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A Semi-automatic Proof of Strong Connectivity
[chapter]

2017
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-319-72308-2_4
fatcat:ntzslyrxoncyzccyslps6xqqmm
*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 ...##
###
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*a*€*A*, then f is s-irresolute. (4)*Strong*s-normality is invariant under irresolute pre-semiclosed ...##
###
Elementary remarks on units in monoidal categories

2006
*
arXiv
*
pre-print

Then we prove that the two notions

arXiv:math/0507349v2
fatcat:tuszktgpdzd75inpmn3hxf2nci
*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. ...##
###
From small-overlap conditions to automatic semigroups
[article]

2010
*
arXiv
*
pre-print

We study the

arXiv:0902.3776v3
fatcat:kklqi4kdn5elzdlhahbqggnaye
*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*. ...##
###
Regular cylindrical algebraic decomposition
[article]

2018
*
arXiv
*
pre-print

We show that

arXiv:1803.04029v1
fatcat:feishuafcra7vig6mrydat4aka
*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. ...##
###
Elementary remarks on units in monoidal categories

2008
*
Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

Then we prove that the two notions

doi:10.1017/s0305004107000679
fatcat:eygc4paefff7ffsytmbpno42bm
*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. ...##
###
Semi-Automatic Measures Of Activity In Selected South Polar Regions Of Mars Using Morphological Image Analysis

2010
*
Zenodo
*

After showing

doi:10.5281/zenodo.34129
fatcat:zyf43oejh5csljmcqdwf5z5ske
*a**proof**of*concept in Aye et.al. (2010), for*a*ROI that is comparable to the one previously used for manual counting in Thomas et.al. (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 ...##
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On symplectic fillings

2004
*
Algebraic and Geometric Topology
*

In particular we show that

doi:10.2140/agt.2004.4.73
fatcat:l6w73la3cfe55hif2rzytdgwmm
*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.) ...##
###
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

1996
*
IEEE Transactions on Automatic Control
*

Abstrucf-This paper addresses the issue

doi:10.1109/9.506242
fatcat:q5kebd75bnaj5gtes25wmb6foa
*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. ...##
###
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. ...##
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STRUCTURE-APPROXIMATING DESIGN OF STABLE PROTEINS IN 2D HP MODEL FORTIFIED BY CYSTEINE MONOMERS

2007
*
Proceedings of the 6th Asia-Pacific Bioinformatics Conference
*

In the

doi:10.1142/9781848161092_0008
fatcat:occul2zocjefjlwlvzpduvhlaq
*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 ...##
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Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in $\mathbb {R}^{2}$

2018
*
Proceedings of the American Mathematical Society
*

This explicit parameterization

doi:10.1090/proc/14087
fatcat:tbcg7fgo4zfnvejekrzpjby6x4
*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. ...
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