Determination of the modulated structure of Sr14/11CoO3 through a (3 + 1)-dimensional space description and using non-harmonic ADPs

1999 ◽  
Vol 55 (6) ◽  
pp. 841-848 ◽  
Author(s):  
O. Gourdon ◽  
V. Petricek ◽  
M. Dusek ◽  
P. Bezdicka ◽  
S.  Durovic ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Atomic Displacement ◽  
Atomic Displacement Parameter ◽  
Third Order ◽  
Modulated Structure ◽  
New Phase ◽  
Space Description ◽  
Three Dimensional Space

Sr14/11CoO3 (i.e. Sr14Co11O33, tetradecastrontium undecacobalt tritriacontaoxide), a new phase in the hexagonal perovskite Sr x CoO3 system, has been prepared and its structure solved from single-crystal X-ray data within the (3 + 1)-dimensional formalism. Sr14/11CoO3 crystallizes in the trigonal symmetry, R3¯m(00γ)0s superspace group with the following lattice parameters: as = 9.508 (2), cs = 2.5343 (7) Å, q = 0.63646 (11)c * and Vs = 198.40 (13) Å3. With the commensurate versus incommensurate test not being conclusive, the structure was considered as commensurate (P32 three-dimensional space group), but refined within the (3 + 1)-dimensional formalism to a residual factor R = 0.0351 for 47 parameters and 1169 independent reflections. Crenel functions were used for the oxygen and cobalt description and a Gram–Charlier expansion up to the third order of the atomic displacement parameter was employed for one Co atom. The structure is similar to that of Sr6/5CoO3, but with a different sequence of the octahedra and trigonal prism polyhedra along the [CoO3] chains. An interesting feature evidenced by the non-harmonic expansion is the displacement of the prismatic Co atoms from the site center, towards the prism rectangular faces.

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

scholarly journals Vector Products As A Tool For The Investigation Of The Isometric Transformation Of Objects

2015 ◽  
Vol 98 (1) ◽  
pp. 60-71
Author(s):  
Ryszard Józef Grabowski
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Vector Product ◽  
Isometric Transformation ◽  
Check Points ◽  
Normal Vectors ◽  
Definition Of ◽  
Three Dimensional Space

Abstract The identification of isometric displacements of studied objects with utilization of the vector product is the aim of the analysis conducted in this paper. Isometric transformations involve translation and rotation. The behaviour of distances between check points on the object in the first and second measurements is a necessary condition for the determination of such displacements. For every three check points about the measured coordinate, one can determine the vector orthogonal to the two neighbouring sides of the triangle that are treated as vectors, using the definition of the vector product in three-dimensional space. If vectors for these points in the first and second measurements are parallel to the studied object has not changed its position or experienced translation. If the termini of vectors formed from vector products treated as the vectors are orthogonal to certain axis, then the object has experienced rotation. The determination of planes symmetric to these vectors allows the axis of rotation of the object and the angle of rotation to be found. The changes of the value of the angle between the normal vectors obtained from the first and second measurements, by exclusion of the isometric transformation, are connected to the size of the changes of the coordinates of check points, that is, deformation of the object. This paper focuses mainly on the description of the procedure for determining the translation and rotation. The main attention was paid to the rotation, due to the new and unusual way in which it is determined. Mean errors of the determined parameters are often treated briefly, and this subject requires separate consideration.

Determination of Sound Velocity in Three-Dimensional Space by Optical Probe

2008 ◽  
Vol 47 (5) ◽  
pp. 3959-3961 ◽  
Author(s):  
Takeshi Ohbuchi ◽  
Koichi Mizutani ◽  
Naoto Wakatsuki ◽  
Hiroyuki Masuyama
Keyword(s):  
Sound Velocity ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Optical Probe ◽  
Three Dimensional Space

In Vivo Determination of the Direction of Rotation and Moment-Angle Relationship of Individual Elbow Muscles

1998 ◽  
Vol 120 (5) ◽  
pp. 625-633 ◽  
Author(s):  
L. Zhang ◽  
J. Butler ◽  
T. Nishida ◽  
G. Nuber ◽  
H. Huang ◽  
...  
Keyword(s):  
Muscle Activation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elbow Flexion ◽  
Joint Movement ◽  
Flexion Extension ◽  
Relationship Of ◽  
Three Dimensional Space

The direction of rotation (DOR) of individual elbow muscles, defined as the direction in which a muscle rotates the forearm relative to the upper arm in three-dimensional space, was studied in vivo as a function of elbow flexion and forearm rotation. Electrical stimulation was used to activate an individual muscle selectively, and the resultant flexion-extension, supination-pronation, and varus-valgus moments were used to determine the DOR. Furthermore, multi-axis moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant submaximal level across different joint positions, which was assumed to result in a constant level of muscle activation. The muscles generate significant moments about axes other than flexion-extension, which is potentially important for actively controlling joint movement and maintaining stability about all axes. Both the muscle DOR and the multi axis moments vary with the joint position systematically. Variations of the DOR and moment-angle relationship across muscle twitches of different amplitudes in a subject were small, while there were considerable variations between subjects.

