1,721,066 research outputs found
Localization of GnRH molecular forms in the brain, pituitary, and testis of the frog, Rana esculenta
No full textMaximal characterisation of local Hardy spaces on locally doubling manifolds
Full text linkWe prove a radial maximal function characterisation of the local atomic Hardy space h1(M) on a Riemannian manifold M with positive injectivity radius and Ricci curvature bounded from below. As a consequence, we show that an integrable function belongs to h1(M) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder cut-offs in terms of an appropriate class of approximations of the identity, which we obtain on arbitrary Ahlfors-regular metric measure spaces and generalises a previous result of A. Uchiyama
Local and non-local Poincaré inequalities on Lie groups
Full text linkWe prove a local (Formula presented.) -Poincaré inequality, (Formula presented.), on non-compact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most exponentially with respect to the radius of the ball, and that if the group is non-doubling, then its growth is indeed, in general, exponential. We also prove a non-local (Formula presented.) -Poincaré inequality with respect to suitable finite measures on the group
BMO Spaces on Weighted Homogeneous Trees
Full text linkWe consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space (V, d, μ) is nondoubling and of exponential growth, hence the classical theory of Hardy and BMO spaces does not apply in this setting. We introduce a space BMO(μ) on (V, d, μ) and investigate some of its properties. We prove in particular that BMO(μ) can be identified with the dual of a Hardy space H1(μ) introduced in a previous work and we investigate the sharp maximal function related with BMO(μ)
Riesz transforms on solvable extensions of stratified groups
Full text linkLet G=N⋊A, where N is a stratified group and A=R acts on N via automorphic dilations. Homogeneous sub-Laplacians on N and A can be lifted to left-invariant operators on G and their sum is a sub-Laplacian Δ on G. Here we prove weak type (1,1), Lp-boundedness for p∈(1,2] and H1→L1 boundedness of the Riesz transforms YΔ−1/2 and YΔ−1Z, where Y and Z are any horizontal left-invariant vector fields on G, as well as the corresponding dual boundedness results. At the crux of the argument are large-time bounds for spatial derivatives of the heat kernel, which are new when Δ is not elliptic
The Sobolev embedding constant on Lie groups
Full text linkIn this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. The bound that we obtain, up to a constant depending only on the group and its sub-Riemannian structure, reduces to the best known bound for the classical inhomogeneous Sobolev embedding constant on Rd. As an application, we prove local and global Moser–Trudinger inequalities
Poincaré inequalities on graphs
Full text linkEvery graph of bounded degree endowed with the counting measure satisfies a local version of L-p-Poincare inequality, p is an element of [1, infinity]. We show that on graphs which are trees the Poincare constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of L-p-Poincare inequality, despite the fact that they are nondoubling measures of exponential growth
Distribution of somatostatin-like immunoreactivity in the brain of the frog, Rana esculenta, during development
No full textNeuropeptide Y: Localization in the brain and pituitary of the developing frog (Rana esculenta)
No full textThe immunohistochemical localization of neuropeptide Y (NPY)-like peptide has been investigated in the peripheral terminal nerve, brain and pituitary of the frog, Rana esculenta, during development. Soon after hatching, a rather simple NPY-immunoreactive (-ir) neuronal system is present, with elements located mainly in the diencephalon. When hind limbs appear and develop, the NPY-neuronal system undergoes considerable elaboration and NPY-ir perikarya appear in several regions of the telencephalon (dorsal, medial, and lateral pallium; medial septum; medioventral telencephalon; anterior preoptic area), diencephalon (ventromedial, central and posterior thalamic nuclei; suprachiasmatic nucleus; infundibulum), mesencephalon (anteroventral mesencephalic tegmentum, and rhombencephalon (central grey, area of the cerebellar and vestibular nuclei). The frequency of NPY-ir neurons increases during larval development, and then decreases in the anterior preoptic area during the metamorphic climax. Dense plexuses of NPY-ir fibers are formed in several brain areas. NPY-ir fibers are found in the peripheral terminal nerve, and ir-neurons through its course along the ventromedial surface of the olfactory bulbs. NPY-ir fiber projections to the median eminence and pars intermedia derive mainly from the ventral infundibular group of NPY-ir neurons, with a contribution from the suprachiasmatic group of NPY neurons. NPY and carboxyl terminal flanking peptide of proneuropeptide Y coexist in the same neurons throughout the brain. The ontogenetic pattern of NPY-ir neuronal system in the brain of Rana esculenta is remarkably different than that reported for Xenopus laevis
Organization of atrial natriuretic factor-like immunoreactive system in the brain of the frog Rana esculenta during development
No full textImmunocytochemical distribution of the atrial natriuretic factor (ANF) has been studied in the brain and pituitary of the anuran Rana esculenta during development and in juvenile animals. Using human ANF and rat α-ANF antisera, immunoreactive cell bodies and nerve fibers were revealed in stage II-III tadpoles and in successive larval stages. Soon after hatching, stages II-III, the ANF-like-immunoreactive elements were confined to the preoptic area-median eminence complex. During successive stages of development, new groups of ANF-immunoreactive cell bodies appeared. In larval stage VI, immunoreactive perikarya were found in the rostral part of the anteroventral area of the thalamus and numerous ANF-like-immunoreactive cells appeared in the pars distalis of the pituitary. In larval stages XIV and XVIII, the distribution of ANF immunoreactivity was virtually similar. The ANF-immunoreactive cells in the preoptic nucleus and in the pituitary pars distalis were comparatively more abundant than in stage VI. During the metamorphic climax (stages XXI-XXII), a new group of ANF-immunoreactive cell bodies appeared in the rostral part of the ventrolateral area of the thalamus. During this stage, ANF-immunoreactive fiber projections were found in the pars intermedia for the first time. However, the pars distalis cells were very weakly immunofluorescent. The pattern of ANF immunoreactivity in the brain ofjuvenile animals was very similar to that described for stages XXI and XXII, whereas the pars distalis cells showed no immunoreactivity. It is conceivable that, early during development, ANF-related peptides may be involved in the regulation of pituitary secretion by means of autocrine mechanisms or may act as a classic pituitary hormone
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