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Clausal Analysis of First-order Proof Schemata
[article]

2017
*
arXiv
*
pre-print

*Proof*schemata are a variant of

*LK*-

*proofs*able to simulate various induction schemes

*in*first-order logic

*by*adding so called

*proof*links to the standard first-order

*LK*-calculus. ...

*In*"Towards a clausal analysis of cut-elimination", it was shown that reductive cut-elimination transforms a given

*LK*-

*proof*

*in*such a way that a subsumption relation holds between the pre- and post-transformation ... Note that

*LKS*-

*proofs*have a free parameter, which when instantiated results

*in*an

*LK*-

*proof*. ...

##
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Page 132 of Phrenological Journal and Science of Health Vol. 77, Issue 3
[page]

1883
*
Phrenological Journal and Science of Health
*

The psycho- logical part of Phrenology might be di-
mh & wee

*lk*...*by*mod- ern scientists. ...##
###
Page 1252 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

*discovery*

*in*

*LK*

*system*

*by*

*analogy*(197- 211); Nobuhiro Inuzuka, Hirohisa Seki and Hidenori Itoh, Effi- cient induction of executable logic programs from examples (212- 224); B. ... Proceedings of the 3rd Asian Computing Science Conference held

*in*Kathmandu, December 9-11, 1997. Edited

*by*R. K. Shyamasundar and K. Ueda. Lecture Notes

*in*Computer Science, 1345. ...

##
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Cut as Consequence

2010
*
History and Philosophy of Logic
*

between a

doi:10.1080/01445340.2010.522365
fatcat:dnibzkfrlfapjkdfxfpaj4d2bm
*system*as a whole and its 'semantics'). ... The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from now dominant views introduced*by*Hilbert, Gödel, Tarski ... Acknowledgments The participants*in*my spring 2009*proof*theory seminar at the University of Notre Dame, with their comments and questions, helped me clarify my reading of Gentzen. ...##
###
The Yangian symmetry of the Hubbard models with variable range hopping

1996
*
Physics Letters A
*

*In*both cases the Yangians are mutually commuting, hence can be combined into a Y(sl_2)⊕Y(sl_2) Yangian. Their mutual commutativity is of dynamical origin. ... This work has been supported

*by*the Japan Society for the ...

*In*

*analogy*to the spin chain case [13] the generator of its Yangian symmetry might be constructed

*by*adding "potential terms" to the second order Yangian generator K α , eq. (29). ...

##
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Focalisation and Classical Realisability
[chapter]

2009
*
Lecture Notes in Computer Science
*

The distinction is motivated

doi:10.1007/978-3-642-04027-6_30
fatcat:lfiecqfw3bezfc7yv2mwy2xmte
*by*the fact that they can be subject to different assumptions during*proof*-search. ...*In*the first part of the paper (Section 2) we give a syntax for LC and LL derived from Curien-Herbelin's calculus, the focalising*system*L (L foc ). ...*Systems*Rules for typing L foc*in*one-sided MALL,*LK*pol and LL are given Fig. 1, 2 and 3 . ...##
###
σ-Set Theory: Introduction to the concepts of σ-antielement, σ-antiset and Integer Space
[article]

2010
*
arXiv
*
pre-print

*In*this paper we develop a theory called σ-Set Theory,

*in*which we present an axiom

*system*developed from the study of Set Theories of Zermelo-Fraenkel, Neumann-Bernays-Godel and Morse-Kelley. ...

*In*σ-Set Theory, we present the proper existence of objects called σ-antielement, σ-antiset, natural numbers, antinatural numbers and generated σ-set

*by*two σ-sets, from which we obtain, among other things ... For all n ∈

*IN*⋆ there exists a unique σ-set m such that {n} ∪ {m} = ∅.

*Proof*. This

*proof*is

*analogous*to the previous one. ...

##
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Page 403 of The American Whig Review Vol. 16, Issue 95
[page]

1852
*
The American Whig Review
*

}not have been more numerous and exact

*in*i its orders of material faculties; nor was the | progre ss of their*discovery*and deification accomplished*by*less observant and judicious | savi ans than those ...*By*the ar gum 1ents of natural useless theology, as de ve loped it Brid lore vater atural & x B Tre atises. and*by*: aj] the ‘ vathen*lk*yori cians, tioned. i ; We make only the first step; as it has been ...##
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A combinatorial computation of the first Pontryagin class of the complex projective plane

