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Theorem proving by analogy — A compelling example
[chapter]

1995
*
Lecture Notes in Computer Science
*

t b

doi:10.1007/3-540-60428-6_22
fatcat:fvxmpfvd3zcedpjktf7g46xody
*Ä*Q P S R P*a*¹ ¶ ¤ T*Ä*X U ¶ Y T*Ä*Q P S R U T · H µ »*a*X U ¶*Å*b µ*a*P t ¹*Ã*º ¤ AE*a*Ç @ È É Ç 1 Ê Ë Í Ì Î r ¹ T*Â**Ä*µ ¶ ¤ T*Ä*Q X 1 ¾ T ¹ ¡ ¾ P*a*¹*Ä*Q X U H p T R p*Ä*P*a*X*Ä*X U µ H Q X U ¶ ... º*a*X ¿ R T ` S R p*Â**a**Â*b*a*X U X · H Q µ µ*Á*Ù b*Ä*Q X U · b µ*Á**Ä*Q X ¦ b Q µ*Â*H y R X ·*Ã*H Q µ µ*Á*v Û Ì G ¶ · P*a*H P Ü R T ` P*a*¹ X U b*Ä*Q P*a*º T*Ä*Q P*a*µ ¹*Ã*b ¿ AE*a*Ç @ Õ Ë Í É µ*À*f X ...##
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Natural Philosophy and Quantum Theory
[article]

2006
*
arXiv
*
pre-print

We also present an

arXiv:quant-ph/0608167v2
fatcat:voqruw5bkrdbrd6do5oft2jcaq
*analogy*with Darwinian evolution in order to pedagogically hint at how one might go about using*a*theory in which one does not even desire to explain correlations*by*invoking common ... We attempt to show how relationalism might help in understanding Bell's*theorem*. ... Jaynes' work-he seemed to understand Bell's*theorem*even without the use of*a*convenient*analogy*. ...##
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Recent Developments in Brill-Noether Theory
[article]

2021
*
arXiv
*
pre-print

Breakthroughs include the proof of the Maximal Rank

arXiv:2111.00351v1
fatcat:ianp7fc2yfau3nslehyrho4shm
*Theorem*, which determines the Hilbert function of the general linear series of given degree and rank on the general curve in M_g, and complete*analogs*... of the standard Brill-Noether*theorems*for curves that are general in Hurwitz spaces. ... The first author was supported*by*NSF DMS-2054135. The second author was supported*by*NSF DMS-2001502 and DMS-2053261. ...##
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Page 2149 of Mathematical Reviews Vol. , Issue 90D
[page]

1990
*
Mathematical Reviews
*

This second part is devoted to functions of three and more variables and gives

*a*result*analogous*to that*proved*in the first part.*A*nontrivial*example*illustrating the method is given. ... The*theorems*require the existence of piecewise continuous auxiliary functions, called Lyapunov functions. The applicability of the results is illustrated*by*two*examples*. ...##
###
Compelling Colorings: A generalization of the dominator chromatic number
[article]

2021
*
arXiv
*
pre-print

We define

arXiv:2105.03694v1
fatcat:umvadvovwnga5pl7kbjxset6se
*a*P-*compelling*coloring as*a*proper coloring of the vertices of*a*graph such that every subset consisting of one vertex of each color has property P. ... The P-*compelling*chromatic number is the minimum number of colors in such*a*coloring. ... Then the set D − {d} is still connected and still dominating,*a*contradiction. qed So we return to*proving*the lower bound for*Theorem*17 and consider*a**compelling*coloring. ...##
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Page 565 of American Society of Mechanical Engineers. Transactions of the American Society of Mechanical Engineers Vol. 79, Issue 3
[page]

1957
*
American Society of Mechanical Engineers. Transactions of the American Society of Mechanical Engineers
*

It is possible, how- ever, to have somewhat less general

*theorems*concerning mono- stability. An*example*of these is the*theorem*stated*by*Dr. Bass in connection with the system [Z,]. ... The present wording (suggested*by*L.*A*. Zadeh) is motivated*by**analogous*designations used in elec- trical engineering practice in connection with multivibrators. ...##
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Page 387 of None Vol. 69, Issue 1796
[page]

1890
*
None
*

Napier’s

*analogies*, Delambre’s*analogies*, Reidt’s*analogies*, Girard’s*theorem*, Lhuilier’s*theorem*, Breitschneider’s*analogies*, isotomic and isogonal conjugates and transversals, in- versions in space, ...*By*G. Chrystal, M.A., LL.D., Professor of Mathematics. Part II. Edinburgh: Black. Solutions of all the*Examples*in*a*Treatise on Algebra,*By*C. ...##
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Protecting Cryptography Against Compelled Self-Incrimination
[article]

