This linear function is applied to determine the absolute head-medium spacing directly through the multiplication of gradient of the linear function and the linear velocity between the head and the medium of the disk drive. More particularly, it relates to a method of measuring the absolute spacing between the medium and the head directly in-situ from the readback signal and the implementation of the method through an apparatus for performing the method disclosed herein. The transducer is also commonly referred to as a head.

So today's lecture is on sorting. We'll be talking about specific sorting algorithms today. I want to start by motivating why we're interested in sorting, which should be fairly easy. Then I want to discuss a particular sorting algorithm that's called insertion sort.

That's probably the simplest sorting algorithm you can write, it's five lines of code. It's not the best sorting algorithm that's out there and so we'll try and improve it.

We'll also talk about merge sort, which is a divide and conquer algorithm and that's going to motivate the last thing that I want to spend time on, which is recurrences and how you solve recurrences.

Typically the recurrences that we'll be looking at in double o six are going to come from divide and conquer problems like merge sort but you'll see this over and over.

So let's talk about why we're interested in sorting. There's some fairly obvious applications like if you want to maintain a phone book, you've got a bunch of names and numbers corresponding to a telephone directory and you want to keep them in sorted order so it's easy to search, mp3 organizers, spreadsheets, et cetera.

So there's lots of obvious applications. There's also some interesting problems that become easy once items are sorted. One example of that is finding a median.

So let's say that you have a bunch of items in an array a zero through n and a zero through n contains n numbers and they're not sorted. When you sort, you turn this into b 0 through n, where if it's just numbers, then you may sort them in increasing order or decreasing order.

Let's just call it increasing order for now. Or if they're records, and they're not numbers, then you have to provide a comparison function to determine which record is smaller than another record. And that's another input that you have to have in order to do the sorting.

So it doesn't really matter what the items are as long as you have the comparison function. Think of it as less than or equal to. And if you have that and it's straightforward, obviously, to check that 3 is less than 4, et cetera.

But it may be a little more complicated for more sophisticated sorting applications. But the bottom line is that if you have your algorithm that takes a comparison function as an input, you're going to be able to, after a certain amount of time, get B 0 n.

Now if you wanted to find the median of the set of numbers that were originally in the array A, what would you do once you have the sorted array B? Isn't there a more efficient algorithm for median? But this is sort of a side effect of having a sorted list. If you happen to have a sorted list, there's many ways that you could imagine building up a sorted list.We also show how to write the equation of a plane from three points that lie in the plane.

Quadric Surfaces – In this section we will be looking at some examples of quadric surfaces. Some examples of quadric surfaces are cones, cylinders, ellipsoids, and elliptic paraboloids.

The ﬁrst law of logarithms Suppose x = an then the equivalent logarithmic forms are loga x = n Using the ﬁrst rule of indices Now the logarithmic form of the statement xy = an+m is loga xy = n + m. we have laws of logarithms. 4. if we want to multiply two numbers together and ﬁnd the .

Write each of the following in terms of log p, log q and log r. The logarithms have the equation y = ax n to logarithmic form, giving a straight line when log y is plotted against log x.

(b) the equation y = A(b x Documents Similar To Topic 2 - Logarithmic and Exponential.

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aeril Deline. Uploaded by.1/5(1). Resources / Answers / Rewrite as a logarithmic GO. Ask a question. 0. Ask a Question Rewrite as a logarithmic equation e^3=x. Need a answer. Logarithmic Equation. Aug 29 | Kaylan from Philadelphia, PA. Subscribe. Comment. 2 Answers by Expert Tutors.

Tutors, sign in to answer this. in logarithmic form.

In this example, the base is 7 and the base moved from the right side of the exponential equation to the left side of the logarithmic equation and the word “log” was added.

Example 5: Write the exponential equation 37 = y 5 in logarithmic form. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy (pdf) | Paperity