Search results for: elliptic integral

Authors: Jinlai Bian, Zailin Yang, Guanxixi Jiang, Xinzhu Li

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The problem of elastic wave propagation in inhomogeneous medium has always been a classic problem. Due to the frequent occurrence of earthquakes, many economic losses and casualties have been caused, therefore, to prevent earthquake damage to people and reduce damage, this paper studies the dynamic response around the circular inclusion in the whole space with inhomogeneous modulus, the inhomogeneity of the medium is reflected in the shear modulus of the medium with the spatial position, and the density is constant, this method can be used to solve the problem of the underground buried pipeline. Stress concentration phenomena are common in aerospace and earthquake engineering, and the dynamic stress concentration factor (DSCF) is one of the main factors leading to material damage, one of the important applications of the theory of elastic dynamics is to determine the stress concentration in the body with discontinuities such as cracks, holes, and inclusions. At present, the methods include wave function expansion method, integral transformation method, integral equation method and so on. Based on the complex function method, the Helmholtz equation with variable coefficients is standardized by using conformal transformation method and wave function expansion method, the displacement and stress fields in the whole space with circular inclusions are solved in the complex coordinate system, the unknown coefficients are solved by using boundary conditions, by comparing with the existing results, the correctness of this method is verified, based on the superiority of the complex variable function theory to the conformal transformation, this method can be extended to study the inclusion problem of arbitrary shapes. By solving the dynamic stress concentration factor around the inclusions, the influence of the inhomogeneous parameters of the medium and the wavenumber ratio of the inclusions to the matrix on the dynamic stress concentration factor is analyzed. The research results can provide some reference value for the evaluation of nondestructive testing (NDT), oil exploration, seismic monitoring, and soil-structure interaction.

Keywords: circular inclusions, complex variable function, dynamic stress concentration factor (DSCF), inhomogeneous medium

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: Vernie C. Convicto, Henry P. Aringa, Wilson I. Barredo

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This study presents a conformational model of the helical structures of globular protein particularly ferritin in the framework of white noise path integral formulation by using Associated Legendre functions, Bessel and convolution of Bessel and trigonometric functions as modulating functions. The model incorporates chirality features of proteins and their helix-turn-helix sequence structural motif.

Keywords: globular protein, modulating function, white noise, winding probability

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Authors: Pradyumna R., Sridhar S., A. Satyanarayana, Alok S. Chauhan, Baig M. A. H.

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Modern turbine engines for aerospace applications need precision investment cast components such as integrally cast rotors and stators, for their hot end turbine stages. Traditionally, these turbines are used as starter engines. In recent times, such engines are also used for strategic missile applications. The rotor/stator castings consist of a central hub (shrouded in some designs) over which a number of aerofoil shaped blades are located. Since these components cannot be machined, investment casting is the only available route for manufacture and hence stringent dimensional aerospace quality has to be in-built in the casting process itself. In the process of investment casting, pattern generation by injection of wax into dedicated dies/moulds is the first critical step. Traditional approach deals in producing individual blades with hub/shroud features through wax injection and assembly of a set of such injected patterns onto a dedicated and precisely manufactured fixture to wax-weld and generate an integral wax pattern, a process known as the ‘segmental approach’. It is possible to design a single-injection die with retractable metallic inserts in the case of untwisted blades of stator patterns without the shroud. Such an approach is also possible for twisted blades of rotors with highly complex design of inter-blade inserts and retraction mechanisms. DMRL has for long established methods and procedures for the above to successfully supply precision castings for various defence related projects. In recent times, urea based soluble insert approach has also been successfully applied to overcome the need to design and manufacture a precision assembly fixture, leading to substantial reduction in component development times. Present paper deals in length various approaches tried and established at DMRL to generate precision wax patterns for aerospace quality turbine rotors and stators. In addition to this, the importance of simulation in solving issues related to wax injection is also touched upon.

