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Stratified Morse theory
Suppose that X is a topological space, f is a real valued function on X, and c is a real number. Then we will denote by X ≤c the subspace of points x in X such that f(x)≤c. The fundamental problem of
Equivariant cohomology, Koszul duality, and the localization theorem
(1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the
Intersection homology II
In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is a
Feedback shift registers, 2-adic span, and combiners with memory
This analysis gives a unified approach to the study of pseudorandom sequences, arithmetic codes, combiners with memory, and the Marsaglia-Zaman random number generator.
Fibonacci and Galois representations of feedback-with-carry shift registers
The d-FCSR, a slight modification of the (Fibonacci) FCSR architecture in which the feedback bit is delayed for d clock cycles before being returned to the first cell of the shift register, admits a more efficient "Galois" architecture.
On the Spectrum of the Equivariant Cohomology Ring
Abstract If an algebraic torus $T$ acts on a complex projective algebraic variety $X$ , then the affine scheme $\text{Spec}\,H_{T}^{*}\left( X;\,\mathbb{C} \right)$ associated with the equivariant
2-Adic Shift Registers
An algebraic framework is described, based on algebra over the 2-adic numbers, in which the sequences generated by FCSRs can be analyzed, in much the same way that algebra over finite fields can be used to analyze LFSR sequences.
An Introduction to Abstract Algebra
This chapter describes a variety of basic algebraic structures that play roles in the generation and analysis of sequences, especially sequences intended for use in communications and cryptography.
Loop Products and Closed Geodesics
We show the Chas-Sullivan product (on the homology of the free loop space of a Riemannian manifold) is related to the Morse index of its closed geodesics. We construct related products in the