Static point-spread function correction dominating higher-order speckle terms at high adaptive correction

At high adaptive correction, the randomly shifting speckles familiar in conventional astronomical imaging become organized into patterns with distinct regularities that may permit partial suppression of the image noise they produce. Mathematically, the phase exponential in the Fourier-optical imaging expression may be expanded in a Taylor series in remnant phase phi, which is small at very high correction, leading to a perturbed point-spread function (PSF) that is a sum of algebraic terms, each of distinct spatial symmetry. At sufficiently high correction, one need deal with only a few of the lowest-order terms. A first-order expansion gives an ideal PSF plus two terms, linear and quadratic, describing the two brightest, physically most relevant kinds of speckle. A second-order expansion gives three new terms, the brightest of which is primarily a static correction to the PSF, with a much smaller true speckle component. When the correction is great enough to isolate individual speckle terms, the two terms from the first-order expansion alone determine the essential physics. A general observational strategy is outlined for reducing speckle noise in highly corrected companion searches, dominated by a few speckle terms of definite spatial symmetry.     

Post-Newtonian approximation for a rotating frame of reference

The field equations of general relativity are solved to post-Newtonian order for a rotating frame of reference. A new method of approximation is used based on a 3+1 decomposition of the equations. The results are expressed explicitly in terms of the gravitational potentials. The space-time is asymptotically flat but not locally flat. The space-time metric contains gravitational terms, inertial terms, and coupled gravitational-inertial terms. The inertial terms in the equation of motion are in agreement with terms obtained by other authors using kinematic methods. The metric and equation of motion reduce to those for an inertial frame of reference under a simple coordinate transformation. The total energy of a particle is given. For the restricted three-body problem this represents the relativistic extension of Jacobi's integral to post-Newtonian order.This article received an honorable mention from the Gravity Research Foundation for the year 1984—Ed.     

Error compensation for mirror symmetry absolute test

A method is proposed to compensate intrinsic error in mirror symmetry absolute test. Because of the limitation of rotation times of flat A, intrinsic error of CNθ terms occurs in reconstructed wavefronts of flats A, B and C. If flat A is rotated to a new azimuthal position, and the wavefront difference between two measurements before and after rotation is calculated, the Zernike coefficients of CNθ terms can be obtained by solving coefficient equations due to rotation invariability of the form of Zernike polynomials in polar coordinates. Therefore, the intrinsic error of CNθ terms may be compensated. Because the amount of CNθ terms is infinite, the compensated terms are decided in terms of the balance between intrinsic error reduction and computational effort. Computer simulation proves the validity of the proposed method.     

Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields.     

On the nonsymmetric,gravitational collapse of an infinite,dust-filled cylinder

Nonsymmetric terms or angle-dependent terms in the power series expansion of Einstein's equations are considered. It is shown, first, that they do not influence the time evolution of the symmetric terms and, second, that they do not remain bounded as the cylinder collapses. However, the major contribution to the density arising from the symmetric terms makes the nonsymmetric contribution progressively more insignificant as the collapse proceeds.     

Intermolecular forces between large molecules: the structure of anthracene stable dimers

Calculations are reported concerning the structure of the anthracene stable dimer. It is shown that the use of an ‘exp-6’ atom-atom potential produces a structure which is definitely not that allowed by the experimental data : this is shown to be due to the absence of any simulation of permanent moment interactions in the atom-atom potentials. A number of conventional methods for calculating the individual terms of the total potential energy are used to estimate the magnitudes of these terms. It is concluded that the resulting relative magnitudes of the individual terms cannot be determined accurately enough to justify the construction of a total potential energy curve. However, by considering the variation of the individual terms with the relative orientation of the two molecules of the dimer, the dominant role of the quadrupole-quadrupole terms in determining the dimer structure is clearly demonstrated.     

A method for selection of significant terms in the assumed solution in a Rayleigh-Ritz analysis

A method is presented which can reduce significantly the size of eigenvalue problems necessary for accurate Rayleigh-Ritz solutions in vibration and buckling problems. Instead of carrying more and more terms in the assumed solution, this method selects terms which are most significant to the eigenvalues of interest. Only the significant terms are used in the eigenvalue problem that is to be solved. The significant terms are chosen by using a Taylor's series approximation of the eigenvalues. The Taylor's series is discussed, the method is explained, and examples of applications of the method are shown which indicate its effectiveness.     

