Search results for: generating functions

Authors: Ahmed Khalil

Abstract:

The discoveries in material sciences create an impulse in renewable energy transmission. Application techniques become more accessible by applied sciences. Variety of materials, application methods, and performance analyzing techniques can convert daily life functions to energy sources. These functions not only include natural sources like sun, wind, or water but also comprise the motion of tools used by human beings. In line with this, vehicles' motion, speed and weights come to the scene as energy sources together with piezoelectric nano-generators beneath the roads. Numerous application examples are put forward with repeated average performance, versus the differentiating challenges depending on geography and project conditions. Such holistic approach provides way for feed backs on research and improvement process of nano-generators beneath asphalt roads. This paper introduces the specific application methods of piezoelectric nano-generator beneath asphalt roads of Ahmadi Township in Kuwait.

Keywords: nano-generator pavements, piezoelectric, renewable energy, transducer

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Authors: Fariha Asif

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The main purpose of this study was to investigate the effectiveness of eclectic approach in teaching of communicative functions. The objectives of the study were to get the information about the use of communicative functions through eclectic approach and to point out the most effective way of teaching functional communication and social interaction with the help of communicative activities through eclectic approach. The next step was to select sample from the selected population. As the research was descriptive so a questionnaire was developed on the basis of hypothesis and distributed to different selected schools of Lahore, Pakistan. Then data was tabulated, analyzed and interpreted through computer by finding percentages of different responses given by teachers to see the results. It was concluded that eclectic approach is effective in teaching communicative functions and communicative functions are better when taught through eclectic approach and communicative activities are more appropriate way of teaching communicative functions. It was found those teachers who were qualified in ELT gave better opinions as compare to those who did not have this degree. Techniques like presentations, dialogues and roleplay proved to be effective for teaching functional communication through communicative activities and also motivate the students not only in learning rules but also in using them to communicate with others.

Keywords: methodology, functions, teaching, ESP

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Hassan Naseh, Javad Roozgard

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This paper represents the methodology based on Artificial Intelligent (AI) applied to Liquid Propellant Engine (LPE) optimization. The AI methodology utilized from Adaptive neural Fuzzy Inference System (ANFIS). In this methodology, the optimum objective function means to achieve maximum performance (specific impulse). The independent design variables in ANFIS modeling are combustion chamber pressure and temperature and oxidizer to fuel ratio and output of this modeling are specific impulse that can be applied with other objective functions in LPE design optimization. To this end, the LPE’s parameter has been modeled in ANFIS methodology based on generating fuzzy inference system structure by using grid partitioning, subtractive clustering and Fuzzy C-Means (FCM) clustering for both inferences (Mamdani and Sugeno) and various types of membership functions. The final comparing optimization results shown accuracy and processing run time of the Gaussian ANFIS Methodology between all methods.

Keywords: ANFIS methodology, artificial intelligent, liquid propellant engine, optimization

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

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In a conventional network, most network devices, such as routers, are dedicated devices that do not have much variation in capacity. In recent years, a new concept of network functions virtualisation (NFV) has come into use. The intention is to implement a variety of network functions with software on general-purpose servers and this allows the network operator to select their capacities and locations without any constraints. This paper focuses on the allocation of NFV-based routing functions which are one of critical network functions, and presents the virtual routing function allocation algorithm that minimizes the total power consumption. In addition, this study presents the useful allocation policy of virtual routing functions, based on an evaluation with a ladder-shaped network model. This policy takes the ratio of the power consumption of a routing function to that of a circuit and traffic distribution between areas into consideration. Furthermore, the present paper shows that there are cases where the use of NFV-based routing functions makes it possible to reduce the total power consumption dramatically, in comparison to a conventional network, in which it is not economically viable to distribute small-capacity routing functions.

Keywords: NFV, resource allocation, virtual routing function, minimum power consumption

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Authors: Yamin Sayyari

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In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: Jose Juan Peña, J. Morales, J. García-Ravelo

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In the search of potential models applied in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf) for displacing and modifying the shape of the potential under study. In order to transcend the scope of hyperbolic functions, in this work, a kind of generalized q-deformed hyperbolic functions (g q-dhf) is presented. By a suitable transformation, through the q deformation parameter, it is shown that these g q-dhf can be expressed in terms of their corresponding standard ones besides they can be reduced to the sc q-dhf. As a useful application of the proposed approach, and considering a class of exactly solvable multi-parameter exponential-type potentials, some new q-deformed quantum interactions models that can be used as interesting alternative in quantum physics and quantum states are presented. Furthermore, due that quantum potential models are conditioned on the q-dependence of the parameters that characterize to the exponential-type potentials, it is shown that many specific cases of q-deformed potentials are obtained as particular cases from the proposal.

