Can the policy Francophonie be considered a manifestation of neocolonialism (on the example of foreign cultural strategy of France in the 1960s)

The subject of this research is the correlation between the policy of neocolonialism and Francophonie in the context of foreign cultural strategy of France in the 1960s. Decolonization forced France to relinquish direct colonial rule and shift towards the policy of “cooperation” on the basis of bilateral agreements with the developing countries, which regulated intergovernmental relations in various spheres. The idea of the universality of French language and cultural values underlied the Agency for Cultural and Technical Cooperation established in 1970. A crucial role in its establishment was played by the political leaders of African countries, who sought benefit from cooperation with France in terms of the development of young sovereign states. Despite this fact, the activity of Francophonie was the object of criticism, and by some researchers, considered a version of French post-colonialism. Analysis is conducted on different interpretations and approaches towards the terms “neo-colonialism” and “Francophonie”. The article employs the unpublished archival documents of the Ministry of Foreign Affairs of France, which determines the scientific novelty. The authors conclude that the equality sign between neo-colonialism and Francophonie seems unreasoned, since the latter has improved the educational, cultural, scientific and technical standard of living in the young sovereign states, contributed to the establishment of their political and administrative and increase of authority on the world stage. The participation of the developing countries in the Agency for Cultural and Technical Cooperation and the leaders of the Western world – France and Canada – consolidated the authority and broadened the experience of the political elite of the third world countries. At the same time, there is no denying that de Gaulle sought to increase the international prestige of the Fifth Republic by strengthening the positions of France in the Francophone world.

Stresses in equilibrium configurations of inextensible nets with slack

The paper deals with nets formed by two families of fibers (cords) which can grow shorter but not longer, in a deformation. The nets are treated as two-dimensional continua in the three-dimensional space. The inextensibility condition places unilateral constraint on the partial derivatives y,1 and y,2 of the deformation [Formula: see text] of the form [Formula: see text] [Formula: see text] There is no deformation energy, the total energy reduces to the potential energy of the net under external forces. Equilibrium configurations are those of minimum energy. The stresses in equilibrium configurations thus reduce to the reactions to the constraints. Nonzero stresses occur only in tense regions where one or two constraints are satisfied with the equality sign. The paper follows the work of Paroni in treating the stress problem via the dual variational problem in the sense of convex analysis. Unlike in the work of Paroni, where stresses are modeled as finitely additive set functions, here a (perhaps more economic) choice of spaces is made that leads to more accessible stresses represented by (countably additive) measures. The present development is made possible by an observation, of independent value, that the space of measures with divergence measure is the dual of another Banach space, in the present context naturally interpreted as the space of strains. Our measures generalize stress fields represented by ordinary functions to account for stress concentrations along folded lines in tension, frequently occurring in equilibrium configurations of the net.

Two uncertainty relations

Heisenberg and Robertson–Schrödinger uncertainty relations for the coordinate and momentum follow from two stronger uncertainty relations. The first uncertainty relation has classical character and its right-hand side can have an arbitrary value greater than or equal to zero. The second uncertainty relation has quantum character and its right-hand side equals h2/4; its existence is related to the existence of the envelop of the wave function. These two uncertainty relations cannot be obviously improved on. The equality sign in the second relation can be achieved for much larger class of the wave functions than in case of the Heisenberg or Robertson–Schrödinger uncertainty relations.

Using research in teaching: Open sentences: some instructional considerations from research

Open sentences such as 21 + N = 59, 9 + N = 17, 18 − N = 9, and so on, occur regularly in elementary school mathematics textbooks. Children learn to solve sentences such as 9 + 6 = N and 38 − 19 = N, where the placeholder is by itself on one side of the equality sign, much earlier than open sentences where the placeholder is in a different position such as 14 − N = 8 or N + 17 = 56. Children's performance is not easily predicted when open sentences of the latter forms are involved. For example, it is not clear which, if any, of the open sentences 24 + N = 58, N + 24 = 58, 58 − N = 24, or N − 24 = 34 children have the most difficulty solving. Which would you predict?

The positive values of inhomogeneous ternary quadratic forms

Let f(x, y, z) be an indefinite ternary quadratic form of signature (2, 1) and determinant d ≠ 0. Davenport [3] has shown that there exist integral x, y, z with, the equality sign being necessary if and only if f is a positive multiple of f1(x, y, z) = x2 + yz.

A Note on a Discriminant Inequality

The following conjecture has been investigated recently by Mordell [1]. “Let z1 , …, zn be any set of n complex numbers. Then1the equality sign being necessary in the case when the z's are at the vertices of a regular n-sided polygon with center at the origin.”