Inversion, multiple

Following the description of the non-gradient SIMBA (selective inverse multiple bond analysis) experiment by one of the authors in 1991 [176], a number of reports describing related methods appeared [177—183]. There have been a few successful applications of SIMBA experiments reported in the literature [70, 184—186] used to establish specific correlations to complete structure assignments. 

It is clear that the operators (ajtl form a group if the set of operators E, R, S,. . . , forms a point group. Every element has an inverse multiplication produces another element o t and every operator takes the system into itself. When the translational vector is defined in an integer representation... 

In the past, the control rod drive stroke was calculated by the operators prior to manual control when approaching criticality. After the installation of the system, it calculates and displays an inverse multiplication curve and the stroke of each control rod subassembly that needs to be driven using the neutron flux and the vertical control rod position. The reliability of this system was validated during a complete operational cycle of the MK-II core. It was also demonstrated that the operation guides provided by the system were very similar to those chosen by the experienced JOYO operators. 

Copp BR, Blunt JW, Munro MHG (1989) A biologically active 1,2,3-trithiane derivative from the New Zealand ascidian Aplidium sp. D. Tetrahedron Lett 30 3703-3706 Copp BR, Ireland CM, Barrows LR (1991) Wakayin a novel cytotoxic pyrroloiminoqui-none alkaloid from the ascidian Clavelina species. J Org Chem 56 4596-4597 Crouch RC, Martin GE (1991) Selective inverse multiple bond analysis. A simple ID experiment for the measurement of long-range heteronuclear coupling constants. J Magn Reson 92 189-194... 

Perhaps the simplest and most obvious way to compute the opmtional space inertia matrix (or its inverse) is by the explicit inversion and multiplication of the Jacobian and joint space inertia matrices as shown in Equations 4.19 and 4.20. We will call this the Explicit Inversion/Multiplication Method. Although we will see that this is not the most efficient approach, it is in standard use today and may serve as a benchmark for new computational approaches. 

Table 4.1 Algorithm for the Ex dicit Inversion/Multiplication Method...

Consequence of the Pseudo Inverse Multiplicative Let X be an interval such that OiX. Then 1 X/X... 

Loadings were taken to 96% of the critical mass as determined by inverse multiplication plots of the three BFj channels. 

If the number of fissile units required for high subcrltical multiplications in a specific lattice type is known as a function of the lattice density, and if a good estimate of the critical number of fissile units for one lattice density Is available, the critical number of fissile units for other densities of that lattice type may be predicted. The number of fissile units required to produce a given inverse multiplication for the unmoderated and moderated arrays as a function of lattice density Is shown in Figs. 1 and 2. (See figures on next page). 

Estimated from least-squares fit Af inverse multiplication measurements. Extrapolation lengths were taken from the measurements on the 1.002 Wt U 23S enriched tubes. 

Estimated from least-squares fit of inverse multiplication measurements. lnnermost seven tubes are 2.1 wt%. 

Inverse Multiplication Monitoring of Sub-critical Reactivity Changes in FTR, S. L. 

These results illustrate that special Instrumentation must be installed in ZPR-Ill for suCh measurements and that these analytical techniques must be applied to the interpretation of Inverse multiplication. data obtained during startup and refueling of FTR. 

Obtained from least-squares fit of "Ijaek-off inverse multiplication measurements. Extrapolation distances are with 0.25 cm. 

Inverse multiplication measurements were made on fully reflected parallelepipeds of the fuel, ranging from... 

The casks were loaded under water. For safety, the inverse multiplication was measured and evaluated daring the loading of each batch. A suitable neutron source and a pulse-type fission chamber were placed in cask positions 11 and 20. Also, one or more pulse-type neutron detectors were placed outside the cask. 

Figure 2 is a typical inverse multiplication curve Early in the loading sequence, Uie curve ajn>eared to be disturbingly steep in all cases, and some interpretative allowance had to be made for the addition of elements in positions that significantly Increased the lattice surface area near the detector. 

Most common mathematical manipulations involve fractions divided by fractions which must be simplified. In the equation for inverse multiplication,... 

Plot inverse multiplication versus Kgff or fuel mass and explain the possible curve shapes. 

A more useful grahpic concept is inverse multiplication,... 

Table 5.5 Variation in Reactivity, Multiplication, and Inverse Multiplication with Kgfi.

A plot of inverse multiplication (1/M = Cq/C constant (1-%)) versus K is a straight line"with a negative slope. If two points on the line are known, all points are known. The line intersects the K axis at 1/M = 0 which means K must equal one and the reactor is critical. By taking only two sets of detector counts while loading fuel, the critical load can be predicted. 

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