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14 results on '"11a"'

1. A Multiplication Formula and Its Application

Author

Zhu, Yongwen

Subjects
Mathematics - Number Theory, 11A, F.2.1
Abstract

This article presents a vertical multiplication formula for calculating the multiplication of any two multi-digit integers, which may be not only used to design the multiplier but also to the mental multiplication. Our algorithm is a generalization of that of Karatsuba and Offman, but it is superior to the latter because the latter is not suitable for oral calculation of multiplication of large integers. These two algorithms are both the vertical multiplication method, but in our algorithm the horizontal subtraction in stead of the horizontal addition used in the Kartsuba algorithm makes the involved numbers are much smaller and their algebraic sum are much smaller too because the positive and negative numbers probably cancel each other out. Because of the above advantages, our vertical multiplication formula allows more practical and efficient multipliers to be designed., Comment: 15 pages, 4 tables, and 23 references

Published
2021

3. Geometric and algebraic interpretation of primitive Pythagorean triples parameters

Author

Aleshkevich, Natalia

Subjects
Mathematics - Number Theory, 11A
Abstract

The paper found a geometric and algebraic interpretation of the parameters m and n from the formulas for obtaining primitive Pythagorean triples, which are solutions of the equation ${x^2+y^2=z^2}$, namely: ${x=m^2-n^2}$, ${y=2mn}$, ${z=m^2+n^2}$. The study was based on the process of building figurate numbers using gnomons. The paper discusses the process of building squares. The addition of the gnomon U to the original square leads to a larger square: ${x^2+U=z^2}$. The first stage of the investigation was the construction of the gnomon U, which is equal to the area of a square ${y^2}$. The construction is based on a generating square with a side equal to an even number. The area of the generating square is represented as the sum of the areas of two equal rectangles in all possible ways. At the same time, using the generating square, the gnomon U and the sides of all squares are also constructed: x, y, z. The second stage of the investigation was to obtain a formula for the parameters m and n through the partition elements t and l of the side of the generating square., Comment: 10 pages, 3 figures

Published
2019

4. A simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem

Author

Daudin, Jean-Jacques and Pierre, Laurent

Subjects
Mathematics - Number Theory, 11A
Abstract

This paper gives a simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the $3x+1$ problem (see \cite{Wirsching} and \cite{Goodwin}). This representation permits to compute all the ascending Collatz sequences $(f^{(i)}(n),\: i=1,b-1)$ with a last value $f^{(b)}(n)=1.$ Other periodic sequences connected to $1$ are also identified.

Published
2018

5. Triangle Area Numbers and Solid Rectangular Numbers

Author

Zelator, Konstantine D.

Subjects
Mathematics - General Mathematics, 11A, A005
Abstract

In this work, we define a triangle area number to be the area number of a triangle whose sides have integer lengths, and whose area is a rational number. In Result 3, on page 17, we prove that every triangle area number is in fact an integer which is a multiple of 6. Certain divisibility and other conditions and formulas are also derived, which the three integer sidelengths must satisfy. On pages 20 and 21, we list all the triangle area numbers not exceeding 999., Comment: 22 pages

Published
2008

6. Certain Properties of Pythagorean Triangles involving the interior diameter, and the exterior diameters

Author

Zelator, Konstantine "Hermes"

Subjects
Mathematics - General Mathematics, 11A, 11D
Abstract

There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is Pythagorean, the four diameters are integers. Consider a Pythagorean triangle with the property that one leglength is a perfect(or integer)square, and with one of the four diameters also a integer square.Of the eight resulting combinations, we prove that only six are possible or can occur. We then completely parametrically describe the six families; each corresponding to one of the six combinations., Comment: 27 pages

Published
2008

7. Survey on Wireless Technology Trade-Offs for the Industrial Internet of Things

Author

Seferagić, Amina, Famaey, Jeroen, De Poorter, Eli, Hoebeke, Jeroen, and Seferagic, Amina

