1. Some well-known examples of tensors in differential geometry are quadratic forms such as metric tensors, and the Riemann curvature tensor.

2. Some well known examples of tensors in geometry are quadratic forms, and the curvature tensor .

3. Antisymmetric tensors are also called skewsymmetric or alternating tensors

4. Antisymmetric and symmetric tensors

5. Antisymmetric and symmetric tensors

6. Antisymmetric and symmetric tensors

7. Then physical quantities appears as 4-component vectors (first rank tensors) or tensors of second rank.

8. The duality between Covariance and contravariance intervenes whenever a vector or tensor quantity is represented by its components, although modern differential geometry uses more sophisticated index-free methods to represent tensors

9. The formulation of such equations is based upon theorems regarding scalarvalued and tensor-valued tensor functions.

10. This is tensor imaging.

11. Wheel bearings, suspension arms and tensors for motor vehicles

12. Therefore,Henckys strain tensor is used.

13. Torch.Clamp (input, *, max, out=None) → Tensor

14. The notation was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential geometry . The tensor calculus achieved broader acceptance with the introduction of Einstein 's theory of general relativity , around 1915, which is formulated completely in the language of tensors.

15. Tensor properties of the Anharmonic oscillator model

16. Bifocal, trifocal and quadrifocal tensors are used to reduce the calculation time.

17. Arguments recently proposed by Kranyš concerning the nondistinguishability between Abraham's and Minkowski's electromagnetic contributions to the total energy-momentum tensor of the same relativistic, thermodynamically closed system are extended to other electromagnetic energy-momentum tensors (as proposed by Grot and Eringen and de Groot and Suttorp).

18. Key words: quantum chemical calculations, computer program, electric field gradient tensor, quadrupolar coupling constant, nuclear magnetic shielding tensor, Euler angles, alkaline earth chloride hydrates.

19. 4 This, the Riemann curvature tensor, quantifies space-time curvature.

20. The pre-averaged Oseen tensor is avoided in the formulation.

21. In this paper, we propose Capuchin, a tensor-based GPU memory management module that reduces the memory foot- print via tensor eviction/prefetching and recomputation

22. Two different basis tensors are introduced permitting to derive Maxwell's equations by one method.

23. The Weyl Curvature tensor has the same symmetries as the Riemann Curvature tensor, but with one extra constraint: its trace (as used to define the Ricci Curvature) must vanish

24. The state variables are the stress, the stretching and the translation tensor.

25. Blind preparation between the sartorius muscle and the tensor fasciae latae muscle.

26. Diffusion tensor imaging (DTI) is a magnetic resonance imaging-based technique.

27. By this procedure we prove the existence of asymmetricg-tensors for paramagnetic centers of triclinic or monoclinic symmetry.

28. The last of the Abductors is called the tensor fascia lata

29. Because of the tidal motion the dispersion tensor is time dependent.

30. The hip Abductor muscles include-Gluteus Medius Gluteus Minimus Tensor Fascia Lata

31. A tensor A that is Antisymmetric on indices i and j has the property that the contraction with a tensor B that is symmetric on indices i and j is identically 0.

32. TensorFlow.js support multiple different Backends that implement tensor storage and mathematical operations

33. Researchers successfully quantified bone mineralisation, complete stiffness tensor and pore network morphology.

34. The intermediate treatment of tensors article attempts to bridge the two extremes, and to show their relationships.

35. The equations define an effective density tensor which couples the fluid and rod accelerations.

36. Regarding biomedical imaging, researchers applied the enhanced resolution algorithms to improve diffusion tensor imaging.

37. But the tensor C ik= A iB k A kB i is Antisymmetric

38. The dynamic equations are deduced from the unified Minkowski–Abraham–Eckart energy-momentum tensor.

39. A quasi-inextensional linear stability theory of shells is derived in tensor notation.

40. A tensor A that is Antisymmetric on indices i and j has the property that the contraction with a tensor B that is symmetric on indices i and j is identically 0.

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

42. In mathematics, calculus, statistics, logic, vectors, tensors and complex analysis, group theory and topology were developed by Westerners.

43. A tensor A that is Antisymmetric on indices i and j has the property that the contraction with a tensor B that is symmetric on indices i and j is identically 0.

