Academic literature on the topic 'Numerology'

One tends to think of the study of pure number as an esoteric pursuit. But for the ancient Maya, particularly when it came to temporal matters, numbers were more than mere devices to tally units of time. In stark contrast to the Western calendar, in the Maya realm of timekeeping the duration between ritual events seems to have mattered as much as the times when the events themselves occurred. Moreover, the manner in which the daykeepers of the Maya codices sequenced the intervals followed well-defined patterns, which reveal an array of motives for the Maya way of structuring time. Among these motives were the need to: a) arrive at or avoid particular lucky or unlucky days; b) accommodate changing seasonal or other astronomical events; and c) set up numerological mirror symmetries, a characteristic that resonates with the Pythagorean philosophy of number. Thus the long-neglected study of Maya number offers insight into the chronological structure underlying ritual process, which finds parallels in contemporary Maya culture.

Las ofrendas quechuas del sur del Perú son platos alimenticios, banquetes destinados principalmente a la pachamama y los apus, pero también elaborados sistemas matemáticos regidos por operaciones sofisticadas. Sirviéndose de dos números fundamentales, el 3 y el 4, los especialistas rituales son capaces de transmitir mensajes polisémicos. Mediante el número 3 aglutinan clientes, parajes y cerros, en suma, «personas» capaces de interactuar entre sí. El 3 aparece en los k’intus de hojas de coca y en las oraciones que se recitan durante el proceso de realizar la ofrenda. Por el contrario, el número 4 no indica relaciones sino formas espaciales: es un operador geométrico que unifica la servilleta ceremonial (unk’uña), el papel envoltorio y el paquete acabado para representar las cuatro direcciones del mundo y hacer de la ofrenda un mundo en miniatura. Gracias a los dos números el ritualista puede recrear el cosmos, establecer convenios con los dioses y definir nuevas situaciones favorables para la vida de sus clientes.
The Quechua offerings in the South of Peru are banquets dedicated to the Pachamama and the Apus, and at the same time, are elaborated mathematical systems controlled by sophisticated operations. Using two principal numbers, 3 and 4, the religious specialist is capable of transmitting polysemic messages. Through the number 3, the religious specialist refers to the people, landscapes and mountains, in sum, to «persons» able to interact among themselves. The number 3 appears in the k’intus, composed of coca leaves, also in the prayers said during the process of the offering ritual. On the contrary, the number 4 does not indicate relationships but spatial forms: it is a geometrical operator that is constructed of the ceremonial square napkin (unk’uña) and paper in which the offering is completely wrapped to make the offering a miniature world, containing the «four directions of the world.» Using these numbers, the religious specialist can recreate the cosmos, establish covenants with the gods and define new situations favorable to the life of Quechuas.

An examination of the influence of medieval numerology and number theory upon the works of the Gawain poet, this essay seeks to connect the importance of numbers to the construction of the four poems. By examining such number theories as the Divine Proportion and marriage numbers, as well as Pythagorean number concepts of masculine and feminine numbers, a clear connection between the literature and the number can be found. The poet not only seeks to use numbers to impart important Christian doctrine to his readers in a subconscious way, he also demonstrates an extreme pre-planning of every line and layout of each poem upon the page. Continuing in current critical traditions of examining this manuscript as whole, "Pearl, " "Patience, " "Cleanness, " and "Sir Gawain and the Green Knight" are shown to join together in an interweaving of connectivity through number pattern and the repetition of important numerological concepts.

This dissertation intends to demonstrate the impact of numerology in every aspect of the lives of ancient precolombian people as well as several contemporary American Indian tribes. For this reason numerology may be viewed as a true science, that is both an esoteric and a philosophical one. Thus, numbers may be looked upon not only as abstract signs, but as all inclusive entities in and of themselves. To the ancients, numerical symbols had an occult connotation that transcended the restrictive boundaries of simple computation. For instance, numerology had an integral role in Maya, Aztec, and some contemporary American Indian religious ceremonies. As an example, the high priests were able to predict future events by making intricate numerological computations. Further still, Maya and Aztec calendars were so accurate that they demonstrated an extraordinary knowledge of astronomical events. In order to accurately study the intricate subject of numerology it was necessary to divide the dissertation in several parts. These parts include a concise discussion of the Maya, the Aztec, and certain contemporary American Indian tribes. A general account of Maya, Aztec, and Contemporary American Indian culture and society was included, using the available data of present day archeological and written documents, in order to accurately describe the philosophy of these people. From an examination of the life and culture of these ancient societies, the basis for their myths of creation and the impact of numerology on those particular myths may be easily ascertained. The conclusion discusses how numerology shaped two great civilizations, that of the Maya and Aztecs, and how these basic esoteric numbers were absorbed and changed, to suit the needs and culture of some present day American Indian tribes.

