# Symbols:D

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### deci-

$\mathrm d$

The Système Internationale d'Unités symbol for the metric scaling prefix deci, denoting $10^{\, -1 }$, is $\mathrm { d }$.

Its $\LaTeX$ code is \mathrm {d} .

### deka-

$\mathrm {da}$

The Système Internationale d'Unités symbol for the metric scaling prefix deka, denoting $10^{\, 1 }$, is $\mathrm { da }$.

Its $\LaTeX$ code is \mathrm {da} .

$\mathrm D$ or $\mathrm d$

The hexadecimal digit $13$.

Its $\LaTeX$ code is \mathrm D  or \mathrm d.

### Roman Numeral

$\mathrm D$ or $\mathrm d$

The Roman numeral for $500$.

Its $\LaTeX$ code is \mathrm D  or \mathrm d.

### Dimension

$\map \dim M$

The dimension of a unitary module $M$ is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ as $\map \dim M$.

The $\LaTeX$ code for $\map \dim M$ is \map \dim M .

### Day

$\mathrm d$

The symbol for the day is $\mathrm {day}$ or $\mathrm d$.

The $\LaTeX$ code for $\mathrm d$ is \mathrm d .

### Differential

$\d$

Symbol used to indicate the differential of a function, used for example to denote the derivative:

$\dfrac \d {\d x} f$

The $\LaTeX$ code for $\dfrac \d {\d x} f$ is \dfrac \d {\d x} f .

### Partial Derivative

$\partial$

Symbol used to indicate the partial derivative of a function, used for example as follows:

$\dfrac \partial {\partial x} \map f {x, y}$

The $\LaTeX$ code for $\dfrac \partial {\partial x} \map f {x, y}$ is \dfrac \partial {\partial x} \map f {x, y} .

### Integral Domain

$D$

Used as a variable denoting the general integral domain.

### Integral Domain as Algebraic Structure

$\struct {D, +, \circ}$

The full specification for an integral domain, where $+$ and $\circ$ are respectively the ring addition and ring product operations.

Its $\LaTeX$ code is \struct {D, +, \circ} .

### Ordered Integral Domain

$\struct {D, +, \circ, \le}$

This specifies an ordered integral domain which is totally ordered by the ordering $\le$.

Its $\LaTeX$ code is \struct {D, +, \circ, \le} .

### Non-Zero Elements of Integral Domain

$D^*$

Let $\struct {D, +, \circ}$ be an integral domain whose zero is $0_D$.

Then $D^*$ denotes the set $D \setminus \set {0_D}$.

Its $\LaTeX$ code is D^* .

### Non-Negative Elements of Ordered Integral Domain

$D_+$

Let $\struct {D, +, \circ, \le}$ be an ordered integral domain whose zero is $0_D$.

Then $D_+$ denotes the set $\set {x \in D: 0_D \le x}$, that is, the set of all positive (that is, non-negative) elements of $D$.

Its $\LaTeX$ code is D_+ .

### Positive Elements of Ordered Integral Domain

$D_+^*$

Let $\struct {D, +, \circ, \le}$ be an ordered integral domain whose zero is $0_D$.

Then $D_+^*$ denotes the set $\set {x \in D: 0_D < x}$, that is, the set of all strictly positive elements of $D$.

Some sources denote this as $D^+$, but this style of notation makes it difficult to distinguish between this and $D_+$.

Its $\LaTeX$ code is D_+^* .

### Electric Displacement Field

$\mathbf D$

The electric displacement field is a vector quantity defined as the electric field strength multiplied by the permittivity of the medium through which it passes:

$\mathbf D = \varepsilon \mathbf E$

where:

$\varepsilon$ is the permittivity of the medium
$\mathbf E$ is the electric field strength

Its $\LaTeX$ code is \mathbf D .

### Divisor Count Function

$\map d n$

Often seen as the symbol used to denote the Divisor Count Function.

This is usually denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ using the symbol as $\sigma_0$ (the Greek letter sigma).

The $\LaTeX$ code for $\map d n$ is \map d n .

### Derangements

$D_n$ or $d_n$

A derangement is a permutation $f: S \to S$ from a set $S$ to itself where:

$\forall s \in S: \map f s \ne s$

That is, a permutation with no fixed points.

If $S$ is finite, the number of derangements is denoted by $D_n$ or $d_n$, where $n = \card S$ (the cardinality of $S$.)

The $\LaTeX$ code for $D_n$ is D_n .

The $\LaTeX$ code for $d_n$ is d_n .

### Determinant

$\det$

The determinant of a square matrix $\mathbf A$ can be denoted $\map \det {\mathbf A}$.

The $\LaTeX$ code for $\map \det {\mathbf A}$ is \map \det {\mathbf A} .

### Divergence Operator

$\operatorname {div}$

Let $R$ be a region of space embedded in a Cartesian coordinate frame.

Let $\mathbf V$ be a vector field acting over $R$.

The divergence of $\mathbf V$ at a point $A$ in $R$ is defined as:

 $\ds \operatorname {div} \mathbf V$ $:=$ $\ds \nabla \cdot \mathbf V$ $\ds$ $=$ $\ds \dfrac {\partial V_x} {\partial x} + \dfrac {\partial V_y} {\partial y} + \dfrac {\partial V_z} {\partial z}$

where:

$\nabla$ denotes the Del operator
$\cdot$ denotes the dot product
$V_x$, $V_y$ and $V_z$ denote the magnitudes of the components of $\mathbf V$ at $A$ in the directions of the coordinate axes $x$, $y$ and $z$ respectively.

The $\LaTeX$ code for $\operatorname {div} \mathbf V$ is \operatorname {div} \mathbf V .

### Decimetre

$\mathrm {dm}$

The symbol for the decimetre is $\mathrm {dm}$:

$\mathrm d$ for deci
$\mathrm m$ for metre.

Its $\LaTeX$ code is \mathrm {dm} .

### Dekametre

$\mathrm {dam}$

The symbol for the dekametre is $\mathrm {dam}$:

$\mathrm {da}$ for deka
$\mathrm m$ for metre.

Its $\LaTeX$ code is \mathrm {dam} .

### Pennyweight

$\mathrm {dwt}$

The symbol for the pennyweight is $\text {dwt}$.

This derives from the Latin denarius, which evolved into the (old) penny.

Its $\LaTeX$ code is \mathrm {dwt} .

### Dyne

$\mathrm {dyn}$

The symbol for the dyne is $\mathrm {dyn}$.

The $\LaTeX$ code for $\mathrm {dyn}$ is \mathrm {dyn} .

### Dyne-Centimetre

$\mathrm {dyn \, cm}$

The symbol for the dyne-centimetre is $\mathrm {dyn \, cm}$.

Its $\LaTeX$ code is \mathrm {dyn \, cm} .

### Electric Flux Density

$\mathbf D$

The usual symbol used to denote electric flux density is $\mathbf D$.

Its $\LaTeX$ code is \mathbf D .

### Dalton

$\mathrm {Da}$

The symbol for the dalton is $\mathrm {Da}$.

The $\LaTeX$ code for $\mathrm {Da}$ is \mathrm {Da} .

### Decibel

$\mathrm {dB}$

The decibel is a unit for comparing levels of power.

The symbol for the decibel is $\mathrm {dB}$.

The $\LaTeX$ code for $\mathrm {dB}$ is \mathrm {dB} .

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