scholarly journals Gaussians never extremize Strichartz inequalities for hyperbolic paraboloids

2021 ◽  
Author(s):  
Emanuel Carneiro ◽  
Lucas Oliveira ◽  
Mateus Sousa
Keyword(s):  
Hyperbolic Paraboloids

Spatial Geometric Cells — Quasipolyhedra

2021 ◽  
pp. 30-38
Author(s):  
A. Efremov ◽  
T. Vereschagina ◽  
Nina Kadykova ◽  
Vyacheslav Rustamyan
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Elementary Cell ◽  
Convex Polyhedra ◽  
Curved Surfaces ◽  
Ancient Times ◽  
Graphical Algorithm ◽  
Opening Up ◽  
Hyperbolic Paraboloids ◽  
Three Dimensional Space

Tiling of three-dimensional space is a very interesting and not yet fully explored type of tiling. Tiling by convex polyhedra has been partially investigated, for example, works [1, 15, 20] are devoted to tiling by various tetrahedra, once tiling realized by Platonic, Archimedean and Catalan bodies. The use of tiling begins from ancient times, on the plane with the creation of parquet floors and ornaments, in space - with the construction of houses, but even now new and new areas of applications of tiling are opening up, for example, a recent cycle of work on the use of tiling for packaging information [17]. Until now, tiling in space has been considered almost always by faceted bodies. Bodies bounded by compartments of curved surfaces are poorly considered and by themselves, one can recall the osohedra [14], dihedra, oloids, biconuses, sphericon [21], the Steinmetz figure [22], quasipolyhedra bounded by compartments of hyperbolic paraboloids described in [3] the astroid ellipsoid and hyperbolic tetrahedra, cubes, octahedra mentioned in [6], and tiling bodies with bounded curved surfaces was practically not considered, except for the infinite three-dimensional Schwartz surfaces, but they were also considered as surfaces, not as bodies., although, of course, in each such surface, you can select an elementary cell and fill it with a body, resulting in a geometric cell. With this work, we tried to eliminate this gap and described approaches to identifying geometric cells bounded by compartments of curved surfaces. The concept of tightly packed frameworks is formulated and an approach for their identification are described. A graphical algorithm for identifying polyhedra and quasipolyhedra - geometric cells are described.

Dual-axis buckling of laminated composite skew hyperbolic paraboloids with openings

2018 ◽  
Vol 40 (10) ◽  
Author(s):  
Abhay Kumar Chaubey ◽  
Ishan Jha ◽  
Ajay Kumar ◽  
Munise Didem Demirbas ◽  
Sudip Dey
Keyword(s):  
Laminated Composite ◽  
Hyperbolic Paraboloids

On the rigidity of triangulated hyperbolic paraboloids

1988 ◽  
Vol 418 (1855) ◽  
pp. 425-452 ◽  
Keyword(s):  
Three Dimensional ◽  
Load Test ◽  
Equilibrium Equations ◽  
Triangulated Surfaces ◽  
Historic Review ◽  
Equilibrium Matrix ◽  
Geometric Arrangements ◽  
Hyperbolic Paraboloids

The paper investigates the rigidity of two classes of three-dimensional pin-jointed assemblies which describe triangulated surfaces of hyperbolic paraboloidal shape: type 1 with straight boundaries, and type 2 with parabolic boundaries. The two arrangements have identical horizontal plans. The investigation begins with a brief historic review of techniques for detecting lack of rigidity. The behaviour of both type-1 and type-2 assemblies depends on the number n of bars on each edge of the structure and, although both geometric arrangements satisfy Maxwell rule (3 j ═ b , where j is the number of joints and b is the number of bars) for any value of n , all type-1 assemblies with n even and greater than 2 and type-2 assemblies with n > 1 are in fact not rigid. This result is first proved for some specific cases by the zero-load test; and then for arbitrary values of n . The equilibrium equations of each joint are written down in terms of a stress function, and are then assembled in an equilibrium matrix whose rank is found by general matrix manipulations. The number of inextensional mechanisms and static redundancies is also obtained. The rigidity of assemblies consisting of four interconnected type-1 hyperbolic paraboloidal sheets is also discussed, and it is concluded that they are equally prone to the same kind of misbehaviour.

Bearing capacity of a canopy composed of hyperbolic paraboloids

1971 ◽  
Vol 7 (10) ◽  
pp. 1114-1118
Author(s):  
A. S. Dekhtyar' ◽  
A. O. Rasskazov
Keyword(s):  
Bearing Capacity ◽  
Hyperbolic Paraboloids

XII.—Paraboloidal Co-ordinates and Laplace's Equation

1963 ◽  
Vol 66 (3) ◽  
pp. 129-139
Author(s):  
F. M. Arscott
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Subsequent Paper ◽  
Laplace’S Equation ◽  
Mathieu Functions ◽  
Laplace's Equation ◽  
Normal Surfaces ◽  
Special Cases ◽  
Hyperbolic Paraboloids

SynopsisIn this paper we examine the general paraboloidal co-ordinate system, in which the normal surfaces are elliptic or hyperbolic paraboloids, including as special cases the “parabolic plate” and the “plate with a parabolic hole”. We then show that normal solutions of Laplace's equation in these co-ordinates are given as products of three Mathieu functions, and apply this to the solution of boundary-value problems for Laplace's equation in these co-ordinates. In a subsequent paper the corresponding treatment of the wave equation will be given.

Compound Forms from Elements with Hyperbolic Surfaces

1994 ◽  
Vol 9 (2) ◽  
pp. 87-98 ◽  
Author(s):  
Anatoly G. Trushcov ◽  
Gennady P. Ivanov
Keyword(s):  
Vertical Load ◽  
Hyperbolic Surfaces ◽  
Box Beams ◽  
Large Eccentricity ◽  
Folded Structures ◽  
Hyperbolic Paraboloids

Interesting results obtained while forming structures with the use of single-petalous hyperbolic paraboloids are presented in this paper. Two main methods of forming compound shells are discussed. Formation possibilities are illustrated by examples, such as box beams and columns with walls made of hypars, bunkers and vertical silos, support elements in foundation that work under vertical load with large eccentricity, folded structures, vaulted and domed radial shells that have various plan views. The structures, mentioned above, are made of hypars with straight edges.

scholarly journals Parametric methods for virtual reconstruction. The hyperbolic paraboloids designed by Félix Candela

2018 ◽  
pp. 18
Author(s):  
Federico Luis Del Blanco García ◽  
Laura Perez Lupi
Keyword(s):  
Parametric Methods ◽  
Research Project ◽  
Scientific Debate ◽  
Educational Role ◽  
Virtual Reconstruction ◽  
Felix Candela ◽  
Hyperbolic Paraboloids ◽  
Selection Of

<p>The paper explains the process used in a research project whose objective was the reconstruction of the hyperbolic-parabolic surfaces of a selection of non-built projects designed by Félix Candela.</p><p>The workflow was based on an automation process.  After setting up the variables and define a procedural design, it has been possible to obtain the variation of the projects designed by Candela.</p><p>The virtual reconstruction was done using models parameterized with Grasshopper and experimentally with Houdini FX.</p><p>The results are valid not only for their scientific debate but also can have an educational role in the fields of geometry and architectural communication.</p>

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