A Networking Approach to Grid Computing
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On Abundancy Index of Some Special Class of Numbers
Sohag J. Math. 4, No. 2, 37-40 (2017) 37 Sohag Journal of Mathematics An International Journal http://dx.doi.org/10.18576/sjm/040202 On Abundancy Index of Some Special Class of Numbers Bhabesh Das1,∗ and Helen K. Saikia2 1 Department of Mathematics, B.P.C.College, Assam, 781127, India 2 Department of Mathematics, Gauhati University, Assam, 781014, India Received: 10 Dec. 2015, Revised: 12 Sep. 2016, Accepted: 23 Sep. 2016 Published online: 1 May 2017 σ(n) σ Abstract: For any positive integer n, abundancy index I(n) is defined as I(n) = n , where (n) is the sum of all positive divisors of n. In this paper, we have discussed non trivial lower and upper bounds of I(n) for some special class of numbers like Quasi perfect numbers, Super hyperperfect numbers, Near perfect numbers and Hyperperfect numbers. Keywords: Quasi perfect number, Super hyperperfect number, Near perfect number, Hyperperfect number p−1 1 Introduction of n. If m = 2 Mp is an even perfect number, where p p both p and Mp = 2 − 1 are primes, then n = 2m, n = 2 m We known divisor function σ(n) is the sum of all positive and n = (2p − 1)m are near perfect numbers. There are divisors of n , including 1 and n itself. The abundancy finitely many near perfect numbers other than these three p index I(n) for any positive integer n is associated with the shapes. The primes of the form Mp = 2 − 1 are called divisor function σ(n) and is defined as Mersenne primes. -
Generalized Perfect Numbers
Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 73–82 Generalized perfect numbers Antal Bege Kinga Fogarasi Sapientia–Hungarian University of Sapientia–Hungarian University of Transilvania Transilvania Department of Mathematics and Department of Mathematics and Informatics, Informatics, Tˆargu Mure¸s, Romania Tˆargu Mure¸s, Romania email: [email protected] email: [email protected] Abstract. Let σ(n) denote the sum of positive divisors of the natural number n. A natural number is perfect if σ(n) = 2n. This concept was already generalized in form of superperfect numbers σ2(n)= σ(σ(n)) = k+1 k−1 2n and hyperperfect numbers σ(n)= k n + k . In this paper some new ways of generalizing perfect numbers are inves- tigated, numerical results are presented and some conjectures are estab- lished. 1 Introduction For the natural number n we denote the sum of positive divisors by arXiv:1008.0155v1 [math.NT] 1 Aug 2010 σ(n)= X d. d|n Definition 1 A positive integer n is called perfect number if it is equal to the sum of its proper divisors. Equivalently: σ(n)= 2n, where AMS 2000 subject classifications: 11A25, 11Y70 Key words and phrases: perfect number, superperfect number, k-hyperperfect number 73 74 A. Bege, K. Fogarasi Example 1 The first few perfect numbers are: 6, 28, 496, 8128, . (Sloane’s A000396 [15]), since 6 = 1 + 2 + 3 28 = 1 + 2 + 4 + 7 + 14 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 Euclid discovered that the first four perfect numbers are generated by the for- mula 2n−1(2n − 1). -
Cluster, Grid and Cloud Computing: a Detailed Comparison
The 6th International Conference on Computer Science & Education (ICCSE 2011) August 3-5, 2011. SuperStar Virgo, Singapore ThC 3.33 Cluster, Grid and Cloud Computing: A Detailed Comparison Naidila Sadashiv S. M Dilip Kumar Dept. of Computer Science and Engineering Dept. of Computer Science and Engineering Acharya Institute of Technology University Visvesvaraya College of Engineering (UVCE) Bangalore, India Bangalore, India [email protected] [email protected] Abstract—Cloud computing is rapidly growing as an alterna- with out any prior reservation and hence eliminates over- tive to conventional computing. However, it is based on models provisioning and improves resource utilization. like cluster computing, distributed computing, utility computing To the best of our knowledge, in the literature, only a few and grid computing in general. This paper presents an end-to- end comparison between Cluster Computing, Grid Computing comparisons have been appeared in the field of computing. and Cloud Computing, along with the challenges they face. This In this paper we bring out a complete comparison of the could help in better understanding these models and to know three computing models. Rest of the paper is organized as how they differ from its related concepts, all in one go. It also follows. The cluster computing, grid computing and cloud discusses the ongoing projects and different applications that use computing models are briefly explained in Section II. Issues these computing models as a platform for execution. An insight into some of the tools which can be used in the three computing and challenges related to these computing models are listed models to design and develop applications is given. -
