scholarly journals On the Theory of a Non-Periodic Quasilattice Associated with the Icosahedral Group

1985 ◽  
Vol 40 (8) ◽  
pp. 775-788
Author(s):  
P. Kramer
Keyword(s):  
Euclidean Space ◽  
General Theory ◽  
Structure Factor ◽  
Point Symmetry ◽  
Space Filling ◽  
Icosahedral Group ◽  
Local Properties ◽  
Global And Local ◽  
Periodic Space

A quasilattice in the euclidean space E3 is generated by dualization of a hexagrid. The construction is based on a general theory of periodic and non-periodic space filling by projection from hypergrids. Global and local properties of the quasilattice are discussed, including the structure factor, the form and packing of the cells, and the point symmetry. The quasilattice is expected to give a description of quasicrystals without periodic order which have recently been found in experiments.

Random tessellations in ℝd

1989 ◽  
Vol 21 (1) ◽  
pp. 37-73 ◽  
Author(s):  
J. Møller
Keyword(s):  
Euclidean Space ◽  
General Theory ◽  
Dimensional Euclidean Space ◽  
Space Filling ◽  
Random Tessellations

This paper presents a general theory of random tessellations (i.e. stochastic aggregates of disjoint and space-filling cells) ind-dimensional Euclidean space. Some particular models of random tessellations are discussed in detail.

Random tessellations in ℝd

1989 ◽  
Vol 21 (01) ◽  
pp. 37-73 ◽  
Author(s):  
J. Møller
Keyword(s):  
Euclidean Space ◽  
General Theory ◽  
Dimensional Euclidean Space ◽  
Space Filling ◽  
Random Tessellations

This paper presents a general theory of random tessellations (i.e. stochastic aggregates of disjoint and space-filling cells) in d-dimensional Euclidean space. Some particular models of random tessellations are discussed in detail.

scholarly journals 22 Year Solar Magnetic Cycle and its relation to Convection Zone Dynamics

2018 ◽  
Vol 13 (S340) ◽  
pp. 9-10 ◽  
Author(s):  
Kiran Jain ◽  
Sushanta Tripathy ◽  
Rudolf Komm ◽  
Frank Hill ◽  
Rosaria Simoniello
Keyword(s):  
Convection Zone ◽  
Magnetic Cycle ◽  
Solar Magnetic Cycle ◽  
Local Properties ◽  
Global And Local

AbstractUsing continuous observations for 22 years from ground-based network GONG and space-borne instruments MDI onboard SoHO and HMI onboard SDO, we report both global and local properties of the convection zone and their variations with time.

scholarly journals Dodecahedral structures with Mosseri–Sadoc tiles

2021 ◽  
Vol 77 (2) ◽  
Author(s):  
Nazife Ozdes Koca ◽  
Ramazan Koc ◽  
Mehmet Koca ◽  
Abeer Al-Siyabi
Keyword(s):  
Euclidean Space ◽  
Golden Ratio ◽  
Root Lattice ◽  
Third Order ◽  
Face To Face ◽  
Icosahedral Group ◽  
3D Space ◽  
Edge Matching ◽  
Inflation Factor

The 3D facets of the Delone cells of the root lattice D 6 which tile the 6D Euclidean space in an alternating order are projected into 3D space. They are classified into six Mosseri–Sadoc tetrahedral tiles of edge lengths 1 and golden ratio τ = (1 + 51/2)/2 with faces normal to the fivefold and threefold axes. The icosahedron, dodecahedron and icosidodecahedron whose vertices are obtained from the fundamental weights of the icosahedral group are dissected in terms of six tetrahedra. A set of four tiles are composed from six fundamental tiles, the faces of which are normal to the fivefold axes of the icosahedral group. It is shown that the 3D Euclidean space can be tiled face-to-face with maximal face coverage by the composite tiles with an inflation factor τ generated by an inflation matrix. It is noted that dodecahedra with edge lengths of 1 and τ naturally occur already in the second and third order of the inflations. The 3D patches displaying fivefold, threefold and twofold symmetries are obtained in the inflated dodecahedral structures with edge lengths τ n with n ≥ 3. The planar tiling of the faces of the composite tiles follows the edge-to-edge matching of the Robinson triangles.

scholarly journals Space-filling Tetrahedra in Euclidean Space

1922 ◽  
Vol 41 ◽  
pp. 49-57 ◽  
Author(s):  
D. M. Y. Sommerville
Keyword(s):  
Euclidean Space ◽  
Triangular Prism ◽  
Space Filling ◽  
Open Mind

In the answer to the book-work question, set in a recent examination to investigate the volume of a pyramid, one candidate stated that the three tetrahedra into which a triangular prism can be divided are congruent, instead of only equal in volume. It was an interesting question to determine the conditions in order that the three tetrahedra should be congruent, and this led to the wider problem – to determine what tetrahedra can fill up space by repetitions. An exhaustive examination of this required one to keep an open mind as regards whether space is euclidean, elliptic, or hyperbolic, and then to pick out the forms which exist in euclidean space.

