The OFFSET Function

The OFFSET reference, rows, columns, height, iv/dfh) function returns a reference offset from a given reference in a one- or two-dimensional range of cells. Thus, although INDEX and OFFSET are similar, INDEX returns only a single value from a one- or two-dimensional range of cells, while OFFSET can return a reference to a range of cells. 

The reference argument can be a reference to a single cell or a range. If reference is a range of cells and the optional arguments height and width are omitted, then OFFSET returns a reference of the same dimensions as reference. To select a single cell, the formula =OFFSET(reference, rows, columns, 1, 1) must be used. 

For an example of using OFFSET, see A Drop-down List Box on a Worksheet in Chapter 8. 

---

Then the AFM is switched to CM-operation, which may require a slight adjustment of the photodiode position. The indentation measurements are carried out at specified location (using the offset function of the scan menu) as detailed in hands-on example 43. 

The yield surface in strain space is a ciruclar cylinder normal to the 11 plane with radius k/2fi and axis offset from the origin by e ", as shown in Fig. 5.7(b). It may be seen that, if the yield function in stress space is independent of pressure, then the yield function in strain space is independent of volume change and vice versa. 

FIGURE 10.71 The ratio of the horizontal component of the fluid velocity to its local maximum u/ u, as a function of t), at x = 0.75 m for the experimental results, the numerical results obtained using the commercial package for the offset and equivalent wall jet models, and the original and modified Verhoff empirical formulae. 

Figure 1.16 Time domain representation and frequency excitation function of a soft pulse. The soft pulse selectively excites a narrow region of a spectral range and leads to a strong offset-dependent amplitude of the excitation function.

A common problem for both methods lies in the use of potentials that do not possess the correct net attractiveness. This can have the consequence that continuum feamres appear shifted in energy. In particular, there is evidence that the LB94 exchange-correlation potential currently used for the B-spline calculations, although possessing the correct asymptotic behavior for ion plus electron, is too attractive, and near threshold features can then disappear below the ionization threshold. An empirical correction can be made, offsetting the energy scale, but this can mean that dynamics within a few electronvolts of threshold get an inadequate description or are lost. There is limited scope to tune the Xa potential, principally by adjustment of the assumed a parameter, but for the B-spline method a preferable alternative for the future may well be use of the SAOP functional that also has correct asymptotic behavior, but appears to be better calibrated for such problems [79]. 

The transfer function of the hidden units in MLF networks is always a sigmoid or related function. As can be seen in Fig. 44.5b, 0, represents the offset, and has the same function as in the simple perceptron-like networks. P determines the slope of the transfer function. It is often omitted in the transfer function since it can implicitly be adjusted by the weights. The main function of the transfer function is modelling the non-linearities in the data. In Fig. 44.11 it can be seen that there are five different response regions in the sigmoidal function ... 

Example 5.3 Derive the closed-loop transfer function of a system with proportional-integral control and a first order process. What is the offset in this system ... 

The result is an ideal PD controller with the choice of xD = xp. See that you can obtain the same result with IMC too. Here, take the process function as the approximate model and it has no parts that we need to consider as having positive zeros. There is no offset the integrating action is provided by Gp. 

Example 7.7 Consider installing a PI controller in a system with a first order process such that we have no offset. The process function has a steady state gain of 0.5 and a time constant of 2 min. Take Ga = Gm = 1. The system has the simple closed-loop characteristic equation ... 

The autocorrelation function G(t) corresponds to the correlation of a time-shifted replica of itself at various time-shifts (t) (Equation (7)).58,65 This autocorrelation defines the probability of the detection of a photon from the same molecule at time zero and at time x. Loss of this correlation indicates that this one molecule is not available for excitation, either because it diffused out of the detection volume or it is in a dark state different from its ground state. Two photons originating from uncorrelated background emission, such as Raman scattering, or emission from two different molecules do not have a time correlation and for this reason appear as a time-independent constant offset for G(r).58... 

The three components of the final magnetization, which are normalized and the function of the offset 5, can be obtained by... 

In a similar way, the overall rotation axis as a function of the offset can be derived from the rotation matrix... 

As shown in Fig. 17, the BSFS, by a double adiabatic decoupling, is not only significantly reduced compared with that by a single adiabatic decoupling but it also becomes linear as a function of the offset as predicted by Eq. (102). This linear BSFS is corrected by the application of a dilated evolution time =[l+(/lnnS/A/)2]h. 

Fig. 10. Plot of partially saturated 2 magnetization as a function of irradiation offset in the offset-saturation experiment. The crosses represent experimental values and the line is the...

A plot of the 2 magnetization (M /Moo) as a function of the irradiation resonance offset is given for an offset saturation experiment on a sample of degassed cyclohexane (CeHn) in CDCI3 at a temperature of 303 K. At this temperature, the cyclohexane resonance was noticeably narrow at 280 K, the linewidth of the cyclohexane resonance was approximately 1.2 Hz, compared to a width of 0.5 Hz for the internal TMS standard. From the resulting values of T and T2, and the measured low-temperature axial-equatorial chemical shift difference of 45.4 Hz at 100 MHz used in eq. (22), the rate at 293 K was determined to be 1.94 x 10 s Thus, rates on the order of 10 or 10 s are accessible in relatively simple systems using the offset-saturation method. 

Figure 10 Critical current criteria as described in Ref. 29. The electric field vs. current density is shown as a function of magnetic field. The electric field criterion is set and the tangent at that intersection to the field vs current curve is extrapolated to obtain the offset Jc.

Both Bm(x) and DM(x) are similarly distorted versions of true background and offset functions that we may identify, respectively, as BT(x) and DT(x). Thus we may write the measured transmittance as... 

---