Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

On the depth of blowup algebras of ideals with analytic deviation one

Let I be an ideal in a local Cohen-Macaulay ring (A, m). Assume I to be generically a complete intersection of positive height. We compute the depth of the Rees algebra and the form ring of I when the analytic deviation of I equals one and its reduction number is also at most one. The formu- las we obtain coincide with the already known formulas for almost complete intersection ideals.

Que cache l'agenda caché [What is behind the hidden agenda?]

The physicians often forget to ask their patients if they would like to discuss other complaints or topics. It is sometimes quite difficult to explore the patient's complaints; while the physicians tend to focus on the immediate problem, the patients may have not only one, but several hidden agendas during a visit. In a caring relation there is a clear advantage to clarify the implicit. The search for the hidden agenda is to improve the care of i) biomedical problems ii) the social quest presented to the physicians. The sentence "Oh, by the way, doctor..." should not be only understood as an information but also as a relational expression and a reaction to the imminent separation from the physician.

Autism in schizophrenia revisited.

The concept of autism is reviewed in its historical evolution. It is suggested that the Bleulerian insistence on the withdrawal component in autism contributed to the decline of its use in adult psychiatry. Phenomenology offers another approach to grasping the nature of autism as a relational (subject-outer world) phenomenon. European phenomenological psychiatry in the field of schizophrenia is introduced and its attempts to reveal the essence of autism are presented. Autism is here considered as a "loss of vital contact with reality" (Minkowski), "inconsistency of natural experience" (Binswanger), or "the global crisis of common sense" (Blankenburg). It is proposed that autism represents dysfunctional perceptual/expressive attunement to the outer world. The usefulness of this concept is briefly examined in relation to the diagnosis and etiopathogenesis of schizophrenia.

L'interprète communautaire: une pièce centrale dans le puzzle de la consultation interculturelle [The community interpreter: a central piece in the puzzle of the intercultural consultation]

As a consequence of growing global migration, physicians in French speaking Switzerland often face communicational difficulties with allophone patients. This paper first discusses advantages and shortcomings of various ways of dealing with this kind of situations. The indication of using professional interpreters will be addressed, as well as some specific therapeutic, linguistic and relational features of triadic consultations involving a physician, a patient and an interpreter. Finally, useful practical information and advices are provided to clinicians in order to help them optimize their consultations with allophone patients.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.

The groups of Poincaré and Galilei in arbitrary dimensional spaces

In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincar algebra. The usual contraction of the Poincar to the Galilei group is seen to be equivalent to a certain coordinate transformation.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

General Interaction Picture from Action Principle for Mechanics

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.