We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [Phys. Rev. E 85, 011120 (2012)], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear fu...

Consider the triangle-free graph process, which starts from the empty graph on n vertices and in every step an edge is added that is chosen uniformly at random from all non-edges that do not form a triangle with the existing edges. We will show that there exists a constant c such that asymptotically almost surely no copy of any fixed finite triangle-free graph on k vertices with at least ck edg...

Nadler. E., Nonnegativity of bivariate quadratic functions on a triangle. Computer Aided Geometric Design 9 (1992) 19.5-205. A necessary and sufficient condition for the nonnegativity of a bivariate quadratic defined on a triangle is presented in terms of the Bernstein-Bkzier form of the function. Keywfords. Nonnegativity, bivariate quadratic function, Bernstein-BCzier form, positiviry preservi...

We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a three-parameter family of inequalities which we call Ceva’s triangle inequalities. Our main result provides the parametrization of the solution set. Mathematics subject classification (2010): Primary 26D07, 51M04; secondary 51M15, 15B48.

The set of security, institutional, economic, scientific-technical, and natural-technological challenges that have arisen before Ukraine as a result the full-scale Russian-Ukrainian war necessitates, in particular, need to substantiate breakthrough measures regarding country's subject participation system international division labor conditions post-war development. One these particularly effec...

Traditional non-linear planners (NOAH, NONLIN, SIPE, ...) construct plans of actions by progressively introducing and partially ordering actions in the initial plan to satisfy a set of constraints. On the other hand, our method, using the triangle table formalism, enables linear planners to easily determine, in linear (over constrained) plans, all actions which can be executed in parallel (remo...

Abstract. We study generation of magnetic fields, involving large spatial scales, by convective plan-forms in a horizontal layer. Magnetic modes and their growth rates are expanded in power series in the scale ratio, and the magnetic eddy diffusivity (MED) tensor is derived for flows, symmetric about the vertical axis in a layer. For convective rolls magnetic eddy correction is demonstrated to ...