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### Towards Grounding of Formulae

Takuto Asakura, André Greiner-Petter, Akiko Aizawa, Yusuke Miyao
2020 Proceedings of the First Workshop on Scholarly Document Processing   unpublished
This flexibility makes it difficult to extract the exact meaning of a mathematical formula. In this project, we will propose a new task direction for grounding mathematical formulae.  ...  A large amount of scientific knowledge is represented within mixed forms of natural language texts and mathematical formulae.  ...  Grounding of Formulae In order to describe the grounding of formulae precisely, we introduce a few linguistic terms for formulae, roughly borrowing from morphology in natural languages (Nida, 1949) :  ...

### The Equivalent Circuits of Composite Lines in the Steady State

A. E. Kennelly
1909 Proceedings of the American Academy of Arts and Sciences
A particular case of this kind is shown in Figure 14 In order to compute the equivalent l~l, ground the line at one end, as at A2 (Figure 14) , and develop the line-angles towards H by preced ing formula  ...  Let us ground the end A2 of the composite line A2D2 (Figure 7). Then by formula (12), the sending-end resistance at B of the section BA grounded, of the section AB, at its end B, is SB = 2 hyps.  ...  Trav erse Tables as used by navigators may also be used with advantage for the resolution of vectors into complex quantities. The following formulas are also useful:  ...

### Page 5 of The Trend in Engineering Vol. 12, Issue 3 [page]

1960 The Trend in Engineering
This supersedes the writer’s efforts to equate intensity as a function of acceleration and period in the 1954 booklet entitled Earthquake Intensity and Related Ground Motion.t| The present attitude toward  ...  of the maximum vibrational velocity of the ground mo- tion.  ...

### Toward a generalization of the logic of grounding

Francesca Poggiolesi, Nissim Francez
2020 THEORIA : an International Journal for Theory, History and Fundations of Science
Such ground-analysis not only serves to extend the applicability of the logic of grounding but also leads to a generalization of [Poggiolesi, 2016]'s definition of the notion of complete and immediate  ...  grounding.  ...  Similar points hold for formulas of the form A, ¬A, where A is either a conjunction or a disjunction: the complexity of the latter Towards a generalization of the logic of grounding cannot be counted as  ...

### Page 380 of The Quarterly Journal of Economics Vol. 39, Issue 3 [page]

1925 The Quarterly Journal of Economics
Newton’s inspired idea was that the moon is all the time falling toward the earth, and that the law or formula of its fall might be the same as that which Galileo had found for the fall of objects toward  ...  the familiar movement of things falling to the ground.  ...

### Page 56 of Daedalus Vol. 45, Issue 3 [page]

1909 Daedalus
To compute the equivalent M of a composite line of m successive sections, ground the line at the A end and develop the line-angles towards the opposite end, following the process of (76).  ...  The process must be repeated after ground- ing the line at the distant end and developing line-angles towards A.  ...

### Page 68 of Manufacturing Engineering Vol. 14, Issue 11 [page]

1944 Manufacturing Engineering
Below are formulas for de- termining movement of roll C toward A and B, where D is equal to the amount ground off. Where one side of the Vee is ground !  ...  Determining the proper front clearance, so that regrinding the face of the tool will not change the form, is-easily done by applying a formula whereby the tangent of the tip up clearance an- gle is multiplied  ...

### Derivation of Special Relativity Transformation Formulas Without Time Slowing and Length Shrinking——Modification of Relativistic Aberration Formula

Sheng Qin
2022 Zenodo
frequency shift formula of the special theory of relativity, the moving mass formula and the velocity transformation formula in the special theory of relativity can be obtained.  ...  At the same time, the biggest innovation of this paper is: (1) The preconditions of the Doppler frequency shift formula are supplemented, and it is pointed out that the Doppler frequency shift formula  ...  annihilate each other to generate two photons of frequency  , which are respectively directed towards the X-axis of the S system.  ...

### Derivation of Special Relativity Transformation Formulas Without Time Slowing and Length Shrinking:Modification of Relativistic Aberration Formula.pdf

Sheng Qin
2022 figshare.com
frequency shift formula of the special theory of relativity, the moving mass formula and the velocity transformation formula in the special theory of relativity can be obtained.  ...  At the same time, the biggest innovation of this paper is: (1) The preconditions of the Doppler frequency shift formula are supplemented, and it is pointed out that the Doppler frequency shift formula  ...  annihilate each other to generate two photons of frequency  , which are respectively directed towards the X-axis of the S system.  ...

### Page 157 of American Meteorological Journal; A Monthly Review of Meteorology and Allied Branches of Study Vol. 4, Issue 4 [page]

1887 American Meteorological Journal; A Monthly Review of Meteorology and Allied Branches of Study
In Part VI we find the temperature extremes of the surface of the ground observed on five minimum thermometers, one on a flat surface and the other four on surfaces having a slope of 45° toward the four  ...  Part IX contains the height of the water at the ground ob- served at 11:30 a. m. on each day of the year. In the appendix Mr.  ...

### Page 198 of AT&T Technical Journal Vol. 27, Issue 2 [page]

1948 AT&T Technical Journal
The use of space diversity may be essential in those localities where strong ground reflections are present.  ...  The formulas will orient the reader in regard to the importance of quantities such as: = Repeater separation Wavelength of signal >same units of length Effective area of each antenna | Noise figure of  ...

### Page 505 of American Water Works Association. Journal Vol. 36, Issue 5 [page]

1944 American Water Works Association. Journal
I Length of well screen, depth of flow toward well, or thickness of water-bearing formation, in feet. S = Angle of slope of ground in de- grees (approximately parallel to the water table).  ...  of the surface or water table, and the length of the screen or depth of flow toward the well.  ...

### Page 632 of Proceedings of the American Philosophical Society Vol. 95, Issue 6 [page]

1951 Proceedings of the American Philosophical Society
(This chapter contains the 185 formulas which the Adhvaryu recites when he places the 185 bricks of the fire-altar, and the 8 formulas which he recites when he puts sand on one of the lines of the ground  ...  ninth or outermost line of that ground, the fifteen bricks that represent the 15 days of the bright fortnight of the month, with the 15 formulas “Samjnana, Vijhana,”’ etc.  ...

### Page 11 of American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers Vol. 78, Issue [page]

1952 American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers
of Technology, was directed toward improvement of the then current design rules.  ...  Although rigorous solutions are possible for particular ground motions applied to particular structures, these solutions are too involved and of too limited significance to be of direct value to the structural  ...

### Heat Transfer via Unconditioned Spaces: The Influence of the Adjustment Factor Evaluation Method

Stefano Bergero, Anna Chiari
2019 TECNICA ITALIANA-Italian Journal of Engineering Science
In the latter case, the influence of thermal bridges between unconditioned rooms (cellars, attics, stairwells) and the outside and the ground is also considered.  ...  of the UNI/TS 11300-1 standard.  ...  ACKNOWLEDGMENT This research was funded by the University of Genoa research project PRA2017.  ...
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