High -energy intake which exceeds energy expenditure leads to the accumulation of triglycerides in adipose tissue, predominantly in large -size adipocytes. This metabolic shift, which drives the liver to produce atherogenic dyslipidemia, is well documented. In addition, an increasing amount of monocytes/macrophages, predominantly the proinflammatory M1- type, cumulates in ectopic adipose tissue. The mechanism of this process, the turnover of macrophages in adipose tissue and their direct atherogenic effects all remain to be analyzed., R. Poledne, I. Králová Lesná, S. Čejková., and Obsahuje bibliografii
For a given bi-continuous semigroup $(T(t))_{t\geq 0}$ on a Banach space $X$ we define its adjoint on an appropriate closed subspace $X^\circ $ of the norm dual $X'$. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology $\sigma (X^\circ ,X)$. We give the following application: For $\Omega $ a Polish space we consider operator semigroups on the space ${\rm C_b}(\Omega )$ of bounded, continuous functions (endowed with the compact-open topology) and on the space ${\rm M}(\Omega )$ of bounded Baire measures (endowed with the weak$^*$-topology). We show that bi-continuous semigroups on ${\rm M}(\Omega )$ are precisely those that are adjoints of bi-continuous semigroups on ${\rm C_b}(\Omega )$. We also prove that the class of bi-continuous semigroups on ${\rm C_b}(\Omega )$ with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if $\Omega $ is not a Polish space this is not the case.
Using the concept of the $ {\mathrm H}_1$-integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.
Let y be observation vector in the usual linear model with expectation Aβ and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic aTy is called invariant estimator for a parametric function ϕ=cTβ if its MSE depends on β only through ϕ. It is shown that aTy is admissible invariant for ϕ, if and only if, it is a BLUE of ϕ, in the case when ϕ is estimable with zero variance, and it is of the form kϕˆ, where k∈⟨0,1⟩ and ϕˆ is an arbitrary BLUE, otherwise. This result is used in the one- and two-way ANOVA models. Our paper is self-contained and accessible, also for non-specialists.