scholarly journals A Small Correction to a Paper of Vandermonde

2021 ◽  
Vol 11 (02) ◽  
pp. 43-53
Author(s):  
Matthew Davis ◽  
Shiv K. Gupta
Keyword(s):  
Small Correction

Rapid horizontal gaze movement in the monkey

1995 ◽  
Vol 73 (4) ◽  
pp. 1632-1652 ◽  
Author(s):  
J. O. Phillips ◽  
L. Ling ◽  
A. F. Fuchs ◽  
C. Siebold ◽  
J. J. Plorde
Keyword(s):  
Eye Movement ◽  
Head Movement ◽  
Vertical Axis ◽  
Head Position ◽  
Head Movements ◽  
Gaze Shifts ◽  
Gaze Shift ◽  
The Gaze ◽  
Small Correction ◽  
Horizontal Gaze

1. We studied horizontal eye and head movements in three monkeys that were trained to direct their gaze (eye position in space) toward jumping targets while their heads were both fixed and free to rotate about a vertical axis. We considered all gaze movements that traveled > or = 80% of the distance to the new visual target. 2. The relative contributions and metrics of eye and head movements to the gaze shift varied considerably from animal to animal and even within animals. Head movements could be initiated early or late and could be large or small. The eye movements of some monkeys showed a consistent decrease in velocity as the head accelerated, whereas others did not. Although all gaze shifts were hypometric, they were more hypometric in some monkeys than in others. Nevertheless, certain features of the gaze shift were identifiable in all monkeys. To identify those we analyzed gaze, eye in head position, and head position, and their velocities at three points in time during the gaze shift: 1) when the eye had completed its initial rotation toward the target, 2) when the initial gaze shift had landed, and 3) when the head movement was finished. 3. For small gaze shifts (< 20 degrees) the initial gaze movement consisted entirely of an eye movement because the head did not move. As gaze shifts became larger, the eye movement contribution saturated at approximately 30 degrees and the head movement contributed increasingly to the initial gaze movement. For the largest gaze shifts, the eye usually began counterrolling or remained stable in the orbit before gaze landed. During the interval between eye and gaze end, the head alone carried gaze to completion. Finally, when the head movement landed, it was almost aimed at the target and the eye had returned to within 10 +/- 7 degrees, mean +/- SD, of straight ahead. Between the end of the gaze shift and the end of the head movement, gaze remained stable in space or a small correction saccade occurred. 4. Gaze movements < 20 degrees landed accurately on target whether the head was fixed or free. For larger target movements, both head-free and head-fixed gaze shifts became increasingly hypometric. Head-free gaze shifts were more accurate, on average, but also more variable. This suggests that gaze is controlled in a different way with the head free. For target amplitudes < 60 degrees, head position was hypometric but the error was rather constant at approximately 10 degrees.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Qibla Direction Correction Test using a Digital Compass and Arduino Microcontroller

2019 ◽  
Vol 8 (2S7) ◽  
pp. 228-230
Keyword(s):  
Spherical Trigonometry ◽  
Arabic Word ◽  
Small Correction ◽  
Arduino Microcontroller ◽  
Yogyakarta City

Qibla is an Arabic word that refers to the direction in which a Muslim establishes prayer. In this study, we made a Qibla-based digital compass and Arduino microprocessor construction. The spherical trigonometry method is used to find out the direction of the Qibla by getting cross lines and longitude. While the direction of the qibla is obtained with the help of a digital compass. The testing of this tool was carried out at the mosque in Indonesia. The results showed that the direction of the Qibla for the Nur Asmaul Husna Mosque (Banten Province) is located at 295.2077026o with a correction of -0.06o . Gedhe Kauman Mosque is (Yogyakarta City) located at 294.7148437owith a correction of -0.35o and the Jami Nurul Muminin mosque is located at 294.0274353o with a correction of -9.74o . A small correction value indicates the accuracy of the Qibla direction

Integration of one-dimensional equations of motions

2020 ◽  
pp. 79-90
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Potential Energy ◽  
Field Change ◽  
One Dimensional ◽  
System A ◽  
Small Correction ◽  
The Law ◽  
The One ◽  
The Given ◽  
Equations Of Motions

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

scholarly journals Small Correction

1986 ◽  
Vol 148 (6) ◽  
pp. 753-753
Author(s):  
Eric W. Fine
Keyword(s):  
Small Correction

scholarly journals The ACCELERATION programme: I. Cosmology with the redshift drift

