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

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. ...

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

1993
*
Journal of The American Mathematical Society
*

One

doi:10.1090/s0894-0347-1993-1179538-2
fatcat:rw4l7dccibbuvdj5au4p6qe6by
*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. ...##
###
Mirror Symmetry and Rational Curves on Quintic Threefolds: A Guide for Mathematicians

1993
*
Journal of The American Mathematical Society
*

One

doi:10.2307/2152798
fatcat:ha47r65zdva4xgxnjhmgxr3clq
*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. ...##
###
On the correspondence between D-branes and stationary supergravity solutions of type II Calabi-Yau compactifications
[article]

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. ...

##
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Hypercomputation by definition

2004
*
Theoretical Computer Science
*

One way to break

doi:10.1016/s0304-3975(03)00638-8
fatcat:p5hy7ivycja6fpah3ouorspogq
*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*...##
###
Hypercomputation by definition

2004
*
Theoretical Computer Science
*

One way to break

doi:10.1016/j.tcs.2003.12.011
fatcat:d3faa6rvkrf2nj3bhywab3nr54
*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*...##
###
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. ...

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

1992
*
arXiv
*
pre-print

We give a mathematical account

arXiv:alg-geom/9202004v1
fatcat:shq3t6k4qrg45hpq7wwyybkzia
*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. ...##
###
The operator-sum-difference representation of a quantum noise channel

2015
*
Quantum Information Processing
*

We consider various applications

doi:10.1007/s11128-015-0965-5
fatcat:hucqfpqksncxtckuuqc5p2czpa
*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. ...##
###
Naïve Thoughts on the Paradox of Gödel

2001
*
Humanistic Mathematics Network Journal
*

AUTHORS CONSULTED ORALLY OR E-WISE

doi:10.5642/hmnj.200101.24.07
fatcat:ft4etr4sgjcv7itraeuxtzgooa
*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. ...##
###
A construction of quintic rings

2004
*
Nagoya mathematical journal
*

We show that

doi:10.1017/s002776300000876x
fatcat:vmp6khdtpfcdpftx57pziuqz6u
*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. ...##
###
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

1995
*
Communications in Mathematical Physics
*

variety P_Σ and

doi:10.1007/bf02101841
fatcat:a2klhlbjsjcanovxqhrdr4nhqe
*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] . ...##
###
The development of Galois theory from Lagrange to Artin

1971
*
Archive for History of Exact Sciences
*

All are

doi:10.1007/bf00327219
fatcat:s3dosqcfjnb6bbkapzvasej2xe
*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. ...##
###
Old mathematical challenges: Precedents to the millennium problems

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. ...

##
###
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. ...

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