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Algorithms is a monthly peer-reviewed open-access scientific journal of mathematics, covering design, analysis, and experiments on algorithms. The journal is published by MDPI and was established in 2008. The founding editor-in-chief was Kazuo Iwama (Kyoto University).. From May 2014 to September 2019, the editor-in-chief was Henning Fernau (Universität Trier). The current editor-in-chief is Frank Werner (Otto-von-Guericke-Universität Magdeburg).
==Abstracting and indexing==
The journal is abstracted and indexed in:
==See also==
Journals with similar scope include:
*ACM Transactions on Algorithms
*Algorithmica
*Journal of Algorithms (Elsevier)
==References==
==External links==
*
Category:Computer science journals
Category:Open access journals
Category:MDPI academic journals
Category:English-language journals
Category:Publications established in 2008
Category:Mathematics journals
Category:Monthly journals | Algorithms (journal) | [
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] |
Telecommunications in Antigua and Barbuda are via media in the telecommunications industry. This article is about communications systems in Antigua and Barbuda.
==Telephone==
Telephones – main lines in use: 37,500 (2006)
:country comparison to the world: 168
Telephones – mobile cellular: 110,200 (2006) (APUA PCS, Cable & Wireless, Digicel)
:country comparison to the world: 177
Telephone system:
domestic: good automatic telephone system
international: 3 fiber optic submarine cables (2 to Saint Kitts and 1 to Guadeloupe); satellite earth station – 1 Intelsat (Atlantic Ocean)
==Radio==
Radio broadcast stations: AM 4, FM 6, shortwave 0 (2002)
{| class="wikitable sortable"
|+ Radio Stations of Antigua and Barbuda
! Band / Freq.
! Call Sign
! Brand
! City of license
! Notes
|-
| AM 620
| V2C
| ABS Radio and TV
| Saint John's, Antigua
| ABS; 5 kW
|-
| AM 1100
| ZDK
| Radio ZDK
| Saint John's, Antigua
| Owner: Grenville Radio; 20 kW
|-
| AM 1160
| Unknown
| Radio Lighthouse
| Saint John's, Antigua
| 10 kW
|-
| AM 1580
| Unknown
| Unknown
| Judge Bay, Antigua
| 50 kW
|-
| FM 88.5
| Unknown
| Power FM
| Saint John's, Antigua
|
|-
| FM 89.7
| Unknown
| Catholic Radio
| Saint John's, Antigua
| 2 kW
|-
| FM 90.5
| V2C-FM
| ABS Radio and TV
| Saint John's, Antigua
| repeats AM 620
|-
| FM 91.1
| Unknown
| Observer Radio
| Saint John's, Antigua
|
|-
| FM 91.9
| Unknown
| Hitz 91.9
| Saint John's, Antigua
|
|-
| FM 92.3
| Unknown
| Radio Lighthouse
| Saint John's, Antigua
| repeats AM | Telecommunications in Antigua and Barbuda | [
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] |
1160
|-
| FM 92.9
| VYBZ-FM
| Vybz FM
| Saint John's, Antigua
|
|-
| FM 93.9
| Unknown
| Caribbean SuperStation
| Saint John's, Antigua
| repeats Caribbean SuperStation from Trinidad
|-
| FM 95.7
| Unknown
| Zoom Radio
| Saint John's, Antigua
|
|-
| FM 97.1
| ZDK
| Radio ZDK
| Saint John's, Antigua
| repeats AM 1100
|-
| FM 98.5
| Unknown
| Red Hot Radio
| Saint John's, Antigua
|
|-
| FM 99.1
| Unknown
| Hit Radio Music Power
| Saint John's, Antigua
|
|-
| FM 100.1
| Unknown (ZDKR-FM?)