Keyphrases describe a document in a coherent and simple way, giving the prospective reader a way to quickly determine whether the document satisfies their information needs. The pervasion of huge amount of information on Web, with only a small amount of documents have keyphrases extracted, there is a definite need to discover automatic keyphrase extraction systems. Typically, a document written by human develops around one or more general concepts or sub-concepts. These concepts or sub-concepts should be structured and semantically related with each other, so that they can form the meaningful representation of a document. Considering the fact, the phrases or concepts in a document are related to each other, a new approach for keyphrase extraction is introduced that exploits the semantic relations in the document. For measuring the semantic relations between concepts or sub-concepts in the document, I present a comprehensive study aimed at using collaboratively constructed semantic resources like Wikipedia and its link structure. In particular, I introduce a graph-based keyphrase extraction system that exploits the semantic relations in the document and features such as term frequency. I evaluated the proposed system using novel measures and the results obtained compare favorably with previously published results on established benchmarks.

The motif of twins is one that permeates strongly throughout the Harry Potter series. Fred and George as a pair are immensely popular with fans, and the “very curious” twinship of Harry and Voldemort’s wands is a relationship greatly explored in the saga. In my paper, I shall further explore this prominent Potter motif and delve into the origins and symbolism behind this twinship. I will also recall the dark conclusion to the tale of the Weasley twins. The death of Fred as related to the series’ theme as a whole and the death of Harry in the attempt to remove his parasitic twin, Voldemort’s unintended horcrux, will be discussed. There will also be exploration of missing and broken twins, for example, where is Romulus since we know a Remus? Why are Padma and Parvati in different houses? What is the symbolism of Harry’s broken wand? I will discuss how Voldemort’s creation of horcruxes is an intentional twinning of his self, and thus a mutation of nature. An exploration of numerology in relation to this twin discussion will also be included. This paper will show that the motif of twins is not just an interesting addition to the Potter novels but rather a tie-in to the story’s core of insisting on duality when the truth is in wholeness.

This thesis supports the Master of Fine Arts exhibition, To End In Silence, at the Slocumb Galleries, East Tennessee State University, March 15-19, 2010. The exhibit consists of fourteen pieces, which are either presented on pedestals or mounted on the wall. To comment on the title of my thesis, it is a description of the state of calm that I strive to embrace during the creation of my work and the unobtrusive yet engaging tone that I hope for each finished composition to project. This paper explores the aesthetic and conceptual transitions in my work, inspired by a period of personal realization and acceptance. Influences discussed include a number of connections to historical practices including Buddhism, Numerology, and Traditional Japanese Aesthetics, as well as the works of contemporary artists, Agnes Martin, Lee Bontecou, and Manfred Muller. Also included is a complete catalogue of works from To End In Silence.