2020
*
IACR Cryptology ePrint Archive
*

We justify our definition

dblp:journals/iacr/SchefflerV20
fatcat:wfixz43efbejrp5ixybzycw6kq
*by*showing that it is consistent with prior court cases. We*prove*that decryption is often not*compellable**by*the government under our definition. ... As*a*result, we initiate the study of protecting cryptographic protocols against the threat of future*compelled*disclosure. ... This material is supported*by**a*Clare Boothe Luce Graduate Research Fellowship,*a*Google PhD Fellowship, the DARPA SIEVE program under Agreement No. ...##
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The Geometric Series in Calculus

1998
*
The American mathematical monthly
*

One approach [2, p. 1621 is to use the Binomial

doi:10.1080/00029890.1998.12004846
fatcat:2ewt666t2vbztobkaqouodqmna
*Theorem*without saying much save for*a*few*examples*. Not exactly convincing! Or should we*prove*the Binomial*Theorem*at this point? Probably not! ... We often hope to say*compelling*things about Riemann sums when we define However, when we try to compute*examples*of simple integrals with*a*uniform partition P of [*a*, b], we can wind up with expressions ...##
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X. On the properties of surfaces of the second degree which correspond to the theorems of Pascal and Brianchon on conic sections

1844
*
The London Edinburgh and Dublin Philosophical Magazine and Journal of Science
*

Chasles~ for

doi:10.1080/14786444408644799
fatcat:fatgybxprfezdeafoequ5qpgqm
*example*, has assigned*a*different*theorem*as the one corresponding to Pascal's. ... The two*theorems*being connected*by*the theory of reciprocal polars, it is sufficient to*prove*one of them, and for the best analytical * I sacrificed nearly*a*score of rabbits for the purpose of determining ...##
###
The New Promise of Analog Computation
[chapter]

2007
*
Lecture Notes in Computer Science
*

we can

doi:10.1007/978-3-540-73001-9_20
fatcat:cg3xnv2vcjg5panxuiisjzwogm
*prove**theorems*of Analysis. ... We show that, using our more or less established framework of inductive definition of real-valued functions (work started*by*Cristopher Moore in [9]) together with ideas and concepts of standard computability ... Acknowledgements We would like to thank Fernando Ferreira for having*compelled*us*a*bit further towards Descriptive Set Theory. ...##
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Obligation, Permission, and Bayesian Orgulity

2019
*
Ergo, An Open Access Journal of Philosophy
*

*A*more

*compelling*version of the Orgulity Argument than Cisewski et al. present is available, however-

*a*point that we make

*by*drawing an

*analogy*with de Finetti's (1974) argument against mandating countable ... We extend Elga's (2016) idea of appealing to finitely additive probability to show that the challenge posed

*by*the Orgulity Argument can be met. ... There are ways to define P directly, without appeal to extension

*theorems*, for

*example*,

*by*letting P be point mass concentrated on some ω P C. 14. ...

##
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Page 377 of Mathematical Reviews Vol. , Issue 2001A
[page]

2001
*
Mathematical Reviews
*

As an

*example*of one of the*theorems*,*a*tiling of*a*3 x 3 square is exhibited consisting of 11 tiles similar to the L-shaped tile T formed*by*three unit squares. ... According to Cauchy’s*theorem*(1813), there is no flexible con- vex polyhedron. In 1977, R. Connelly found the first*example*of*a*flexible polyhedron without self-intersections. ...##
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On Gunther's stress functions for couple stresses

1967
*
Quarterly of Applied Mathematics
*

'

doi:10.1090/qam/99904
fatcat:mqr4lzgjl5g3dmgzv5bsd6o2py
*A*Cosserat [1] continuum is an*example*of such*a*material. ... The following*theorem*, which provides*a*solution of Eqs. (5.1), may be confirmed*by*direct substitution.*a*and (? ...##
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An impossibility theorem for amalgamating evidence

2011
*
Synthese
*

I

doi:10.1007/s11229-011-9973-x
fatcat:pjsktrmbqrbovifmuiwgt64mji
*prove*that this is so, and end*by*discussing the plausibility of the axioms required for the*theorem*. ... Once the*analogy*between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face*a**theorem*similar to Arrow's. ... To the extent that one finds the Independence axiom*a*generally*compelling*desideratum, one ought to be troubled*by*this*example*. ...
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