Cubic structures and ideal class groups

We establish a generalization of Breen’s theory of cubic structures on line bundles over group schemes. We study such “n-cubic structures” inductively using multiextensions. As a result we obtain information on the set of isomorphism classes of line bundles with n-cubic structures over finite multiplicative group schemes over Spec (Z) by relating this set to certain corresponding eigenspaces of ideal class groups of cyclotomic fields.

Implementing Volatility Trades in the Athens Derivatives Exchange

The purpose of this paper is to demonstrate how investors can benefit from volatility by constructing portfolios of options and futures based on the FTSE/ASE-20 ADEX listed derivatives. Furthermore, this paper provides an insight into the risks associated with such trades as well as addresses the question of whether such a trade can be profitable when transaction costs and margin requirements are taken into account. Its purpose is to serve as a practical guide to trading volatility using data from the Athens Derivative Exchange. The design of an infoormation systems prototype based on selected trades to measure the expected return on each given trade is also demonstrated. You can use Access or SQL to build the prototype.(In this case I used MSAccess)

Network-Level Performance Evaluation of a Two-Relay Cooperative Random Access Wireless System

In wireless networks relay nodes can be used to assist the users' transmissions to reach their destination. Work on relay cooperation, from a physical layer perspective, has up to now yielded well-known results. This paper takes a different stance focusing on network-level cooperation. Extending previous results for a single relay, we investigate here the benefits from the deployment of a second one. We assume that the two relays do not generate packets of their own and the system employs random access to the medium; we further consider slotted time and that the users have saturated queues. We obtain analytical expressions for the arrival and service rates of the queues of the two relays and the stability conditions. We investigate a model of the system, in which the users are divided into clusters, each being served by one relay, and show its advantages in terms of aggregate and throughput per user. We quantify the above, analytically for the case of the collision channel and through simulations for the case of Multi-Packet Reception (MPR), and we provide insight on when the deployment of a second relay in the system can yield significant advantages.Comment: Submitted for journal publicatio

Ανάπτυξη Συστήματος Διαχείρισης Ποιότητας σε φροντιστήριο μέσης εκπαίδευσης σύμφωνα με τις απαιτήσεις του ISO 9001:2008 και της Τ.Π 1433 του ΕΛΟΤ

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Εφαρμοσμένες Μαθηματικές Επιστήμες

On tamely ramified G\mathcal G-bundles on curves

We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and simply-connected, we show that such group schemes can be written as invariants of reductive group schemes over a tame cover of the curve. We relate the torsors under the Bruhat-Tits group scheme and torsors under the reductive group scheme over the cover which are equivariant for the action of the covering group. For this, we develop a theory of local types for such equivariant torsors. We also relate the moduli stacks of torsors under the Bruhat-Tits group scheme and equivariant torsors under the reductive group scheme over the cover. In an Appendix, B. Conrad provides a proof of the Hasse principle for adjoint groups over function fields with finite field of constants.Comment: with an Appendix by B. Conrad, 35pp. Some corrections, added a hypothesis at small characteristics. To appear in Algebraic Geometr

p-adic shtukas and the theory of global and local Shimura varieties

We establish basic results on p-adic shtukas and apply them to the theory of local and global Shimura varieties, and on their interrelation. We construct canonical integral models for (local, and global) Shimura varieties of Hodge type with parahoric level structure.Comment: 96 pp, comments welcom