| Sun FM
| Saint John's, Antigua
|
|-
| FM 101.5
| Unknown
| Second Advent Radio
| Saint John's, Antigua
| 20 watts
|-
| FM 102.3
| Unknown
| Variety Radio
| Saint John's, Antigua
|
|-
| FM 103.1
| Unknown
| Life FM
| Codrington, Barbuda
| 1 kW
|-
| FM 103.9
| Unknown
| Life FM
| Saint John's, Antigua
| repeats 103.1 Codrington
|-
| FM 104.3
| Unknown
| Nice FM
| Codrington, Barbuda
|
|-
| FM 107.3
| Unknown
| Crusader Radio
| Saint John's, Antigua
|
|-
| SW 3.255 mHz
| V2C
| ABS Radio and TV
| Saint John's, Antigua
| Repeats AM 620
|}
Radios: 36,000 (1997)
==Television==
Television broadcast stations: 2 (1997) (including ABS-TV)
Televisions: 31,000 (1997)
==Internet==
Internet Service Providers (ISPs): Cable & Wireless, Antigua Computer Technologies (ACT), Antigua Public Utilities Authority (APUA INET)
Internet hosts: 2,215 (2008)
:country comparison to the world: 140
Internet users: 60,000 (2007)
:country comparison to the world: 158
Country codes: AG
== Demographics ==
{| class="wikitable sortable"
|+Internet Users by Ethnicity
! rowspan="2" |Q48 Ethnic
! colspan="3" |Q55 Internet Use
|-
!Yes
!No
!Don't know/Not stated
|-
|African descendent
|47.42%
|50.74%
|1.84%
|-
|Caucasian/White
|83.27%
|16.03%
|0.70%
|-
|East Indian/India
|58.66%
|40.08%
|1.26%
|-
|Mixed (Black/White)
|64.34%
|33.35%
|2.31%
|-
|Mixed (Other)
|61.22%
|37.62%
|1.16%
|-
|Hispanic
|31.78%
|66.80%
|1.42%
|-
|Syrian/Lebanese
|60.77%
|36.76%
|2.48%
|-
|Other
|59.46%
|39.71%
|0.83%
|-
|Don't | Telecommunications in Antigua and Barbuda | [
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] |
know/Not stated
|20.58%
|70.61%
|8.81%
|-
!Total
!48.35%
!49.81%
!1.84%
|}
{| class="wikitable sortable"
|+Household internet access by ethnicity
! rowspan="2" |Q48 Ethnic
! colspan="3" |Q25 4 Internet access
|-
!No
!Yes
!Don't know/not declared
|-
|African descendent
|51.99%
|38.20%
|9.81%
|-
|Caucasian/White
|14.56%
|82.83%
|2.61%
|-
|East Indian/India
|36.63%
|54.93%
|8.44%
|-
|Mixed (Black/White)
|39.47%
|54.60%
|5.93%
|-
|Mixed (Other)
|41.76%
|51.53%
|6.71%
|-
|Hispanic
|67.68%
|20.56%
|11.76%
|-
|Syrian/Lebanese
|29.48%
|69.39%
|1.13%
|-
|Other
|34.02%
|58.96%
|7.02%
|-
|Don't know/Not stated
|53.86%
|27.58%
|18.56%
|-
!Total
!50.83%
!39.61%
!9.57%
|}
==See also==
*Antigua and Barbuda
*History of telecommunication
*List of telecommunications terminology
*Outline of telecommunication
==References==
==External links==
* Antigua and Barbuda, SubmarineCableMap.com
Antigua and Barbuda
Antigua | Telecommunications in Antigua and Barbuda | [
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] |
This article is about communications systems in Anguilla.
==Telephone==
Telephones – main lines in use: 6,200 (2002)
:country comparison to the world: 212
Telephones – mobile cellular: 1,800 (2002)
:country comparison to the world: 211
Telephone system:
Domestic: Modern internal telephone system
International: EAST CARIBBEAN FIBRE SYSTEM ECFS (cable system)
microwave radio relay to island of Saint Martin (Guadeloupe and Netherlands Antilles)
==Mobile phone (GSM)==
Mobile phone operators:
FLOW (Anguilla) Ltd. – GSM and UMTS 850 and 1900 MHz, LTE 700 MHz with Island-wide coverage
Digicel (Anguilla) Ltd. – GSM and UMTS 850 to 1900 MHz, LTE 700 MHz
Mobiles: ? (2007)
==Radio==
Radio broadcast stations: AM 3, FM 7, shortwave 0 (2007)
{| class="wikitable sortable"
|+ Radio Stations of Anguilla
! Band / Freq.
