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1. These, also, will be vector fields in space.

2. A new method of gravity gradient vector field for quantitative determination of field source is described in this paper.

3. Well, if you know that your vector field is defined everywhere in a simply connected region, then you don't have to worry about this question of, can I apply Green's theorem to the inside?

4. Using vector algebra and vector field theory, we calculated the total moment of magnetic force acted on a coil carrying current in uniform magnetic field.

5. We present a novel approach for vector field guided solid texture synthesis from 2 D examples.

6. Vector field visualization is an important part of visualization in scientific computing.

7. It says that the work done by a vector field along a closed curve can be replaced by a double integral of curl F.

8. Here we calculate the edge flow vector field by using cubic B spline function.

9. Sound wave has information about scalar field and vector field. But pressure sensor was predominant in underwater acoustic field for a long time.

10. If you take a vector field that is a constant vector field where everything just translates then there is no divergence involved because the derivatives will be zero.

11. OK, so in particular, if you have a vector field that's defined everywhere the plane, then you take any closed curve.

12. And so now, remember, curl of a vector field in space is going to be another vector expression. It has three components.

13. The electric current density vector field also satisfies superposition principle, some applications thereof are introduced.

14. That is a vector field in which the trajectories are going to be circles centered in the z-axis and our vector field is just going to be tangent to each of these circles.

15. In order to accommodate different vector field, the sample image is rotated and zoomed.

15. Wish you can benefit from sentencedict.com and make progress everyday!

16. If I take a constant vector field, so everything translates at the same speed, 0 then obviously when you take the partial derivatives 0 you will just get a bunch of zeros so the curl will be zero.

17. The way that Q moves is completely determined by the Hamiltonian vector field.

18. So, the divergence theorem gives us a way to compute the flux of a vector field for a closed surface.

19. You know it's automatically OK because if you have a closed curve, then the vector field is, I mean, if a vector field is defined on the curve it will also be defined inside.

20. In this paper, a general formula for information content of random vector field under certain subjective condition is derived.

21. an exact differential. Or, if you don't like exact differentials, a the corresponding vector field with i, j and k instead, a gradient field. Let's just apply the criterion.

22. So, in fact, the actual optimal statement you can make is if a vector field is defined in a simply connected region, and its curl is zero, then it's a gradient field.

23. In this paper, we consider some planar quintic Hamiltonian vector field with Z3-equivariant property, get its global phase portraits, and classify its parameter space.

24. In this paper, cluster analysis and fuzzy classification methods for vector field are presented, with an example and preliminary discussion.

25. OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.

26. Let's not worry too much about it. For accuracy we need our vector field to be defined in a simply connected region.

27. In order to alter the integral length automatically(sentencedict.com), the paper uses a method of variational integral length to trace vector field depending on the emanative degree of vector field.

28. Starting from Helmholtz's theorem, the uniqueness conditions of scalar field are obtained based on the fact that the scalar field can be regarded as a special example of vector field.

29. All kinds of ways of kickball, such as perpendicular bisector kickball method, vector field kickball method, are introduced and the implement methods are given, too.

30. Let's say that I have a plane curve and a vector field in the plane.