Distances/Vectors
< DistancesIn mathematics and physics, a vector is a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.
Theoretical vectors
Def.
- "a quantity that has both magnitude and direction"[1]
- "the signed difference between two points"[2] or
- an "ordered tuple representing a directed quantity or the signed difference between two points"[2]
is called a vector.
Unit vectors
Notation: let 
denote a unit vector in the ith direction.
Def. a "vector with length 1"[3] is called a unit vector
Force vectors
A force vector is a force defined in two or more dimensions with a component vector in each dimension which may all be summed to equal the force vector. Similarly, the magnitude of each component vector, which is a scalar quantity, may be multiplied by the unit vector in that dimension to equal the component vector.
where 
is the magnitude of the force in the ith direction parallel to the x-axis.
Research
Hypothesis:
- For a vector, the direction can be stated and the magnitude is arbitrary.
Control groups
The findings demonstrate a statistically systematic change from the status quo or the control group.
“In the design of experiments, treatments [or special properties or characteristics] are applied to [or observed in] experimental units in the treatment group(s).[4] In comparative experiments, members of the complementary group, the control group, receive either no treatment or a standard treatment.[5]"[6]
Proof of concept
Def. a “short and/or incomplete realization of a certain method or idea to demonstrate its feasibility"[7] is called a proof of concept.
Def. evidence that demonstrates that a concept is possible is called proof of concept.
The proof-of-concept structure consists of
- background,
- procedures,
- findings, and
- interpretation.[8]
See also
References
- ↑ Paul G (22 December 2003). "vector, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-08-10.
- 1 2 "vector, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. 24 July 2015. Retrieved 2015-08-10.
- ↑ "unit vector, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. Retrieved 2015-08-10.
- ↑ Klaus Hinkelmann, Oscar Kempthorne (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (2nd ed.). Wiley. ISBN 978-0-471-72756-9. http://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover.
- ↑ R. A. Bailey (2008). Design of comparative experiments. Cambridge University Press. ISBN 978-0-521-68357-9. http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579.
- ↑ "Treatment and control groups, In: Wikipedia". San Francisco, California: Wikimedia Foundation, Inc. May 18, 2012. Retrieved 2012-05-31.
- ↑ "proof of concept, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. November 10, 2012. Retrieved 2013-01-13.
- ↑ Ginger Lehrman and Ian B Hogue, Sarah Palmer, Cheryl Jennings, Celsa A Spina, Ann Wiegand, Alan L Landay, Robert W Coombs, Douglas D Richman, John W Mellors, John M Coffin, Ronald J Bosch, David M Margolis (August 13, 2005). "Depletion of latent HIV-1 infection in vivo: a proof-of-concept study". Lancet 366 (9485): 549-55. doi:10.1016/S0140-6736(05)67098-5. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1894952/. Retrieved 2012-05-09.
External links
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