Quotient Technique Research Articles

Parallel high-radix nonrestoring division

An algorithm for high-radix nonrestoring division is proposed which combines a cost-efficient quotient estimation technique with collapsing of the division into one operation each iteration. The quotient estimation technique is a direct combinatorial algorithm which allows a more generalized partial remainder than similar studies. In addition, the successor partial remainder is calculated directly from the previous partial remainder. The intermediate steps of calculating the next quotient estimate, multiplying it by the divisor, and then subtracting the result from the previous remainder are telescoped into one step. This is possible due to the use of simple direct combinatorial equations for the quotient estimate. Thus, one operation is used to generate the next remainder from the previous remainder. This operation is similar to a multiplication with a reduced carry propagate adder. This algorithm reduces the latency of each iteration to less than the delay of one multiplication. Thus, high-radix nonrestoring division is possible with a low latency and no need for an off-chip ROM to hold a quotient estimate. >

The application of the dispersion quotient technique for particle size and density measurements behind an electron beam scrubber

The application of the dispersion quotient technique for particle size and density measurements behind an electron beam scrubber

Cross-Hauling and Nonsurvey Input—Output Models: Some Lessons from Small-Area Timber Economies

Nonsurvey input—output models, especially those constructed by means of pool and quotient techniques, are suspect when applied to the case of cross-hauling. This is well known. But the US Department of Agriculture (USDA) Forest Service, through its IMPLAN model, and the US Department of Commerce (USDC), through its RIMSII model, encourage the application of pool and quotient nonsurvey models in cases where cross-hauling is likely to occur. In a study of the timber economy of the West-central Idaho Highlands we show the error caused by ignoring cross-hauling in estimates of logger—sawmill trade. We argue that pool and quotient techniques, used in nonsurvey models such as IMPLAN and RIMSII, should not be applied to a single county situation, or to any aggregation of counties that is not, in some sense, a functional economic area. This applies in many cases to full state models. We close by noting that in many applications of pool and quotient nonsurvey input—output methods, technique may be substituting for thought.

A spectroscopic determination of the velocity dispersion in the Galactic bulge

view Abstract Citations (9) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Spectroscopic Determination of the Velocity Dispersion in the Galactic Bulge Freeman, K. C. ; de Vaucouleurs, G. ; de Vaucouleurs, A. ; Wainscoat, R. J. Abstract The velocity dispersion of the K giant population in the Galactic bulge has been measured. Two fields in the brightest parts of the great Sagittarius cloud whose lines of sight pass within 0.5 and 0.7 kpc from the Galactic center were observed on three nights each to produce high signal-to-noise sky-subtracted spectra of the 4965-5400 A region at 1.2 A resolution. The velocity dispersions in the two fields derived by the Fourier quotient technique are, respectively 118 and 129 km/s, with a weighted mean of 122 + or - 7 (m.e.), in excellent agreement with the mean velocity dispersion previously derived from the kinematics of 'test particles', such as globular clusters, RR Lyrae and Mira-type variables, and planetary nebulae. This result confirms the validity of the Fourier quotient method applied to the integrated spectra of the unresolved bulges of external galaxies. The central velocity dispersion of the galactic bulge is 128 + or - 7 km/s. Publication: The Astrophysical Journal Pub Date: February 1988 DOI: 10.1086/166027 Bibcode: 1988ApJ...325..563F Keywords: Astronomical Spectroscopy; Galactic Bulge; Galactic Nuclei; Milky Way Galaxy; Velocity Distribution; Globular Clusters; K Stars; Mira Variables; Planetary Nebulae; Spectrum Analysis; Astrophysics; GALAXIES: FORMATION; GALAXIES: INTERNAL MOTIONS; GALAXIES: NUCLEI; GALAXIES: THE GALAXY full text sources ADS | data products SIMBAD (3)