Determination of Arbitrary Tooth Displacements

1978 ◽  
Vol 57 (5-6) ◽  
pp. 663-674 ◽  
Author(s):  
R.J. Pryputniewicz ◽  
C.J. Burstone ◽  
W.W. Bowley
Keyword(s):  
Dimensional Space ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Double Exposure ◽  
Maxillary Central Incisor ◽  
Modern Technique ◽  
Hologram Interferometry ◽  
Component Loading ◽  
Three Dimensional Space

The noninvasive, modern technique based on the method of double-exposure hologram interferometry was used to measure arbitrary displacements of teeth in the three dimensional space. The experimental studies were carried out on an idealized model of the maxillary central incisor. The results show that the experimental data, based on component loading, are inadequate to accurately predict tooth displacement from an arbitrary force acting in the three dimensional space.

PROBLEM S5 FOR THE THIRD-ORDER HYPERBOLIC EGUATION IN A THREE-DIMENSIONAL SPACE

2020 ◽  
Author(s):  
Irina Nikolaevna Rodionova ◽  
◽  
S.A. Sevastyanova ◽  
Keyword(s):  
Special Class ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Hyperbolic Type ◽  
Darboux Problem ◽  
Third Order ◽  
The Third ◽  
Class Of Functions ◽  
Three Dimensional Space

The article presents a method for solving the boundary value for the complete equation of the thirdorder hyperbolic type with variable coefficients. The solution to the problem posed is based on the solution of the Darboux problem in a special class of functions obtained by the authors. The problem is reduced to a set of uniquely solvable Volterra integral equations, by virtue of which its solution can be obtained in explicit form.

scholarly journals Three-dimensional nanostructure determination from a large diffraction data set recorded using scanning electron nanodiffraction

IUCrJ ◽  
2016 ◽  
Vol 3 (5) ◽  
pp. 300-308 ◽  
Author(s):  
Yifei Meng ◽  
Jian-Min Zuo
Keyword(s):  
Dimensional Space ◽  
Large Angle ◽  
Three Dimensional ◽  
Dark Field ◽  
Data Set ◽  
Angle Rotation ◽  
Diffraction Patterns ◽  
Scanning Electron ◽  
Three Dimensional Space

A diffraction-based technique is developed for the determination of three-dimensional nanostructures. The technique employs high-resolution and low-dose scanning electron nanodiffraction (SEND) to acquire three-dimensional diffraction patterns, with the help of a special sample holder for large-angle rotation. Grains are identified in three-dimensional space based on crystal orientation and on reconstructed dark-field images from the recorded diffraction patterns. Application to a nanocrystalline TiN thin film shows that the three-dimensional morphology of columnar TiN grains of tens of nanometres in diameter can be reconstructed using an algebraic iterative algorithm under specified prior conditions, together with their crystallographic orientations. The principles can be extended to multiphase nanocrystalline materials as well. Thus, the tomographic SEND technique provides an effective and adaptive way of determining three-dimensional nanostructures.

scholarly journals Spatial context effects at different scales: A formal model for egocentric contexts in two- and three-dimensional space

2018 ◽  
Author(s):  
Steffen Hillmert
Keyword(s):  
General Model ◽  
Context Effects ◽  
Formal Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Spatial Context ◽  
Optimal Range ◽  
Scientific Disciplines ◽  
Three Dimensional Space

Spatial context effects are a topic in many scientific disciplines. This paper examines which conceptual steps are necessary for determining the extension, or the appropriate scale, of relevant spatial environments when contexts can be analytically disaggregated into context elements. Adequate models of scale need to specify not only the distance-dependent relevance of context elements but also their distribution and an adequate combination. In this way, it becomes possible to understand why non-monotonic patterns in scale-related context effects have been repeatedly found in spite of common assumptions of distance decay in relevance. In many cases, a distance-related maximum of (aggregate) context relevance can be expected, so that there is an “optimal” range for the measurement of context effects. It is also important to distinguish between applications in two- and three-dimensional space. This general model helps to specify the steps necessary for the determination of spatial context patterns and to identify unrealistic assumptions.

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