[ES] La estandarización de la Quinta Generación de redes móviles o 5G, ha concluido este año 2020. No obstante, en el año 2014 cuando la ITU empezó el proceso de estandarización IMT-2020, una de las principales interrogantes era cuál sería la forma de onda sobre la cual se construiría la capa física de esta nueva generación de tecnologías. El 3GPP se comprometió a entregar una tecnología candidata al proceso IMT-2020, y es así como dentro de este proceso de deliberación se presentaron varias formas de onda candidatas, las cuales fueron evaluadas en varios aspectos hasta que en el año 2016 el 3GPP tomó una decisión, continuar con CP-OFDM (utilizada en 4G) con numerología flexible. Una vez decidida la forma de onda, el proceso de estandarización continuó afinando la estructura de la trama, y todos los aspectos intrínsecos de la misma. Esta tesis acompañó y participó de todo este proceso. Para empezar, en esta disertación se evaluaron las principales formas de onda candidatas al 5G. Es así que se realizó un análisis teórico de cada forma de onda, destacando sus fortalezas y debilidades, tanto a nivel de implementación como de rendimiento. Posteriormente, se llevó a cabo una implementación real en una plataforma Software Defined Radio de tres de las formas de onda más prometedoras (CP-OFDM, UFMC y OQAM-FBMC), lo que permitió evaluar su rendimiento en términos de la tasa de error por bit, así como la complejidad de su implementación. Esta tesis ha propuesto también el uso de una solución armonizada como forma de onda para el 5G y sostiene que sigue siendo una opción viable para sistemas beyond 5G. Dado que ninguna de las forma de onda candidatas era capaz de cumplir por sí misma con todos los requisitos del 5G, en lugar de elegir una única forma de onda se propuso construir un transceptor que fuese capaz de construir todas las principales formas de onda candidatas (CP-OFDM, P-OFDM, UFMC, QAM-FBMC, OQAM-FBMC). Esto se consiguió identificando los bloques comunes entre las formas de onda, para luego integrarlos junto con el resto de bloques indispensables para cada forma de onda. La motivación para esta solución era tener una capa física que fuese capaz de cumplir con todos los aspectos del 5G, seleccionando siempre la mejor forma de onda según el escenario. Esta propuesta fue evaluada en términos de complejidad, y los resultados se compararon con la complejidad de cada forma de onda. La decisión de continuar con CP-OFDM con numerología flexible como forma de onda para el 5G se puede considerar también como una solución armonizada, ya que al cambiar el prefijo cíclico y el número de subportadoras, cambian también las prestaciones del sistema. En esta tesis se evaluaron todas las numerologías propuestas por el 3GPP sobre cada uno de los modelos de canal descritos para el 5G (y considerados válidos para sistemas beyond 5G), teniendo en cuenta factores como la movilidad de los equipos de usuario y la frecuencia de operación; para esto se utilizó un simulador de capa física del 3GPP, al que se hicieron las debidas adaptaciones con el fin de evaluar el rendimiento de las numerologías en términos de la tasa de error por bloque. Finalmente, se presenta un bosquejo de lo que podría llegar a ser la Sexta Generación de redes móviles o 6G, con el objetivo de entender las nuevas aplicaciones que podrían ser utilizadas en un futuro, así como sus necesidades. Completado el estudio llevado a cabo en esta tesis, se puede afirmar que como se propuso desde un principio la solución, tanto para el 5G como para beyond 5G, la solución es la armonización de las formas de onda. De los resultados obtenidos se puede corroborar que una solución armonizada permite alcanzar un ahorro computacional entre el 25-40% para el transmisor y del 15-25% para el receptor. Además, fue posible identificar qué numerología CP-OFDM es la más adecuada para cada escenario, lo que permitiría optimizar el diseño y despliegue de las redes 5G. Esto abriría la puerta a hacer lo mismo con el 6G, ya que en esta tesis se considera que será necesario abrir nuevamente el debate sobre cuál es la forma de onda adecuada para esta nueva generación de tecnologías, y se plantea que el camino a seguir es optar por una solución armonizada con distintas formas de onda, en lugar de solo una como sucede con el 5G.
[CA] L'estandardització de la Quinta Generació de xarxes mòbils o 5G, ha conclòs enguany 2020. No obstant això, l'any 2014 quan la ITU va començar el procés d'estandardització IMT-2020, uns dels principals interrogants era quina seria la forma d'onda sobre la qual es construiria la capa física d'esta nova generació de tecnologies. El 3GPP es va comprometre a entregar una tecnologia candidata al procés IMT-2020, i és així com dins d'este procés de deliberació es van presentar diverses formes d'onda candidates, les quals van ser avaluades en diversos aspectes fins que l'any 2016 el 3GPP va prendre una decisió, continuar amb CP-OFDM (utilitzada en 4G) amb numerología flexible. Una vegada decidida la forma d'onda, el procés d'estandardització va continuar afinant la frame structure (no se m'ocorre nom en espanyol), i tots els aspectes intrínsecs de la mateixa. Esta tesi va acompanyar i va participar de tot este procés. Per a començar, en esta dissertació es van avaluar les principals formes d'onda candidates al 5G. És així que es va realitzar una anàlisi teòrica de cada forma d'onda, destacant les seues fortaleses i debilitats, tant a nivell d'implementació com de rendiment. Posteriorment, es va dur a terme una implementació real en una plataforma Software Defined Radio de tres de les formes d'onda més prometedores (CP-OFDM, UFMC i OQAM-FBMC), la qual cosa va permetre avaluar el seu rendiment en termes de la taxa d'error per bit, així com la complexitat de la seua implementació. Esta tesi ha proposat també l'ús d'una solució harmonitzada com a forma d'onda per al 5G i sosté que continua sent una opció viable per a sistemes beyond 5G. Atés que cap de les forma d'onda candidates era capaç de complir per si mateixa amb tots els requeriments del 5G, en compte de triar una única forma d'onda es va proposar construir un transceptor que fóra capaç de construir totes les principals formes d'onda candidates (CP-OFDM, P-OFDM, UFMC, QAM-FBMC, OQAM-FBMC). Açò es va aconseguir identificant els blocs comuns entre les formes d'onda, per a després integrar-los junt