1. The sine function, hyperbolic tangent, and other non-linear variations on these basic ideas have also been used.

2. In a hyperbolic plane an unlimited number of lines can pass through the point and not meet the given line.

3. Karl Gauss pioneered hyperbolic geometry.

4. The initial boundary value problem for nonlinear hyperbolic equation in three dimensional domain with moving boundary is studied.

5. Impulse hyperbolic partial differential equation oscillation higher order Laplace operator.

6. Elliptical, hyperbolic and parabolic interpolation algorithms are introduced in this dissertation, which are based on central angle division.

7. The hyperbolic function method has been used to study new exact travelling wave solutions for a class of nonlinear evolution equation.

8. In this article holomorphic curves in the complex hyperbolic space are discussed.

9. Two fdmilies Of characteristic lines in the hyperbolic region are not orthogonal.

10. Reducer used Gleason hyperbolic Drive, from single to multi - level multilevel transmission.

11. The convergence analysis for the second order hyperbolic equation with the P 1 - nonconforming finite element is discussed.

12. Furthermore, a hyperbolic function model of calculating the economic loss and the approach to determine the model's parameters are established for river basins.

13. The hyperbolic conservation laws with relaxation appear in many physical systems such as nonequilibrium gas dynamics, flood flow with friction, magnetohydrodynamics, etc.

14. So what is this hyperbolic geometry that corals and sea slugs embody?

15. The results show that the hyperbolic microlens a better coupling - performance.

16. The hyperbolic function method was used to study new exact travelling wave solutions for a class of nonlinear evolution equation.

17. So he theorized that, for democracies, waging war had a hyperbolic boomerang-like effect on society.

18. Tony Scott directs this movie to maximum shock effect with big images, loud music and hyperbolic confrontations.

19. In this paper, we prove the existence of the global solutions of Cauchy problem for quasi-linear hyperbolic equation without convexity condition.

20. Results show that it's rational to illustrate the relationship between skin friction and relative displacement by hyperbolic function.

21. This guidance law avoids the chattering of line-of-sight angular rate of attack missile by introducing the hyperbolic tangent function .

22. Explore to see if the following theorems of plane geometry still hold true under hyperbolic geometry.

23. An artificial boundary numerical method for the exterior problems of the hyperbolic equation is considered.

23. try its best to gather and make good sentences.

24. The results obtained shows the intrinsic difference of the neutral hyperbolic equations from hyperbolic equation.

25. In this paper, some GE schemes for the first order hyperbolic equation with constant coefficients are given. Then we analysis the stability and the error.

26. Spiral bevel gears carbide skiving cutter has designed by method of inclination cut and straight line profile, and the generating surface of cutter is hyperbolic but conic.

27. This paper has given the global uniqueness theory of solutions for a class of inverse problem in 1-D Wave equation of hyperbolic type.

28. According to the data statistics of max transformation aside of pit to time, the paper established 3 typical hyperbolic function of displacement to time (depth).

29. The nonexistence of global weak solution to elliptic equation and the evolution equation, together with the nonexistence of local weak solution to hyperbolic equation is contained in this paper.

30. The relation between piping resistance and dry density may be expressed by a hyperbolic function.

31. The dynamic secant elastic modulus is introduced to analyze the test data, and the results indicate that the dynamic secant elastic modulus-strain curves of all test models are hyperbolic type.

32. This model consists the hyperbolic partial differential equations, boundary conditions and cyclical conditions of the system.

33. This article analyses the reason of hyperbolic error in cutting cone by using arc front form tool, and offers some methods to eliminate or reduce the hyperbolic error.

34. Since 1950' s, the research of numerical method for hyperbolic conservation laws is one of key research directions in computational mathematics.

35. By means of interpolating wavelets theory, we construct an self - adaptive algorithm to solve twodimensional hyperbolic PDEs.

36. Sufficient conditions are obtained for oscillation of solutions of a class nonlinear delay systems of hyperbolic partial differential equation.

37. Methods Based on dynamic error correction BP using artificial neural network with Hyperbolic Tangent function as activation function and the number of hidden node six.

38. The relationship between the differentiability of solution of Cauchy problem of weak—hyperbolic differential equationand its lower term is studied in this paper.

