Real Analysis on Intervals

Choudary, A. D. R.; Niculescu, Constantin P.

doi:10.1007/978-81-322-2148-7

Cited by 33 publications

(27 citation statements)

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“…F2.2 is cleaved by a variety of IgA1Ps from Gram-negative pathogens, including H. influenzae. 30 We previously demonstrated the compatibility of F2.2 with a 384-well HTS format using Neisseria meningitidis IgA1P. With that protease, we observed good signal-to-noise ratio and reproducibility, with a Z′-factor of 0.70.…”

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confidence: 70%

Small-Molecule Inhibitors of Haemophilus influenzae IgA1 Protease

et al. 2019

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Newly identified, non-typable H. influenza strains represent a serious threat to global health. Due to the increasing prevalence of antibiotic resistance, virulence factors have emerged as potential therapeutic targets that would be less likely to promote resistance. IgA1 proteases are secreted virulence factors of many Gram-negative human pathogens. These enzymes play important roles in tissue invasion as well as evasion of the immune response, yet there has been limited work on pharmacological inhibitors. Here we report the discovery of the first small molecule, non-peptidic inhibitors of H. influenzae IgA1 proteases. We screened over 47,000 compounds in a biochemical assay using recombinant protease, and identified a hit compound with micromolar potency. Preliminary SAR produced additional inhibitors, two of which showed improved inhibition and selectivity for IgA protease over other serine proteases. We further showed dose-dependent inhibition against four different IgA1 protease variants collected from clinical isolates. These data support further development of IgA protease inhibitors as potential therapeutics for antibacterialresistant H. influenza strains. The newly-discovered inhibitors also represent valuable probes for exploring the roles of these proteases in bacterial colonization, invasion, and infection of mucosal tissues.

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confidence: 70%

Small-Molecule Inhibitors of Haemophilus influenzae IgA1 Protease

et al. 2019

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“…Lemma 6.1. The abelianization ab: F → F/F (2) induces a factor of (M, {ϕ w t } t∈R ) which is isomorphic to a linear flow {ϕ t } t∈R on T 2 .…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

“…which expresses M as a bundle over the torus T 2 with fibers isomorphic to Λ\ΛF (2) . The differential of the induced projection ab : M → T 2 on M maps the vector field w = w 0 f 0 + · · · + w d f d ∈ f to a vector field on T 2 , which gives the linear flow ϕ t (x 0 , x 1 ) = (x 0 , x 1 ) + t(w 0 , w 1 ).…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

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Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows

Ravotti¹

2018

Ergod. Th. Dynam. Sys.

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We consider suspension flows over uniquely ergodic skew-translations on a d-dimensional torus T d , for d ≥ 2. We prove that there exists a set R of smooth functions, which is dense in the space C (T d ) of continuous functions, such that every roof function in R which is not cohomologous to a constant induces a mixing suspension flow. We also construct a dense set of mixing examples which is explicitly described in terms of their Fourier coefficients. In the language of nilflows on nilmanifolds, our result implies that, for every uniquely ergodic nilflow on a quasi-abelian filiform nilmanifold, there exists a dense subspace of smooth time-changes in which mixing occurs if and only if the time-change is not cohomologous to a constant. This generalizes a theorem by Avila, Forni and Ulcigrai (J. Diff. Geom., 2011) for the classical Heisenberg group.In this section, we present the general structure of the proof of Theorem 1.1-(a), stating some intermediate results, which are proved in later sections.Let T be a uniquely ergodic skew-translation as in (1.1). If we denote by E j the image of the linear map (A − Id) j , we have a filtration of R d into rational subspacesUp to a linear isomorphism, we can assume that the basis {e 1 , . . . , e d } of Z d is adapted to the filtration above, in particular {e d0+1 , . . . , e d } is a basis of E k , where d − d 0 = dim E k . Since T is not a rotation, k ≥ 1 and 1 ≤ d 0 ≤ d − 1. We remark that w ∈ E j for j ≥ 1 if and only if there exists v ∈ E j−1 such that v(A − Id) = w, i.e. vA = v + w. In particular,

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“…Condition (2) is the main estimate describing the growth of the function φ, while (1) simply means that φ is a modulus of continuity and (3) is of technical nature. Condition (3) implies that φ is a modulus that is at least Hölder with some positive exponent α. Since, in applications, we are interested in moduli very close to Lipschitz, the condition (3) is not restrictive.…”

Section: Introductionmentioning

confidence: 99%

Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

Goldstein¹,

Hajłasz²

2018

Ann. Acad. Sci. Fenn. Math.

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We construct an a.e. approximately differentiable homeomorphism of a unit n-dimensional cube onto itself which is orientation preserving, has the Lusin property (N) and has the Jacobian determinant negative a.e. Moreover, the homeomorphism together with its inverse satisfy a rather general sub-Lipschitz condition, in particular it can be bi-Hölder continuous with an arbitrary exponent less than 1.2010 Mathematics Subject Classification. Primary 46E35; Secondary 26B05, 26B10, 26B35, 74B20.

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Real Analysis on Intervals

Cited by 33 publications

References 0 publications

Small-Molecule Inhibitors of Haemophilus influenzae IgA1 Protease

Small-Molecule Inhibitors of Haemophilus influenzae IgA1 Protease

Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows

Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian

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