amb la resta de blocs indispensables per a cada forma d'onda. La motivació per a esta solució era tindre una capa física que fóra capaç de complir amb tots els aspectes del 5G, seleccionant sempre la millor forma d'onda segons l'escenari. Esta proposta va ser avaluada en termes de complexitat, i els resultats es van comparar amb la complexitat de cada forma d'onda. La decisió de continuar amb CP-OFDM amb numerología flexible com a forma d'onda per al 5G es pot considerar també com una solució harmonitzada, ja que al canviar el prefix cíclic i el número de subportadores, canvien també les prestacions del sistema. En esta tesi es van avaluar totes les numerologías propostes pel 3GPP sobre cada un dels models de canal descrits per al 5G (i considerats vàlids per a sistemes beyond 5G), tenint en compte factors com la mobilitat dels equips d'usuari i la freqüència d'operació; per a açò es va utilitzar un simulador de capa física del 3GPP, a què es van fer les degudes adaptacions a fi d'avaluar el rendiment de les numerologías en termes de la taxa d'error per bloc. Finalment, es presenta un esbós del que podria arribar a ser la Sexta Generació de xarxes mòbils o 6G, amb l'objectiu d'entendre les noves aplicacions que podrien ser utilitzades en un futur, així com les seues necessitats. Completat l'estudi dut a terme en esta tesi, es pot afirmar que com es va proposar des d'un principi la solució, tant per al 5G com per a beyond 5G, la solució és l'harmonització de les formes d'onda. dels resultats obtinguts es pot corroborar que una solució harmonitzada permet aconseguir un estalvi computacional entre el 25-40% per al transmissor i del 15-25% per al receptor. A més, va ser possible identificar què numerología CP-OFDM és la més adequada per a cada escenari, la qual cosa permetria optimitzar el disseny i desplegament de les xarxes 5G. Açò obriria la porta a fer el mateix amb el 6G, ja que en esta tesi es considera que serà necessari obrir novament el debat sobre quina és la forma d’onda adequada per a esta nova generació de tecnologies, i es planteja que el camí que s’ha de seguir és optar per una solució harmonitzada amb distintes formes d’onda, en compte de només una com succeïx amb el 5G.
[EN] The standardization of the Fifth Generation of mobile networks or 5G is still ongoing, although the first releases of the standard were completed two years ago and several 5G networks are up and running in several countries around the globe. However, in 2014 when the ITU began the IMT-2020 standardization process, one of the main questions was which would be the waveform to be used on the physical layer of this new generation of technologies. The 3GPP committed to submit a candidate technology to the IMT-2020 process, and that is how within this deliberation process several candidate waveforms were presented. After a thorough evaluation regarding several aspects, in 2016 the 3GPP decided to continue with CP-OFDM (used in 4G) but including, as a novelty, the use of a flexible numerology. Once the waveform was decided, the standardization process continued to fine-tune the frame structure and all the intrinsic aspects of it. This thesis accompanied and participated in this entire process. To begin with, this dissertation evaluates the main 5G candidate waveforms. Therefore, a theoretical analysis of each waveform is carried out, highlighting its strengths and weaknesses, both at the implementation and performance levels. Subsequently, a real implementation on a Software Defined Radio platform of three of the most promising waveforms (CP-OFDM, UFMC, and OQAM-FBMC) is presented, which allows evaluating their performance in terms of bit error rate, as well as the complexity of its implementation. This thesis also proposes the use of a harmonized solution as a waveform for 5G and argues that it remains a viable option for systems beyond 5G. Since none of the candidate waveforms was capable of meeting on its own with all the requirements for 5G, instead of choosing a single waveform, this thesis proposes to build a transceiver capable of building all the main waveforms candidates (CP-OFDM, P-OFDM, UFMC, QAM-FBMC, OQAM-FBMC). This is achieved by identifying the common blocks between the waveforms and then integrating them with the rest of the essential blocks for each waveform. The motivation for this solution is to have a physical layer that is capable of complying with all aspects of beyond 5G technologies, always selecting the best waveform according to the scenario. This proposal is evaluated in terms of complexity, and the results are compared with the complexity of each waveform. The decision to continue with CP-OFDM with flexible numerology as a waveform for 5G can also be considered as a harmonized solution, since changing the cyclic prefix and the number of subcarriers, changes also the performance of the system. In this thesis, all the numerologies proposed by the 3GPP are evaluated on each of the channel models described for 5G (and considered valid for beyond 5G systems), taking into account factors such as the mobility of the user equipment and the operating frequency. For this, a 3GPP physical layer simulator is used, and proper adaptations are made in order to evaluate the performance of the numerologies in terms of the block error rate. Finally, a sketch of what could become the Sixth Generation of mobile networks or 6G is presented, with the aim of understanding the new applications that could be used in the future, as well as their needs. After the completion of the study carried out in this thesis, it can be said that, as stated from the beginning, for both 5G and beyond 5G systems, the solution is the waveform harmonization. From the results obtained, it can be corroborated that a harmonized solution allows achieving computational savings between 25-40% for the transmitter and 15-25% for the receiver. In addition, it is possible to identify which CP-OFDM numerology is the most appropriate for each scenario, which would allow optimizing the design and deployment of 5G networks. This would open the door to doing the same with 6G, i.e., a harmonized solution with different waveforms, instead of just one as in 5G.
Flores De Valgas Torres, FJ. (2020). Study on Air Interface Variants and their Harmonization for Beyond 5G Systems [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/164442
TESIS