Existence of regular solutions for nonlinear Signorini's problems

The aim of this paper is to prove the existence of a Lipschitz solution for nonlinear obstacle problems with quadratic growth in the gradient and Signorini’s boundary conditions. For the linear Signorini’s problem, existence and regularity results have been given by Brezis [S], and by Hanouzet and Joly [13]; in particular, the last two authors apply a dual estimation technique, consisting of estimating the conormal derivative of the solution as a measure on the boundary. For the nonlinear Signorini’s problem of the type considered in this paper, no existence results for weak solutions are known; the only results available are due to Frehse [lo], and refer to the interior regularity of arbitrary bounded weak solutions. To obtain the existence of a (Lipschitz) weak solution in the present nonlinear quadratic case, global estimates up to the boundary are needed. Let us remark incidentally that C’ regularity up to the boundary of the weak solution was previously obtained by da Veiga [2], da Veiga and Conti [3], by Giaquinta and Modica [15], using a direct variational approach; however, they only allow a sublinear growth in the gradient. In this case the existence of weak solutions can be obtained by standard methods. Our proof of the existence of a weak solution, in the case of quadratic growth in the gradient, relies on an a priori estimate up to the boundary of the Lipschitz norm for C’ n Hz arbitrary solution u, which is obtained in Section 3. We at first estimate the derivatives of u in the interior of the domain and its tangential derivatives on the boundary, adapting the differential quotient technique of Frehse to the present situation in which

Droplet formation and growth in condensing binary vapours

An earlier model of the droplet growth in unary condensation is extended for binary mixtures. The theoretical results are compared with measurements in the driver section of a shock tube using ethanol/water systems. Droplet radii and concentration are determined by means of the dispersion quotient technique. Particle size in the range of 0.1–1 μm and particle densities between 10 11 and 10 14 m −3 were determined. Theoretical and experimental results are in good agreement under the conditions chosen.

Note on Non-Survey Input-Output Models for Multicounty Regions: Reply

The comment by Bernat on my pragmatic solution to a problem that occurs in using the simple location quotient (SLQ) technique to estimate input-output multipliers raises an interesting estimation issue not addressed in the comment or my paper (1980). My purposes in this reply are to assert that there still is a multicounty problem in interpretation of SLQ based I-0 multipliers and to identify potential downward bias in SLQ based multipliers associated with neglect of within region specialization.

Dynamics of the stellar component of the bulge of M31

view Abstract Citations (65) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dynamics of the STELAR component of the bulge of M 31. McElroy, D. B. Abstract The present study of the rotation and velocity dispersion fields of the stellar component of the bulge region of M31 indicates that the Fourier quotient technique is useful in the determination of velocities and their dispersions, even on photographic spectra. An apparent symmetry is found to be present in the rotation curves in the region whose R value is less than 10 arcsec. The position of discrete dust features shown on enhanced photography correlates with small perturbations in the rotation curves. The gas and stellar components have different intrinsic rotational velocities in the bulge, suggesting only weak coupling, if any, between the two systems. No clear dynamical evidence is noted for the presence of a barlike structure in the bulge of M31. Publication: The Astrophysical Journal Pub Date: July 1983 DOI: 10.1086/161142 Bibcode: 1983ApJ...270..485M Keywords: Andromeda Galaxy; Galactic Rotation; Spiral Galaxies; Stellar Motions; Line Spectra; Radial Velocity; Spectrum Analysis; Tables (Data); Velocity Distribution; Astrophysics full text sources ADS | data products NED (1)

Velocity dispersions in the bulges of spiral and S0 galaxies. II Further observations and a simple three-component model for spiral galaxies

