Search results for: chaos theory
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 330

Search results for: chaos theory

330 Chaos Theory and Application in Foreign Exchange Rates vs. IRR (Iranian Rial)

Authors: M. A. Torkamani, S. Mahmoodzadeh, S. Pourroostaei, C. Lucas

Abstract:

Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.

Keywords: Chaos, Exchange Rate, Nonlinear Models.

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329 Direct Democracy and Social Contract in Ancient Athens

Authors: Nicholas Kyriazis, Emmanouil Marios L. Economou, Jr, Loukas Zachilas

Abstract:

In the present essay, a model of choice by actors is analysedby utilizing the theory of chaos to explain how change comes about. Then, by using ancient and modern sources of literature, the theory of the social contract is analysed as a historical phenomenon that first appeared during the period of Classical Greece. Then, based on the findings of this analysis, the practice of direct democracy and public choice in ancient Athens is analysed, through two historical cases: Eubulus and Lycurgus political program in the second half of the 4th century. The main finding of this research is that these policies can be interpreted as an implementation of a social contract, through which citizens were taking decisions based on rational choice according to economic considerations.

Keywords: Chaos theory, public choice, social contract, 4th century BC. Athens.

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328 Chua’s Circuit Regulation Using a Nonlinear Adaptive Feedback Technique

Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

Abstract:

Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.

Keywords: Chaos, adaptive control, nonlinear control, Chua's circuit.

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327 Investigation of a Transition from Steady Convection to Chaos in Porous Media Using Piecewise Variational Iteration Method

Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab

Abstract:

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.

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326 Neural Network Learning Based on Chaos

Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.

Keywords: learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.

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325 An Evolutionary Statistical Learning Theory

Authors: Sung-Hae Jun, Kyung-Whan Oh

Abstract:

Statistical learning theory was developed by Vapnik. It is a learning theory based on Vapnik-Chervonenkis dimension. It also has been used in learning models as good analytical tools. In general, a learning theory has had several problems. Some of them are local optima and over-fitting problems. As well, statistical learning theory has same problems because the kernel type, kernel parameters, and regularization constant C are determined subjectively by the art of researchers. So, we propose an evolutionary statistical learning theory to settle the problems of original statistical learning theory. Combining evolutionary computing into statistical learning theory, our theory is constructed. We verify improved performances of an evolutionary statistical learning theory using data sets from KDD cup.

Keywords: Evolutionary computing, Local optima, Over-fitting, Statistical learning theory

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324 Fundamental Concepts of Theory of Constraints: An Emerging Philosophy

Authors: Ajay Gupta, Arvind Bhardwaj, Arun Kanda

Abstract:

Dr Eliyahu Goldratt has done the pioneering work in the development of Theory of Constraints. Since then, many more researchers around the globe are working to enhance this body of knowledge. In this paper, an attempt has been made to compile the salient features of this theory from the work done by Goldratt and other researchers. This paper will provide a good starting point to the potential researchers interested to work in Theory of Constraints. The paper will also help the practicing managers by clarifying their concepts on the theory and will facilitate its successful implementation in their working areas.

Keywords: Drum-Buffer-Rope, Goldratt, ProductionScheduling, Theory of Constraints.

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323 Chaotic Oscillations of Diaphragm Supported by Nonlinear Springs with Hysteresis

Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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322 Assessing the Relation between Theory of Multiple Algebras and Universal Algebras

Authors: Mona Taheri

Abstract:

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the basic relation and the fundamental algebra in question. In this study, by stating the characteristic theorem of multiple algebras, we show that the theory of multiple algebras is a natural extension of the theory of universal algebras.

