1 Let us think about Euclidean geometry first.

2 Previously, Euclidean geometry had stated that parallel lines never meet.

3 For example, recall that in Euclidean geometry the sum of the angles of any triangle is always 1800.

4 But a postulate in a Euclidean system must be accepted in order to maintain the integrity of the whole.

5 It is also mathematics, of course, but Euclidean geometry is by no means the only conceivable mathematical geometry.

6 However, certain ideas taken from ordinary Euclidean geometry are very helpful for us.

7 Why do I refer to Euclidean geometry as a physical theory rather than a branch of mathematics?

8 We choose the Euclidean distance as a similarity coefficient.

9 In the case of non - Euclidean geometry he published no definitive work.

10 Some application of the extended Euclidean algorithm are also given.

11 All the process of clustering based on the Euclidean distance among data vectors.

12 He has been using a mathematical technique called the "Euclidean path integral".

13 Euclidean geometry is not only the leader of the civilization of ancient Greek but also the brilliant achievements of axiomatic approach in mathematics.

14 In this paper, empirical euclidean likelihood ratio statistics are constructed for parametric in a nonlinear model. And prove strong consistency and asymptotic normality of the estimation.

15 The euclidean norm of an n - vector x with real or complex components is defined as following.

16 The essential property and developmental course of Euclidean space, symplectic space and bogus space are studied.

17 To avoid the technical difficulties in actually performing the sum over histories, these curved space-times must be taken to be Euclidean.

18 These principles can be applied to energise and bring to life the hard edges of Euclidean geometry and of the drawing board.

19 However, this revelation did not bring about the destruction of Euclidean geometry, it simply added to it.

20 The common conclusion was the uniqueness and necessity of Euclidean geometry.

21 Entering in details of cluster number 41 , Table 5 reports the customer with the largest Euclidean distance from the prototype.

22 The error performance of continuous phase modulation (CPM) with optimal coherent detection depends on the minimum squared Euclidean distance (MSED).

23 The finite temperature and chemical potential axial anomalies in Euclidean space are studied within the framework of Perturbation theory.

24 These observations allow one to formalize the definition of reflection: a reflection is an involutive isometry of an Euclidean space whose set of fixed points is an affine subspace of codimension 1.

25 It was this concept that Riemann generalized, thereby opening up new vistas in non - Euclidean geometry.

26 Lorentzian wormholes are mainly studied in semiclassical gravity and Euclidean wormholes are studied in particle physics.

27 The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied.

28 The Lorentz transformation of orthogonal bases is derived by means of matrix Euclidean four dimension space.

29 Numerical results show that there is no matching issue for an OOK system using binary linear block code because its bijection between Hamming distance and Euclidean distance.

30 The specular reflection is a very important linear transformation in Euclidean space, and it has a special geometrical explanation in geometrical space.

31 A new RS ( Reed - Solomon ) code decoding algorithm based on the Euclidean Divi - sion is presented.

32 The results showed that this method could be used to reconstruct the surgical scene in a close Euclidean space.

33 Complex network can be tangible objects in the Euclidean space, such as electric power grids, the Internet, highways or subway systems, and the neural network.

34 Different from the Euclidean distance, Mahalanobis distance is independent of the scale of the features and can reflect the internal structure.

35 The paper introduces the one of non- Euclidean geometry - hyperbolic geometry into special theory of relativity.

36 In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.

37 Economics is not a straightforward discipline like Newtonian mechanics or Euclidean geometry.

37 try its best to gather and create good sentences.

38 A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.

39 In addition, we prove the performance ratio of the convex hull insertion for the traveling salesman problem in Euclidean plane has the upper bound about a logarithmic function of the number of nodes.

40 Using some fundamental definition and theorem of unitary space, this paper comes to several conclusions of Hermitian matrix which is parallel to symmetric matrix of Euclidean space.

41 Mathematically it corresponds to a linear transformation for a set of points in the Euclidean space.

42 Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclidof Alexandria.

43 A nonexistence theorem is established for F-harmonic map with finite F-energy from Euclidean space to any Riemannian manifold.

44 The technique supports Euclidean distance measure and L - shift Euclidean distance measure.

45 A united method for greatest common factor and least common multiple of two elements in Euclidean ring is given.

46 The ideal element is a bridge that Euclidean space geometry transits to projection geometry, a cornerstone in project geometry.

47 This method include 3 D Euclidean distance transform, computer the Hessian matrix in every voxel, and visibility test.

