let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

Let $R$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎Let $M$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎Then $M$ has a direct decomposition $M=oplus_{iin I} M_i$‎,‎where each $M_i$ is noetherian quasi-projective and each‎‎endomorphism ring $End(M_i)$ is local‎.

In a group G, we denote the (cyclic) group of powers of some g ∈ G by 〈g〉 = {g : k ∈ Z}. If G = 〈g〉, then G itself is cyclic, with g as a generator. Examples of infinite cyclic groups include Z, with (additive) generator 1, and the group 2Z of integral powers of the real number 2, with generator 2. The most basic examples of finite cyclic groups are Z/(m) with (additive) generator 1 and μm = {z...

We study the kinematic distributions of top–antitop quark (tt̄) pairs produced at the Tevatron, including the effects of initial state and final state multiple soft gluon emission, using the Collins–Soper–Sterman resummation formalism. The resummed results are compared with those predicted by the showering event generator PYTHIA for various distributions involving the tt̄ pair and the individual ...

Every pseudorandom generator is in particular a one-way function. If we only consider part of the output of the pseudorandom generator is this still one-way? Here is a general setting formalizing this question. Suppose G : {0, 1} → {0, 1} is a pseudorandom generator with stretch `(n). Let MR ∈ {0, 1}m(n)×`(n) be a linear operator computable in polynomial time given randomness R. Consider the fu...

A stream cipher generator can not be considered as suitable for stream ciphers applications unless its output sequences have large periods, large linear complexities and possess certain randomness properties. The use of clock-controlled shift registers in keystream generators appears to be a good way of achieving sequences with these properties. In this thesis we look at clock-controlled genera...

We demonstrate how virtually all common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the equivalence of the well-known generator problem, “Is every separably-acting von Neumann algebra singly-generated?”, with the formally stronger questions, “Is ev...

Cryan and Miltersen [8] recently considered the question of whether there can be a pseudorandom generator in NC, that is, a pseudorandom generator that maps n-bit strings to m-bit strings such that every bit of the output depends on a constant number k of bits of the seed. They show that for k = 3, if m ≥ 4n + 1, there is a distinguisher; in fact, they show that in this case it is possible to b...

We investigate some properties of approximately quasi inner generalized dynamics and quasi approximately inner generalized derivations on modules. In particular, we prove that if A is a C*-algebra, is the generator of a generalized dynamics on an A-bimodule M satisfying and there exist two sequences of self adjoint elements in A such that for all in a core for , , then is approx...