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The geometric continuity
2014
Godisnjak Uciteljskog fakulteta u Vranju
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Сажетак: Циљ рада је савремено заснивање геометријске теорије непрекидности, која се темељи на двема аксиомама четврте групе -Архимедовом и Канторовом аксиомом. Доказане су разне последице Архимедове и Канторове аксиоме, попут Канторове и Дедекиндове теореме. Дат је посебан осврт на Хилбертово аксиоматско заснивање геометрије, које уместо Канторове аксиоме користи аксиому линеарне потпуности. На крају, рад илуструје употребу аксиома непрекидности и њихових последица у доказивању неких теорема.
doi:10.5937/gufv1405039s
fatcat:pej4w5rpkncmrpqsbhwcqqmxde
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... ључне речи: Аксиоме непрекидности, Архимедова аксиома, Канторова аксиома, Дедекиндова теорема, Аксиома линеарне потпуности.
A GEOMETRIC REPRESENTATION (Continued)
1918
Mathematics Teacher
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a geometric representation. ...
2(25
-
2g
-
3)'
(49)
(50)
For
>
, symmetry requires that there shall be in addition to
the continuous positive real value of y also negative values for
special values of x, as for
2p -f-I ...
fatcat:yqw4mptaf5f3zelhy6ueu2axae
Continuity and geometric logic
2014
Journal of Applied Logic
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Following Grothendieck's view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. ...
The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers and maps as bundles. ...
To put it another way, the geometric mathematics has an intrinsic continuity (since geometric morphisms are the continuous maps between toposes). ...
doi:10.1016/j.jal.2013.07.004
fatcat:hn25epegnzdrvpf252l2disf5m
Building geometrically continuous splines
[article]
2015
arXiv
pre-print
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With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions ...
Lastly, a comprehensive example is presented, and practical perspectives of geometric continuity are discussed. ...
Geometric continuity [6] , [10] , [24] is a general technique to produce visually smooth surfaces in Computer Aided Geometric Design (CAGD). ...
arXiv:1510.07475v1
fatcat:qozmpwoucvbzzpaebwflnz7xy4
Geometric continuous patch complexes
1989
Computer Aided Geometric Design
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A theory of geometric continuity of arbitrary order is presented. Conditions of geometric continuity at a vertex where a number of patches meet are investigated. ...
Geometric continuous patch complexes are introduced as the appropriate setting for the representation of surfaces in CAGD. ...
The basic concepts of geometric continuity, geometric characterisations of first and second order continuity and the reparameterization approach for continuity of arbitrary order, were already introduced ...
doi:10.1016/0167-8396(89)90006-x
fatcat:7caq3jc5bzauxiie36jc2btlk4
The geometric mean criterion continued
1979
Journal of Banking & Finance
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The cost measured in these probabilities can be calculated for decisions which for utility reasons or otherwise do not maximize the geometric mean. ...
My main interest has been in the tfiird goal -the maximization of the expected growth rate or, what is the same thing, ~ maximization of G, the geometric mean of the probability distribution of returns ...
doi:10.1016/0378-4266(79)90024-4
fatcat:wjduea4sfrgnrbeqeyrnvlzsdm
Geometrization of continuous characters of Z_p^×
[article]
2011
arXiv
pre-print
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Thus, we think of L ψ as the geometrization of ψ. ...
We propose to think of K χ := Tr −1 n (χ) as the geometrization of χ, when χ : Z × p → Q × ℓ is a continuous character of depth n. We do not discuss how to vary n in the present text. ...
arXiv:1012.0213v2
fatcat:jrwr7sscjbarjcyvpshl2hoxmq
Geometric Model Checking of Continuous Space
[article]
2022
arXiv
pre-print
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Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models ...
Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence. ...
This is the key for introducing a novel geometric model checking technique to analyse continuous space. ...
arXiv:2105.06194v2
fatcat:w6sqisekjndgrnhrsydoaokftq
The Development of Geometrical Methods (Continued)
1905
Mathematical Gazette
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But I must now point out another stimulus to great progress in geometrical research. ...
(To be continued.) This content downloaded from 129.16.69.49 on Mon, 28 Dec 2015 12:10:53 UTC All use subject to JSTOR Terms and Conditions
* Krummungsschwerpunkt [Tr.]. ...
doi:10.2307/3602736
fatcat:vmbrbdsptjefbnu3j3jwr54mom
The Development of Geometrical Methods (Continued)
1905
Mathematical Gazette
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THE DEVELOPMENT OF GEOMETRICAL METHODS. XI. HERE, again, in this infinitesimal branch of Geometry we find the two tendencies which I pointed out in connection with the geometry of finite quantities. ...
METHODS. 161 THE DEVELOPMENT OF GEOMETRICAL METHODS. 161 course on a given surface. ...
The aim of this book, as stated by the author, is to give in a compact form a treatment of so much of the Science of Dynamics as should DEVELOPMENT OF GEOMETRICAL METHODS. 161 THE DEVELOPMENT OF GEOMETRICAL ...
doi:10.2307/3602529
fatcat:oh3i7zauabg4pkk74tyimrtibm
The Development of Geometrical Methods (Continued)
1905
Mathematical Gazette
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THE DEVELOPMENT OF GEOMETRICAL METHODS. XIII. ...
By continuing the study of these special transformations, Lie was led to construct progressively his masterly theory of continuous groups of transformations, and to bring to light the important role played ...
doi:10.2307/3603882
fatcat:q5sz3emuvjfifexe4lazvvyzae
Geometric continuity and convex combination patches
1987
Computer Aided Geometric Design
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2 C reader should note that the concept of 'geometric continuity', now being considered within the field of c.a.g.d., has already been addressed by the subject of differential topology. ...
This result, 2 C 2 C which may seem surprising, has serious implications for the development of 2 C surface patches for computer aided geometric design (c.a.g.d) based on convex combination ideas. ...
doi:10.1016/0167-8396(87)90026-4
fatcat:jtwgq3zsqzhxvol3cszn62c4d4
Geometric Proof of Riemann Conjecture (Continued)
2021
Advances in Pure Mathematics
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We shall continue to complete the geometric analysis of ξ in section 3. ...
of Geometric Analysis In previous papers [7] [8] [9] , we have proposed geometric analysis and proved three results: Theorem 1. ...
doi:10.4236/apm.2021.119051
fatcat:cnfx4yjiknf6fdx4gdksltn4tu
A Theory of Geometrical Relations (Continued)
1913
American Journal of Mathematics
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If K is collinear with an edge of /y, then the theorem is easily verified by theorem 26 and A Theory of Geometrical Relations. definition 2. ...
XLIII (1893). t To complete, therefore, the system 3K3 for euclidean geometry, we must first add to this system an axiom of Dedekind continuity. The latter may be expressed in a variety of ways; ? ...
doi:10.2307/2370203
fatcat:r6dzk5vw6zfahdjfrwcbo54yfa
Geometric effects in continuous-media percolation
1982
Physical Review B (Condensed Matter)
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The discrepancies occur in part because the components of a continuous-media percolating system can have various geometric shapes and correlated arrangements, features that are difficult to model by any ...
The paper concludes with a discussion of possible implications for three-dimensional continuous-media percolating systems. ...
The discrepancies occur in part because the components of a continuous-media percolating system can have various geometric shapes and correlated arrangements, features that are difficult to model by any ...
doi:10.1103/physrevb.26.1331
fatcat:qilu4ne6jvab7fpqdqbe3tpkyu
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