scholarly journals Constructive geometric generating of concave pyramids of fourth sort

2021 ◽  
Vol 49 (4) ◽  
pp. 1047-1054
Author(s):  
Slobodan Mišić ◽  
Marija Backović
Keyword(s):  
Axial Symmetry ◽  
Equilateral Triangle ◽  
Common Vertex ◽  
Geometric Methods ◽  
Unit Space ◽  
Unit Cells ◽  
The Common ◽  
Polar Distribution

The paper presents the results of the study of the new set of polihedra, the Concave pyramids of the fourth sort, the construction procedures for generating them and their possible application. Correspondingly to the method of generating the Concave cupolae of fourth sort, the Concave pyramids of fourth sort have the similar logic of origination, and their counterpart in regular faced convex pyramids. They are characterised by the polygonal base, deltahedral surface net, obtained by folding the planar net of unilateral triangles, the polar distribution of the unit space cells with common apex - the top of the Concave pyramid. Polihedral surface of the planar net of Concave pyramids is produced by polar distribution of unit cells, consisting of a spatial sexagon and spatial pentagon - six, or five, unilateral triangles grouped around the common vertex. In the deltahedral surface, the two neighbouring unit cells are joined by means of a unilateral triangle in the zone of the polygonal base and a spatial quadrangle with which they share common sides. The criterion of face regularity is respected, as well as the criterion of multiple axial symmetry. The sort of the Concave pyramids is determined by the number of equilateral triangle rows in thus obtained polyhedron's net. The parameters of the solids were determined constructively by geometric methods.

The crystal structure of myoglobin. VI. Seal myoglobin

1960 ◽  
Vol 258 (1293) ◽  
pp. 181-201 ◽  
Keyword(s):  
Tertiary Structure ◽  
Heavy Atom ◽  
Three Dimensional ◽  
Sperm Whale ◽  
Fourier Synthesis ◽  
Heavy Atoms ◽  
Isomorphous Replacement ◽  
Unit Cells ◽  
The Common ◽  
Sperm Whale Myoglobin

Myoglobin from the common seal ( Phoca vitulina ) when crystallized from ammonium sulphate forms monoclinic crystals with space group the unit cell, a = 57·9Å, b = 29·6Å, c = 106·4Å, β = 102°15', contains four molecules. The method of isomorphous replacement has been used in an investigation of the centrosymmetric b -axis projection in which it has been possible to determine signs for nearly all the h0l reflexions having spacings greater than 4Å. Three independent heavy-atom derivatives were employed and the signs so determined have been used to compute a map of the electron density projected on the (010) plane. This projection has been interpreted in terms of the molecule of sperm-whale myoglobin, as deduced by Bodo, Dintzis, Kendrew & Wyckoff (1959) from a three-dimensional Fourier synthesis to 6Å resolution. The results of the interpretation show that the two myoglobin molecules are very similar in form (tertiary structure) in spite of the differences in their amino-acid composition. The relative orientation of the two unit cells with respect to the myoglobin molecule is given and a comparison is made of the positions of the heavy atoms in each molecule.

Spherical Symmetry in the Theory of Elasticity

1958 ◽  
Vol 25 (1) ◽  
pp. 136-140
Author(s):  
F. Goded
Keyword(s):  
General Solution ◽  
Stress Tensor ◽  
Axial Symmetry ◽  
Spherical Symmetry ◽  
Stress Function ◽  
Theory Of Elasticity ◽  
Plane Symmetry ◽  
The Subject ◽  
The Common

Abstract Part 1 of the paper presents a study of the common characteristics of both plane symmetry and axial symmetry in the theory of elasticity; viz., the form of the stress tensor and the existence of further analogous symmetries. In Part 2, the subject deals with the possibility of the existence of further analogous symmetries which are found to be possible only in some specific cases. In particular, spherical symmetry is treated. The method of obtaining the stress function of this new symmetry and the equation which this function must satisfy also are discussed, together with the stresses expressed by means of this stress function. The paper ends with a brief review of a general solution of the stress function and an example of the application of this stress function to a given problem.

scholarly journals Novel kind of decagonal ordering in Al74Cr15Fe11

2020 ◽  
Author(s):  
Haikun Ma ◽  
Zhanbing He ◽  
Hua Li ◽  
Tiantian Zhang ◽  
Shuang Zhang ◽  
...  
Keyword(s):  
Scanning Transmission Electron Microscopy ◽  
Dark Field ◽  
High Angle ◽  
Decagonal Quasicrystal ◽  
Transmission Electron ◽  
Aperiodic Order ◽  
Scanning Transmission ◽  
Unit Cells ◽  
Annular Dark Field ◽  
The Common

Abstract A high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) study of the intermetallic compound Al74Cr15Fe11 reveals a novel kind of aperiodic order. In contrast to the common quasi-unit-cells based on Gummelt decagons, the present structure is related to a covering formed by Andritz decagons, which can also be described by a Hexagon-Bowtie (HB) tiling. This is the first observation of a decagonal quasicrystal with a structure significantly differing from the ones known so far.

