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Abstract in This Paper, D-Strong and Almost D-Strong Near-Rings Ha
Periodica Mathematica Hungarlca Vol. 17 (1), (1986), pp. 13--20 D-STRONG AND ALMOST D-STRONG NEAR-RINGS A. K. GOYAL (Udaipur) Abstract In this paper, D-strong and almost D-strong near-rings have been defined. It has been proved that if R is a D-strong S-near ring, then prime ideals, strictly prime ideals and completely prime ideals coincide. Also if R is a D-strong near-ring with iden- tity, then every maximal right ideal becomes a maximal ideal and moreover every 2- primitive near-ring becomes a near-field. Several properties, chain conditions and structure theorems have also been discussed. Introduction In this paper, we have generalized some of the results obtained for rings by Wong [12]. Corresponding to the prime and strictly prime ideals in near-rings, we have defined D-strong and almost D-strong near-rings. It has been shown that a regular near-ring having all idempotents central in R is a D-strong and hence almost D-strong near-ring. If R is a D-strong S-near ring, then it has been shown that prime ideals, strictly prime ideals and com- pletely prime ideals coincide and g(R) = H(R) ~ ~(R), where H(R) is the intersection of all strictly prime ideals of R. Also if R is a D-strong near-ring with identity, then every maximal right ideal becomes a maximal ideal and moreover every 2-primitive near-ring becomes a near-field. Some structure theorems have also been discussed. Preliminaries Throughout R will denote a zero-symmetric left near-ring, i.e., R -- Ro in the sense of Pilz [10]. -
Quarterly Report on the Political Situation in Georgia and Related Foreign Malign Influence
REPORT QUARTERLY REPORT ON THE POLITICAL SITUATION IN GEORGIA AND RELATED FOREIGN MALIGN INFLUENCE 2021 EUROPEAN VALUES CENTER FOR SECURITY POLICY European Values Center for Security Policy is a non-governmental, non-partisan institute defending freedom and sovereignty. We protect liberal democracy, the rule of law, and the transatlantic alliance of the Czech Republic. We help defend Europe especially from the malign influences of Russia, China, and Islamic extremists. We envision a free, safe, and prosperous Czechia within a vibrant Central Europe that is an integral part of the transatlantic community and is based on a firm alliance with the USA. Authors: David Stulík - Head of Eastern European Program, European Values Center for Security Policy Miranda Betchvaia - Intern of Eastern European Program, European Values Center for Security Policy Notice: The following report (ISSUE 3) aims to provide a brief overview of the political crisis in Georgia and its development during the period of January-March 2021. The crisis has been evolving since the parliamentary elections held on 31 October 2020. The report briefly summarizes the background context, touches upon the current political deadlock, and includes the key developments since the previous quarterly report. Responses from the third sector and Georgia’s Western partners will also be discussed. Besides, the report considers anti-Western messages and disinformation, which have contributed to Georgia’s political crisis. This report has been produced under the two-years project implemented by the Prague-based European Values Center for Security Policy in Georgia. The project is supported by the Transition Promotion Program of The Czech Ministry of Foreign Affairs and the Emerging Donors Challenge Program of the USAID. -
Georgia: Background and U.S
Georgia: Background and U.S. Policy Updated September 5, 2018 Congressional Research Service https://crsreports.congress.gov R45307 SUMMARY R45307 Georgia: Background and U.S. Policy September 5, 2018 Georgia is one of the United States’ closest non-NATO partners among the post-Soviet states. With a history of strong economic aid and security cooperation, the United States Cory Welt has deepened its strategic partnership with Georgia since Russia’s 2008 invasion of Analyst in European Affairs Georgia and 2014 invasion of Ukraine. U.S. policy expressly supports Georgia’s sovereignty and territorial integrity within its internationally recognized borders, and Georgia is a leading recipient of U.S. aid in Europe and Eurasia. Many observers consider Georgia to be one of the most democratic states in the post-Soviet region, even