Search results for: chaotic mapping
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 461

Search results for: chaotic mapping

221 Best Proximity Point Theorems for MT-K and MT-C Rational Cyclic Contractions in Metric Spaces

Authors: M. R. Yadav, A. K. Sharma, B. S. Thakur

Abstract:

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

Keywords: Cyclic contraction, rational cyclic contraction, best proximity point and complete metric space.

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220 Educational Experiences in Engineering in the COVID-19 Era and Their Comparative Analysis: Spain, March-June 2020

Authors: Borja Bordel, Ramón Alcarria, Marina Pérez

Abstract:

In March 2020, in Spain, a sanitary and unexpected crisis caused by COVID-19 was declared. All of a sudden, all degrees, classes and evaluation tests and projects had to be transformed into online activities. However, the chaotic situation generated by a complex operation like that, executed without any well-established procedure, led to very different experiences and, finally, results. In this paper, we are describing three experiences in two different Universities in Madrid. On the one hand, the Technical University of Madrid, a public university with little experience in online education was considered. On the other hand, Alfonso X el Sabio University, a private university with more than five years of experience in online teaching was involved. All analyzed subjects were related to computer engineering. Professors and students answered a survey and personal interviews were also carried out. Besides, the professors’ workload and the students’ academic results were also compared. From the comparative analysis of all these experiences, we are extracting the most successful strategies, methodologies, and activities. The recommendations in this paper will be useful for courses during the next months when the sanitary situation is still affecting an educational organization. While, at the same time, they will be considered as input for the upcoming digitalization process of higher education.

Keywords: educational experience, online education, higher education digitalization, COVID, Spain

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219 A Robust LS-SVM Regression

Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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218 A Review on Marine Search and Rescue Operations Using Unmanned Aerial Vehicles

Authors: S. P. Yeong, L. M. King, S. S. Dol

Abstract:

There have been rigorous research and development of unmanned aerial vehicles in the field of search and rescue (SAR) operation recently. UAVs reduce unnecessary human risks while assisting rescue efforts through aerial imagery, topographic mapping and emergency delivery. The application of UAVs in offshore and nearshore marine SAR missions is discussed in this paper. Projects that integrate UAV technology into their systems are introduced to highlight the great advantages and capabilities of UAVs. Scenarios where UAVs could provide invaluable assistance are also suggested.

Keywords: Marine SAR, nearshore, offshore, search and rescue, UAS, UAV.

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217 Bayesian Geostatistical Modelling of COVID-19 Datasets

Authors: I. Oloyede

Abstract:

The COVID-19 dataset is obtained by extracting weather, longitude, latitude, ISO3666, cases and death of coronavirus patients across the globe. The data were extracted for a period of eight day choosing uniform time within the specified period. Then mapping of cases and deaths with reverence to continents were obtained. Bayesian Geostastical modelling was carried out on the dataset. The study found out that countries in the tropical region suffered less deaths/attacks compared to countries in the temperate region, this is due to high temperature in the tropical region.

Keywords: COVID-19, Bayesian, geostastical modelling, prior, posterior.

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216 Automatic Vehicle Location Systems

Authors: S.A. Mahdavifar, G.R. Sotudeh., K. Heydari

Abstract:

In this article, a single application is suggested to determine the position of vehicles using Geographical Information Systems (GIS) and Geographical Position Systems (GPS). The part of the article material included mapping three dimensional coordinates to two dimensional coordinates using UTM or LAMBERT geographical methods, and the algorithm of conversion of GPS information into GIS maps is studied. Also, suggestions are given in order to implement this system based on web (called web based systems). To apply this system in IRAN, related official in this case are introduced and their duties are explained. Finally, economy analyzed is assisted according to IRAN communicational system.

Keywords: GIS-GPS-UTM-LAMBERT.

