An instance of umbral methods in representation theory: the parking function module

We test the umbral methods introduced by Rota and Taylor within the theory of representation of symmetric group. We define a simple bijection between the set of all parking functions of length $n$ and the set of all noncrossing partitions of $\{1,2,...,n\}$. Then we give an umbral expression of the Frobenius characteristic of the parking function module introduced by Haiman that allows an explicit relation between this symmetric function and the volume polynomial of Pitman and Stanley

Cumulants and convolutions via Abel polynomials

We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state a explicit connection between boolean and free convolution

Methane dry reforming over nickel perovsikite catalysts

In recent years dry reforming of methane (DRM) has received considerable attention as a promising alternative to steam reforming for synthesis gas (H2 and CO) production. This process could be industrially advantageous, yielding a syngas with a H2/CO ratio close to 1, suitable for Fischer-Tropsch synthesis to liquid hydrocarbons and for production of valuable oxygenated chemicals. The major drawback of the process is the endothermicity of the reaction that implies the use of a suitable catalyst to work at relatively low temperatures (923-1,023 K). Higher temperatures would make the process unaffordable for an industrial development and would increase the risk of undesirable side reactions, such as coke formation, that are the main causes of catalyst deactivation. In this work the activity of nickel perovskite catalysts were studied and the results were compared with rhodium perovskite. It is well known that rhodium is very active and stable for dry reforming but its high cost makes its utilization limited. The Ni, due to its low cost, is a promising substitute even if it is more susceptible to coking. The perovskite structure allows a high dispersion of the metal into the catalyst increasing the catalytic activity. In this work the Ni perovskite was obtained with two methods (auto-combustion and modified citrate methods). The results pointed out that the Ni perovskite obtained with the auto-combustion method is a promising route for the use of Ni in this process. The experimental tests show that with Ni catalyst very good activity can be achieved from temperature of 973 K

Biocrude production by hydrothermal liquefaction of olive residue

Hydrothermal liquefaction (HTL) converts biomass into a crude bio-oil by thermally and hydrolytically decomposing the biomacromolecules into smaller compounds. The crude bio-oil, or biocrude, is an energy dense product that can potentially be used as a substitute for petroleum crudes. Liquefaction also produces gases, solids, and water-soluble compounds that can be converted to obtain valuable chemical species or can be used as energy vectors. The process is usually performed in water at 250°C-370°C and under pressures of 4-22 MPa: depending on the adopted pressure and temperature the process can be carried out in sub-critical or super-critical conditions. In the conditions reached in hydrothermal reactors, water changes its properties and acts as a catalyst for the biomass decomposition reactions. One of the main advantages of this process is that the energy expensive biomass-drying step, required in all the thermochemical processes, is not necessary, allowing the use of biomass with high moisture content such as microalgae or olive residue and grape mark. In this work, the feasibility of a hydrothermal process conducted under sub-critical conditions to obtain a bio-oil from the residue of olive oil production is investigated. The experimental tests were performed at 320°C and about 13 MPa, using a biomass to water weight ratio of 1:5. The influence of two different catalysts on the bio-oil yield and quality was investigated: CaO and a zeolite (faujasite-Na). CaO allows the increase of bio-oil yields, while the selected zeolite enhances the deoxygenation reactions, thus improving the bio-oil quality in terms of heating value