Bruns–Gubeladze K-Groups for Quadrangular Pyramid

Popelensky, Th. Yu.; Приходько, М. В.

doi:10.1007/s10958-016-2808-z

Cited by 2 publications

(1 citation statement)

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“…Initiate thinking : try to demonstrate the actual trajectory of the moving point through the intersection of plane geometry proof and analytic geometry proof [5] . Using the proven trajectory properties [6,7] , construct a model and apply this type of curve to the field of UAV communication.…”

Section: Introduce Research Ideasmentioning

confidence: 99%

Quadrangular pyramid curve trajectory for communication performance optimization

Xia,

Luo,

Hou

2023

Third International Conference on Signal Image Processing and Communication (ICSIPC 2023)

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Based on the definition of ellipse: the sum of the distances from the plane to the fixed point F1 and F2 is equal to the trajectory of the moving point P with a constant ( greater than |F1F2| ). It is extended to the study of the trajectory of the point with the distance from the moving point to the three lines and the fixed value, and the corresponding coefficients are added before the distance from the point to the three lines, so that the sum is fixed, that is k1⋅ d(P,l1)+k2⋅ d(P,l2)+k3 ⋅ d(P,l3) = M(M ≥ 0). With the help of drawing software to make the trajectory, based on analytic geometry and Auto CAD, a class of quadrilateral pyramid curve trajectory is obtained, which is a geometric projection similar to the conical curve. The trajectory can be intercepted on the quadrilateral pyramid with a rectangular bottom surface, and then the relationship between the variables in the curve trajectory equation is studied. In the variation, the third straight line is changed into a fixed point, and the obtained trajectory is a conic curve with the point as the focus. In addition, in the study of eccentricity, a triangle model is established to determine what kind of curve the trajectory will be. This kind of curve can be applied to the field of UAV communication. Combined with the relevant knowledge of mathematical analysis, the practicability of this kind of curve for signal enhancement and trajectory optimization is further studied from the perspectives of uniform distribution and Gaussian distribution. Finally, Monte-Carlo simulation and covariance verification are used to prove the help and role of pyramid curve in industry and information field.

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Section: Introduce Research Ideasmentioning

confidence: 99%