1, This, the Riemann curvature tensor, quantifies space-time curvature.

2, The Ricci tensor has a non-zero divergence which can be removed by a simple subtraction.

3, The dominant term in the stress-energy tensor is therefore the energy density Too.

4, The resulting tensor equation is automatically valid under all general transformations.

5, Under a general transformation which demonstrates that this tensor is the same in all frames.

6, Firstly, physical laws must be expressible as tensor equations so that they remain valid under transformations to any accelerated frame.

7, There are a number of other tensor properties which are needed in Chapters 6 and 7.

8, B is termed the left Cauchy-Green deformation tensor, both terms having obvious origins in the definitions given above.

9, Some differential geometry and tensor analysis is needed in order to appreciate the full flavour of the theory.

10, The curvature tensor can be identified by using an approach that was introduced in Chapter 3.

11, In this case the rotation tensor R is equal to the direction, cosine L. Example 10.

12, The metric tensor requires one transformation for each of its indices.

13, Einstein also recognized that the stress-energy tensor provided the appropriate tensor description for the distribution and flow of energy in space-time.

14, Gravity gradient tensor; Forward; Edge extraction.

15, Conservation of Mass. Conservation of Momentum. Stress Tensor.

16, We derive the relations between physical and tensor components.

17, Tensor algebra is tied to coordinates.

18, But tensor product wavelets has a number of drawbacks.

19, In addition to the usual material,(http:///tensor.html) it contains useful chapters on electromagnetism and relativistic fluids and introduces the reader to tensor notation.

20, Consequently we can use the quotient theorem to prove that is a tensor.

21, We shall now briefly bring out the relationship between the Gaussian curvature and the Riemann curvature tensor.

22, A more compact way of writing this is where the components form a square matrix: is called a metric tensor.

23, For vacuum solutions, in these regions at most one component, either 4 or 0, of the curvature tensor is non-zero.

24, This leads to the definition of stress as a tensor quantity of rank 2.

25, Appendix B contains more details on the mathematical properties of the Riemann tensor.

26, In Chapter 5 we discovered that physical laws expressed as tensor equations automatically retain their form under general transformations.

27, Applying the usual procedure to obtain this in another frame we obtain so that transforms as a rank 2 tensor.

28, This equation has a different, but still diagonal, metric tensor.

29, A more complete and compact description of curvature in n dimensions is embodied in the Riemann tensor.

30, This can not be a curvature singularity, since the curvature tensor on it is zero.

31, The equivalent permeability tensor of rock mass, which has single set of fractures, is deduced.

32, The anterior iliofemoral approach utilizes the interval between the sartorius muscle and the tensor fascia lata muscle.

33, Non - tensor multivariate wavelets was wildly used in pattern recognition and texture analysis and edge detection.

34, In this paper, a fast algorithm for image interpolation based on the tensor product of matrices is presented, which transforms the vector interpolation model to matrix form.

35, Based on two-dimensional tensor product B-spline wavelet on the interval(BSWI), a class of flat shell elements was constructed with good performance.

36, The rank of matrix which two matrices act right semi - tensor product is given.

37, Accounting the key point of building dynamic model to be setting up 2 steps tensor T(subscript ia) and 3 steps tenser T(subscript ibc) and assembling the equivalent mass matrix.

38, The electromagnetic force of the machine was numerically investigated via virtual work method and Maxwell stress tensor method.

39, A theorem on natural equivalences between a right exact additive functor F which preserves sums and some tensor functor ?B over functor categories is given.

40, The induced spanning subgraph was employed in studying the property of the graph of decomposable tensor.

41, In this paper(), the irreducible tensor basis method in group representation theory is studied further.

42, Furthermore, the semi module of fractions is represented as the extension of scalars, which is defined by a tensor product.

43, In addition, the spheric tensor illustrates better angular dependence of the density function.

44, The researchers looked at the connections in two areas of the brain that control language and social behavior. They used a technique called diffusion tensor imaging.

45, Furthermore, the centroid of a tensor product of a simple Lie triple system and a polynomial ring is completely determined.

46, The existence of a tensor product is proved in the left quasi-normal band category, and the relationship with the tensor product in the semi-group category is provided.

47, The tensor tympani muscle, middle meningeal artery and mandibular nerve are good landmarks to predict and identify the horizontal segment of the internal carotid artery.

48, First, we characterize graphs whose tensor product and lexicographic product admit nowhere-zero 3-flows.

49, The main factors such as pressure, the third invariant of stress tensor, strain hardening and softening, stain rate and tensile damage have been taken into account in the constitutive model.

49, try its best to gather and build good sentences.

50, The anterior approach utilizes the interval between the sartorius and tensor fascia.

