Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers

We consider three examples of weekly perturbed centers which do not have {\it geometrical equivalence}: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: $dH(x,y)+\epsilon(f(x,y)dy-g(x,y)dx)=0$, with $H(x,y)={1/2}(x^2+y^2)$. This reduction allows us to find the Melnikov function, $M(h)=\int_{H=h}fdy-gdx$, associated to each particular problem. We obtain the information on the bifurcation curves of the limit cycles by solving explicitly the equation $M(h)=0$ in each case.Comment: 17 pages, 0 figure

Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials

Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of functions that are special cases of the given polynomials. The method is based on expanding integrals in one or two points of the complex plane, these points being saddle points of the phase functions of the integrands

Hermite polynomials in asymptotic representations of generalized Bernoulli,Euler, Bessel and Buchholz polynomials

This is a second paper on finite exact representations of certain polynomials in terms of Hermite polynomials. The representations have asymptotic properties and include new limits of the polynomials, again in terms of Hermite polynomials. This time we consider the generalized Bernoulli, Euler, Bessel and Buchholz polynomials. The asymptotic approximations of these polynomials are valid for large values of a certain parameter. The representations and limits include information on the zero distribution of the polynomials. Graphs are given that indicate the accuracy of the first term approximations

Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials

This is the second paper on finite exact representations of certain polynomials in terms of Hermite polynomials. The representations have asymptotic properties and include new limits of the polynomials, again in terms of Hermite polynomials. This time we consider the generalized Bernoulli, Euler, Bessel and Buchholz polynomials. The asymptotic approximations of these polynomials are valid for large values of a certain parameter. The representations and limits include information on the zero distribution of the polynomials. Graphs are given that indicate the accuracy of the first term approximations

The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis

Many limits are known for hypergeometric orthogonal polynomials that occur in the Askey scheme. We show how asymptotic representations can be derived by using the generating functions of the polynomials. For example, we discuss the asymptotic representation of the Meixner-Pollaczek, Jacobi, Meixner, and Krawtchouk polynomials in terms of Laguerre polynomials

Japan’s Science and Technology Diplomacy: Society 5.0 and its International Projection

Japan is the third largest economy on the planet but lacks coercive capacity due to Article 9 of its Constitution, which prevents it from having an army and declaring war. This means that it can only rely on persuasion to influence the international sphere and achieve its political objectives. One of the tools it has for this purpose is public diplomacy, which is diplomacy exercised through non-traditional means such as communication, art and culture. One branch of public diplomacy is science and technology diplomacy (S&T Diplomacy), which consists of collaboration in these areas with other nations to strengthen their international projection, as well as the dissemination of scientific knowledge and technology transfer between nations. S&T diplomacy has become a major focus for Japan of its diplomatic action since it launched the Society 5.0 project in 2016, which sought to revolutionize Japan’s economy, society and governance through technology. This S&T diplomacy has the potential to not only strengthen Japan’s external action, but also to transform its industries and research while it is transforming the infrastructures of Japan’s partner nations, like the construction of subway and high-speed rail networks in India. This article will first analyze the theoretical framework of public diplomacy and science and technology diplomacy. Next, Japan’s public diplomacy will be studied by comparing The Soft Power 30 and Global Soft Power Index. Finally, Japanese science and technology diplomacy will be analyzed by assessing the initiatives contained in the Japanese Society 5.0 project