On Recurrence Formulae of Solid Spherical Monogenics

2008 ◽  
Author(s):  
S. Bock ◽  
K. Gürlebeck
Keyword(s):  
Spherical Monogenics ◽  
Recurrence Formulae

scholarly journals UNIVERSAL CALABI–YAU ALGEBRA: TOWARDS AN UNIFICATION OF COMPLEX GEOMETRY

2003 ◽  
Vol 18 (30) ◽  
pp. 5541-5612 ◽  
Author(s):  
F. ANSELMO ◽  
J. ELLIS ◽  
D. V. NANOPOULOS ◽  
G. VOLKOV
Keyword(s):  
Lie Algebras ◽  
Complex Geometry ◽  
Algebraic Approach ◽  
Higher Dimensions ◽  
Normal Algebra ◽  
Natural Extensions ◽  
Recurrence Formulae ◽  
Different Dimensions ◽  
Arbitrary Dimensions

We present a universal normal algebra suitable for constructing and classifying Calabi–Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions, related to Batyrev's reflexive polyhedra, and their n-ary combinations. It also includes a "dual" construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi–Yau spaces in arbitrary dimensions with Weierstrass, K3, etc., fibrations. Our approach also yields simple algebraic relations between chains of Calabi–Yau spaces in different dimensions, and concrete visualizations of their singularities related to Cartan–Lie algebras. This Universal Calabi–Yau algebra is a powerful tool for deciphering the Calabi–Yau genome in all dimensions.

(iv) Note on the Recurrence Formulae for the Moments of the Point Binomial

Biometrika ◽  
1934 ◽  
Vol 26 (1-2) ◽  
pp. 261-264
Author(s):  
A. A. K. AYYANGAR
Keyword(s):  
Recurrence Formulae

scholarly journals Hyper-Wiener indices of polyphenyl chains and polyphenyl spiders

2019 ◽  
Vol 17 (1) ◽  
pp. 668-676
Author(s):  
Tingzeng Wu ◽  
Huazhong Lü
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Wiener Index ◽  
Upper And Lower Bounds ◽  
Extremal Graphs ◽  
Recurrence Formulae

Abstract Let G be a connected graph and u and v two vertices of G. The hyper-Wiener index of graph G is $\begin{array}{} WW(G)=\frac{1}{2}\sum\limits_{u,v\in V(G)}(d_{G}(u,v)+d^{2}_{G}(u,v)) \end{array}$, where dG(u, v) is the distance between u and v. In this paper, we first give the recurrence formulae for computing the hyper-Wiener indices of polyphenyl chains and polyphenyl spiders. We then obtain the sharp upper and lower bounds for the hyper-Wiener index among polyphenyl chains and polyphenyl spiders, respectively. Moreover, the corresponding extremal graphs are determined.

scholarly journals Recurrence Formulae for the Functions which represent Solutions of the Differential Equation:

1914 ◽  
Vol 33 ◽  
pp. 107-117
Author(s):  
H. T. Flint
Keyword(s):  
Differential Equation ◽  
Positive Integer ◽  
In Series ◽  
Recurrence Formulae ◽  
Image Position

The contents of this paper were suggested by a discussion of the equation:in a paper by Glaisher which appears in the Philosophical Transactions, 1881, Part III.The solutions in series of (1) are:and in the paper referred to it is shewn that the coefficients of hp+1 in the expansions of and of satisfy equation (1) when p is a positive integer.

scholarly journals Orthogonal basis for spherical monogenics by step two branching

2011 ◽  
Vol 41 (2) ◽  
pp. 161-186 ◽  
Author(s):  
R. Lávička ◽  
V. Souček ◽  
P. Van Lancker
Keyword(s):  
Orthogonal Basis ◽  
Spherical Monogenics
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