This book is a collection of essays reporting the successes, failures, and barriers contributing to a lack of educational access in developing countries. The international contributors to this volume work in communities that are in the front lines of the battle to achieve universal access to education for everyone.

This topic reflects the behavioral characteristics and the measurement of first class air travel worldwide. Airlines in the East are pushing the boundaries and investing heavily on their first class cabins and potentially competes for their premium passenger. On the other hand, first class market in the western part of the world has been disappearing for decades and rather replaced with improved business class cabins. The worldwide shock of most recent economic crisis had a downward impact on the premium air (...) travel and the post economic impacts were followed by some carriers cutting their first class capacity. The purpose of this research is to highlight whether first class make sense for the airlines to retain? This study is carried out with the research that some airlines have specifically targeted their routes that can fill expensive first class seats, and these were reflected by the strong presence of global business centers whereas others were diminishing due to less lucrative demand. This research will also show the complexity of airline hard product around the world and how they encounter to retain their premium passenger. (shrink)

Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano Arithmetic, Bull. of (...) the LMS 14 285–293]) and Harvey Friedman [S.G. Simpson, Non-provability of certain combinatorial properties of finite trees, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 87–117; R. Smith, The consistency strength of some finite forms of the Higman and Kruskal theorems, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 119–136] who produced the first mathematically interesting independence results in Ramsey theory and well-order and well-quasi-order theory .In this article we investigate Friedman-style principles of combinatorial well-foundedness for the ordinals below ε0. These principles state that there is a uniform bound on the length of decreasing sequences of ordinals which satisfy an elementary recursive growth rate condition with respect to their Gödel numbers.For these independence principles we classify their phase transitions, i.e. we classify exactly the bounding conditions which lead from provability to unprovability in the induced combinatorial well-foundedness principles.As Gödel numbering for ordinals we choose the one which is induced naturally from Gödel’s coding of finite sequences from his classical 1931 paper on his incompleteness results.This choice makes the investigation highly non-trivial but rewarding and we succeed in our objectives by using an intricate and surprising interplay between analytic combinatorics and the theory of descent recursive functions. For obtaining the required bounds on count functions for ordinals we use a classical 1961 Tauberian theorem of Parameswaran which apparently is far remote from Gödel’s theorem. (shrink)