Semiclassical limit for Schr\"odinger equations with magnetic field and Hartree-type nonlinearities

The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.Comment: 34 page

Developmental Regulation of Small-Conductance Ca²⁺-Activated K⁺ Channel Expression and Function in Rat Purkinje Neurons

Calcium transients play an important role in the early and later phases of differentiation and maturation of single neurons and neuronal networks. Small-conductance calcium-activated potassium channels of the SK type modulate membrane excitability and are important determinants of the firing properties of central neurons. Increases in the intracellular calcium concentration activate SK channels, leading to a hyperpolarization of the membrane potential, which in turn reduces the calcium inflow into the cell. This feedback mechanism is ideally suited to regulate the spatiotemporal occurrence of calcium transients. However, the role of SK channels in neuronal development has not been addressed so far. We have concentrated on the ontogenesis and function of SK channels in the developing rat cerebellum, focusing particularly on Purkinje neurons. Electrophysiological recordings combined with specific pharmacological tools have revealed for the first time the presence of an afterhyperpolarizing current (I_{AHP}) in immature Purkinje cells in rat cerebellar slices. The channel subunits underlying this current were identified as SK2 and localized by in situ hybridization and subunit-specific antibodies. Their expression level was shown to be high at birth and subsequently to decline during the first 3 weeks of postnatal life, both at the mRNA and protein levels. This developmental regulation was tightly correlated with the expression of I_{AHP} and the prominent role of SK2 channels in shaping the spontaneous firing pattern in young, but not in adult, Purkinje neurons. These results provide the first evidence of the developmental regulation and function of SK channels in central neurons

Joan Roís de Corella i els límits de la literatura

In a text that anticipates and sums up part of the thesis defended in Joan Roís de Corella: La importància de dir-se honest [the importance of being honest], the author shows the poet as creator of an autonomous literary fiction basedon the mimesis of Aristotle' s Poètics, which distances the reader from the text and at the same time generates cathartis,piety and moral reflection

Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

Role of anisotropy in the F\"orster energy transfer from a semiconductor quantum well to an organic crystalline overlayer

We consider the non-radiative resonant energy transfer from a two-dimensional Wannier exciton (donor) to a Frenkel exciton of a molecular crystal overlayer (acceptor). We characterize the effect of the optical anisotropy of the organic subsystem on this process. Using realistic values of material parameters, we show that it is possible to change the transfer rate within typically a factor of two depending on the orientation of the crystalline overlayer. The resonant matching of donor and acceptor energies is also partly tunable via the organic crystal orientation.Comment: 6 pages, 8 figure

Els orígens familiars dels Cartellà al llarg de deu generacions (s. X-XIV)

L'estudi pretén investigar els ascendents familiars de Guillem Galceran de Cartellà i de la seva esposa Blanca de Creixell, detallant els arbres genealògics de les tres famílies principals que els componen: els Hostoles, a més dels Cartellà i dels Creixell. L'anàlisi detallada i la recopilació de tota la documentació disponible, molta de la qual inèdita, és aquí presentada de forma abreujada, permet aclarir molts punts fins ara dubtosos d'aquestes genealogies i proporciona materials de notable interès per a la construcció d'un relat històric als comtats de Besalú i de Barcelona, especialment per als segles xi-xii, a més de les estratègies matrimonials i del paper de les tres nissagues en la història local i general de Catalunya, així com l'origen de la figura del senescal.The aim of this paper is to study the ancestors of Guillem Galceran de Cartellà and his wife Blanca d'Hostoles with a detailed examination of the genealogical trees of the three main families: Hostoles, Cartellà and Creixell. This detailed analysis, and the compilation of all available documents, many of them previously unpublished, presented as a summary, helps to clarify many of the doubts regarding these genealogies, as well as providing useful material to construct the historical narrative of the counties of Besalú and Barcelona, especially for the 11th and 12th centuries, in addition to the matrimonial strategies employed and the role played by these three families in the local and general history of Catalonia, as well as the origins of the position of «seneschal» (steward)

Variations in pulp/tooth area ratio as an indicator of age: a preliminary study

This paper details for age determination of adult from single rooted theeth. The sample consisted of 100 Italians white Caucasioan patients (46 men, 54 womwn) aged between 18 and 72 years. The single rooted maxillary right canine was utilized in this preliminary study. Pulp/root ration, tooth length ratio, pulp/root area and pulp/root width ratios at three different levels were computed. Pearson's correlation coefficients between age and these variables showed that the ratio between pulp and tooth area correlated best with age (r2 = 0,85). Stepwise multiple regression models yielded a linear relationship between pulp/root width at mid-root level and chronological age and a linear relationship when pulp/tooth area was compared to age. Statistical analysis indicated that these two variables explain 84,9% of variations in estimated chronological age. The median of the absolute value of residual errors between actual and estimated ages was less than four years

Age estimation in children by measurement of open apices in teeth

This paper concerns a method for estimating the age of children based on their teeth. The sample consisted of 455 Italian white children (213 boys, 242 girls) aged between 5 and 15 years. The purpose of the present investigation was to present a method for assessing chronological age based on the relationship between age and measurement of the open apices in teeth. Pearson\u2019s correlation coefficients between age and these variables showed that the correlations between age and the open apices in teeth were significant and negative. Furthermore, gender and the number of teeth with the apical end of the root canals completely closed (N0) showed a significant correlation with chronological age. With the aid of a stepwise multiple regression model, a linear relationship between open apices, N0, and age was shown. Statistical analysis indicated that these morphological variables explain 83.6% of the variations in estimated chronological age. The median of residual errors between the actual and estimated ages was 120.035 years [interquartile range (IQR)=1.18 years]

On fractional Schrodinger equations with Hartree type nonlinearities

Goal of this paper is to study the following doubly nonlocal equation in the case of general nonlinearities of Berestycki-Lions type. We prove existence of ground states and we obtain regularity and asymptotic decay of general solutions, extending some results by Moroz and Van Schaftingen