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The geometric continuity

Marko Stankovic
2014 Godisnjak Uciteljskog fakulteta u Vranju  
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.
more » ... ључне речи: Аксиоме непрекидности, Архимедова аксиома, Канторова аксиома, Дедекиндова теорема, Аксиома линеарне потпуности.
doi:10.5937/gufv1405039s fatcat:pej4w5rpkncmrpqsbhwcqqmxde

A GEOMETRIC REPRESENTATION (Continued)

E. D. Roe
1918 Mathematics Teacher  
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

Steven Vickers
2014 Journal of Applied Logic  
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]

Raimundas Vidunas
2015 arXiv   pre-print
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

Jörg M. Hahn
1989 Computer Aided Geometric Design  
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

Henry A. Latané
1979 Journal of Banking & Finance  
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]

Clifton Cunningham, Masoud Kamgarpour
2011 arXiv   pre-print
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]

Nick Bezhanishvili and Vincenzo Ciancia and David Gabelaia and Gianluca Grilletti and Diego Latella and Mieke Massink
2022 arXiv   pre-print
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)

G. Darboux
1905 Mathematical Gazette  
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)

G. Darboux
1905 Mathematical Gazette  
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)

G. Darboux
1905 Mathematical Gazette  
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

John A. Gregory, Jörg M. Mahn
1987 Computer Aided Geometric Design  
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)

Chuanmiao Chen
2021 Advances in Pure Mathematics  
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)

Arthur Richard Schweitzer
1913 American Journal of Mathematics  
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

Ping Sheng, R. V. Kohn
1982 Physical Review B (Condensed Matter)  
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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