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215 Mathematical Analysis of EEG of Patients with Non-fatal Nonspecific Diffuse Encephalitis

Authors: Mukesh Doble, Sunil K Narayan

Abstract:

Diffuse viral encephalitis may lack fever and other cardinal signs of infection and hence its distinction from other acute encephalopathic illnesses is challenging. Often, the EEG changes seen routinely are nonspecific and reflect diffuse encephalopathic changes only. The aim of this study was to use nonlinear dynamic mathematical techniques for analyzing the EEG data in order to look for any characteristic diagnostic patterns in diffuse forms of encephalitis.It was diagnosed on clinical, imaging and cerebrospinal fluid criteria in three young male patients. Metabolic and toxic encephalopathies were ruled out through appropriate investigations. Digital EEGs were done on the 3rd to 5th day of onset. The digital EEGs of 5 male and 5 female age and sex matched healthy volunteers served as controls.Two sample t-test indicated that there was no statistically significant difference between the average values in amplitude between the two groups. However, the standard deviation (or variance) of the EEG signals at FP1-F7 and FP2-F8 are significantly higher for the patients than the normal subjects. The regularisation dimension is significantly less for the patients (average between 1.24-1.43) when compared to the normal persons (average between 1.41-1.63) for the EEG signals from all locations except for the Fz-Cz signal. Similarly the wavelet dimension is significantly less (P = 0.05*) for the patients (1.122) when compared to the normal person (1.458). EEGs are subdued in the case of the patients with presence of uniform patterns, manifested in the values of regularisation and wavelet dimensions, when compared to the normal person, indicating a decrease in chaotic nature.

Keywords: Chaos, Diffuse encephalitis, Electroencephalogram, Fractal dimension, Fourier spectrum.

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214 Existence of Iterative Cauchy Fractional Differential Equation

Authors: Rabha W. Ibrahim

Abstract:

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

Keywords: Fractional calculus, fractional differential equation, Cauchy equation, Riemann-Liouville fractional operators, Volterra integral equation, non-expansive mapping, iterative differential equation.

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213 Method for Concept Labeling Based on Mapping between Ontology and Thesaurus

Authors: Kazuki Sonoda, Masahiro Hori

Abstract:

When designing information systems that deal with large amount of domain knowledge, system designers need to consider ambiguities of labeling termsin domain vocabulary for navigating users in the information space. The goal of this study is to develop a methodology for system designers to label navigation items, taking account of ambiguities stems from synonyms or polysemes of labeling terms. In this paper, we propose a method for concept labeling based on mappings between domain ontology andthesaurus, and report results of an empirical evaluation.

Keywords: Concept Labeling, Ontology, Thesaurus, VocabularyProblem

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212 Hydrochemical Contamination Profiling and Spatial-Temporal Mapping with the Support of Multivariate and Cluster Statistical Analysis

Authors: S. Barbosa, M. Pinto, J. A. Almeida, E. Carvalho, C. Diamantino

Abstract:

The aim of this work was to test a methodology able to generate spatial-temporal maps that can synthesize simultaneously the trends of distinct hydrochemical indicators in an old radium-uranium tailings dam deposit. Multidimensionality reduction derived from principal component analysis and subsequent data aggregation derived from clustering analysis allow to identify distinct hydrochemical behavioral profiles and generate synthetic evolutionary hydrochemical maps.

Keywords: Contamination plume migration, K-means of PCA scores, groundwater and mine water monitoring, spatial-temporal hydrochemical trends.

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211 Transmission Model for Plasmodium Vivax Malaria: Conditions for Bifurcation

Authors: P. Pongsumpun, I.M. Tang

Abstract:

Plasmodium vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the patients where it is able to re-infect the patient after a passage of time. During this stage, the patient is classified as being in the dormant class. The model to describe the transmission of P. vivax malaria consists of a human population divided into four classes, the susceptible, the infected, the dormant and the recovered. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P. vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number G is less than one. If G is greater than one the endemic state E1 is stable. The conditions for the endemic equilibrium state E1 to be a stable spiral node are established. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic state. It is shown that the limit cycle and chaotic behaviors can only be achieved with unrealistic parameter values.

Keywords: Equilibrium states, Hopf bifurcation, limit cyclebehavior, local stability, Plasmodium Vivax, time delay.

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210 AGENTMAP: A Conceptual Meta-Model of Interacting Simulations

Authors: Thomas M. Prinz Wilhelm R. Rossak, Kai Gebhardt

Abstract:

A straightforward and intuitive combination of single simulations into an aggregated master-simulation is not trivial. There are lots of problems, which trigger-specific difficulties during the modeling and execution of such a simulation. In this paper we identify these problems and aim to solve them by mapping the task to the field of multi agent systems. The solution is a new meta-model named AGENTMAP, which is able to mitigate most of the problems and to support intuitive modeling at the same time. This meta-model will be introduced and explained on basis of an example from the e-commerce domain.

Keywords: Multi Agent System, Agent-based Simulation, Distributed Systems, Meta-models.

