# Geometrical approach to the argumentum of bijection of one coordinate-threshold reflection

( Pp. 26-30)

More about authors

Litvinenko Vitaly Sergeevich
sotrudnik FGUP «NII «KVANT»

Federal State Unitary Enterprise Scientific Research Institute KVANT Nikonov Vladimir G. Doctor of Engineering, Professor; member at the Presidium

Russian Academy of Natural Sciences

Moscow, Russian Federation

Federal State Unitary Enterprise Scientific Research Institute KVANT Nikonov Vladimir G. Doctor of Engineering, Professor; member at the Presidium

Russian Academy of Natural Sciences

Moscow, Russian Federation

Abstract:

The application of threshold operations is the perspective direction of the construction of discrete information processing nodes considering the potential possibility of realization of calculating the scalar product directly in the carrier signal, for instance, perspective optical computing medium. The article analyzes the reflection of bijective binary vectors with simple implementation of both the initial and inverse transformation by means of so-called quasi-hadamard matrices A
n in threshold basis. Currently bijection of such reflection is empirically shown for n = 4, 6, 8, however there was no relevant strict proof. The first relevant proof based on the study of the geometrical properties of the reflection generated by quasi-hadamard matrice A
4 is provided in this work. During the proof it was found that it is unique and possible as proposed only for n = 4. The article highlights the interesting features of its geometrical interpretation together with the proof of important applied statement about bijection of reflection generated by quasi-hadamard matrice A
4.

How to Cite:

Litvinenko V.S., Nikonov V.G., (2015), GEOMETRICAL APPROACH TO THE ARGUMENTUM OF BIJECTION OF ONE COORDINATE-THRESHOLD REFLECTION. Computational Nanotechnology, 4 => 26-30.

Reference list:

Belevitch, V. Theorem of 2n-terminal networks with application to conference telephony. 1950. vol. 26, pp. 231-244.

Goethals, J.M., and Seidel, J.J. Orthogonal matrices with zero diagonal. Canadian Journal of Mathematics. 1967. vol. 19, pp. 1001-1010.

Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. 2003. T. 1, 2.

Nikonov V.G., Sarantsev A.V. Metody kompaktnoy realizatsii biektivnykh otobrazheniy, zadannykh regulyarnymi sistemami odnotipnykh bulevykh funktsiy // Vestnik Rossiyskogo universiteta druzhby narodov. Seriya: Prikladnaya i komp yuternaya matematika. 2003. T. 2. № 1. S. 94-105.

Nikonov V.G., Sarantsev A.V. Postroenie i klassifikatsiya regulyarnykh sistem odnotipnykh funktsiy // Informatsionnye tekhnologii v nauke, obrazovanii, telekommunikatsii i biznese: materialy XXXI Mezhdunarodnoy konferentsii. T. 5 iz Pril. 1. - M.:.Akademiya estestvoznaniya, 2004. S. 173-174.

Nikonov V.G., Sidorov E.S. O sposobe postroeniya vzaimno odnoznachnykh otobrazheniy pri pomoshchi kvaziadamarovykh matrits // Vestnik Moskovskogo gosudarstvennogo universiteta lesa - Lesnoy vestnik. 2009. №2 (65).

Goethals, J.M., and Seidel, J.J. Orthogonal matrices with zero diagonal. Canadian Journal of Mathematics. 1967. vol. 19, pp. 1001-1010.

Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. 2003. T. 1, 2.

Nikonov V.G., Sarantsev A.V. Metody kompaktnoy realizatsii biektivnykh otobrazheniy, zadannykh regulyarnymi sistemami odnotipnykh bulevykh funktsiy // Vestnik Rossiyskogo universiteta druzhby narodov. Seriya: Prikladnaya i komp yuternaya matematika. 2003. T. 2. № 1. S. 94-105.

Nikonov V.G., Sarantsev A.V. Postroenie i klassifikatsiya regulyarnykh sistem odnotipnykh funktsiy // Informatsionnye tekhnologii v nauke, obrazovanii, telekommunikatsii i biznese: materialy XXXI Mezhdunarodnoy konferentsii. T. 5 iz Pril. 1. - M.:.Akademiya estestvoznaniya, 2004. S. 173-174.

Nikonov V.G., Sidorov E.S. O sposobe postroeniya vzaimno odnoznachnykh otobrazheniy pri pomoshchi kvaziadamarovykh matrits // Vestnik Moskovskogo gosudarstvennogo universiteta lesa - Lesnoy vestnik. 2009. №2 (65).

Keywords:

bijective mapping, threshold function, multidimensional cones, quasidemocracy matrix.

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