منابع مشابه
Nonnegative approximations of nonnegative tensors
We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious näıve Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative parafac, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Brègman diverge...
متن کاملNonnegative Approximations of Nonnegative Tensors
We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious näıve Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative parafac, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Brègman diverge...
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We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$, where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$, with $d(n)$ denoting the number of positive divisors of $n$. Also, we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.
متن کاملMaximal nonnegative perturbation of a nonnegative matrix
is known to be stable if and only if ρ(A) < 1. Models of real world dynamical phenomena often involve positive quantities. A dynamical system (1) is called positive if any trajectory of the system starting in the positive orthant R+ remains in R+. In this case, the matrix A has only real positive entries. In many cases, it may be useful to consider systems with a known “nominal” part A and a un...
متن کاملHomology of zero-divisors
Let R be a commutative ring with unity. The set Z(R) of zero-divisors in a ring does not possess any obvious algebraic structure; consequently, the study of this set has often involved techniques and ideas from outside algebra. Several recent attempts, among them [2], [3] have focused on studying the so-called zero-divisor graph ΓR, whose vertices are the zero-divisors of R, with xy being an ed...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1968
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1968-0219751-3