Hill Case Research Articles

Close Reading on a Global Scale

Close Reading on a Global Scale

Speech and Sensuality; Speech and Separation: Commentary on Paper by Sarah Hill

This discussion attends to the way the author addresses issues of bilingualism, multiple self-states, primary nonverbal attachments, and the complexity of countertransference identifications in a treatment with several overlapping language worlds. Language or rather speech practice is considered as a carrier of object ties, as a repository of affect and unconscious meaning. I approach Hill's clinical report by thinking about how Hill situates aspects of identity within particular language worlds. Why exactly is it that language demarcates identity, the distinctions of self and other, and the positioning of identity in history so acutely? We see that language has amazing constitutive power in this case, a case where language and attachment, language and early loss, language and traumatic memory, and language and development are so intertwined. This discussion also takes on the author's use of her countertransference and her dream material illuminate conflicts and ruptures in a treatment with a French-speaking patient. Various theories of language and the philosophy of language as well as attachment theory are used to examine the dynamics and processes in Sarah Hill's case. I consider also the role of a lost language world in the analyst's early childhood may have pressed powerfully on the treatment.

The Precautionary Principle, Epidemiology and the Ethics of Delay

Ethics tells us: do good and do no harm and invokes the norms of justice, equity and respect for autonomy in protecting and promoting health and well-being. The Precautionary Principle, a contemporary re-definition of Bradford Hill's case for action, gives us a common sense rule for doing good by preventing harm to public health from delay: when in doubt about the presence of a hazard, there should be no doubt about its prevention or removal. It shifts the burden of proof from showing presence of risk to showing absence of risk, aims to do good by preventing harm, and subsumes the upstream strategies of the DPSEEA (Driving Forces Pressure Stress Exposure Effect Action) model and downstream strategies from molecular epidemiology for detection and prevention of risk. The Precautionary Principle has emerged because of the ethical import of delays in detection of risks to human health and the environment. Ethical principles, the Precautionary Principle, the DPSEEA model and molecular epidemiology all imply re-emphasizing epidemiology's classic rôle for early detection and prevention. Delays in recognizing risks from past exposures and acting on the findings (e.g., cigarette smoking and lung cancer, asbestos, organochlorines and endocrine disruption, radiofrequency, raised travel speeds) were examples of failures that were not only scientific, but ethical, since they resulted in preventable harm to exposed populations. These may delay results from, among other things, external and internal determinants of epidemiologic investigations of hazard and risk, including misuse of tests of statistical significance. Furthermore, applying the Precautionary Principle to ensure justice, equity, and respect for autonomy raises questions concerning the short-term costs of implementation to achieve long-term goals and the principles that guide compensation.

Students as Context in Mathematics Reform: The Story of Two Upper-Elementary Teachers

This case study describes 2 experienced upper-elementary school teachers-Joe Scott and Karen Hill-who for the past 4 years have attempted to implement elements of educational reform in mathematics as part of a statewide effort in California. This statewide effort, which began with the adoption of a curriculum framework similar to the one recommended by the National Council of Teachers of Mathematics, involved changes in textbooks, teacher in-service programs, and statewide assessment. The 2 teachers, not surprisingly, brought important strengths and weaknesses to this effort. This article, which draws on 5 years of interview and observational data, focuses on a complex factor that is both a strength and a weakness: Scott and Hill's attentiveness to learners' needs. Scott views learners' needs largely through the prism of a fixed set of curricular demands. In Hill's case, attentiveness to student needs means focusing on an equally hard and fast set of demands-mathematical ability-albeit originating from the student side of the student-curriculum divide. Implications of these differing views of what students need on the reform effort are developed.