Grid Computing: What Is It, and Why Do I Care?*
Grid Computing: What Is It, and Why Do I Care?* Ken MacInnis <[email protected]> * Or, “Mi caja es su caja!” (c) Ken MacInnis 2004 1 Outline Introduction and Motivation Examples Architecture, Components, Tools Lessons Learned and The Future Questions? (c) Ken MacInnis 2004 2 What is “grid computing”? Many different definitions: Utility computing Cycles for sale Distributed computing distributed.net RC5, SETI@Home High-performance resource sharing Clusters, storage, visualization, networking “We will probably see the spread of ‘computer utilities’, which, like present electric and telephone utilities, will service individual homes and offices across the country.” Len Kleinrock (1969) The word “grid” doesn’t equal Grid Computing: Sun Grid Engine is a mere scheduler! (c) Ken MacInnis 2004 3 Better definitions: Common protocols allowing large problems to be solved in a distributed multi-resource multi-user environment. “A computational grid is a hardware and software infrastructure that provides dependable, consistent, pervasive, and inexpensive access to high-end computational capabilities.” Kesselman & Foster (1998) “…coordinated resource sharing and problem solving in dynamic, multi- institutional virtual organizations.” Kesselman, Foster, Tuecke (2000) (c) Ken MacInnis 2004 4 New Challenges for Computing Grid computing evolved out of a need to share resources Flexible, ever-changing “virtual organizations” High-energy physics, astronomy, more Differing site policies with common needs Disparate computing needs -
Cloud Computing Over Cluster, Grid Computing: a Comparative Analysis
Journal of Grid and Distributed Computing Volume 1, Issue 1, 2011, pp-01-04 Available online at: http://www.bioinfo.in/contents.php?id=92 Cloud Computing Over Cluster, Grid Computing: a Comparative Analysis 1Indu Gandotra, 2Pawanesh Abrol, 3 Pooja Gupta, 3Rohit Uppal and 3Sandeep Singh 1Department of MCA, MIET, Jammu 2Department of Computer Science & IT, Jammu Univ, Jammu 3Department of MCA, MIET, Jammu e-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract—There are dozens of definitions for cloud Virtualization is a technology that enables sharing of computing and through each definition we can get the cloud resources. Cloud computing platform can become different idea about what a cloud computing exacting is? more flexible, extensible and reusable by adopting the Cloud computing is not a very new concept because it is concept of service oriented architecture [5].We will not connected to grid computing paradigm whose concept came need to unwrap the shrink wrapped software and install. into existence thirteen years ago. Cloud computing is not only related to Grid Computing but also to Utility computing The cloud is really very easier, just to install single as well as Cluster computing. Cloud computing is a software in the centralized facility and cover all the computing platform for sharing resources that include requirements of the company’s users [1]. software’s, business process, infrastructures and applications. Cloud computing also relies on the technology II. CLUSTER COMPUTING of virtualization. In this paper, we will discuss about Grid computing, Cluster computing and Cloud computing i.e. -
“Grid Computing”
VISHVESHWARAIAH TECHNOLOGICAL UNIVERSITY S.D.M COLLEGE OF ENGINEERING AND TECHNOLOGY A seminar report on “Grid Computing” Submitted by Nagaraj Baddi (2SD07CS402) 8th semester DEPARTMENT OF COMPUTER SCIENCE ENGINEERING 2009-10 1 VISHVESHWARAIAH TECHNOLOGICAL UNIVERSITY S.D.M COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF COMPUTER SCIENCE ENGINEERING CERTIFICATE Certified that the seminar work entitled “Grid Computing” is a bonafide work presented by Mr. Nagaraj.M.Baddi, bearing USN 2SD07CS402 in a partial fulfillment for the award of degree of Bachelor of Engineering in Computer Science Engineering of the Vishveshwaraiah Technological University Belgaum, during the year 2009-10. The seminar report has been approved as it satisfies the academic requirements with respect to seminar work presented for the Bachelor of Engineering Degree. Staff in charge H.O.D CSE (S. L. DESHPANDE) (S. M. JOSHI) Name: Nagaraj M. Baddi USN: 2SD07CS402 2 INDEX 1. Introduction 4 2. History 5 3. How Grid Computing Works 6 4. Related technologies 8 4.1 Cluster computing 8 4.2 Peer-to-peer computing 9 4.3 Internet computing 9 5. Grid Computing Logical Levels 10 5.1 Cluster Grid 10 5.2 Campus Grid 10 5.3 Global Grid 10 6. Grid Architecture 11 6.1 Grid fabric 11 6.2 Core Grid middleware 12 6.3 User-level Grid middleware 12 6.4 Grid applications and portals. 13 7. Grid Applications 13 7.1 Distributed supercomputing 13 7.2 High-throughput computing 14 7.3 On-demand computing 14 7.4 Data-intensive computing 14 7.5 Collaborative computing 15 8. Difference: Grid Computing vs Cloud Computing 15 9. -
