Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

BIOMATERIAIS DE TITÂNIO: PERSPECTIVAS DE APLICAÇÃO

O titânio pode ser utilizado como biomaterial devido a sua biocompatibilidade, resistência à corrosão e propriedades mecânicas. Amostras de Ti-puro Nacional e Importada foram cortadas, embutidas, lixadas e polidas. A avaliação microestrutural e tamanho de grãos utilizando microscópio OptikaB-1000 revelou que o Ti-puro Nacional e Importado apresentam grãos homogêneos de 10 e 10,32μm, respectivamente, e estrutura cristalina alfa equiaxial. As microdurezas das amostras de Ti-puro Nacional e Importado obtidas com microdurômetro revelaram média de 171,4 e 168,6 Vickers (HV), respectivamente. Os resultados obtidos demonstraram que as amostras de Ti-puro Nacional e Importado são semelhantes tanto em propriedades mecânicas como estruturais

Synthetic approach from polypyrrole nanotubes to nitrogen doped pyrolyzed carbon nanotubes for asymmetric supercapacitors

Pseudocapacitive materials are highly capable to achieve high energy density integrated with high power electrostatic capacitive materials. However, finding a suitable electrostatic capacitive material to integrate with pseudocapacitive material in order to achieve high energy density with good rate capability is still a challenge. Herein, we are providing a novel synthetic approach starting from the synthesis of polypyrrole nanotubes (PPy-NTs) and ending up at the carbonization of PPy-NTs to obtain N-doped carbon nanotubes (N-CNTs). With highly porous nature of PPy-NTs and great graphitic texture with copious heteroatom functionalities, N-CNTs significantly promoted the faradic pseudo-capacitors, demonstrating high single-electrode capacitance over 332 F/g and 228 F/g in 1 M HSO aqueous solution. Further, a novel asymmetric supercapacitor with PPy-NTs as positive and N-CNTs as negative electrode has been fabricated. This PPy-NTs//N-CNTs cell effectively provides high operation voltage (1.4 V) and hence high energy density over 28.95 W h/kg (0.41 mW h/cm) with a high power density of 7.75 kW/kg (113 mW/cm) and cyclic stability of 89.98% after 2000 cycles

A pp-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil representation, on the space $\mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $\rho_{M}$-action of a general element of $Mp_{2}(\mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $\rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{\mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(\mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{\mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(\mathbb{Z})$ just gives the $p$-part of $\rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(\mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated.Comment: 29 pages, shortened a lo

Effect of temporary cements on the shear bond strength of luting cements

OBJECTIVE: The purpose of this study was to evaluate, by shear bond strength (SBS) testing, the influence of different types of temporary cements on the final cementation using conventional and self-etching resin-based luting cements. Material and Methods: Forty human teeth divided in two halves were assigned to 8 groups (n=10): I and V (no temporary cementation); II and VI: Ca(OH)2-based cement; III and VII: zinc oxide (ZO)-based cement; IV and VIII: ZO-eugenol (ZOE)-based cement. Final cementation was done with RelyX ARC cement (groups I to IV) and RelyX Unicem cement (groups V to VIII). Data were analyzed statistically by ANOVA and Tukey's test at 5% significance level. RESULTS: Means were (MPa): I - 3.80 (&plusmn;1.481); II - 5.24 (&plusmn;2.297); III - 6.98 (&plusmn;1.885); IV - 6.54 (&plusmn;1.459); V - 5.22 (&plusmn;2.465); VI - 4.48 (&plusmn;1.705); VII - 6.29 (&plusmn;2.280); VIII - 2.47 (&plusmn;2.076). Comparison of the groups that had the same temporary cementation (Groups II and VI; III and VII; IV and VIII) showed statistically significant difference (p<0.001) only between Groups IV and VIII, in which ZOE-based cements were used. The use of either Ca(OH)2-based (Groups II and VI) or ZO-based (Groups III and VII) cements showed no statistically significant difference (p>0.05) for the different luting cements (RelyX TM ARC and RelyX TM Unicem). The groups that had no temporary cementation (Groups I and V) did not differ significantly from each other either (p>0.05). CONCLUSION: When temporary cementation was done with ZO- or ZOE-based cements and final cementation was done with RelyX ARC, there was an increase in the SBS compared to the control. In the groups cemented with RelyX Unicem, however, the use of a ZOE-based temporary cement affected negatively the SBS of the luting agent used for final cementation

Intense Synaptic Activity Enhances Temporal Resolution in Spinal Motoneurons

In neurons, spike timing is determined by integration of synaptic potentials in delicate concert with intrinsic properties. Although the integration time is functionally crucial, it remains elusive during network activity. While mechanisms of rapid processing are well documented in sensory systems, agility in motor systems has received little attention. Here we analyze how intense synaptic activity affects integration time in spinal motoneurons during functional motor activity and report a 10-fold decrease. As a result, action potentials can only be predicted from the membrane potential within 10 ms of their occurrence and detected for less than 10 ms after their occurrence. Being shorter than the average inter-spike interval, the AHP has little effect on integration time and spike timing, which instead is entirely determined by fluctuations in membrane potential caused by the barrage of inhibitory and excitatory synaptic activity. By shortening the effective integration time, this intense synaptic input may serve to facilitate the generation of rapid changes in movements

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs