10,335 research outputs found
Agrawali, Kayali ja Saxena teoreem algarvulisuse kohta
No full textThis bachelor’s thesis gives an overview about prime numbers and different
methods how to determine if an integer is prime or composite. It is based on Andrew
Granville’s article "It is easy to determine if a given integer is prime", where
he introduces and gives a proof of the primality theorem of Agrawal, Kayal and
Saxena. The theorem was first published in 2002 in a paper "PRIMES is in P" by
Manindra Agrawal, Neeraj Kayal and Nitin Saxena.
This thesis consists of 3 parts. In the first part, the main definitions are given
that are used throughout the whole thesis. The second part gives some examples
about different theorems which have been used to determine primality before the
theorem of Agrawal, Kayal and Saxena. In the third part we give a detailed proof
of the main theorem of the thesis. It is formulated as follows.
For a given integer n 2, let r be a positive integer < n, for which n has
order > (log2 n)2 (mod r). Then n is prime if and only if
1) n is not a perfect power,
2) n does not have any prime factor r,
3) (x + a)n xn + a mod (n; xr =< 1) for each integer a, 1 a
p
r log n.
Based on this theorem M. Agrawal, N. Kayal and N. Saxena created a deterministic
primality-proving algorithm. This algorithm determines whether a positive
integer n is prime or composite within polynomial time with respect to the number
of digits of n
Towards Blackbox Identity Testing of Log-Variate Circuits
No full textDerandomization of blackbox identity testing reduces to extremely special circuit models. After a line of work, it is known that focusing on circuits with constant-depth and constantly many variables is enough (Agrawal,Ghosh,Saxena, STOC'18) to get to general hitting-sets and circuit lower bounds. This inspires us to study circuits with few variables, eg. logarithmic in the size s.
We give the first poly(s)-time blackbox identity test for n=O(log s) variate size-s circuits that have poly(s)-dimensional partial derivative space; eg. depth-3 diagonal circuits (or Sigma wedge Sigma^n). The former model is well-studied (Nisan,Wigderson, FOCS'95) but no poly(s2^n)-time identity test was known before us. We introduce the concept of cone-closed basis isolation and prove its usefulness in studying log-variate circuits. It subsumes the previous notions of rank-concentration studied extensively in the context of ROABP models
Neelam Saxena Chandra: A Literary Luminary Bridging Languages and Genres
No full textNeelam Saxena Chandra, a prolific bilingual author, discusses her journey in poetry, literary influences, and creative process. She reflects on poetry as a medium for emotional expression and social change, sharing insights into her works, inspirations, and thoughts on gender sensitization and evolving poetic forms in contemporary literature
Groundnut Production in Central Asia and Caucasus Countries: Outlook for the future
No full textThis book comprises Proceedings of a Workshop held at Tashkent, Uzbekistan, in Nov.
1999, organized jointly by ICRISAT and CGIAR-CAC Program Facilitation Unit, Tashkent,
Uzbekistan. Scientists from six countries of the Central Asia and Caucasus region
participated in the workshop. The first chapter discusses the groundnut and briefly
describes current groundnut research and development at ICRISAT. The next six
chapters document facts about the current status of groundnut production in these CAC
countries. The constraints and opportunities for expansion of groundnut production have
been listed. Spatial distribution of the crop in these countries on an ecoregional scale and
potential areas for expansion have been shown using maps developed on geographic
information systems. The final chapter is an overall synthesis, with suggested priorities
and future areas of research to enhance and stabilize groundnut yield and production in
the CAC region
A Dynamic Hybrid Scheduling Algorithm with Clients' Departure for Impatient Clients in Heterogeneous Environments
No full textPush less and pull the current highest demanded data item to decrease the waiting time in asymmetric communication environments
No full textA hybrid scheduling that effectively combines broadcasting for very popular data (push data) and dissemination upon-request for less popular data (pull data) in asymmetric communication environments is introduced. In this solution, the server continuously broadcasts one push item and disseminates one pull item. The clients send their requests to the server, which queues-up them for the pull items. At any instant of time, the item to be broadcast is designated applying a pure-push scheduling, while the item to be pulled is the one stored in the pull-queue, which has accumulated, so far, the highest number of pending requests. The value of the average expected waiting time spent by a client in the hybrid system is evaluated analytically, and the cut-off point between push and pull items is chosen so that such a waiting time is minimized. It is found out that by doing so the cut off point decreases to a value, which is much less than the total number of items present in the system, improving upon the average waiting time spent by a client in a pure push system and also on that spent in some of the hybrid systems already proposed in literature
K.P. Saxena, Muslim Law as Administered in India and Pakistan, 3e éd.
No full textK.P. Saxena, Muslim Law as Administered in India and Pakistan, 3e éd.. In: Revue internationale de droit comparé. Vol. 13 N°3, Juillet-septembre 1961. pp. 691-692
K.P. Saxena, Muslim Law as Administered in India and Pakistan, 3e éd.
No full textK.P. Saxena, Muslim Law as Administered in India and Pakistan, 3e éd.. In: Revue internationale de droit comparé. Vol. 13 N°3, Juillet-septembre 1961. pp. 691-692
Les villes de l'Uttar Pradesh : Sudha Saxena, Trends of Urbanisation in Uttar Pradesh
No full textDupuis Jacques. Les villes de l'Uttar Pradesh : Sudha Saxena, Trends of Urbanisation in Uttar Pradesh. In: Annales de Géographie, t. 81, n°443, 1972. pp. 112-113
Saxena (S.K.) - Nationalization and Industrial Conflict : Example of British Coal-Mining.
No full textLhomme Jean. Saxena (S.K.) - Nationalization and Industrial Conflict : Example of British Coal-Mining.. In: Revue économique, volume 8, n°3, 1957. p. 516
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