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For a continuous Hamiltonian H : (x , p , u) ∈ T ⁎ R n × R → R , we consider the asymptotic behavior of associated Hamilton–Jacobi equations with state-constraint { H (x , D u , λ u) ≤ C λ , x ∈ Ω λ ⊂ R n , H (x , D u , λ u) ≥ C λ , x ∈ Ω ‾ λ ⊂ R n , as λ → 0 +. When H satisfies certain convex, coercive and monotone conditions, the domain Ω λ : = (1 + r (λ)) Ω keeps bounded, star-shaped for all λ > 0 with lim λ → 0 + ⁡ r (λ) = 0 , and lim λ → 0 + ⁡ C λ = c (H) equals the ergodic constant of H (⋅ , ⋅ , 0) , we prove the convergence of solutions u λ to a specific solution of the critical equation { H (x , D u , 0) ≤ c (H) , x ∈ Ω ⊂ R n , H (x , D u , 0) ≥ c (H) , x ∈ Ω ‾ ⊂ R n. We also discuss the generalization of such a convergence for equations with more general C λ and Ω λ. [ABSTRACT FROM AUTHOR]

Let Ω be a bounded open subset of R n and H (x , p) : Ω × R n → R be a continuous Hamiltonian that is convex in the second argument. We study the asymptotic behavior, as λ → 0 + , of the state-constraint Hamilton–Jacobi equation (S λ) { ϕ (λ) u λ (x) + H (x , D u λ (x)) ⩽ 0 in (1 + r (λ)) Ω , ϕ (λ) u λ (x) + H (x , D u λ (x)) ⩾ 0 on (1 + r (λ)) Ω ‾ , and the corresponding additive eigenvalues, or ergodic constant (E λ) { H (x , D v λ (x)) ⩽ c (λ) in (1 + r (λ)) Ω , H (x , D v λ (x)) ⩾ c (λ) on (1 + r (λ)) Ω ‾. Here, ϕ (λ) , r (λ) : (0 , ∞) → R are continuous functions such that ϕ is nonnegative and lim λ → 0 + ⁡ ϕ (λ) = lim λ → 0 + ⁡ r (λ) = 0. We obtain both convergence and non-convergence results for the convex Hamilton–Jacobi equations. Moreover, we provide a very first result on the asymptotic expansion of the additive eigenvalue c (λ) as λ → 0 +. The main tool we use is a duality representation of solution with viscosity Mather measures. [ABSTRACT FROM AUTHOR]

We study the additive eigenvalues on changing domains, along with the associated vanishing discount problems. We consider the convergence of the vanishing discount problem on changing domains for a general scaling type Ω λ = (1 + r (λ)) Ω with a continuous function r and a positive constant λ. We characterize all solutions to the ergodic problem on Ω in terms of r. In addition, we demonstrate that the additive eigenvalue λ ↦ c Ω λ on a rescaled domain Ω λ = (1 + λ) Ω possesses one-sided derivatives everywhere. Additionally, the limiting solution can be parameterized by a real function, and we establish a connection between the regularity of this real function and the regularity of λ ↦ c Ω λ . We provide examples where higher regularity is achieved. [ABSTRACT FROM AUTHOR]

Abstract: Postprandial glucagon-like peptide-1 (GLP-1) secretion can act as a meal termination signal in animals and humans. We tested the hypothesis that the postprandial changes in plasma GLP-1 concentrations are associated with changes in the human brain activity in response to satiety by performing a post-hoc analysis of a cross-sectional study of neuroanatomical correlates of hunger and satiation using 15O-water positron-emission tomography (PET). Forty-two subjects (22M/20F, age 31±8 years) spanning a wide range of adiposity (body fat: 7–44%) were included in this analysis. Outcome measures included changes in PET-measured regional cerebral blood flow (rCBF) and plasma concentrations of GLP-1, glucose, insulin, and free-fatty acids (FFA), elicited by the administration of a satiating amount of a liquid formula meal. The peak postprandial increases in plasma GLP-1 concentrations were correlated with increases in rCBF in the left dorsolateral prefrontal cortex (including the left middle and inferior frontal gyri), previously implicated in PET studies of human satiation, and the hypothalamus, previously implicated in the regulation of food intake in animal and human studies, both before and after adjustment for sex, age, body fat, and changes in plasma glucose, insulin, and serum FFA concentrations. The postprandial GLP-1 response is associated with activation of areas of the human brain previously implicated in satiation and food intake regulation. [Copyright &y& Elsevier]

Abstract: ZnO substrate crystals from two different sources, and epitaxial layers have been studied by SEM, AFM, photoluminescence and EPR. Although fabricated by the same growth principle, i.e. the hydrothermal technique, the substrates differ in terms of purity and structural quality. In the PL spectra of all samples the dominating emission originates from the donor bound exciton (BE) recombination positioned at about 3361 meV. The temperature dependence of the spectra confirms the assignment of the free exciton emission in the purest sample, the line at 3376 meV evolves into a broad peak at higher temperatures, probably including both A and B excitons. Another FE-related emission appears as a shoulder on the high-energy side of FEA,B above 40 K. It is expected and associated with the crystal-field split-off counterpart of the valence band. Free-exciton related emission in the less pure sample can only be seen if the temperature is above 45 K. At all bound excitons are quenched and the spectrum in both samples consists of the free exciton no-phonon lines and their replicas. However, the emission from the pure samples is several orders of magnitude stronger than that from the other sample, which indicates strong non-radiative quenching of the excitons in the latter sample. The EPR measurements reveal a possible scenario of impurity re-arrangement, e.g. annealing at 950 ∘C may dissociate existing complexes and release Fe as isolated ions. The AFM and SEM investigations of an epilayer grown by MOCVD on one of the studied substrates have indicated growth instabilities and structural irregularities, thus pointing to the need for substrate quality and epitaxial process optimization. [Copyright &y& Elsevier]

Abstract: Obesity is accompanied by damage to several tissues. Overweight is a risk factor for Alzheimer''s disease and other neurodegenerative disorders. Whether structural abnormalities associated with excess body fat may also occur in the brain is unknown. We sought to determine to what extent excess body fat is associated with regional alterations in brain structure using voxel-based morphometry (VBM), a whole-brain unbiased technique based upon high-definition 3D magnetic resonance imaging (MRI) scans normalized into a common standard space and allowing for an objective assessment of neuroanatomical differences throughout the brain. We studied 24 obese (11 male, 13 female; age: 32 ± 8 years; body mass index [BMI]: 39.4 ± 4.7 kg/m2) and 36 lean (25 male, 11 female; mean age: 33 ± 9 years; BMI: 22.7 ± 2.2 kg/m2) non-diabetic Caucasians. In comparison with the group of lean subjects, the group of obese individuals had significantly lower gray matter density in the post-central gyrus, frontal operculum, putamen, and middle frontal gyrus (P < 0.01 after adjustment for sex, age, handedness, global tissue density, and multiple comparisons). BMI was negatively associated with GM density of the left post-central gyrus in obese but not lean subjects. This study identified structural brain differences in human obesity in several brain areas previously involved in the regulation of taste, reward, and behavioral control. These alterations may either precede obesity, representing a neural marker of increased propensity to gaining weight, or occur as a consequence of obesity, indicating that also the brain is affected by increased adiposity. [Copyright &y& Elsevier]