Keywords: die/mold and fixtures, integral rotor/stator, investment casting, wax patterns, simulation

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Authors: S. R. Nayaka, Putta Swamy

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Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

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Authors: A. Y. Purnama, N. Yasufuku

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The bridge structure is a building that has to be maintained, especially for the elastomeric bearing. The girder of the bridge needs to be lifted upward to maintain this elastomeric bearing, that needs high cost. Nowadays, integral abutment bridges are becoming popular. The integral abutment bridge is less costly because the elastomeric bearings are eliminated, which reduces the construction cost and maintenance costs. However, when this elastomeric bearing removed, the girder movement due to environmental thermal forces directly support by pile foundation, and it needs to be considered in the design. In case of pile foundation in a stiff soil, in the top area of the pile cannot move freely due to the fixed condition by soil stiffness. Pre-bored pile system can be used to increase the flexibility of pile foundation using a pre-bored hole that filled with elastic materials, but the behavior of soil-pile interaction and soil response due to this system is still rarely explained. In this paper, an experimental study using small-scale laboratory model test conducted in a half size model. Single flexible pile model embedded in sandy soil with the pre-bored ring, which filled with the filler material. The testing box made from an acrylic glass panel as observation area of the pile shaft to monitor the displacement of the pile during the lateral loading. The failure behavior of the soil inside the pre-bored ring and around the pile shaft was investigated to determine the point of pile rotation and the movement of this point due to the pre-bored ring system along the pile shaft. Digital images were used to capture the deformations of the soil and pile foundation during the loading from the acrylic glass on the side of the testing box. The results were presented in the form of lateral load resistance charts against the pile shaft displacement. The failure pattern result also established due to the cyclic lateral loading. The movement of the rotational point was measured due to the pre-bored system filled with appropriate filler material. Based on the findings, design considerations for pre-bored pile system due to cyclic lateral loading can be introduced.

Keywords: failure behavior, pre-bored pile system, cyclic lateral loading, sandy soil

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: stochastic integrals, single–server queue model, catastrophes, busy period

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Authors: Salman Piri

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In this study, a two-dimensional lattice Boltzmann method (LBM) was considered for the numerical simulation of fluid flow in a channel. Also, the Lagrangian method was used for particle tracking in one-way coupling. Three hundred spherical particles with specific diameters were released in the channel entry and an elliptical object was placed in the channel for flow obstruction. The effect of gravity, the drag force, the Saffman lift and the Brownian forces were evaluated in the particle motion trajectories. Also, the effect of the geometrical parameter, ellipse aspect ratio, and the flow characteristic or Reynolds number was surveyed for the transport and deposition of particles. Moreover, the influence of particle diameter between 0.01 and 10 µm was investigated. Results indicated that in small Reynolds, more inertial and gravitational trapping occurred on the obstacle surface for particles with larger diameters. Whereas, for nano-particles, influenced by Brownian diffusion and vortices behind the obstacle, the inertial and gravitational mechanisms were insignificant and diffusion was the dominant deposition mechanism. In addition, in Reynolds numbers larger than 400, there was no significant difference between the deposition of finer and larger particles. Also, in higher aspect ratios of the ellipse, more inertial trapping occurred for particles of larger diameter (10 micrometers), while in lower cases, interception and gravitational mechanisms were dominant.

Keywords: ellipse aspect elito, particle tracking diffusion, lattice boltzman method, larangain particle tracking

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Authors: Mohammad Rajabalinejad

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Safety is often seen as a requirement or a performance indicator through the design process, and this does not always result in optimally safe products or systems. This paper suggests integrating the best safety practices with the design process to enrich the exploration experience for designers and add extra values for customers. For this purpose, the commonly practiced safety standards and design methods have been reviewed and their common blocks have been merged forming Safety Cube. Safety Cube combines common blocks for design, hazard identification, risk assessment and risk reduction through an integral approach. An example application presents the use of Safety Cube for design of machinery.

Keywords: safety, safety cube, product, system, machinery, design

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Authors: Walid Abdallah, Noureddine Boudriga

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Wireless sensor networks have shown their effectiveness in the deployment of many critical applications especially in the military domain. Border surveillance is one of these applications where a set of wireless sensors are deployed along a country border line to detect illegal intrusion attempts to the national territory and report this to a control center to undergo the necessary measures. Regarding its nature, this wireless sensor network can be the target of many security attacks trying to compromise its normal operation. Particularly, in this application the deployment and location of sensor nodes are of great importance for detecting and tracking intruders. This paper proposes a location-based authentication and key distribution mechanism to secure wireless sensor networks intended for border surveillance where the key establishment is performed using elliptic curve cryptography and identity-based public key scheme. In this scheme, the public key of each sensor node will be authenticated by keys that depend on its position in the monitored area. Before establishing a pairwise key between two nodes, each one of them must verify the neighborhood location of the other node using a message authentication code (MAC) calculated on the corresponding public key and keys derived from encrypted beacon messages broadcast by anchor nodes. We show that our proposed public key authentication and key distribution scheme is more resilient to node capture and node replication attacks than currently available schemes. Also, the achievement of the key distribution between nodes in our scheme generates less communication overhead and hence increases network performances.

