Complexes of elliptic cylinders with a characteristic manifold of the generator element in the form of coordinate straight lines

2019 ◽  
pp. 82-87
Author(s):  
M. Kretov
Keyword(s):  
Three Dimensional ◽  
Parameter Family ◽  
Coordinate Plane ◽  
Coordinate Line ◽  
The Third ◽  
Characteristic Manifold ◽  
Coordinate Vector ◽  
Line Congruence ◽  
Focal Variety ◽  
Straight Lines

The complex (three-parameter family) of elliptic cylinders is investigated in the three-dimensional affine space, in which the characteristic multiplicity of the forming element consists of three coordinate axes. The focal variety of the forming element of the considered variety is geometrically characterized. Geometric properties of the complex under study were obtained. It is shown that the studied manifold exists and is determined by a completely integrable system of differential equations. It is proved that the focal variety of the forming element of the complex consists of four geometrically characterized points. The center of the ray of the straight-line congruence of the axes of the cylinder, the indicatrix of the second coordinate vector, the second coordinate line and one of the coordinate planes are fixed. The indicatrix of the first coordinate vector describes a one-parameter family of lines with tangents parallel to the second coordinate vector. The end of the first coordinate vector describes a one-parameter family of lines with tangents parallel to the third coordinate vector. The indicatrix of the third coordinate vector and its end describe congruences of planes parallel to the first coordinate plane. The points of the first coordinate line and the first coordinate plane describe one-parameter families of planes parallel to the coordinate plane indicated above.

Differentiable mapping generated by elliptic parabo­loid complexes

2020 ◽  
pp. 76-80
Author(s):  
M. V. Kretov
Keyword(s):  
Existence Theorem ◽  
Three Dimensional ◽  
Tangent Plane ◽  
Scientific Conference ◽  
Differentiable Mapping ◽  
Systems Of Equations ◽  
Elliptic Paraboloid ◽  
The Third ◽  
Canonical Frame ◽  
Coordinate Vector

In three-dimensional equiaffine space, we consider a differentiable map generated by complexes with three-parameter families of elliptic paraboloids according to the method proposed by the author in the mate­rials of the international scientific conference on geometry and applica­tions in Bulgaria in 1986, as well as in works published earlier in the sci­entific collection of Differ. Geom. Mnogoobr. Figur. The study is carried out in the canonical frame, the vertex of which coincides with the top of the generating element of the manifold, the first two coordinate vectors are conjugate and lie in the tangent plane of the elliptic paraboloid at its vertex, the third coordinate vector is directed along the main diameter of the generating element so that the ends are, respectively, the sums of the first and third, and also the sums of the second and third coordinate vec­tors lay on a paraboloid, while the indicatrixes of all three coordinate vec­tors describe lines with tangents, parallel to the first coordinate vector. The existence theorem of the mapping under study is proved, according to which it exists and is determined with the arbitrariness of one function of one argument. The systems of equations of the indicatrix and the main directions of the mapping under consideration are obtained. The indicatrix and the cone of the main directions of the indicated mapping are geomet­rically characterized.

Singularities of line congruences

2003 ◽  
Vol 133 (6) ◽  
pp. 1341-1359 ◽  
Author(s):  
Shyuichi Izumiya ◽  
Kentaro Saji ◽  
Nobuko Takeuchi
Keyword(s):  
Three Dimensional ◽  
Parameter Family ◽  
General Line ◽  
Line Congruence ◽  
Lagrangian Singularities ◽  
Generic Singularities ◽  
Two Parameter

A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

scholarly journals Modeling of dense well block point bar architecture based on geological vector information: A case study of the third member of Quantou Formation in Songliao Basin

2021 ◽  
Vol 13 (1) ◽  
pp. 39-48
Author(s):  
Chao Luo ◽  
Ailin Jia ◽  
Jianlin Guo ◽  
Wei Liu ◽  
Nanxin Yin ◽  
...  
Keyword(s):  
River Sediments ◽  
Three Dimensional ◽  
Songliao Basin ◽  
Point Bar ◽  
Meandering River ◽  
Architecture Model ◽  
The Third ◽  
Continuous Convergence ◽  
Vector Information ◽  
Architecture Modeling

Abstract Although stochastic modeling methods can achieve multiple implementations of sedimentary microfacies model in dense well blocks, it is difficult to realize continuous convergence of well spacing. Taking the small high-sinuosity meandering river sediments of the third member of Quantou Formation in Songliao Basin as an example, a deterministic modeling method based on geological vector information was explored in this article. Quantitative geological characteristics of point bar sediments were analyzed by field outcrops, modern sediments, and dense well block anatomy. The lateral extension distance, length, and spacing parameters of the point bar were used to quantitatively characterize the thickness, dip angle, and frequency of the lateral layer. In addition, the three-dimensional architecture modeling of the point bar was carried out in the study. The established three-dimensional architecture model of well X24-1 had continuous convergence near all wells, which conformed to the geological knowledge of small high-sinuosity meandering river, and verified the reliability of this method in the process of geological modeling in dense well blocks.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

