisfying the...
A determinant formula from random walks
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...
A determinant of Ostrowski.
A Generalization of the Matrix-Tree Theorem.
A high-tech proof of the Mills-Robbins-Rumsey determinant formula.
A matrix derivation of a representation theorem for (tr Ap)1/p.
A matrix derivation of a well-known representation theorem for (tr Ap)1/p is given, which is the solution of a restricted maximization problem. The paper further gives a solution of the corresponding restricted minimization problem.
A matrix inequality for Möbius functions.
A new determinant expression of the zeta function for a hypergraph.
A new proof of Löwner's theorem on monotone matrix functions.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review 49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A new series of conjectures and open questions in optimization and matrix analysis
We present below a new series of conjectures and open problems in the fields of (global) Optimization and Matrix analysis, in the same spirit as our recently published paper [J.-B. Hiriart-Urruty, Potpourri of conjectures and open questions in Nonlinear analysis and Optimization. SIAM Review49 (2007) 255–273]. With each problem come a succinct presentation, a list of specific references, and a view on the state of the art of the subject.
A new upper bound for the eigenvalues of the continuous algebraic Riccati equation.
A note on linear discrepancy.
A note on the determinant of a Toeplitz-Hessenberg matrix
The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.
A Note on the Permanental Roots of Bipartite Graphs
It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing...
A note on the trace inequality for products of Hermitian matrix power.