Keywords: diatomic molecules, exponential-type potentials, hyperbolic functions, q-deformed potentials

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Authors: Smita Sonker

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Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Fakharuddin Ibrahim, Jamaludin Md. Ali, Ahmad Ramli

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In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G¹ continuity. The conditions considered are known as the G¹ Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

Keywords: data interpolation, rational ball curve, hermite condition, continuity

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Sunyoung Park

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Context: Talent management is a strategic approach that has received considerable attention in recent years to improve employee competency and organizational performance in many organizations. The implementation of talent management involves identifying objectives and positions within the organization, developing a pool of high-potential employees, and establishing appropriate HR functions to promote high employee and organizational performance. This study aims to investigate the relationship between talent management, HR functions, employee competency, and organizational performance in the South Korean context. Research Aim: The main objective of this study is to investigate the structural relationships among talent management, human resources (HR) functions, employee competency, and organizational performance. Methodology: To achieve the research aim, this study used a quantitative research method. Specifically, a total of 1,478 responses were analyzed using structural equation modeling based on data obtained from the Human Capital Corporate Panel (HCCP) survey in South Korea. Findings: The study revealed that talent management has a positive influence on HR functions and employee competency. Additionally, HR functions directly affect employee competency and organizational performance. Employee competency was found to be related to organizational performance. Moreover, talent management and HR functions indirectly affect organizational performance through employee competency. Theoretical Importance: This study provides empirical evidence of the relationship between talent management, HR functions, employee competency, and organizational performance in the South Korean context. The findings suggest that organizations should focus on developing appropriate talent management and HR functions to improve employee competency, which, in turn, will lead to better organizational performance. Moreover, the study contributes to the existing literature by emphasizing the importance of the relationship between talent management and HR functions in improving organizational performance.

Keywords: employee competency, HR functions, organizational performance, talent management

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Authors: Dylan Santos De Pinho, Nabil Ouerhani

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Energy consumption of machine-tools is becoming critical for machine-tool builders and end-users because of economic, ecological and legislation-related reasons. Many machine-tool builders are seeking for solutions that allow the reduction of energy consumption of machine-tools while preserving the same productivity rate and the same quality of machined parts. In this paper, we present the first results of a project conducted jointly by academic and industrial partners to reduce the energy consumption of a Swiss-Type lathe. We employ genetic algorithms to find optimal machining parameters – the set of parameters that lead to the best trade-off between energy consumption, part quality and tool lifetime. Three main machining process parameters are considered in our optimization technique, namely depth of cut, spindle rotation speed and material feed rate. These machining process parameters have been identified as the most influential ones in the configuration of the Swiss-type machining process. A state-of-the-art multi-objective genetic algorithm has been used. The algorithm combines three fitness functions, which are objective functions that permit to evaluate a set of parameters against the three objectives: energy consumption, quality of the machined parts, and tool lifetime. In this paper, we focus on the investigation of the fitness function related to energy consumption. Four different energy consumption related fitness functions have been investigated and compared. The first fitness function refers to the Kienzle cutting force model. The second fitness function uses the Material Removal Rate (RMM) as an indicator of energy consumption. The two other fitness functions are non-deterministic, learning-based functions. One fitness function uses a simple Neural Network to learn the relation between the process parameters and the energy consumption from experimental data. Another fitness function uses Lasso regression to determine the same relation. The goal is, then, to find out which fitness functions predict best the energy consumption of a Swiss-Type machining process for the given set of machining process parameters. Once determined, these functions may be used for optimization purposes – determine the optimal machining process parameters leading to minimum energy consumption. The performance of the four fitness functions has been evaluated. The Tornos DT13 Swiss-Type Lathe has been used to carry out the experiments. A mechanical part including various Swiss-Type machining operations has been selected for the experiments. The evaluation process starts with generating a set of CNC (Computer Numerical Control) programs for machining the part at hand. Each CNC program considers a different set of machining process parameters. During the machining process, the power consumption of the spindle is measured. All collected data are assigned to the appropriate CNC program and thus to the set of machining process parameters. The evaluation approach consists in calculating the correlation between the normalized measured power consumption and the normalized power consumption prediction for each of the four fitness functions. The evaluation shows that the Lasso and Neural Network fitness functions have the highest correlation coefficient with 97%. The fitness function “Material Removal Rate” (MRR) has a correlation coefficient of 90%, whereas the Kienzle-based fitness function has a correlation coefficient of 80%.