view Abstract Citations (76) References (54) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Velocity dispersions in the bulges of spiral and S0 galaxies. II. Further observations and a simple three-component model for spiral galaxies. Whitmore, B. C. ; Kirshner, R. P. Abstract We have obtained velocity dispersions for 24 galaxies in the Virgo cluster to supplement our earlier results. A 2000 channel intensified Reticon scanner has again been used on the 1.3 m telescope of McGraw-Hill Observatory, and a Fourier quotient technique has been employed to yield dispersions. We have confirmed our earlier result that spiral bulges exhibit a relation between total luminosity and velocity dispersion with the form L ∝ σ4, but with velocity dispersions that are 17 ± 8% smaller than elliptical galaxies at the same absolute magnitude. However, possible systematic errors may still affect the reality of this gap. The scatter in the L ∝ σ4 relationship is substantially larger for the spiral bulges than for the elliptical galaxies. This larger scatter probably indicates that spiral bulges comprise a more heterogeneous sample than do elliptical galaxies. We also find that the bulge components of SO galaxies follow a L ∝ σ4 relation with no gap with the ellipticals. The similarity in this relation for the spheroidal components of spiral, SO, and elliptical galaxies indicates that the systems are dynamically similar. We have compared our velocity dispersions with rotational velocities determined from neutral hydrogen widths. For a totally bulge dominated spiral the ratio of the asymptotic rotational velocity to the velocity dispersion is about 1.4. This suggests that the mass responsible for producing the flat rotation curves (presumably the "halo") resides in a spheroidal component rather than in the disk. Our study also substantiates our earlier result that the massive halo is not merely an extension of the bulge, but is a separate dynamical component for most of our galaxies. A simple three-component model has been constructed to aid in the interpretation of this data. These models provide an independent indication of the existence of massive halos in spiral galaxies. Publication: The Astrophysical Journal Pub Date: November 1981 DOI: 10.1086/159346 Bibcode: 1981ApJ...250...43W Keywords: Astronomical Models; Dispersions; Elliptical Galaxies; Galactic Nuclei; Galactic Structure; Spiral Galaxies; Galactic Rotation; Luminosity; Tables (Data); Virgo Galactic Cluster; Astrophysics full text sources ADS | data products NED (64) SIMBAD (61)

The dispersion quotient technique in submicron particle size analysis

The dispersion quotient technique in submicron particle size analysis

Reading Difficulties in Arithmetical Computation

Arithmetical computation, although seemingly farther di vorced from reading than from the solution of verbal problems, does involve certain specific skills in the field of reading. In connection with an extensive study of special instruction and motivation in reading, the writer was brought face to face with certain striking facts concerning the r?le of reading as a factor in success in solving examples in arithmetic. During the school year, 1923-24, a study of achievement quotient technique was conducted in the public schools of Rad cliff, Iowa, under the direction of Professors Ruch and Horn of the State University of Iowa. But part of this study is reported here. During this investigation emphasis was placed upon in struction in reading, but no variation from the typical programs for arithmetic or any other school subject was permitted. Dur ing the third week in September the Stanford Achievement Test, Form A, was administered to all the pupils from the third to the eighth grades, inclusive. At the end of the first semester Form B of this test was given, and at the end of the second semester Form A was repeated. Since a period of eight and one-half months separated the two testings by Form A, the direct carry over of familiarity or practice effects was, in all probability, negligible. When checking the results of these tests, the writer was struck by the fact that the pupils' gains in arithmetical computation were as great or greater than those in reading, although reading had received additional motivation and instruction. Roughly speak ing, gains of one and one-half to more than two years were scored in computation. This fact suggested the value of a de tailed study of the errors made by the pupils on the initial and final testings. A considerable proportion of the actual errors 287

Spelling Age Computed from the Score on Fifty Percent Lists

In a study of the accomplishment of school children, in which the quotient technique was used, it became necessary to deter mine the spelling ages of pupils of the elementary grades. Age norms were available for such product tests as the Woody-McCall Mixed Fundamentals, the Trabue-Kelley Completion Test Exer cises, the Thorndike Visual Vocabulary Scales,2 and the Thorn dike-McCall Reading Scales. In spelling, however, there were no age norms. It was, therefore, necessary either to establish them or to adopt some technique which would be equally valid in determining spelling age. Conversion of the grade norms for the fifty percent lists of the Buckingham Extension of the Ayres Spelling Scale into age norms, and the adaptation of Van Wagenen's3 Table I so as to determine, from the pupils' scores on these lists, the point of fifty percent success and failure, would fulfill the need.

The achievement quotient technique.

The achievement quotient technique.