A uniqueness principle for up ≤ (−Δ)α 2u in the Euclidean space

2016 ◽  
Vol 18 (06) ◽  
pp. 1650019 ◽  
Author(s):  
Y. Wang ◽  
J. Xiao
Keyword(s):  
Weak Solution ◽  
Euclidean Space ◽  
Fractional Order ◽  
Elliptic Equations ◽  
Differential Inequality ◽  
Nonlinear Elliptic Equations ◽  
Local Behavior ◽  
Nonlinear Elliptic ◽  
Global And Local ◽  
Appl Math

This paper establishes such a uniqueness principle that under [Formula: see text] the fractional order differential inequality [Formula: see text] has the property that if [Formula: see text] then a non-negative weak solution to [Formula: see text] is unique, and if [Formula: see text] then the uniqueness of a non-negative weak solution to [Formula: see text] occurs when and only when [Formula: see text], thereby innovatively generalizing Gidas–Spruck’s result for [Formula: see text] in [Formula: see text] discovered in [B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525–598].

scholarly journals System dynamics models as decision-making tools in agritourism

Agricultura ◽  
2016 ◽  
Vol 13 (1-2) ◽  
pp. 5-10 ◽  
Author(s):  
Tadeja Jere Jakulin
Keyword(s):  
Decision Making ◽  
System Dynamics ◽  
Social Factors ◽  
Qualitative And Quantitative ◽  
Causal Connections ◽  
Local Properties ◽  
Dynamics Models ◽  
Global And Local ◽  
And Training ◽  
Develop System

Abstract Agritourism as a type of niche tourism is a complex and softly defined phaenomenon. The demands for fast and integrated decision regarding agritourism and its interconnections with environment, economy (investments, traffic) and social factors (tourists) is urgent. Many different methodologies and methods master softly structured questions and dilemmas with global and local properties. Here we present methods of systems thinking and system dynamics, which were first brought into force in the educational and training area in the form of different computer simulations and later as tools for decision-making and organisational re-engineering. We develop system dynamics models in order to present accuracy of methodology. These models are essentially simple and can serve only as describers of the activity of basic mutual influences among variables. We will pay the attention to the methodology for parameter model values determination and the so-called mental model. This one is the basis of causal connections among model variables. At the end, we restore a connection between qualitative and quantitative models in frame of system dynamics.

scholarly journals Multi-sensor Aerosol Products Sampling System (MAPSS)

2012 ◽  
Vol 5 (5) ◽  
pp. 913-926 ◽  
Author(s):  
M. Petrenko ◽  
C. Ichoku ◽  
G. Leptoukh
Keyword(s):  
Atmospheric Aerosols ◽  
Integrated Analysis ◽  
Sampling System ◽  
Sampling Methodology ◽  
Multiple Sensors ◽  
Direct Cross ◽  
Local Properties ◽  
Complete Set ◽  
Global And Local ◽  
Level 2

Abstract. Global and local properties of atmospheric aerosols have been extensively observed and measured using both spaceborne and ground-based instruments, especially during the last decade. Unique properties retrieved by the different instruments contribute to an unprecedented availability of the most complete set of complimentary aerosol measurements ever acquired. However, some of these measurements remain underutilized, largely due to the complexities involved in analyzing them synergistically. To characterize the inconsistencies and bridge the gap that exists between the sensors, we have established a Multi-sensor Aerosol Products Sampling System (MAPSS), which consistently samples and generates the spatial statistics (mean, standard deviation, direction and rate of spatial variation, and spatial correlation coefficient) of aerosol products from multiple spaceborne sensors, including MODIS (on Terra and Aqua), MISR, OMI, POLDER, CALIOP, and SeaWiFS. Samples of satellite aerosol products are extracted over Aerosol Robotic Network (AERONET) locations as well as over other locations of interest such as those with available ground-based aerosol observations. In this way, MAPSS enables a direct cross-characterization and data integration between Level-2 aerosol observations from multiple sensors. In addition, the available well-characterized co-located ground-based data provides the basis for the integrated validation of these products. This paper explains the sampling methodology and concepts used in MAPSS, and demonstrates specific examples of using MAPSS for an integrated analysis of multiple aerosol products.

Sign in / Sign up

Export Citation Format

Share Document