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209 Innovative Activity and Development: Analyzing Firm Data from Eurozone Country-Members

Authors: Ilias A. Makris

Abstract:

In this work, we attempt to associate firm characteristics with innovative activity. We collect microdata from listed firms of selected Eurozone Country-members, after the beginning of 2007 financial crisis. The following literature, several indicators of growth and performance were selected and tested for their ability to interpret innovative activity. The main scope is to examine the possible differences in performance and growth between innovative and non-innovative firms, during a severe recession. Additionally to that, a special focus will be held on whether macroeconomic performance and national innovation system, determines the extent of innovators' performance. Preliminary findings, through correlation matrices and non-parametric tests, strongly indicate the positive relation between innovative activity and most of the measures used (profitability, size, employment), confirming that even during a recessionary period, innovative firms not only survive but also seem to succeed better economic results in almost all indexes relative to non-innovative. However, even though innovators seem to perform better in all economies examined, the extent of that performance seems to be strongly affected by the supportive mechanisms (financial and structural) that their country provides. Thus, it is clear, that the technologically intensive 'gap' between European South and North, during the economic crisis, became chaotic, due to the harsh austerity measures and reduced budgets in those countries, even in sectors with high potentials in economic activity and employment, impairing the effects of crisis and enhancing the vicious circle of recession.

Keywords: Eurozone, innovative activity, development, firm performance, non-parametric tests.

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208 Sustainable Walkability and Place Identity

Authors: Marichela Sepe

Abstract:

The sustainability of a place depends on a series of factors which contribute to the quality of life, sense of place and recognition of identity. An activity like walking, which in itself is obviously ''sustainable'', can become non sustainable if the context in which it is carried out does not meet the conditions for an adequate quality of life. This work is aimed at proposing the analytical method of Place Maker to identify the elements that do not feature in traditional mapping and which constitute the contemporary identity of the places, and the relative complex map to represent those elements and support sustainable urban identity design. The method's potential for areas with a predominantly pedestrian vocation is illustrated by means of the case study of the Ramblas in Barcelona.

Keywords: Place-identity, PlaceMaker, sustainability, walkability.

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207 Research on the Optimization of the Facility Layout of Efficient Cafeterias for Troops

Authors: Qing Zhang, Jiachen Nie, Yujia Wen, Guanyuan Kou, Peng Yu, Kun Xia, Qin Yang, Li Ding

Abstract:

Background: A facility layout problem (FLP) is an NP-complete (non-deterministic polynomial) problem, for which is hard to obtain an exact optimal solution. FLP has been widely studied in various limited spaces and workflows. For example, cafeterias with many types of equipment for troops cause chaotic processes when dining. Objective: This article tried to optimize the layout of a troops’ cafeteria and to improve the overall efficiency of the dining process. Methods: First, the original cafeteria layout design scheme was analyzed from an ergonomic perspective and two new design schemes were generated. Next, three facility layout models were designed, and further simulation was applied to compare the total time and density of troops between each scheme. Last, an experiment of the dining process with video observation and analysis verified the simulation results. Results: In a simulation, the dining time under the second new layout is shortened by 2.25% and 1.89% (p<0.0001, p=0.0001) compared with the other two layouts, while troops-flow density and interference both greatly reduced in the two new layouts. In the experiment, process completing time and the number of interferences reduced as well, which verified corresponding simulation results. Conclusion: Our two new layout schemes are tested to be optimal by a series of simulation and space experiments. In future research, similar approaches could be applied when taking layout-design algorithm calculation into consideration.

Keywords: Troops’ cafeteria, layout optimization, dining efficiency, AnyLogic simulation, field experiment

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206 A Compact Pi Network for Reducing Bit Error Rate in Dispersive FIR Channel Noise Model

Authors: Kavita Burse, R.N. Yadav, S.C. Shrivastava, Vishnu Pratap Singh Kirar

Abstract:

During signal transmission, the combined effect of the transmitter filter, the transmission medium, and additive white Gaussian noise (AWGN) are included in the channel which distort and add noise to the signal. This causes the well defined signal constellation to spread causing errors in bit detection. A compact pi neural network with minimum number of nodes is proposed. The replacement of summation at each node by multiplication results in more powerful mapping. The resultant pi network is tested on six different channels.

Keywords: Additive white Gaussian noise, digitalcommunication system, multiplicative neuron, Pi neural network.

