Search results for: The Szasz-Mirakjan-Kantorovich operators

Authors: Mohammed Husein Mohammad Rashid

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For a bounded linear operator T acting on a complex infinite dimensional Hilbert space ℋ, we say that T is ∗-class A operator (abbreviation T∈A*) if |T²|≥ |T*|². In this article, we prove the following assertions:(i) we establish some conditions which imply the normality of ∗-class A; (ii) we consider ∗-class A operator T ∈ ℬ(ℋ) with reducing kernel such that TX = XS for some X ∈ ℬ(K, ℋ) and prove the Fuglede-Putnam type theorem when adjoint of S ∈ ℬ(K) is dominant operators; (iii) furthermore, we extend the asymmetric Putnam-Fuglede theorem the class of ∗-class A operators.

Keywords: fuglede-putnam theorem, normal operators, ∗-class a operators, dominant operators

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Authors: Tulin Coskun

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We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: G. S. Thakur

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In this paper, four new operators (O1, O2, O3, O4) are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. These operators are useful for different operation on hesitant fuzzy sets. The various theorems are proved using the new operators. The study of the proposed new operators has opened a new area of research and applications.

Keywords: vague sets, hesitant fuzzy sets, intuitionistic fuzzy set, fuzzy sets, fuzzy multisets

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Authors: Shams Alyusof

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This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: Preeti Sharma

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This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied.

Keywords: Lupas-Durrmeyer operators, polya distribution, weighted approximation, rate of convergence, modulus of continuity

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Authors: Arkady Kitover

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We obtain a complete description of semi-Fredholm spectra of operators of the form (T f)(z) = w(z)f(B(z) acting on the disk algebra in the case when B is either elliptic or double parabolic finite Blaschke product and w has no zeros on the unit circle. Actually, in this case the lower semi-Fredholm spectrum is a disk, and the upper semi-Fredholm spectrum is a circle. We consider some examples and discuss some unsolved problems Our results hint on the possibility of interesting connections between the spectral properties of weighted composition operators and complex dynamics.

Keywords: weighted composition operators, essential spectra, Blaschke products, Julia set

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Authors: Anna Sikharulidze, Gia Sirbiladze

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For the evaluation of unreliability levels of movement on the closed routes in the vehicle routing problem, the fuzzy operators family is constructed. The interactions between routing factors in extreme conditions on the roads are considered. A multi-criteria decision-making model (MCDM) is constructed. Constructed aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are proved. Connections between the operators and the compositions of dual triangular norms are described. The conjugate connections between the constructed operators are shown. Operators reflect interactions among all the combinations of the factors in the fuzzy MCDM process. Several variants of constructed operators are used in the decision-making problem regarding the assessment of unreliability and possibility levels of movement on closed routes.

Keywords: vehicle routing problem, associated probabilities of a fuzzy measure, choquet integral, fuzzy aggregation operator

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Safeer Hussain Khan

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In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves and generalizes corresponding results in the literature in two ways: the iterative process is faster, operators are more general. In the end, we indicate that the results can also be proved with the iterative process with error terms.

Keywords: contractive-like operator, iterative process, fixed point, strong convergence

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Authors: Safeer Hussain Khan, H. Fukhar-ud-Din

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The concept of quasi-contractive type operators was given by Berinde and extended by Imoru and Olatinwo. They named this new type as contractive-like operators. On the other hand, Xu and Noo introduced a three-step-one-mappings iterative process which can be seen as a generalization of Mann and Ishikawa iterative processes. Approximating common fixed points has its own importance as it has a direct link with minimization problem. Motivated by this, in this paper, we first extend the iterative process of Xu and Noor to the case of three-step-three-mappings and then prove a strong convergence result using contractive-like operators for this iterative process. In general, this generalizes corresponding results using Mann, Ishikawa and Xu-Noor iterative processes with quasi-contractive type operators. It is to be pointed out that our results can also be proved with iterative process involving error terms.

Keywords: contractive-like operator, iterative process, common fixed point, strong convergence

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: Francis Padi, Solomon Nunoo, John Kojo Annan

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The paper "Survey on Fiber Optic Deployment for Telecommunications Operators in Ghana: Coverage Gap, Recommendations and Research Directions" presents a comprehensive survey on the deployment of fiber optic networks for telecommunications operators in Ghana. It addresses the challenges encountered by operators using microwave transmission systems for backhauling traffic and emphasizes the advantages of deploying fiber optic networks. The study delves into the coverage gap, provides recommendations, and outlines research directions to enhance the telecommunications infrastructure in Ghana. Additionally, it evaluates next-generation optical access technologies and architectures tailored to operators' needs. The paper also investigates current technological solutions and regulatory, technical, and economical dimensions related to sharing mobile telecommunication networks in emerging countries. Overall, this paper offers valuable insights into fiber optic network deployment for telecommunications operators in Ghana and suggests strategies to meet the increasing demand for data and mobile applications.

