Dupin Cyclide and Second-Order Curves. Part 1

2016 ◽  
Vol 4 (2) ◽  
pp. 19-28 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Second Order ◽  
Descriptive Geometry ◽  
Analytical Equation ◽  
Not Given ◽  
Academic Literature ◽  
Order Curve ◽  
Plane Passing ◽  
Dupin Cyclide ◽  
The One ◽  
Order Smoothness

Making smooth shapes of various products is caused by the following requirements: aerodynamic, structural, aesthetic, etc. That’s why the review of the topic of second-order curves is included in many textbooks on descriptive geometry and engineering graphics. These curves can be used as a transition from the one line to another as the first and second order smoothness. Unfortunately, in modern textbooks on engineering graphics the building of Konik is not given. Despite the fact that all the second-order curves are banded by a single analytical equation, geometrically they unites by the affiliation of the quadric, projective unites by the commonality of their construction, in the academic literature for each of these curves is offered its own individual plot. Considering the patterns associated with Dupin cyclide, you can pay attention to the following peculiarity: the center of the sphere that is in contact circumferentially with Dupin cyclide, by changing the radius of the sphere moves along the second-order curve. The circle of contact of the sphere with Dupin cyclide is always located in a plane passing through one of the two axes, and each of these planes intersects cyclide by two circles. This property formed the basis of the graphical constructions that are common to all second-order curves. In addition, considered building has a connection with such transformation as the dilation or the central similarity. This article considers the methods of constructing of second-order curves, which are the lines of centers tangent of the spheres, applies a systematic approach.

Properties of Dupin Cyclide and Their Application. Part 4: Applications

2016 ◽  
Vol 4 (1) ◽  
pp. 21-33 ◽  
Author(s):  
Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Dense Packing ◽  
Descriptive Geometry ◽  
Practical Application ◽  
Surfaces Of Revolution ◽  
Special Cases ◽  
Dupin Cyclide ◽  
Different Diameters

In the first and second parts of the work there were considered mainly properties of Dupin cyclide, and given some examples of their application: three ways of solving the problem of Apollonius using only compass and ruler, using the identified properties of cyclide; it is determined that the focal surfaces of Dupin cyclid are degenerated in the lines and represent curves of the second order – herefrom Dupin cyclide can be defined by conic curve and a sphere whose center lies on the focal curve. Polyconic compliance of these focal curves is identified. The formation of the surface of the fourth order on the basis of defocusing curves of the second order is shown. In this issue of the journal the reader is invited to consider the practical application of Dupin cyclide’s properties. The proposed solution of Fermat’s classical task about the touch of the four spheres by the fifth with a ruler and compass, i.e., in the classical way. This task is the basis for the problem of dense packing. In the following there is an application of Dupin cyclide as a transition pipe element, providing smooth coupling of pipes of different diameters in places of their connections. Then the author provides the examples of Dupin cyclide’s application in the architecture as a shell coating. It is shown how to produce membranes from the same cyclide’s modules, from different modules of the same cyclide, from the modules of different cyclides, from cyclides with the inclusion of other surfaces, special cases of cyclides in the educational process. The practical application of the last problem found the place in descriptive geometry at the final geometrical education of architects in the "Construction of surfaces". Here such special cased of cyclides as conical and cylindrical surfaces of revolution.

Representations of Dupin Cyclides

2017 ◽  
Vol 5 (3) ◽  
pp. 11-24 ◽  
Author(s):  
Николай Сальков ◽  
Nikolay Sal'kov
Keyword(s):  
Second Order ◽  
Single Parameter ◽  
Geometric Constructions ◽  
Order Curve ◽  
Computer Technologies ◽  
Special Cases ◽  
Dupin Cyclide ◽  
Dupin Cyclides ◽  
Confocal Conics

We know very little about such an interesting surface as Dupin cyclide. It belongs to channel surfaces, its special cases are tor, conical and cylindrical surfaces of rotation. It is known that Dupin cyclides are the only surfaces whose focal surfaces, that are surfaces consisting of sets of curvatures centers points, have been degenerated in second-order curves. Two sets give two confocal conics. That is why any study of Dupin cyclides is of great interest both scientific and applied. In the works devoted to Dupin cyclide and published in the "Geometry and Graphics" journal, are presented various properties of cyclides, and demonstrated application of these surfaces in various industries, mostly in construction. Based on the cyclides’ properties in 1980s have been developed numerous inventions relating to devices for drawing and having the opportunity to be applied in various geometric constructions with the use of computer technologies. In the present paper have been considered various options for representation of Dupin cyclides on a different basis – from the traditional way using the three given spheres unto the second-order curves. In such a case, if it is possible to represent four cyclides by three spheres, and when cyclide is represented by the second-order curve (konic) and the sphere their number is reduced to two, then in representation of cyclide by the conic and one of two cyclide’s axes a single Dupin cyclide is obtained. The conic itself without any additional parameters represents the single-parameter set of cyclides. Representations of Dupin cyclides by ellipse, hyperbola and parabola have been considered. The work has been sufficiently illustrated.

