Elliptical Figures Research Articles

FRANCIS G. PEASE AND THE FIRST GALACTIC ROTATION CURVES (1916‒1922)

With the 60-inch reflector at Mount Wilson Observatory, Francis G. Pease obtained the first measurements of the rotation curves of two nearly edge-on spiral galaxies, NGC 4594 (the Sombrero Galaxy) and NGC 224 (the Andromeda Galaxy) in 1916 and 1918, respectively. Pease aligned the spectrograph's slit with the major axes of the galaxies' foreshortened elliptical figures and obtained direct measurements of the Doppler-induced radial velocity components along their axes. This technique originally had been applied in 1895 by James E. Keeler to a rotational analysis of the rings of Saturn. By subtracting out the radial velocities of their centers, Pease obtained their rotational velocities as a function of distance away from the centers. This enabled him to determine that linear relationships existed in both cases, whereby these objects appeared to show evidence of solid-body rotations out to (and beyond) the limits that could be observed spectroscopically (about 2.5 arcminutes from their centers). These relationships contradicted the behaviors of planets that orbited our Sun, and indicated that the objects' mass distributions likewise increased in direct proportion away from the centers. Pease's dynamical results were applied in two independent cases (by Ernst J. Öpik and Knut Lundmark) to a greater understanding of the distance and nature of the 'spiral nebulae' in the aftermath of the 'Great Debate'. Yet, the remaining questions posed by Pease's data were not effectively answered for two decades (or more) until Horace W. Babcock extended spectroscopic investigations into the disk region of the Andromeda Galaxy and showed that those stellar velocities were largely independent of their distances from the center. Along with many other examples, this finding was later confirmed by Vera Rubin and her colleagues and has become one of the leading forms of evidence for the existence of dark matter in galaxies.

Handwritten Gregg Shorthand Recognition

Gregg shorthand is a form of stenography that was invented by John Robert Gregg in 1888. Like cursive longhand, it is completely based on elliptical figures and lines that bisect them. Gregg shorthand is the most popular form of pen stenography in the United States and its Spanish adaptation is fairly popular in Latin America. With the invention of dictation machines, shorthand machines, and the practice of executives writing their own letters on their personal computers, the use of shorthand has gradually declined in the business and reporting world. However, Gregg shorthand is still in use today. The need to process documents on paper by computer has led to an area of research that may be referred to as Document Image Understanding (DIU).The goal of DIU system is to convert a raster image representation of a document. For Example, A hand written Gregg shorthand character or word is converted into an appropriate Symbolic Character in a computer (It may be a scanned character or online written character).Thus it involves many disciplines of computer science including image processing, pattern recognition, natural language processing, artificial intelligence, neural networks and database system. The ultimate goal of this paper is to recognize hand written Gregg shorthand character and Gregg shorthand word.

The free librations of Mercury and the size of its inner core

[1] The predicted period of the free libration of Mercury's mantle, if fully decoupled from the core, is approximately 12 yr. If the innermost part of the core is solid, this period is altered and a second free mode is possible. The period of these two modes depend on the mean solar torque acting on the elliptical figures of the mantle and inner core, and also on the gravitational torque they exert on one another. We show that one mode is well approximated by the free gravitational oscillation between the mantle and inner core that would occur in the absence of a solar torque; its period is as small as 4 yr depending on inner core size and other model parameters. The second free mode consists of an in-phase libration of the mantle and inner core. When the inner core is small, the period of this mode coincides with that of the decoupled free mantle libration of 12 yr. However, the period lengthens considerably when the inner core radius is larger than 1000 km, and can be as high as approximately 19 yr if Mercury's core is almost fully solidified. These modes should affect Mercury's libration dynamics at decadal timescale. This suggests that, in principle, constraints on the size of Mercury's inner core may be extracted from its long term libration motion, though in practice this may be difficult given data limitations.

Intermittency in preplanned elbow movements persists in the absence of visual feedback.

