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Planning diagonalization proofs [chapter]

Lassaad Cheikhrouhou
1997 Lecture Notes in Computer Science  
In this paper we give an account on how to systematically construct and plan diagonalization proofs: (i) by nding an indexing relation, (ii) by constructing a diagonal element, and (iii) by making the  ...  Proof planning is a novel knowledge-based approach for proof construction, which supports the incorporation of mathematical knowledge and the common mathematical proof techniques of a particular mathematical  ...  Planning Diagonalization Proofs We shall now present the main methods for the construction of proof plans for diagonalization and describe how these methods can be applied.  ... 
doi:10.1007/3540634932_31 fatcat:vfa5mksr6jcuzoyobtypqbpyxy

Planning diagonalization proofs [chapter]

Lassaad Cheikhrouhou, Jörg Siekmann
1998 Lecture Notes in Computer Science  
doi:10.1007/bfb0057443 fatcat:aomhzqodg5hezmxbdhrpmg6yci

Page 352 of RIBA [Royal Institute of British Architects] Journal Vol. 9, Issue 13 [page]

1902 RIBA [Royal Institute of British Architects] Journal  
He finds a proof of this in my figure 12,* which shows how the diagonal ribs at their springing cover part of the mouldings of the arches of the choir arcade.  ...  This plan can only be explained by the conclusion that the shafts were planned to receive the ribs of th existing vaults.  ... 

A Tropical Count of Binodal Cubic Surfaces [article]

Madeline Brandt, Alheydis Geiger
2019 arXiv   pre-print
If a floor plan has separated nodes, C 2 cannot have a right string. Proof.  ...  Proof. If the conic in a floor plan has two node germs, it passes only through 3 points of the point configuration.  ... 
arXiv:1909.09105v1 fatcat:56n4uccotzhjbjsmpruzm3bdle

Tropical floor plans and enumeration of complex and real multi-nodal surfaces [article]

Hannah Markwig, Thomas Markwig, Kristin Shaw, Eugenii Shustin
2019 arXiv   pre-print
These surfaces are close to tropical limits which we characterize combinatorially, introducing the concept of floor plans for multinodal tropical surfaces.  ...  The concept of floor plans is similar to the well-known floor diagrams (a combinatorial tool for tropical curve counts): with it, we keep the combinatorial essentials of a multinodal tropical surface which  ...  Proof.  ... 
arXiv:1910.08585v1 fatcat:n3r53nusljb2jimkoybjro5mem

Two Layer 3D Floor Planning [article]

Paul Horn, Gabor Lippner
2012 arXiv   pre-print
Floor planning is a central notion in chip-design, and with recent advances in 3D integrated circuits, understanding 3D floor plans has become important.  ...  A 3D floor plan is a non-overlapping arrangement of blocks within a large box.  ...  general 3D plans without diagonal corners is only exponential.  ... 
arXiv:1210.4595v1 fatcat:azy7l75bobaqdiko6wootljs6q

Two Layer 3D Floor Planning

Paul Horn, Gabor Lippner
2013 Electronic Journal of Combinatorics  
Floor planning is a central notion in chip-design, and with recent advances in 3D integrated circuits, understanding 3D floorplans has become important.  ...  general 3D plans without diagonal corners is only exponential.  ...  Proof. The top and bottom planes are 2D floor plans with blocks from T ∪ D and B ∪ D respectively.  ... 
doi:10.37236/2816 fatcat:m57hq6bld5egnpeeaak4ktfzta

Corrigendum to the paper "Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings"

Moosa Gabeleh
2021 Demonstratio Mathematica  
The purpose of this short note is to present a correction of the proof of the main result given in the paper "Equivalence of the existence of best proximity points and best proximity pairs for cyclic and  ...  Also, every two parallel segments in the Euclidian plan 2 have the diagonal property.  ...  Proof.  ... 
doi:10.1515/dema-2021-0007 fatcat:6gciosjvcnaexj47g32cstigjq

Page 443 of School Science and Mathematics Vol. 45, Issue 394 [page]

1945 School Science and Mathematics  
each vertex is the point of intersection of the diagonals?)  ...  A class which limits the work to the study of theorems (whose proofs are presented in the textbook) and to simple exercises (like: if the diagonals of a parallelogram are 8 in. and 10 in., how far from  ... 

