Multiplying operators

Q. What are the main differences between an electron multiplier operated in pulse counting and analogue mode ... 

There is a definition of how to multiply operations we apply them successively. The product of any two is one of the remaining ones. In other words, this collection of operations is self-sufficient, all its possible products being already within itself. This is sometimes called the property of closure. 

The most common transducers for ICP-MS are electron multipliers. The discrete dynode electron multiplier operates much like the photomultiplier transducer for ultraviolet/visible radiation, discussed in Section 25A-4. Electrons strike a cathode, where secondary electrons are emitted. These are attracted to dynodes that are each held at a successively higher positive voltage. Electron multipliers with up to 20 dynodes are available. These devices can multiply the signal strength by a factor of up to 10. ... 

The tandem MS includes a quadrupole mass filter, an octopole ion guide," a second quadrupole mass filter, and an ion detector. The ions from the flow tube are focused through electrostatic lenses into the first quadrupole, where a particular reactant ion is selected. These ions are then focused into the octopole, which passes through a cell that contains the collision gas. From the octopole, the dissociated and unreacted ions are focused into a second quadrupole for mass analysis. The detector is an electron multiplier operating in pulse-counting mode. 

On arrival at the ion source, the pyrolyzate gas is subjected to bombardment by electrons with a nominal energy of 25 eV in classic El mass spectrometry. The resultant charged molecules produced are transmitted by the quadrupole, and a mass spectrum of the pyrolysate is recorded by an electron multiplier operating in pulsecounting mode. 

One multiply operated patient who had pre-operative cauda equina syndrome twice, does wear a bilateral drop foot brace for L5 nerve root deficit though she no longer takes any narcotic medication. She was deeply habituated on narcotics prior to the surgical procedure. 

Static analysis takes many forms, each one tailored to address a particular problem in the safety or profitability of optimization. One such problem is constant propagation—discovering variables whose run-time values can be determined at compile time. If the compiler can discover that x always has the value 2 at a particular point in the program, it can specialize the code that uses x to reflect that knowledge. In particular, if x has the value 2 in an expression x y, it can replace the expression with 2 y or with y + y, either of which may be faster than a generic multiply. (The former avoids referring to x, with a possible memory reference, while the latter also replaces the multiply operation with an addition, which may be cheaper.)... 

Fig. 1. Number of floating point multiply operations of new computers versus their first year of availability...

Figure 4.18 Schematic example of Pulse Height Distribution analysis carried out for 4500 eV secondary ions impinging on an ETP Discrete Dynode Electron Multiplier operated at the listed voltages. Pulse counting was carried out using custom built ECL logic pre-amplifier/discriminator units. Discriminator voltage in this case should be set at 5 mV. Reproduced with permission from van der Heide and Fichter (1998) Copyright 1998 John Wiley and Sons.

Condition 4. The multiplieation operation is associative, because operator multiplication is always associative. 

In this code there are two multiply operations. Yet it is clear by inspection that only one of the multiply operations is active at any one instance. Clearly it would be wasteful to implement two large multipliers when only one is needed. This is what is meant by resource sharing. By creating a single multiplier with a permanent input a surrounded by selector logic to select input b if a = 1 or d otherwise would result in a smaller circuit. The reader will have noticed that alternative resource sharing is possible in this example as if a =1 then c = b. 

The multiplier is not pipelined and therefore a complete parallel multiply operation must be complete within one machine cycle. 

The basic principles of discrete-dynode electron multiplier operation are shown schematically in Figure 3.1. When an ion strikes the first dynode of a discrete-dynode electron multiplier (or conversion dynode) it liberates secondary electrons. The electron-optics of the dynodes then accelerates these electrons to the next dynode in the multiplier, which in turn produces a greater number of secondary electrons. This process is repeated at each subsequent dynode, generating a cascade of millions of electrons, which are finally captured (as an output pulse , hence the term pulse counting) at the multiplier output electrode. The gain of an electron multiplier can be defined as the average number of electrons collected at the multiplier s output electrode for each input ion that initiates an electron cascade. Similarly, it can be described as the current measured from the output divided by the input ion current. It should be noted that this second definition includes the ion detection efficiency of the multiplier. 

Figure 3.7 Typical analog gain linearity curve plotted as a function oftheoutputcurrent for a 21-dynode electron multiplier operated at a gain of 5 x 10 . In this case the multiplier bias current is 70/nA.

A typical detection system for measuring currents from a multiplier operated in analog mode is shown in Figure 3.15. 

With most present ICP-MS instruments, a quadrupole mass analyzer is used (Fig. 5.2). This device provides essentially unit mass resolution and can be scanned and switched rapidly between peaks of interest. The mass-selected ions are detected with an electron multiplier operated in either a pulse counting mode (for trace constituents) or in an analog... 

On the secondary side of the step-up transformer a ten-stage voltage multiplier operates delivering approximately + 1000 volts, if 10 volts are present on the base of the QlOl emitter follower. 

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