Specification for metric dimensions of toroidal sealing rings ('O'-rings) and their housings

Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.

Download Full-text

A multispectral 3D-Endoscope for Cholesteatoma Removal

Current Directions in Biomedical Engineering ◽

10.1515/cdbme-2020-3065 ◽

2020 ◽

Vol 6 (3) ◽

pp. 257-260

Author(s):

Eric L. Wisotzky ◽

Jean-Claude Rosenthal ◽

Anna Hilsmann ◽

Peter Eisert ◽

Florian C. Uecker

Keyword(s):

Multispectral Imaging ◽

Narrow Band ◽

Tissue Classification ◽

Step Size ◽

3D Endoscope ◽

Before And After ◽

Overlay Technique ◽

Ct Data ◽

Metric Dimensions ◽

20 Nm

AbstractWe present a stereo-multispectral endoscopic prototype using a filter-wheel to guide the removal of cholesteatoma tissue in the middle ear. An image-based method is used that combines multispectral tissue classification for the detection of tissue to be removed and 3Dreconstruction to determine its metric dimensions. The multispectral illumination used for tissue classification ranges from λ = 400 nm to λ = 500 nm with step-size of 20 nm, which results in six different narrow-band illumination modes. For classical RGB imaging and metric calculations, a broadband illumination mode is applied before and after the narrow-band illumination. The spectral information is augmented into the broadband mode using an overlay technique. The combination of multispectral imaging with stereoscopic 3D-reconstruction results in new valuable visualization of intraoperative data. This allows to generate a 3D-model of the patients anatomy highlighting the identified malicious tissue and compare the anatomical dimensions with pre-operative CT data.

Download Full-text

A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1971_013_052_02 ◽

1971 ◽

Vol 13 (5) ◽

pp. 330-343 ◽

Cited By ~ 1

Author(s):

D. F. Sheldon

Keyword(s):

Equations Of Motion ◽

Physical Parameters ◽

Recent Experience ◽

Wind Tunnel Testing ◽

Stability Derivatives ◽

Direct Indication ◽

Metric Dimensions ◽

Set Up ◽

The Stability ◽

Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

Download Full-text

Metric Dimensions Of Graphs

10.20944/preprints202106.0392.v1 ◽

2021 ◽

Author(s):

Henry Garrett

Keyword(s):

Metric Dimensions ◽

General Graphs

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

Download Full-text

Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

Contemporary Mathematics and Applications (ConMathA) ◽

10.20473/conmatha.v1i2.17383 ◽

2020 ◽

Vol 1 (2) ◽

pp. 64

Author(s):

Nurma Ariska Sutardji ◽

Liliek Susilowati ◽

Utami Dyah Purwati

Keyword(s):

Graph Theory ◽

Cartesian Product ◽

Metric Dimension ◽

Star Graph ◽

Product Graph ◽

Path Graph ◽

Strong Metric Dimension ◽

Metric Dimensions ◽

Development Result ◽

Corona Product

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

Download Full-text

Une table de correspondance granulometrique "dimensions metriques-dimensions phi-temps de sedimentation standards"

BSGF - Earth Sciences Bulletin ◽

10.2113/gssgfbull.s7-iii.4.383 ◽

1961 ◽

Vol S7-III (4) ◽

pp. 383-386 ◽

Cited By ~ 2

Author(s):

Andre Rosfelder

Keyword(s):

Linear Dimensions ◽

Metric Dimensions

Abstract Devises a table for granulometric correlation of sediments, in which metric dimensions, logarithmic expressions of linear dimensions, and settling velocities serve as parameters.

Download Full-text