986 research outputs found
Periodic solutions for Boussinesq systems in weak-Morrey spaces
We prove the existence and polynomial stability of periodic mild solutions
for Boussinesq systems in critical weak-Morrey spaces for dimension
. Those systems are derived via the Boussinesq approximation and
describe the movement of an incompressible viscous fluid under natural
convection filling the whole space . Using certain dispersive
and smoothing properties of heat semigroups on Morrey-Lorentz spaces as well as
Yamazaki-type estimate on block spaces, we prove the existence of bounded mild
solutions for the linear equations corresponding to the Boussinesq system.
Then, we establish a Massera-type theorem to obtain the existence and
uniqueness of periodic solutions to corresponding linear equations on the
half-line by using a mean-ergodic method. Next, using fixed point arguments, we
can pass from linear equations to prove the existence uniqueness and polynomial
stability of such solutions for Boussinesq systems. Finally, we apply the
results to Navier-Stokes equations.Comment: 18 page
On stability problem for the stationary Boussinesq system in Morrey-type spaces
In this paper we establish the asymptotic stability of steady solutions for
the Boussinesq systems in the framework of Cartesian product of critical
weak-Morrey spaces on , where . In our strategy,
we first establish the continuity for the long time of the bilinear terms
associated with the mild solutions of the Boussinesq systems, i.e., the
bilinear estimates by using only the norm of the present spaces. As a direct
consequence, we obtain the existence of global small mild solutions and
asymptotic stability of steady solutions of the Boussinesq systems in the class
of continuous functions from to the Cartesian product of critical
weak-Morrey spaces. Our techniques consist interpolation of operators, duality,
heat semigroup estimates , Holder and Young inequalities in block spaces (based
on Lorentz spaces) that are preduals of Morrey-Lorentz spaces. Our results are
generalized the previous ones of the steady Boussinesq systems in weak-
spaces obtained by Hishida [T. Hishida, {\it On a class of Stable Steady flow
to the Exterior Convection Problem}, Journal of Differential Equations, Vol.
141, Iss. 1 (1997), pages 54-85] and Ferreira et al. [L.C.F. Ferreira and E.J.
Villamizar-Roa, {\it On the stability problem for the Boussinesq equations in
weak- spaces}, Commun. Pure Appl. Anal. (2010), Vol. 9, No. 3, pages
667-684] and of the Navier-Stokes equations in Morrey spaces obtained by Kozono
et al. [H. Kozono and M. Yamazaki, {\it The stability of small stationary
solutions in Morrey Spaces of the Navier-Stokes equation}, Indiana University
Mathematics Journal, Vol. 44, No. 4 (1995), pages 1307-1336].Comment: 17 page
Dynamics of evoked and spontaneous calcium transients in synaptic boutons of neocortical pyramidal neurons
In response to an action potential (AP), a transient rise in the
intracellular calcium concentration ([Ca2+]i) causes transmitter
release from nerve terminals. As the spatiotemporal dynamics of
this calcium rise can affect the efficacy and plasticity of
synaptic connections, it is essential to understand their
determinants. To characterise factors that shape calcium
transients in neocortical synaptic boutons, layer 5 pyramidal
cells in the rat somatosensory cortex were filled through the
patch pipette with a fluorescent calcium indicator for the
measurement of [Ca2+]i.
For accurate calculation of [Ca2+]i from the fluorescence
intensity, the calcium binding affinities (Kd) of the indicators
were measured in vitro, in solutions that were similar to the
patch-clamp internal solution. These solutions were made with
various concentrations of calcium chloride, but a constant
concentration of a calcium buffer. The resultant free [Ca2+] was
measured with a calcium-selective macroelectrode. It was found
that the Kd values of the calcium indicators were considerably
different from those previously published or provided by the
manufacturers.