Computer Systems Architecture
CS 352H: Computer Systems Architecture Topic 14: Multicores, Multiprocessors, and Clusters University of Texas at Austin CS352H - Computer Systems Architecture Fall 2009 Don Fussell Introduction Goal: connecting multiple computers to get higher performance Multiprocessors Scalability, availability, power efficiency Job-level (process-level) parallelism High throughput for independent jobs Parallel processing program Single program run on multiple processors Multicore microprocessors Chips with multiple processors (cores) University of Texas at Austin CS352H - Computer Systems Architecture Fall 2009 Don Fussell 2 Hardware and Software Hardware Serial: e.g., Pentium 4 Parallel: e.g., quad-core Xeon e5345 Software Sequential: e.g., matrix multiplication Concurrent: e.g., operating system Sequential/concurrent software can run on serial/parallel hardware Challenge: making effective use of parallel hardware University of Texas at Austin CS352H - Computer Systems Architecture Fall 2009 Don Fussell 3 What We’ve Already Covered §2.11: Parallelism and Instructions Synchronization §3.6: Parallelism and Computer Arithmetic Associativity §4.10: Parallelism and Advanced Instruction-Level Parallelism §5.8: Parallelism and Memory Hierarchies Cache Coherence §6.9: Parallelism and I/O: Redundant Arrays of Inexpensive Disks University of Texas at Austin CS352H - Computer Systems Architecture Fall 2009 Don Fussell 4 Parallel Programming Parallel software is the problem Need to get significant performance improvement Otherwise, just use a faster uniprocessor, -
Strategies for Managing Business Disruption Due to Grid Computing
Strategies for managing business disruption due to Grid Computing by Vidyadhar Phalke Ph.D. Computer Science, Rutgers University, New Jersey, 1995 M.S. Computer Science, Rutgers University, New Jersey, 1992 B.Tech. Computer Science, Indian Institute of Technology, Delhi, 1989 Submitted to the MIT Sloan School of Management in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Management of Technology at the Massachusetts Institute of Technology June 2003 © 2003 Vidyadhar Phalke All Rights Reserved The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part Signature of Author: MIT Sloan School of Management 9 May 2003 Certified By: Starling D. Hunter III Theodore T. Miller Career Development Assistant Professor Thesis Supervisor Accepted By: David A. Weber Director, Management of Technology Program 2 Strategies for managing business disruption due to Grid Computing by Vidyadhar Phalke Submitted to the MIT Sloan School of Management on May 9 2003 in partial fulfillment of the requirements for the degree of Master of Science in the Management of Technology ABSTRACT In the technology centric businesses disruptive technologies displace incumbents time and again, sometimes to the extent that incumbents go bankrupt. In this thesis we would address the issue of what strategies are essential to prepare for and to manage disruptions for the affected businesses and industries. Specifically we will look at grid computing that is poised to disrupt (1) certain Enterprise IT departments, and (2) the software industry in the high-performance and web services space. -
On Perfect Numbers and Their Relations 1 Introduction
Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 27, 1337 - 1346 On Perfect Numbers and their Relations Recep G¨ur 2000 Evler Mahallesi Boykent Sitesi E Blok 26/7 Nevsehir, Turkey [email protected] Nihal Bircan Technische Universitaet Berlin Fakultaet II Institut f¨ur Mathematik MA 8 − 1 Strasse des 17. Juni 136 D-10623 Berlin, Germany [email protected] Abstract In this paper, we get some new formulas for generalized perfect numbers and their relationship between arithmetical functions φ, σ concerning Ore’s harmonic numbers and by using these formulas we present some examples. Mathematics Subject Classification: 11A25, 11A41, 11Y70 Keywords: perfect number, 2-hyperperfect number, Euler’s totient function, Ore harmonic number 1 Introduction In this section, we aimed to provide general information on perfect numbers shortly. Here and throughout the paper we assume m, n, k, d, b are positive integers and p is prime. N is called perfect number, if it is equal to the sum of its proper divisors. The first few perfect numbers are 6, 28, 496, 8128,... since, 6 = 1+2+3 28 = 1+2+4+7+14 496 = 1+2+4+8+16+31+62+124+248 Euclid discovered the first four perfect numbers which are generated by the formula 2n−1(2n−1), called Euclid number. In his book ’Elements’ he presented the proof of the formula which gives an even perfect number whenever 2n −1is 1338 Recep G¨ur and Nihal Bircan prime. In order for 2n −1 to be a prime n must itself be a prime. -
Identities for Near and Deficient Hyperperfect Numbers
