Determination of All Systems of Equations Which Admit a Given $$r$$ r -term Group

2015 ◽  
pp. 235-255
Author(s):  
Sophus Lie
Keyword(s):  
Systems Of Equations

Synthesis of Planetary Gears by Means of Artificial Intelligence Approach ‒ Graph-Theoretical Modeling

2010 ◽  
Vol 164 ◽  
pp. 243-248 ◽  
Author(s):  
Józef Drewniak ◽  
Stanisław Zawiślak
Keyword(s):  
Research Work ◽  
Planetary Gear ◽  
Systems Of Equations ◽  
Modes Of Operation ◽  
Planetary Gears ◽  
Intelligence Approach ◽  
Artificial Intelligence Approach ◽  
Selection Of ◽  
Structure Layout

Graph-based modeling of planetary gears was applied in the presented research work for their synthesis. The tailored Hsu and contour graphs were used. Graphs encode the structure (layout) of a planetary gear and upon them - the systems of equations can be generated. These systems enable determination of rotational velocities of planetary gear elements. The method is algorithmic and simple. It allows for an easy comparison of different design solutions and selection of the most appropriate one. The list of the possible modes of operation for an exemplary planetary gear is also provided in the paper.

On the determination of the zones of influence and dependence for three-dimensional boundary-layer equations

1971 ◽  
Vol 48 (2) ◽  
pp. 397-404 ◽  
Author(s):  
K. C. Wang
Keyword(s):  
Boundary Layer ◽  
Hyperbolic System ◽  
Parabolic System ◽  
Three Dimensional ◽  
Similar Type ◽  
Systems Of Equations ◽  
Boundary Layer Equations ◽  
General Systems ◽  
Dimensional Boundary

The zones of influence and dependence for three-dimensional boundary-layer equations first studied by Raetz are re-examined from the viewpoint of the subcharacteristics. It is shown that in contrast, the zones of influence and dependence for a totally hyperbolic system are determined by the characteristics; for the present parabolic system of three-dimensional boundary-layer equations, the zones are determined by the characteristics and subcharacteristics. The same idea should be applicable to more general systems of equations of similar type.

scholarly journals Water waves over arrays of horizontal cylinders: band gaps and Bragg resonance

2011 ◽  
Vol 670 ◽  
pp. 504-526 ◽  
Author(s):  
C. M. LINTON
Keyword(s):  
Band Gap ◽  
Water Waves ◽  
Band Gaps ◽  
Circular Cylinders ◽  
Approximate Determination ◽  
Systems Of Equations ◽  
Periodic Arrays ◽  
Horizontal Cylinders ◽  
Band Gap Structure

The existence of a band-gap structure associated with water waves propagating over infinite periodic arrays of submerged horizontal circular cylinders in deep water is established. Waves propagating at right angles to the cylinder axes and at an oblique angle are both considered. In each case an exact linear analysis is presented with numerical results obtained by solving truncated systems of equations. Calculations for large finite arrays are also presented, which show the effect of an incident wave having a frequency within a band gap – with the amount of energy transmitted across the array tending to zero as the size of the array is increased. The location of the band gaps is not as predicted by Bragg's law, but we show that an approximate determination of their position can be made very simply if the phase of the transmission coefficient for a single cylinder is known.

scholarly journals Modelling hydraulic mixture movement along the extraction chamber bottom in case of hydraulic washout of the tuff-stone

2020 ◽  
Vol 201 ◽  
pp. 01011 ◽  
Author(s):  
Zinovii Malanchuk ◽  
Viktor Moshynskyi ◽  
Petro Martyniuk ◽  
Sergii Stets ◽  
Daniyar Galiyev
Keyword(s):  
Process Performance ◽  
Contact Strength ◽  
Systems Of Equations ◽  
Mixture Flow ◽  
Volcanic Tuff ◽  
Hydraulic Mining ◽  
Extraction Chamber ◽  
Transportation Capacity ◽  
Chamber Bottom

This paper presents the research results of the pulp movement process along the extraction chamber bottom to the suction pipe of the pulp lifting device in case of downhole hydraulic mining the volcanic tuff-stone. The washout process and hydraulically operated transportation of the tuff-stone hydraulic mixture, when forming the extraction chamber, have been studied under various conditions and methods of exposure. As a result, the dominant parameters have been determined influencing the hydrodynamic washout technology as well as tuff-stone hydraulic mixture lifting to the alluviation map. The dependences have been substantiated of the washout process performance and transportation capacity of the hydraulic mixture flow on the determined parameters. To calculate the process of pulp flow-over along the extraction chamber bottom to the intaking hydraulic elevator headwall, the systems of equations have been determined based on the modelling the movement of tuff-stone hydraulic mixture along the extraction chamber bottom during hydraulic washout. The dependences of the contact strength of the tuff-stone samples mined by downhole method on the time spent in water are presented, resulting in determination of the tuff-stone weakening coefficient and the degree of its saturation with water.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

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