! Call Sign
! Brand
! City of license
! Notes
|-
| AM 690 kHz
| Unknown
| Caribbean Beacon
| The Valley
| Religious broadcaster
|-
| AM 1500 kHz
| Unknown
| Caribbean Beacon
| The Valley
| 2.5 kW repeater
|-
| AM 1610 kHz
| Unknown
| Caribbean Beacon
| The Valley
| 200 kW repeater
|-
| FM 92.9 MHz
| Unknown
| Klass 92.9
| The Valley
|
|-
| FM 93.3 MHz
| Unknown
| Rainbow FM
| The Valley
| Caribbean Music, News
|-
| FM 95.5 MHz
| Unknown
| Radio Anguilla
| The Valley
| Public broadcaster
|-
| FM 97.7 MHz
| Unknown
| Heart Beat Radio/Up Beat Radio
| The Valley
| 30 kW, Caribbean Music, News
|-
| FM 99.3 MHz
| ZNBR-FM
| NBR – New Beginning Radio / Grace FM
| The Valley
| 5 kW, Religious broadcaster
|-
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] |
FM 100.1 MHz
| Unknown
| Caribbean Beacon
| The Valley
| Religious broadcaster
|-
| FM 100.9 MHz
| Unknown
| CBN – Country Broadcast Network
| The Valley
| 3 kW
|-
| FM 103.3 MHz
| Unknown
| Kool FM
| The Valley
| Religious broadcaster, Urban Caribbean
|-
| FM 105.1 MHz
| ZRON-FM
| Tradewinds Radio
| The Valley
| 5 kW, Caribbean Music, News
|-
| FM 106.7 MHz
| unknown
| VOC – Voice Of Creation
| Sachasses
| Religious broadcaster
|-
| FM 107.9 MHz
| unknown
| GEM Radio Network
| The Valley
| Repeater (Trinidad)
|-
| SW 6090 kHz
| Unknown
| Caribbean Beacon
| The Valley
| Religious
|-
| SW 11775 kHz
| Unknown
| Caribbean Beacon
| The Valley
| Religious
|}
Radios: 3,000 (1997)
==Television==
Television broadcast stations: 1 (1997)
Televisions: 1,000 (1997)
==Internet==
Internet country code: .ai (Top level domain)
Internet Service Providers (ISPs): 2 (FLOW – , Digicel Anguilla – )
Internet hosts: 269 (2012)
:country comparison to the world: 192
Internet: users: 12,377 (2018)
:country comparison to the world: 206
==See also==
*Anguilla
* FLOW (Anguilla) Ltd.
== References ==
== External links ==
* Public Utilities Commission of Anguilla
* Anguilla, SubmarineCableMap.com
Category:Communications in Anguilla
Anguilla
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] |
Acoustic theory is a scientific field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach.
For sound waves of any magnitude of a disturbance in velocity, pressure, and density we have
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot \mathbf{v} + \nabla\cdot(\rho'\mathbf{v}) & = 0 \qquad \text{(Conservation of Mass)} \\
(\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0 \qquad \text{(Equation of Motion)}
\end{align}
In the case that the fluctuations in velocity, density, and pressure are small, we can approximate these as
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot \mathbf{v} & = 0 \\
\frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p'& = 0
\end{align}
Where \mathbf{v}(\mathbf{x},t) is the perturbed velocity of the fluid, p_0 is the pressure of the fluid at rest, p'(\mathbf{x},t) is the perturbed pressure of the system as a function of space and time, \rho_0 is the density of the fluid at rest, and \rho'(\mathbf{x}, t) is the variance in the density of the fluid over space and time.
