Analytical expansion of the earth's zonal potential in terms of ks regular elements

1997 ◽  
Vol 66 (2) ◽  
pp. 181-190 ◽  
Author(s):  
M.A. Sharaf ◽  
A.S. Saad
Keyword(s):  
Regular Elements ◽  
Analytical Expansion ◽  
Ks Regular Elements

scholarly journals Zonal Harmonics of the Gravity Field in Def-Variables

1999 ◽  
Vol 172 ◽  
pp. 455-456
Author(s):  
Ignacio Aparicio ◽  
Luis Floría
Keyword(s):  
Gravity Field ◽  
Celestial Mechanics ◽  
Elliptic Type ◽  
Eccentric Anomaly ◽  
Regular Elements ◽  
Zonal Harmonics ◽  
Satellite Problem ◽  
Independent Variable ◽  
Analytical Expansion ◽  
Ks Regular Elements

To take advantage of the linear and regular formulation and treatment of Celestial Mechanics problems (Kustaanheimo & Stiefel 1965; Stiefel & Scheifele 1971; Deprit, Elipe & Ferrer 1994), Sharaf & Saad (1997) have given an analytical expansion of the Earth’s gravitational zonal potential in terms of Kustaanheimo-Stiefel (KS) regular elements (Stiefel & Scheifele 1971, §19), with special emphasis on its application to elliptic-type two-body orbits and, consequently, using a generalized (elliptic) eccentric anomaly as the independent variable.Motivated by these and other considerations based on the definition and use of KS elements, and following a treatment similar to that of Stiefel & Scheifele (1971, §19), we develop element equations corresponding to a DEF-formulation of the satellite problem under the effect of the zonal potential.

scholarly journals THE SMOOTHNESS OF ORBITAL MEASURES ON NONCOMPACT SYMMETRIC SPACES

2021 ◽  
pp. 1-20
Author(s):  
SANJIV KUMAR GUPTA ◽  
KATHRYN E. HARE
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Continuous Measure ◽  
Convolution Product ◽  
Absolutely Continuous ◽  
Regular Elements ◽  
Connected Subgroup ◽  
Decay Properties ◽  
Absolutely Continuous Measure ◽  
Special Case

Abstract Let $G/K$ be an irreducible symmetric space, where G is a noncompact, connected Lie group and K is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$ continuous orbital measures has its density function in $L^{2}(G)$ and hence is an absolutely continuous measure with respect to the Haar measure. The number r is approximately the rank of $G/K$ . For the special case of the orbital measures, $\nu _{a_{i}}$ , supported on the double cosets $Ka_{i}K$ , where $a_{i}$ belongs to the dense set of regular elements, we prove the sharp result that $\nu _{a_{1}}\ast \nu _{a_{2}}\in L^{2},$ except for the symmetric space of Cartan class $AI$ when the convolution of three orbital measures is needed (even though $\nu _{a_{1}}\ast \nu _{a_{2}}$ is absolutely continuous).

scholarly journals ON MATRIX KP AND SUPER-KP HIERARCHIES IN THE HOMOGENEOUS GRADING

1996 ◽  
Vol 11 (18) ◽  
pp. 3257-3295 ◽  
Author(s):  
F. TOPPAN
Keyword(s):  
Power Series ◽  
Symmetric Spaces ◽  
Unexpected Result ◽  
Hermitian Symmetric Spaces ◽  
Regular Elements ◽  
Symmetry Properties ◽  
Alternating Sums ◽  
Spectral Parameter Power Series ◽  
Special Limit ◽  
Free Parameters

Constrained KP and super-KP hierarchies of integrable equations (generalized NLS hierarchies) are systematically produced through a Lie-algebraic AKS matrix framework associated with the homogeneous grading. The role played by different regular elements in defining the corresponding hierarchies is analyzed, as well as the symmetry properties under the Weyl group transformations. The coset structure of higher order Hamiltonian densities is proven. For a generic Lie algebra the hierarchies considered here are integrable and essentially dependent on continuous free parameters. The bosonic hierarchies studied in Refs. 1 and 2 are obtained as special limit restrictions on Hermitian symmetric spaces. In the supersymmetric case the homogeneous grading is introduced consistently by using alternating sums of bosons and fermions in the spectral parameter power series. The bosonic hierarchies obtained from [Formula: see text] and the supersymmetric ones derived from the N=1 affinization of sl (2), sl (3) and osp (1|2) are explicitly constructed. An unexpected result is found: only a restricted subclass of the sl (3) bosonic hierarchies can be supersymmetrically extended while preserving integrability.

scholarly journals Simplex algebras and their representation

1973 ◽  
Vol 14 (2) ◽  
pp. 136-144
Author(s):  
M. S. Vijayakumar
Keyword(s):  
Left Ideal ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Principal Component ◽  
Nonempty Interior ◽  
Regular Elements ◽  
Maximal Left Ideal ◽  
The Relationship ◽  
Order Identity ◽  
Real Matrices

