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A Semi-automatic Proof of Strong Connectivity [chapter]

Ran Chen, Jean-Jacques Lévy
2017 Lecture Notes in Computer Science  
We present a formal proof of the classical Tarjan-1972 algorithm for finding strongly connected components in directed graphs.  ...  The Why3 system allows the description of programs in a Why3-ML programming language (a first-order programming language with ML syntax) and provides interfaces to various state-of-the-art automatic provers  ...  Acknowledgments Thanks to the Why3 group at Inria-Saclay/LRI-Orsay for very valuable advices, to Cyril Cohen and Laurent Théry for their fantastic expertise in Coq proofs, to Claude Marché for many corrections  ... 
doi:10.1007/978-3-319-72308-2_4 fatcat:ntzslyrxoncyzccyslps6xqqmm

Page 5042 of Mathematical Reviews Vol. , Issue 87i [page]

1987 Mathematical Reviews  
It is shown that the following statements are equivalent: (a) f is s-irresolute. (b) If V is a semi-open subset of Y such that Y —V is connected, then f~!(V) is semi-open.  ...  (sel(A) denotes the semiclosure of A.) (3) If {U,:a€ 4} is a semi-open cover of X and f|U, is s-irresolute for each aA, then f is s-irresolute. (4) Strong s-normality is invariant under irresolute pre-semiclosed  ... 

Elementary remarks on units in monoidal categories

Joachim Kock
2006 arXiv   pre-print
Then we prove that the two notions of units are equivalent in a strong functorial sense.  ...  To start, we describe the semi-monoidal category of all possible unit structures on a given semi-monoidal category and observe that it is contractible (if nonempty).  ...  Part of this work was carried out while I was a postdoc at 6.7 Remark.  ... 
arXiv:math/0507349v2 fatcat:tuszktgpdzd75inpmn3hxf2nci

From small-overlap conditions to automatic semigroups [article]

Uri Weiss
2010 arXiv   pre-print
We study the connection between small-overlap conditions and automaticity of semigroups.  ...  For these hyperbolic-like conditions we show how to construct an automatic structure. Furthermore, we show that the naive approach of considering just geodesics fails in our case.  ...  A straightforward generalization of the proof of the main theorem shows that in fact the semi-groups considered in the main theorem are bi-automatic.  ... 
arXiv:0902.3776v3 fatcat:kklqi4kdn5elzdlhahbqggnaye

Regular cylindrical algebraic decomposition [article]

J.H. Davenport, A.F. Locatelli, G.K. Sankaran
2018 arXiv   pre-print
We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set is a regular cell decomposition, in any dimension and independently of the method by which P is constructed  ...  We also show the same for S of dimension at most 3 and P a strong cylindrical algebraic decomposition that is locally boundary simply connected: this is a purely local extra condition.  ...  Proof: A strong c.a.d. P of R n is closure finite, so we just need to show that C ⊂ S is a regular cell.  ... 
arXiv:1803.04029v1 fatcat:feishuafcra7vig6mrydat4aka

Elementary remarks on units in monoidal categories

2008 Mathematical proceedings of the Cambridge Philosophical Society (Print)  
Then we prove that the two notions of units are equivalent in a strong functorial sense.  ...  To start, we describe the semi-monoidal category of all possible unit structures on a given semi-monoidal category and observe that it is contractible (if nonempty).  ...  Note that for strong monoidal functors, both condition (24) and (25) are automatic, so the definition reduces to 3.4 in this case. Proof of Proposition 6.2.  ... 
doi:10.1017/s0305004107000679 fatcat:eygc4paefff7ffsytmbpno42bm

Semi-Automatic Measures Of Activity In Selected South Polar Regions Of Mars Using Morphological Image Analysis

K.-Michael Aye, Ganna Portyankina, Antoine Pommerol, Nicolas Thomas
2010 Zenodo  
After showing a proof of concept in Aye (2010), for a ROI that is comparable to the one previously used for manual counting in Thomas (2009), we now will show results of these semi-automatically  ...  This ROI was chosen for its strong visual variability in ground features.  ...  Covering of fan rims by blue halos (Pommerol, COSPAR 2010) Numbers and areas of Ithaca fans F a n m a t e r ia l s in k s in t o ic e Inca City's fan physics seem to be dominated more by local inclined  ... 
doi:10.5281/zenodo.34129 fatcat:zyf43oejh5csljmcqdwf5z5ske