Two main determinants of the intracellular calcium dynamics are
the capacity of endogenous calcium buffers and the activity of
calcium sequestration mechanisms. By measuring the peak amplitude
of single AP-evoked calcium transients with different
concentrations of OGB-1 or OGB-6F, a value of 7 was estimated for
the calcium-binding ratio of endogenous buffers. Thus, in
response to a single AP and in the absence of exogenous buffers,
[Ca2+]i was raised by 5.3 microM, with a total change of
approximately 50 microM. The rate constant of calcium
sequestration (0.60 per s) was estimated from the slow decay time
constant of the measured transients. The initial fast decay did
not prolong when intracellular calcium uptake was inhibited, or
speed up during repetitive stimulation. These findings suggest
that calcium-induced calcium release (CICR), buffer saturation,
and a non-linear calcium transporter were not the main cause of
the bi-exponential decay. A 3D model of a bouton en passant
showed that diffusion of calcium into the axon was likely the
underlying mechanism. During high-frequency stimulation, CICR
contributed to a supralinear summation of [Ca2+]i.
Spontaneous increases in [Ca2+]i have been observed in several
nerve terminals. They have been implicated in a number of
cellular processes, including calcium homeostasis and spontaneous
transmitter release. Here, the high-affinity calcium indicator
OGB-1 was used to monitor small changes in [Ca2+]i. Spontaneous
calcium transients (sCaTs) were observed at a frequency of around
0.2 per min. The increase in [Ca2+]i associated with each sCaT
was 1.4–2.3 microM, in the absence of exogenous buffers. It was
hypothesised that sCaTs arose from calcium release from
presynaptic stores. In support of this, caffeine increased the
average frequency of sCaTs by approximately 90%. The amplitude
and kinetics of sCaTs identified in caffeine and in the control
condition were not different from each other, suggesting that the
majority of sCaTs might have been a result of calcium release
through ryanodine receptors. The functional consequence(s) of
sCaTs in neocortical synaptic boutons remains to be determined
Dispersion and nonlinearity properties of small solid-core photonic fibers with As2Se3 substrate
Characteristics of As2Se3 photonic crystal fibers (PCFs) with a solid-core and small-core diameter are numerically investigated in the long-wavelength range (from 2 to 10 μm). A full modal analysis and optical properties of designed photonic crystal fibers with lattice constant Λ and filling factor d/Λ are presented in terms of chromatic dispersion, effective refractive index, nonlinear coefficients, and confinement loss. The simulation results show that a high nonlinear coefficient of 4410.303 W–1·km–1 and a low confinement loss of 10−20 dB·km–1 can simultaneously be achieved in the proposed PCFs at a 4.5 μm wavelength. Chromatic dispersions are flat. The values of dispersion increase with increasing filling factor d/Λ and decrease with the increase in lattice constant Λ. In particular, some chromatic dispersion curves also cut the zero-dispersion line at two points. The flat dispersion feature, high nonlinearity, and small confinement loss of the proposed photonic crystal fiber structure make it suitable for supercontinuum
Growth, survival and food utilization efficiency of longfin batfish (<em>Platax teira</em> Forsskål, 1775) larvae reared under different salinity levels
Salinity is crucial in fish larval rearing. In longfin batfish (Platax teira), little research has been conducted regarding the specific effects of salinity on growth, survival, deformity, and food utilization efficiency. This study aimed to determine the optimal salinity level for larval rearing of the longfin batfish by testing five different salinity levels (10, 15, 20, 25, and 30‰). Larvae of 1.5 cm in length and 0.2 g/fish in weight were stocked in cylindrical fiberglass tanks (300 L) at a density of 1 fish/L. The fish were fed to meet their dietary requirement and divided into four daily feedings. Each treatment was replicated three times over a 28-day period of rearing. The results revealed that salinity significantly influenced the growth (length, weight, biomass), and food utilization efficiency of the longfin batfish larvae. Overall, larvae reared at salinity levels of 15-20‰ exhibited superior performance compared to those exposed to salinity levels of 10, 25, and 30‰. However, salinity did not affect the coefficient of variation, survival, and deformity. From these findings, it is recommended to rear longfin batfish larvae at a salinity of 15-20‰ to achieve optimal growth and food utilization efficiency. This study provides valuable insights for longfin batfish larval rearing guidance, contributing to the aquaculture development of this economically valuable species
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