scholarly journals The effect of the distribution of variable characteristics determining the asymmetry of the sealing rings sliding surfaces on the values of friction loss coefficients and other selected parameters of oil film

2017 ◽  
Vol 171 (4) ◽  
pp. 107-116
Author(s):  
Piotr WRÓBLEWSKI
Keyword(s):  
Friction Loss ◽  
Common Vertex ◽  
Cylinder Wall ◽  
Bearing Surface ◽  
Oil Film ◽  
Sliding Surfaces ◽  
Asymmetric Shape ◽  
Loss Coefficients ◽  
The Common ◽  
Mathematical Relationships

The article presents the results of research on the effect of the change in coordinates that determine the location of the common vertex of the parabolas and ellipses demonstrating the asymmetric shape of the rings sliding surfaces on the change in the thickness of oil film, the amount of scraped oil, and the oil left on the cylinder wall, once a set of selected sealing rings has passed, as well as the results concerning friction losses. Mathematical relationships of the asymmetric shapes of the rings sliding surfaces were presented, and the values of coefficients characterizing selected parameters of oil film and friction losses were determined. It was confirmed that there is a large dependence of the coordinate values of the vertices determining the asymmetric shapes of these surfaces on the condition and cooperation between piston rings and the cylinder bearing surface, and mainly on the amount of the oil scraped in the selected engine strokes.

Analysis of multiple solutions in powder pattern indexing: the common reciprocal metric tensor approach

2011 ◽  
Vol 44 (4) ◽  
pp. 812-819 ◽  
Author(s):  
Herbert Kroll ◽  
Diedrich Stöckelmann ◽  
Rolf Heinemann
Keyword(s):  
Multiple Solutions ◽  
Coincidence Site Lattice ◽  
Powder Pattern ◽  
Metric Tensor ◽  
Site Lattice ◽  
Reciprocal Vector ◽  
Orientation Matrix ◽  
Unit Cells ◽  
The Common

Powder pattern indexing routines frequently yield multiple solutions,i.e.different reciprocal lattices and unit cells. Here, a method is suggested that reveals whether or not there are numerical and geometric relationships between the solutions. It is based on the detection of a reciprocal vector triplet that is common to two or more proposed reciprocal lattices. Hence, the method can be termed a common reciprocal metric tensor approach. If no such common tensor exists, the different reciprocal lattices are unrelated, but if one exists the lattices are either in a sublattice/superlattice or in a coincidence-site lattice relationship, depending on the character of the respective orientation matrix. Furthermore, the approach can also be used to generate, from a given indexing solution, further valid indexing solutions that could also be produced by indexing routines.

Geometry in three dimensions over GF (3)

1954 ◽  
Vol 222 (1149) ◽  
pp. 262-286 ◽  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Galois Field ◽  
The Other ◽  
Three Dimensions ◽  
Common Vertex ◽  
Line Geometry ◽  
Fundamental Properties ◽  
The Common ◽  
Three Dimensional Space

The object of this paper is to give some account of the geometry of the three-dimensional space S wherein the co-ordinates belong to a Galois field K of 3 marks. A description of the fundamental properties of quadrics is sufficiently long for one paper, and so an account of the line geometry is deferred. The early paragraphs (§§ 1 to 4) are necessarily concerned with geometry on a line or in a plane. A line consists of 4 points; these are self-projective under all 4! permutations. A plane consists of 13 points and has the same number, 234, of triangles, quadrangles, quadri-laterals and non-singular conics. A diagram is helpful, especially when we consider sections by planes in S . The space S has 40 points. Non-singular quadrics are of two kinds: either ruled, when we call them hyperboloids, or non-ruled, when we call them ellipsoids. A hyperboloid H consists of 16 points and has a pair of reguli; the 24 points of S not on H are the vertices of 6 tetra-hedra that form two allied desmic triads. The ellipsoid F is introduced in § 12; it consists of 10 points, the other 30 points of S being separated into two batches of 15 between which there is a symmetrical (3, 3) correspondence. Either batch can be arranged as a set of 6 pentagons, each of the 15 points being the common vertex of 2 of these. The pentagons of either set have all their edges tangents of F and, with their polar pentahedra, have significant properties and interrelations. By no means their least important attribute is that they afford, with F , so apposite a domain of operation for the simple group of order 360. In §§ 23 to 26 are described the operations of the group in this setting. Thereafter the 36 separations of the 10 points of F into complementary pentads are discussed, no 4 of either pentad being coplanar. During the work constructions for an ellipsoid are encountered; one is in § 16, another in § 30.

