11,413 research outputs found
Приближение непрерывных функций интерполяционными многочленами
No full text[Saxena R. B.; Saxena R.; Саксена Р. Б.]English. Bulgarian, Russian summar
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
Некоторые интерполяционные свойства лежандровых и ультрасферических полиномов
No full text[Saxena R. B.; Саксена Р. Б.]English. Russian, Bulgarian summar
Genetic Enhancement in Major Food Legumes: An Overview
No full textFarming communities, around the world, who earn their livelihoods through their hard work with limited resources and many times under unfriendly and risky agricultural environments are the main providers of plant proteins to masses by cultivating legumes. Besides proteins, legumes also contain valuable vitamins, mineral and fibre necessary for nutritional security. Globally, over a dozen legume species are cultivated in different agro-ecologies and cropping systems, but seven of them, namely, soybean (Glycine max), groundnut (Arachis hypogaea), cowpea (Vigna unguiculata), common bean (Phaseolus vulgaris), chickpea (Cicer arietinum), lentil (Lens culinaris) and pigeonpea (Cajanus cajan), hold promise with respect to their adaptation, productivity, international trade and consumer preferences. Legumes as a group, unfortunately, carry a tag of low productivity, and in spite of reasonable research efforts in general, their yield enhancement goals still remain unfulfilled. For this bottleneck various factors such as lack of high yielding cultivars, low research priority, inadequate inputs, relegation of the crops to second-grade lands, disease and insect losses and use of the age-old research tools and technologies can be held responsible. It seems that legume researchers have already lost valuable time and opportunities to provide farmers with high yielding cultivars with wide adaptation and incurring least damage due to biotic and abiotic stresses. Presently, the adverse effects of climate changes are also looming large, and hence, there is compelling need to re-emphasize the research priorities on a global basis. To highlight the importance of legumes to the human race and to make the legumes (including pulses) affordable to the poor, the 68th session of the UN General Assembly declared 2016 as the “International Year of Pulses”. It seems now the time is ripe to revisit the production trends and key constraints facing legumes and develop smart R&D plans, keeping in view the recent developments in the fields of genomics, genetic engineering/editing, crop breeding, agronomy and technology transfer. Therefore, there was a need to document these advances that can help the research community to develop a road map. In view of this, we have brought the experts working in different areas of legumes together to document their experiences and provide a road map through this book
On some interpolatory properties of Legendre polynomials. III
No full text[Saxena R. B.; Саксена Р. Б.]Englis
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
On the Use of the Polynomial Annihilation Edge Detection for Locating Cracks in Beam-Like Structures
No full textA crack in a structure causes a discontinuity in the first derivative of the mode shapes: On this basis, a numerical method for detecting discontinuities in smooth piecewise functions and their derivatives, based on a polynomialannihilation technique, has been applied to the problem of crack detection and localisation in beam-like structures for which only post-damage mode shapes are available. Using a finite-element model of a cracked beam, the performance of this methodology has been analysed for different crack depths and increasing amounts of noise. Given the crack position, a procedure to estimate its depth is also proposed and corresponding results show
Functional relations involving generalized H-function
No full textA number of papers have appeared in literature in which certain functional relations associated with hypergeometric functions and Digamma function ψ(z) are derived. In order to unify and extend the existing results due to Kalla [7]. Kalla and Ross [9], Al-Saqabi and Kalla [1], Nishimoto and Saxena [12], Srivastava and Nishimoto [17] and Pandey and Srivastava [14] etc., the author establishes two functional relations between ψ(z) and generalized H -function due to Inayat-Hussain [6]. The results obtained are of general character and provide extension and unification of functional relations of various hypergeometric functions available in literature. Existence conditionsand computable representation of the H -function are also investigated.<br /
Grundlagen der Peritonealdialyse
No full textNeben der Hämodialyse und der Nierentransplantation ist die Peritonealdialyse ein weiteres Nierenersatzverfahren, das aktuell in unseren Breitengraden zu selten angewandt wird
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