Construction of Doubly Periodic Solutions via the Poincare-Lindstedt Method in the case of Massless Phi^4 Theory

Doubly periodic (periodic both in time and in space) solutions for the Lagrange-Euler equation of the (1+1)-dimensional scalar Phi^4 theory are considered. The nonlinear term is assumed to be small, and the Poincare-Lindstedt method is used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leading-order term is taken in the form of a Jacobi elliptic function. It have been proved that the choice of elliptic cosine with fixed value of module k (k=0.451075598811) as the leading-order term puts the principal resonance to zero and allows us constructed (with accuracy to third order of small parameter) the asymptotic solution in the standing wave form. To obtain this leading-order term the computer algebra system REDUCE have been used. We have appended the REDUCE program to this paper.Comment: 16 pages, LaTeX 2.09. This paper have been published in the Electronic Proceedings of the Fourth International IMACS Conference on Applications of Computer Algebra (ACA'98) {Prague (Czech Republic)} at http://math.unm.edu/ACA/1998/sessions/dynamical/verno

Focal Randomization: An optimal mechanism for the evaluation of R&D

In most countries, governments intervene in the process of R&D by financing a substantial part of it. The mechanism employed for choosing the projects to be financed is a committee composed of experts who evaluate projects in their field of specialization, and decide which ones should be funded. This mechanism for evaluating projects is conservative. Proposals of new ideas are too often rejected, and inventions are commonly thrown out of the set of potential projects. In this paper, I propose a mechanism that will allow less conformity: focal randomization. Focal randomization mechanism (FRM) states that projects which are unanimously ranked at the top by all reviewers, will be adopted. Projects perceived as valueless by all are rejected, while projects that are ranked differently will be randomized. I compare the average return under the present and proposed mechanism. I examine under which conditions this new mechanism is preferable, and its consequences on economic growth.

Density in Ws,p(Ω;N)W^{s,p}(\Omega ; N)

Let $\Omega$ be a smooth bounded domain in ${\mathbb R}^n$, 0\textless{}s\textless{}\infty and 1\le p\textless{}\infty. We prove that $C^\infty(\overline\Omega\, ; {\mathbb S}^1)$ is dense in $W^{s,p}(\Omega ; {\mathbb S}^1)$ except when 1\le sp\textless{}2 and $n\ge 2$. The main ingredient is a new approximation method for $W^{s,p}$-maps when s\textless{}1. With 0\textless{}s\textless{}1, 1\le p\textless{}\infty and sp\textless{}n, $\Omega$ a ball, and $N$ a general compact connected manifold, we prove that $C^\infty(\overline\Omega \, ; N)$ is dense in $W^{s,p}(\Omega \, ; N)$ if and only if $\pi\_{[sp]}(N)=0$. This supplements analogous results obtained by Bethuel when $s=1$, and by Bousquet, Ponce and Van Schaftingen when $s=2,3,\ldots$ [General domains $\Omega$ have been treated by Hang and Lin when $s=1$; our approach allows to extend their result to s\textless{}1.] The case where s\textgreater{}1, $s\not\in{\mathbb N}$, is still open.Comment: To appear in J. Funct. Anal. 49

Fertility, Non-Altruism and Economic Growth: Industrialization in the Nineteenth Century

This paper presents a model of fertility, which is specific for the industrialization that took place during the nineteenth century and which was concurrent with the demographic transition that occurred over the period. While previous research on demographic transition assumed altruism as the main element explaining the increase in fertility rates, this paper does not, since altruism seems irrelevant over this period. The relationship between parents and children is part of a whole set of values and social norms that evolved over time and were affected by changes in the economic environment. In the nineteenth century, parental behavior was not compatible with altruism. I therefore present a model that suits the social norms of the nineteenth century. The value that seems to correspond to the legal system and social norms regarding the parent-child relationship of the period of industrialization is perpetuation. Due to a budget constraint on workers, perpetuation is displayed differently in different social classes. This paper will therefore focus on the interaction between the different social classes and show how industrialization is linked to demographic transition.altruism; social classes; demographic transition; capital; proletariat; fertility; growth.

Is Privatization Necessary to achieve Quality of Universities?

