Currents elements

The current element of a relay is wound for a wide range of current settings in terms of the rated secondary current of the CT, such as 10-80% for a ground fault protection, 50-200% for an overcurrent and 300-800% for a short-circuit protection. At lower current settings, while the VA requirement for the operation of the relay will remain the same, the VA capacity of the CT will decrease in a square proportion of the current. A CT of a correspondingly higher VA level would therefore be necessary to obtain the reduced VA level. 

No bold face will be used for the subscript X of T,x. The current element (il, i2) of can be rewritten as S(Xn Xi2)—S(Xil)S(Xi2). The condensed form of the covariance-matrix is obtained by using the outer product defined in Section 2.1... 

We should be aware that the variables now appear row-wise, so that the current element xf of 1 is the jth measurement of the ith variable. 

Variances and covariances can be lumped together into the n x n symmetric sample covariance or dispersion matrix S (or ) with current element siU2 such that... 

The symmetric sample correlation matrix R (or p) is similarly defined by its current element... 

Let us define X as the m x n matrix with current element xi and the vector ym as the vector with element yt. The m-vector S of residuals <5, is... 

Defining the current element of the matrix A by the following expressions... 

The mxn matrix A of phase compositions is defined by its current element atj, such as... 

M. Rambaut and J. P. Vigier, Ampere forces considered as collective non-relativistic limit of the sum of all Lorentz interactions acting on individual current elements Possible consequences for electromagnetic discharge stability and Tokamak behavior, Phys. Lett. A 148(5), 229-238 (1990). 

Estimate from current element L,-(x, y) center Estimate from left element L,(x — 1, y) left... 

In other words, we could average the data from the four neighboring elements as well as the current element. Omitting the current element from the averaging operation may lead to... 

Figure 10.6 A 3 x 3 mesh of processing elements is initialized with numbers from 1 to 9. The sequence shows what happens if we continue to average the data from neighboring elements. The current element was not included in the averaging operation.

The second step fades the color at the current element into the current average. This can also be viewed as a force that pulls the average into the direction of the color at the current element. Figure 10.8 shows the computed local average color for two different input images. 

Figure 10.7 Oscillatory behavior might result if we do not include the current element into the averaging operation (top). If the current element is also averaged, the oscillatory behavior disappears (bottom).

The first interpolation method (a) calculates the color Cp at point P by interpolating the data from positions A and B. Let cA and cg be the pixel color at positions A and B. Let a be the direction of the gradient at the current element. Then the color at position P can be calculated as... 

Let a(front), a(back), a(left), and a(right) be the interpolated colors of the rotated coordinate system. Let c(x, y) be the color at the current element. Now we can calculate local space average color a, for color band i by averaging the colors obtained from the left and the right along the line of constant illumination ... 

Figure 12.8 Care must be taken at the border elements. The pixel values outside of the grid of processing elements are unknown. No assumption should be made about these pixel values. Therefore, we only average the data of the current element and the interpolated value along the line of constant illumination.

Now that we know the position of the center of the curvature, we can calculate the points where the unit circle around the current element and the circle that describes the curvature intersect. This is illustrated in Figure 12.12. Let us assume that the center of the curvature is located at point (0, r). This simplifies the calculation of the two points of intersection. We have to calculate the two point of intersection Pi and P2. The following two equations describe both circles. 

Finally, the color from the current element is slowly faded into the result... 

Fig. 9.2 Magnetic induction arising from a current element.

The SI equations of electromagnetic theory are usually used with physical quantities in SI units, in particular the four units m, kg, s, and A for length, mass, time and electric current. The basic equations for the electrostatic force between charges Qx and Q2, and for the electromagnetic force between current elements It dlx and I2 d/2, in vacuum, are written... 

In the more usual description of the emu system only three base units and three independent dimensions are used. The dimension (electric current) is defined to be the same as that of (force)1/2, so that 1 (emu of current)2 = lgcms 2 = l dyn. The (emu of current) then disappears as a unit, and the constant /i0(ir) is dimensionless and equal to 1, so that it may be omitted from all equations. Thus equation (4b) for the force between current elements in vacuum, for example, becomes simply... 

This is the current element of the infinite symmetric matrix C (see Table 1), the elements of which decay rapidly apart from the diagonal and tend to be constant values on each line parallel to the diagonal. If this line is marked by k such that I / - /1 = k, the limiting value for large i and / is ... 

Afh (q) is the current element of a matrix A (q) called the constraint-matrix. A (q) is a real symmetric matrix whose diagonal elements are positive it depends on the generalized coordinates as variables and parametrically on the constraints. This matrix possesses an inverse since det A(q) = 0 is not possible it would correspond to a supplementary relationship between the coordinates only, i.e a supplementary holonomic constraint. 

Relation (5.89) gives the value of each element of matrix (XX ), where the symbol dj]j represents a current element, as shown in relation (5.88),... 

Find Qpfc, the absolutely largest current element in column k that lies in a row not yet selected for pivoting. If Qpfc is negligible, skip to step 4 otherwise, accept it as the pivot for stage k and go to step 2. 

Reciprocity relation (8.138) shows that the electric field component excited at r" in the direction of b by an electric current element a at r is identical with the electric field component excited at r in the direction of a by an electric current element b at r". 

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