It has been observed for nearly 100 years that visually guided human movements appear to be composed of submovements, intermittently executed overlapping segments. This paper presents experiments to investigate the pervasiveness of movement intermittency and, in particular, whether it is exclusively due to visual feedback. With and without visual feedback, human subjects were asked to 1) move with constant velocity and 2) draw elliptical figures on a phase-plane display (showing velocity vs. position) that required cyclic movements at different frequencies. In both tasks, we found that removal of visual feedback did not significantly change movement intermittency. Subjects were unable to generate movements at constant speed. In addition, subjects moved less smoothly when drawing slower phase-plane ellipses. Furthermore, elliptical phase-plane figures were not always drawn at the frequency suggested by the center of the display. Instead, subjects moved more slowly than the tall (fast) ellipse displays suggested, and faster than the wide (slow) displays suggested. These results show that 1) movement intermittency is not exclusively due to visual feedback and 2) may in fact be a fundamental feature of movement behavior.

A quantitative description of dynamic left ventricular geometry in anaesthetized rats using magnetic resonance imaging.

We report a functional application of magnetic resonance imaging (MRI) for the quantitative description of left ventricular geometry through systole and diastole in normal anaesthetized Wistar rats that might be applicable for the analysis of chronic changes resulting from pathological conditions. Images of cardiac anatomy were acquired through planes both parallel and perpendicular to the principal cardiac axis at times that were synchronized to the R wave of the electrocardiogram. The images of the transverse sections were assembled into three-dimensional representations of left ventricular geometry at consecutive time points through the cardiac cycle. This confirmed the geometrical coherence of the data sets, that each slice showed circular symmetry, and that the images were correctly aligned with the appropriate anatomical axes. Different models for the three-dimensional geometry of the left ventricle were then tested against the epi- and endocardial surfaces reconstructed from images of the transverse sections of the left ventricle in both systole and diastole using least-squares minimizations in three dimensions. In agreement with previous reports in the human heart, an elliptical figure of revolution offered an optimal fit to the epicardial and endocardial geometry for the rat heart in diastole. This was in preference to models that used spherical, quartic or parabolic geometries. However, in contrast to contraction in the human heart, all these geometrical representations broke down during systolic ejection in the rat heart. We therefore introduced a more general hybrid model which described left ventricular geometry in terms of the variation of the radii r(z), independently determined for each slice, with its position z along the principal cardiac axis. The resulting function r(z) could then be described by a simple ellipsoid of revolution not only during diastole, but also throughout ventricular ejection. The findings also ruled out alternative geometrical representations. It was then possible additionally to reconstruct the luminal and total left ventricular volumes, wall thicknesses and ejection fractions through the cardiac cycle and to confirm that the predicted total ventricular wall volume was conserved throughout the cardiac cycle. Our hybrid model of cardiac geometry may thus be useful for non-invasive serial studies of chronic pathological changes that use the rat as a model experimental system.

Figural modulation of visuo-spatial neglect: A case study

We report a case of severe left visuo-spatial neglect consequent upon right-hemisphere stroke. In Experiment 1, horizontal and vertical (radial) line bisection is performed; the patient displays left neglect and “altitudinal” (radial) neglect, placing his transections too far to the right and to the top, respectively. In Experiment 2, the patient is required to place a dot at the centre of squares and circles, the horizontal and vertical extents of which are identical to the length of the lines employed in Experiment 1. Performance is now extremely accurate. In Experiment 3, the height of the rectangular or elliptical figure whose midpoint is to be estimated is held constant whilst length varies. In Experiment 4, the length of the figure is held constant whilst height is varied. Both manipulations exert a profound, lawful influence on the patient's estimate of each figure's midpoint. We provide some preliminary hypotheses concerning how configurational constraints may affect perceptual and attentional processes in visual neglect.

Surface Tension in the Developing Mammal: Anisotropic Tension Generation in the Dorsal Skin of the Perinatal Rat

It is common knowledge that skin biopsies retract following excision. The direction and the magnitude of this retraction is thought to be related to the field of tension previously experienced by the skin sections in vivo. We utilized this phenomenon to investigate the ontogeny, directionality, and regulation of skin tension in the perinatal rat from gestational day 20 to postnatal day 6. In this study, geometrically-precise biopsies (circles and rectangles) were excised from the dorsal skin of perinatal rats and placed in tissue culture media. The excised skin sections rapidly exhibited changes in shape (to ellipses and helices). These resulting conformations were characterized with regard to selected spatial attributes; i.e., the ratio of major to minor axes for elliptical figures and the "winding number" for helices. This simple methodological approach allowed the following conclusions: 1) skin retraction in the rat is anisotropic and is maximal in the rostral-caudal direction; 2) skin retraction is inversely related to postnatal age and to ambient temperature; 3) retraction is inhibited by in vivo treatment with epidermal growth factor (EGF) as well as by metabolic poisons such as sodium azide; 4) retraction is augmented in vitro by calcium chloride. Overall, these data support the hypothesis of a metabolically active, temperature-dependent, anisotropically organized retractile mechanism in the dorsal skin of the perinatal rat.

