Arbitrary Origin Research Articles

Efficient timestamp input and output

AbstractIn this paper we provide efficient algorithms for converting between timestamp values that signify some number of seconds from an arbitrary origin, and character strings specifying Gregorian dates, such as ‘January 1, 1993’. We give several algorithms that explore a range of time and space trade‐offs. Unlike previous algorithms, those discussed here have a constant time cost over a greatly extended range of timestamp values. These algorithms are especially useful in operating systems and in database management systems.

An eigenvalue theory of circular birefringence and dichroism in a non-magnetic chiral medium

By means of known constitutive relations for the D and H fields, which include both electric quadrupole and magnetic dipole terms, an eigenvalue theory is developed for electromagnetic wave propagation in an absorbing chiral medium. The theory allows the polarization eigenvectors to be determined, which the medium supports, and also their refractive indices and absorption coefficients. Uniaxial and cubic crystals, as well as an ideal gas, are treated in this way, and expressions are derived for their circular birefringence and dichroism in terms of property tensors of the medium. These expressions are shown to be independent of the arbitrary origin to which the multipole moments are referred. The theory is also applicable to artificial chiral materials which are optically active in the microwave regime.

A novel approach to the identification of microcrystals with electrons

Measurement of conventional-cell data requires observations along several specific zone axes in most cases. On the contrary, as shown in and outlined below, primitive-cell data can be extracted ab-initio, without trial-and-error, from single CBED patterns exposed along any zone axis, and displaying at least ZOLZ and first-order Laue-zone (FOLZ) spots.The CRYSTDAT database, which is up-to-date and accessible on-line, contains over 180,000 entries, each with cell data, chemistry and reference to published work for a compound. It can be searched for primitive cell data and partial chemistry. In combination with the previous remark, this shows that crystallites can be identified from single CBED patterns, and from partial chemical information obtained on them by Energy-Dispersive X-ray spectroscopy.CBED patterns are analyzed as follows. Two-dimensional (xP.vP) cartesian coordinates are measured for centers of all diffraction spots on the CBED film from an arbitrary origin. To each Bragg spot P on the film corresponds a scaied reciprocal vector FS with projections on the three axes:

Frequency of quadrupole mode oscillations of spheroidal liquid drops in an acoustic field.

Ultrasonic levitation of liquid drops in air has been used [Y. Tian etal., J. Colloid Interface Sci. (submitted)] as a technique for measurement of the rheological properties (viscosity, interfacial tension, elasticity) of liquid surfaces and interfaces. The unavoidable deformation and asymmetry caused by the intensity of the sound field needed to levitate millimeter-sized water drops in air in a 1-g environment gives rise to a change in the frequency of quadrupole mode shape oscillations from the spherical value. This complicates measurements of rheological properties. Thus the frequency change due to the interaction with the sound field has been modeled. Using a unique conservation of energy approach, the shift due strictly to geometrical deformation of arbitrary origin is derived. Then realistic values of deformation and corresponding radiation force for typical cases are considered, modifying the previously obtained frequency shift values. Results are compared to experimental values obtained for millimeter-sized drops levitated ultrasonically in air in a 1-g field. [Work supported by NASA through JPL Contract No. 958722.]

4984157 System and method for displaying oblique planar cross sections of a solid body using tri-linear interpolation to determine pixel position dataes

A method and apparatus for displaying arbitrary cross-sectional views of a three-dimensional body from a regular array of values of at least one physical property in the interior of the body includes making physical property measurements with such systems as computerized tomographic x-ray systems, or magnetic resonance imaging systems. Cut planes are defined by the user as displacement from, and rotations from, an arbitrary coordinate origin in the data space. An initial plane of pixel positions of arbitrary density is displaced and rotated to correspond to the cut plane. The values for the physical property at the pixel positions are interpolated from the surrounding measurements of actual values. Cross-sectional images are thereby supplied interactively in real time to support, for example, ongoing surgical procedures.

Solution of selfconsistent equations for superconducting glasses: a new universal ratio, critical exponent ?=1, and behaviour in magnetic fields

From higher order selfconsistent equations we derive a mean field theory of Ising- and XY-like superconducting glass phases. Detailed results include: the superconducting glass order parameter(s) (SGOP) at zero temperature, the critical temperatureT scg, and their universal ratio 0.64 for a class of poor conductors aboveT scg, the SGOP-decay nearT scg with critical exponent β=1 and slope 6/π, general conditions forT scg/T BCS, and incomplete depression ofT scg(H) in a magnetic field withT scg(H) approaching a high-field saturation value given by InT scg(∞)/T scg(0)) = −1/4>v 2<ρ 2 . We consider models with homogeneous and with inhomogeneous attractive couplingv of arbitrary origin.

