scholarly journals The Family of Global Attractors for a Generalized Kirchhoff Equations

2021 ◽  
Vol 11 (07) ◽  
pp. 789-806
Author(s):  
Guoguang Lin ◽  
Xiaomei Liu
Keyword(s):  
Global Attractors ◽  
Kirchhoff Equations ◽  
The Family

Equi-exponential attraction and rate of convergence of attractors with application to a perturbed damped wave equation

2014 ◽  
Vol 144 (1) ◽  
pp. 13-51 ◽  
Author(s):  
Alexandre N. Carvalho ◽  
Jan W. Cholewa ◽  
Tomasz Dłotko
Keyword(s):  
Wave Equation ◽  
Rate Of Convergence ◽  
Global Attractors ◽  
Damped Wave Equation ◽  
Continuity Properties ◽  
Compact Semigroups ◽  
The Family ◽  
Bounded Dissipative ◽  
Attraction Property ◽  
Abstract Framework

We consider a family of bounded dissipative asymptotically compact semigroups depending on a parameter, and study the continuity properties of the corresponding family of its global attractors. We exploit the idea of the uniform exponential attraction property to discuss the continuity properties of the family of attractors and estimate the rate of convergence of the approximating attractors to the limit one. Showing a range of applications of an abstract framework, we focus much of our attention on a perturbed damped wave equation. In this latter case our results involve nonlinearities with critical exponents, for which the continuity of the family of attractors is concluded, including the rate of convergence and the regularity of the limit attractor. This complements the results in the literature.

scholarly journals Existence and continuity of global attractors for ternary mixtures of solids

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mirelson M. Freitas ◽  
Anderson J. A. Ramos ◽  
Baowei Feng ◽  
Mauro L. Santos ◽  
Helen C. M. Rodrigues
Keyword(s):  
Global Attractors ◽  
Nonlinear Damping ◽  
Ternary Mixtures ◽  
Small Perturbations ◽  
Time Dynamics ◽  
The Family ◽  
Long Time ◽  
Finite Fractal Dimension ◽  
Dense Set ◽  
Long Time Dynamics

<p style='text-indent:20px;'>In this paper, we study the long-time dynamics of a system modelinga mixture of three interacting continua with nonlinear damping, sources terms and subjected to small perturbations of autonomousexternal forces with a parameter <inline-formula><tex-math id="M1">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula>, inspired by the modelstudied by Dell' Oro and Rivera [<xref ref-type="bibr" rid="b12">12</xref>]. We establish astabilizability estimate for the associated gradient dynamicalsystem, which as a consequence, implies the existence of a compactglobal attractor with finite fractal dimension andexponential attractors. This estimate is establishedindependent of the parameter <inline-formula><tex-math id="M2">\begin{document}$ \epsilon\in[0,1] $\end{document}</tex-math></inline-formula>. We also prove thesmoothness of global attractors independent of the parameter<inline-formula><tex-math id="M3">\begin{document}$ \epsilon\in[0,1] $\end{document}</tex-math></inline-formula>. Moreover, we show that the family of globalattractors is continuous with respect to the parameter <inline-formula><tex-math id="M4">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> ona residual dense set <inline-formula><tex-math id="M5">\begin{document}$ I_*\subset[0,1] $\end{document}</tex-math></inline-formula> in the same sense proposed inHoang et al. [<xref ref-type="bibr" rid="b15">15</xref>].</p>

Triassic sponges (Sphinctozoa) from Hells Canyon, Oregon

1988 ◽  
Vol 62 (03) ◽  
pp. 419-423 ◽  
Author(s):  
Baba Senowbari-Daryan ◽  
George D. Stanley
Keyword(s):  
Endemic Species ◽  
Upper Triassic ◽  
Island Arc ◽  
Tropical Island ◽  
The Family ◽  
Wallowa Terrane ◽  
Unique Condition ◽  
Hells Canyon