as the country faces ongoing governance challenges. The center-left Georgian Dream party has more than a three-fourths supermajority in parliament, allowing it to rule with only limited checks and balances. Although Georgia faces high rates of poverty and underemployment, its economy in 2017 appeared to enter a period of stronger growth than the previous four years. The Georgian Dream won elections in 2012 amid growing dissatisfaction with the former ruling party, Georgia: Basic Facts Mikheil Saakashvili’s center-right United National Population: 3.73 million (2018 est.) Movement, which came to power as a result of Comparative Area: slightly larger than West Virginia Georgia’s 2003 Rose Revolution. In August 2008, Capital: Tbilisi Russia went to war with Georgia to prevent Ethnic Composition: 87% Georgian, 6% Azerbaijani, 5% Saakashvili’s government from reestablishing control Armenian (2014 census) over Georgia’s regions of South Ossetia and Abkhazia, Religion: 83% Georgian Orthodox, 11% Muslim, 3% Armenian which broke away from Georgia in the early 1990s to Apostolic (2014 census) become informal Russian protectorates. -
Survey on Political Attitudes August 2020 Demographics 1. There Are A
Survey on Political Attitudes August 2020 Demographics 1. There are a number of ethnic groups living in Georgia. Which ethnic group do you consider yourself a part of? [Interviewer! Do not read. One answer only.] Armenian 1 Azerbaijani 2 Georgian 3 Other Caucasian ethnicity (Abkhazian, Lezgin, Ossetian, etc.) 4 Russian 5 Kurd or Yezidi 6 Other ethnicity 7 (Don’t know) -1 (Refuse to answer) -2 2. What is the highest level of education you have achieved to date? [Interviewer! Do not read. Correspond.] 1 Did not obtain a nine year diploma 2 Nine year diploma 3 High school diploma (11 or 12 years) 4 Vocational/technical degree 5 Bachelor’s degree/5 years diploma 6 Any degree above bachelor’s (Don’t know) -1 (Refuse to answer) -2 3. Which of the following best describes your situation? Please tell me about the activity that you consider to be primary. [Interviewer! Read out. Only one answer that corresponds with the respondent’s main activity.] I am retired and do not work 1 I am a student and do not work 2 I am a housewife and do not work 3 I am unemployed 4 I work full or part-time, including seasonal 5 jobs I am self-employed, including seasonal jobs 6 I am disabled and cannot work 7 Other 8 (Don’t know) -1 (Refuse to answer) -2 4. How often do you use the Internet? Do you use the Internet … [READ OUT] Every day, 1 At least once a week, 2 At least once a month, 3 Less often, 4 or Never? 5 [DO NOT READ] I don’t know what the Internet is. -
Neural Networks and the Search for a Quadratic Residue Detector
Neural Networks and the Search for a Quadratic Residue Detector Michael Potter∗ Leon Reznik∗ Stanisław Radziszowski∗ [email protected] [email protected] [email protected] ∗ Department of Computer Science Rochester Institute of Technology Rochester, NY 14623 Abstract—This paper investigates the feasibility of employing This paper investigates the possibility of employing ANNs artificial neural network techniques for solving fundamental in the search for a solution to the quadratic residues (QR) cryptography problems, taking quadratic residue detection problem, which is defined as follows: as an example. The problem of quadratic residue detection Suppose that you have two integers a and b. Then a is is one which is well known in both number theory and a quadratic residue of b if and only if the following two cryptography. While it garners less attention than problems conditions hold: [1] such as factoring or discrete logarithms, it is similar in both 1) The greatest common divisor of a and b is 1, and difficulty and importance. No polynomial–time algorithm is 2) There exists an integer c such that c2 ≡ a (mod b). currently known to the public by which the quadratic residue status of one number modulo another may be determined. This The first condition is satisfied automatically so long as ∗ work leverages machine learning algorithms in an attempt to a 2 Zb . There is, however, no known polynomial–time (in create a detector capable of solving instances of the problem the number of bits of a and b) algorithm for determining more efficiently. A variety of neural networks, currently at the whether the second condition is satisfied. -
