Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group.

In this paper, sufficient conditions are obtained for the nonexistence of solutions to the Cauchy problems for ultra-parabolic equations involving fractional Laplacian operator. The nonexistence result is also extended to the corresponding system. The results to such problems are derived in the Heisenberg group. The proofs of our nonexistence theorems are based on the nonlinear capacity method. This method is based on the choice of a suitable test function in the weak formulation of the considered problems.

The nonexistence of the Other and the contemporany symptoms of children / A inexistência do outro e os sintomas contemporâneos da criança

RESUMO: O objetivo deste artigo é discutir as mudanças apresentadas na sintomatologia das crianças no mundo contemporâneo, sintomatologia esta marcada pelas manifestações no corpo e pela primazia do gozo. Partindo da tese da inexistência do Outro, busca-se extrair suas consequências teóricas e clínicas para as manifestações do sofrimento na criança. Discutem-se a presença do gozo do Um separado do Outro e seu modo de manifestação nos sintomas das crianças. Evidencia-se a importância, no tratamento da criança, da constituição de um Outro que permita extrair o falasser de seu gozo solitário.

Abstract: This article aims to discuss the changes presented in children's symptomatology in the contemporary world. These symptoms are marked by manifestations in the body and the primacy of jouissance. Based on the thesis of the nonexistence of the Other, we seek to extract its theoretical and clinical consequences for the manifestations of suffering in children. The work discusses the presence of jouissance of the One separated from the Other and how it manifests in children's symptoms. It highlights the importance of the constitution of an Other that allows extracting the parlêtre from their solitary jouissance for the treatment of children.

On Finite Energy Solutions of 4-harmonic and ES-4-harmonic Maps.

4-harmonic and ES-4-harmonic maps are two generalizations of the well-studied harmonic map equation which are both given by a nonlinear elliptic partial differential equation of order eight. Due to the large number of derivatives it is very difficult to find any difference in the qualitative behavior of these two variational problems. In this article we prove that finite energy solutions of both 4-harmonic and ES-4-harmonic maps from Euclidean space must be trivial. However, the energy that we require to be finite is different for 4-harmonic and ES-4-harmonic maps pointing out a first difference between these two variational problems.

Why psychological accounts of personal identity can accept a brain death criterion and biological definition of death.

Psychological accounts of personal identity claim that the human person is not identical to the human animal. Advocates of such accounts maintain that the definition and criterion of death for a human person should differ from the definition and criterion of death for a human animal. My contention is instead that psychological accounts of personal identity should have human persons dying deaths that are defined biologically, just like the deaths of human animals. Moreover, if brain death is the correct criterion for the death of a human animal, then it is also the correct criterion for the death of a human person. What the nonidentity of persons and animals requires is only that they have distinct criteria for ceasing to exist.

Nonexistence of global solutions of abstract wave equations with high energies.

We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are given improving known results in the literature.

BETWEEN KNOWING AND BELIEVING: SALVAGING ILLUSION'S RIGHTFUL PLACE IN PSYCHOANALYSIS.

Illusion has historically received insufficient psychoanalytic attention, even though it plays an indispensable and adaptive role that helps protect individuals from becoming traumatized by the most psychically noxious aspects of reality. Trauma is mitigated by an individual's knowing about the existence of such realities yet simultaneously believing them non-existent, with neither position granted exclusivity. Psychoanalytic theory is surprisingly predicated on the employment of illusions that picture an individual capable of controlling the potentially traumatic actions of others, just so long as the individual effectively manages his own intrapsychic processes (wishes, fantasies, impulses, etc.). The role of illusion in everyday life is highlighted.