Normal Basis of the Maximal Real Subfield of a Circular Field

2019 ◽  
Vol 40 (5) ◽  
pp. 630-639 ◽  
Author(s):  
I. G. Galyautdinov ◽  
E. E. Lavrentyeva
Keyword(s):  
Normal Basis ◽  
Circular Field

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

Optimisation of Magnification Levels for near Infrared Chemical Imaging of Blending of Pharmaceutical Powders

2007 ◽  
Vol 15 (3) ◽  
pp. 137-151 ◽  
Author(s):  
Hua Ma ◽  
Carl A. Anderson
Keyword(s):  
Near Infrared ◽  
Image Data ◽  
Principal Component ◽  
Chemical Imaging ◽  
Field Of View ◽  
Pharmaceutical Dosage Forms ◽  
Component Distribution ◽  
Circular Field ◽  
Pharmaceutical Powder ◽  
Magnification Level

A critical parameter in the evaluation of pharmaceutical dosage forms by hyperspectral imaging is the level of magnification. If the magnification (as set by the optical objective) is inadequate to resolve the relevant features, then the value of the imaging is diminished; if the magnification level is greater than is required, then the field of view is unnecessarily reduced. The purpose of this study was to determine an optimum magnification level for the study of powder mixing. Relevant features in this system include distribution of individual components within samples and the overall content of a given sample. In the present study, three magnification levels of near infrared (NIR) chemical imaging objectives were evaluated for their effects on imaging a blend of pharmaceutical materials (powders). High, medium and low objective magnification levels were investigated by comparing the resulting blend surface images of a two-component (salicylic acid and lactose) pharmaceutical powder mixture. Multiple images from high and medium magnification were concatenated so that an equivalent field of view was obtained for all magnification levels. Univariate images, principal component analysis score images, partial least squares predicted images and spectra extracted from different intensity regions in the area images were analysed qualitatively and quantitatively for comparison. A series of images spanning a strip across the centre of the circular field were collected at each magnification level and compared with respect to surface features elucidated and area of blend surface imaged. Analyses of images indicate that the three magnification levels delineate the component distribution for this particular powder system similarly. Images obtained at the low magnification level demonstrated adequate resolution and provided the broadest view of the blend surface. It is concluded that the low optical magnification level was adequate for the system being studied and is the preferred mode for pharmaceutical powder blend image data collection for this system.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

scholarly journals ON THE NORMAL BASIS THEOREMS AND THE EXTENSION DIMENSION

1964 ◽  
Vol 18 (1-2) ◽  
pp. 81-88 ◽  
Author(s):  
Kazuo Kishimoto ◽  
Takesi Onodera ◽  
and Hisao TOMINAGA
Keyword(s):  
Normal Basis ◽  
Extension Dimension
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