An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms
In this article, a comprehensive analysis of the approach known as Split-Step Wavelet Parabolic Equation (SSW-PE) in modeling radio wave propagation is presented. The SSW-PE introduces innovations, such as the application of narrow-angle and wideangle approaches, referred to as NAPE and WAPE, respec...
- Autores:
-
Alexandre Rocha
Parada Rozo, Diego Andres
Tami, Diego
Dinael Guevara
Rego, Cassio
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2024
- Institución:
- Universidad Francisco de Paula Santander
- Repositorio:
- Repositorio Digital UFPS
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.ufps.edu.co:ufps/9180
- Acceso en línea:
- https://repositorio.ufps.edu.co/handle/ufps/9180
- Palabra clave:
- Split-Step Wavelet (SSW-PE) Approach
Parabolic equation
Radio Wave Propagation
- Rights
- openAccess
- License
- Está bajo una licencia Creative Commons Atribución 4.0 Internacional (CC BY 4.0)
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An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| title |
An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| spellingShingle |
An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms Split-Step Wavelet (SSW-PE) Approach Parabolic equation Radio Wave Propagation |
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An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| title_full |
An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| title_fullStr |
An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| title_full_unstemmed |
An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| title_sort |
An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet Transforms |
| dc.creator.fl_str_mv |
Alexandre Rocha Parada Rozo, Diego Andres Tami, Diego Dinael Guevara Rego, Cassio |
| dc.contributor.author.none.fl_str_mv |
Alexandre Rocha Parada Rozo, Diego Andres Tami, Diego Dinael Guevara Rego, Cassio |
| dc.subject.proposal.eng.fl_str_mv |
Split-Step Wavelet (SSW-PE) Approach Parabolic equation Radio Wave Propagation |
| topic |
Split-Step Wavelet (SSW-PE) Approach Parabolic equation Radio Wave Propagation |
| description |
In this article, a comprehensive analysis of the approach known as Split-Step Wavelet Parabolic Equation (SSW-PE) in modeling radio wave propagation is presented. The SSW-PE introduces innovations, such as the application of narrow-angle and wideangle approaches, referred to as NAPE and WAPE, respectively. Furthermore, the SSW-PE demonstrates the incorporation of refractivity variations, modifications in terrain modeling for better representation, and considerations of surface boundary conditions. In addition to its innovative aspects, this study aims to provide a complete guide for effectively replicating the algorithm, thereby promoting the advancement of propagation studies using wavelets. The effectiveness and applicability of this approach are validated through comparative studies with well-established solutions, including the Discrete Mixed Fourier Transform (DMFT) version of the Split-Step Parabolic Equation (SSPE) method. Comparisons with measurements from real propagation cases are also conducted. Statistical analysis confirms the innovative potential of the SSW-PE algorithm, which also offers computational efficiency for rapid and consistent simulations. Thus, this article contributes to a comprehensive and innovative analysis, providing tangible resources for the research community interested in expanding this methodology. |
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2024 |
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2024-02-21 |
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2025-03-06T15:25:16Z |
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2025-03-06T15:25:16Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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eng |
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eng |
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Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 23, No. 1, e2024279458, Mar 2024 DOI: https://dx.doi.org/10.1590/2179-10742024v23i1279458 |
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Journal of microwaves optoelectronics and electromagnetic applications |