2019 ◽  
Vol 492 (2) ◽  
pp. 2044-2057
Author(s):  
Ryan Cooke
Keyword(s):  
Local Density ◽  
Current Data ◽  
Cosmological Redshift ◽  
Star Forming ◽  
Star Forming Regions ◽  
Neutral Gas ◽  
Small Correction ◽  
Redshift Drift ◽  
Universal Expansion ◽  
Order Of Magnitude

ABSTRACT Detecting the change of a cosmological object’s redshift due to the time evolution of the Universal expansion rate is an ambitious experiment that will be attempted with future telescope facilities. In this paper, we describe the ACCELERATION programme, which aims to study the properties of the most underdense regions of the Universe. One of the highlight goals of this programme is to prepare for the redshift drift measurement. Using the EAGLE cosmological hydrodynamic simulations, we estimate the peculiar acceleration of gas in galaxies and the Lyα forest. We find that star-forming ‘cold neutral gas’ exhibits large peculiar acceleration due to the high local density of baryons near star-forming regions. We conclude that absorption by cold neutral gas is unlikely to yield a detection of the cosmological redshift drift. On the other hand, we find that the peculiar accelerations of Lyα forest absorbers are more than an order of magnitude below the expected cosmological signal. We also highlight that the numerous low H i column density systems display lower peculiar acceleration. Finally, we propose a new ‘Lyα cell’ technique that applies a small correction to the wavelength calibration to secure a relative measurement of the cosmic drift between two unrelated cosmological sources at different redshifts. For suitable combinations of absorption lines, the cosmological signal can be more than doubled, while the affect of the observer peculiar acceleration is mitigated. Using current data of four suitable Lyα cells, we infer a limit on the cosmological redshift drift to be $\dot{v}_{\rm obs}\lt 65~{\rm m~s}^{-1}~{\rm yr}^{-1}$ (2σ).

KLEIN–DUNHAM POTENTIAL ENERGY FUNCTIONS IN SIMPLIFIED ANALYTICAL FORM

1960 ◽  
Vol 38 (2) ◽  
pp. 217-230 ◽  
Author(s):  
W. R. Jarmain
Keyword(s):  
Potential Energy ◽  
Equivalent Form ◽  
Analytical Form ◽  
Spectroscopic Constants ◽  
Dissociation Limit ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Small Correction ◽  
Correction Terms ◽  
Surprising Discovery

A simple formula, based originally on the work of Klein and Rees, is developed for calculating potential energy curves, except near the dissociation limit, for electronic states of diatomic molecules. Classical turning points r1,2 are given as functions of vibrational quantum number (V ≡ ν + 1/2), with coefficients depending on observed spectroscopic constants, in the form[Formula: see text]where[Formula: see text]For most states convergence is rapid, but as a rule more so for heavy molecules than for light molecules. Assuming it to be close to the 'true' potential, such a representation affords a convenient means of assessing the accuracy of the Morse or other empirical potential function. Morse curves have also been fitted by least squares to Klein–Rees turning points.Term-by-term comparison between the inverted Dunham series and an equivalent form of the above has led to the surprising discovery that if Dunham's small correction terms are neglected, Klein and Dunham potentials are mathematically identical. This is contrary to the generally held belief that the two should be used in mutually exclusive regions. In the present form these series exhibit better behavior over a wider range than a series giving potential energy as a function of internuclear separation.

Small correction required when applying the Hertzian contact model to instrumented indentation data

2001 ◽  
Vol 16 (5) ◽  
pp. 1280-1286 ◽  
Author(s):  
J. L. Hay ◽  
P. J. Wolff
Keyword(s):  
Mechanical Properties ◽  
Contact Model ◽  
Hertzian Contact ◽  
Test Material ◽  
Contact Radius ◽  
Test Surface ◽  
Instrumented Indentation ◽  
Hardness Testing ◽  
Small Correction ◽  
Hertzian Contact Model

Instrumented indentation testing (IIT) is a relatively new form of mechanical testing which significantly expands on the capabilities of traditional hardness testing. In an IIT experiment, an indenter of known mechanical properties is pressed into contact and then withdrawn from a test material. The fundamental measurements during an IIT experiment are the applied load and the resulting penetration of the indenter into the test surface. The Hertzian contact model, or a derivative thereof, is often employed to relate these measurements to interesting mechanical properties of the test material. This article argues for a small correction to the Hertzian contact model when applied to instrumented indentation data. The magnitude of the correction primarily depends on Poisson's ratio of the test material and the contact radius normalized by the radius of the indenter tip. Neglecting this correction can cause significant errors in the calculation of elastic modulus and hardness from instrumented indentation data.