Received: 03.01.2016 Year: 2017, Pages: 01-12 Published: 13.04.2017 Original Article** Identities for Near and Deficient Hyperperfect Numbers Bhabesh Das1;* <[email protected]> Helen K.Saikia2 <[email protected]> 1Department of Mathematics,B.P.C.College,781127,Assam,India 2Department of Mathematics,Gauhati University,781014,Assam,India Abstaract − It is well-known that a positive integer n is said to be k−hyperperfect number if k + 1 k − 1 σ(n) = n + ; k k where k is a positive integer and σ(n) is the sum of all positive divisors of n. We call a number n is near k−hyperperfect number if k + 1 k − 1 σ(n) = n + + d k k and decient k−hyperperfect number if k + 1 k − 1 σ(n) = n + − d; k k where d is a proper divisor of n. In this paper, for any prime number q, we present two classes of near (q − 1)−hyperperfect number and one class of decient (q − 1)−hyperperfect number with two distinct prime factors and also present some numerical results. Keywords − Perfect number, Hyperperfect number, Near perfect number, Decient perfect number. **Edited by A. D. Godase (Editor-in-Chief). *Corresponding Author. Indian Journal in Number Theory, 2017, 01-12 2 1 Introduction For any positive integer n, divisor function σ(n) denote the sum of all positive divisors of n, X σ(n) = d: djn Denition 1.1. A positive integer n is called perfect number, if σ(n) = 2n. All known perfect numbers are even. The Euclid-Euler theorem gives the general form of even perfect numbers. -
Contributions to Desktop Grid Computing Gilles Fedak
Contributions to Desktop Grid Computing Gilles Fedak To cite this version: Gilles Fedak. Contributions to Desktop Grid Computing : From High Throughput Computing to Data-Intensive Sciences on Hybrid Distributed Computing Infrastructures. Calcul parallèle, distribué et partagé [cs.DC]. Ecole Normale Supérieure de Lyon, 2015. tel-01158462v2 HAL Id: tel-01158462 https://hal.inria.fr/tel-01158462v2 Submitted on 7 Dec 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Copyright University of Lyon Habilitation `aDiriger des Recherches Contributions to Desktop Grid Computing From High Throughput Computing to Data-Intensive Sciences on Hybrid Distributed Computing Infrastructures Gilles Fedak 28 Mai 2015 Apr`esavis de : Christine Morin Directeur de Recherche, INRIA Pierre Sens Professeur, Universit´eParis VI Domenico Talia Professeur, University of Calabria Devant la commission d'examen form´eede : Vincent Breton Directeur de Recherche, CNRS Christine Morin Directeur de Recherche, INRIA Manish Parashar Professeur, Rutgers University Christian Perez Directeur de Recherche, INRIA Pierre Sens Professeur, Universit´eParis VI Domenico Talia Professeur, University of Calabria Contents 1 Introduction 9 1.1 Historical Context . .9 1.2 Contributions . 13 1.3 Summary of the Document . 16 2 Evolution of Desktop Grid Computing 19 2.1 A Brief History of Desktop Grid and Volunteer Computing . -
Resume Ivo Janssen
Ivo J. Janssen 13266 Kerrville Folkway Austin, TX 78729 (512) 750-9455 / [email protected] Objective To be part of a successful professional services team in a pre-sales and post-sales architecture and deployment role. Summary I'm an experienced, enthusiastic and skilled professional services consultant with experience in architecting and supporting large-scale enterprise software, with extensive experience in designing and implementing custom solutions as part of pre- and post sales support activities in diverse industry verticals across five continents. I'm as comfortable in designing and coding in an engineering role as I am in on-site planning, executing and troubleshooting customer deployments in a professional services role, as well as in participating in sales calls and drafting proposals in a sales engineering role. I'm able to adapt to new environments quickly and rapidly become proficient with new systems, tools and skills. I'm a good team player who thinks beyond the problem at hand instead of following the established paths in order to find a better solution that meets both current and future needs. Professional experience • Virtual Bridges , Austin, TX, USA (Nov 2010 – present) Senior Solution Architect o Solution architect for VDI product line. • Initiate Systems / IBM , Austin, TX, USA (Sep 2008 – Nov 2010) Senior Consultant o Senior implementation engineer for Healthcare sector of Master Data Management product line. o Responsibilities include requirements gathering, product installation and configuration, custom coding, connectivity scripting on Windows and Unix, database performance tuning, customer training workshops, pre/post-sales support. o Successfully architected, implemented and brought live custom implementation projects for major hospital systems and labs in the US, including customers with up to 250 million records (1TB database) connected to 20 auxiliary systems.