In this work we study classical bouncing solutions in the context of Formula omitted gravity in a flat FLRW background using a perfect fluid as the only matter content. Our investigation is based on ...introducing an effective fluid through defining effective energy density and pressure; we call this reformulation as the "effective picture". These definitions have been already introduced to study the energy conditions in Formula omitted gravity. We examine various models to which different effective equations of state, corresponding to different Formula omitted functions, can be attributed. It is also discussed that one can link between an assumed Formula omitted model in the effective picture and the theories with generalized equation of state (EoS). We obtain cosmological scenarios exhibiting a nonsingular bounce before and after which the Universe lives within a de-Sitter phase. We then proceed to find general solutions for matter bounce and investigate their properties. We show that the properties of bouncing solution in the effective picture of Formula omitted gravity are as follows: for a specific form of the Formula omitted function, these solutions are without any future singularities. Moreover, stability analysis of the nonsingular solutions through matter density perturbations revealed that except two of the models, the parameters of scalar-type perturbations for the other ones have a slight transient fluctuation around the bounce point and damp to zero or a finite value at late times. Hence these bouncing solutions are stable against scalar-type perturbations. It is possible that all energy conditions be respected by the real perfect fluid, however, the null and the strong energy conditions can be violated by the effective fluid near the bounce event. These solutions always correspond to a maximum in the real matter energy density and a vanishing minimum in the effective density. The effective pressure varies between negative values and may show either a minimum or a maximum.
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The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection ...is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
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Among postmenopausal women with osteoporosis and a high risk of fracture, treatment with the monoclonal antibody romosozumab for 12 months followed by alendronate resulted in a significantly lower ...risk of fracture than alendronate for 12 months followed by alendronate.
This study shows that in postmenopausal women with low bone mineral density, the monoclonal antibody romosozumab, which binds to sclerostin, an osteoblast-activity inhibitor, was associated with ...increased bone mineral density and bone formation and decreased bone resorption.
Osteoporosis is characterized by low bone mass and defects in microarchitecture that are responsible for decreased bone strength and increased risk of fracture.
1
Antiresorptive drugs for osteoporosis increase bone mineral density and prevent the progression of structural damage but may not restore bone structure. Stimulation of bone formation is necessary to achieve improvements in bone mass, architecture, and strength.
Sclerostin, encoded by the gene
SOST,
is an osteocyte-secreted glycoprotein that has been identified as a pivotal regulator of bone formation. By inhibiting the Wnt and bone morphogenetic protein signaling pathways, sclerostin impedes osteoblast proliferation and function, thereby decreasing bone formation. . . .
Ionospheric F2 region peak densities (NmF2) are expected to have a positive correlation with total electron content (TEC), and electron densities usually show an anticorrelation with electron ...temperatures near the ionospheric F2 peak. However, during the 17 March 2015 great storm, the observed TEC, NmF2, and electron temperatures of the storm‐enhanced density (SED) over Millstone Hill (42.6°N, 71.5°W, 72° dip angle) show a quiet different picture. Compared with the quiet time ionosphere, TEC, the F2 region electron density peak height (hmF2), and electron temperatures above ~220 km increased, but NmF2 decreased significantly within the SED. This SED occurred where there was a negative ionospheric storm effect near the F2 peak and below it, but a positive storm effect in the topside ionosphere. Thus, this SED event was a SED in TEC but not in NmF2. The very low ionospheric densities below the F2 peak resulted in a much reduced downward heat conduction for the electrons, trapping the heat in the topside in the presence of heat source above. This, in turn, increased the topside scale height so that even though electron densities at the F2 peak were depleted, TEC increased in the SED. The depletion in NmF2 was probably caused by an increase in the density of the molecular neutrals, resulting in enhanced recombination. In addition, the storm time topside ionospheric electron density profiles were much closer to diffusive equilibrium than the nonstorm time profiles, indicating less daytime plasma flow between the ionosphere and the plasmasphere.
Key Points
A SED in TEC but not in NmF2
Storm time topside ionospheric electron density profiles were in diffusive equilibrium
Increase in the topside but decrease in bottom side ionosphere
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Demonstrates how anyone in math, science, and engineering can master DFT calculationsDensity functional theory (DFT) is one of the most frequently used computational tools for studying and predicting ...the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems.Density Functional Theory: A Practical Introductionoffers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to students from a variety of backgrounds. The book therefore offers several features that have proven to be helpful in enabling students to master the subject, including:Problem sets in each chapter that give readers the opportunity to test their knowledge by performing their own calculationsWorked examples that demonstrate how DFT calculations are used to solve real-world problemsFurther readings listed in each chapter enabling readers to investigate specific topics in greater depthThis text is written at a level suitable for individuals from a variety of scientific, mathematical, and engineering backgrounds. No previous experience working with DFT calculations is needed.
On the notions of upper and lower density Leonetti, Paolo; Tringali, Salvatore
Proceedings of the Edinburgh Mathematical Society,
02/2020, Volume:
63, Issue:
1
Journal Article
Peer reviewed
Open access
Abstract
Let
$\mathcal {P}(\mathbf{N})$
be the power set of
N
. We say that a function
$\mu ^\ast : \mathcal {P}(\mathbf{N}) \to \mathbf{R}$
is an upper density if, for all
X
,
Y
⊆
N
and
h
,
k
∈
N
+
..., the following hold: (
f1
)
$\mu ^\ast (\mathbf{N}) = 1$
; (
f2
)
$\mu ^\ast (X) \le \mu ^\ast (Y)$
if
X
⊆
Y
; (
f3
)
$\mu ^\ast (X \cup Y) \le \mu ^\ast (X) + \mu ^\ast (Y)$
; (
f4
)
$\mu ^\ast (k\cdot X) = ({1}/{k}) \mu ^\ast (X)$
, where
k
·
X
: = {
kx
:
x
∈
X
}; and (
f5
)
$\mu ^\ast (X + h) = \mu ^\ast (X)$
. We show that the upper asymptotic, upper logarithmic, upper Banach, upper Buck, upper Pólya and upper analytic densities, together with all upper
α
-densities (with
α
a real parameter ≥ −1), are upper densities in the sense of our definition. Moreover, we establish the mutual independence of axioms (
f1
)–(
f5
), and we investigate various properties of upper densities (and related functions) under the assumption that (
f2
) is replaced by the weaker condition that
$\mu ^\ast (X)\le 1$
for every
X
⊆
N
. Overall, this allows us to extend and generalize results so far independently derived for some of the classical upper densities mentioned above, thus introducing a certain amount of unification into the theory.
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