Keywords: multiple algebras , universal algebras

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321 Use of Item Response Theory in Medical Surgical Nursing Achievement Examination

Authors: Rita C. Ramos

Abstract:

Medical Surgical Nursing is one of the major subjects in nursing. This study examined the validity and reliability of the achievement examination utilizing the Classical Test Theory and Item Response Theory. The study answered the following objectives specifically : ( a) To establish the validity and reliability of the achievement examination utilizing Classical Test Theory and Item Response Theory ; ( b ) To determine the dimensionality measure of items and ( c ) to compare the item difficulty and item discrimination of the Medical Surgical Nursing Achievement examination using Classical Test Theory ( CTT ) and Item Response Theory ( IRT ). The developed instrument was administered to fourth year nursing students (N= 136) of a private university in Manila. The findings yielded the following results: The achievement examination is reliable both using CTT and IRT. The findings indicate person and item statistics from two frameworks are quite alike. The achievement examination formed a unidimensional construct.

Keywords: Achievement Examination, Item Response Theory, Medical Surgical, Nursing.

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320 PZ: A Z-based Formalism for Modeling Probabilistic Behavior

Authors: Hassan Haghighi

Abstract:

Probabilistic techniques in computer programs are becoming more and more widely used. Therefore, there is a big interest in the formal specification, verification, and development of probabilistic programs. In our work-in-progress project, we are attempting to make a constructive framework for developing probabilistic programs formally. The main contribution of this paper is to introduce an intermediate artifact of our work, a Z-based formalism called PZ, by which one can build set theoretical models of probabilistic programs. We propose to use a constructive set theory, called CZ set theory, to interpret the specifications written in PZ. Since CZ has an interpretation in Martin-L¨of-s theory of types, this idea enables us to derive probabilistic programs from correctness proofs of their PZ specifications.

Keywords: formal specification, formal program development, probabilistic programs, CZ set theory, type theory.

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319 Predicting Dietary Practice Behavior among Type 2 Diabetics Using the Theory of Planned Behavior and Mixed Methods Design

Authors: D.O. Omondi, M.K. Walingo, G.M. Mbagaya, L.O.A. Othuon

Abstract:

This study applied the Theory of Planned Behavior model in predicting dietary behavior among Type 2 diabetics in a Kenyan environment. The study was conducted for three months within the diabetic clinic at Kisii Hospital in Nyanza Province in Kenya and adopted sequential mixed methods design combing both qualitative and quantitative phases. Qualitative data was analyzed using grounded theory analysis method. Structural equation modeling using maximum likelihood was used to analyze quantitative data. The results based on the common fit indices revealed that the theory of planned behavior fitted the data acceptably well among the Type 2 diabetes and within dietary behavior {χ2 = 223.3, df = 77, p = .02, χ2/df = 2.9, n=237; TLI = .93; CFI =.91; RMSEA (90CI) = .090(.039, .146)}. This implies that the Theory of Planned Behavior holds and forms a framework for promoting dietary practice among Type 2 diabetics.

Keywords: Dietary practice, Kenya, Theory of PlannedBehavior, Type 2 diabetes, Mixed Methods Design.

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318 A Multi-Signature Scheme based on Coding Theory

Authors: Mohammed Meziani, Pierre-Louis Cayrel

Abstract:

In this paper we propose two first non-generic constructions of multisignature scheme based on coding theory. The first system make use of the CFS signature scheme and is secure in random oracle while the second scheme is based on the KKS construction and is a few times. The security of our construction relies on a difficult problems in coding theory: The Syndrome Decoding problem which has been proved NP-complete [4].

Keywords: Post-quantum cryptography, Coding-based cryptography, Digital signature, Multisignature scheme.

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317 A Vortex Plate Theory of Hovering Animal Flight

Authors: Khaled. M. Faqih

Abstract:

A model of vortex wake is suggested to determine the induced power during animal hovering flight. The wake is modeled by a series of equi-spaced rigid rectangular vortex plates, positioned horizontally and moving vertically downwards with identical speeds; each plate is generated during powering of the functionally wing stroke. The vortex representation of the wake considered in the current theory allows a considerable loss of momentum to occur. The current approach accords well with the nature of the wingbeat since it considers the unsteadiness in the wake as an important fluid dynamical characteristic. Induced power in hovering is calculated as the aerodynamic power required to generate the vortex wake system. Specific mean induced power to mean wing tip velocity ratio is determined by solely the normal spacing parameter (f) for a given wing stroke amplitude. The current theory gives much higher specific induced power estimate than anticipated by classical methods.