Symmetry properties of the macroscopic scalar potential

This Communication examines the group properties of the macroscopic scalar potential of an alkali halide derived previously by Ritter and Markham. The potential has the form σ i f i ( r) q i , where f i is a function of space and q i is a normal coordinate. It does not consider in detail the properties of the potential at a site, since Ritter and Markham omit all higher order terms in an expansion. This makes the origin arbitrary. The potential has space group symmetry. One desires point group symmetry when working with point imperfections. Hence, here we consider the point group symmetry of the σ i f i 2( r) without regards to the q i 's. We believe that f 2 i is more appropriate than just the f i . Our interest is limited to the Φ + 1, Φ + 3, Φ - 4 and Φ + 5 irreducible representations of O h , and the lengthy calculations were made only for KCl. The γ + 1 part of the potential dominates, especially near the arbitrary origin where the other parts of the potential go to zero.

Statistical geometric analysis of packing of paired helical filaments in neurofibrillary tangles of Alzheimer's disease

The tangles of abnormal fibers known as paired helical filaments (PHF), which occur in neurons of persons suffering from Alzheimer's disease, possess limited regions of quasi-crystalline ordering interspersed with regions of randomly oriented fibers. Analysis of the quasi-crystalline zones of tangles, as visualized in longitudinal orientation in thin sections, indicated that a paracrystalline order may characterize the packing of PHF in tangles. Para-crystals may be defined as structures in which each pair of molecules is associated with uniquely spaced positions with a low probability that the molecules occupy these positions. In a paracrystal of the first kind, the probability of the molecules occupying these positions is independent of the distance from an arbitrary origin. In a paracrystal of the second type, positional indeterminancy increases with increasing distance. Myelin is a paracrystal of the second kind. The purpose of this paper is to present evidence concerning the paracrystalline nature of PHF in Alzheimer tangles based on analyses of variance of PHF interfilament spacing.

A Minimum Chi-Square Method for Developing a Common Metric in Item Response Theory

The θ scale in item response theory has arbitrary unit and origin. When a group of items is calibrated twice, estimates from one calibration must be trans formed to the metric of the other. A new method is presented for doing so. It is simpler than an earlier method based on test characteristic curves, and makes more complete use of available information.

Space as a ?bucket of dust?

A pregeometry of space is considered, in which the only structure imposed on individual points is a uniform probability of adjacency between any two arbitrarily chosen points. This probability is not specified (but only assumed small) and neither is the total number of points specified (but is assumed large). It is shown that the most likely distribution of points has similarities with a closed three-dimensional space of constant positive curvature, in particular, the number of points at a given distance from an arbitrary origin is proportional to sine-squared of the distance from that origin.

Probability density for diffusion on fractals

We propose an asymptotic formula for the probability density ${P}_{F}(x,t)$ that a random walker starts at an arbitrary origin on a fractal at time 0 and arrives at site $x$ at time $t$. We have numerically verified the proposed form for ${P}_{F}$ by testing a composition rule for probabilities which requires that the walker must have been on some site of the fractal at any intermediate time. We further write a Wiener integral representation of ${P}_{F}$.

Cooperative plasticity due to the motion of disorientation and phase separation boundaries

As has already been noted above, the theory of planar defects organically includes the mechanics of twinning, grain boundaries, Somigliani dislocations, translational dislocations, disclination, and dispiration. The fundamental propositions of the theory and methods of giving the tensor T are listed in Table 4. The mathematical formalism remains the same throughout, and it is applicable to both discrete objects (it is then necessary to conserve the δ-function apparatus), and to a continuous (then appropriate “smoothing” is needed, which usually reduces to replacement of the multiplication procedure by the normal n or by the direction Τ, to operations of finding the gradient, divergence, and curl of regular expressions, and “discarding” the δ-functional), In particular, the problem of thermoelasticity is formulated successfully by such a method in the terminology of the present theory. In a broad sence of the word, the development of the theory should be perceived as an extension of the concept of imperfection to “defects” of sufficiently arbitrary origin. A completely developed formalism was worked out earlier for just linear defects; in the symbols used here, for the case b=b0 + Ω X (r − r0) for constant b0,Ω, and r0, and without taking account of processes on the boundary S if the linear defect contained such a feature. Let us emphasize that to describe three-dimensional “defects” occurring because of homogeneous distortion Β = Τδ (V)., it is sufficient to use the apparatus of just the theory of planar defects since the fundamental phenomena are associated with precisely the presence of boundaries and in a formal plane, with the spatial derivatives of Β, they are always expressed in terms of the functional δ (S), while in the case of finite surface gradients in terms of δ(L). The time derivatives of the distortion T, i.e., $$\dot T$$ is written down in the developed representations in terms of the form $$\dot \alpha = n \times T\delta (S), \dot \eta = (\dot \alpha \times \nabla )^s $$ with all the resulting consequences.

