The words “spectral sequence” strike fear into the hearts of many hardened mathematicians. These notes will attempt to demonstrate that spectral sequences are not so scary, and also very powerful. This is an unfinished handout for my algebraic topology class. In particular I did not have time to reproduce here the little spectral sequence diagrams showing where all the arrows go. For a comprehe...

For a function f 2 L p ?1; 1], 0 < p < 1, with nitely many sign changes, we construct a sequence of polynomials P n 2 n which are copositive with f and such that kf ? P n k p C! ' (f; (n + 1) ?1) p , where ! ' (f; t) p denotes the Ditzian-Totik modulus of continuity in L p metric. It was shown by S. P. Zhou that this estimate is exact in the sense that if f has at least one sign change, then ! ...

Recently the first author presented exact formulas for the number of 2-periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2-periodic binary sequence. A crucial role for the analysis played the Chan-Games algorithm. We use a more s...

We explore a variation of the isoperimetric problem in which integer subsets take the role of geometric figures. More specifically, we consider the sequence P (n) introduced by Miller et al. and described in OEIS A186053. We provide the first exact formulas for P (n) including recursive relations via auxiliary functions as well as concise and satisfying representations and even quasi-explicit f...

In this paper, within the framework of Method Differential Constraints, celebrated p-system is studied. All possible constraints compatible with original governing system are classified. solving compatibility conditions between and appended differential constraint, several model laws for pressure p(v) characterised. Therefore, analysis developed in paper has been carried out case physical inter...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...