scholarly journals On the representation of integers by binary forms

2019 ◽  
Vol 375 (1-2) ◽  
pp. 133-163
Author(s):  
C. L. Stewart ◽  
Stanley Yao Xiao
Keyword(s):  
Binary Forms ◽  
Representation Of Integers

scholarly journals On the representation of integers by binary forms

1961 ◽  
Vol 6 (3) ◽  
pp. 333-363 ◽  
Author(s):  
D. Lewis ◽  
Kurt Mahler
Keyword(s):  
Binary Forms ◽  
Representation Of Integers

scholarly journals Representation of integers by cyclotomic binary forms

2018 ◽  
Vol 184 (1) ◽  
pp. 67-86 ◽  
Author(s):  
Étienne Fouvry ◽  
Claude Levesque ◽  
Michel Waldschmidt
Keyword(s):  
Binary Forms ◽  
Representation Of Integers

Contributions to the theory of diophantine equations I. On the representation of integers by binary forms

1968 ◽  
Vol 263 (1139) ◽  
pp. 173-191 ◽  
Keyword(s):  
Diophantine Equation ◽  
Diophantine Equations ◽  
Binary Form ◽  
Effective Algorithm ◽  
Algebraic Numbers ◽  
Binary Forms ◽  
Integer Coefficients ◽  
Representation Of Integers

An effective algorithm is established for solving in integers x, y any Diophantine equation of the type/( x, y ) = m , where/ denotes an irreducible binary form with integer coefficients and degree at least 3. The magnitude, relative to m, of the bound furnished by the algorithm for the size of all the solutions of the equation is investigated, and, in consequence, there is obtained the first generally effective improvement on the well known result of Liouville (1844) concerning the accuracy with which algebraic numbers can be approximated by rationals.

Teaching Bach's Binary Forms

Bach ◽  
2018 ◽  
Vol 49 (2) ◽  
pp. 281
Author(s):  
Brody
Keyword(s):  
Binary Forms

scholarly journals Isolation of viable Babesia bovis merozoites to study parasite invasion

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hassan Hakimi ◽  
Masahito Asada ◽  
Takahiro Ishizaki ◽  
Shinichiro Kawazu
Keyword(s):  
Control Strategies ◽  
Specific Inhibitor ◽  
Babesia Bovis ◽  
Parasite Development ◽  
Mammalian Host ◽  
Bovine Babesiosis ◽  
Binary Forms ◽  
Parasite Invasion ◽  
Dependent Protein ◽  
Basic Biology

AbstractBabesia parasite invades exclusively red blood cell (RBC) in mammalian host and induces alterations to host cell for survival. Despite the importance of Babesia in livestock industry and emerging cases in humans, their basic biology is hampered by lack of suitable biological tools. In this study, we aimed to develop a synchronization method for Babesia bovis which causes the most pathogenic form of bovine babesiosis. Initially, we used compound 2 (C2), a specific inhibitor of cyclic GMP-dependent protein kinase (PKG), and a derivative of C2, ML10. While both inhibitors were able to prevent B. bovis egress from RBC and increased percentage of binary forms, removal of inhibitors from culture did not result in a synchronized egress of parasites. Because using PKG inhibitors alone was not efficient to induce a synchronized culture, we isolated viable and invasive B. bovis merozoites and showed dynamics of merozoite invasion and development in RBCs. Using isolated merozoites we showed that BbVEAP, VESA1-export associated protein, is essential for parasite development in the RBC while has no significant role in invasion. Given the importance of invasion for the establishment of infection, this study paves the way for finding novel antigens to be used in control strategies against bovine babesiosis.

scholarly journals Representation by binary forms

1967 ◽  
Vol 6 (2) ◽  
pp. 157-184 ◽  
Author(s):  
Warren May
Keyword(s):  
Binary Forms

Thue equations that simultaneously fail the Hasse principle

2021 ◽  
pp. 1-10
Author(s):  
PALOMA BENGOECHEA
Keyword(s):  
Positive Integer ◽  
Hasse Principle ◽  
Fixed Degree ◽  
Binary Forms ◽  
Absolute Value ◽  
Positive Proportion ◽  
The Absolute

Abstract We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.

Binary Forms with a Vanishing Covariant of Weight Four Or Five

1933 ◽  
Vol s1-8 (3) ◽  
pp. 182-187
Author(s):  
Alfred Young
Keyword(s):  
Binary Forms
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