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A New Understanding on the Problem That the Quintic Equation Has No Radical Solutions

Xiaochun Mei
2020 Advances in Pure Mathematics  
In order to prove the effectiveness of radical extension group of automorphism mapping for the cubic and quartic equations, in the Galois's theory, some algebraic relations among the roots of equations  ...  It is proved in this paper that Abel's and Galois's proofs that the quintic equations have no radical solutions are invalid.  ...  The Theory of Radical Extension of General Cubic Equation Is Invalid The theory of radical extension is only a formal thing.  ... 
doi:10.4236/apm.2020.109032 fatcat:yitrin36hzcn7fa453roeppjvi

Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians

David R. Morrison
1993 Journal of The American Mathematical Society  
One of the important unsolved problems in the theory is to determine this relationship precisely.  ...  Specifying a superconformal field theory of this type also determines cubic forms Sym 3 H-I,I(X) -+ C and Sym 3 HI,I(X) -+ C.  ...  We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold.  ... 
doi:10.1090/s0894-0347-1993-1179538-2 fatcat:rw4l7dccibbuvdj5au4p6qe6by

Mirror Symmetry and Rational Curves on Quintic Threefolds: A Guide for Mathematicians

David R. Morrison
1993 Journal of The American Mathematical Society  
One of the important unsolved problems in the theory is to determine this relationship precisely.  ...  Specifying a superconformal field theory of this type also determines cubic forms Sym 3 H-I,I(X) -+ C and Sym 3 HI,I(X) -+ C.  ...  We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold.  ... 
doi:10.2307/2152798 fatcat:ha47r65zdva4xgxnjhmgxr3clq

On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications [article]

Frederik Denef
2000 arXiv   pre-print
In this talk, I review how four dimensional stationary supergravity solutions that are more general than spherically symmetric black holes emerge naturally in the low energy description of BPS states in  ...  type II Calabi-Yau compactifications.  ...  We will follow the manifestly duality invariant formalism of [16] . Consider type-IIB string theory compactified on a Calabi-Yau manifold X.  ... 
arXiv:hep-th/0010222v1 fatcat:lgrvzs7g3bhwdk7g3ogzmheb4i

Hypercomputation by definition

B WELLS
2004 Theoretical Computer Science  
One way to break the impasse is to predicate that the theory is computable-in other words, hypercomputation by deÿnition.  ...  The dilemma of a decidable but not recursive set presents an impasse to standard computability theory.  ...  of this paper, to Jack Copeland for fostering a broader interest in hypercomputation and historical computers and for proposing speciÿc projects in both, to Carol Cleland for encouraging expression of  ... 
doi:10.1016/s0304-3975(03)00638-8 fatcat:p5hy7ivycja6fpah3ouorspogq

Hypercomputation by definition

Benjamin Wells
2004 Theoretical Computer Science  
One way to break the impasse is to predicate that the theory is computable-in other words, hypercomputation by deÿnition.  ...  The dilemma of a decidable but not recursive set presents an impasse to standard computability theory.  ...  of this paper, to Jack Copeland for fostering a broader interest in hypercomputation and historical computers and for proposing speciÿc projects in both, to Carol Cleland for encouraging expression of  ... 
doi:10.1016/j.tcs.2003.12.011 fatcat:d3faa6rvkrf2nj3bhywab3nr54

On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications [chapter]

2003 Mirror Symmetry IV  
In this talk, I review how four dimensional stationary supergravity solutions that are more general than spherically symmetric black holes emerge naturally in the low energy description of BPS states in  ...  type II Calabi-Yau compactifications.  ...  Part of this work was done in collaboration with Brian Greene and Mark Raugas.  ... 
doi:10.1090/amsip/033/14 fatcat:bihb57yrcng2vmmtnb26haqnpe

Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians [article]

David R. Morrison
1992 arXiv   pre-print
We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold.  ...  Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new q-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the "mirror  ...  One of the important unsolved problems in the theory is to determine this relationship precisely.  ... 
arXiv:alg-geom/9202004v1 fatcat:shq3t6k4qrg45hpq7wwyybkzia