Subjects
bluetooth low energy (ble), Computer science, COMMUNICATION, Review, 02 engineering and technology, lcsh:Chemical technology, LoRa, Biochemistry, Analytical Chemistry, law.invention, IEEE 802, Bluetooth, law, 0202 electrical engineering, electronic engineering, information engineering, lcsh:TP1-1185, wirelesshart, Instrumentation, Wireless network, Physics, Time Slotted Channel Hopping (TSCH), Industrial Internet of Things (IIoT), Narrowband IoT (NB-IoT), Atomic and Molecular Physics, and Optics, NETWORKS, Chemistry, Systems engineering, 11ah, 11a, Engineering sciences. Technology, IEEE 802.11ah, Low Energy (BLE), ble long range, Technology and Engineering, ieee 802.11ah, industrial internet of things (iiot), AUTOMATION, narrowband iot (nb-iot), Wireless, ISA100, Electrical and Electronic Engineering, BLE Long Range, wifi halow, WirelessHART, business.industry, 020208 electrical & electronic engineering, isa100.11a, 020206 networking & telecommunications, Automation, IEEE 802.11AH, ISA100.11a, Software deployment, time slotted channel hopping (tsch), WiFi HaLow, business, REQUIREMENTS, lora
Abstract

Aside from vast deployment cost reduction, Industrial Wireless Sensor and Actuator Networks (IWSAN) introduce a new level of industrial connectivity. Wireless connection of sensors and actuators in industrial environments not only enables wireless monitoring and actuation, it also enables coordination of production stages, connecting mobile robots and autonomous transport vehicles, as well as localization and tracking of assets. All these opportunities already inspired the development of many wireless technologies in an effort to fully enable Industry 4.0. However, different technologies significantly differ in performance and capabilities, none being capable of supporting all industrial use cases. When designing a network solution, one must be aware of the capabilities and the trade-offs that prospective technologies have. This paper evaluates the technologies potentially suitable for IWSAN solutions covering an entire industrial site with limited infrastructure cost and discusses their trade-offs in an effort to provide information for choosing the most suitable technology for the use case of interest. The comparative discussion presented in this paper aims to enable engineers to choose the most suitable wireless technology for their specific IWSAN deployment.

Published
2020
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8. Certain Properties of Pythagorean Triangles involving the interior diameter, and the exterior diameters

Author

Zelator, Konstantine \\'Hermes\\'

Subjects
11A, 11D, General Mathematics (math.GM), FOS: Mathematics, Mathematics - General Mathematics
Abstract

There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is Pythagorean, the four diameters are integers. Consider a Pythagorean triangle with the property that one leglength is a perfect(or integer)square, and with one of the four diameters also a integer square.Of the eight resulting combinations, we prove that only six are possible or can occur. We then completely parametrically describe the six families; each corresponding to one of the six combinations., 27 pages

Published
2008

9. Influencia del tamaño de paquetes sobre la pérdida de paquetes en un enlace UDP/IP/IEEE 802.11a

Author

Noroño Rodríguez, Nomar Alexander, Fermín, José R., Noroño Rodríguez, Nomar Alexander, and Fermín, José R.

Abstract

La presente investigación tiene como objetivo estudiar la influencia del tamaño de paquetes sobre la pérdida de paquetes en un enlace UDP/IP/IEEE 802.11a. Se emplearon métodos indirectos de medición, utilizando un generador de tráfico comercial bajo ambiente Windows XP. Para el diseño experimental se estableció un enlace punto a punto a través del cual se enviaron ráfagas de diferentes tamaños de paquetes equidistantes entre sí. Se determinó que la pérdida de paquetes es sensible al tamaño de los mismos, satisfaciendo la Ley de Probabilidad de Pareto. Esto puede ser debido a la característica intrínseca del protocolo UDP., The purpose of this work is to study the influence of packet size on packet loss in a UDP/IP/IEEE 802.11a link. The capture was performed via indirect methods of measurement, employing commercial software tools under Windows XP. For the experimental design, a point-to-point link was implemented, through which, sequences of packets of different size has being transmitted. It was determined that the packet loss is sensible on the packet size, following the Pareto´s Law. This could be due to an intrinsic property of the UDP protocol itself.

