A perfectly one-factorable (P1F) regular graph is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. The case of cubic graphs is treated. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. A description of this class was obtained by Kotzig in 1962. It is the purpose of t...

In 1937, Von Neumann [1] established the famous coincidence theorem. Since then, the coincidence theorem was generalized in many directions. Browder [2] first proved some basic coincidence theorems for a pair of set-valued mappings in compact setting of topological vector spaces and gave some applications to minimax inequalities and variational inequalities. Recently, Ding [3] established some ...

This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a...

The purpose of discussed optimal valid partitioning (OVP) methods is uncovering of ordinal or continuous explanatory variables effect on outcome variables of different types. The OVP approach is based on searching partitions of explanatory variables space that in the best way separate observations with different levels of outcomes. Partitions of single variables ranges or two-dimensional admiss...

Given a set of individuals, a collection of admissible subsets, and a cost associated to each of these subsets, the Set Partitioning Problem (SPP) consists in selecting admissible subsets to build a partition of the individuals that minimizes the total cost. This combinatorial optimization problem has been used to model dozens of problems arising in specific domains of Artificial Intelligence a...

in this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. we obtain the classes of admissible estimators. the result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized laplace and other distributions.

We apply multiple machine learning methods to obtain concise rules that are highly predictive of scientifically meaningful classes in hydrating plaster over multiple time periods. We use three dimensional data obtained through X-ray microtomography at greater than one micron resolution per voxel at five times in the hydration process: powder, after 4 hours, 7 hours, 15.5 hours, and after 6 days...