Grouping Miller–Nicely by linear vector space rotations

2004 ◽  
Vol 115 (5) ◽  
pp. 2427-2427
Author(s):  
Suvrat Budhlakoti ◽  
Jont B. Allen ◽  
Erik Larsen
Keyword(s):  
Vector Space ◽  
Linear Vector ◽  
Linear Vector Space

Modeling Interferometric Structures with Birefringent Elements: A Linear Vector-Space Formalism

2013 ◽  
Author(s):  
Nicholas J. Frigo ◽  
Vincent J. Urick ◽  
Frank Bucholtz
Keyword(s):  
Vector Space ◽  
Linear Vector ◽  
Space Formalism ◽  
Linear Vector Space

scholarly journals On Rotor calculus, I

1966 ◽  
Vol 6 (4) ◽  
pp. 402-423 ◽  
Author(s):  
H. A. Buchdahl
Keyword(s):  
Vector Space ◽  
Lorentz Transformation ◽  
Real World ◽  
Three Dimensional ◽  
Linear Vector ◽  
Complex Rotation ◽  
Starting Point ◽  
Complex Linear ◽  
Definition Of ◽  
Linear Vector Space

SummaryIt is known that to every proper homogeneous Lorentz transformation there corresponds a unique proper complex rotation in a three-dimensional complex linear vector space, the elements of which are here called “rotors”. Equivalently one has a one-one correspondence between rotors and self- dual bi-vectors in space-time (w-space). Rotor calculus fully exploits this correspondence, just as spinor calculus exploits the correspondence between real world vectors and hermitian spinors; and its formal starting point is the definition of certain covariant connecting quantities τAkl which transform as vectors under transformations in rotor space (r-space) and as tensors of valence 2 under transformations in w-space.

Series Expansions in Linear Vector Space

1941 ◽  
Vol 63 (1) ◽  
pp. 87 ◽  
Author(s):  
Orrin Frink
Keyword(s):  
Vector Space ◽  
Series Expansions ◽  
Linear Vector ◽  
Linear Vector Space

scholarly journals Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhaolin Jiang ◽  
Tingting Xu ◽  
Fuliang Lu
Keyword(s):  
Differential Equations ◽  
Vector Space ◽  
Ordinary Differential Equations ◽  
Cyclic Group ◽  
Functional Equations ◽  
Circulant Matrix ◽  
Circulant Matrices ◽  
Linear Vector ◽  
Skew Circulant ◽  
Linear Vector Space

The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra ofn×ncomplex skew-circulant matrices are displayed in this paper.

scholarly journals Paleochronic reversion in Psophocarpus: Dynamics II, rhizogeny on floral anatomic fields

2018 ◽  
Author(s):  
Edward G F Benya
Keyword(s):  
Vector Field ◽  
Vector Space ◽  
Ground State ◽  
Linear Vector ◽  
Generative Phase ◽  
Axial Transformation ◽  
Linear Vector Space

Paleochronic reversion is confirmed in Psophocarpus as a basic floral ground state. That state can expand to include dynamics T (g,,h) ) of axial expansion (AE) as a permutation (T X ) phase beginning as phyllotactic floral phylloid (T Phyld ) and/or axial decompression (T Axl ) manifest as linear elongation (T Long ) and/or rotation (T Rtn ) and/or latitudinal (TS Lat ) expansion. Organ regions present a continuum as a vector space LT Axl of floral axial transformation. A generative phase of meristem activity (T (Rz, SAM, Infl) ) can follow. Experiments with 49 phylloid and/or phyllome paleochronically reverted flowers presented varying degrees of phyllotactic permutation involving development of a pericladial stalk (PCL) and/or inter-bracts stem (IBS) and/or activated pedicel (PdcL) and/or gynophore (Gnf), Cupule-like (Gnf)/Cupl-Lk) elongation. A meristem generative function included rhizogeny as root site generation (RSG) at the calyx (Cl), PCL, bracts (Bt), IBS, PdcL and/or Gnf/Cupl-Lk regions manifest as eigenvector functions as RSG whose density of generation was associated with permutation of the ground state. A continuum of pedicel to calyx regions constitutes a subset [PdcL,Cl] of a linear vector space [Bt,Crpl]=T X → [PdcL,Crpl]=LT Axl whose extension is defined within the space: ∑ F PdcL + F Bt (1,,z) ± S IBS (1,,x) + F PCL (1,,w) + F Cl + F Gyncm ± S Gnf ± S Cupl-Lk = L T Axl . The vector space LT Axl transforms to a master vector field (F [c,..,d] ) of generated Euclidian eigenvectors so that: LT Axl → F [c,..,d]

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