scholarly journals APLIKASI INTEGRAL UNTUK MEMBUKTIKAN RUMUS KELILING LINGKARAN

2021 ◽  
Vol 9 (1) ◽  
pp. 17-23
Author(s):  
Ayyidatul Imaniyah ◽  
Keto Susanto ◽  
Andika Setyo Budi Lestari
Keyword(s):  
Integral Formula ◽  
Polar Coordinates ◽  
Single Integral

Integral can be used to determine several quantities, one of them is to determine the length of a curve in the plane. It can be applied to prove the circumference formula of a circle. This research aims to explain how to prove the circumference formula of a circle using a single integral expressed in both cartesian and polar coordinates. The method used in this research is a study of literature. The result of this research shows that proving the circumference of a circle can be done by determining the implicit derivative of the circle equation. Then, the circle equation and its implicit derivative are substituted into the integral formula for determining the length of the curve in both cartesian and polar coordinates so that the circumference formula of a circle is obtained.

Rayleigh's problem for a semi-infinite plate

1950 ◽  
Vol 46 (1) ◽  
pp. 127-140 ◽  
Author(s):  
L. Howarth
Keyword(s):  
Viscous Incompressible Fluid ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Leading Edge ◽  
The Other ◽  
Polar Coordinates ◽  
Infinite Plane ◽  
Quarter Plane ◽  
Single Integral ◽  
Approximate Expressions

The problem considered in this paper is the fluid motion arising from a thin semi-infinite plate started to move impulsively from rest (in viscous incompressible fluid at rest) with a velocity, subsequently maintained uniform, parallel to the edge. Two solutions are given, one obtained in polar coordinates is in the form of an infinite series, whilst the other, derived operationally in parabolic coordinates, leads to a single integral for the velocity distribution. The former is convenient for computation in the vicinity of the edge, the latter being more convenient elsewhere.A hypothesis originally introduced by Rayleigh after he had discussed the corresponding flow for an infinite plane has been used here to draw deductions about the steady flow past a quarter-plane whose leading edge is normal to the direction of flow and also to obtain approximate expressions for the effect of the edges on the skin friction of a sufficiently broad rectangle whose length is parallel to the incident stream.

Non-Polar Variation of Latitude

1972 ◽  
Vol 1 ◽  
pp. 93-101 ◽  
Author(s):  
S. Yumi
Keyword(s):  
Polar Motion ◽  
Polar Coordinates ◽  
Normal Variation ◽  
Latitude Variation ◽  
Local Trend

ABSTRACTAnalysing the residual latitude of the station, local trend in latitude variation other than by the polar motion was found.Residual latitude was calculated for each of 26 stations which gave the continuous records of observation during 6 years comprising — 1962 — 1967 as a difference between observed variation of latitude and – normal variation calculated by the polar coordinates Iderived from all the results of 26 stations.As far as the results during these six years are concerned, local trend at any station it seemed to be expressed in terms of 3λ.Assumed effect of local trend on the coordinates values of the instantaneous pole is also discussed.

An integral formula for the even part of the texture function or « the apparition of the fπ and fω ghost distributions »

1982 ◽  
Vol 43 (2) ◽  
pp. 189-195 ◽  
Author(s):  
Claude Esling ◽  
Jacques Muller ◽  
Hans-Joachim Bunge
Keyword(s):  
Integral Formula

The solution problem of Dirihle for equation of Laplace in polar coordinates by method Monte Carlo

2018 ◽  
Vol 2 ◽  
pp. 114-122
Author(s):  
Yu.I. Nikolayenko ◽  
◽  
V.G. Ilvovsky ◽  
S.V. Moiseenko ◽  
◽  
...  
Keyword(s):  
Monte Carlo ◽  
Polar Coordinates ◽  
Solution Problem

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

scholarly journals Approach to hand posture recognition based on hand shape features for human–robot interaction

2021 ◽  
Author(s):  
Jing Qi ◽  
Kun Xu ◽  
Xilun Ding
Keyword(s):  
Gaussian Mixture ◽  
Human Robot Interaction ◽  
Polar Coordinates ◽  
Support Vector ◽  
Hand Posture ◽  
Data Set ◽  
Hand Shape ◽  
Hand Posture Recognition ◽  
Hand Segmentation ◽  
Posture Recognition

AbstractHand segmentation is the initial step for hand posture recognition. To reduce the effect of variable illumination in hand segmentation step, a new CbCr-I component Gaussian mixture model (GMM) is proposed to detect the skin region. The hand region is selected as a region of interest from the image using the skin detection technique based on the presented CbCr-I component GMM and a new adaptive threshold. A new hand shape distribution feature described in polar coordinates is proposed to extract hand contour features to solve the false recognition problem in some shape-based methods and effectively recognize the hand posture in cases when different hand postures have the same number of outstretched fingers. A multiclass support vector machine classifier is utilized to recognize the hand posture. Experiments were carried out on our data set to verify the feasibility of the proposed method. The results showed the effectiveness of the proposed approach compared with other methods.

scholarly journals The surface layer integral method for the modelling of the radial gravity gradient component over sea surface

2019 ◽  
Vol 9 (1) ◽  
pp. 127-132
Author(s):  
D. Zhao ◽  
Z. Gong ◽  
J. Feng
Keyword(s):  
Surface Layer ◽  
Integral Method ◽  
Integral Formula ◽  
Radial Component ◽  
Second Order ◽  
Sea Surface ◽  
Gravity Potential ◽  
Gravity Gradient ◽  
Disturbing Potential ◽  
Gradient Component

Abstract For the modelling and determination of the Earth’s external gravity potential as well as its second-order radial derivatives in the space near sea surface, the surface layer integral method was discussed in the paper. The reasons for the applicability of the method over sea surface were discussed. From the original integral formula of disturbing potential based on the surface layer method, the expression of the radial component of the gravity gradient tensor was derived. Furthermore, an identity relation was introduced to modify the formula in order to reduce the singularity problem. Numerical experiments carried out over the marine area of China show that, the modi-fied surface layer integral method effectively improves the accuracy and reliability of the calculation of the second-order radial gradient component of the disturbing potential near sea surface.

scholarly journals Polar Coordinates View on KM-Arcs

2021 ◽  
Author(s):  
Kanat Abdukhalikov ◽  
Duy Ho
Keyword(s):  
Polar Coordinates
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