scholarly journals Students’ Responses To Different Representations Of A Vector Addition Question

2010 ◽  
Author(s):  
Jeffrey M. Hawkins ◽  
John R. Thompson ◽  
Michael C. Wittmann ◽  
Eleanor C. Sayre ◽  
Brian W. Frank ◽  
...  
Keyword(s):  
Vector Addition

Dipole Moments of para-Substituted N-Phenylsulfonyl-N'-Allylthioureas

1995 ◽  
Vol 60 (5) ◽  
pp. 856-862
Author(s):  
Gejza Suchár ◽  
Ivan Danihel
Keyword(s):  
Dipole Moments ◽  
Vector Addition ◽  
Stretching Vibrations

Dipole moments of a series of para-substituted N-phenylsulfonyl-N'-allylthioureas were determined. Comparison of the experimentally found dipole moments with those calculated by vector addition of bond and group moments has shown that (E) conformation at the N-C bonds is preferred. The same result was obtained from the N-H stretching vibrations. The results are compatible with a synperiplanar arrangement at the C-C bond of the allyl moiety.

scholarly journals Vector Arithmetic in the Triangular Grid

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 373
Author(s):  
Khaled Abuhmaidan ◽  
Monther Aldwairi ◽  
Benedek Nagy
Keyword(s):  
Coordinate System ◽  
Triangular Grid ◽  
Vector Addition ◽  
Plane Space ◽  
Physical Simulations ◽  
Rectangular Grids ◽  
Cartesian Coordinate ◽  
Zero Sum ◽  
Coordinate Geometry ◽  
Point Lattice

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

TRANSFORMATION AMPLITUDES FOR VECTOR ADDITION OF ANGULAR MOMENTUM; (j3mm′|j3JM)

1952 ◽  
Vol 30 (3) ◽  
pp. 253-256 ◽  
Author(s):  
G. S. Colladay ◽  
R. E. Sells ◽  
D. L. Falkoff
Keyword(s):  
Angular Momentum ◽  
Quantum Mechanical ◽  
Angular Momenta ◽  
Vector Addition

The transformation amplitudes for the quantum-mechanical vector addition of angular momenta, [Formula: see text] are given.

A r-maximal vector space not contained in any maximal vector space

1978 ◽  
Vol 43 (3) ◽  
pp. 430-441 ◽  
Author(s):  
J. Remmel
Keyword(s):  
Vector Space ◽  
Quotient Space ◽  
Independent Set ◽  
Scalar Multiplication ◽  
Effective Procedure ◽  
Natural Numbers ◽  
Infinite Dimensional ◽  
Vector Addition ◽  
Zero Vector

In [4], Metakides and Nerode define a recursively presented vector space V∞. over a (finite or infinite) recursive field F to consist of a recursive subset U of the natural numbers N and operations of vector addition and scalar multiplication which are partial recursive and under which V∞ becomes a vector space. Throughout this paper, we will identify V∞ with N, say via some fixed Gödel numbering, and assume V∞ is infinite dimensional and has a dependence algorithm, i.e., there is a uniform effective procedure which determines whether any given n-tuple v0, …, vn−1 from V∞ is linearly dependent. Given a subspace W of V∞, we write dim(W) for the dimension of W. Given subspaces V and W of V∞, V + W will denote the weak sum of V and W and if V ∩ W = {0) (where 0 is the zero vector of V∞), we write V ⊕ W instead of V + W. If W ⊇ V, we write W mod V for the quotient space. An independent set A ⊆ V∞ is extendible if there is a r.e. independent set I ⊇ A such that I − A is infinite and A is nonextendible if it is not the case that A is extendible.

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