Keywords: wireless sensor networks, border surveillance, security, key distribution, location-based

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Authors: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Ahmed AlNouss, Salim Ahmed

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Process control refers to the techniques to control the variables in a process in order to maintain them at their desired values. Advanced process control (APC) is a broad term within the domain of control where it refers to different kinds of process control and control related tools, for example, model predictive control (MPC), statistical process control (SPC), fault detection and classification (FDC) and performance assessment. APC is often used for solving multivariable control problems and model predictive control (MPC) is one of only a few advanced control methods used successfully in industrial control applications. Advanced control is expected to bring many benefits to the plant operation; however, the extent of the benefits is plant specific and the application needs a large investment. This requires an analysis of the expected benefits before the implementation of the control. In a real plant simulation studies are carried out along with some experimentation to determine the improvement in the performance of the plant due to advanced control. In this research, such an exercise is undertaken to realize the needs of APC application. The main objectives of the paper are as follows: (1) To apply MPC to a number of simulations set up to realize the need of MPC by comparing its performance with that of proportional integral derivatives (PID) controllers. (2) To study the effect of controller parameters on control performance. (3) To develop appropriate performance index (PI) to compare the performance of different controller and develop novel idea to present tuning map of a controller. These objectives were achieved by applying PID controller and a special type of MPC which is dynamic matrix control (DMC) on the multi-tanks process simulated in loop-pro. Then the controller performance has been evaluated by changing the controller parameters. This performance was based on special indices related to the difference between set point and process variable in order to compare the both controllers. The same principle was applied for continuous stirred tank heater (CSTH) and continuous stirred tank reactor (CSTR) processes simulated in Matlab. However, in these processes some developed programs were written to evaluate the performance of the PID and MPC controllers. Finally these performance indices along with their controller parameters were plotted using special program called Sigmaplot. As a result, the improvement in the performance of the control loops was quantified using relevant indices to justify the need and importance of advanced process control. Also, it has been approved that, by using appropriate indices, predictive controller can improve the performance of the control loop significantly.

Keywords: advanced process control (APC), control loop, model predictive control (MPC), proportional integral derivatives (PID), performance indices (PI)

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Authors: Maya Jaber

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Climate change is one of the biggest challenges that require immediate attention and mitigation for the continued prosperity of human existence. The transformation will need to occur that is top-down and bottom-up on holistic scales. A new way of thinking will need to be adopted that is innovative, human-centric, and global. Designers and researchers are vital leaders in this movement that can help guide other practitioners in the strategy development, critical thinking process, and alignment of transformative solutions. Holistic critical thinking strategies will be essential to change behaviors and cultures for future generations' survival. This paper will discuss these topics associated with Dr. Jaber's research.

Keywords: environmental social governance (ESG), integral design thinking (IDT), organizational transformation, sustainability management

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Authors: Janet Fernandez

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Reading is both for aesthetic and efferent purposes. In order for reading comprehension to take place, the reader needs to be able to make meaningful connections and enjoy the reading process. The notion of reading comprehension is discussed along with the plausible causes of poor reading comprehension abilities among primary school children. Among the major contributing causes are imaging, lack of schemata, selection of reading materials, and habits of the readers. Instruction methods are an integral part of making reading comprehension a meaningful experience, hence several models are presented for the classroom practitioner. Suggestions on how primary school children can improve their reading comprehension skills are offered.

Keywords: children, improve, reading comprehension, meaningful strategies

Procedia PDF Downloads 464

Authors: Ibrahim M. Metwally

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Have you ever thought that earth was not the same earth we live on? Was it bigger or smaller? Was it a great continent surrounded by huge ocean as Alfred Wegener (1912) claimed? Earth is the most amazing planet in our Milky Way galaxy and may be in the universe. It is the only deformed planet that has a variable orbit around the sun and the only planet that has water on its surface. How did earth deformation take place? What does cause earth to deform? What are the results of earth deformation? How does its orbit around the sun change? First earth size computation can be achieved only considering the quantum of iron and nickel rested into earth core. This paper introduces a new theory “Earth expansion Theory”. The principles of “Earth Expansion Theory” are leading to new approaches and concepts to interpret whole earth dynamics and its geological and environmental changes. This theory is not an attempt to unify the two divergent dominant theories of continental drift, plate tectonic theory and earth expansion theory. The new theory is unique since it has a mathematical derivation, explains all the change to and around earth in terms of geological and environmental changes, and answers all unanswered questions in other theories. This paper presents the basic of the introduced theory and discusses the mechanism of earth expansion and how it took place, the forces that made the expansion. The mechanisms of earth size change from its spherical shape with radius about 3447.6 km to an elliptic shape of major radius about 6378.1 km and minor radius of about 6356.8 km and how it took place, are introduced and discussed. This article also introduces, in a more realistic explanation the formation of oceans and seas, the preparation of river formation. It also addresses the role of iron in earth size enlargement process within the continuum mechanics framework.