Two Upper Triassic sphinctozoan sponges of the family Sebargasiidae were recovered from silicified residues collected in Hells Canyon, Oregon. These sponges areAmblysiphonellacf.A. steinmanni(Haas), known from the Tethys region, andColospongia whalenin. sp., an endemic species. The latter sponge was placed in the superfamily Porata by Seilacher (1962). The presence of well-preserved cribrate plates in this sponge, in addition to pores of the chamber walls, is a unique condition never before reported in any porate sphinctozoans. Aporate counterparts known primarily from the Triassic Alps have similar cribrate plates but lack the pores in the chamber walls. The sponges from Hells Canyon are associated with abundant bivalves and corals of marked Tethyan affinities and come from a displaced terrane known as the Wallowa Terrane. It was a tropical island arc, suspected to have paleogeographic relationships with Wrangellia; however, these sponges have not yet been found in any other Cordilleran terrane.

Electron Microscopy of Mycoplasma Pneumoniae

1971 ◽  
Vol 29 ◽  
pp. 258-259 ◽  
Author(s):  
E. S. Boatman ◽  
G. E. Kenny
Keyword(s):  
Electron Microscopy ◽  
Light Microscopy ◽  
Growth Phase ◽  
Hela Cells ◽  
Sulfonic Acid ◽  
Gamma Globulin ◽  
Horse Serum ◽  
Morphological Aspects ◽  
The Family

Information concerning the morphology and replication of organism of the family Mycoplasmataceae remains, despite over 70 years of study, highly controversial. Due to their small size observations by light microscopy have not been rewarding. Furthermore, not only are these organisms extremely pleomorphic but their morphology also changes according to growth phase. This study deals with the morphological aspects of M. pneumoniae strain 3546 in relation to growth, interaction with HeLa cells and possible mechanisms of replication.The organisms were grown aerobically at 37°C in a soy peptone yeast dialysate medium supplemented with 12% gamma-globulin free horse serum. The medium was buffered at pH 7.3 with TES [N-tris (hyroxymethyl) methyl-2-aminoethane sulfonic acid] at 10mM concentration. The inoculum, an actively growing culture, was filtered through a 0.5 μm polycarbonate “nuclepore” filter to prevent transfer of all but the smallest aggregates. Growth was assessed at specific periods by colony counts and 800 ml samples of organisms were fixed in situ with 2.5% glutaraldehyde for 3 hrs. at 4°C. Washed cells for sectioning were post-fixed in 0.8% OSO4 in veronal-acetate buffer pH 6.1 for 1 hr. at 21°C. HeLa cells were infected with a filtered inoculum of M. pneumoniae and incubated for 9 days in Leighton tubes with coverslips. The cells were then removed and processed for electron microscopy.

Exposure of protein VP7 on the surface of bluetongue virus

1990 ◽  
Vol 48 (3) ◽  
pp. 600-601
Author(s):  
A.D. Hyatt
Keyword(s):  
Bluetongue Virus ◽  
Structural Proteins ◽  
Major Constituent ◽  
Outer Coat ◽  
Virus Particles ◽  
Antibody Recognition ◽  
The Core ◽  
The Family ◽  
Electron Microscopical ◽  
Physical Accessibility

Bluetongue virus (BTV) is the type species os the genus orbivirus in the family Reoviridae. The virus has a fibrillar outer coat containing two major structural proteins VP2 and VP5 which surround an icosahedral core. The core contains two major proteins VP3 and VP7 and three minor proteins VP1, VP4 and VP6. Recent evidence has indicated that the core comprises a neucleoprotein center which is surrounded by two protein layers; VP7, a major constituent of capsomeres comprises the outer and VP3 the inner layer of the core . Antibodies to VP7 are currently used in enzyme-linked immunosorbant assays and immuno-electron microscopical (JEM) tests for the detection of BTV. The tests involve the antibody recognition of VP7 on virus particles. In an attempt to understand how complete viruses can interact with antibodies to VP7 various antibody types and methodologies were utilized to determine the physical accessibility of the core to the external environment.

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