Pachystigmus Hellén, 1927 : a substitute name for Noserus Foerster, 1863 (Hymenoptera: Braconidae), not Noserus LeConte, 1862 (Coleoptera: Zopheridae)

By establishing the date of its first publication, Noserus Foerster, 1863 (Hymenoptera, Braconidae) is shown to be a junior primary homonym of Noserus LeConte, 1862 (Coleoptera, Zopheridae). The substitute name for Noserus Foerster is that of its subjective synonym, Pachystigmus Hellén, 1927 [type species: Pachystigmus nitidulus Hellén, 1927]. Other described species in the genus are: Pachystigmus facialis (Foerster, 1863) New Combination; P. similis (Szépligeti, 1896) New Combination, P. nitidulus Hellén, 1927, P. gigas (Tobias, 1964)New Combination, P. occipitalis (Belokobylskij, 1986) New Combination, P. olgensis (Belokobylskij, 1994) New Combination, and P. sculpturator (Belokobylskij, 1999) New Combination

Relatively computably enumerable reals

A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above.Comment: 5 pages. Significant changes from earlier versio

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

International Sourcing, Product Complexity and Intellectual Property Rights

In this paper, we propose the technological complexity of a product and the level of Intellectual Property Rights (IPRs) protection to be the co-determinants of the mode through which multinational firms purchase their goods. We study the choice between intra-firm trade and outsourcing given heterogeneity at the product- (complexity), firm- (productivity) and country- (IPRs) level. Our findings suggest that the above three dimensions of heterogeneity are crucial for complex goods, where firms face a trade-off between higher marginal costs in the case of trade with an affiliate and higher imitation risks in the case of sourcing from an independent supplier. We test these predictions by combining data from a French firm-level survey on the mode choice for each transaction with a newly developed complexity measure at the product-level. Our fractional logit estimations confirm the proposition that although firms are generally reluctant to source highly complex goods from outside the firm’s boundaries, they do so when a strong IPR regime in the host country guarantees the protection of their technology