51, Objective To test and verify the disconnection theory in conduction aphasia with diffusion tensor imaging.

52, Since 1993, transposition of tensor facia lata was practiced in 102 cases. The results were good.

53, If the legs tend to turn outward, the tensor fascia lata and the front part of the gluteus medius muscles at the front and highest point of the hip bones work to turn them inward.

54, There exist a resistance tensor and a conductance tensor respectively form of second order.

55, In this paper, we will study the tensor product of matrices over a Chain semiring, and.

56, Using the parameterized quark propagator proposed by us in our previous publication, the quark vacuum condensates and tensor susceptibility of QCD vacuum have been calculated.

57, Objective To establish visualization methods of the commissural fibers in the human brain by using diffusion tensor tractography, and to investigate the coherence with known anatomy.

58, Finally, the essential commutant of tensor product of operator algebras is discussed.

59, The G 1 continuity conditions between tensor product B spline surfaces with single interior knots are studied.

60, The lesser petrosal nerve comes from the tympanic plexus running between cochlear window and vestibular window, over recess of tensor sympani muscle and toward otogaglion .

61, It consist of computation of fundamental matrix in two views and of trifocal tensor in three views .

62, The volume integral equation method based on tensor Greens function is used to modeling the transient electromagnetic responses from a reservoir in a layered formation.

63, The induced gauge field if the curvature tensor of fiber bundle.

64, According to the definition of stress tensor and by means of the tensor calculation rule and the concerned stipulations the equivalent theorem of shearing stress is proved in this paper.

65, The trifocal tensor is the mathematical expression of trifocal geometry, it has strict constraints to correspondence points and lines in three images.

66, In this paper we turn out the coherent-state expression of energy-momentum stress tensor in two dimensional Schwarzschild black holes. The results have been discussed as well.

67, Objective To investigate the feasibility of applying diffusion tensor imaging (DTI)-based arcuate fasciculus tractography and intraoperative arcuate fasciculus navigation for neurosurgery.

68, The tensor fascia lata and gluteus medius turn the thigh bone inward, balancing the turning-out force of the gluteus maximus.

69, Objective To exhibit the fibers of cheirokinesthetic center, and to demonstrate fiber changes of agraphia with diffusion tensor imaging and fiber tracking technique.

70, The complete stress tensor of regional stress field is obtained based on the genetic algorithm; and the result is satisfactory.

71, The energy density of the 4-dimensional spacetime is supposed to be dominated by incoherent radiation and the energy-momentum tensor of the internal subspace is a step function.

72, To rectify the geometric deformation of diffusion - tensor imaging ( DTI ) by non - rigid registration.

73, Then the expression of damage-dependent elasticity tensor is deduced and the constitutive equations of damaged rock are built by using an equivalent state.

74, Using the theory of damage mechanics and fracture mechanics, the damage tensor, effective stress tensor and damage strain, etc. of rock mass are defined, propagation equation of damage is developed.

75, Based on three dimensional finite element analyses of magnetic fields, the cogging torque of a prototype motor is calculated using the virtual work and Maxwell stress tensor methods.

76, This paper analyses the physical sence of effective mass of energy band electron and also discusses its tensor.

77, An instrument based on microcomputer and grating tensor can be used to test and analyse the gear-driven error of various ratio gear trains on the spot.

78, Firstly, structure tensor information was used to improve the LBF model, so that a new level set model was constructed with structure tensor information.

79, To overcome the disadvantage of converting permeability coefficients method, the formulas to calculate tensor of karst conduit in global coordinate system are deduced.

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

80, This paper introduces a new concept-mechanical energy flow, studies stress tensor in energy flow and an application of mechanical energy density conservative points in dynamical systems is discussed.

81, The electric and magnetic fields have been amalgamated into electromagnetic field tensor.

82, The invariant tensor under projective transformations of semi - symmetric metric - recurrent connections is obtained.

83, This paper studies the reflection theory for multi-component colloidal suspension systems and presents the method of deriving the rotational diffusion tensor.

84, For wool fibres, Sirolan TENSOR can supply fibre bundle tenacity ( BS ) and bundle extension (BE) , but has some limitations on the analysis of the measured tensile curves of fibre bundles.

85, Objective To explore the effects of bone grafts with muscular pedicles of both musculus tensor fascia lata and musculus sartorius in treating femoral neck fracture(TSFFN).

86, Thereinto, the problem of matching feature points and feature lines introduce the trifocal tensor as the constraint condition.

87, Taking advantage of tensor, succinct writing and artistic form, it discusses generalized Hook's Law from the anisotropic linear elastomer to the isotropic linear elastomer.

88, Furthermore, we shall give Pinching-estimate for general equation and the proof of n-dimensional for the Laplace equation and an application of Hamilton tensor maximum principle.

