Search results for "Lemma"

Atomic Decomposition of Weighted Besov Spaces

1996

We find the atomic decomposition of functions in the weighted Besov spaces under certain factorization conditions on the weight. Introduction. After achieving the atomic decomposition of Hardy spaces (see [8,22, 33]), many of the function saces have been shown to admit similar decompositions. Let us mention the decomposition of B.M.O. (see [32, 25]), Bergman spaces (see [9, 23]), the predual of Bloch space (see [ 11]), Besov spaces (see [15, 4, 10]), Lipschitz spaces (see [18]), Triebel-Lizorkin spaces (see [16, 31]),... They are obtained by quite different methods, but there is a unified and beautiful approach to get the decomposition for most of the spaces. This is the use of a formula du…

Glycemic Variability, Glycated Hemoglobin, and Cardiovascular Complications: Still a Dilemma in Clinical Practice

2021

Dystrophin-deficiency increases the susceptibility to doxorubicin-induced cardiotoxicity

2007

Background and aim: The clinical use of doxorubicin (DOX) and other anthracyclines is limited by a dosage-dependent cardiotoxicity, which can lead to cardiomyopathy. The role of the individual genetic makeup in this disorder is poorly understood. Alterations in genes encoding cardiac cytoskeleton or sarcolemma proteins may increase the susceptibility to doxorubicin-related cardiotoxicity. Methods: Female dystrophin-deficient mice (MDX) and age-matched wild-type mice underwent chronic treatment with doxorubicin. Cardiac function and tissue damage were assessed by echocardiography and histopathology, respectively. Gene expression changes were investigated using microarrays. Results: DOX treat…

Reversible stress-induced lipid body formation in fast twitch rat myofibers

2012

We analyzed the existence of lipid bodies (LBs) in the fast twitch rat flexor digitorum brevis (FDB) myofibers and found that these structures were scarce. However, isolation procedure of the myofibers, heath shock, viral infection or the glycosylation inhibitor tunicamycin induced formation of the LBs, which were stationary structures flanking Z lines. We next infected FDB myofibers with recombinant Semliki Forest virus expressing caveolin 3-yellow fluorescent protein (cav3-YFP) since this chimeric protein was targeted to the LBs facilitating their further analysis. Photobleaching experiments showed that the LBs recovered cav 3-YFP extremely slowly, indicating that they were not continuous…

Protein targeting to the plasma membrane of adult skeletal muscle fiber: an organized mosaic of functional domains.

2001

The plasma membrane of differentiated skeletal muscle fibers comprises the sarcolemma, the transverse (T) tubule network, and the neuromuscular and muscle-tendon junctions. We analyzed the organization of these domains in relation to defined surface markers, beta-dystroglycan, dystrophin, and caveolin-3. These markers were shown to exhibit highly organized arrays along the length of the fiber. Caveolin-3 and beta-dystroglycan/dystrophin showed distinct, but to some extent overlapping, labeling patterns and both markers left transverse tubule openings clear. This labeling pattern revealed microdomains over the entire plasma membrane with the exception of the neuromuscular and muscle-tendon j…

Religious Engagement and the Migration Issue: Towards Reconciling Political and Moral Duty

2020

The increasingly acknowledged post-secular perspective has resulted in the emergence of some new approaches theorizing this phenomenon. One such approach has been the concept of religious engagement, which calls for the redefinition of the perception of religious non-state actors towards including them as important partners in the process of identifying and realizing political goals. According to this view, due to the multidimensional role played by religious communities and non-state religious actors, they need to be recognized as pivotal in creating a new form of knowledge generated through encounter and dialogue of the political decision-makers with these subjects. Among numerous others,…

4-Manifold topology I: Subexponential groups

1995

The technical lemma underlying the 5-dimensional topological s-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ~-null immersions of disks. These conjectures are theorems precisely for those fundamental groups ("good groups") where the ~l-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two opera- tions: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.

On Banaschewski functions in lattices

1991

hold for all x, y ~ X. We call such a function z a Banaschewski function or a B-function on X. A lattice L is a B-lattice or antitonely complemented, if there is a B-function defined on the whole lattice L. For instance, Boolean lattices as well as orthocomplemented lattices are B-lattices. On the other hand, a B-lattice is not necessarily Boolean or orthocomplemented, although a distributive B-lattice is a Boolean lattice. It is shown later that a matroid (geometric) lattice is also a B-lattice. Naturally, our results include the lemma of Banaschewski [ 1, Lemma 4], by which the lattice of the subspaces of a vector space is a B-lattice. It should be emphasized that a B-function is supposed…

Size of Sets with Small Sensitivity: A Generalization of Simon’s Lemma

2015

We study the structure of sets \(S\subseteq \{0, 1\}^n\) with small sensitivity. The well-known Simon’s lemma says that any \(S\subseteq \{0, 1\}^n\) of sensitivity \(s\) must be of size at least \(2^{n-s}\). This result has been useful for proving lower bounds on the sensitivity of Boolean functions, with applications to the theory of parallel computing and the “sensitivity vs. block sensitivity” conjecture.

Extension of a Schur theorem to groups with a central factor with a bounded section rank

2013

Abstract A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.