Abstract In a recent work of Anderson and Hu, the authors constructed measure that was p-adic q-adic doubling, for any primes p q, yet not doubling. This relied heavily on developed number theory framework. Here we develop this framework further, which yields is m-adic n-adic doubling coprime $m,n$, Additionally, show several new applications to intersection weight function classes.

The feature map represented by the set of weight vectors of the basic SOM (Self-Organizing Map) provides a good approximation to the input space from which the sample vectors come. But the timedecreasing learning rate and neighborhood function of the basic SOM algorithm reduce its capability to adapt weights for a varied environment. In dealing with non-stationary input distributions and changi...

In a weighted sum model such as the Analytic Hierarchy Process, a set function value is constructed from the weights of the model. In this paper, we use relative individual scores to propose a set function that shows the features of an alternative. The set function value for the alternative is calculated by averaging the values of the set function representation of the weights generated when th...

In wireless sensor networks, one of most important issues is data collection from sensors to sink. Many researchers employ a mathematical formula to select the next forwarding node in the network-wide manner. We are motivated that surrounding environments for nodes are different in time and space. Because different situations of nodes are not considered for selecting the next forwarding node, t...

Let Cλ n(x), n = 0, 1, . . . , λ > −1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal in (−1, 1) with respect to the weight function (1−x2)λ−1/2. Denote by xnk(λ), k = 1, . . . , n, the zeros of Cλ n(x) enumerated in decreasing order. In this short note we prove that, for any n ∈ IN , the product (λ+1)xn1(λ) is a convex function of λ if λ ≥ 0. The result is applied to obtain some ...

Let Cλ n(x), n = 0, 1, . . . , λ > −1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal in (−1, 1) with respect to the weight function (1−x2)λ−1/2. Denote by xnk(λ), k = 1, . . . , n, the zeros of Cλ n(x) enumerated in decreasing order. In this short note we prove that, for any n ∈ IN , the product (λ+1)xn1(λ) is a convex function of λ if λ ≥ 0. The result is applied to obtain some ...

In several domains it is common to have data from different, but closely related problems. For instance, in manufacturing many products follow the same industrial process but with different conditions; or in industrial diagnosis, where there is equipment with similar specifications. In these cases, it is common to have plenty of data for some scenarios but very little for other. In order to lea...