We present a spectral analysis of continuous scaling algorithm for matrix and operator scaling. The main result is that if the input or has gap, then natural gradient flow linear convergence. This implies simple descent also convergence under same assumption. gap condition closely related to notion quantum expander studied in information theory. provides bounds on some important quantities prob...

Customer churn is a grave problem for all mobile operators. Early identification of customers from the risk group could help retain them in the operator's network. This paper introduces a set of potential churn factors on which data can be relatively easily extracted from the operator’s databases and analyzed using the SAS® Enterprise Guide®. A multi-stage research procedure utilizing such real...

The Koopman operator allows for handling nonlinear systems through a globally linear representation. In general, the is infinite-dimensional – necessitating finite approximations which there no overarching framework. Although are principled ways of learning such approximations, they in many instances overlooked favor of, often ill-posed and unstructured methods. Also, theory has long-standing c...

By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.