Published
2012

10. Calidad de servicio entre sistemas autónomos con enlaces a 5.7 GHz y servicios de última milla inalámbricos con el uso de IPv6

Author

Acurero, Alfredo, Bracho, David, Rincón, Carlos, Wu, Jianfeng, Acurero, Alfredo, Bracho, David, Rincón, Carlos, and Wu, Jianfeng

Abstract

El estudio de conectividad inalámbrica entre Sistemas Autónomos no ha sido muy explorado, por lo que se busca asociar el nuevo protocolo de direccionamiento IPv6 con dicha problemática. Consecuentemente, se analizó el comportamiento del protocolo IPv6 en Sistemas Autónomos conectados por enlaces de 5.7 GHz usando parámetros de medición de Calidad de Servicio (QoS) y nodos móviles en los extremos. Aplicando los principios de Bisquerra (2000), la metodología constó de cuatro (4) fases: recopilación de información, diseño de topologías de pruebas, rutinas de medición y recopilación de los resultados y análisis estadístico. Del análisis-comparativo entre el protocolo IPv6 e IPv4 se desprende que IPv6 presentó en general un menor desempeño frente a IPv4, pero mediante el uso del método estadístico ANOVA se concluye que a causas de diferencias no considerables, IPv6 no influye significativamente en el rendimiento, considerando factible su uso en una red con las características estudiadas.

Published
2012

11. Influencia de la radiación solar sobre el desempeño de las redes wi-fi en la banda de los 5 ghz (802.11a)

Author

Chávez, Carlos Orlando and Chávez, Carlos Orlando

Abstract

The fundamental intention of this investigation was the analysis of the influence of the solar radiation on the Wi-Fi networks performance that operate in the 5 GHz band (802.11a), with the purpose of determining to what extent the incident solar radiation affects the performance of these networks in terms of throughput and the percentage of lost packages. For the data collection of performance a test Wi-Fi network was designed and implemented operating in the 5 GHz band formed in Ad-Hoc mode and, with the aid of a wireless sniffer, throughput and loss of package were obtained; at the same time the data of solar radiation provided by the weather station of the Faculty of Architecture and Design of the University of Zulia was analyzed. The obtained results indicate that the solar radiation exerts a significant influence on the performance of the Wi-Fi networks that operate in the 5 GHz band. In order to reach this conclusion, a performance index was created based on throughput and the loss of packages that, once quantified, was tabulated together with the values solar radiation values later to make a statistical analysis of regression and correlation of variables. The obtained finding serves as reference to companies as to network professionals, in order that they take in consideration this meteorological parameter at the moment of implementing networks that operate in the 5 GHz bands in geographical areas with the climatic characteristics of the Maracaibo., El propósito fundamental de esta investigación fue el análisis de la influencia de la radiación solar sobre el desempeño de las redes WI-FI que operan en la banda de los 5 GHz (802.11a), con el fin de determinar en qué medida la radiación solar incidente afecta el desempeño de estas redes en términos de throughput y porcentaje de paquetes perdidos. Para la recolección de datos de desempeño se diseñó e implementó una red WI-FI de prueba operando en la banda de 5 GHz configurada en modo Ad-Hoc donde, con la ayuda de un sniffer inalámbrico, se obtuvieron las métricas del throughput y pérdida de paquetes; a la vez que se analizaron los datos de radiación solar suministrados por la estación meteorológica de la Facultad de Arquitectura y Diseño de la Universidad del Zulia. Los resultados obtenidos mediante el análisis estadístico de correlación y regresión de variables, indican que la radiación solar ejerce una significativa influencia sobre el desempeño de las redes Wi-Fi que operan en la banda de 5 GHz. El hallazgo obtenido sirve de referencia tanto a empresas como a profesionales de redes, para que tomen en consideración este parámetro meteorológico a la hora de implementar estas redes que operen en la banda de 5 GHz en áreas geográficas con las características climáticas de la ciudad de Maracaibo.

Published
2007

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