Keywords: earth size, earth expansion, continuum mechanics, continental and ocean formation

Procedia PDF Downloads 447

Authors: Ewelina Zdebska

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A social worker is an integral part of an interdisciplinary team working with the child and his family in a terminal state. Social support is an integral part of the medical procedure in the care of hospice. This is the basis and prerequisite of full treatment and good care of the child - patient, whose illness often finds at least the expected period of his life when his personal and legal issues are not regulated, and the family burdened with the problem requires care and support specialists - professionals. Hospice for Children in Krakow: a palliative care team operating in the province of Krakow and Malopolska, conducts specialized care for terminally ill children in place of their residence from the time when parents and doctors decided to end of treatment in hospital, allows parents to carry out medical care at home, provides parents social and legal assistance and provides care, psychological support and friendship to families throughout the life of the child's illness and after his death, as long as it is needed. The social worker in a hospice does not bear the burden of solving social problems, which is the responsibility of other authorities, but provides support possible and necessary at the moment. The most common form of assistance is to provide information on benefits, which for the child and his family may be subject to any treatment and fight for the life and health of a child. Employee assists in the preparation and completion of documents, requests to increase the degree of disability because of progressive disease or Allowance care because of the inability to live independently. It works in settling all the issues with the Department of Social Security, as well as with the Municipal and District Team Affairs of disability. Seeking help and support using multi-faceted childcare. With the Centres for Social Welfare contacts are also often on the organization of additional respite care for the sick at home (care), especially in the work of the other members of the family or if the family can not cope with the care and needs extra help. Hospice for Children in Cracow completing construction of Poland's first Respite Care Centre for chronically and terminally ill children, will be an open house where children suffering from chronic and incurable diseases and their families can get professional help, whenever - when they need it. The social worker has to pick up a very important role in caring for a terminally ill child. His presence gives a little patient and family the opportunity to be at this difficult time together while organizing assistance and support.

Keywords: social worker, care, terminal care, hospice

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Authors: José Luiz da Silva Neto, Renato Sipelli Silva, Érick Aragão Ribeiro

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The automation of industrial processes plays a vital role in industries today, becoming an integral and important part of the industrial process and modern production. The process control systems are designed to maximize production, reduce costs and minimize risks in production. However, these systems are generally not deployed methodologies and planning. So that this article describes the development of an automation system of a kitchen preparation of chemicals in the textile industry based on a retrofitting methodology that provides more quality into the process at a lower cost.

Keywords: automation, textile industry, kitchen chemical, information integration

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Authors: N. Ben-Mahmoud, M. Elfandi, A. Shallof

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This paper presents a methodology to design multivariable PID controllers for multi-input and multi-output systems. The proposed control strategy, which is centralized, combines of PID controllers. The proportional gains in the P controllers act as tuning parameters of (SISO) in order to modify the behavior of the loops almost independently. The design procedure consists of three steps: first, an ideal decoupler including integral action is determined. Second, the decoupler is approximated with PID controllers. Third, the proportional gains are tuned to achieve the specified performance. The proposed method is applied to representative processes.

Keywords: boiler turbine, MIMO, PID controller, control by decoupling, anti wind-up techniques

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Authors: A. Benbouali, H. Saidi, A. Derrouazin, T. Bessaad

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Aerial robotics is a very exciting research field dealing with a variety of subjects, including the attitude control. This paper deals with the control of a four rotor vertical take-off and landing (VTOL) Unmanned Aerial Vehicle. The paper presents a mathematical model based on the approach of Lagrange for the flight control of an autonomous quad-rotor. It also describes the controller architecture which is based on PID regulators. The control method has been simulated in closed loop in different situations. All the calculation stages and the simulation results have been detailed.