This thesis deals with complex processes, relationships and phenomena which go beyond the assumed and accepted materialistic perception of the world in general and the process of architectural design specifically. It clarifies and actually redefine the sustainability from a point of higher universal principles forming our environment. At the beginning this thesis presents an extensive knowledge base of existing holistic design systems including Feng-shui, sacred geometry, geomancy or numerology. The purpose is to build and establish a solid foundation for understanding and further research as well as objectively interpreting lesser known topics as a whole. On the basis of intersecting information through the above mentioned topics we specify the hypothesis which proposes the pre-existence of one unifying design matrix of harmonic structures in architecture. The structure of its verification takes us from an analysis of the science of human perception to systems of self-similar contextual references of animated and inanimated forms. These systems of emergent form and flow are basically known as fractals, and could be expressed in both mathematical and geometrical languages. The thesis research then consists of analysing chosen examples of urban and architectural scale in sense of fractality, symbolism and geometrical matrices. We include and integrate the research of associated and relevant phenomena in pedagogical practice, and a case study of the application of fractals in development of a chosen town. From the results of this thesis we abstract five non-dogmatic guidelines or tenets for architectural design; which are supported by experimental verification on some of the author´s buildings. These tenets stand as pillars of implosive architecture. This kind of architecture in context of transcendental overlaps means a possibility of how to bring our anthropogenic environment closer to the natural and harmonic code of the Universe.