Inferring Structure from Motion in Two-View and Multiview Displays

Perception ◽  
1993 ◽  
Vol 22 (12) ◽  
pp. 1441-1465 ◽  
Author(s):  
Jeffrey C Liter ◽  
Myron L Braunstein ◽  
Donald D Hoffman
Keyword(s):  
Relative Motion ◽  
Apparent Motion ◽  
Structure From Motion ◽  
Three Dimensional ◽  
Rigid Motion ◽  
Parameter Family ◽  
Image Motion ◽  
Heuristic Analysis

Five experiments were conducted to examine constraints used to interpret structure-from-motion displays. Theoretically, two orthographic views of four or more points in rigid motion yield a one-parameter family of rigid three-dimensional (3-D) interpretations. Additional views yield a unique rigid interpretation. Subjects viewed two-view and thirty-view displays of five-point objects in apparent motion. The subjects selected the best 3-D interpretation from a set of 89 compatible alternatives (experiments 1–3) or judged depth directly (experiment 4). In both cases the judged depth increased when relative image motion increased, even when the increased motion was due to increased simulation rotation. Subjects also judged rotation to be greater when either simulated depth or simulated rotation increased (experiment 4). The results are consistent with a heuristic analysis in which perceived depth is determined by relative motion.

Imaging Cracks in Bones Using Acoustic Nonlinearity: A Simulation Study

2011 ◽  
Vol 97 (5) ◽  
pp. 728-733
Author(s):  
Yang Liu ◽  
Xiasheng Guo ◽  
Zhao Da ◽  
Dong Zhang ◽  
Xiufen Gong
Keyword(s):  
Time Reversal ◽  
Three Dimensional ◽  
Harmonic Component ◽  
Ultrasonic Signal ◽  
Long Bone ◽  
Third Harmonic ◽  
Acoustic Nonlinearity ◽  
The Third ◽  
Nonlinear Approach ◽  
Radial Depth

This article proposes an acoustic nonlinear approach combined with the time reversal technique to image cracks in long bones. In this method, the scattered ultrasound generated from the crack is recorded, and the third harmonic nonlinear component of the ultrasonic signal is used to reconstruct an image of the crack by the time reversal process. Numerical simulations are performed to examine the validity of this approach. The fatigue long bone is modeled as a hollow cylinder with a crack of 1, 0.1, and 0.225 mm in axial, radial and circumferential directions respectively. A broadband 500 kHz ultrasonic signal is used as the exciting signal, and the extended three-dimensional Preisach-Mayergoyz model is used to describe the nonclassical nonlinear dynamics of the crack. Time reversal is carried out by using the filtered third harmonic component. The localization capability depends on the radial depth of the crack.

A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?

2009 ◽  
Vol 18 (5) ◽  
pp. 691-705 ◽  
Author(s):  
GYÖRGY ELEKES ◽  
MIKLÓS SIMONOVITS ◽  
ENDRE SZABÓ
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Simple Application ◽  
Quadratic Number ◽  
General Sufficient Condition ◽  
Family Of Curves ◽  
Unit Circles ◽  
Triple Points ◽  
Straight Lines ◽  
Special Case

We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)

The selection of the main axis and the forming plane in automatic profiling and stamping lines

2021 ◽  
pp. 44-48
Author(s):  
O.M. Koryagina
Keyword(s):  
Main Axis ◽  
Labor Costs ◽  
Simple Shape ◽  
Small Thickness ◽  
Advantages And Disadvantages ◽  
The Third ◽  
Large Length ◽  
Straight Lines ◽  
Light Profiles ◽  
Selection Of

The article defines the main axis and the profiling plane in automatic profiling and stamping lines. Specific recommendations are given for choosing the position of the main axis and the profiling plane, depending on the configuration of the manufactured parts of the roll-formed section. Under the general name of profiling in the practice of stamping works, it is meant to obtain rigid and light profiles of large length and various configurations from sheet blanks. Profiling is carried out in four ways: in dies on crank presses, in dies on special bending presses, on universal bending machines (edging machines), on profiling roller machines. The first method, profiling on crank presses, is used for complex semi-closed and open profiles of relatively small length, if there are no special bending presses or profiling machines. The second method, profiling on special bending presses, is used for open and semiclosed profiles up to 5 mm long. The advantage of such presses is the possibility of using simple, and therefore cheap, tools in the manufacture. The third method, profiling on universal bending machines (edging machines), is used for bending parts (profiles of a simple shape in straight lines with different coupling radii determined by the radius of the machine ruler, for which the latter has a set of rulers). Bending machines allow bending materials of small thickness. Low productivity and the need for physical labor costs limit the use of these machines. The fourth method, profiling on roller machines, is used for open, semi-closed and closed profiles. The essence of the profiling process is to gradually change the profile drawing of a flat belt to a given profile when it is moved sequentially through several pairs of shaped rollers arranged sequentially one after the other in the same plane and rotating at the same speed. The article describes in detail the fourth method; the advantages and disadvantages are noted.

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