Revisiting the moduli space of semistable G-bundles over elliptic curves

We show that the moduli space of semistable G-bundles on an elliptic curve for a reductive group G is isomorphic to a power of the elliptic curve modulo a certain Weyl group which depend on the topological type of the bundle. This generalises a result of Laszlo to arbitrary connected components and recovers the global description of the moduli space due to Friedman--Morgan--Witten and Schweigert. The proof is entirely in the realm of algebraic geometry and works in arbitrary characteristic.Comment: 21pages, one table. To appear in Annales de l'Institut Fourie

Comment on "Statistical Distribution for Generalized Ideal Gas of Fractional-Statistics Particles", Phys. Rev. Lett. {\bf 73}, 922 (1994)

In Phys. Rev. Lett. 67, 937 (1991) [1], Haldane introduced the fruitful concept of fractional exclusion statistics (FES). One of the most influential papers in which the thermodynamics of FES systems was deduced is Y.-S. Wu, Phys. Rev. Lett. 73, 922 (1994). Unfortunately, some important, but eventually subtle, properties of the exclusion statistics parameters were overlooked in the original paper [1] and in all the papers after that, including [2]. This omission makes the thermodynamics of FES systems inconsistent when mutual exclusion statistics is manifesting in the system. By this Comment I want to point-out this error--an error that persisted for such a long time--and to give the correct statistical mechanics interpretation of FES.Comment: 1 page, submitted to PR

Further Properties and Applications of Koszul Pairs

Koszul pairs were introduced in [arXiv:1011.4243] as an instrument for the study of Koszul rings. In this paper, we continue the enquiry of such pairs, focusing on the description of the second component, as a follow-up of the study in [arXiv:1605.05458]. As such, we introduce Koszul corings and prove several equivalent characterizations for them. As applications, in the case of locally finite $R$-rings, we show that a graded $R$-ring is Koszul if and only if its left (or right) graded dual coring is Koszul. Finally, for finite graded posets, we obtain that the respective incidence ring is Koszul if and only if the incidence coring is so.Comment: part of the first versio

THE HUMAN RESOURCES MANAGEMENT IN THE CONTEXT OF THE ECONOMIC CRISIS

Crisis periods are creating acute tensioned situations in the relationships between people, not only in the organizations that are in need to stint their activities, but also in institutions that are not so affected by the crisis. This happens because in the new context we can find a lot of apprehensions in the minds of citizens, especially regarding the labor force. In these conditions the Human Resources management is facing difficulties regarding limitation decisions for a part of the personnel. On the other hand, the economic crisis has also some positive aspects for the Human Resources management because it allows the existence an adequacy filter, a constancy of employees, the reinforcement of discipline in institutions, a growth of productivity, an increase in people‟s responsibilities and even the attenuation of income pressure. All of these things can be capitalized for the interest of institutions. At the same time the crisis can be a rupture between the old and the new, it can stimulate creativity, it can determine the reorganization and increase the efficiency of activities, it can lead to an orientation towards new technologies, methods and products highly demanded on the market. This paper analyzes and estimates the attitudes manifested by Romanian Human Resources managers that are facing the current socio-economic crisis. It shows what people can do to decrease the effects of the crisis and also their perception regarding the manifestation forms of the economic crisis, the changes that are necessary for a good administration of the human resources which would lead to a minimum loss in this area, so that the closure of the crisis should not be accompanied by an absence of human resources.human resources, economic crisis, managerial activities, human relationships, small and average enterprises, economic development