A Scalable System-On-A-Chip Architecture for Prime Number Validation
A SCALABLE SYSTEM-ON-A-CHIP ARCHITECTURE FOR PRIME NUMBER VALIDATION Ray C.C. Cheung and Ashley Brown Department of Computing, Imperial College London, United Kingdom Abstract This paper presents a scalable SoC architecture for prime number validation which targets reconfigurable hardware This paper presents a scalable SoC architecture for prime such as FPGAs. In particular, users are allowed to se- number validation which targets reconfigurable hardware. lect predefined scalable or non-scalable modular opera- The primality test is crucial for security systems, especially tors for their designs [4]. Our main contributions in- for most public-key schemes. The Rabin-Miller Strong clude: (1) Parallel designs for Montgomery modular arith- Pseudoprime Test has been mapped into hardware, which metic operations (Section 3). (2) A scalable design method makes use of a circuit for computing Montgomery modu- for mapping the Rabin-Miller Strong Pseudoprime Test lar exponentiation to further speed up the validation and to into hardware (Section 4). (3) An architecture of RAM- reduce the hardware cost. A design generator has been de- based Radix-2 Scalable Montgomery multiplier (Section veloped to generate a variety of scalable and non-scalable 4). (4) A design generator for producing hardware prime Montgomery multipliers based on user-defined parameters. number validators based on user-specified parameters (Sec- The performance and resource usage of our designs, im- tion 5). (5) Implementation of the proposed hardware ar- plemented in Xilinx reconfigurable devices, have been ex- chitectures in FPGAs, with an evaluation of its effective- plored using the embedded PowerPC processor and the soft ness compared with different size and speed tradeoffs (Sec- MicroBlaze processor. -
Gakharia Resigns, International Partners React to Ongoing Events
“Impartial, Informative, Insightful” GEL 3.00 #034 (4838) FRIDAY, FEBRUARY 19, 2021 WWW.MESSENGER.COM.GE POLITICS Gakharia resigns, international partners GD nominates Defense react to ongoing events Minister Gharibashvili as PM candidate for second term FORMER PM RESIGNED OVER THE ISSUE OF MELIA’S SENTENCING. FULL STORY ON Page 2 POLITICS EU, US Embassy call to avoid escalation FULL STORY ON Page 3 Giorgi Gakharia has resigned as the Prime Minister of the country BY NIKA GAMTSEMLIDZE National Movement would be a danger- On Sunday, the Tbilisi City Court noted that he appreciated the decision ous political move and it would end up made a decision to arrest Melia for the of the former Prime Minister and said iorgi Gakharia announced his deci- escalating the already unstable and violation of the conditions of the bail. that there is an urgent need for the gov- G sion to resign as Georgian Prime polarized political situation. This has led to mass protests in the ernment to start thinking about snap Minister yesterday. Gakaria cited dif- The Former Prime Minister of the country, and the international partners elections. ferences of opinion within the Georgian country has also criticized Nika Melia for of Georgia reacted harshly. Melia noted that Gakharia’s decision Dream team over Nika Melia’s arrest not disregarding the law and once again The opposition of the country is de- essentially means that he is admitting warrant. As the former PM said, the said that he is responsible for encourag- manding snap elections and welcomes that the government of the country is arrest of the chairman of the United ing protests on June 20, 2019. -
Diffie-Hellman Key Exchange
Public Key Cryptosystems - Diffie Hellman Public Key Cryptosystems - Diffie Hellman Get two parties to share a secret number that no one else knows Public Key Cryptosystems - Diffie Hellman Get two parties to share a secret number that no one else knows Receiver Sender Public Key Cryptosystems - Diffie Hellman Get two parties to share a secret number that no one else knows Can only use an insecure communications channel for exchange Receiver Sender Attacker Public Key Cryptosystems - Diffie Hellman Get two parties to share a secret number that no one else knows Can only use an insecure communications channel for exchange p,g Receiver Sender p: prime & (p-1)/2 prime g: less than p n = gk mod p Attacker for all 0<n<p and some k (see