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205 A Semantic Web Based Ontology in the Financial Domain

Authors: S. Banerjee

Abstract:

The paper describes design of an ontology in the financial domain for mutual funds. The design of this ontology consists of four steps, namely, specification, knowledge acquisition, implementation and semantic query. Specification includes a description of the taxonomy and different types mutual funds and their scope. Knowledge acquisition involves the information extraction from heterogeneous resources. Implementation describes the conceptualization and encoding of this data. Finally, semantic query permits complex queries to integrated data, mapping of these database entities to ontological concepts.

Keywords: Ontology, Semantic Web, Mutual Funds.

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204 Soft Connected Spaces and Soft Paracompact Spaces

Authors: Fucai Lin

Abstract:

Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft closed mapping, soft open mappings, soft connected spaces and soft paracompact spaces. We also redefine the concept of soft points such that it is reasonable in soft topological spaces. Moreover, some basic properties of these concepts are explored.

Keywords: soft sets, soft open mappings, soft closed mappings, soft connected spaces, soft paracompact spaces.

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203 A Neurofuzzy Learning and its Application to Control System

Authors: Seema Chopra, R. Mitra, Vijay Kumar

Abstract:

A neurofuzzy approach for a given set of input-output training data is proposed in two phases. Firstly, the data set is partitioned automatically into a set of clusters. Then a fuzzy if-then rule is extracted from each cluster to form a fuzzy rule base. Secondly, a fuzzy neural network is constructed accordingly and parameters are tuned to increase the precision of the fuzzy rule base. This network is able to learn and optimize the rule base of a Sugeno like Fuzzy inference system using Hybrid learning algorithm, which combines gradient descent, and least mean square algorithm. This proposed neurofuzzy system has the advantage of determining the number of rules automatically and also reduce the number of rules, decrease computational time, learns faster and consumes less memory. The authors also investigate that how neurofuzzy techniques can be applied in the area of control theory to design a fuzzy controller for linear and nonlinear dynamic systems modelling from a set of input/output data. The simulation analysis on a wide range of processes, to identify nonlinear components on-linely in a control system and a benchmark problem involving the prediction of a chaotic time series is carried out. Furthermore, the well-known examples of linear and nonlinear systems are also simulated under the Matlab/Simulink environment. The above combination is also illustrated in modeling the relationship between automobile trips and demographic factors.

Keywords: Fuzzy control, neuro-fuzzy techniques, fuzzy subtractive clustering, extraction of rules, and optimization of membership functions.

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202 Enhancement Approaches for Supporting Default Hierarchies Formation for Robot Behaviors

Authors: Saeed Mohammed Baneamoon, Rosalina Abdul Salam

Abstract:

Robotic system is an important area in artificial intelligence that aims at developing the performance techniques of the robot and making it more efficient and more effective in choosing its correct behavior. In this paper the distributed learning classifier system is used for designing a simulated control system for robot to perform complex behaviors. A set of enhanced approaches that support default hierarchies formation is suggested and compared with each other in order to make the simulated robot more effective in mapping the input to the correct output behavior.

Keywords: Learning Classifier System, Default Hierarchies, Robot Behaviors.

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201 GIS-based Approach for Land-Use Analysis: A Case Study

Authors: M. Giannopoulou, I. Roukounis, A. Roukouni.

Abstract:

Geographical Information Systems are an integral part of planning in modern technical systems. Nowadays referred to as Spatial Decision Support Systems, as they allow synergy database management systems and models within a single user interface machine and they are important tools in spatial design for evaluating policies and programs at all levels of administration. This work refers to the creation of a Geographical Information System in the context of a broader research in the area of influence of an under construction station of the new metro in the Greek city of Thessaloniki, which included statistical and multivariate data analysis and diagrammatic representation, mapping and interpretation of the results.

Keywords: Databases, Geographical information systems (GIS), Land-use planning, Metro stations

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200 Model of Obstacle Avoidance on Hard Disk Drive Manufacturing with Distance Constraint

Authors: Rawinun Praserttaweelap, Somyot Kiatwanidvilai

Abstract:

Obstacle avoidance is the one key for the robot system in unknown environment. The robots should be able to know their position and safety region. This research starts on the path planning which are SLAM and AMCL in ROS system. In addition, the best parameters of the obstacle avoidance function are required. In situation on Hard Disk Drive Manufacturing, the distance between robots and obstacles are very serious due to the manufacturing constraint. The simulations are accomplished by the SLAM and AMCL with adaptive velocity and safety region calculation.

Keywords: Obstacle avoidance, simultaneous localization and mapping, adaptive Monte Carlo localization, KLD sampling.

