The aim of this paper is to gain explicit information about the multiplicative structure of l∗l, where l is the connective Adams summand. Our approach differs from Kane’s or Lellmann’s because our main technical tool is the MU -based Künneth spectral sequence. We prove that the algebra structure on l∗l is inherited from the multiplication on a Koszul resolution of l∗BP . Introduction Our goal i...

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper’s algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is inreased.

We present various comments on a question about systems over rings posed in a recent note by Sharma, proving that a ring R is pole-assignable if and only if, for every reachable system (F,G), G contains a rank-one summand of the state space. We also provide a generalization to deal with dynamic feedback.

We provide a new algorithm for indefinite nested summation which is applicable to summands involving unspecified sequences x(n). More than that, we show how to extend Karr’s algorithm to a general summation framework by which additional types of summand expressions can be handled. Our treatment of unspecified sequences can be seen as a first illustrative application of this approach.

In this paper, we prove the following result conjectured by Z.-W. Sun: (2n− 1) ( 3n n ) ∣∣∣∣ n ∑ k=0 ( 6k 3k )( 3k k )( 6(n− k) 3(n− k) )( 3(n− k) n− k ) by showing that the left-hand side divides each summand on the right-hand side.

in this paper we study the duality of bessel and g-bessel sequences in hilbertspaces. we show that a bessel sequence is an inner summand of a frame and the sum of anybessel sequence with bessel bound less than one with a parseval frame is a frame. next wedevelop this results to the g-frame situation.

It is shown how the performance of Zeilberger’s algorithm and its q-version for proving (q-)hypergeometric summation identities can be dramatically improved by a frequently missed optimization on the programming level and by applying certain kinds of substitutions to the summand. These methods lead to computer proofs of identities for which all existing programs have failed so far.

We prove large deviation results for Minkowski sums of iid random compact sets where we assume that the summands have a regularly varying distribution. The result confirms the heavy-tailed large deviation heuristics: “large” values of the sum are essentially due to the “largest” summand.

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group SL2, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands. Various other related results are obtained, and numerous examples are computed. Introduction We study the structure of L ⊗ L where L,L are simple modules for the algeb...