{{Numbered block|:|<math>y=ax+b</math>|Eq. 3}}

{{Numbered block|:|<math>ax^2+bx+c=0</math>|Eq. 3}}

{{Numbered block|:|<math>\Psi(x_1,x_2)=U(x_1)V(x_2)</math>|1}}

{{Numbered block|:|Fe<sup>3+</sup> + H<sub>2</sub>O<sub>2</sub> → Fe<sup>2+</sup> + HOO<sup>•</sup> + H<sup>+</sup>|2}}

{{Numbered block|:|<chem>H+ + CO3^2- -> HCO3^-</chem>|3}}

{{Numbered block||<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3.5}}

{{Numbered block|:|<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|1}}

{{Numbered block|::|<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|13.7}}

{{Numbered block|:::|<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|1.2}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=3.5|RawN=.}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<3.5>|RawN=.}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=[3.5]|RawN=.}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3='''[3.5]'''|RawN=.}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>|RawN=.}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<math>(3.5)</math>|RawN=.}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''(3.5)'''</Big>|RawN=.|LnSty=1px dashed red}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''(3.5)'''</Big>|RawN=.|LnSty=3px dashed #0a7392}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>|RawN=.|LnSty=3px solid green}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>|RawN=.|LnSty=5px dotted blue}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>|RawN=.|LnSty=0px solid green}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>|RawN=.|LnSty=5px none green}}

{{Numbered block|1=:|2=<math>\mathbf{a}(t)=\frac{d}{dt}\mathbf{v}(t)</math>|3=<Big>'''[3.5]'''</Big>|RawN=.|LnSty=3px double green}}

The following equations

${\displaystyle 3x+2y-z=1}$

${\displaystyle 2x-2y+4z=-2}$

${\displaystyle -2x+y-2z=0}$

form a system of three equations.

The following equations

${\displaystyle 3x+2y-z=1}$

(1)

${\displaystyle 2x-2y+4z=-2}$

(2)

${\displaystyle -2x+y-2z=0}$

(3)

form a system of three equations.

The following equations

${\displaystyle 3x+2y-z=1}$

(1)

${\displaystyle 2x-2y+4z=-2}$

(2)

${\displaystyle -2x+y-2z=0}$

(3)

form a system of three equations.

The following equations

${\displaystyle 3x+2y-z=1}$

(1)

${\displaystyle 2x-2y+4z=-2}$

(2)

${\displaystyle -2x+y-2z=0}$

(3)

form a system of three equations.

• ${\displaystyle 3x+2y-z=1}$
• ${\displaystyle 2x-2y+4z=-2}$
• ${\displaystyle -2x+y-2z=0}$

1. ${\displaystyle 3x+2y-z=1}$
2. ${\displaystyle 2x-2y+4z=-2}$
3. ${\displaystyle -2x+y-2z=0}$

(mouse over the row you want to highlight)

${\displaystyle a^{2}+b^{2}=(a+bi)(a-bi)}$ (1)

${\displaystyle a^{2}-b^{2}=(a+b)(a-b)}$ (2)

${\displaystyle e^{ix}=\cos x+i\sin x}$ (3)

${\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1}$ (4)

${\displaystyle \sin(2\theta )=2\sin \theta \cos \theta }$ (5)

[[Image:Bnet_fan2.png|frame|right|Fig.1: Bayesian Network representation of Eq.(6)]]
[[Image:Bnet_fan2.png|frame|left|Fig.1: Bayesian Network representation of Eq.(6)]]
<br><br>A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of
variables and their probabilistic independencies. For example, a Bayesian network could represent the
probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute
the probabilities of the presence of various diseases.
{{Numbered block|1=:|2=<math>
P(a, b, \lambda) = P(a| \lambda) P(b | \lambda) P(\lambda)\,
</math>,|3='''Eq.(6)'''|RawN=.}}

A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of variables and their probabilistic independencies. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

${\displaystyle P(a,b,\lambda )=P(a|\lambda )P(b|\lambda )P(\lambda )\,}$,

Eq.(6)

[[Image:Bnet_fan2.png|frame|right|Fig.1: Bayesian Network representation of Eq.(6)]]
[[Image:Bnet_fan2.png|frame|left|Fig.1: Bayesian Network representation of Eq.(6)]]
<br><br>A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of
variables and their probabilistic independencies. For example, a Bayesian network could represent the
probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute
the probabilities of the presence of various diseases.
{{clear}}
{{Numbered block|1=:|2=<math>
P(a, b, \lambda) = P(a| \lambda) P(b | \lambda) P(\lambda)\,
</math>,|3='''Eq.(6)'''|RawN=.}}

A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of variables and their probabilistic independencies. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

${\displaystyle P(a,b,\lambda )=P(a|\lambda )P(b|\lambda )P(\lambda )\,}$,

Eq.(6)

<dl><dd>
{|
|<math>(f * g)[n]\,</math>&nbsp; &nbsp; &nbsp; 
|{{Numbered block||<math>\stackrel{\mathrm{def}}{=}\sum_{m=-\infty}^{\infty} f[m]\cdot g[n - m]\,</math>|
3=<span style="color:darkred">'''(Eq.1)'''</span>|RawN=.}}
|-
|
|<math>= \sum_{m=-\infty}^{\infty} f[n-m]\cdot g[m].\,</math> &nbsp; &nbsp; &nbsp; ([[Convolution#Commutativity|commutativity]])
|}
</dd></dl>

${\displaystyle (f*g)[n]\,}$	${\displaystyle {\stackrel {\mathrm {def} }{=}}\sum _{m=-\infty }^{\infty }f[m]\cdot g[n-m]\,}$ (Eq.1)
	${\displaystyle =\sum _{m=-\infty }^{\infty }f[n-m]\cdot g[m].\,}$       (commutativity)