The purpose of this study is to analyze the relationship between privatization in higher education and the quality of universities. An interesting fact is that of the top 10 universities in the US, nine are private. Previous studies have claimed that there is a relationship between the privatization of universities and their quality, since countries with a high proportion of private resources have superior universities. The purpose of this paper is to analyze if indeed this supposed relationship is due to empirical regularities between quality and ownership, or whether the two are unrelated. The analysis presented herein is based on data collected on 508 universities in 40 countries. I show that flexibility is the important element affecting quality, and not ownership per se.Higher Education, quality, privatization, ranking

The BBM formula revisited

In this paper, we revise the BBM formula due to J. Bourgain, H. Brezis, and P. Mironescu in [1]

Why do Students Migrate? Where do they Migrate to?

The flow of students has grown very rapidly these last decades, and in some regions, has become twice as important as the flows of those seeking work. The purpose of this study is to explore the elements affecting students’ decision on migration. The two main elements affecting migration are wages, and quality of education. It should be stressed that the countries with the highest-quality education are not necessarily those with high wages. Therefore there is a need to explore whether it is quality of higher education or wage levels that determine the direction of student flows. First, we develop a simple two-stage model relating decisions on educational choices to those on job search. Our model shows that student migration is towards countries with the highest quality of higher education. In the second part of this study, we empirically investigate our theoretical model using a panel data on European OECD countries. We use the Bologna process to outline which of the elements, wages or educational quality, determines the direction of flows. We find strong evidence of concentration of students in countries with high-quality education and not in high-wage countries.Migration, Human capital, Students, higher education, Bologna process, Brain drain.

On the optimality of shape and data representation in the spectral domain

A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant-Fischer min-max principle adapted to our case. % The theorem we present supports the new trend in geometry processing of treating geometric structures by using their projection onto the leading eigenfunctions of the decomposition of the LBO. Utilisation of this result can be used for constructing numerically efficient algorithms to process shapes in their spectrum. We review a couple of applications as possible practical usage cases of the proposed optimality criteria. % We refer to a scale invariant metric, which is also invariant to bending of the manifold. This novel pseudo-metric allows constructing an LBO by which a scale invariant eigenspace on the surface is defined. We demonstrate the efficiency of an intermediate metric, defined as an interpolation between the scale invariant and the regular one, in representing geometric structures while capturing both coarse and fine details. Next, we review a numerical acceleration technique for classical scaling, a member of a family of flattening methods known as multidimensional scaling (MDS). There, the optimality is exploited to efficiently approximate all geodesic distances between pairs of points on a given surface, and thereby match and compare between almost isometric surfaces. Finally, we revisit the classical principal component analysis (PCA) definition by coupling its variational form with a Dirichlet energy on the data manifold. By pairing the PCA with the LBO we can handle cases that go beyond the scope defined by the observation set that is handled by regular PCA

Changes in the Recruitment and Education of the Power Elites in Twentieth Century Western Democracies

The aim of this paper is to examine the evolution of recruitment of elites and to investigate the nature of the links between recruitment and training of elites and economic development. We show that there was a key shift at the turn of the nineteenth century in the way the Western world trained its elites, with a second shift taking place after World War II, when meritocracy became the basis for recruitment of elites. Although meritocratic selection should result in the best being chosen, we show that meritocratic recruitment leads to class stratification and auto-recruitment. We analyze whether stratification resulting from meritocratic selection is optimal for the development of a country, and show that it is dependent on the type of technological changes occurring in the country.elite; auto-recruitment; training; education; meritocracy; stratification; economic growth

Was the Korean slave market efficient?

Over the decades, the traditional condemnation of slavery has been based not only on philosophical argumentation and moral values, but also on the conjecture that slavery was inefficient. This position led to one of the most passionate debates in economic history on the efficiency of the US slave market. This question of efficiency has not been analyzed on the slave market in Korea. The aim of this paper is to analyze the efficiency of the Korean slave market by examining the behavior of slave prices during the period 1689-1893. In order to do so, we collected long-run series of slave prices from nationwide surveys of more than 25 public and private historical records. We then tested whether the slave market was efficient using the arbitrage asset equation. We found slavery to have been efficient most of the time.arbitrage asset equation; efficient markets; Korea; slave