scholarly journals Quantum mechanical effects in reactions involving hydrogen

1935 ◽  
Vol 148 (864) ◽  
pp. 241-250 ◽  
Keyword(s):  
Correction Term ◽  
Classical Mechanics ◽  
Potential Curve ◽  
Quantum Mechanical ◽  
Small Correction ◽  
Classical Behaviour ◽  
The Difference ◽  
Quantum Mechanical Effects ◽  
Simple Equations ◽  
Approximate Treatment

It has been shown in a previous paper that classical mechanics are not adequate to treat the transition of a hydrogen atom or proton across an energy barrier of the dimensions commonly met with in chemical reaction. The treatment given was based on an exact solution of the Schrödinger equation and a type of potential curve having no discontinuities in slope, but owing to the laborious nature of the computations involved, no attempt was made to investigate quantitatively the effect of variations in the heat of activation, the width of the barrier, or the mass of the particle. The present paper describes an approximate treatment leading to simple equations which can be applied directly to investigate these points. In a recent paper, Wigner has given a method of treatment applicable to any form of potential curve. His final equations are, however, only valid for the case in which the difference between the quantum mechanical and classical results can be expressed as a small correction term, and cannot be applied when there are large deviations from classical behaviour.

Quadronium and quantum electrodynamics

1996 ◽  
Vol 74 (7-8) ◽  
pp. 527-533 ◽  
Author(s):  
James J. Griffin
Keyword(s):  
Quantum Electrodynamics ◽  
Composite Particle ◽  
Bound State ◽  
Heavy Ion ◽  
Annihilation Rate ◽  
Small Correction ◽  
Order Matrix Element ◽  
Nucleus Scattering ◽  
Electron Magnetic Moment ◽  
Rule Out

The composite-particle scenario is a phenomenology that can organize the data of the "sharp lepton problem" posed by heavy-ion and (β+ + atom) studies. It hypothesizes a new composite particle (of mass ~3mc2) as the source of the observed sharp energy (e+e−) decay pairs. Available data rule out the possibilities that the source is a new elementary particle or that it is a quasi-bound state of (e+e−). Occam's razor therefore currently favors the quadronium structure, Q0 = (e+e+e−e−). Implications of quadronium for high-precision quantum electrodynamics (QED) are considered, and calculated and (or) measured deviations in QED that are sensitive to the existence of Q0 are identified. In particular, for the electron magnetic-moment anomaly, a(e) = (ge − 2)/2, a Q0–pole effects a small correction to the contributions of O(α4), which is therefore small compared to the largest current (theoretical) uncertainty. For photon–photon scattering, Q0 corrects the leading order matrix element, and allows resonant Q0 creation in photon–nucleus scattering. Finally, a Q0 bound state corrects the O(α) correction to the leading 3γ annihilation rate of triplet positronium. Therefore Q0 may contribute significantly to this decay rate, which is currently in a 10σ discrepancy with experiment. A current experimental gap is the lack of corroborative data on the sharp (Γ ≤ 2.1 keV) 330.1 keV electrons reported by Sakai from irradiations of U and Th with β+-decay positrons. A study of these (and (or) their expected partner positrons of the same energy) in collisions of (~3 MeV) beam positrons (or electrons) upon high-Z neutral atoms could fill this gap. Similar studies with positrons of 660–795 keV would test the expectation that recoilless resonance creation of the Q0 source of these pairs is also possible.

The loss of activity of pyrethrum. II

1934 ◽  
Vol 24 (4) ◽  
pp. 598-626 ◽  
Author(s):  
F. Tattersfield ◽  
J. T. Martin
Keyword(s):  
The Other ◽  
Acid Method ◽  
Small Correction ◽  
Two Samples ◽  
Residual Amount ◽  
Before And After ◽  
Artificial Illumination

Summary1. The loss of activity of pyrethrum flowers and preparations has been studied.2. The degree of concordance between the content of pyrethrin I, as determined by the acid method, and the insecticidal value of pyrethrinised dusts, before and after exposure to air and artificial illumination, has been statistically examined. The pyrethrin I values, corrected for a small residual amount of extraneous matter, indicate fairly closely the degree of activity of the samples. The loss of pyrethrins on exposure has been traced out quantitatively.3. A comparison was made between two samples of pyrethrum flowers, one rich and the other poor in pyrethrins, in order to determine the degree of concordance between the pyrethrin I content and their toxicity. The pyrethrin I value as determined by the acid method, subject to a small correction, gave a good indication of the relative activities of the samples.

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