Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange’s method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscover...

An n–criteria problem with a finite set of vector valuations is considered. An optimality principle of this problem is given by an integer-valued parameter s, which is varied from 1 to n−1. At that, the majority and Pareto optimality principles correspond to the extreme values of the parameter. Sufficient conditions, under which the problem of finding efficient valuations corresponding to the p...

To a real Hilbert space and a one-parameter group of orthogonal transformations we associate a C∗-algebra which admits a free quasi-free state. This construction is a freeprobability analog of the construction of quasi-free states on the CAR and CCR algebras. We show that under certain conditions, our C∗-algebras are simple, and the free quasi-free states are unique. The corresponding von Neuma...

Water famously expands upon freezing, foreshadowed by a negative coefficient of expansion of the liquid at temperatures close to its freezing temperature. These behaviors, and many others, reflect the energetic preference for local tetrahedral arrangements of water molecules and entropic effects that oppose it. Here, we provide theoretical analysis of mesoscopic implications of this competition...

It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work, we further test this proposal for another generalization of the Lennard-Jones pair potential. ...

Dependences of low temperature behavior and anisotropy of various physical quantities for pure unconventional superconductors upon a particular form of momentum direction dependence for the superconducting order parameter (within the framework of the same symmetry type of superconducting pair-ing) are considered. A special attention is drawn to the possibility of different multiplicities of the...