Properties of Padovan Sequence

Among several types of famous sequences that exist in all branches of mathematics, Padovan sequence is one of such sequences possessing amusing properties. In this paper, we shall discuss about Padovan Sequence and determine a special number called Plastic number. We also derive the ratio of its (n+1)st term to the nth term as n is very large, which is called “Limiting Ratio”. Finally we discuss the geometrical interpretation of the terms of Padovan sequence.

2021 IEEE 5th International Conference on Cryptography, Security and Privacy (CSP) ◽

Analysis and Improvements to the Special Number Field Sieve for Discrete Logarithm Problems

10.1109/csp51677.2021.9357589 ◽

2021 ◽

Author(s):

Liwei Liu ◽

Maozhi Xu ◽

Guoqing Zhou

Keyword(s):

Number Field ◽

Discrete Logarithm ◽

Number Field Sieve ◽

A geometrical interpretation of the addition of nodes to an interpolatory quadrature rule while preserving positive weights

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113430 ◽

2021 ◽

Vol 391 ◽

pp. 113430

Author(s):

L.M.M. van den Bos ◽

B. Sanderse

Keyword(s):

Quadrature Rule ◽

Positive Weights ◽

Interpolatory Quadrature

Geometrical interpretation of the multi-point flux approximation L-method

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.1926 ◽

2009 ◽

Vol 60 (11) ◽

pp. 1173-1199 ◽

Cited By ~ 13

Author(s):

Yufei Cao ◽

Rainer Helmig ◽

Barbara I. Wohlmuth

Keyword(s):

Flux Approximation

Physical and geometrical interpretation of theϵ≤0Szekeres models

Physical Review D ◽

10.1103/physrevd.77.023529 ◽

2008 ◽

Vol 77 (2) ◽

Cited By ~ 28

Author(s):

Charles Hellaby ◽

Andrzej Krasiński

Keyword(s):

Geometrical Interpretation

Why the Auto Doffer Special Number?

Journal of the Textile Machinery Society of Japan ◽

10.4188/jte1955.11.169 ◽

1965 ◽

Vol 11 (5-6) ◽

pp. 169-169

Author(s):

Kiyohisa Fujino

Keyword(s):

The deformation multiplicity of a map germ with respect to a Boardman symbol

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500001244 ◽

2001 ◽

Vol 131 (5) ◽

pp. 1003-1022 ◽

Cited By ~ 5

Author(s):

C. Bivià-Ausina ◽

J. J. Nuño-Ballesteros

Keyword(s):

Algebraic Multiplicity ◽

Homogeneous Map

We define the deformation multiplicity of a map germ f: (Cn, 0) → (Cp, 0) with respect to a Boardman symbol i of codimension less than or equal to n and establish a geometrical interpretation of this number in terms of the set of Σi points that appear in a generic deformation of f. Moreover, this number is equal to the algebraic multiplicity of f with respect to i when the corresponding associated ring is Cohen-Macaulay. Finally, we study how algebraic multiplicity behaves with weighted homogeneous map germs.

Austrian Poetry 1945-1980. Special Number of the Literary Review 25 (Winter 1982)

The German Quarterly ◽

10.2307/405686 ◽

1983 ◽

Vol 56 (2) ◽

pp. 290

Author(s):

Jerry Glenn ◽

Beth Bjorklund ◽

Adolf Opel

Keyword(s):

Algorithms for Stochastic Games with Geometrical Interpretation

Management Science ◽

10.1287/mnsc.15.7.399 ◽

1969 ◽

Vol 15 (7) ◽

pp. 399-415 ◽

Cited By ~ 41

Author(s):

M. A. Pollatschek ◽

B. Avi-Itzhak

Keyword(s):

Stochastic Games ◽

Geometrical Interpretation

SOME ALGEBRAICAL, COMBINATORIAL AND ANALYTICAL PROPERTIES OF PARAGRASSMANN VARIABLES

International Journal of Modern Physics A ◽

10.1142/s0217751x05025127 ◽

2005 ◽

Vol 20 (20n21) ◽

pp. 4797-4819 ◽

Cited By ~ 3

Author(s):

MATTHIAS SCHORK

Keyword(s):

Differential Equations ◽

Fibonacci Numbers ◽

Delta Function ◽

Generalized Fibonacci Numbers ◽

Analytical Properties ◽

Witten Index ◽

Grassmann Variables

Some algebraical, combinatorial and analytical aspects of paragrassmann variables are discussed. In particular, the similarity of the combinatorics involved with those of generalized exclusion statistics (Gentile's intermediate statistics) is stressed. It is shown that the dimensions of the algebras of generalized grassmann variables are related to generalized Fibonacci numbers. On the analytical side, some of the simplest differential equations are discussed and a suitably generalized Berezin integral as well as an associated delta-function are considered. Some remarks concerning a geometrical interpretation of recent results about fractional superconformal transformations involving generalized grassmann variables are given. Finally, a quantity related to the Witten index is discussed.

III. Octonions

Proceedings of the Royal Society of London ◽

10.1098/rspl.1895.0071 ◽

1896 ◽

Vol 59 (353-358) ◽

pp. 169-181

Keyword(s):

Linear Function ◽

Geometrical Interpretation

Octonions is a name adopted for various reasons in place of Clifford’s Bi- quaternions . Formal quaternions are symbols which formally obey all the laws of the quaternion symbols , q (quaternion), x (scalar), ρ (vector) ϕ (linear function in both its ordinary meanings), ϕ' (conjugate of ϕ ), i, j, k, ζ , K q , S q , T q , U q , V q . Octonions are in this sense formal quaternions. Each octonion symbol, however, requires for its specification just double the number of scalars required for the corresponding quaternion symbol. Thus, of every quaternion formula involving the above symbols there is a geometrical interpretation more general than the ordinary quaternion one, an octonion interpretation.