Keywords: vortex theory, hovering flight, induced power, Prandlt's tip theory.

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316 Mechanical Structure Design Optimization by Blind Number Theory: Time-dependent Reliability

Authors: Zakari Yaou, Lirong Cui

Abstract:

In a product development process, understanding the functional behavior of the system, the role of components in achieving functions and failure modes if components/subsystem fails its required function will help develop appropriate design validation and verification program for reliability assessment. The integration of these three issues will help design and reliability engineers in identifying weak spots in design and planning future actions and testing program. This case study demonstrate the advantage of unascertained theory described in the subjective cognition uncertainty, and then applies blind number (BN) theory in describing the uncertainty of the mechanical system failure process and the same time used the same theory in bringing out another mechanical reliability system model. The practical calculations shows the BN Model embodied the characters of simply, small account of calculation but betterforecasting capability, which had the value of macroscopic discussion to some extent.

Keywords: Mechanical structure Design, time-dependent stochastic process, unascertained information, blind number theory.

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315 Authoritarian Parenting Received from Mothers Reveals Individual Differences in Preschooler's False-belief, but not in Advanced Theory of Mind

Authors: Alejandra Rodríguez Villalobos, Michael Padilla-Mora, Jaime Fornaguera Trías

Abstract:

Remarkable changes, like the progress in the ability to understand others' minds, can be identified in several socio-cognitive dimensions between age four and seven. Recently, the parenting attitudes have been considerate as one of the potential extrinsic modifiers of these important developmental aspects. The aim of present study is to explore the relationship among authoritarian parenting attitudes and individual differences in Theory of Mind performance. The study included ninety-two Costarrican preschoolers. Six False-belief tasks, an Advanced Theory of Mind test and the Parenting Attitudes Inventory were used. The results demonstrate that participants with high and low Authoritarian Parenting Received differ in their performance on First and Second Order False-belief tasks, but not in Advanced Theory of Mind tasks. Theoretical considerations about possible explanations regarding these results are discussed and methodological limitations are considered to shed light over future directions.

Keywords: Authoritarian parenting, cognitive development, false- belief, individual differences, theory of mind, parenting.

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314 Decision-Making Criteria of PPP Projects: Stakeholder Theoretic Perspective

Authors: Xueqin Shan, Wenhua Hou, Xiaosu Ye, Chuanming Wu

Abstract:

Any decision-making is based on certain theory. Taking the public rental housing in Chongqing municipality as an example, this essay states that the stakeholder theory can provide innovative criteria and evaluation methods for Public Private Partnership (PPP) projects. It gives an analysis of how to choose decision-making criteria for different stakeholders in the PPP model and what measures to take to meet the criteria to form “symbiotic" decision-making mode through contracts and to boost the application of PPP model in large-scale public programs in China.

Keywords: PPP, Stakeholder Theory, Stakeholders, Decision- making Criteria

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313 A New Measurable Definition of Knowledge in New Growth Theory

Authors: Mohammad Ali Molaei

Abstract:

New Growth Theory helps us make sense of the ongoing shift from a resource-based economy to a knowledge-based economy. It underscores the point that the economic processes which create and diffuse new knowledge are critical to shaping the growth of nations, communities and individual firms. In all too many contributions to New (Endogenous) Growth Theory – though not in all – central reference is made to 'a stock of knowledge', a 'stock of ideas', etc., this variable featuring centre-stage in the analysis. Yet it is immediately apparent that this is far from being a crystal clear concept. The difficulty and uncertainty of being able to capture the value associated with knowledge is a real problem. The intent of this paper is introducing new thinking and theorizing about the knowledge and its measurability in new growth theory. Moreover the study aims to synthesize various strain of the literature with a practical bearing on knowledge concept. By contribution of institution framework which is found within NGT, we can indirectly measure the knowledge concept. Institutions matter because they shape the environment for production and employment of new knowledge

Keywords: Institution Framework, Knowledge, New GrowthTheory (NGT)