1994
*
Geometriae Dedicata
*

but it can be so realized

doi:10.1007/bf01264030
fatcat:ofcmuujyevgjxgazs7ef4xfgby
*by*a star-shaped polytope, and the space of all such realizations is not connected. ... The conditions of the original formula must be modified since the 8-vertex triangulation of the 3-sphere link of each vertex cannot be realized as the complex of faces of a convex polytope*in*4-space, ... The*proof*that (ngt~6)g and nj~; belong to the same component of CFo (*Lk*(i j ) ) is*analogous*. ...##
###
Geometry of Higher Helicities

2003
*
Moscow Mathematical Journal
*

results related to Arnold's theorem on the asymptotic Hopf invariant on three-dimensional manifolds and recent work on linking of a vector field with a foliation, the asymptotic crossing number, short path

doi:10.17323/1609-4514-2003-3-3-989-1011
fatcat:bmsexkstubd5znxlsktd5ibpry
*systems*... The author is grateful for kind hospitality to the ESI*in*Vienna, the IHES*in*Bures-sur-Yvette, and Ecole Polytechnique*in*Paris, where this paper was written. Special thanks go to V. Kaimanovich, M. ...*Proof*.*lk*ξ (F) = M*lk*ξ (x, F) µ = M lim T →∞ 1 T*lk*(Γ T (x), F) µ = M lim T →∞ 1 T*lk*(g [0,T ] x , F) µ = M lim T →∞ 1 T g [0,T ] x d −1 β µ = M lim T →∞ 1 T T 0 i ξ (d −1 β)dt µ. ...##
###
Revisiting Generalizations of the Dehn–Sommerville Relations
[article]

2021
*
arXiv
*
pre-print

Our

arXiv:2108.13145v2
fatcat:b2y6rbrairfebcgmwxmnzbmoyi
*proofs*are uniform, and are based on two simple evaluations of the h̃-polynomial: one that recovers the f̃-polynomial, and one that counts faces according to certain multiplicities. ...*In*addition, we present Dehn–Sommerville relations for reciprocal complexes and general balanced simplicial complexes; which slightly generalize some of the previous results. ... ACKNOWLEDGEMENTS Part of the results*in*this manuscript were initially included*in*a preliminary preprint available at [3] , which was split*in*two papers afterwards. ...##
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Triple linking numbers and surface systems
[article]

2017
*
arXiv
*
pre-print

We give a refined value group for the collection of triple linking numbers of links

arXiv:1709.08478v1
fatcat:y5ntoxfe4rawvgokpwiswewvnm
*in*the 3-sphere. ... Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the links admit homeomorphic surface*systems*. ... MN and PO were supported*by*CIRGET postdoctoral fellowships. MP was supported*by*an NSERC*Discovery*grant. Surface*systems*Definition 2.1. ...##
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Concordance invariance of Levine-Tristram signatures of links
[article]

2018
*
arXiv
*
pre-print

*In*particular [GL15] inspired the question that led to this paper. We also thank the referee for helpful feedback. M. Powell is supported

*by*an NSERC

*Discovery*grant. M. ... Nagel is supported

*by*a CIRGET Postdoctoral Fellowship. ... That is, the sum of the entries

*in*each row and

*in*each column of the matrix

*Lk*L is zero. We will use this observation

*in*the

*proof*below. Lemma 5.4. ...

##
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Exact simulation of coupled Wright–Fisher diffusions

2021
*
Advances in Applied Probability
*

Finally, the algorithm's complexity is derived and its performance demonstrated

doi:10.1017/apr.2021.9
fatcat:txaiwpqrpva7lmbl4ycf2xconu
*in*a simulation study. ... Once a candidate is accepted, the remainder of the path can be recovered*by*sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. ... summands*in*(7.2). 2 ( 1 21 + |θ |) z j x j .The*proof*for the general (d − 1)-dimensional case follows*analogously*. ...##
###
XVI. Properties of the trapezium

1826
*
The Philosophical Magazine
*

*LK*: EL. LD. :: CB.BK: EB.BD. PROP. IV. (Fig. 1.) Let the points E C KD lie

*in*the circumference of a circle; then AE:AK:: (~L:

*LK*:: EL: LD::AC: CD. Dem.--

*By*cireleAE. AD : AC. AK : : CL. LD: EL. ...

*In*like manner is the second

*analogy*demonstrated. Q.E.D. Cot. Hence also CE 2 : KD 2 : : CL. LE : KL. LD, : : CA. AE : KA. AD, and CK ~ : ED ~ : : CL.

*LK*: EL. LD :: BC.BK: EB. BD. PROP. ...

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