We prove a number of conjectures recently stated by P. Barry, related to the paperfolding sequence and Rueppel sequence. Furthermore, we study regularity sequences involved in paper, that for all q≥2, consisting positive integers whose odd part is form 4k+1 not q-regular. Finally establish 2-regularity two Hankel determinants.

We propose a framework for solving equational and membership constraints for terms built over individual, sequence, function, and context variables and flexible arity symbols. Each membership constraint couples a variable with a regular expression on terms or contexts. There can be several membership constraints with the same constrained variable, and expressions may contain variables themselve...

4. N. Jacobson, Abstract derivations and Lie algebras, Trans. Amer. Math. Soc. 42 (1937), 206-224. 5. — , p-Algebras of exponent p, Bull. Amer. Math. Soc. 43 (1937), 667-670. 6. , Galois theory of purely inseparable fields of exponent one, Amer. J. Math. 46(1944), 645-648. 7. , Lectures in abstract algebra, Vol. I l l , Van Nostrand, Princeton, N. J., 1964. 8. O. Zariski and P. Samuel, Commutat...

A spectral sequence is constructed whose nonzero E1-terms are the Witt groups of the residue fields of a regular scheme X, arranged in Gersten-Witt complexes, and whose limit is the four global Witt groups of X. There are several immediate consequences concerning purity for Witt groups of low-dimensional schemes. The Witt groups of punctured spectra of regular local rings are also computed. Let...

In 1911, Steinhaus presented the following theorem: if A is a regular matrix then there exists a sequence of 0’s and 1’s which is not A-summable. In 1943, R. C. Buck characterized convergent sequences as follows: a sequence x is convergent if and only if there exists a regular matrix A which sums every subsequence of x. In this paper, definitions for “subsequences of a double sequence” and “Pri...