Influence of poles on equioscillation in rational approximation

The error curve for rational best approximation of f ∈ C[−1, 1] is characterized by the well-known equioscillation property. Contrary to the polynomial case, the distribution of these alternations is not governed by the equilibrium distribution. It is known that these points need not to be dense in [−1, 1]. The reason is the influence of the distribution of the poles of the rational approximants. In this paper, we generalize the results known so far to situations where the requirements for the degrees of numerators and denominators are less restrictive.Крива похибок для раціонального найкращого наближення f∈C[−1,1] характеризується відомою властивістю еквіосциляцій. На відміну від поліноміального випадку розподіл цих змін знаку не визначається рівноважним розподілом. Відомо, що ці точки не обов'язково мають бути щільними в [−1,1], що зумовлено впливом розподілу полюсів раціональних наближень. У даній роботі узагальнено відомі результати на випадки, де на степені чисельників та знаменників накладаються менш жорсткі умови

Quasirelativistic quasilocal finite wave-function collapse model

A Markovian wave function collapse model is presented where the collapse-inducing operator, constructed from quantum fields, is a manifestly covariant generalization of the mass density operator utilized in the nonrelativistic Continuous Spontaneous Localization (CSL) wave function collapse model. However, the model is not Lorentz invariant because two such operators do not commute at spacelike separation, i.e., the time-ordering operation in one Lorentz frame, the "preferred" frame, is not the time-ordering operation in another frame. However, the characteristic spacelike distance over which the commutator decays is the particle's Compton wavelength so, since the commutator rapidly gets quite small, the model is "almost" relativistic. This "QRCSL" model is completely finite: unlike previous, relativistic, models, it has no (infinite) energy production from the vacuum state. QRCSL calculations are given of the collapse rate for a single free particle in a superposition of spatially separated packets, and of the energy production rate for any number of free particles: these reduce to the CSL rates if the particle's Compton wavelength is small compared to the model's distance parameter. One motivation for QRCSL is the realization that previous relativistic models entail excitation of nuclear states which exceeds that of experiment, whereas QRCSL does not: an example is given involving quadrupole excitation of the $^{74}$Ge nucleus.Comment: 10 pages, to be published in Phys. Rev.

A Hierarchical Multiple-Level Approach to the Assessment of Interpersonal Relatedness and Self-Definition: Implications for Research, Clinical Practice, and DSM Planning

Extant research suggests there is considerable overlap between so-called 2-polarities models of personality development; that is, models that propose that personality development evolves through a dialectic synergistic interaction between 2 key developmental tasks across the life span—the development of selfdefinition on the one hand and of relatedness on the other. These models have attracted considerable research attention and play a central role in DSM planning. This article provides a researcher- and clinicianfriendly guide to the assessment of these personality theories. We argue that current theoretical models focus on issues of relatedness and self-definition at different hierarchically organized levels of analysis; that is (a) at the level of broad personality features, (b) at the motivational level (i.e., the motivational processes underlying the development of these dimensions), and (c) at the level of underlying internal working models or cognitive affective schemas, and the specific interpersonal features and problems in which they are expressed. Implications for further research and DSM planning are outlined

Motion Tomography of a single trapped ion

A method for the experimental reconstruction of the quantum state of motion for a single trapped ion is proposed. It is based on the measurement of the ground state population of the trap after a sudden change of the trapping potential. In particular, we show how the Q function and the quadrature distribution can be measured directly. In an example we demonstrate the principle and analyze the sensibility of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to the Lamb-Dicke Limit and works in one or more dimensions.Comment: 4 pages, Revtex format, 4 postscript figures, changed typographical error

Effective-range approach and scaling laws for electromagnetic strength in neutron-halo nuclei

We study low-lying multipole strength in neutron-halo nuclei. The strength depends only on a few low-energy constants: the neutron separation energy, the asymptotic normalization coefficient of the bound state wave function, and the scattering length that contains the information on the interaction in the continuum. The shape of the transition probability shows a characteristic dependence on few scaling parameters and the angular momenta. The total E1 strength is related to the root-mean-square radius of the neutron wave function in the ground state and shows corresponding scaling properties. We apply our approach to the E1 strength distribution of 11Be.Comment: 4 pages, 1 figure (modified), additional table, extended discussion of example, accepted for publication in Phys. Rev. Let

On the Divergence Phenomenon in Hermite–Fejér Interpolation

AbstractGeneralizing results of L. Brutman and I. Gopengauz (1999, Constr. Approx.15, 611–617), we show that for any nonconstant entire function f and any interpolation scheme on [−1, 1], the associated Hermite–Fejér interpolating polynomials diverge on any infinite subset of C\[−1, 1]. Moreover, it turns out that even for the locally uniform convergence on the open interval ]−1, 1[ it is necessary that the interpolation scheme converges to the arcsine distribution