Keywords: quad-rotor, lagrange approach, proportional integral derivate (PID) controller, Matlab/Simulink

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Authors: Andrey V. Timofeev

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The paper presents new results concerning selection of optimal information fusion formula for ensembles of C-OTDR channels. The goal of information fusion is to create an integral classificator designed for effective classification of seismoacoustic target events. The LPBoost (LP-β and LP-B variants), the Multiple Kernel Learning, and Weighing of Inversely as Lipschitz Constants (WILC) approaches were compared. The WILC is a brand new approach to optimal fusion of Lipschitz Classifiers Ensembles. Results of practical usage are presented.

Keywords: Lipschitz Classifier, classifiers ensembles, LPBoost, C-OTDR systems

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Authors: Hajara Abdulkarim Aliyu, Abdulbasid Ismail Isa

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This research paper studies electrohydraulic system for its role in position and motion control system and develops as mathematical model describing the behaviour of the system. The research further proposes Fuzzy logic and conventional PID controllers in order to achieve both accurate positioning of the payload and overall improvement of the system performance. The simulation result shows Fuzzy logic controller has a superior tracking performance and high disturbance rejection efficiency for its shorter settling time, less overshoot, smaller values of integral of absolute and deviation errors over the conventional PID controller at all the testing conditions.

Keywords: electrohydraulic, fuzzy logic, modelling, NZ-PID

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Authors: Gebreegziabher Hailu Gebrecherkos

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This study explores the derivatives of functions defined by I-functions of two variables and their connections to generalized M-series. We begin by defining I-functions, which are generalized functions that encompass various special functions, and analyze their properties. By employing advanced calculus techniques, we derive new formulas for the first and higher-order derivatives of I-functions with respect to their variables; we establish some derivative formulae of the I-function of two variables involving generalized M-series. The special cases of our derivatives yield interesting results.

Keywords: I-function, Mellin-Barners control integral, generalized M-series, higher order derivative

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Nassim Ourabia, Malika Ourabia

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A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The technique obtains closed form expressions for the equivalent circuits which are used to model these discontinuities. Then it would be easy to handle and to characterize complicated structures like T and Y junctions, truncated junctions, arbitrarily shaped junctions, cascading junctions, and more generally planar multiport junctions. Another advantage of this method is that the edge line concept for arbitrary shape junctions operates with real parameters circuits. The validity of the method was further confirmed by comparing our results for various discontinuities (bend, filters) with those from HFSS as well as from other published sources.

Keywords: CAD analysis, contour integral approach, microwave circuits, s-parameters

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Authors: C. S. Bianca Sabrina, N. Egidio Raimundo, L. Alexandre Baratella, C. H. João Paulo

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This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values.

Keywords: controllers, drones, quadcopter, stability

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Authors: Ritu Sarsoha

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According to World Summit 2002 health is an integral component of sustainable development. Due to overpopulation and lack of employment opportunities in villages and small towns, the rural youth tend to migrate to the big cities causing mushrooming of slums. These slums lack most of the basic necessities of life particularly regarding environmental pollution and appropriate health care system. Present paper deals with the socio-economic and environmental status of people living in slum area of Chandigarh which has now grown as a big city today as it has become a hub for the migrants from U. P. and Bihar. Here is a case study of Colony no. 5 of Chandigarh which is divided into more than one block.

Keywords: slum, socio-economic, environment pollution, health

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Authors: Ogunrinde Roseline Bosede, Ogunrinde Rowland Rotimi

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Just as the development of ideas of early mathematics was essentially motivated by social needs, the invention of the computer was equally inspired by social needs. The early years of the twenty-first century have been remarkable in advances in mathematical and computer sciences. Mathematical and computer sciences work are fast becoming an increasingly integral and essential components of a growing catalogues of areas of interests in biology, business, military, medicine, social sciences, advanced design, advanced materials, climate, banking and finance, and many other fields of disciplines. This paper seeks to highlight the trend and impacts of the duo in the technological advancements being witnessed in our today's world.

Keywords: computer, impacts, mathematics, modern society

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Authors: Roland Lachmayer, Mahtab Afsari

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Research is the cornerstone for advancement of human communities. So that it is one of the indexes for evaluating advancement of countries. Research projects are usually cost and time-consuming and do not end in result in short term. Project scheduling is one of the integral parts of project management. The present article offers a new method by using C# and Matlab software to solve Fuzzy GERT networks for Exclusive-OR kind of nodes to schedule the network. In this article we concentrate on flowcharts that we used in Matlab to show how we apply Matlab to schedule Exclusive-OR nodes.

Keywords: research projects, fuzzy GERT, fuzzy CPM, CPM, α-cuts, scheduling

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Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino

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Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

Procedia PDF Downloads 197