Gluing copulas

We present a new way of constructing bivariate copulas, by recalling and gluing two (or more) copulas. Examples illustrate how this construction can be applied to build complicated copulas from simple ones. --

A measure of mutual complete dependence

--

A scalar product for copulas

--

Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory

We consider Lagrangian submanifolds lying on a fiberwise strictly convex hypersurface in some cotangent bundle or, respectively, in the domain bounded by such a hypersurface. We establish a new boundary rigidity phenomenon, saying that certain Lagrangians on the hypersurface cannot be deformed (via Lagrangians having the same Liouville class) into the interior domain. Moreover, we study the "non-removable intersection set" between the Lagrangian and the hypersurface, and show that it contains a set with specific dynamical behavior, known as Aubry set in Aubry-Mather theory.Comment: The main new point of this revised and substantially enlarged version, with G.P. Paternain as new co-author, is the relation between non-removable intersections and Aubry-Mather theor

Human capital – the basis for enterprise development

У статті проаналізовано запропоновану НБУ концепцію нової моделі валютного регулювання, яка не передбачає диференціацію моделей регулювання залежно від поточного стану фінансової системи країни. Автором запропоновано підхід до валютного регулювання, який передбачає наявність трьох сценаріїв реалізації, які включають антикризове, посткризове та регулювання валютного ринку за умов поступального розвитку. На основі аналізу тенденції розвитку валютного ринку України протягом останніх років, яка має характерні повторювані кризові прояви, запропоновано власну концепцію антикризового регулювання.The article analyses the concept proposed by the NBU for a new model of currency regulation, which does not involve differentiation of regulatory models depending on the current state of the financial system of the country. The author proposes an approach to currency regulation, which involves the existence of three scenarios of implementation, which include anti-crisis, post-crisis, and currency market regulation in the context of steady development. Based on the analysis of development tendencies of the foreign exchange market in Ukraine in recent years, which has characteristic recurrent crisis manifestations, the author proposed his own concept of anti-crisis regulation

Gluing copulas

We present a new way of constructing bivariate copulas, by rescaling and gluing two (or more) copulas. Examples illustrate how this construction can be applied to build complicated copulas from simple ones