This paper establishes a relationship (Theorem 4.1) between the approaches of A. C. Thompson [8, 9] and E. G. Effros [2] to the representation of simplex algebras, that is, real unital Banach algebras that are simplex spaces with the unit for order identity. It proves that the (nonempty) interior of the associated cone is contained in the principal component of the set of all regular elements of the algebra. It also conjectures that each maximal ideal (in the order sense—see below) of a simplex algebra contains a maximal left ideal of the algebra. This conjecture and other aspects of the relationship are illustrated by considering algebras of n × n real matrices.

scholarly journals A note on Noetherian orders in Artinian rings

1979 ◽  
Vol 20 (2) ◽  
pp. 125-128 ◽  
Author(s):  
A. W. Chatters
Keyword(s):  
Noetherian Ring ◽  
Quotient Ring ◽  
Triangular Matrix ◽  
Idempotent Element ◽  
Noetherian Rings ◽  
Central Idempotent ◽  
Matrix Rings ◽  
Regular Elements ◽  
Zero Divisors ◽  
Left And Right

Throughout this note, rings are associative with identity element but are not necessarily commutative. Let R be a left and right Noetherian ring which has an Artinian (classical) quotient ring. It was shown by S. M. Ginn and P. B. Moss [2, Theorem 10] that there is a central idempotent element e of R such that eR is the largest Artinian ideal of R. We shall extend this result, using a different method of proof, to show that the idempotent e is also related to the socle of R/N (where N, throughout, denotes the largest nilpotent ideal of R) and to the intersection of all the principal right (or left) ideals of R generated by regular elements (i.e. by elements which are not zero-divisors). There are many examples of left and right Noetherian rings with Artinian quotient rings, e.g. commutative Noetherian rings in which all the associated primes of zero are minimal together with full or triangular matrix rings over such rings. It was shown by L. W. Small that if R is any left and right Noetherian ring then R has an Artinian quotient ring if and only if the regular elements of R are precisely the elements c of R such that c + N is a regular element of R/N (for further details and examples see [5] and [6]). By the largest Artinian ideal of R we mean the sum of all the Artinian right ideals of R, and it was shown by T. H. Lenagan in [3] that this coincides in any left and right Noetherian ring R with the sum of all the Artinian left ideals of R.

Inverse complements and strongly unit regular elements

2021 ◽  
pp. 2250190
Author(s):  
Umashankara Kelathaya ◽  
Savitha Varkady ◽  
Manjunatha Prasad Karantha
Keyword(s):  
Partial Order ◽  
Regular Element ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Order Unit ◽  
Regular Elements ◽  
Strongly Regular ◽  
Minus Partial Order

In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.

scholarly journals Green's relations for regular elements of sandwich semigroups, II; semigroups of continuous functions

1978 ◽  
Vol 25 (1) ◽  
pp. 45-65 ◽  
Author(s):  
K. D. Magill ◽  
S. Subbiah
Keyword(s):  
Continuous Functions ◽  
Maximal Subgroups ◽  
Green’S Relations ◽  
Boolean Ring ◽  
Regular Elements ◽  
Ring Homomorphisms ◽  
Special Cases ◽  
Green's Relations ◽  
Sandwich Semigroup ◽  
Sandwich Semigroups

AbstractA sandwich semigroup of continuous functions consists of continuous functions with domains all in some space X and ranges all in some space Y with multiplication defined by fg = foαog where α is a fixed continuous function from a subspace of Y into X. These semigroups include, as special cases, a number of semigroups previously studied by various people. In this paper, we characterize the regular elements of such semigroups and we completely determine Green's relations for the regular elements. We also determine the maximal subgroups and, finally, we apply some of these results to semigroups of Boolean ring homomorphisms.

scholarly journals Grid convergence study of a cyclone separator using different mesh structures

2017 ◽  
Vol 23 (3) ◽  
pp. 311-320 ◽  
Author(s):  
R.A.F. Oliveira ◽  
G.H. Justi ◽  
G.C. Lopes
Keyword(s):  
Pressure Drop ◽  
Collection Efficiency ◽  
Fluid Dynamic ◽  
Two Phase ◽  
Mesh Structure ◽  
Pressure Drops ◽  
Regular Elements ◽  
Grid Convergence ◽  
Grid Convergence Index ◽  
Mesh Structures

In a cyclone design, pressure drop and collection efficiency are two important performance parameters to estimate its implementation viability. The optimum design provides higher efficiencies and lower pressure drops. In this paper, a grid independence study was performed to determine the most appropriate mesh to simulate the two-phase flow in a Stairmand cyclone. Computational fluid dynamic (CFD) tools were used to simulate the flow in an Eulerian-Lagrangian approach. Two different mesh structure, one with wall-refinement and the other with regular elements, and several mesh sizes were tested. The grid convergence index (GCI) method was applied to evaluate the result independence. The CFD model results were compared with empirical correlations from bibliography, showing good agreement. The wall-refined mesh with 287 thousand elements obtained errors of 9.8% for collection efficiency and 14.2% for pressure drop, while the same mesh, with regular elements, obtained errors of 8.7% for collection efficiency and 0.01% for pressure drop.

Determination of analytical expansion from numerical field data

2010 ◽  
Vol 110 (9) ◽  
pp. 1198-1204 ◽  
Author(s):  
Tomáš Radlička ◽  
Bohumila Lencová
Keyword(s):  
Field Data ◽  
Analytical Expansion
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