39. After affirming the existence of non-Fourier effect, the hyperbolic equation suited for describing rapidity heat transfer process inside propellant is obtained.

40. The authors show that the hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

41. Based on the analysis of crude oil thixotropy data de- noised by DSWT, a novel four-parameter hyperbolic thixotropy model was put forward.

42. Based on CORDIC algorithm, research reveals how to calculate hyperbolic function by simple hardware.

43. The correlation between ε r and other influential factors a hyperbolic trend.

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

45. The pedestrian overbridge of Haidian Park is located in Beijing Haidian Park, whose steel-concrete continous beam is a bifilar and hyperbolic through box beam.

46. A hyperbolic grid generation method based on upwind scheme has been developed.

47. Diffractions appear as hyperbolic or umbrella-shaped events on a seismic profile.

48. Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping.

49. This general solution consists of either the combinations of trigonometric and hyperbolic functions, or algebraic polynomials.

50. Two mathematic methods are presented to prove that 2-parameter hyperbolic model and exponential model are the superior limit and lower limit of the corresponding new 3-parameter model respectively.

51. From many tests it is concluded that the joint loading, unloading and reloading follow hyperbolic responses, and result in irrecoverable closure deformation with hardening of the joints.

52. We define the distance from a point to a hyperbolic pattern such that detection becomes feasible.

53. An attempt to offer a new treatment of end point error in precipitation titration by using hyperbolic sine function is given in this paper.

53. is a online sentence dictionary, on which you can find nice sentences for a large number of words.

54. Exponential, hyperbolic, and harmonic curve equations are often used to mathematically express the decline curve.

55. Having analyzed and compared some typical solutions to the hyperbolic decline equation, this paper presents a new statistical analytical sieve method.

56. In order to obtain the exact and clear image edge of a heart, the enhancement with hyperbolic function is used in which the constant C is 0.5 or 1.

57. The initial value problem for a nonlinear hyperbolic equation is studied. The existence and uniqueness of the global strong solution to the problem are proved.

58. The hyperbolic conservation laws with relaxation appear in many physical systems floodwith friction, magnetohydrodynamics, etc.

59. For the research on shear deformation characteristics of the discontinuous plane, the hyperbolic function is adopted to describe the shear deformation curve, and the key factors are discussed.

60. The paper studied the impact of velocity analysis and NMO correction based on hyperbolic equation on stack velocity and to time and presented improvement method.

61. Linear triangular element is considered to solve second order hyperbolic equations on anisotropic meshes in 2 - D.

62. The method is an implicit iterative scheme with a hyperbolic sine transform for the matric potential.

63. Starting from paraxial wave equation, analytical propagation expressions of hyperbolic secant pulsed beams with narrowband and broadband are derived.

64. A general class of solutions to nonlinear scalar equations with static cylindrical symmetry is obtained in the form of a hyperbolic function series.

65. Meanwhile, the similar results are obtained for hyperbolic equation under semidiscrete scheme with above elements.

66. In this paper, we show the domain of the existence of the solution on Goursat problem for quasi—linear hyperbolic equation and obtain the Theorem of the existence and uniqueness in above domain.

67. Popp and some experiments, biological photon delayed radiation intensity obeys the hyperbolic function with time.

68. Hyperbolic navigation systems were first implemented as ground-based navigation systems operating in the medium and long-wave radio frequency spectrum like LORAN, DECCA or OMEGA.

69. By analyzing the principle of hyperbolic navigation based on the time difference of arrival(TDOA), the hyperbolic navigation system, which stations are constituted of multi-ultrasonic sensors is used.

70. A class of nonconforming finite elements are applied to hyperbolic equation with semidiscretization on anisotropic meshes, the optimal error estimates are derived.

71. The numeric solution! of hyperbolic equation by FEA indicates that the deductions should comply with the acoustic parameters such as sound velocity, vibration range, wave shape etc.

72. The linear displacement discontinuity model for wave propagation across fracture is extended to nonlinear model, the hyperbolic elastic model(BB model).

73. Telegraph equations, can be looked as cascade connection of two-port network of lumped circuit of transmission line, is a hyperbolic partial differential equations.

74. The dynamic behaviour of a simply supported hyperbolic flat thin shell subjected to a simple harmonic excitation is studied in the paper.

