Time-Averaging for Weakly Nonlinear CGL Equations with Arbitrary Potentials

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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Evolution of High-Order Weakly Nonlinear Wave with Bottom Topography Change

Journal of Japan Society of Civil Engineers Ser B2 (Coastal Engineering) ◽

10.2208/kaigan.76.2_i_1 ◽

2020 ◽

Vol 76 (2) ◽

pp. I_1-I_6

Author(s):

Zuorui LYU ◽

Nobuhito MORI ◽

Hiroaki KASHIMA

Keyword(s):

Nonlinear Wave ◽

Bottom Topography ◽

High Order ◽

Weakly Nonlinear

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TAPHONOMY AND TIME AVERAGING OF MOLLUSCAN DEATH ASSEMBLAGES IN FLORIDA SPRINGS AND RIVERS

10.1130/abs/2018am-322285 ◽

2018 ◽

Author(s):

Kristopher M. Kusnerik ◽

◽

Harley Means ◽

Roger W. Portell ◽

Michal Kowalewski

Keyword(s):

Time Averaging ◽

Death Assemblages ◽

Florida Springs

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A robust algorithm for source number detection based on space-time averaging techniques

10.1049/cp.2009.0353 ◽

2009 ◽

Author(s):

Ruiyan Du ◽

Jinkuan Wang ◽

Fulai Liu ◽

Bin Wang

Keyword(s):

Space Time ◽

Time Averaging ◽

Robust Algorithm ◽

Source Number ◽

Averaging Techniques

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Activity of Specialized Biomolecules against Gram-Positive and Gram-Negative Bacteria

Antibiotics ◽

10.3390/antibiotics9060314 ◽

2020 ◽

Vol 9 (6) ◽

pp. 314 ◽

Cited By ~ 1

Author(s):

Tânia D. Tavares ◽

Joana C. Antunes ◽

Jorge Padrão ◽

Ana I. Ribeiro ◽

Andrea Zille ◽

...

Keyword(s):

Cell Morphology ◽

Time Averaging ◽

Gram Negative Bacteria ◽

Gram Positive ◽

Intracellular Space ◽

Gram Negative ◽

Tea Tree ◽

Minimal Inhibitory Concentrations ◽

Agar Diffusion Test ◽

Short Period

The increased resistance of bacteria against conventional pharmaceutical solutions, the antibiotics, has raised serious health concerns. This has stimulated interest in the development of bio-based therapeutics with limited resistance, namely, essential oils (EOs) or antimicrobial peptides (AMPs). This study envisaged the evaluation of the antimicrobial efficacy of selected biomolecules, namely LL37, pexiganan, tea tree oil (TTO), cinnamon leaf oil (CLO) and niaouli oil (NO), against four bacteria commonly associated to nosocomial infections: Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli and Pseudomonas aeruginosa. The antibiotic vancomycin and silver nanoparticles (AgNPs) were used as control compounds for comparison purposes. The biomolecules were initially screened for their antibacterial efficacy using the agar-diffusion test, followed by the determination of minimal inhibitory concentrations (MICs), kill-time kinetics and the evaluation of the cell morphology upon 24 h exposure. All agents were effective against the selected bacteria. Interestingly, the AgNPs required a higher concentration (4000–1250 μg/mL) to induce the same effects as the AMPs (500–7.8 μg/mL) or EOs (365.2–19.7 μg/mL). Pexiganan and CLO were the most effective biomolecules, requiring lower concentrations to kill both Gram-positive and Gram-negative bacteria (62.5–7.8 μg/mL and 39.3–19.7 μg/mL, respectively), within a short period of time (averaging 2 h 15 min for all bacteria). Most biomolecules apparently disrupted the bacteria membrane stability due to the observed cell morphology deformation and by effecting on the intracellular space. AMPs were observed to induce morphological deformations and cellular content release, while EOs were seen to split and completely envelope bacteria. Data unraveled more of the potential of these new biomolecules as replacements for the conventional antibiotics and allowed us to take a step forward in the understanding of their mechanisms of action against infection-related bacteria.

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