48 Given the vectors, one can calculate the distance between two items using measures such as the Manhattan Distance, Euclidean distance, or cosine similarity.

49 The method of fundamental solutions(MFS), one of the radial basis function(RBF) methods, employs the fundamental solutions to the governing differential operator as the Euclidean distance based RBF.

50 The non - Euclidena geometries were in effect subordinated to Euclidean geometry.

51 The simulation results showed that the minimum Euclidean distance and channel capacity were dependent on relative radii and were independent of relative phase.

52 In the third chapter, we discuss the annealing process on the Euclidean space.

53 A few good necessary and sufficient conditions are given by using inner product and length relation for antisymmetric transformation on Euclidean space.

54 On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space, this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.

55 Euclidean norm theory was used to select and optimize the contractors during the evaluation work of the construction projects.

56 A new method to deform surfaces using radial basis function is proposed by replacing the Euclidean distance as geodesic distance.

57 Instructed here Euclidean algorithm, modulus arithmetic as well as the input and output of big numbers.

58 The Euclidean distance is usually chosen as the similarity measure in the conventional K-means clustering algorithm, which usually relates to all attributes.

59 Fractal Geometry is an expanding and deepening system of Euclidean geometry and essentially a new Weltanschauung and methodology.

60 Lastly, we extend Erd s - Mordell inequality to n dimensional Euclidean space E ~ n ( n 3 ).

61 Another simple synthetic proof of finiteness of areas of asymptotic triangles in non - Euclidean geometry is given.

62 Extended Euclidean Algorithm is selected to realize inversion from the standpoint of saving time.

63 By analysing computational complexity, the improved algorithm only requires half a computation required by original Euclidean algorithm, and has high computing precision.

64 A new non-Euclidean distance was introduced to replace the Euclidean distance in the IPCM, and then a new fuzzy clustering, called novel improved possibilistic C-means(NIPCM)clustering was proposed.

65 Based on Euclidean algorithm, this paper gives a new method that can judge similar zero and pole points of a system model and conception of similarly.

66 This article starts with the definition of the Euclidean Geometry and the Non-Euclidean Geometry.

67 The FPGA simulation results show that the modified Euclidean algorithm is feasible.

68 In this part , a centerline extraction based on 3 D Euclidean distance transform is presented.

69 During the recognition phase, Euclidean Distance representing VQ distortion in this project is calculated.

70 Furthermore, a conjecture on further generalization to higher dimension case or general Euclidean space is proposed which requires further study.

71 In this paper, we study the scalarization over Euclidean Jordan algebra vector optimization problem.

72 For instance, it's also the square of the Euclidean norm on R2, the length of a two-dimensional vector, a part of the triangle inequality, and quite a bit more.

72 try its best to gather and build good sentences.

73 In this course we will introduce the basic properties about curves and surfaces in three dimensional Euclidean space.

74 A 2 - D complete Euclidean distance transform algorithm based on contour - stripped is presented in the paper.

75 Each innovation destined to dwarf the one extensive accomplishment of the Greeks - Euclidean geometry.

76 The Euclidean distance is usually chosen as the similarity measure in the conventional K-NN algorithm, which usually relates to all attributes.

77 We prefer the form (5.16.7) since it is in conformity with the definition of scalar product in a complex Euclidean space.

78 The minimum squared Euclidean distance ( MSED ) of 2-ary multi - k continuous - phase frequency - shift keying ( CPFSK ) signal is presented.

79 First, the counterparts of the points on image in camera coordinate system (CCS) are found by utilizing two properties, namely collinearity and Euclidean distance invariability.

80 The TCQ algorithm takes advantage of convolution code, and enlarges the Euclidean distances among quantized data by expanding data dimensions.

81 It has been proved that the nature of independence exists in the axiomatic system of Group, Euclidean space, distance space and topological space.

82 A speech emotion recognition method is also presented based on weighted Euclidean distance template matching, in which the weights of features are calculated by the method of contribution analysis.

83 It is revealed that the paradox solution in Euclidean space is just a solution in symplectic space in the Jordan form which can easily be obtained by conventional mathematical means.

84 Distance-based and density-based clustering algorithms in Euclidean space can be used in this framework.

85 It seems that the proof of Pythagoras's theorem comes pretty much from just consulting the ideas of Euclidean triangle, the exhume of Euclidean geometry and simply doing inferences from those.