field extensions
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PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260362
Author(s):  
Denise Wetzel ◽  
Judith Ungewiss ◽  
Michael Wörner ◽  
Helmut Wilhelm ◽  
Ulrich Schiefer

Significance Horizontal visual field extension was assessed for red and white stimuli in subjects with protanopia using semi-automated kinetic perimetry. In contrast to a conventional anomaloscope, the “red/white dissociation ratio” (RWR) allows to describe protanopia numerically. For the majority of subjects with protanopia a restriction for faint red stimuli was found. Purpose Comparing the horizontal visual field extensions for red and white stimuli in subjects with protanopia and those with normal trichromacy and assessing the related intra-subject intra-session repeatability. Methods The subjects were divided into groups with protanopia and with normal trichromacy, based on color vision testing (HMC anomaloscope, Oculus, Wetzlar/FRG). Two stimulus characteristics, III4e and III1e, according to the Goldmann-classification, were presented with semi-automated kinetic perimetry (Octopus 900 perimeter, Haag-Streit, Köniz/CH). They moved along the horizontal meridian, with an angular velocity of 3°/s towards the visual field center, starting from either the temporal or nasal periphery. If necessary, a 20° nasal fixation point offset was chosen to capture the temporal periphery of the visual field. For each condition the red/white dissociation ratio (RWR); Pat Appl. DPMA DRN 43200082D) between the extent of the isopter for red (RG610, Schott, Mainz/ FRG) and white stimuli along the horizontal meridian was determined. Results All data are listed as median/interquartile range: Five males with protanopia (age 22.1/4.5 years) and six males with normal trichromacy (control group, age 30.5/15.2 years) were enrolled. The RWR is listed for the right eye, as no clinically relevant difference between right and left eye occurred. Protanopes’ RWR for mark III4e (in brackets: control group) was 0.941/0.013 (0.977/0.019) and for mark III1e 0.496/0.062 (0.805/0.051), respectively. Conclusions In this exploratory “proof-of-concept study” red/white dissociation ratio perimetry is introduced as a novel technique aiming at assessing and quantifying the severity of protanopia. Further effort is needed to understand the magnitude of the observed red-/white dissociation and to extend this methodology to a wider age range of the sample and to anomalous trichromacies (protanomalia) with varying magnitude.


2021 ◽  
Vol 2021 (12) ◽  
pp. 045
Author(s):  
Katsuki Aoki ◽  
Yusuke Manita ◽  
Shinji Mukohyama

Abstract A Poincarè invariant, local scalar field theory in which the Lagrangian and the equation of motion contain only up to second-order derivatives of the fields is called generalized Galileon. The covariant version of it in four dimensions is called Horndeski theory, and has been vigorously studied in applications to inflation and dark energy. In this paper, we study a class of multi-field extensions of the generalized Galileon theory. By imposing shift and SO(N) symmetries on all the currently known multi-Galileon terms in general dimensions, we find that the structure of the Lagrangian is uniquely determined and parameterized by a series of coupling constants. We also study tensor perturbation in the shift-symmetric SO(3) multi-Galileon theory in four dimensions. The tensor perturbations can obtain a mass term stemming from the same symmetry breaking pattern as the solid inflation. We also find that the shift-symmetric SO(3) multi-Galileon theory gives rise to new cubic interactions of the tensor modes, suggesting the existence of a new type of tensor primordial non-Gaussianity.


2021 ◽  
Vol 33 (2) ◽  
Author(s):  
Chad Awtrey ◽  
James R. Beuerle ◽  
Hanna Noelle Griesbach
Keyword(s):  

2021 ◽  
Vol 107 ◽  
pp. 23-66
Author(s):  
Sergei A. Abramov ◽  
Manuel Bronstein ◽  
Marko Petkovšek ◽  
Carsten Schneider

2021 ◽  
Author(s):  
Lhoussain El Fadil ◽  
Mohamed Faris

Polynomial factorization over a field is very useful in algebraic number theory, in extensions of valuations, etc. For valued field extensions, the determination of irreducible polynomials was the focus of interest of many authors. In 1850, Eisenstein gave one of the most popular criterion to decide on irreducibility of a polynomial over Q. A criterion which was generalized in 1906 by Dumas. In 2008, R. Brown gave what is known to be the most general version of Eisenstein-Schönemann irreducibility criterion. Thanks to MacLane theory, key polynomials play a key role to extend absolute values. In this chapter, we give a sufficient condition on any monic plynomial to be a key polynomial of an absolute value, an irreducibly criterion will be given, and for any simple algebraic extension L=Kα, we give a method to describe all absolute values of L extending ∣∣, where K is a discrete rank one valued field.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
David Loeffler

Abstract We study GL 2 ⁡ ( F ) {\operatorname{GL}_{2}(F)} -invariant periods on representations of GL 2 ⁡ ( A ) {\operatorname{GL}_{2}(A)} , where F is a non-archimedean local field and A / F {A/F} a product of field extensions of total degree 3. For irreducible representations, a theorem of Prasad shows that the space of such periods has dimension ⩽ 1 {\leqslant 1} , and is non-zero when a certain ε-factor condition holds. We give an extension of this result to a certain class of reducible representations (of Whittaker type), extending results of Harris–Scholl when A is the split algebra F × F × F {F\times F\times F} .


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