Nutation and the Oppolzer's Terms

Two fundamental frames of reference are used in the study of the rotation of the Earth: the nonrotating celestial coordinate system XYZ attached to the directions to stars and/or extragalactic sources, and the terrestrial coordinate system xyz attached in “a prescribed way” to several points (observatories) on the surface of the Earth or to the pencil of unit vectors drawn from an arbitrary origin parallel to the local verticals at these points.

Classification for Market Segmentation: An Improved Linear Model for Solving Problems of Arbitrary Origin

A current problem in marketing research involves the use of scale measures of consumer characteristics to develop homogeneous classifications of consumers. The quality of these classification efforts is influenced by the nature of the scales, which are frequently characterized by arbitrary origin and variance. This paper draws on recent developments in classification methodology to propose and illustrate an integrative classification methodology which overcomes some of the current problems of classification approaches.

Analytical evaluation of magnetic multipole moment integrals for Slater-type orbitals

A general formula has been established for the magnetic multipole moment integrals over Slater-type orbitals. These integrals with an arbitrary origin of the magnetic multipole moment operator are expressed in terms of the well known A and B functions.

Calculations of magnetic susceptibility of polyatomic molecules

The magnetic susceptibility of H2O, NH3, and CH4 molecules has been evaluated within the framework of coupled and uncoupled Hartree–Fock perturbation theories for the Fock–Dirac density matrix, employing several basis sets of gaugeless Gaussian functions. The results provided by the largest basis sets are in good agreement with experiment as well as with other ab initio calculations. Quantities necessary to assess the degree of gauge independence of the susceptibility and to evaluate this property for an arbitrary gauge origin are also reported. The reliability of the uncoupled approach suggested here is systematically analyzed by investigating the upper bounds to the error affecting the geometric approximation to the paramagnetic susceptibility. The results demonstrate the practicality of the simple and inexpensive uncoupled scheme with respect to the cumbersome coupled method.

Semiautomatic processing of neurophysiological data: Part I—A device for measuring potential intervals from film

This paper describes the operation and construction of an electromechanical device designed to make measurements on oscillograph recordings of nerve or muscle potentials for subsequent computer analysis. The device consists of a motor-driven shaft which moves the record past a fixed cursor, and an electronic counter which records the movements of the shaft, thereby providing a cumulative tally of the distance of the current position of the cursor from some arbitrary origin on the record. When the device is connected to a paper tape punch, the operator can punch the distance measurement associated with each potential along the record onto the tape. The format of data on the tape readily allows further analysis by computer.

Study of Diffuse Scattering by Means of High Resolution Structure Images

Disorders in crystals with relatively simple structures which gave diffuse scattering have been extensively studied by X-ray or neutron diffraction methods. All these investigations were based on traditional diffraction methods and observations were made in reciprocal space (note observable diffraction intensities can be considered only in terms of interatomic vectors) and therefore the results obtained there leaves considerable ambiguity, particularly when we try to derive an actual model of the disordered crystals. A solution of this problem will be given only by knowing all atom positions in an assembly of atoms and for this case the observable diffracted intensity is given bywhere (xi,yi) and (xj,yj) represent position vectors of the i th and j th atoms with scattering factors fi and fj from an arbitrary origin. On the other hand, a crystal containing imperfections can be defined by

Westwanderung and the lunar tidal couple: Modulation of convection by Bulge Stress

Wegener concluded that the Earth's surface has suffered regionally variable westward displacement. Modern data support Wegener's conclusion, but a causative mechanism has not been evident. The retarding torque is too small to distort the viscous Earth. At the same time difficulty has been experienced in explaining the large value of the astronomically detected tidal dissipation. We have examined the effect of the secular rotational strain imposed by tidal bulge formation on convection in the mantle of arbitrary origin. The dissipation as measured by the lag in the bodily tides appears adequate to explain the missing part of the dissipation, some 8.5 × 1026 erg yr−1, without recourse to an unidentified mechanism in the seas. The convection must itself be influenced by the external force system. The effect to be expected is that circulation resulting in westward displacement at surface must be fostered at the expense of circulation in other directions. The history of the tidal couple, if this is based on dissipation in the mantle, is likely to differ greatly from that of a couple based on dissipation in the seas.

On the use of contour maps in the analysis of spread of communicable disease.

The co-ordinates of the dwellings where cases of variola minor (alastrim) occurred during a small epidemic were used in a worked example of contour mapping of disease spread. The contoured variable was the date of onset, relative to an arbitrary base date, of the case introducing the disease into each of twenty-two households. Three contour maps prepared with slightly different computer programmes or dates exhibited similar concentric loops whose centres were close to the first infected household. The average rate of spread of the disease was estimated by regression of the number of days to onset of the first case in the household on the average distance from an arbitrary origin to the relevant contour line. The calculated average rate of spread was 1.22 metres per day. An additional map was contoured using the cumulative number of cases as the contoured variable, relative to the onset of the example epidemic.