THE ASYMPTOTIC DENSITY OF FINITE
... The following classical result can be found, for example, in [11]. Theorem 2.2 (Milnor, Efremovich, Švarc). If Γ is a group acting properly discontinuously and cocompactly by isometries on a proper geodesic metric space X, then Γ is quasi-isometric to X. More precisely, for any x0 ∈ X, the mapping ...
... The following classical result can be found, for example, in [11]. Theorem 2.2 (Milnor, Efremovich, Švarc). If Γ is a group acting properly discontinuously and cocompactly by isometries on a proper geodesic metric space X, then Γ is quasi-isometric to X. More precisely, for any x0 ∈ X, the mapping ...
CHAPTER 3: Cyclic Codes
... We show that all cyclic codes C have the form C = f(x) for some f(x) Rn. Theorem Let C be a non-zero cyclic code in Rn. Then • there exists unique monic polynomial g(x) of the smallest degree such that • C = g(x) • g(x) is a factor of xn -1. Proof (i) Suppose g(x) and h(x) are two monic polyno ...
... We show that all cyclic codes C have the form C = f(x) for some f(x) Rn. Theorem Let C be a non-zero cyclic code in Rn. Then • there exists unique monic polynomial g(x) of the smallest degree such that • C = g(x) • g(x) is a factor of xn -1. Proof (i) Suppose g(x) and h(x) are two monic polyno ...
FMROT.pdf
... it is not useful in and of itself, it appears to be very useful as a means towards other ends, and in fact has been used in a number of other protocols by a number of different researchers [1]-[3]. In [4], Rabin proposed a protocol for the oblivious transfer. It was intended that the protocol be cor ...
... it is not useful in and of itself, it appears to be very useful as a means towards other ends, and in fact has been used in a number of other protocols by a number of different researchers [1]-[3]. In [4], Rabin proposed a protocol for the oblivious transfer. It was intended that the protocol be cor ...
IFP near-rings - Cambridge University Press
... PROOF. Suppose A' has no sub-semi-group in N*. Then each element of N is nilpotent. In this case Q(N) is precisely the set of all nilpotent elements of N. Assume that N has sub-semi-groups in N*. Let {Ka}aeA be the family of maximal sub-semi-groups in N*. Since each Ka contains no nilpotent elements ...
... PROOF. Suppose A' has no sub-semi-group in N*. Then each element of N is nilpotent. In this case Q(N) is precisely the set of all nilpotent elements of N. Assume that N has sub-semi-groups in N*. Let {Ka}aeA be the family of maximal sub-semi-groups in N*. Since each Ka contains no nilpotent elements ...
ALGEBRAIC SYSTEMS BIOLOGY: A CASE STUDY
... Cellular decisions such as cell division, specialization and cell death are governed by a rich repertoire of complex signals that are produced by other cells and/or stimuli. In order for a cell to come to an appropriate decision, it must sense its external environment, communicate this information t ...
... Cellular decisions such as cell division, specialization and cell death are governed by a rich repertoire of complex signals that are produced by other cells and/or stimuli. In order for a cell to come to an appropriate decision, it must sense its external environment, communicate this information t ...
3.1 Solving linear equations Introduction
... 1. (a) The general form is ax + b = 0 where a and b are known numbers and x represents the unknown quantity. (b) A root is a value for the unknown which satisfies the equation. Back to the theory ...
... 1. (a) The general form is ax + b = 0 where a and b are known numbers and x represents the unknown quantity. (b) A root is a value for the unknown which satisfies the equation. Back to the theory ...
Uniform finite generation of the rotation group
... The fact that SO(3) is uniformly finitely generated by T+ and S0 is a simple consequence of its being compact; an elegant proof of this involving Baire category theory was suggested to the author by R. B. Burckel and is included in the Appendix. The goal of this paper is to compute the order of gene ...
... The fact that SO(3) is uniformly finitely generated by T+ and S0 is a simple consequence of its being compact; an elegant proof of this involving Baire category theory was suggested to the author by R. B. Burckel and is included in the Appendix. The goal of this paper is to compute the order of gene ...
Joint Reductions, Tight Closure, and the Briancon
... holds in any equicharacteristic regular local ring, not necessarily of characteristic p. In general, it is false that for each ideal Z in an arbitrary ring there exists an integer I such that for all positive integers n, the integral closure of Z’+n is contained in I”. For example, if R = k[.X’, Y]/ ...
... holds in any equicharacteristic regular local ring, not necessarily of characteristic p. In general, it is false that for each ideal Z in an arbitrary ring there exists an integer I such that for all positive integers n, the integral closure of Z’+n is contained in I”. For example, if R = k[.X’, Y]/ ...
23. Group actions and automorphisms Recall the definition of an
... Theorem 23.12. The outer automorphism group of Sn is trivial unless n = 6 when it is isomorphic to Z2 . Lemma 23.13. If φ : Sn −→ Sn is an automorphism of Sn which sends a transposition to a transposition then φ is an inner automorphism. Proof. Since any automorphism permutes the conjugacy classes, ...
... Theorem 23.12. The outer automorphism group of Sn is trivial unless n = 6 when it is isomorphic to Z2 . Lemma 23.13. If φ : Sn −→ Sn is an automorphism of Sn which sends a transposition to a transposition then φ is an inner automorphism. Proof. Since any automorphism permutes the conjugacy classes, ...