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312 Modality and Redundancy Effects on Music Theory Learning Among Pupils of Different Anxiety Levels

Authors: Soon Fook Fong, Aldalalah, M. Osamah

Abstract:

The purpose of this study was to investigate effects of modality and redundancy principles on music theory learning among pupils of different anxiety levels. The lesson of music theory was developed in three different modes, audio and image (AI), text with image (TI) and audio with image and text (AIT). The independent variables were the three modes of courseware. The moderator variable was the anxiety level, while the dependent variable was the post test score. The study sample consisted of 405 third-grade pupils. Descriptive and inferential statistics were conducted to analyze the collected data. Analyses of covariance (ANCOVA) and Post hoc were carried out to examine the main effects as well as the interaction effects of the independent variables on the dependent variable. The findings of this study showed that medium anxiety pupils performed significantly better than low and high anxiety pupils in all the three treatment modes. The AI mode was found to help pupils with high anxiety significantly more than the TI and AIT modes.

Keywords: Modality, Redundancy, Music theory, Cognitivetheory of multimedia learning, Cognitive load theory, Anxiety.

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311 Control of Chaotic Dynamical Systems using RBF Networks

Authors: Yoichi Ishikawa, Yuichi Masukake, Yoshihisa Ishida

Abstract:

This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.

Keywords: Chaos, nonlinear plant, radial basis function network.

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310 Partial Stabilization of a Class of Nonlinear Systems Via Center Manifold Theory

Authors: Ping He

Abstract:

This paper addresses the problem of the partial state feedback stabilization of a class of nonlinear systems. In order to stabilization this class systems, the especial place of this paper is to reverse designing the state feedback control law from the method of judging system stability with the center manifold theory. First of all, the center manifold theory is applied to discuss the stabilization sufficient condition and design the stabilizing state control laws for a class of nonlinear. Secondly, the problem of partial stabilization for a class of plane nonlinear system is discuss using the lyapunov second method and the center manifold theory. Thirdly, we investigate specially the problem of the stabilization for a class of homogenous plane nonlinear systems, a class of nonlinear with dual-zero eigenvalues and a class of nonlinear with zero-center using the method of lyapunov function with homogenous derivative, specifically. At the end of this paper, some examples and simulation results are given show that the approach of this paper to this class of nonlinear system is effective and convenient.

Keywords: Partial stabilization, Nonlinear critical systems, Centermanifold theory, Lyapunov function, System reduction.

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309 Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers

Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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308 Finding Equilibrium in Transport Networks by Simulation and Investigation of Behaviors

Authors: Gábor Szűcs, Gyula Sallai

Abstract:

The goal of this paper is to find Wardrop equilibrium in transport networks at case of uncertainty situations, where the uncertainty comes from lack of information. We use simulation tool to find the equilibrium, which gives only approximate solution, but this is sufficient for large networks as well. In order to take the uncertainty into account we have developed an interval-based procedure for finding the paths with minimal cost using the Dempster-Shafer theory. Furthermore we have investigated the users- behaviors using game theory approach, because their path choices influence the costs of the other users- paths.

Keywords: Dempster-Shafer theory, S-O and U-Otransportation network, uncertainty of information, Wardropequilibrium.

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307 Belief Theory-Based Classifiers Comparison for Static Human Body Postures Recognition in Video

Authors: V. Girondel, L. Bonnaud, A. Caplier, M. Rombaut

Abstract:

This paper presents various classifiers results from a system that can automatically recognize four different static human body postures in video sequences. The considered postures are standing, sitting, squatting, and lying. The three classifiers considered are a naïve one and two based on the belief theory. The belief theory-based classifiers use either a classic or restricted plausibility criterion to make a decision after data fusion. The data come from the people 2D segmentation and from their face localization. Measurements consist in distances relative to a reference posture. The efficiency and the limits of the different classifiers on the recognition system are highlighted thanks to the analysis of a great number of results. This system allows real-time processing.

Keywords: Belief theory, classifiers comparison, data fusion, human motion analysis, real-time processing, static posture recognition.

