Publications by Year: Submitted

A LAnKe (also known as a Filippov algebra or a Lie algebra of the n-th kind) is a vector space equipped with a skew-symmetric n-linear form that satisfies the generalized Jacobi identity. Friedmann, Hanlon, Stanley and Wachs have shown that the symmetric group acts on the multilinear part of the free LAnKe on 2n-1 generators as an irreducible representation. They announced that the multilinear component on 3n-2 generators decomposes as a direct sum of two irreducible symmetric group representations and a proof was given recently in a subsequent paper by Friedmann, Hanlon and Wachs. In the present paper we provide a proof of the later statement. The two proofs are substantially different.

A LAnKe (also known as a Lie algebra of the th kind, or a Filippov algebra) is a vector space equipped with a skew-symmetric -linear form that satisfies the generalized Jacobi identity. The symmetric group  acts on the multilinear part of the free LAnKe on  generators, where  is the number of brackets, by permutation of the generators. The corresponding representation was studied by Friedmann, Hanlon, Stanley and Wachs, who asked whether for , its irreducible decomposition contains no summand whose Young diagram has at most  columns. The answer is affirmative if $k \le 3$. In this paper, we show that the answer is affirmative for all $k$

Loneliness represents a negative feeling that arises when individuals perceive a discrepancy between actual and desired social relationships. Using a qualitative approach, the present study explored the meanings and personal experiences of loneliness in children and early adolescents in Italy. Participants included 139 children and early adolescents aged 8–14 years (M = 10.76 years, SD = 1.71; 70 girls, 57.6%) who completed an online semi-structured interview. Results from the descriptive analysis provided evidence of the multidimensional nature of loneliness, defined and experienced through different dimensions (e.g., cognitive, emotional, and regarding interpersonal context). Additionally, participants discussed loneliness in relation to both their family and peers. Some children and adolescents expressed experiencing loneliness voluntarily. Children and early adolescents reported to feel sadness, anger and other emotions as boredom, happiness, and fear in associations with loneliness. Gender and grade differences were also found. Primary school children and boys defined and experienced loneliness using the physical separation dimension. Middle school childrens defined more frequently loneliness using the cognitive dimension. Overall, the present study offers a richer understanding of the meanings and experiences of loneliness in youth and highlights the importance of considering developmental, gender, and cultural factors when studying loneliness.

We analyze the impact of the institutional environment on the leverage of European listed SMEs for the period 2005-2018. We use a broad range of institutional quality, judicial efficiency and corruption measures, along with several firm-specific and macro control variables, to identify different transmission channels on leverage. By performing a panel data analysis into the fixed effects filter estimator framework, along with several model specifications and robustness tests, the results show that better institutions, stronger judicial effectiveness and higher corruption decrease leverage. In terms of active transmission channels, increased investment under regimes of better institutional quality tends to increase leverage. Higher judicial efficiency accompanied by increased profitability tends to decrease, while higher institutional quality accompanied by higher investments tends to increase leverage, bringing more bank credit. Increasing profitability under regimes of decreased corruption decreases leverage. This last finding is even more pronounced for medium enterprises, as opposed to micro enterprises. The most significant factors associated with leverage are profitability, asset structure, cost of borrowing, stock market development and size, while an age effect is rejected. Pecking order theory seems to better fit the European SMEs capital structure choices under several institutional states.

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Given a filtration of the module of vector fields on a smooth manifold, we define a pseudodifferential calculus where the order of a vector field is given by the filtration. We show that pseudodifferential operators have a well-defined principal symbol for a subset of the unitary representations of the osculating groups. We prove a Rockland-type theorem, showing that the invertibility of the principal symbol is equivalent to maximal hypoellipticity. This answers affirmatively a conjecture due to Helffer and Nourrigat.

Trades are important objects in combinatorial design theory that may be realized as certain elements of kernels of inclusion matrices. Total trades were introduced recently by Ghorbani, Kamali and Khosravshahi, who showed that over a field of characteristic zero the vector space of trades decomposes into a direct sum of spaces of total trades. In this paper, we show that the vector space spanned by the permutations of a total trade is an irreducible representation of the symmetric group. As a corollary, the previous decomposition theorem is recovered. Also, a basis is obtained for the module of total trades in the spirit of Specht polynomials. More generally, in the second part of the paper we consider intersection matrices and determine the irreducible decompositions of their images. This generalizes previously known results concerning ranks of special cases.