Keywords: adaptive machining, genetic algorithms, smart manufacturing, parameters optimization

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Authors: Nicolae Pascu

Abstract:

Aside from being a fundamental tool in Complex analysis, Schwarz Lemma-which was finalized in its most complete form at the beginning of the last century-generated an important area of research in various fields of mathematics, which continues to advance even today. We present some properties of analytic functions in the half-plane which satisfy the conditions of the classical Schwarz Lemma (Carathéodory functions) and obtain a generalization of the well-known Aleksandrov-Sobolev Lemma for analytic functions in the half-plane (the correspondent of Schwarz-Pick Lemma from the unit disk). Using this Schwarz-type lemma, we obtain a characterization for the entire class of Carathéodory functions, which might be of independent interest. We prove two monotonicity properties for Carathéodory functions that do not depend upon their normalization at infinity (the hydrodynamic normalization). The method is based on conformal mapping arguments for analytic functions in the half-plane satisfying appropriate conditions, in the spirit of Schwarz lemma. According to the research findings in this paper, our main results give estimates for the modulus and the argument for the entire class of Carathéodory functions. As applications, we give several extensions of Julia-Wolf-Carathéodory Lemma in a half-strip and show that our results are sharp.

Keywords: schwarz lemma, Julia-wolf-caratéodory lemma, analytic function, normalization condition, caratéodory function

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Authors: Madina Hamiane

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Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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Authors: Prat Yotyawilai, Taratip Suwannasart

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Business Process Model and Notation (BPMN) is more important in the business process and creating functional models, and is a standard for OMG, which becomes popular in various organizations and in education. Researches related to software testing based on models are prominent. Although most researches use the UML model in software testing, not many researches use the BPMN Model in creating test cases. Therefore, this research proposes a design of a tool for generating test cases from the BPMN. The model is analyzed and the details of the various components are extracted before creating a flow graph. Both details of components and the flow graph are used in generating test cases.

Keywords: software testing, test case, BPMN, flow graph

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Authors: F. Maass, P. Martin, J. Olivares

Abstract:

The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Sang Beom Kim, Kyung Ju Kim, Myung Hoon Cho, Ji Hoon Kim, Soo Hyung Kim

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In this study, we systematically investigated the effect of nanoscale energetic materials in formulations of aluminum nanoparticles (Al NPs; heat source)/copper oxide nanoparticles (CuO NPs; oxidizer) on the combustion and gas-generating properties of sodium azide microparticles (NaN3 MPs; gas-generating agent) for potential applications in gas generators. The burn rate of the NaN3 MP/CuO NP composite powder was only ~0.3 m/s. However, the addition of Al NPs to the NaN3 MP/CuO NP matrix caused the rates to reach ~5.3 m/s, respectively. In addition, the N2 gas volume flow rate generated by the ignition of the NaN3 MP/CuO NP composite powder was only ~0.6 L/s, which was significantly increased to ~3.9 L/s by adding Al NPs to the NaN3 MP/CuO NP composite powder. This suggested that the highly reactive NPs, with the assistance of CuO NPs, were effective heat-generating sources enabling the complete thermal decomposition of NaN3 MPs upon ignition. Al NPs were highly effective in the gas generators because of the increased reactivity induced by the reduced particle size. Finally, we successfully demonstrated that a homemade airbag with a specific volume of ~140 mL could be rapidly and fully inflated by the thermal activation of nanoscale energetic material-added gas-generating agents (i.e., NaN3 MP/Al NP/CuO NP composites) within the standard time of ~50 ms for airbag inflation.