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Alexandre RochaParada Rozo, Diego AndresTami, DiegoDinael GuevaraRego, Cassio2025-03-06T15:25:16Z2025-03-06T15:25:16Z2024-02-21https://repositorio.ufps.edu.co/handle/ufps/9180In this article, a comprehensive analysis of the approach known as Split-Step Wavelet Parabolic Equation (SSW-PE) in modeling radio wave propagation is presented. The SSW-PE introduces innovations, such as the application of narrow-angle and wideangle approaches, referred to as NAPE and WAPE, respectively. Furthermore, the SSW-PE demonstrates the incorporation of refractivity variations, modifications in terrain modeling for better representation, and considerations of surface boundary conditions. In addition to its innovative aspects, this study aims to provide a complete guide for effectively replicating the algorithm, thereby promoting the advancement of propagation studies using wavelets. The effectiveness and applicability of this approach are validated through comparative studies with well-established solutions, including the Discrete Mixed Fourier Transform (DMFT) version of the Split-Step Parabolic Equation (SSPE) method. Comparisons with measurements from real propagation cases are also conducted. Statistical analysis confirms the innovative potential of the SSW-PE algorithm, which also offers computational efficiency for rapid and consistent simulations. Thus, this article contributes to a comprehensive and innovative analysis, providing tangible resources for the research community interested in expanding this methodology.18 Páginasapplication/pdfengJournal of microwaves optoelectronics and electromagnetic applicationsBrasilJournal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 23, No. 1, e2024279458, Mar 2024 DOI: https://dx.doi.org/10.1590/2179-10742024v23i1279458Vol.23 No.1 (2024)181. (2024)123Está bajo una licencia Creative Commons Atribución 4.0 Internacional (CC BY 4.0)https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessAtribución 4.0 Internacional (CC BY 4.0)http://purl.org/coar/access_right/c_abf2https://www.scielo.br/j/jmoea/a/bHQHrTBQWshQjHMFCpZWXyS/An Efficient and Accurate Algorithm for Electromagnetic Wave Propagation Modeling Based on Wavelet TransformsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Split-Step Wavelet (SSW-PE) ApproachParabolic equationRadio Wave PropagationT. S. Rappaport, Y. Xing, G. R. MacCartney, A. F. Molisch, E. Mellios, and J. Zhang, “Overview of millimeter wave communications for fifth-generation (5g) wireless networks-with a focus on propagation models,” IEEE Transactions on Antennas and Propagation, vol. 65, no. 12, pp. 6213-6230, 2017.H. Zhou, A. Chabory, and R. Douvenot, “A Fast Wavelet-to-Wavelet Propagation Method for the Simulation of Long- Range Propagation in Low Troposphere,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 3, pp. 2137-2148, 2022.D. Parada, C. G. Rego, D. Guevara, A. Navarro, G. L. Ramos, and R. Oliveira, “A modified radiopropagation multipath model for constant refractivity gradient profiles,” Journal of Microwaves, Optoelectronics and Electromagnetic Applications, vol. 22, no. 2, p. 298-312, 2023.G. Dockery, “Modeling electromagnetic wave propagation in the troposphere using the parabolic equation,” IEEE Transactions on Antennas and Propagation, vol. 36, no. 10, pp. 1464-1470, 1988.C. Dartora and K. Nobrega, “Study of gaussian and bessel beam propagation using a new analytic approach,” Optics Communications, vol. 285, no. 5, pp. 510-516, 2012.G. Apaydin and L. Sevgi, Radio wave propagation and parabolic equation modeling John Wiley & Sons, Ltd, 2017.P. Zhang, L. Bai, Z. Wu, and L. Guo, “Applying the parabolic equation to tropospheric groundwave propagation: A review of recent achievements and significant milestones.” IEEE Antennas and Propagation Magazine, vol. 58, no. 3, pp. 31-44, 2016.M. Leontovich and V. Fzck", “Solution of propagation of electromagnetic waves along the earth’s surface by the method of parabolic equations,” Journal of Physics USSR vol. 10 pp. 13-23, 1946.D. J. Thomson and N. R. Chapman, “A wide-angle split-step algorithm for the parabolic equation,” The Journal of the Acoustical Society of America, vol. 74, no. 6, pp. 1848-1854, 1983.O. Ozgun, G. Apaydin, M. Kuzuoglu, and L. Sevgi, “Petool: Matlab-based one-way and two-way split-step parabolic equation tool for radiowave propagation over variable terrain,” Computer