There is an optimal way of increasing certain cardinal invariants of the

For a filter over a regular cardinal, least functions and the consequent notion of weak normality are described. The following two results, which make a basic connection between the existence of least functions and irregularity of ultrafilters, are then proved: Let U be a uniform ultrafilter over a regular cardinal k. (a) If k = \+, then U is not (\, \ )-regular iff V has a least function / suc...

A computationally fast and optimally smooth method for generating a probability density of y given x that models given data points is described and illustrated. This method interpolates in that the mean function intersects the points and the variance function is zero at the points. It is fast and optimal in that it is produced by the smallest number of maximally-smooth Gaussian radial interpola...

This is an expository paper giving a complete proof of a theorem of Saharon Shelah: If 2n < @! for all n < !, then 2! < @!4 .

We prove that every compact space X is a Čech-Stone compactification of a normal subspace of cardinality at most d(X)t(X), and some facts about cardinal invariants of compact spaces.

In [9] and [12] we have introduced and studied a new paradigm for cardinal interpolation which is related to the theory of multivariate polysplines. In the present paper we show that this is related to a new sampling paradigm in the multivariate case, whereas we obtain a Shannon type function S (x) and the following Shannon type formula:

Although primarily defined by their cardinal antigen-presenting function, dendritic cells (DCs) are also equipped with cytotoxic properties. We have recently reported that DCs activated by IFNγ-secreting Th-1 lymphocytes can kill cancer cells and subsequently present the acquired tumor-derived antigens to T lymphocytes both in vitro and in vivo.

We present a new interactive algorithm allowing to solve the inconsistencies problem, when the preferences of a decision maker cannot be representable by a numerical function. This algorithm is based on technics of linear programming and the type of preferences we use are cardinal information.