The operator-sum-difference representation of a quantum noise channel

S. Omkar, R. Srikanth, Subhashish Banerjee
2015 Quantum Information Processing  
We consider various applications of the formalism: the Kraus repesentation of the 2-qubit amplitude damping channel, the noise resulting from a 2-qubit system interacting dissipatively with a vacuum bath  ...  The price to pay is that the sufficient number of Kraus operators is d^4 instead of d^2, sufficient in the Kraus representation.  ...  For polynomials upto quartic degree, the associated Galois group is solvable, but for quintic and above, unsolvable cases exist.  ... 
doi:10.1007/s11128-015-0965-5 fatcat:hucqfpqksncxtckuuqc5p2czpa

Naïve Thoughts on the Paradox of Gödel

Philip Davis
2001 Humanistic Mathematics Network Journal  
AUTHORS CONSULTED ORALLY OR E-WISE The author wishes to thank these individuals who graciously answered the questions I put to them:  ...  Many of these, in number theory especially, have been listed in such books as Daniel Shanks' Solved and Unsolved Problems in Number Theory and Richard Guy's Unsolved Problems in Number Theory.  ...  ., Gershgorin's theorem in matrix theory, or indeed for any of the theorems employed routinely in daily research.  ... 
doi:10.5642/hmnj.200101.24.07 fatcat:ft4etr4sgjcv7itraeuxtzgooa

A construction of quintic rings

Anthony C. Kable, Akihiko Yukie
2004 Nagoya mathematical journal  
We show that the ring of integers of every quintic number field lies in the image of the map.  ...  AbstractWe construct a discriminant-preserving map from the set of orbits in the space of quadruples of quinary alternating forms over the integers to the set of isomorphism classes of quintic rings.  ...  out the references mentioned in Section 4.  ... 
doi:10.1017/s002776300000876x fatcat:vmp6khdtpfcdpftx57pziuqz6u

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

Victor V. Batyrev, Duco van Straten
1995 Communications in Mathematical Physics  
variety P_Σ and the system of differential operators annihilating the special hypergeometric function Φ_0 depending on the fan Σ.  ...  In this context, the Mirror Symmetry phenomenon can be interpreted as the following twofold characterization of the series Φ_0.  ...  Morrison whose numerous remarks concerning a preliminary version of the paper helped us to give precise references on his work, especially on the forthcoming papers [18, 35] .  ... 
doi:10.1007/bf02101841 fatcat:a2klhlbjsjcanovxqhrdr4nhqe

The development of Galois theory from Lagrange to Artin

B. Melvin Kiernan
1971 Archive for History of Exact Sciences  
All are dependent on ABEL'S work and are, in general, attempts to simplify and clarify his work, either on the unsolvability of the general quintic or on determining particular solvable equations.  ...  These contradictions complete ABEL'S proof of the algebraic unsolvability of the general quintic equation.  ... 
doi:10.1007/bf00327219 fatcat:s3dosqcfjnb6bbkapzvasej2xe

Old mathematical challenges: Precedents to the millennium problems

Sergio Segura de León
2017 Mètode Science Studies Journal: Annual Review  
of variations; and the incidence of the problems posed by David Hilbert in 1900, focusing on the first problem in the list: the continuum hypothesis.  ...  With this pretext, we present three moments in the history of mathematics that were important for the development of new lines of research.  ...  This might be the first significant theorem in his theory, and it shows that there are different types of infinity. The fact that most real numbers are irrational is a consequence of this.  ... 
doi:10.7203/metode.8.9076 fatcat:lrrrbs3mtzdnllajjyleik54h4

Abstracts of papers

1930 Bulletin of the American Mathematical Society  
The importance of the transformation depends on this fact, since it follows almost at once that any sufficiently general quintic can be reduced to the Brioschi form.  ...  Ingram: Systems of integral equations and their Fredholm solutions. The system of integral equations of the previous paper has, formally, two solutions of Fredholm type for v and two for u.  ... 
doi:10.1090/s0002-9904-1930-04895-8 fatcat:dygavt3ixzhmhndwcvxky5m3mq
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