# Content mathml  (Page 3/3)

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The eq operator is used to write equations. It is used in the same way as any other operator. That is, itis the first child of an apply. It takes two (or more) children which are the two quantities that are equal to eachother. For example, " $a$ times $b$ plus $a$ times $c$ equals $a$ times the quantity $b$ plus $c$ " would be written as shown. <m:math> <m:apply> <m:eq/> <m:apply> <m:plus/> <m:apply> <m:times/> <m:ci>a</m:ci> <m:ci>b</m:ci> </m:apply> <m:apply> <m:times/> <m:ci>a</m:ci> <m:ci>c</m:ci> </m:apply> </m:apply> <m:apply> <m:times/> <m:ci>a</m:ci> <m:apply> <m:plus/> <m:ci>b</m:ci> <m:ci>c</m:ci> </m:apply> </m:apply> </m:apply> </m:math> This will display as $ab+ac=a(b+c)$ .

## Integrals

The operator for an integral is int . However, unlike the operators and functions discussed above, it haschildren that define the independent variable that you integrate with respect to ( bvar ) and the interval over which the integral is taken (use either lowlimit and uplimit , or interval , or condition ). lowlimit and uplimit (which go together), interval , and condition are just three different ways of denoting the integrands. Don't forget that the bvar, lowlimit , uplimit , interval , and condition children take token elements as well. The following is "the integral of $f$ of $x$ with respect to $x$ from 0 to $b$ ." <m:math> <m:apply> <m:int/> <m:bvar><m:ci>x</m:ci></m:bvar> <m:lowlimit><m:cn>0</m:cn></m:lowlimit> <m:uplimit><m:ci>b</m:ci></m:uplimit> <m:apply> <m:ci type='fn'>f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as $\int_{0}^{b} f(x)\,d x$ .

## Derivatives

The derivative operator is diff . The derivative is done in much the same way as the integral. That is, youneed to define a base variable (using bvar ). The following is "the derivative of the function $f$ of $x$ , with respect to $x$ ." <m:math> <m:apply> <m:diff/> <m:bvar> <m:ci>x</m:ci> </m:bvar> <m:apply> <m:ci type="fn">f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as $\frac{d f(x)}{d x}}$ .

To apply a higher level derivative to a function, add a degree tag inside of the bvar tag. The degree tag will contain the order of the derivative. Thefollowing shows "the second derivative of the function $f$ of $x$ , with respect to $x$ ." <m:math> <m:apply> <m:diff/> <m:bvar> <m:ci>x</m:ci> <m:degree><m:cn>2</m:cn></m:degree> </m:bvar> <m:apply><m:ci type="fn">f</m:ci> <m:ci>x</m:ci> </m:apply> </m:apply> </m:math> This will display as $\frac{d^{2}f(x)}{dx^{2}}$ .

## Vector and matrices

Vectors are created as a combination of other elements using the vector tag. <m:math> <m:vector> <m:apply> <m:plus/> <m:ci>x</m:ci> <m:ci>y</m:ci> </m:apply> <m:ci>z</m:ci> <m:cn>0</m:cn> </m:vector> </m:math> This will display as $\left(\begin{array}{c}x+y\\ z\\ 0\end{array}\right)$ .

Matrices are done in a similar manner. Each matrix element contains several matrixrow elements. Then each matrixrow element contains several other elements. <m:math> <m:matrix> <m:matrixrow> <m:ci>a</m:ci> <m:ci>b</m:ci> <m:ci>c</m:ci> </m:matrixrow> <m:matrixrow> <m:ci>d</m:ci> <m:ci>e</m:ci> <m:ci>f</m:ci> </m:matrixrow> <m:matrixrow> <m:ci>g</m:ci> <m:ci>h</m:ci> <m:ci>j</m:ci> </m:matrixrow> </m:matrix> </m:math> This will display as $\begin{pmatrix}a & b & c\\ d & e & f\\ g & h & j\\ \end{pmatrix}$ .

There are also operators to take the determinant and the transpose of a matrix as well as to select elements fromwithin the matrix.

## Entities

The use of MathML character entity references in Connexions content is deprecated .

MathML defines its own entities for many special characters used in mathematical notation. While the entity references have the advantage of being mnemonic with respect to the characters they stand for, they also entail some technical limitations, and so their use in Connexions content is deprecated. Please use the UTF-8-encoded Unicode characters themselves where possible, or, failing that, the XML Unicode character references for the characters. At some time in the future, the Connexions repository system will likely convert entity references and character references silently to the UTF-8-encoded Unicode characters they stand for. See 6.2.1 Unicode Character Data from the XML Specification for more information. The MathML specification contains a list of character entities with their corresponding Unicode code points .

There are character picker utilities available to help you select and paste UTF-8 characters into applications like Connexions. If you are running Microsoft Windows, the Windows accessory Character Map can help you. The "Lucida Sans Unicode" font seems to have a good selection of mathematical operators and special characters. Under Linux, the charmap utility and GNOME applet provide access to all Unicode characters.

## Other resources

There is a lot more that can be done with Content MathML. Especially if you are planning on writing a lot of ContentMathML, it is well worth your time to take a look at the MathML specification .

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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