On symplectic fillings

John B Etnyre
2004 Algebraic and Geometric Topology  
In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic manifold.  ...  We also relate properties of the open book decomposition of a contact manifold to its possible fillings.  ...  (Note a Stein manifold always has a connected boundary so there is no notion of holomorphically semi-fillable.)  ... 
doi:10.2140/agt.2004.4.73 fatcat:l6w73la3cfe55hif2rzytdgwmm

Page 1043 of The Electrical Review Vol. 60, Issue 1544 [page]

1907 The Electrical Review  
—Drrect-CuRRENT Moror-GENERATOR. generator set, consisting of one of their semi-enclosed p.c. motors coupled to a semi-enclosed p.c. generator, both mounted upon a common bed-plate.  ...  Essentially it consists of a “Leitner” variable- speed dynamo, an automatic switch and a small battery of accumu- lators.  ... 

Page 937 of POWER Vol. 75, Issue 25 [page]

1932 POWER  
This valve is arranged with a small ‘ opening to allow the air and other Fig. 2—Two types of Strong inverted- bucket steam traps fitted with the anti- balancing device, the semi-steel above and the forged-steel  ...  In Fig. 1 the valve is shown full open, in Fig. 2 automatically closed after the water attempts to enter a broken or dis- connected _ radia- tor, and in Fig. 3 in partly closed position for equal- ization  ... 

Page 169 of Mathematical Reviews Vol. 37, Issue 1 [page]

1969 Mathematical Reviews  
The proof goes by showing that a neighborhood of B will also be ANE. When Y is metrizable, (Y, B) is automatically semi- canonical, ANE coincides with ANR, and the theorem re- duces to one of A. H.  ...  Theorem: Assume that (Y, B) is semi-canonical, B is a strong neighborhood deformation retract of Y, and both B and Y — B are ANE (for metric pairs); then Y is an ANE.  ... 

Global and semi-global stabilizability in certain cascade nonlinear systems

J.H. Braslavsky, R.H. Miidleton
1996 IEEE Transactions on Automatic Control  
Abstrucf-This paper addresses the issue of global and semi-global stabilizability of an important class of nonlinear systems, namely, a cascade of a linear, controllable system followed by an asymptotically  ...  It is also known, however, that when the linear "connection" to the nonlinear system is nonminimum phase, i.e., it has zeros with positive real part, then global or semi-global stabilizability may be impossible  ...  Fu and A. Feuer for key suggestions in the development of these results.  ... 
doi:10.1109/9.506242 fatcat:q5kebd75bnaj5gtes25wmb6foa

Page 401 of Mathematical Reviews Vol. , Issue 84a [page]

1984 Mathematical Reviews  
In this note, we propose to give a direct proof of the complex version of Motzkin’s transposition theorem for polyhedral cones, using Farkas’ theorem. The method of proof coincides with that of J.  ...  The authors show that their variant of this algorithm converges to a strong Kuhn- Tucker-point of the problem locally R-quadratically.  ... 


2007 Proceedings of the 6th Asia-Pacific Bioinformatics Conference  
In the proof we will make an efficient use of a computational tool 2DHPSolver which significantly speeds up the progress in the technical part of the proof.  ...  The inverse protein folding problem is that of designing an amino acid sequence which has a prescribed native protein fold.  ...  a much deeper case analysis. 2DHPSolver: a semi-automatic prover 2DHPSolver is a tool for proving the uniqueness of a protein design in 2D square lattice under the HP, HPC or strong HPC models. 2DHPSolver  ... 
doi:10.1142/9781848161092_0008 fatcat:occul2zocjefjlwlvzpduvhlaq

Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in $\mathbb {R}^{2}$

Julien Guillod, Peter Wittwer
2018 Proceedings of the American Mathematical Society  
This explicit parameterization of the weak solutions allows us to prove a weak-strong uniqueness theorem for small data.  ...  As a corollary, we obtain infinitely many weak solutions in R^2 parameterized by this mean velocity, which is reminiscent of the expected convergence of the velocity field at large distances to any prescribed  ...  Šverák for valuable comments and suggestions on a preliminary version of the manuscript. This research was partially supported by the Swiss National Science Foundation grants 161996 and 171500.  ... 
doi:10.1090/proc/14087 fatcat:tbcg7fgo4zfnvejekrzpjby6x4
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