From Sheaf Cohomology to the Algebraic de Rham Theorem

Let X be a smooth complex algebraic variety with the Zariski topology, and let Y be the underlying complex manifold with the complex topology. Grothendieck's algebraic de Rham theorem asserts that the singular cohomology of Y with complex coefficients can be computed from the complex of sheaves of algebraic differential forms on X. This article gives an elementary proof of Grothendieck's algebraic de Rham theorem, elementary in the sense that we use only tools from standard textbooks as well as Serre's FAC and GAGA papers.Comment: 53 pages; this version replaces an earlier version submitted in August 2013. Some misprints have been correcte

Decomposition, purity and fibrations by normal crossing divisors

We give a simple geometric proof of the decomposition theorem in terms of Thom-Whitney stratifications by reduction to fibrations by normal crossings divisors over the strata and explain the relation with the local purity theorem an unpublished result of Deligne and Gabber.Comment: arXiv admin note: text overlap with arXiv:1302.581

The antagonist and protagonist approaches of televising extremism and terrorism

This paper illuminates a current issue related to reporting extremism and terrorism because the developments in the communication technology and the spawn of television stations that seek scoop have allowed the extremists and terrorists not only to transmit their messages, but also to recruit followers and entice supporters throughout the world. Owing to this emerged problem, this paper answers the following question: can the mainstream media televise extremism and terrorism and what is the suitable approach in this regard? To approach this question, this paper reviews the existing literature and debate related to reporting extremism and terrorism. Guided by agenda-setting theory, it adopts a qualitative approach and focuses in the analysis on two contemporary cases aired by Australian broadcasters to verify the argument that the media should be professional and responsible in the cases related to reporting extremism and terrorism. This paper concludes that the media may maximize the publicity of the extremists and terrorists and consequently it may allow them to achieve their agendas. Drawing on these findings, this paper develops models related to the significance of media to the extremists and terrorists and their targeted audiences. Thus, it presents a set of recommendations can be adopted by the media outlets when they report extremism and terrorism

Performance Enhancement of Multiuser Time Reversal UWB Communication System

UWB communication is a recent research area for indoor propagation channels. Time Reversal (TR) communication in UWB has shown promising results for improving the system performance. In multiuser environment, the system performance is significantly degraded due to the interference among different users. TR reduces the interference caused by multiusers due to its spatial focusing property. The performance of a multiuser TR communication system is further improved if the TR filter is modified. In this paper, multiuser TR in UWB communication is investigated using simple TR filter and a modified TR filter with circular shift operation. The concept of circular shift in TR is analytically studied. Thereafter, the channel impulse responses (CIR) of a typical indoor laboratory environment are measured. The measured CIRs are used to analyze the received signal peak power and signal to interference ratio (SIR) with and without performing the circular shift operation in a multiuser environment

On the Succinct Representation of Equivalence Classes

Given a set of n elements that are partitioned into equivalence classes, we study the problem of assigning unique labels to these elements in order to support the query that asks whether the elements corresponding to two given labels belong to the same equivalence class. This problem has been studied by Katz et al., Alstrup et al., and Lewenstein et al.. Lewenstein et al. showed that with no auxiliary data structure, a label space of size nlg(n) is necessary and sufficient to represent the equivalence relation. They also showed that if the labels were to be assigned from the set [n], a data structure of square root of n bits is necessary and sufficient to represent the equivalence relation and to answer the equivalence query in O(lg(n)) time. In this thesis, we give an improved data structure that uses O(square root of n) bits and can answer queries in constant time, when the label space is of size n. Moreover, we study the case where we allow the label space to be of size cn for any constant c > 1. We show that with such a label space, a data structure of O(lg(n)) bits is necessary and sufficient to represent the equivalence relation and to answer the equivalence query in constant time. We believe that our work can trigger further work on tradeoffs between label space and auxiliary data structure space for other labeling problems

Letter From Beirut.

It has been raining all week, persistent drizzle unlike the brief downpours that are more typical of Beirut. The city is slumbering. El-Zein am staying with his parents. His father goes out less often. His mother is snuggled under the blankets. She hopes the war won’t happen. The kettle is boiling like a purring cat. The house is quiet. Rain is the soporific of cities.Australia Council, La Trobe University, National Library of Australia, Holding Redlich, Arts Victori