Neste trabalho, recorremos à metodologia da transformada de Laplace a fim de mostrar a sua importância na abordagem de uma classe de equações diferenciais fracionárias. Em particular, apresentamos aplicações desta metodologia ao discutirmos possíveis generalizações de certos problemas físicos no campo da viscoelasticidade linear e osciladores harmônicos, comprovando que o uso do cálculo fracionário em modelagem e resolução de problemas usualmente abordados pelo cálculo de ordem inteira oferece vantagens promissoras para nos fornecer formulações mais consistentes com os dados experimentais.

In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible generalizations of certain physical problems in linear viscoelasticity and harmonic oscillators, proving that fractional calculus is well suited for the modelling and solving of problems usually treated by ordinary integer calculus, with the promissing advantages of being able to provide more accurate theoretical predictions to fit experimental data.

Denervation of the colon is protective against the colon cancer; however, the mechanisms involved are unknown. We tested the hypothesis that the denervated colonic mucosa could be less responsive to the action of the chemical carcinogen dimethylhydrazine (DMH). Three groups of 32 male Wistar rats were treated as follows: group 1 (G1) had the colon denervated with 0.3 mL 1.5 mM benzyldimethyltetradecylammonium (benzalkonium chloride, BAC); G2 received a single ip injection of 125 mg/kg DMH; G3 was treated with BAC + the same dose and route of DMH. A control group (Sham, N = 32) did not receive any treatment. Each group was subdivided into four groups according to the sacrifice time (1, 2, 6, and 12 weeks after DMH). Crypt fission index, ß-catenin accumulated crypts, aberrant crypt foci, and cell proliferation were evaluated and analyzed by ANOVA and the Student t-test. G3 animals presented a small number of aberrant crypt foci and low crypt fission index compared to G2 animals after 2 and 12 weeks, respectively. From the second week on, the index of ß-catenin crypt in G3 animals increased slower than in G2 animals. From the 12th week on, G2 animals presented a significant increase in cell proliferation when compared to the other groups. Colonic denervation plays an anticarcinogenic role from early stages of colon cancer development. This finding can be of importance for the study of the role of the enteric nervous system in the carcinogenic process.

The probability of a compound residual hot hypernucleus formation at the end of pre-equilibrium phase of high energy photonuclear reactions is calculated with a time dependent Monte Carlo Multicollisional Cascade (MCMC) approach. The emission of hadrons during the rapid phase of the reaction is discussed and characteristics of the residual nucleus are obtained. Results for mass and charge distributions of the formed hot hypernucleus are shown and its excitation energy is discussed.