Keywords: nanoenergetic materials, aluminum nanoparticles, copper oxide nanoparticles, gas generators

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Shun Horikoshi, Tohru Kawabe

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This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis

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Authors: Haojie Wang, Xun Li, Rui Yin

Abstract:

In order to solve the memorization overfitting in the meta-learning MAML algorithm, a method of generating mutually exclusive tasks based on data augmentation is proposed. This method generates a mutex task by corresponding one feature of the data to multiple labels, so that the generated mutex task is inconsistent with the data distribution in the initial dataset. Because generating mutex tasks for all data will produce a large number of invalid data and, in the worst case, lead to exponential growth of computation, this paper also proposes a key data extraction method, that only extracts part of the data to generate the mutex task. The experiments show that the method of generating mutually exclusive tasks can effectively solve the memorization overfitting in the meta-learning MAML algorithm.

Keywords: data augmentation, mutex task generation, meta-learning, text classification.

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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Authors: Chantima Wangsomchok

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The main purposes of this study are (1) to test the students’ communicative competence within six main functions: greeting, parting, thanking, offering, requesting and suggesting, (2) to employ error analysis in the students’ communicative competence within those functions, and (3) to compare the characteristics of the error found from the investigation. The subjects of the study is 328 first-year undergraduates taking the Foundation English course in the first semester of the 2008 academic year at Suan Sunandha Rajabhat University. This study found that while the subjects showed high communicative competence in the use of the following three functions: greeting, thanking, and offering, they seemed to show poor communicative competence in suggesting, requesting and parting instead. In addition, this study found that the grammatical errors were likely to be most frequently found in the parting function. In the same way, the type of errors which were less frequently found was in the functions of thanking and requesting respectively. Instead, the students tended to have high pragmatic failure in the use of greeting and suggesting functions.

Keywords: error analysis, functions of English language, communicative competence, cognitive science

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Authors: Haojie Wang, Xun Li, Rui Yin

Abstract:

In order to solve the memorization overfitting in the model-agnostic meta-learning MAML algorithm, a method of generating mutually exclusive tasks based on data augmentation is proposed. This method generates a mutex task by corresponding one feature of the data to multiple labels so that the generated mutex task is inconsistent with the data distribution in the initial dataset. Because generating mutex tasks for all data will produce a large number of invalid data and, in the worst case, lead to an exponential growth of computation, this paper also proposes a key data extraction method that only extract part of the data to generate the mutex task. The experiments show that the method of generating mutually exclusive tasks can effectively solve the memorization overfitting in the meta-learning MAML algorithm.

Keywords: mutex task generation, data augmentation, meta-learning, text classification.

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Authors: Zsolt Lipcsey, Sampson Marshal Imeh

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We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to ascertain the relevance of the concept of independence. There are cases where the concept of independence fails to be useful for this purpose. One would expect the basic element to be the maximal independent subset of a given semigroup. However, we construct examples for semigroups where finite basis exist and the basis is larger than the number of independent elements.

Keywords: generating sets, independent set, rank, cyclic semigroup, basis, commutative

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Authors: Niroshan K. Walgama Wellalage, Tieling Zhang, Richard Dwight

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State-based Markov deterioration models (SMDM) sometimes fail to find accurate transition probability matrix (TPM) values, and hence lead to invalid future condition prediction or incorrect average deterioration rates mainly due to drawbacks of existing nonlinear optimization-based algorithms and/or subjective function types used for regression analysis. Furthermore, a set of separate functions for each condition state with age cannot be directly derived by using Markov model for a given bridge element group, which however is of interest to industrial partners. This paper presents a new approach for generating Homogeneous SMDM model output, namely, the Modified Weibull approach, which consists of a set of appropriate functions to describe the percentage condition prediction of bridge elements in each state. These functions are combined with Bayesian approach and Metropolis Hasting Algorithm (MHA) based Markov Chain Monte Carlo (MCMC) simulation technique for quantifying the uncertainty in model parameter estimates. In this study, factors contributing to rail bridge deterioration were identified. The inspection data for 1,000 Australian railway bridges over 15 years were reviewed and filtered accordingly based on the real operational experience. Network level deterioration model for a typical bridge element group was developed using the proposed Modified Weibull approach. The condition state predictions obtained from this method were validated using statistical hypothesis tests with a test data set. Results show that the proposed model is able to not only predict the conditions in network-level accurately but also capture the model uncertainties with given confidence interval.

Keywords: bridge deterioration modelling, modified weibull approach, MCMC, metropolis-hasting algorithm, bayesian approach, Markov deterioration models

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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