Elbert Walker Article
Dr. Author Jones
At this Address The Date
This article illustrates many features of a mathematics article, but we do not explain the spurious appearance of the formula in this abstract.
Sample Mathematics and Text
This short sample document illustrates the typeset appearance of in-line and displayed mathematics in documents. It also illustrates five levels
of section headings and three kinds of lists. Finally, the document includes entries for a manual bibliography and an appendix.
In-line and Displayed Mathematics
The expression is in-line mathematics, while the numbered equation
is displayed and automatically numbered as equation .
Let be a Hilbert space, be a closed bounded convex subset of , a nonexpansive self map of . Suppose that as , for each , and . Then for each in , converges weakly to a fixed point of .
Two sets of LATEX parameters govern mathematical displays.
LATEX automatically selects the spacing depending on the surrounding
line lengths. The spacing above and below a display depends on whether the lines above or below are short or long, as shown
in the following examples.
A short line above: and a short line below.
A long line above may depend on your margins as will a long line below. This line is long enough to illustrate the spacing for mathematical displays, regardless
of the margins.
Mathematics in section heads
Mathematics can appear in section heads. Note that mathematics in section heads may cause difficulties in typesetting styles with running headers
or table of contents entries.
Theorems, Lemmata, and Other Theorem-like Environments
A number of theorem-like environments is available. The following lemma is a well-known fact on differentiation of asymptotic expansions of analytic
functions.
Let be an analytic function in . If admits the representation for inside a cone then
Change for . Then and
Fix , and let be a circle with radius . It follows from () that
where for the remainder we have
Therefore as , , and hence by the Cauchy theorem () implies
that implies ()
by substituting back for .
Section Headings
Use the section tag for major sections, such as
the one just above. Four additional heading levels are available, as shown below.
Subsection
This text appears under a subsection heading.
Subsubsection
This text appears under a subsubsection.
Paragraph
This text appears under a paragraph heading.
Subparagraph
This text appears under a subparagraph. The subparagraph is
the lowest heading level.
Included below is
Table
to demonstrate cross referencing a table.
The table caption will appear in the list of tables, if
used. LATEX will
position this floating table to best take advantage of the flow of the surrounding text.
Head
|
Head
|
Head
|
entry
|
entry
|
entry
|
entry
|
entry
|
entry
|
entry
|
entry
|
entry
|
Table caption text here.
Lists
Bullet, numbered and description list environments are available. Lists, which can extend four levels deep, look like this:
Numbered list item 1. Numbered list item 2.
A numbered list item under a list item.
The typeset appearance for this level is often different from the screen appearance. The typeset appearance often uses parentheses around the
level indicator. Another numbered list item under a list item.
Third level numbered list item under a list item.
Fourth and final level of numbered list items allowed.
Bullet item 1. Bullet item 2.
Second level bullet item.
Third level bullet item.
Fourth and final level bullet item.
Description List Each description list item has a lead-in followed
by the item. Double-click the lead-in box to enter or customize the text of the lead-in. Bunyip
Mythical beast of Australian Aboriginal legends.
Tags
You can apply the logical markup tag Emphasized.
You can apply the visual markup tags Bold, Italics, Roman, Sans Serif, Slanted,
Small Caps, and Typewriter.
You can apply the special, mathematics only, tags , , and . Note that blackboard bold and calligraphic are correct only when applied to uppercase letters A through
Z.
You can apply the size tags tiny, scriptsize, footnotesize, small,
normalsize, large, Large, LARGE, huge and Huge.
Following is a group of paragraphs marked as Short Quote. This environment is appropriate for a short quotation or a sequence of short quotations.
The only thing we have to fear is fear itself. Franklin D. Roosevelt, Mar. 4, 1933
Ask not what your country can do for you; ask what you can do for your country. John F. Kennedy, Jan. 20. 1961
There is nothing wrong with America that cannot be cured by what is right with America. William J. “Bill” Clinton,
Jan. 21, 1993
Use the Verbatim tag when you want LATEX to preserve
spacing, perhaps when including a fragment from a program such as:
#include <iostream> // < > is used for standard libraries.
void main(void) // "main" method always called first.
{
cout << "Hello World."; // Send to output stream.
}
About the Bibliography
Following the text of this article is a short manual bibliography. This sample bibliography has no relationship to the previous text, but it shows
sample citations such as ,
and . You can also have multiple citations appear together.
Here is an example: .
dunford N. Dunford and J. Schwartz, Functional Analysis, v.
2, John Wiley and Sons, New York, 1963. HB98a Harstad, K. and Bellan, J., ``Isolated
fluid oxygen drop behavior in fluid hydrogen at rocket chamber pressures'', Int. J. Heat Mass Transfer, 1998a, 41, 3537-3550
HB98b Harstad, K. and Bellan, J., ``The Lewis number under supercritical conditions'',
Int. J. Heat Mass Transfer, in print Hirsh64 Hirshfelder,
J. O., Curtis, C. F. and Bird, R. B., Molecular Theory of Gases and Liquids, John Wiley and Sons, Inc., 1964 Prausnitz86
Prausnitz, J., Lichtenthaler, R. and de Azevedo, E., Molecular thermodynamics for fluid-phase equilibrium, Prentice -Hall, Inc., 1986 Reid87
Reid, R. C., Prausnitz, J. M. and Polling, B. E., The Properties of Gases and Liquids, 4th Edition, McGraw-Hill Book Company, 1987
An Appendix
Because appendices may contain material that is supplementary rather than integral to the main text , many styles use a different numbering system
for equations that appear in the appendices.
The quadratic equation shown as equation is used to demonstrate how equations are numbered in the appendix.