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981.
Text
Over a period of sixteen years elliptic curve cryptography went from being an approach that many people mistrusted or misunderstood to being a public key technology that enjoys almost unquestioned acceptance. We describe the sometimes surprising twists and turns in this paradigm shift, and compare this story with the commonly accepted Ideal Model of how research and development function in cryptography. We also discuss to what extent the ideas in the literature on “social construction of technology” can contribute to a better understanding of this history.Video
For a video summary of this paper, please visit http://www.youtube.com/watch?v=HHFFvfDoTK4. 相似文献982.
In the present paper, we obtain new results on universality as applications of hybrid universality and almost-periodicity in its half-plane of absolute convergence. By using these, we show the universality for Euler products of Igusa type, Euler-Zagier multiple zeta-functions and Tornheim-Hurwitz type of double zeta-functions. 相似文献
983.
Akinari Hoshi 《Journal of Number Theory》2011,131(11):2135-2150
Let m?−1 be an integer. We give a correspondence between integer solutions to the parametric family of cubic Thue equations
X3−mX2Y−(m+3)XY2−Y3=λ 相似文献
984.
Daniel Simson 《Journal of Pure and Applied Algebra》2011,215(1):13-34
Integral quadratic forms q:Zn→Z, with n≥1, and the sets Rq(d)={v∈Zn;q(v)=d}, with d∈Z, of their integral roots are studied by means of mesh translation quivers defined by Z-bilinear morsifications bA:Zn×Zn→Z of q, with Z-regular matrices A∈Mn(Z). Mesh geometries of roots of positive definite quadratic forms q:Zn→Z are studied in connection with root mesh quivers of forms associated to Dynkin diagrams An,Dn,E6,E7,E8 and the Auslander-Reiten quivers of the derived category Db(R) of path algebras R=KQ of Dynkin quivers Q. We introduce the concepts of a Z-morsification bA of a quadratic form q, a weighted ΦA-mesh of vectors in Zn, and a weighted ΦA-mesh orbit translation quiver Γ(Rq,ΦA) of vectors in Zn, where Rq?Rq(1) and ΦA:Zn→Zn is the Coxeter isomorphism defined by A. The existence of mesh geometries on Rq is discussed. It is shown that, under some assumptions on the morsification bA:Zn×Zn→Z, the set admit a ΦA-orbit mesh quiver , where ΦA:Zn→Zn is the Coxeter isomorphism defined by A. Moreover, splits into three infinite connected components , , and , where are isomorphic to a translation quiver Z⋅Δ, with Δ an extended Dynkin quiver, and has the shape of a sand-glass tube. 相似文献
985.
Mark Tomforde 《Journal of Pure and Applied Algebra》2011,215(4):471-484
Given a directed graph E we describe a method for constructing a Leavitt path algebra LR(E) whose coefficients are in a commutative unital ring R. We prove versions of the Graded Uniqueness Theorem and Cuntz-Krieger Uniqueness Theorem for these Leavitt path algebras, giving proofs that both generalize and simplify the classical results for Leavitt path algebras over fields. We also analyze the ideal structure of LR(E), and we prove that if K is a field, then LK(E)≅K⊗ZLZ(E). 相似文献
986.
B.A.F. Wehrfritz 《Journal of Pure and Applied Algebra》2011,215(5):1112-1115
Suppose G is either a soluble (torsion-free)-by-finite group of finite rank or a soluble linear group over a finite extension field of the rational numbers. We consider the implications for G if G has an automorphism of finite order m with only finitely many fixed points. For example, if m is prime then G is a finite extension of a nilpotent group and if m=4 then G is a finite extension of a centre-by-metabelian group. This extends the special cases where G is polycyclic, proved recently by Endimioni (2010); see [3]. 相似文献
987.
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective lines; this is illustrated by various applications. 相似文献
988.
Guangbin Zhuang 《Journal of Pure and Applied Algebra》2011,215(12):2912-2922
Let H be a pointed Hopf algebra over an algebraically closed field of characteristic zero. If H is a domain with finite Gelfand-Kirillov dimension greater than or equal to two, then H contains a Hopf subalgebra of Gelfand-Kirillov dimension two. 相似文献
989.
Jonas T. Hartwig 《Journal of Pure and Applied Algebra》2011,215(10):2352-2377
We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coefficient ring R), which is assumed to carry an involution of the form X∗=Y, R∗⊆R. We prove that a weight module V is pseudo-unitarizable iff it is isomorphic to its finitistic dual V?. Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necessary and sufficient conditions for an indecomposable weight module to be isomorphic to its finitistic dual, and thus to be pseudo-unitarizable. Some examples are given, including Uq(sl2) for q a root of unity. 相似文献
990.
For R a commutative Noetherian ring, wide and Serre subcategories of finitely generated R-modules have been classified by their support. This paper studies general torsion classes and introduces narrow subcategories. These are closed under fewer operations than wide and Serre subcategories, but still for finitely generated R-modules both narrow subcategories and torsion classes are classified using the same support data. Although for finitely generated R-modules all four kinds of subcategories coincide, they do not coincide in the larger category of all R-modules. 相似文献