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306 Structural Study of Boron - Nitride Nanotube with Magnetic Resonance (NMR) Parameters Calculation via Density Functional Theory Method (DFT)

Authors: Asadollah Boshra, Ahmad Seif, Mehran Aghaei

Abstract:

A model of (4, 4) single-walled boron-nitride nanotube as a representative of armchair boron-nitride nanotubes studied. At first the structure optimization performed and then Nuclear Magnetic Resonance parameters (NMR) by Density Functional Theory (DFT) method at 11B and 15N nuclei calculated. Resulted parameters evaluation presents electrostatic environment heterogeneity along the nanotube and especially at the ends but the nuclei in a layer feel the same electrostatic environment. All of calculations carried out using Gaussian 98 Software package.

Keywords: Boron-nitride nanotube, Density Functional Theory, Nuclear Magnetic Resonance (NMR).

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305 The Story of Mergers and Acquisitions: Using Narrative Theory to Understand the Uncertainty of Organizational Change

Authors: Philip T. Roundy

Abstract:

This paper examines the influence of communication form on employee uncertainty during mergers and acquisitions (M&As). Specifically, the author uses narrative theory to analyze how narrative organizational communication affects the three components of uncertainty – decreased predictive, explanatory, and descriptive ability. It is hypothesized that employees whose organizations use narrative M&A communication will have greater predictive, explanatory, and descriptive abilities than employees of organizations using non-narrative M&A communication. This paper contributes to the stream of research examining uncertainty during mergers and acquisitions and argues that narratives are an effective means of managing uncertainty in the mergers and acquisitions context.

Keywords: Narrative Theory, Mergers and Acquisitions, Employee Uncertainty.

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304 Stability of Functionally Graded Beams with Piezoelectric Layers Based on the First Order Shear Deformation Theory

Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Stability, Functionally graded beam, First order shear deformation theory, Piezoelectric layer.

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303 Prediction Method of Extenics Theory for Assessment of Bearing Capacity of Lateritic Soil Foundation

Authors: Wei Bai, Ling-Wei Kong, Ai-Guo Guo

Abstract:

Base on extenics theory, the statistical physical and mechanical properties from laboratory experiments are used to evaluate the bearing capacity of lateritic soil foundation. The properties include water content, bulk density, liquid limit, cohesion, and so on. The matter-element and the dependent function are defined. Then the synthesis dependent degree and the final grade index are calculated. The results show that predicted outcomes can be matched with the in-situ test data, and a evaluate grade associate with bearing capacity can be deduced. The results provide guidance to assess and determine the bearing capacity grade of lateritic soil foundation.

Keywords: Lateritic soil, bearing capacity, extenics theory, plate loading test.

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302 Variation of Uncertainty in Steady And Non-Steady Processes Of Queuing Theory

Authors: Om Parkash, C.P.Gandhi

Abstract:

Probabilistic measures of uncertainty have been obtained as functions of time and birth and death rates in a queuing process. The variation of different entropy measures has been studied in steady and non-steady processes of queuing theory.

Keywords: Uncertainty, steady state, non-steady state, trafficintensity, monotonocity

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301 Modified Diffie-Hellman Protocol By Extend The Theory of The Congruence

Authors: Rand Alfaris, Mohamed Rushdan MD Said, Mohamed Othman, Fudziah Ismail

Abstract:

This paper is introduced a modification to Diffie- Hellman protocol to be applicable on the decimal numbers, which they are the numbers between zero and one. For this purpose we extend the theory of the congruence. The new congruence is over the set of the real numbers and it is called the “real congruence" or the “real modulus". We will refer to the existing congruence by the “integer congruence" or the “integer modulus". This extension will define new terms and redefine the existing terms. As the properties and the theorems of the integer modulus are extended as well. Modified Diffie-Hellman key exchange protocol is produced a sharing, secure and decimal secret key for the the cryptosystems that depend on decimal numbers.

Keywords: Extended theory of the congruence, modified Diffie- Hellman protocol.

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