We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Bi...

The paper concentrates on electrocardiographic (ECG) signal analysis for the sake of acquiring proper heartbeat datasets for further detection and recognition of anomalies in an ECG signal. The analysis is based on the distribution of the voltage extreme values of the signal and the time distribution of proper extreme values. The main assumption of the work is creation of as efficient and fast ...

We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we an extension metrics, which states that if $X$ is space, $A$ closed subset $X$, and $d$ metric generates the same topology $A$, then there exists such $D$ $D|_{A^{2}}=d$. Moreover, retraction, ca...

We have undertaken a long term program to measure high precision proper motions of nearby Galactic globular cluster (GC) stars using multi-epoch observations with the WFPC2 and the ACS cameras on-board the Hubble Space Telescope. The proper motions are used to study the internal cluster kinematics, and to obtain accurate cluster distances. In this paper, we also show how the proper motions of t...

?1. Historical introduction. The modern problem of infinity was first raised by Aristotle who held (at least on the popular interpretation2) that infinite sets exist potentially (i.e. one more number can always be counted, one more division can always be made in a line segment) but not actually (i.e. the numbers or divisions cannot all exist at one time). In fact, Aristotle not only held that c...

This paper introduces a new two-parameter family of dwarf spheroidal (dSph) galaxy models. The mass distribution has a Plummer profile and falls like R−4 in projection in agreement with the star-count data. The first free parameter controls the velocity anisotropy, the second controls the dark matter content. The dark matter distribution can be varied from one extreme of mass-follows-light thro...

Proper consistency is defined by the properties that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used w...