We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature (n−1, 1) is “thin”, namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg’s theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many ...

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in n . Also, for symmetric second-order ordinary differential operators we show that lim sup t→c (pq′)′/q2 = θ < 2 where c is a singular point guarantees separation of −(py′)′ + qy on its minimal domain and extend this criterion to the partial ...

The problem of obtaining the optimum design, which is able to discriminate between several rival models has been considered in this paper. We give an optimality-criterion, using a Bayesian approach. This is an extension of the Bayesian KL-optimality to more than two models. A modification is made to deal with nested models. The proposed Bayesian optimality criterion is a weighted average, where...

Let $d(n)$ and $d^*(n)$ be, respectively, the number of divisors unitary an integer $n\geq 1.$ A divisor $d$ is to be said if it prime over $\frac{n}{d}.$ In this paper, we study mean value function $D(n)=\frac{d(n)}{d^*(n)}$ in arithmetic progressions $ \left\lbrace l+mk \mid m\in\mathbb{N}^* \text{ } (l, k)=1 \right\rbrace;$ leads back real $x\mapsto S(x;k,l)=\underset{n\equiv l[k]}{\sum\limi...

This paper presents the application of a signal intensity independent registration criterion for 2D rigid body registration of medical images using 1D binary projections. The criterion is defined as the weighted ratio of two projections. The ratio is computed on a pixel per pixel basis and weighting is performed by setting the ratios between one and zero pixels to a standard high value. The mea...

We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type A). One criterion uses totally nonnegative polynomials and the other uses Schur functions. The Bruhat order on Sn is often defined by comparing two permutations π = π(1) · · ·π(n) and σ = σ(1) · · ·σ(n) according to the following criterion: π ≤ σ if σ is obtainable from π by a sequence ...

We address the question "when local image of a map is well defined" and answer it in case holomorphic germs with target $(\bC^{2}, 0)$. prove criterion for $(X, x)\to (Y, y)$ to be locally open, solving conjecture by Huckleberry all dimensions.

Logistic regression models with n observations and q linearly-independent covariates are shown to have Fisher information volumes which are bounded below by π and above by ( n q ) π. This is proved with a novel generalization of the classical theorems of Pythagoras and de Gua, which is of independent interest. The finding that the volume is always finite is new, and it implies that the volume c...

This is a three part paper. Optimality of source-channel separation for communication with a fidelity criterion when the channel is compound as defined in [1] and general as defined in [2] is proved in Part I. It is assumed that random codes are permitted. The word “universal” in the title of this paper refers to the fact that the channel model is compound. The proof uses a layered black-box or...

A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group G of cardinality K that is not free but is X -free. A conjecture in infinitary logic concern71 n ing free abelian groups is also ve...