http://gauss.ececs.uc.edu/Courses/c6053/lectures/Math/Group/group.html) Public Key Cryptosystems - Diffie Hellman A safe prime p: p = 2q + 1 where q is also prime Example: 479 = 2*239 + 1 If p is a safe prime, then p-1 has large prime factor, namely q. If all the factors of p-1 are less than logcp, then the problem of solving the discrete logarithm modulo p is in P (it©s easy). Therefore, for cryptosystems based on discrete logarithm (such as Diffie-Hellman) it is required that p-1 has at least one large prime factor. Public Key Cryptosystems - Diffie Hellman A strong prime p: p is large p-1 has large prime factors (p = aq+1 for integer a and prime q) q-1 has large prime factors (q = br+1 for integer b, prime r) p+1 has large prime factors. -
News Digest on Georgia
NEWS DIGEST ON GEORGIA January 27-29 Compiled by: Aleksandre Davitashvili Date: January 30, 2020 Occupied Regions Abkhazia Region 1. Aslan Bzhania to run in so-called presidential elections in occupied Abkhazia Aslan Bzhania, Leader of the occupied Abkhazia region of Georgia will participate in the so-called elections of Abkhazia. Bzhania said that the situation required unification in a team that he would lead. So-called presidential elections in occupied Abkhazia are scheduled for March 22. Former de-facto President of Abkhazia Raul Khajimba quit post amid the ongoing protest rallies. The opposition demanded his resignation. The Cassation Collegiums of Judges declared results of the September 8, 2019, presidential elections as null and void (1TV, January 28, 2020). Foreign Affairs 2. EU Special Representative Klaar Concludes Georgia Visit Toivo Klaar, the European Union Special Representative for the South Caucasus and the crisis in Georgia, who visited Tbilisi on January 20-25, held bilateral consultations with Georgian leaders. Spokesperson to the EU Special Representative Klaar told Civil.ge that this visit aimed to discuss the current situation in Abkhazia and Tskhinvali Region/South Ossetia, as well as ―continuing security and humanitarian challenges on the ground,‖ in particular in the context of the Tskhinvali crossing points, which ―remain closed and security concerns are still significant.‖ Several issues discussed during the last round of the Geneva International Discussions (GID), which was held in December 2019, were also raised during his meetings. ―This visit allows him to get a better understanding of the Georgian position as well as to pass key messages to his interlocutors,‖ Toivo Klaar‘s Spokesperson told Civil.ge earlier last week (Civil.ge, January 27, 2020). -
WHAT IS the BEST APPROACH to COUNTING PRIMES? Andrew Granville 1. How Many Primes Are There? Predictions You Have Probably Seen
WHAT IS THE BEST APPROACH TO COUNTING PRIMES? Andrew Granville As long as people have studied mathematics, they have wanted to know how many primes there are. Getting precise answers is a notoriously difficult problem, and the first suitable technique, due to Riemann, inspired an enormous amount of great mathematics, the techniques and insights penetrating many different fields. In this article we will review some of the best techniques for counting primes, centering our discussion around Riemann's seminal paper. We will go on to discuss its limitations, and then recent efforts to replace Riemann's theory with one that is significantly simpler. 1. How many primes are there? Predictions You have probably seen a proof that there are infinitely many prime numbers. This was known to the ancient Greeks, and today there are many different proofs, using tools from all sorts of fields. Once one knows that there are infinitely many prime numbers then it is natural to ask whether we can give an exact formula, or at least a good approximation, for the number of primes up to a given point. Such questions were no doubt asked, since antiquity, by those people who thought about prime numbers. With the advent of tables of factorizations, it was possible to make predictions supported by lots of data. Figure 1 is a photograph of Chernac's Table of Factorizations of all integers up to one million, published in 1811.1 There are exactly one thousand pages of factorization tables in the book, each giving the factorizations of one thousand numbers. For example, Page 677, seen here, enables us to factor all numbers between 676000 and 676999. -
What Will Be the Renewed World After Defeating Coronavirus?