Physics Communications, vol. 182, no. 12, pp. 2638-2654, 2011.M. Levy, Parabolic Equation Methods for Electromagnetic Wave Propagation IET, 2000, vol. 45.R. Kuttler and G. D. Dockery, “Theoretical description of the parabolic approximation/fourier split-step method of representing electromagnetic propagation in the troposphere,” Radio Science, vol. 26, no. 02, pp. 381-393, 1991.F. Claerbout, “Fundamentals of geophysical data processing,” International Series in the Earth and Planetary Sciences, 1985.M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Applied Optics, vol. 17, no. 24, pp. 3990-3998, 1978.M. D. Collins and R. B. Evans, “A two-way parabolic equation for acoustic backscattering in the ocean,” The Journal of the Acoustical Society of America, vol. 91, no. 3, pp. 1357-1368, 1992.A. Iqbal and V. Jeoti, “A split step wavelet method for radiowave propagation modelling in tropospheric ducts,” in 2011 IEEE International RF & Microwave Conference, 2011.H. Zhou, R. Douvenot, and A. Chabory, “Modeling the long-range wave propagation by a split-step wavelet method,” Journal of Computational Physics, vol. 402, p. 109042, 2020.]T. Bonnafont, R. Douvenot, and A. Chabory, “A local split-step wavelet method for the long range propagation simulation in 2d,” Radio Science, vol. 56, no. 2, pp. 1-11, 2021.S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.0]I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 909-996, 1988.O. Ozgun, M. Kuzuoglu, G. Apaydin, and L. Sevgi, “Two-way split-step parabolic equation algorithm for tropospheric propagation: Tests and comparisons,” in 2010 10th Mediterranean Microwave Symposium, pp. 14-17, 2010.]S. Mallat, A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way, 3rd ed. USA: Academic Press, Inc., 2008.C. Union, ITU-R P.453-14 The radio refractive index: its formula and refractivity data, ITU Recommendation”, 2019.]P. Zhang, L. Bai, Z. Wu, and F. Li, “Effect of window function on absorbing layers top boundary in parabolic equation,” in Asia-Pacific Conference on Antennas and Propagation, pp. 849-852, 2014.]D. Dockery and J. Kuttler, “An improved impedance-boundary algorithm for fourier split-step solutions of the parabolic wave equation,” IEEE Transactions on Antennas and Propagation, vol. 44, no. 12, pp. 1592-1599, 1996.6]J. R. Kuttler and R. Janaswamy, “Improved fourier transform methods for solving the parabolic wave equation,” Radio Science, vol. 37, no. 2, pp. 1-11, 2002.]J. Hviid, J. Andersen, J. Toftgard, and J. Bojer, “Terrain-based propagation model for rural area-an integral equation approach,” IEEE Transactions on Antennas and Propagation, vol. 43, no. 1, pp. 41-46, 19958]C. Garcia Batista and C. Gonçalves do Rego, “A high-order unconditionally stable fdtd-based propagation method,” IEEE Antennas and Wireless Propagation Letters, vol. 12, pp. 809-812, 2013.R. Oliveira, G. L. Ramos, and C. G. do Rego, “Predição de cobertura radioelétrica usando métodos de equação parabólica em ambiente metroviário urbano na faixa de vhf,” in Programa de Pós-Graduação em Engenharia Elétrica - PPGEE, 2021.]E. Territorial, Satélites de Monitoramento, 2023.ORIGINALdescarga.pdfdescarga.pdfArtículo de Investigaciónapplication/pdf1357029https://repositorio.ufps.edu.co/bitstreams/56ae0180-c6f1-4dc8-915d-4e7c88f91c00/download2001b2b0fcc34432bb6efd9327926894MD51trueAnonymousREADLICENSElicense.txtlicense.txttext/plain; charset=utf-814828https://repositorio.ufps.edu.co/bitstreams/d0ee8bb4-19cd-44f3-8d44-e48b506eeb2d/download2f9959eaf5b71fae44bbf9ec84150c7aMD52falseAnonymousREADTEXTdescarga.pdf.txtdescarga.pdf.txtExtracted texttext/plain55481https://repositorio.ufps.edu.co/bitstreams/75b614cb-2d2a-4f2b-8ba7-b1971ab982d9/download708d48be6fb692bdfc3fcf27b29aeaf3MD53falseAnonymousREADTHUMBNAILdescarga.pdf.jpgdescarga.pdf.jpgGenerated Thumbnailimage/jpeg14785https://repositorio.ufps.edu.co/bitstreams/4abbfe5b-a768-4f99-807f-3f617a62cd20/download88818b59846278d7fedf4ce98f6107bfMD54falseAnonymousREADufps/9180oai:repositorio.ufps.edu.co:ufps/91802025-03-07 03:05:02.219https://creativecommons.org/licenses/by/4.0/Está bajo una licencia Creative Commons Atribución 4.0 Internacional (CC BY 4.0)open.accesshttps://repositorio.ufps.edu.coRepositorio Universidad Francisco de Paula 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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