In the case that the velocity is irrotational (\nabla\times \mathbf{v} = 0), | Acoustic theory | [
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we then have the acoustic wave equation that describes the system:
:
\frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2} - \nabla^2\phi = 0
Where we have
:
\begin{align}
\mathbf{v} & = -\nabla \phi \\
c^2 & = (\frac{\partial p}{\partial \rho})_s\\
p' & = \rho_0\frac{\partial \phi}{\partial t}\\
\rho' & = \frac{\rho_0}{c^2}\frac{\partial \phi}{\partial t}
\end{align}
==Derivation for a medium at rest==
Starting with the Continuity Equation and the Euler Equation:
:
\begin{align}
\frac{\partial \rho}{\partial t} +\nabla\cdot \rho\mathbf{v} & = 0 \\
\rho\frac{\partial \mathbf{v}}{\partial t} + \rho(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p & = 0
\end{align}
If we take small perturbations of a constant pressure and density:
:
\begin{align}
\rho & = \rho_0+\rho' \\
p & = p_0 + p'
\end{align}
Then the equations of the system are
:
\begin{align}
\frac{\partial}{\partial t}(\rho_0+\rho') +\nabla\cdot (\rho_0+\rho')\mathbf{v} & = 0 \\
(\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla (p_0+p') & = 0
\end{align}
Noting that the equilibrium pressures and densities are constant, this simplifies to
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\nabla\cdot \rho'\mathbf{v} & = 0 \\
(\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} | Acoustic theory | [
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] |
+ (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0
\end{align}
===A Moving Medium===
Starting with
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{w}+\nabla\cdot \rho'\mathbf{w} & = 0 \\
(\rho_0+\rho')\frac{\partial \mathbf{w}}{\partial t} + (\rho_0+\rho')(\mathbf{w}\cdot\nabla)\mathbf{w} + \nabla p' & = 0
\end{align}
We can have these equations work for a moving medium by setting \mathbf{w} = \mathbf{u} + \mathbf{v}, where \mathbf{u} is the constant velocity that the whole fluid is moving at before being disturbed (equivalent to a moving observer) and \mathbf{v} is the fluid velocity.
In this case the equations look very similar:
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\mathbf{u}\cdot\nabla\rho' + \nabla\cdot \rho'\mathbf{v} & = 0 \\
(\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{u}\cdot\nabla)\mathbf{v} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0
\end{align}
Note that setting \mathbf{u} = 0 returns the equations at rest.
==Linearized Waves==
Starting with the above given equations of motion for a medium at rest:
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\nabla\cdot \rho'\mathbf{v} & = 0 \\
(\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0
\end{align}
Let us now take \mathbf{v},\rho',p' to all be small quantities.
In the case | Acoustic theory | [
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that we keep terms to first order, for the continuity equation, we have the \rho'\mathbf{v} term going to 0. This similarly applies for the density perturbation times the time derivative of the velocity. Moreover, the spatial components of the material derivative go to 0. We thus have, upon rearranging the equilibrium density:
:
\begin{align}
\frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot \mathbf{v} & = 0 \\
\frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0
\end{align}
Next, given that our sound wave occurs in an ideal fluid, the motion is adiabatic, and then we can relate the small change in the pressure to the small change in the density by
:
p' = (\frac{\partial p}{\partial \rho_0})_s\rho'
Under this condition, we see that we now have
:
\begin{align}
\frac{\partial p'}{\partial t} +\rho_0(\frac{\partial p}{\partial \rho_0})_s\nabla\cdot \mathbf{v} & = 0 \\
\frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0
\end{align}
Defining the speed of sound of the system:
:
c \equiv \sqrt{(\frac{\partial p}{\partial \rho_0})_s}
Everything becomes
:
\begin{align}
\frac{\partial p'}{\partial t} +\rho_0c^2\nabla\cdot \mathbf{v} & = 0 \\
\frac{\partial \mathbf{v}}{\partial t} | Acoustic theory | [
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] |
+ \frac{1}{\rho_0}\nabla p' & = 0
\end{align}
===For Irrotational Fluids===
In the case that the fluid is irrotational, that is \nabla\times\mathbf{v} = 0, we can then write \mathbf{v} = -\nabla\phi and thus write our equations of motion as
:
\begin{align}
\frac{\partial p'}{\partial t} -\rho_0c^2\nabla^2\phi & = 0 \\
-\nabla\frac{\partial\phi}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0
\end{align}
The second equation tells us that
:
p' = \rho_0 \frac{\partial \phi}{\partial t}
And the use of this equation in the continuity equation tells us that
:
\rho_0\frac{\partial^2 \phi}{\partial t} -\rho_0c^2\nabla^2\phi = 0
This simplifies to
:
\frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2} -\nabla^2\phi = 0
Thus the velocity potential \phi obeys the wave equation in the limit of small disturbances. The boundary conditions required to solve for the potential come from the fact that the velocity of the fluid must be 0 normal to the fixed surfaces of the system.
Taking the time derivative of this wave equation and multiplying all sides by the unperturbed density, and then using the fact that p' = \rho_0 \frac{\partial \phi}{\partial t} tells us that
:
\frac{1}{c^2}\frac{\partial^2 p'}{\partial t^2} -\nabla^2p' = 0
Similarly, | Acoustic theory | [
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