Let BðEÞ be the complex Banach algebra of all bounded linear operators on a complex Banach space E: For n-tuples A ¼ ðA1, . . . ,AnÞ and B ¼ ðB1, . . . ,BnÞ of operators on E, let RA, B denote the operator on BðEÞ defined by RA, BðXÞ ¼ Pn i¼1AiXBi : For A, B 2 BðEÞ, we put UA, B ¼ RðA, BÞ, ðB,AÞ: In this note, we prove that co Xn i¼1 ii : ð1, . . . , nÞ 2 VðAÞ, ð1, . . . , nÞ 2 VðBÞ ( ) W0ðRA, BjJÞ where VðÞ is the joint spatial numerical range, W0ðÞ is the algebraic numerical range and J is a norm ideal of BðEÞ: We shall show that this inclusion becomes an equality when RA, B is taken to be a derivation. Also, we deduce that wðUA, BjJÞ 2ð ffiffiffi2 p 1ÞwðAÞwðBÞ, for A,B 2 BðEÞ and J is a norm ideal of BðEÞ, where wðÞ is the numerical radius. On the other hand, in the particular case when E is a Hilbert space, we shall prove that the lower estimate bound kUA, BjJk 2ð ffiffiffi2 p 1ÞkAkkBk holds, if one of the following two conditions is satisfied: (i) J is a standard operator algebra of BðEÞ and A,B 2 J: (ii) J is a norm ideal of BðEÞ and A, B 2 BðEÞ:
Mokrani K, Fournier PE, Dalichaouche M, Tebbal S, Aouati A, Raoult D. Reemerging threat of epidemic typhus in Algeria. Journal of Clinical Microbiology [J Clin Microbiol], ISSN: 0095-1137, PMID: 15297561, AugJournal of Clinical Microbiology [J Clin Microbiol], ISSN: 0095-1137, PMID: 15297561, Aug. 2004;42 :pp 3898-900.Abstract
We report a case of epidemic typhus in a patient from the Batna region of Algeria, who presented with generalized febrile exanthema. The clinical diagnosis was confirmed by serological cross-adsorption followed by Western blotting. Our report emphasizes the threat of epidemic typhus in the highlands of Algeria.
Hardware fault tolerance is an important consideration in critical distributed real-time embedded systems and has been extensively researched. In these systems, critical real-time constraints must be satisfied even in the presence of hardware component failures. Our goal is to propose a solution to automatically produce a fault-tolerant distributed schedule of a given algorithm onto a given distributed architecture, according to real-time constraints. The distributed architectures we consider have bidirectional point-to-point communication links. Our solution is a list scheduling heuristics, based on disjoint paths to tolerate a fixed number of arbitrary processor and communication link failures. Because of the resource limitation in embedded systems, our heuristics implements a software solution based on the active replication technique, where each operation of the algorithm is replicated on different processors. With a detailed example, we show the techniques used to satisfy the real-time constraints and tolerate the failure of processor and communication links. Simulations show the efficiency of our method compared with other heuristics found in the literature.
Let B(H) be the C ∗-algebra of all bounded linear operators on a complex Hilbert space H, S be an invertible and selfadjoint operator in B(H) and let (I, . I ) denote a norm ideal of B(H). In this note, we shall show the following inequality: ∀X ∈ I : SXS −1 − S −1XS I (SS −1 − 1)SXS −1 + S −1XS I .