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199 A Unified Framework for a Robust Conflict-Free Robot Navigation

Authors: S. Veera Ragavan, V. Ganapathy

Abstract:

Many environment specific methods and systems for Robot Navigation exist. However vast strides in the evolution of navigation technologies and system techniques create the need for a general unified framework that is scalable, modular and dynamic. In this paper a Unified Framework for a Robust Conflict-free Robot Navigation System that can be used for either a structured or unstructured and indoor or outdoor environments has been proposed. The fundamental design aspects and implementation issues encountered during the development of the module are discussed. The results of the deployment of three major peripheral modules of the framework namely the GSM based communication module, GIS Module and GPS module are reported in this paper.

Keywords: Localization, Sensor Fusion, Mapping, GIS, GPS, and Autonomous Mobile Robot Navigation.

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198 Energy Efficient Resource Allocation in Distributed Computing Systems

Authors: Samee Ullah Khan, C. Ardil

Abstract:

The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.

Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.

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197 Accurate HLA Typing at High-Digit Resolution from NGS Data

Authors: Yazhi Huang, Jing Yang, Dingge Ying, Yan Zhang, Vorasuk Shotelersuk, Nattiya Hirankarn, Pak Chung Sham, Yu Lung Lau, Wanling Yang

Abstract:

Human leukocyte antigen (HLA) typing from next generation sequencing (NGS) data has the potential for applications in clinical laboratories and population genetic studies. Here we introduce a novel technique for HLA typing from NGS data based on read-mapping using a comprehensive reference panel containing all known HLA alleles and de novo assembly of the gene-specific short reads. An accurate HLA typing at high-digit resolution was achieved when it was tested on publicly available NGS data, outperforming other newly-developed tools such as HLAminer and PHLAT.

Keywords: Human leukocyte antigens, next generation sequencing, whole exome sequencing, HLA typing.

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196 Geographic Information System Mapping of Roadway Lighting and Traffic Accidents

Authors: Riad Saraiji, Scott Sizer, Emily Yance-Houser, Felix Bermejo

Abstract:

The use of a Geographic Information System (GIS) in roadway lighting to show the state of street-lighting and nighttime accident is demonstrated. Geographical maps were generated showing colored streets based on how much of the street's length is illuminated. The night to daytime accidents ratio at intersections were found along with the state of lighting at those intersections. The result is a method to show the state of street-lighting at roads and intersections and a quick guide for decision makers to implement strategies for better street-lighting to reduce night time traffic accidents in a particular district.

Keywords: GIS. Roadway lighting, Traffic Accidents

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195 Convergence of a One-step Iteration Scheme for Quasi-asymptotically Nonexpansive Mappings

Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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194 Demand and Price Evolution Forecasting as Tools for Facilitating the RoadMapping Process of the Photonic Component Industry

Authors: T. Kamalakis, I. Neokosmidis, D. Varoutas, T. Sphicopoulos

Abstract:

The photonic component industry is a highly innovative industry with a large value chain. In order to ensure the growth of the industry much effort must be devoted to road mapping activities. In such activities demand and price evolution forecasting tools can prove quite useful in order to help in the roadmap refinement and update process. This paper attempts to provide useful guidelines in roadmapping of optical components and considers two models based on diffusion theory and the extended learning curve for demand and price evolution forecasting.

Keywords: Roadmapping, Photonic Components, Forecasting, Diffusion Theory.

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193 A New Robust Stability Criterion for Dynamical Neural Networks with Mixed Time Delays

Authors: Guang Zhou, Shouming Zhong

Abstract:

In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.

Keywords: Neural networks, Delayed systems, Lyapunov function, Stability analysis.

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192 Elasto-Plastic Behavior of Rock during Temperature Drop

Authors: N. Reppas, Y. L. Gui, B. Wetenhall, C. T. Davie, J. Ma

Abstract:

A theoretical constitutive model describing the stress-strain behavior of rock subjected to different confining pressures is presented. A bounding surface plastic model with hardening effects is proposed which includes the effect of temperature drop. The bounding surface is based on a mapping rule and the temperature effect on rock is controlled by Poisson’s ratio. Validation of the results against available experimental data is also presented. The relation of deviatoric stress and axial strain is illustrated at different temperatures to analyze the effect of temperature decrease in terms of stiffness of the material.

Keywords: Bounding surface, cooling of rock, plasticity model, rock deformation, elasto-plastic behavior.

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