组合数学方法推引原子谱项（Ⅲ）非等效组态的谱项及其微机处理

讨论了推引非等效组态原子谱项的组合数学方法和矢量加和法，并编制了ＢＡＳＩＣ语言程序，在微机上快速推求非等效组态的谱项。     

Fine structure of the exciton spectrum in GaSe

New optical spectra near the fundamental edge of GaSe have been measured at low temperatures. The observed fine structure is explained in terms of transitions to excitonic groundstates and excited states, in terms of phonon replica of exciton ground states and in terms of excitons bound to intrinsic point defects.     

New Terms for Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.     

“Exact” shell model calculations and linked nuclear effective interactions

It is shown that so-called “exact” shell model calculations of spectra (diagonalizations) contain important unlinked terms which are due to space truncation. These terms render less interesting a comparison between the “exact” calculation of spectra and model space calculations with effective interactions containing linked terms only. The spectral calculations were performed in mass 6. The lowest order unlinked terms which arise in the “exact” calculation were calculated in mass 6 and mass 18.     

Antiprotonic helium

Recent measurements of the 2p and 3d atomic levels and lifetimes in antiprotonic helium seem to indicate an inconsistency, when interpreted in terms of an optical potential based on parameters extracted from heavier antiprotonic atoms. Here it is shown that this inconsistency is removed, when the data is described in terms of a multiple scattering formalism that treats correctly the number of nucleons and their correlations in the rescattering terms.     

Peculiarities in the behavior of the entropy diameter for molecular liquids as the reflection of molecular rotations and the excluded volume effects

The behavior of the diameter of the coexistence curve in terms of the entropy and the corresponding diameter are investigated. It is shown that the diameter of the coexistence curve in terms of the entropy is sensitive to the change in the character of the rotational motion of the molecule in liquid phase which is governed by the short range correlations. The model of the compressible effective volume is proposed to describe the phase coexistence both in terms of the density and the entropy.     

Gauge invariance and corrections to deep inelastic scaling

The asymptotic behavior of the correction terms to scaling for the deep inelastic structure functions is analysed in the covariant parton model. It is shown by consideration of the ω→ 1 limit that the non-canonical secondary terms from the “hand-bag” diagram cannot be made gauge invariant. The large ω behavior of the terms is also considered, and it is concluded that scale breaking effects are likely to be significant at large values of ω.     

Non-standard aspects of Minkowski causal logic

The Minkowski causal logic, which is already known to be a complete orthomodular lattice, is found to be also an atomistic and irreducible logic, but to have no other essential properties to be represented in terms of all the subspace of some Hilbert space. Alternative representation of the logic in terms of subspaces of a real vector space or of the states in terms of probability measures are suggested.     

Virtual Compton Scattering off Spin-Zero Particles at Low Energies

We discuss the low-energy behaviour of the virtual Compton scattering amplitude off a spin-zero target. We first compare various methods of obtaining a low-energy expression based either on the soft-photon approximation or the use of Ward-Takahashi identities. We point out that structure-dependent terms are defined with respect to a low-energy approximation of the pole terms, which commonly is separated from the full amplitude. We derive a general expression for the structure-dependent terms in an expansion in terms of the momenta and of the initial and final virtual photon, respectively, up to and including terms of order . At order two terms appear that are related to the usual electric and magnetic polarizabilities of real Compton scattering. At order we find nine new structures of which five can only be determined using virtual photons. Received October 23, 1997; accepted for publication December 29, 1997     

The compressible hybrid RANS/LES formulation using an additive operator

In this work, the compressible governing equations for the hybrid Reynolds-averaged/large-eddy simulations are formally derived by applying a hybrid filter to the Navier–Stokes equations. This filter is constructed by linearly combining the Reynolds-average (RANS) and large-eddy simulation (LES) operators with a continuous blending function. The derived hybrid equations include additional terms that represent the interactions between RANS and LES formulations. The relevance of these terms is investigated in flat-plate turbulent boundary layer simulations and indicate that these additional terms play a fundamental role in compensating for the turbulence that is neither modeled nor resolved in the transition region between RANS and LES. Results also show that when the additional terms are included, the calculations are not very sensitive to the blending function implemented in the hybrid filter. In the contrary, when these terms are neglected and a step function is implemented in the hybrid filter, nonphysical discontinuities are predicted in the flow statistics.