Mg(OH)2 Crystals Synthesized by CHM Method

2011 ◽  
Vol 688 ◽  
pp. 153-157
Author(s):  
Lin Hong Cao ◽  
Shun Hua Zhi ◽  
Ning Hui Wang
Keyword(s):  
Crystal Growth ◽  
High Temperature ◽  
Temperature Increase ◽  
Raw Materials ◽  
Nitrate Concentration ◽  
Magnesium Nitrate ◽  
Common Vertex ◽  
Vertex Angle ◽  
Polar Plane ◽  
The Common

Using Mg(NO3)2·6H2O as raw materials, Mg(OH)2 crystals were synthesized by a composite-hydroxide-mediated(CHM) method at 160-200 °C for 24 h. Hexagonal plates Mg(OH)2 crystal were formed at high content of magnesium nitrate. The size of the plates increased to 5-15 μm while the content of magnesium nitrate was 30 mmol. The strength of (001) plane became stronger than (101) plane with the high content of magnesium nitrate, and this tendency became more obvious at high magnesium nitrate concentration. It is explained that the more Mg2+ ion fill the polar plane. The strength of (001) plane became stronger than (101) plane at high temperature. It can be explained Mg(OH)2 crystal become more steady with more non-polar plane at high temperature, and the shape of the sample showed a change from irregular to cubic shape with heated temperature increase. It indicates that the Mg(OH)2 crystal growth benefits from high temperature. It is conjectured that the connecting of the [Mg(OH)6]4+ basic units with the common edges change into common vertex angle.

scholarly journals SOLVING APPLIED PROBLEMS OF AUTOMATING THE PREPARATION OF MODERN TECHNOLOGICAL PROCESSES OF MECHANICAL PROCESSING

2019 ◽  
pp. 97-102
Author(s):  
Viktor Dubchak
Keyword(s):  
Equilateral Triangle ◽  
Machine Tools ◽  
Internal Combustion Engines ◽  
Combustion Engines ◽  
Mechanical Processing ◽  
Technological Processes ◽  
Different Types ◽  
Common Center ◽  
The Common ◽  
The Difference

The article proposes a technique for solving applied problems for the preparation of technological processes of mechanical processing on machine tools with numerical programmed control (CNC) of different types of profiled surfaces with the aim of ensuring their further precise connection. In particular, the question of the optimal coverage of the “circle” profile with the common center of these profiles by the “equilateral triangle” profile is investigated. These tasks are relevant in the processing of parts of rotary-piston internal combustion engines, parts of profile joints with equiaxial contour and in other similar technologies. In the work, the value of the function determining the difference of areas, according to which these profiles do not coincide, was obtained, the function was investigated for extremality, two points of its extremum were determined in the domain of definition, it was shown that at one of these points the function acquires a minimum . The conditions for such an extremal coverage of one profile in accordance with another profile are established, figures are given for the formulation and solution of the problem, conclusions are made.

scholarly journals Novel kind of decagonal ordering in Al74Cr15Fe11

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Haikun Ma ◽  
Zhanbing He ◽  
Hua Li ◽  
Tiantian Zhang ◽  
Shuang Zhang ◽  
...  
Keyword(s):  
Microscopy Study ◽  
Dark Field ◽  
Electron Microscopy Study ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Unit Cells ◽  
Annular Dark Field ◽  
Quasiperiodic Structure ◽  
The Common ◽  
Bow Tie

AbstractA high-angle annular dark field scanning transmission electron microscopy study of the intermetallic compound Al74Cr15Fe11 reveals a quasiperiodic structure significantly differing from the ones known so far. In contrast to the common quasi-unit-cells based on Gummelt decagons, the present structure is related to a covering formed by Lück decagons, which can also be described by a Hexagon-Bow-Tie tiling.

scholarly journals Actively Tunable Metalens Array Based on Patterned Phase Change Materials

2019 ◽  
Vol 9 (22) ◽  
pp. 4927 ◽  
Author(s):  
Wei Bai ◽  
Ping Yang ◽  
Shuai Wang ◽  
Jie Huang ◽  
Dingbo Chen ◽  
...  
Keyword(s):  
Phase Change ◽  
Adaptive Optics ◽  
Phase Change Materials ◽  
Phase State ◽  
Large Area ◽  
Dynamic Display ◽  
Unit Cells ◽  
The Common ◽  
First Time ◽  
Change Material

Recently, the metalens has been investigated for its application in many fields due to its advantages of being much smaller than a conventional lens and is compatible with nano-devices. Although metalenses have extraordinary optical performance, it is still not enough in some occasions such as wavefront detection for adaptive optics and display for large area applications. Using a metalens array is an ideal solution to solve these problems. Unfortunately, the common metalens array cannot be adjusted once it is fabricated, which limits its range of application. In this article, we designed an actively tunable metalens array for the first time by arranging the patterned phase change material Ge2Sb2Te5 (GST) appropriately. For the metalens array designed at the wavelength of 4.6 μm, it had excellent broadband performance in the range from 4.5 μm to 5.2 μm. On the other hand, by tuning the phase state of GST, the focus and display of the metalens array can be controlled, acting as switching on or off. Furthermore, any graphics constructed with patterned focal spots can be achieved when the metalens array has sufficient secondary unit cells. The proposed metalens may have potential application value in the adaptive optics and dynamic display field.

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