Dynamics of binary asteroids: I. Hill's case

Recent observations suggest that binary or multiple asteroids could exist ( T. C. Van Flandern, E. F. Tedesco, and R. P. Binzel, 1979, Satellites of Asteroids (T. Gehrels, Ed.), pp 443–465 ; A. Cellino et. al., 1985, Astron. Astrophys. 144, 355–362 ; S. J. Weidenschilling, P. Paolicchi, and V. Zappalà, submitted for publication). However, because of the smal size of such objects and also because of their distance from the Earth, direct observations are nearly impossible. Indeed, their mere existence is still challenged. We present here a study of the dynamics of these objects. Our aim is to assess whether or not they are dynamically stable. More specifically, we investigate the trajectories of Hill's problem to describe the effect of the solar perturbations on the relative motion of a binary asteroid.

Generalized hill's problem Lagrangian Hill's case

In this paper, we investigate a generalization of the Hill's problem to the case where no restriction is made about the nature of the field of force perturbing two small bodies in gravitational interaction. We apply the general equations obtained to the dynamics of two bodies located in the vicinity of the triangular lagrangian points of the restricted three-body problem.

Geometry of KDV (2): Three examples

Let Q be a 1-dimensional Schroedinger operator with spectrum bounded from - infinity. By addition I mean a map of the form Q ..-->.. Q' = Q - 2D/sup 2/1g e with Qe = lambdae, lambda to the left of spec Q, and either integral/sub - infinity//sup 0/ e/sup 2/ or integral/sub 0//sup infinity/ e/sup 2/ finite. The additive class of Q is obtained by composite addition and a subsequent closure; it is a substitute for the KDV invariant manifold even if the individual KDV flows have no existence. KDV(1) = McKean (1987) suggested that the additive class of Q is the same as its unimodular spectral class defined in terms of the 2 x 2 spectral weight dF by fixing (a) the measure class of dF, and (b) the value of ..sqrt..det dF. The present paper verifies this for (1) the scattering case, (2) Hill's case, and (3) when the additive class is finite-dimensional (Neumann case).

Hill's case of the averaged problem of three bodies and the stability of plane orbits: PMM vol. 41, n≗ 2, 1977, pp. 234–244

Hill's case of the averaged problem of three bodies and the stability of plane orbits: PMM vol. 41, n≗ 2, 1977, pp. 234–244

Non-restricted double-averaged three body problem in Hill's case

A limiting case of the problem of three bodies (m 0,m 1,m 2) is considered. The distance between the bodiesm 0 andm 1 is assumed to be much less than that between their barycenter and the bodym 2 so that one may use Hill's approximation for the potential of interaction between the bodiesm 1 andm 2. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm 1 andm 2, describes the secular evolution of the orbits in the first approximation of the perturbation theory. As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out. The set of initial data is found, for which a collision between the bodiesm 0 andm 1 takes place. The region of the parameters of the problem is determined, for which plane retrograde motion is unstable. In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.

Libration effects for retrograde satellites in the restricted three-body problem

Numerical explorations of the restricted problem have shown that for stable large nonperiodic retrograde satellite orbits, the motion can be decomposed into a fast ‘reference motion’ and a slow libration aroundB 2 We study here this libration in the circular plane Hill's case, for which the ‘reference motion’ is elliptic. We establish the equations of motion for the coordinates of the centre of this ellipse. We find two integrals of motion: the first is the semi-major axis of the ellipse; the second is essentially Jacobi's integral, translated into the new coordinates. We give a formula for the period of the libration and we find its limiting value for small libration amplitudes. A numerical verification gives very good agreement for all these results.

Retrograde Satellites in the Circular Plane Restricted Three-Body Problem

Characteristics and stability of simple-periodic retrograde satellites of the lighter body are presented for Hill's case and for all values of the mass ratio m2/(m1+m2) between 0 and 0.5.

Presumption of Deliberation and Premeditation. The Doctrine of Hunter Hill's Case

Presumption of Deliberation and Premeditation. The Doctrine of Hunter Hill's Case

Periodic Orbits in Hill's Case. Third Paper (Periodic Ejectional Orbit)

Periodic Orbits in Hill's Case. Third Paper (Periodic Ejectional Orbit)

Periodic Orbits in Hill's Case. Second Paper (Retrograde Variational Orbits)

Periodic Orbits in Hill's Case. Second Paper (Retrograde Variational Orbits)