エッジベクトル場における楕円形状検出

エッジベクトル場における楕円形状検出

Seismology and geodesy of the sun: Solar geodesy

Measurements of the elliptical figure of the sun made in 1966 are analyzed on an hourly basis. This analysis yields an improved measure of the previously found solar distortion, rotating rigidly with a sidereal period of 12.38+/-0.10 days. It also yields a set of residùals used to search for signals due to low-frequency solar oscillations.

Study on Cytology of Urinary Transitional Cell Carcinoma

In 1962, Umiker reported the difficulty of cytological diagnosis of voided urine, especially in class III group. Up to the present, it seems that this problem has been not resolved.We performed a statistical analysis and a karyomethric examination using available materials for cytology of Sakai Municipal Hospital from 1974 to 1977. Our statistical data were similar to Umiker's. In 84% we observed desquamated cell clusters in the voided urine of patients with transitional cell carcinoma. Consequently we conducted a karyometry on cells in clusters in the voided urine of patients with transitional cell carcinomas grade III, II, I and false positive. Totally 33 patients were karyometrically examined.The discriminant point between transitional cell carcinoma grade I and grade II was determined by the comparison of nuclear sizes (p<0.01). In examination of two more cells in a transitional cell cluster, if the sum of long diameter and short diameter of a tumor cell nucleus is 2.5 times larger than that of lymphocyte, the cell cluster is considered to belong to transitional cell carcinoma grade II or grade III. The comparison of the nuclear diameters among them, however, did not seem to be easy under microscope. Therefore we tried to convert the length to the dimensions concerning the discriminant point, using the ratio of long diameter/short diameter of the tumor cell nucleus with the size of discriminant point, that of the lymphocyte's nucleus of average size in the urine and the discriminant value of the sum of long and short diameters of tumor cell nucleus.Consequently, in case that observed more than two cells 6 times larger than a lymphocyte's nucleus in a transitional cell cluster, we suspected transitional cell carcinoma grade II or III. But in microscopic examination, when we put lymphocyte's figure on a tumor cell nucleus in the above condition, we are just able to place four lymphocytes on it, because we cannot put six figures of almost circle like lymphocyte on an elliptical figure like a nucleus of transitional cell carcinoma without an unfilled space.In this study the renewed transitional cells with clear cell dysplasia, renal tubular epithelium and glandular epithelium were excluded out of the karyometric examination of transitional cell carcinoma. Additionally we studied on the features of nuclei in all groups of transitional cell carcinomas grade III, II, I, false positive and negative respectively.The result concerning the karyometrical differentiation between transitional cell carcinoma grade I and grade II should be evaluated as a preliminary one, because the condition of desquamated cells, e. g. shrinkage, swelling, or other degenerative changes, could not be uniform as long as we would use the voided urine as materials and because the number of cases examined karyometrically were not enough to settle the conclusion. So we continued to confirm the above results in the practice of urine cytology almost for two years.In other words, we conducted supplementarily the urinocytological examination cytology from January 1978 to October 1979 on the basis of the above results.As result, we obtained more accurate information of urinary cytology in class V, IV, II follow up, II and I. In fact, a correct diagnosis could be made 94% in class V, IV and 83% in class H follow up, while the former 86%, the latter 55% in the previous data. However a correct diagnosis rate became lower in class III.The result in class III suggests that it is very difficult to distinguish between transitional cell carcinoma grade I and hyperplasia of non-malignant transitional epithelium only by the estimation of nuclear sizes.

Functional equivalence of masking and cue reduction in perception of shape at a slant

In a backward masking paradigm Epstein, Hatfield, and Muise (1977) found that presentation of a frontoparallel pattern mask caused the perceived shape of elliptical figures which were rotated in depth to conform to a projective shape function. The current study extended the masking function by examining the effect of a mask which was partially or wholly cotemporal with the target. The study also assessed the functional equivalence of the masking treatment and the conventional treatment for minimizing depth information. Reports of perceived shape and perceived orientation were obtained under three conditions: binocular without mask, binocular with mask, monocular without mask. Under the first condition, perceived shape conformed to objective shape and perceived orientation was proportional to objective orientation. Under the latter two conditions, perceived shape was in very close agreement to projective shape and the two functions did not differ. Orientation was underestimated greatly under both conditions. We concluded that the effect of the mask on perceived shape is mediated by its effect on encoding of orientation information, although an additional effect on the subsequent stage of shape-slant integration cannot be excluded.

