We say that a Banach space X satisfies the "descent spectrum equality" (in short, DSE) whenever, for every bounded linear operator T on X, the descent spectrum of T as an operator coincides with the descent spectrum of T as an element of the algebra of all bounded linear operators on X. We prove that the DSE is fulfilled by 1 , all Hilbert spaces, and all Banach spaces which are not isomorphic to any of their proper quotients (so, in particular, by the hereditarily indecomposable Banach spaces [8]), but not by p, for 1 < p ≤ ∞ with p = 2. Actually, a Banach space is not isomorphic to any of its proper quotients if and only if it is not isomorphic to any of its proper complemented subspaces and satisfies the DSE.

In this work, we study binary linear distinct weight codes (DW-code). We give a complete classification of [ ] 2 , n k-DW-codes and enumerate their equivalence classes in terms of the number of solutions of specific Diophantine Equations. We use the Q-extension program to provide examples.

If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.

<p>This paper proposes a novel discrete bio-inspired chicken swarm optimization algorithm (CSO) to solve the problem of the traveling salesman problem (TSP) which is one of the most known problems used to evaluate the performance of the new metaheuristics. This problem is solved by applying a local search method 2-opt in order to improve the quality of the solutions. The DCSO as a swarm system of the algorithm increases the level of diversification, in the same way the hierarchical order of the chicken swarm and the behaviors of chickens increase the level of intensification. In this contribution, we redefined the basic different operators and operations of the CSO algorithm. The performance of the algorithm is tested on a symmetric TSP benchmark dataset from TSPLIB library. Therefore, the algorithm provides good results in terms of both optimization accuracy and robustness comparing to other metaheuristics.</p>

No abstract