89, Uses the sourceless magnetic damping tensor to control winding tension.

90, In this article, a new analysis method of network topology for power semiconductor swith circuits-method of tensor transformation, is presented.

91, We have dealt with effective conductivity tensor of the composites with local anisotropic components.

92, The trifocal tensor can eliminate the wrong matches while the epipolar geometry algorithms of feature point and line match can not find them.

93, A nodal analysis method for calculating inertial tensor of rotors is described in this paper.

94, Objective To investigate the pathogenesis of the abnormal diffusion in the white matter tracts in patients with neuromyelitis optics (NMO) using diffusion tensor imaging (DTI).

95, Then we use the expressions to the calculation of the axial vector, vector and tensor vacuum susceptibilities.

96, Normal pressure tensor keeps at zero in the whole simulated zone.

97, Objective To study morphology in the application of transplanting tensor fascia lata.

98, Transformation of unitary operators between two classes is presented according to tensor product transposition similarity theory.

99, The sound-conducting apparatus in the middle-ear of domestic fowls includes the membrana tympani, columella, musculus tensor tympani and several ligaments.

100, General results on centroids of Lie triple systems are developed. Centroids of the tensor product of a Lie triple system and a unital commutative associative algebra are studied.

101, The symmetry of the permittivity tensor is found to be based on the first law of thermodynamics and the non-wastage condition.

102, The major contents include tensor analysis, principle of equivalence, Riemann geometry ...

103, To improve the accuracy, the tensor product weight function which has rectangular influence domain is picked out.

104, A dual relationship between stress tensor and displacement grads tensor is presented.

105, The spacetime structure is expressed by the metric tensor and the metric tensor is confirmed by the Einstein field equation in the general relativity theory.

106, And physical quantities are divided into the scalar quantity, the vector and the tensor.

107, In this paper, the problem of electromagnetic stress tensor of the oblate spheroidal conductor in an electric field is studied.

108, Since the Spline Toolbox can handle splines with vector coefficients, it is easy to implement interpolation or approximation to gridded data by tensor product splines.

109, Brittle deformation in the late stage is mainly marked by tensor - shear faulting.

110, The subscapular artery has a definite and strong branch to the infraspinatus muscle,(http:///tensor.html) and a long collateral branch to the long head of the triceps cervical and the tensor antebrachii.

111, Based on observation and investigation insitu, a method is presented to solve equivalent permeability tensor of rock mass during excavation.

112, A physical quantity that is transformed in this manner is a second - order tensor.

113, By simple tensor techniques, a large amount of simultaneous equations are solved successfully.

114, A general mathematical model of carrier - based aircraft ski jump take - off is derived based on tensor.

115, In this paper we turn out the coherent-state expression of energy-momentum stress tensor in two dimensional Schwarzschild black holes.

116, From the basic formula of coulomb force and ampere force, together with the concept of electric stress tensor, the mathematic formula of electric force and magnetic force is deduced in this article.

117, This paper mainly researches the application that one uses the trifocal tensor to get feature points and feature lines.

118, Finally, through the approximate analysis, the approximate representation on the rotation tensor and stretch tensor is proposed.

119, The anterolateral approach utilizes the interval between the tensor fascia and the gluteus medius .

120, A result of fundamental importance has been proved with regard to the matrix representation of symmetrizing operator on tensor space.

121, Using total scattering cross section and Raman tensor, we make thorough discuss in geometry arrangement about how to measure the spectrum line of the crystal.

122, The present paper offers two proofs of the representation theorem for linear, isotropic tensor functions of a skew argument. The first proof is new.

123, Based a method is presented to solve equivalent permeability tensor of rock mass during excavation.

124, To characterize relative orientation between the loading direction and material fabric(), an anisotropic variable expressed by the joint invariants of the stress tensor and fabric tensor is introduced.

125, This paper discussed the basic form of the wave-vector surface and normal mode of nonreciprocal gyrotropic dielectric tensor.

126, "The auditory area of her brain started taking over the somatosensory area, " says Ro, who used diffusion tensor imaging, which focuses on the brain's white matter connections, to spot the change.

127, Natural frequencies and natural modes are determined by the null-field integral formulation in conjunction with degenerate kernels, tensor rotation and Fourier series.

128, The superficial and deep fascia over the sartorius muscle are divided, medial to the tensor fascia lata muscle.

129, The method for calculating equivalent permeability tensor is introduced, the criterions for determining the tensor validity are presented.

130, This means that constitutive equations must be framed in tensor language.

131, It is indicated that the third-order nonlinear elastic coefficient tensor for quasicrystals with ten-fold symmetry axis has an arbitrary rotation symmetry about the ten-fold axis.