Geometric Aid in Teaching Rectilinear Correlation

THE PURPOSE of this paper is to present a simple geometric aid for use in the teaching of rectilinear correlation. The coefficient of correlation may be concerned with the relationship between a number of variables. In the materials to follow, the concern will be with just two variables, X and Y. A c o n v e nient means of indicating the concept of correlation is by a diagram in which the X variable is plotted on the horizontal axis and the Y variable on the ver tical axis. If the points within the axes scatter in an upward direction from left to right, in a manner which indicates that X and Y tend to vary together, a positive correlation is present. If the scatter is downward from left to right, a negative correla tion is present, indicating that X and Y tend to vary inversely. If there appears to be no trend pres ent, then zero correlation is indicated. A convenient way of teaching rectilinear corre lation is to consider the scattering present as de scribing an ellipse. An ellipse is completely de fined by its major and minor axes. The m a j or axis is the long axis, and the minor axis is the short axis. An ellipse varies in shape with two interesting limiting cases. One limit occurs when the major and minor axes are equal; then the fig ure is a circle. The other extreme is when the minor axis is equal to zero and the major axis is finite, in which case we have a straight line. First, plot the points on the correlation chart, or scatter diagram. Thus one obtains an approx imate elliptical figure by drawing a curve which encloses most points and passes through some of the outer points. Next draw a single straight line through the long axis of the figure. This line rep resents the trend of the scattering points. For descriptive purposes this can be handled quickly by inspection of the scatter and crudely drawing a line by hand. (A more precise method would be to draw the lines representing the regression of Y on X and X on Y, and then to use a line which is intermediate between the two to represent the trend. ) This line would be the major axis of the ellipse. The minor axis would be a line drawn perpendicular to this line at its center. Having drawn the scatteringof the points to represent an ellipse, we then determine the mag nitude of t h e relationship. This magnitude could be determined exactly by an appropriate formula available. The approximate magnitude, however, could be ascertained by looking at the ratio of the minor axis to the major axis, provided the two axes are drawn to the same scale. As the minor axis goes to zero (or the major axis gets very large relative to the minor axis), this ratio will also go to zero, and the correlation coefficient will vary toward one. When the minor axis equals zero and the major axis is finite, the ratio also equals zero, the coefficient is one, no spread is present, and we have a single straight line?with perfect corre lation. (An exception occurs when the slope of the line representing the major axis equals zero. In this case, the Y variable equals a constant value for every X, and the line is parallel to the X axis. Thus, there is no change in Y with a change in X; Y remains the same. In this case, even though the minor axis is zero and the ratio is zero, the correlation coefficient would be zero because no

Totalregistrierendes Fadenpendel für die absolute Schwerebestimmung

The thread pendulum previously was found to have remarkable advantages in avoiding systematical errors with regard to absolute gravity determination. To assure, on account of the present claims, the whole force of conviction, full recording of energy transformation seems to be indispensable. Two influences on the period of the pendulum, as yet remained without consideration, habe been treated: theFoucault revolution and the elliptical figure of the swing whenever occurring — which may be considered as a contribution to the movement of the spherical pendulum. In order to prepare the final measurements a number of introducing steps are to be regarded. Le pendule a fil, discute precedemment, a ete trouve superieur a cause de manque des erreurs systematiques pour la determination de la gravite. Au but d'assurer une precision convaincante en raison des pretentions modernes, l'enregistrement total de la transformation energetique est retenue indispensable. Deux influences a la periode oscillatoire du pendule, jusqu'a present restees sans consideration, ont ete examinees: la revolution deFoucault et la figure elliptique d'oscillation. Les deux, proposees comme supplements au mouvement du pendule spherique. En outre la preparation des mesures definitives exige de considerer un nombre de demarches introductives.

On Extending the Compass and Increasing the Tone of Stringed Instruments, with Especial Reference to the Author's and Mr. Meeson's Elliptical Tension-Bars

On Extending the Compass and Increasing the Tone of Stringed Instruments, with Especial Reference to the Author's and Mr. Meeson's Elliptical Tension-Bars