Good strategies for the iterated prisoner's dilemma: Smale vs. Markov

Ethan Akin
2017 Journal of Dynamics & Games  
Proof. The lines j and Switch( j ) meet the diagonal at a common point (Q, Q) = j ∩ Switch( j ). To the right of {s X = Q} the line j lies below the diagonal, because A is below the diagonal.  ...  Suppose that π(S, T ) = 0, π(T, S) = 1 and π(s) = 1 when s lies on the diagonal. If both X and Y play Smale plans which satisfy these conditions then for any initial plays, lim s N = (R, R). Proof.  ... 
doi:10.3934/jdg.2017014 fatcat:pi7acwbohfha7corfhy6pokbgm

Page 957 of The Journal of the Operational Research Society Vol. 49, Issue 9 [page]

1998 The Journal of the Operational Research Society  
Theorem 1 7,,;, = min(y;,2) < < max(n,, 42) = Nmax- Proof = qn, + (1 — q)nz = No + (nN, — N2)q. Three con- ditions prevail to complete the proof.  ...  blocks to the total number of elements in the diagonal blocks in the final matrix, 7, is the ratio of number of Os in the off- diagonal blocks to the total number of elements in the off- diagonal blocks  ... 

Good Strategies for the Iterated Prisoner's Dilemma : Smale vs. Markov [article]

Ethan Akin
2017 arXiv   pre-print
Proof: The lines j and Switch( j ) meet the diagonal at a common point (Q, Q) = j ∩ Switch( j ). To the right of {s X = Q} the line j lies below the diagonal, because A is below the diagonal.  ...  Proof: Assume that both plans are adopted by time N * . Let L 0 (s) = s Y − s X . That is, L 0 is the affine function associated with the diagonal separation line. Let L 1 (s) = s X + s Y − T − S.  ... 
arXiv:1610.05262v2 fatcat:abnede5g2vcdxnxomru24rsgc4

Flip Paths Between Lattice Triangulations [article]

William Sims, Meera Sitharam
2021 arXiv   pre-print
Diagonal flip paths between triangulations have been studied in the combinatorial setting for nearly a century.  ...  One application of flip paths to Euclidean distance geometry and Moebius geometry is a recent, simple, constructive proof by Connelly and Gortler of the Koebe-Andreev-Thurston circle packing theorem that  ...  diagonal edges.  ... 
arXiv:2008.11292v3 fatcat:uik6emwvyrdevgnekus4ucjaw4

Page 76 of American Architect and Architecture Vol. 150, Issue 2653 [page]

1937 American Architect and Architecture  
In this type of construction, columns should be rectangular in plan with their long axes perpendieular to the walls.  ...  This treatment allows the building to be of very light construction without concrete exterior walls and still to be earthquake-proof up to heights of six or seven stories.  ... 

On the Codimension One Motion Planning Problem

J.-P. Gauthier, V. Zakalyukin
2005 Journal of dynamical and control systems  
In this paper, we improve the results of [5] related to motion planning problems for corank one sub-Riemannian (SR) metrics.  ...  case, or under certain nonvanishing condition (C) in the analytic case) is, in fact, always true under condition (C), on the complement of a subset of codimension infinity, in the set of C ∞ "motion planning  ...  Proof. The proof is based upon the homotopy method (standard in real C ∞ singularity theory).  ... 
doi:10.1007/s10883-005-0002-6 fatcat:t4auucrnsnao7dkfsnkbvpjxle
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