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/340105525 What will be the renewed World after defeating Coronavirus? Thesis · March 2020 DOI: 10.13140/RG.2.2.13783.83364 CITATIONS READS 0 296 1 author: Revaz Lordkipanidze International Charity Scientific-Research Partnership of Physical Persons 791 PUBLICATIONS 11,135 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Global Platform To Showcase Your Research View project Politic-Economical and Physic-Mathematical Interpretations for Perfect Competitions and Effective Markets View project All content following this page was uploaded by Revaz Lordkipanidze on 23 March 2020. The user has requested enhancement of the downloaded file. Revaz Lordkipanidze What will be the renewed World after defeating Coronavirus? Tbilisi International Charity Scientific-Research Partnership of Physical Persons 2020 Dedicated to the Professionalism in the All - current American Reform of the "Protective Wall of a Stronger Economy", Progressive changes in Georgia and whole Eurasian space, author’s Colleagues (Harvard, St. Petersburg and Tbilisi State Universities) in Justice and World Machine- Building Economics, fantastically wise friends of University of Patriarchate (Georgia), the Open Door Center (US: ODC), American Economic Association, New York Academy of Political Science, New York Academy of Sciences, California Academy of Sciences, very needful for World progress ResearchGate, our dear Open Wikipedia, Genius Experienced and Young Managers of Georgian Technical University, Mayo Clinic (US) and the University Geomedi (Georgia). The present work (Thesis) is prepared for students and wider readers, also providing some help to interested professionals. The work is continuations of the researches under blessing in the Saint Church Qashveti by Great Spiritual Father Saba (Ghvtiso Shalikashvili). -
Local Prime Factor Decomposition of Approximate Strong Product Graphs
Local Prime Factor Decomposition of Approximate Strong Product Graphs Von der Fakultät für Mathematik und Informatik der Universität Leipzig angenommene DISSERTATION zur Erlangung des akademischen Grades DOCTOR RERUM NATURALIUM (Dr. rer. nat.) im Fachgebiet Informatik vorgelegt von Diplom Wirtschaftsmathematiker Marc Hellmuth geboren am 25. Juni 1980 in Nordhausen Die Annahme der Dissertation wurde empfohlen von: 1. Professor Dr. Peter F. Stadler (Leipzig, Deutschland) 2. Professor Dr. Sandi Klavžar (Ljubljana, Slowenien) Die Verleihung des akademischen Grades erfolgt mit Bestehen der Vertei- digung am 22.04.2010 mit dem Gesamtprädikat summa cum laude. Acknowledgements Let me thank you very much !! peter F. stadler and wilfried imrich paula werner kloeckl, daniel merkle, lydia gringmann, maribel hernandez-rosales, steve hoffmann, phil ostermeier, kon- stantin klemm, sven findeisz, and the entire beerinformatics community my family christine rahn, marlen pelny, dietrich becker, gilbert spiegel, min choe, and my old friends in nordhausen jens steuck and petra pregel josef leydold, manja marz, sonja prohaska, and martin middendorf ... and all other persons that are in the closed neighborhood of mine !! Abstract In practice, graphs often occur as perturbed product structures, so-called approximate graph products. The practical application of the well-known prime factorization algorithms is therefore limited, since most graphs are prime, although they can have a product-like structure. This work is concerned with the strong graph product. Since strong product graphs G contain subgraphs that are itself products of subgraphs of the underlying factors of G, we follow the idea to develop local approaches that cover a graph by factorizable patches and then use this information to derive the global factors.