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- B Mazur, E Krebbers, S Tingey
- Science
- 1999

The composition of oils, proteins, and carbohydrates in seeds of corn, soybean, and other crops has been modified to produce grains with enhanced value. Both plant breeding and molecular technologies have been used to produce plants carrying the desired traits. Genomics-based strategies for gene discovery, coupled with high-throughput transformation… (More)

- B Mazur, K Rubin, A Silverberg
- 2008

If V is a commutative algebraic group over a field k, O is a commutative ring that acts on V , and I is a finitely generated free O-module with a right action of the absolute Galois group of k, then there is a commutative algebraic group I ⊗O V over k, which is a twist of a power of V . These group varieties have applications to cryptography (in the cases… (More)

Let E be an elliptic curve over ij. A celebrated theorem of Mordell asserts that E(ij) , the (abelian) group of rational points of E, is finitely generated. By the rank of E we mean the rank of E(ij). Thus the rank of E is positive if and only if E possesses an infinity of rational points. Relatively few general qualitative assertions can be made about the… (More)

- B. MAZUR
- 2009

In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence,… (More)

- B. Mazur, K. A. Ribet
- 2003

In the theory of automorphic representations of a reductive algebraic group G over a number field K, it is broadly — but not always — true that irreducible representations occurring in L(GA/GK) occur with multiplicity one. In a classical special case (G = GL(2), K = Q, and where we restrict attention to automorphic representations which are holomorphic,… (More)

Contents 1. Introduction 307 2. Universal unfoldings 309 3. Special, general, very general, generic... 313 4. Moduli: Parameters describing the deformations of a mathematical structure 314 (1). Classifying ellipses in the plane up to Euclidean congruence. 314 (2). Deforming Riemann surfaces. 315 5. Moduli and lattices 317 6. Lattices in real vector spaces… (More)

- B Mazur
- Science
- 1983

- Elżbieta Macauley, Tim Macauley, +11 authors Agostino Cortesi
- 2014

There is a trade-off in Supply Chain Management Systems between efficiency and demand variability. When no variation occurs in consumer need, order cycle, product portfolios, and in distribution lead time, then the supply chain would be just a routine business process. Unfortunately, in practice this is not often the case. Thus, ranking demand variability… (More)

- Elżbieta Macauley, Tim Macauley, +11 authors Agostino Cortesi
- 2014

This article presents the problem of consensus determining postulates defined in decision support systems. The consensus determining methods and the general postulates for consensus estimation and their characteristics are presented in the first part. Next, the definitions of new postulates pertaining to decisions support systems were elaborated, and the… (More)

We report on the discovery of eleven multimode SX Phoenicis–type blue stragglers in the field of the southern globular cluster NGC 3201. In these variables both radial and non-radial modes are excited. For three variables the derived period ratio is close to that observed in SX Phoenicis itself, suggesting that these stars are pulsating in the fundamental… (More)