Subtraction writing operators

The second equality follows from die fact that gomg from Bto AB involves subtracting a c -niunber from B and that c -niunber can be taken outside the trace. The resulting trace is the trace of a conmuitator, which vanishes. The invariance of the trace to cyclic pennutations of the order of the operators is used in the third equality. It is straightforward to write... 

You aren t told if Matt makes more or less than Mike. Letting Matt s salary be represented by x, you write the absolute value equation lx-165,0001 = 10,000. Solve two different linear equations. One equation assumes that the result in the absolute value operation is positive, and the other assumes that it s negative. The first equation is written x- 165,000 = 10,000. Solving for x, you get x = 175,000. The other equation is formed by negating the expression inside the absolute value. You get -(x - 165,000) = 10,000 which becomes -x + 165,000 = 10,000. Subtract 165,000 from each side and divide by -1, and you get x = 155,000. So Matt makes either 175,000 or 155,000. 

To find the variation—not the differential—of a function. Let y be the given function. Write y + By in place of y, and subtract the new function from the old, and there you have it. We at once recognize the formal analogy of the operation with the process of differentiation. Thus, if... 

Several interesting operations with Equations 5 now suggest themselves. Writing 5a for each of the liquid phases 1 and 2, and then subtracting, we obtain... 

Let H and H, be the operators obtained when t>(r,) in (15.106) is replaced by v (r,) and Wi,(r,), respectively, where and (r,) differ by more than a constant. Prove that the ground-state wave functions ij/o and of these Hamiltonians must be different functions. Hint Assume they are the same function, write the Schrodinger equations for H and H/, subtract one equation from the other, and show that this leads to w (r,) — fc(r,) equals a constant, thereby contradicting the given information and proving that the two wave functions cannot be equal. 

Reg is a register, sel is a selector, and is a don t-care. Recall that operators are extended to mappings for instance, the term Q-1 denotes mapping subtraction over Q and an infinite sequence of Is. Expanding Q in the defining expression for R, with some retiming and distribution of —1 through sel, we can write... 

Step 5. To write a balanced net cell reaction, subtract the left half-reaction from the right half-reaction. This operation is equivalent to reversing the halfreaction and adding.)... 

We will examine this using the Cartesian system. We write out each operator product and subtract ... 

---