Smooth solutions to the abc equation: the xyz Conjecture

This paper studies integer solutions to the ABC equation A+B+C=0 in which none of A, B, C has a large prime factor. Set H(A,B, C)= max(|A|,|B|,|C|) and set the smoothness S(A, B, C) to be the largest prime factor of ABC. We consider primitive solutions (gcd(A, B, C)=1) having smoothness no larger than a fixed power p of log H. Assuming the abc Conjecture we show that there are finitely many solutions if p<1. We discuss a conditional result, showing that the Generalized Riemann Hypothesis (GRH) implies there are infinitely many primitive solutions when p>8. We sketch some details of the proof of the latter result.Comment: 21 pages, presented at 26th Journees Arithmetiques, 2009; v2 added new examples 1.2, updated references; v3 changed title, more examples added, notation changes, v4 corrects misprints in Conj. 3.1, Thm. 4.3 statement, 25 page

Counting Smooth Solutions to the Equation A+B=C

This paper studies integer solutions to the Diophantine equation A+B=C in which none of A, B, C have a large prime factor. We set H(A, B,C) = max(|A|, |B|, |C|), and consider primitive solutions (gcd}(A, B, C)=1) having no prime factor p larger than (log H(A, B,C))^K, for a given finite K. On the assumption that the Generalized Riemann hypothesis (GRH) holds, we show that for any K > 8 there are infinitely many such primitive solutions having no prime factor larger than (log H(A, B, C))^K. We obtain in this range an asymptotic formula for the number of such suitably weighted primitive solutions.Comment: 35 pages latex; v2 corrected misprint

Electrostatic Structures in Space Plasmas: Stability of Two-dimensional Magnetic Bernstein-Greene-Kruskal Modes

Electrostatic structures have been observed in many regions of space plasmas, including the solar wind, the magnetosphere, the auroral acceleration region, and in association with shocks, turbulence, and magnetic reconnection. Due to potentially large amplitude of electric fields within these structures, their effects on particle heating, scattering, or acceleration can be important. One possible theoretical description of some of these structures is the concept of Bernstein-Greene-Kruskal (BGK) modes, which are exact nonlinear solutions of the Vlasov-Poisson system of equations in collisionless kinetic theory. BGK modes have been studied extensively for many decades, predominately in one dimension (1D), although there have been observations showing that some of these structures have clear 3D features. While there have been approximate solutions of higher dimensional BGK modes, an exact 3D BGK mode solution in a finite magnetic field has not been found yet. Recently we have constructed exact solutions of 2D BGK modes in a magnetized plasma with finite magnetic field strength in order to gain insights of the ultimate 3D theory [Ng, Bhattacharjee, and Skiff, Phys. Plasmas 13, 055903 (2006)]. Based on the analytic form of these solutions, as well as Particle-in-Cell (PIC) simulations, we will present numerical studies of their stability for different levels of background magnetic field strength.Comment: Submitted to AIP Journal Proceedings for "Tenth Annual International Astrophysics Conference

Can multi-stakeholder initiatives improve global supply chains? Improving deliberative capacity with a stakeholder orientation

Global multi-stakeholder initiatives (MSIs) are important instruments that have the potential to improve the social and environmental sustainability of global supply chains. However, they often fail to comprehensively address the needs and interests of various supplychain participants. While voluntary in nature, MSIs have most often been implemented through coercive approaches, resulting in friction among their participants and in systemic problems with decoupling. Additionally, in those cases in which deliberation was constrained between and amongst participants, collaborative approaches have often failed to materialize. Our framework focuses on two key aspects of these breakdowns: assumptions about the orientation of MSI participants, and the deliberation processes that participants use to engage with each other to create these initiatives and sustain them over time. Drawing from stakeholder and deliberation theories, we revisit the concept of MSIs and show how their deliberative capacity may be enhanced in order to encourage participants to collaborate voluntarily

Towards an Institutional Knowledge Repository (IKR) at IGCAR

The collective acquired information of an organization is called the ‘institutional knowledge’. The centralized Knowledge Repository uses standard taxonomies to consolidate information into one place allowing knowledge to be searched and retrieved with maximum efficiency and accuracy. Many organizations have realized the value of institutional knowledge and already initiated knowledge management systems that collect, store, redistribute, utilize and ultimately leverage the institutional knowledge for the benefit of the organization. All the organizations, in particular the R&D institutions like IGCAR need to build knowledge repository on its specific areas of interest. Once created, the IKR will act as a vehicle for knowledge dissemination, sharing and transfer. This paper gives a comprehensive view on building IKR at IGCAR

User interface design and development: the role of open source systems

Open Source movement has tremendously influenced Information industry, in particular the Digital Library Environment where the Information Systems and services are inevitable. This has helped the Library and Information Centers in developing User Interface to render web based services to the patrons. Wherever the network infrastructure and the target users are in place, the design and development of IR user interface using Open Source system for a specific application is very much possible. This paper highlights the role of Open Source Systems in detail and explains a prototype IR User Interface which was developed in-house at Indira Gandhi Centre for Atomic Research, Kalpakkam

Ellipsometric Studies on Silver Telluride Thin Films

Silver telluride thin films of thickness between 45 nm and 145 nm were thermally evaporated on well cleaned glass substrates at high vacuum better than 10 – 5 mbar. Silver telluride thin films are polycrystalline with monoclinic structure was confirmed by X-ray diffractogram studies. AFM and SEM images of these films are also recorded. The phase ratio and amplitude ratio of these films were recorded in the wavelength range between 300 nm and 700 nm using spectroscopic ellipsometry and analysed to determine its optical band gap, refractive index, extinction coefficient, and dielectric functions. High absorption coefficient determined from the analysis of recorded spectra indicates the presence of direct band transition. The optical band gap of silver telluride thin films is thickness dependent and proportional to square of reciprocal of thickness. The dependence of optical band gap of silver telluride thin films on film thickness has been explained through quantum size effect. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2371

Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.Comment: 18 pages, 10 figure