Identifying various types of definitions

1. In addition to the examination of historical records, a study of the geologic record of past seismic activities, called paleoseismology, can be used to evaluate the occurrence and size of earthquakes in the region. Geomorphic (surface landform) and trench studies may reveal the number of past seismic events, slip per event, and timing of the events at a specific fault.

2. It should be noted that cell phones are not necessarily the same as car phones, i.e., devices intended for permanent installation in the vehicle and which may have separate handset/dial units.

3. The uncertainty associated with the energy obtained from other types of nonutility generators (NUGs), i.e., thermal and hydro, is relatively small compared to that associated with wind.

4. Average raw scores on IQ tests have been rising for years (Flynn, 1984, 1987, 1999), by an estimated three IQ points per decade (Neisser 1998). This rise, known as the Flynn effect, has received much attention, though its exact nature was recently questioned.

5. Phytoremediation is the direct use of living green plants for in situ, or in place, risk reduction for contaminated soil, sediments, and groundwater.

6. Procrastination refers to deliberately putting off one’s intended actions.

7. Tax evasion is defined as intentionally paying fewer taxes than the law requires, as a deliberate act of noncompliance.

8. Software watermarking is a process in which identifying information is embedded into a file, enabling authors to control the distribution of and verify ownership of their digital information. The purpose of software watermarking is to protect the intellectual property that belongs to the author.

9. Road pricing is a transportation control measure that requires motorists to pay directly for using a particular roadway or driving in a particular area. Economists have long advocated road pricing as an efficient and fair way to pay roadway costs and encourage more efficient transportation. Road pricing has three general objectives: revenue generation, a reduction in pollution, and congestion management. One simple road pricing instrument is area licensing, which requires a motorist to purchase a permit to take a vehicle into a designated urban area during peak traffic hours.

10. Collecting, defined as the process of actively, selectively, and passionately acquiring and possessing things removed from ordinary use and perceived as part of a set of nonidentical objects or experiences (Belk 1995), is an acquisitive, possessive, and materialistic pursuit.

(Examples 1 to 10 are taken from Swales and Feak. 2004. Academic Writing for Graduate Students. The University of Michigan Press. pp. 53-54.) 11. Quantum numbers are numerical descriptions that, when taken together, describe a given electron in a given atom. There are four quantum numbers for every electron. The first, called the principal quantum number, describes the energy level of the electron. The second, called the orbital quantum number, describes the shape of the orbit in which the electron moves. The third, called the magnetic quantum number, describes the electron’s orientation in space. The fourth, called the spin, describes the clockwise or counterclockwise spin of the electron around its own axis. Together, the four numbers describe an electron, and no two electrons in an atom can have the same four quantum numbers.

12. When writing extremely large or small numbers, you may sometimes have so many digits that you cannot read them or even pronounce whatever words it may take to say them. (What comes after trillions?) To more easily write those very large or small numbers, mathematicians use a method called scientific notation. To write a number in scientific notation, you move the decimal point from its present location one place to the right of the first digit that is not a zero. In other words, you write the number so that it has a value between 1 and 10, rounding off as necessary. Then you multiply the number by 10 raised to the power equal to the number of places that the decimal point was moved. If you move the decimal point from the right to the left, the exponent is positive. For example, 9,238,648,500 written in scientific notation is 9.24×109. On the other hand, if you move the decimal point from the left to the right, the exponent is negative. For example, 0.00000092 written in scientific notation is 9.2×10-7. So scientific notation makes numbers shorter and easier to read and mathematical operations easier to complete.

(Examples 11 and 12 are from Sharon Sorenson. 2000. Webster’s New World Student Writing Handbook. fourth edition. Wiley Publishing.)

13. If m and n are positive integers then by a matrix of size m by n, or an m × n matrix, we shall mean a rectangular array consisting of mn numbers in a boxed display consisting of m rows and n columns.

We shall often find it convenient to abbreviate a matrix to simply

[xij] m × n and refer to xij as the (i, j)-th element or the (i, j)-th entry of the matrix. Thus the expression X = [xij] m × n will be taken to mean that ‘X is the m × n matrix whose (i, j)-th element is xij.’

If A = [aij] m × n and B = [bij] p × q then we shall say that A and B are equal (and write A = B) if and only if (1) m = p and n = q;

(2) aij = bij for all i, j. The algebraic system that we shall develop for matrices will have many of the familiar properties enjoyed by the system of real numbers. However, as we shall see, there are some very striking differences.

Given m × n matrices A = [aij] and B = [bij] we define the sum A + B to be the m × n matrix whose (i, j)-th element is aij + bij. Note that the sum A + B is defined only when A and B are of the same size; and to obtain this sum we simply add corresponding entries, thereby obtaining a matrix again of the same size. (Blyth and Robertson. 2002. Basic Linear Algebra. second edition. Springer Verlag.)