75. After 10 years of research, they proved earlier this year that a curved shape called a hyperbolic paraboloid, which they and others had been folding for years, doesn't actually exist.

76. This paper is devoted to design a variable size block cipher (VSBC) based on the first-order hyperbolic equation with mixed initial-boundary conditions.

77. If the hydraulic noise in the, valve plate is required to be eliminated, the characteristics of preloading and pre-releasing of the cylinder must be hyperbolic type.

78. The shock response of hyperbolic tangent system is investigated under the action of forward sawtooth pulse.

79. The relationship between suction strength and suction was a hyperbolic feature.

80. According to the interpolation principle of time division of an arc, a hyperbolic interpolation algorithm and a parabolic interpolation algorithm based on central angle division are developed.

81. The authors showthe hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

82. Hyperbolic conservation laws with stiff source terms could describe the effect of relaxation as in the kinetic theory of gases, water waves and traffic flows, etc.

83. Then fit heat output curve by exponential function and hyperbolic function, and solved heat output coefficient of different composition ratio cement.

84. The results obtained shows the intrinsic difference type hyperbolic equations with variable time - lag from hyperbolic equations.

85. By using this method, automatic drawing is realized in designing different form turning tools which minimizes the hyperbolic error, increases the design speed and improves drawing quality.

86. Finally, we construct 3 D highly directive antenna based on the hyperbolic medium.

87. In this Paper, a new tyPe of hyperbolic coal furnace of Pearlite expansion is discussed according to the principle of fluidics. Living examples are used for verification.

88. The discovery of hyperbolic space ushered in the field of mathematics that is called non-Euclidean geometry.

89. In this paper, we obtain the global exact controllability for a class of multidimensional semilinear hyperbolic equations with a superlinear nonlinearity.

90. This paper presents a class of quadratic non - uniform hyperbolic B - spline curves with multiple shape parameters.

91. Hamiltonian schemes of four order rod vibration equation are considered and hyperbolic function tanh( x ) is applied.

92. Hyperbolic gear oil is recommended to be used in the differential gears in driving axles.

93. By starting from the paraxial wave equation, the analytical expression of the ultrashort Hyperbolic Secant pulsed beam are deduced.

94. In this paper, the values of the hyperbolic function term in the equation of the 1.5th order differential electroanalysis with DME are calculated by using a TP803 microcomputer.

95. Due to the hyperbolic properties of convection-dominate dispersion equations, the central difference formula often cause numerical dispersion and oscillation even it has two-order precision in space.

96. Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied.

97. The blow-up property of a nonlinear damped hyperbolic equation, which describes the motion of the neo-Hookean elastomer rod, is proven.

98. It concludes the works as follows:(1) The dynamic stress-strain curves of both soft clay and LCES are hyperbolic type.

99. Furthermore, the methods and results in this paper can be extended to the problem for a class of hyperbolic type systems.

100. The shock response of hyperbolic tangent system is investigated under the action of final peak saw tooth shock pulse.

101. The breakage volumetric strain of rockfill is positive and increases with the increase of axial strain in a trend of hyperbolic curve.

102. A class of exact solutions of the Dirac equation are obtained for an electron in the electromagnetic field of a wave guide formed by two pairs of hyperbolic cylinders.

103. Husain Haqqani, Pakistan's ambassador to Washington, has dismissed such warnings as hyperbolic and accused US officials and analysts of being guilty of a "panic reaction".

104. The initial-boundary value problem for hyperbolic equation in one-dimensional domain with moving boundary is studied.

105. The paper introduces the one of non-euclidean geometry - hyperbolic geometry into special theory of relativity.

106. The method and results of this paper can be extended to the problems for a class of hyperbolic type systems as well.

107. This paper explores three ruled surfaces geometry properties about columnar surface, cone surface and hyperbolic paraboloid.

107. try its best to gather and create good sentences.

108. An hyperbolic function was proposed as a load transfer function to analyze the load transfer mechanism of a single pile.

109. Figure 11.3.3–3 Family of hyperbolic flow potentials in the meridional stress plane.

110. This paper discusses the research we have done into the oscillation of the solutions to a neutral type hyperbolic equation under the third boundary condition.