44. Antisymmetric represents the symmetry of a tensor that is Antisymmetric in all its slots

45. More generally, we give a criterion of graded Coherentness of the tensor algebra T_ …

46. It is shown in the paper that tensor analysis is more general than usually claimed.

47. For use in accelerated frames with reference to GR it is usual to write them in a covariant form by means of tensors.

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

49. New techniques, such as quantitative susceptibility mapping (QSM) and susceptibility tensor imaging (STI) allow improved differentiation between blood residues and calcifications and provide an alternative imaging method for fiber tractography with respect to diffusion tensor imaging.

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

51. Littlewood's 4/3 inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory.

52. It can be shown easily that an Antisymmetric second-order tensor has an matrix like this: (C ik

53. A differentiation of structures within the brain stem is possible by the use of diffusion tensor imaging (DTI).

54. For Cl and Co the principal axes of the field gradient tensor in the crystal have been determined.

55. To have this ability, a cosmetic tensor principle must respond to different technological and biochemical requirements.

56. This paper presents an analysis on the stress tensor in non-heat conducting nematic liquid crystals.

57. The structure of these compact objects was investigated using different theories of gravity, the scalar tensor theories.

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

59. Along with axial stress and radial stress, Circumferential stress is a component of the stress tensor in cylindrical coordinates.

60. 9 The Ricci tensor has a non-zero divergence which can be removed by a simple subtraction.

61. To this end, they employed structural magnetic resonance imaging (MRI), diffusion tensor imaging and resting-state functional MRI.

62. It is suggested that abnormal contractions (e.g. tonic contractions) of the tympanic tensor muscle may trigger neurogenic inflammation.

63. 30 We shall now briefly bring out the relationship between the Gaussian curvature and the Riemann curvature tensor.

64. Up to 0.5% cash back  · The NVIDIA Ampere architecture builds upon these innovations by bringing new precisions—Tensor Float (TF32) and Floating Point 64 (FP64)—to accelerate and simplify AI adoption and extend the power of Tensor Cores to HPC

65. Chapter 6 is an introduction to the construction of C*-Algebras using direct limits and tensor products of given C*-Algebras.

66. Anatomy of hip abduction The hip Abductor muscles include the gluteus medius, gluteus minimus, and tensor fasciae latae (TFL)

67. De.wikipedia.org Für ihn folgt die Asymmetrie der Koeffizientenmatrix und die 0 auf der Diagonalen wie beim kovarianten Tensor.

68. The energy and momentum derived within general relativity by Noether's prescriptions do not make a real tensor for this reason.

69. Affine scheme, the spectrum of prime ideals of a commutative ring Affine morphism, a morphism of schemes such that the pre-image of an open Affine subscheme is Affine; Affine space, an abstract structure that generalises the Affine-geometric properties of Euclidean space; Affine tensor, a tensor belonging to an Affine coordinate system

70. It is also shown that the dyad is just the outer product of two vectors, and the relationship between dyads and tensors can be accordingly set up.

71. This constant would restore to the general theory's description of space-time an invariant metric tensor for the fabric of space/existence.

72. The problem is governed by the aspect ratioA, the Rayleigh numberRa, the anisotropy ratioR and the orientation angle θ of the permeability tensor.

73. The key feature of Capuchin is that it makes memory man- agement decisions based on dynamic tensor access pattern tracked at runtime.

74. Up to 0.5% cash back  · Tensor Cores enable mixed-precision computing, dynamically adapting calculations to accelerate throughput while preserving accuracy

75. The development of algebraic topology during the 1940s gave additional incentive for the development of a purely algebraic treatment of the tensor product.

76. More generally, we give a criterion of graded Coherentness of the tensor algebra T_{A}(M) of a certain class of bi-module M

77. More generally, we give a criterion of graded Coherentness of the tensor algebra T_{A}(M) of a certain class of bi-module M

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

79. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski spacetime, displays covariant symmetries, and enables calculations of boosts and spatial rotations without matrices or tensors.

80. Patient specific tumor location, defined by contrast-enhancement, was combined with diffusion tensor imaging derived tractography to determine the location of axons intersecting tumor enhancement (Axites)