In this paper one proposes a new simple combination rule, similar to Dempster’s rule, but the normalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass matrix; in the case when all sets are empty the conflict is redistributed to the disjunctive form of them all (which in many cases coincides with the total ignorance). A general formula is proposed t...

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current understanding are indicated.

Abstract. Let Ω ⊆ R have minimal Gaussian surface area among all sets satisfying Ω = −Ω with fixed Gaussian volume. Let A = Ax be the second fundamental form of ∂Ω at x, i.e. A is the matrix of first order partial derivatives of the unit normal vector at x ∈ ∂Ω. For any x = (x1, . . . , xn+1) ∈ R, let γn(x) = (2π)−n/2e 2 1+···+x 2 n+1. Let ‖A‖2 be the sum of the squares of the entries of A, and...

Let A be a m ×m complex matrix with zero trace and let ε > 0. Then there are m ×m matrices B and C such that A = [B, C] and ‖B‖‖C‖ ≤ Kεm‖A‖ where Kε depends only on ε. Moreover, the matrix B can be taken to be normal.

We study eigenfunctions φj and eigenvalues Ej of the Dirichlet Laplacian on a bounded domain Ω ⊂ Rn with piecewise smooth boundary. We bound the distance between an arbitrary parameter E > 0 and the spectrum {Ej} in terms of the boundary L2-norm of a normalized trial solution u of the Helmholtz equation (∆ + E)u = 0. We also bound the L2-norm of the error of this trial solution from an eigenfun...

The index of matrix A in Cn.n is equivalent to the dimension of largest Jor-dan block corresponding to the zero eigenvalue of A. In this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.

We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the determinant polynomial) come in families that include representatives with normal forms. These normal forms will be useful both to develop new efficient algorithms a...

We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of joint distributions); and relate these notions to the matrix distribution, another invariant of measurable functions found earlier, which is a random matrix...