Immunohistochemistry Particularities of Retroperitoneal Tumors

2018 ◽  
Vol 69 (7) ◽  
pp. 1813-1816 ◽  
Author(s):  
Ovidiu Gabriel Bratu ◽  
Radu Dragos Marcu ◽  
Bogdan Socea ◽  
Tiberiu Paul Neagu ◽  
Camelia Cristina Diaconu ◽  
...  
Keyword(s):  
Clinical Presentation ◽  
Histopathological Examination ◽  
Good Reason ◽  
Definitive Diagnosis ◽  
Histological Type ◽  
Not Given ◽  
Medical Specialties ◽  
Retroperitoneal Tumors ◽  
Extreme Variability ◽  
The One

Retroperitoneal space is called sometimes no man�s land�and for a good reason: this is disputed anatomical territory for many surgical and medical specialties. Their wide histological diversity and unspecific clinical presentation make them a challenge for the surgeon. In order to improve their detection immunohistochemistry seems to show promising results. Methods of detection have evolved over time to identify as much as possible the histological type of tumor. Because of this extreme variability immunohistochemistry through its various markers is the one that often sets the definitive diagnosis, the simple histopathological examination being insufficient. This paper aims to highlight the main markers used in retroperitoneal tumors. As it can be seen there is a huge histologic areal for these tumors. Some have proven some of them still not. Given the fact that there is a tendency toward personalized therapy it is imperative to identify the histological type of tumor as soon as possible.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

As-Rigid-As-Possible Stereo under Second Order Smoothness Priors

2014 ◽  
pp. 112-126 ◽  
Author(s):  
Chi Zhang ◽  
Zhiwei Li ◽  
Rui Cai ◽  
Hongyang Chao ◽  
Yong Rui
Keyword(s):  
Second Order ◽  
Order Smoothness

A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

2001 ◽  
Vol 699 ◽  
Author(s):  
D.S. McLachlan ◽  
C. Chiteme ◽  
W.D. Heiss ◽  
Junjie Wu
Keyword(s):  
Experimental Data ◽  
Ac Conductivity ◽  
Volume Fraction ◽  
Power Laws ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Equation ◽  
Scaling Properties ◽  
First Order ◽  
Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

A Simple Practical Criterion to Guarantee Second Order Smoothness of Blend Surfaces

1989 ◽  
Author(s):  
J. Pegna ◽  
F.-E. Wolter
Keyword(s):  
Second Order ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Common Boundary ◽  
First Order ◽  
Computer Aided ◽  
The Common ◽  
Blend Surfaces ◽  
Continuous Curves ◽  
Order Smoothness

Abstract Computer Aided Geometric Design of surfaces sometimes presents problems that were not envisioned by mathematicians in differential geometry. This paper presents mathematical results that pertain to the design of second order smooth blending surfaces. Second order smoothness normally requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve Theorem proved here shows that, for the blend to be second order smooth when it is already first order smooth, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. This property may be helpful to the designer since linkage curves can be constructed from low order piecewise continuous curves.

One-Stop Government Portals

2013 ◽  
Vol 9 (3) ◽  
pp. 74-95 ◽  
Author(s):  
Thomas Kohlborn ◽  
Erwin Fielt ◽  
Maximillian Boentgen
Keyword(s):  
Access Point ◽  
Pragmatic Approach ◽  
Academic Literature ◽  
Body Of Knowledge ◽  
Provision Of Services ◽  
One Stop ◽  
Cost Efficient ◽  
The One ◽  
Government Portal ◽  
Service Data

E-government is seen as a promising approach for governments to improve their service towards citizens and become more cost-efficient in service delivery. This is often combined with one-stop government, which is a citizen-oriented approach stressing integrated provision of services from multiple departments via a single access point, the one-stop government portal. While the portal concept is gaining prominence in practice, there is little known about its status in academic literature. This hinders academics in building an accumulated body of knowledge around the concept and makes it hard for practitioners to access relevant academic insights on the topic. The objective of this study is to identify and understand the key themes of the one-stop government portal concept in academic, e-government research. A holistic analysis is provided by addressing different viewpoints: social-political, legal, organizational, user, security, service, data and information, and technical. As an overall finding, the authors conclude that there are two different approaches: a more pragmatic approach focuses on quick wins in particular related to usability and navigation and a more ambitious, transformational approach having far reaching social-political, legal, and organizational implications.

scholarly journals Location Modeling of Final Palaeolithic Sites in Northern Germany

Geosciences ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 430 ◽  
Author(s):  
Wolfgang B. Hamer ◽  
Daniel Knitter ◽  
Sonja B. Grimm ◽  
Benjamin Serbe ◽  
Berit Valentin Eriksen ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Extended Period ◽  
Second Order ◽  
Order Effects ◽  
Interaction Patterns ◽  
Spatial Effects ◽  
Point Distribution ◽  
Location Modeling ◽  
Second Order Effects ◽  
The One

Location modeling, both inductive and deductive, is widely used in archaeology to predict or investigate the spatial distribution of sites. The commonality among these approaches is their consideration of only spatial effects of the first order (i.e., the interaction of the locations with the site characteristics). Second-order effects (i.e., the interaction of locations with each other) are rarely considered. We introduce a deductive approach to investigating such second-order effects using linguistic hypotheses about settling behavior in the Final Palaeolithic. A Poisson process was used to simulate a point distribution using expert knowledge of two distinct hunter–gatherer groups, namely, reindeer hunters and elk hunters. The modeled points and point densities were compared with the actual finds. The G-, F-, and K-function, which allow for the identification of second-order effects of varying intensity for different periods, were applied. The results reveal differences between the two investigated groups, with the reindeer hunters showing location-related interaction patterns, indicating a spatial memory of the preferred locations over an extended period of time. Overall, this paper shows that second-order effects occur in the geographical modeling of archaeological finds and should be taken into account by using approaches such as the one presented in this paper.

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