Keywords: survey on fiber optic deployment, coverage gap, recommendations, research directions

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Authors: Özlem Öksüzer

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In this paper, we introduce variation detracting property of Kantorovich-Stancu type operators in the space of functions of bounded variation. These problems are studied with respect to the variation seminorm.

Keywords: Kantorovich-Stancu type operators, variation seminorm, variation detracting property, absolutely continuous function

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Authors: Rana Gill, Chandandeep Kaur

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Segmentation of images can be implemented using different fundamental algorithms like edge detection (discontinuity based segmentation), region growing (similarity based segmentation), iterative thresholding method. A comprehensive literature review relevant to the study gives description of different techniques for vehicle number plate detection and edge detection techniques widely used on different types of images. This research work is based on edge detection techniques and calculating threshold on the basis of five edge operators. Five operators used are Prewitt, Roberts, Sobel, LoG and Canny. Segmentation of characters present in different type of images like vehicle number plate, name plate of house and characters on different sign boards are selected as a case study in this work. The proposed methodology has seven stages. The proposed system has been implemented using MATLAB R2010a. Comparison of all the five operators has been done on the basis of their performance. From the results it is found that Canny operators produce best results among the used operators and performance of different edge operators in decreasing order is: Canny>Log>Sobel>Prewitt>Roberts.

Keywords: segmentation, edge detection, text, extracting characters

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Authors: Mehdi Jafari Matehkolaee

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In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

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Authors: Giulio Nisoli, Jonas Brüngger, Karin Hostettler, Nicole Stoller, Katrin Fischer

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Technical operators in the railway domain are experts responsible for the supervisory control of the railway power grid as well as of the railway tunnels. The technical systems used to master these demanding tasks are constantly increasing in their degree of automation. It becomes therefore difficult for technical operators to maintain the control over the technical systems and the processes of their job. In particular, the operators must have the necessary experience and knowledge in dealing with a malfunction situation or unexpected event. For this reason, it is of growing importance that the skills relevant for the execution of the job are maintained and further developed beyond the basic training they receive, where they are educated in respect of technical knowledge and the work with guidelines. Training methods aimed at improving the cognitive skills needed by technical operators are still missing and must be developed. Goals of the present study were to identify which are the relevant cognitive skills of technical operators in the railway domain and to define which topics should be addressed by the training of these skills. Observational interviews were conducted in order to identify the main tasks and the organization of the work of technical operators as well as the technical systems used for the execution of their job. Based on this analysis, the most demanding tasks of technical operators could be identified and described. The cognitive skills involved in the execution of these tasks are those, which need to be trained. In order to identify and analyze these cognitive skills a cognitive task analysis (CTA) was developed. CTA specifically aims at identifying the cognitive skills that employees implement when performing their own tasks. The identified cognitive skills of technical operators were summarized and grouped in training topics. For every training topic, specific goals were defined. The goals regard the three main categories; knowledge, skills and attitude to be trained in every training topic. Based on the results of this study, it is possible to develop specific training methods to train the relevant cognitive skills of the technical operators.

Keywords: cognitive skills, cognitive task analysis, technical operators in the railway domain, training topics

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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: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: B. Falah, N. E. Abakouy

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Due to its high computational cost, mutation testing has been neglected by researchers. Recently, many cost and mutants’ reduction techniques have been developed, improved, and experimented, but few of them has relied the possibility of reducing the cost of mutation testing on the program type of the application under test. This paper is a comparative study between four operators’ selection techniques (mutants sampling, class level operators, method level operators, and all operators’ selection) based on the program code type of each application under test. It aims at finding an alternative approach to reveal the effect of code type on mutation testing score. The result of our experiment shows that the program code type can affect the mutation score and that the programs using polymorphism are best suited to be tested with mutation testing.

Keywords: equivalent mutant, killed mutant, mutation score, mutation testing, program code type, software testing

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Authors: Odile Amoncou, Djedje-Kossu Zahui

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The increased demand for digital communications during the COVID-19 pandemic has seen an unprecedented surge in new telecom infrastructure around the world. The expansion has been more remarkable in countries with developing telecom infrastructures. Particularly, the three telecom operators in Cote d’Ivoire, Orange CI, MTN CI, and MOOV Africa, have considerably scaled up their exploitation technologies and capacities in terms of towers, fiber optic installation, and customer service hubs. The trend will likely continue upward while expanding the carbon footprint of the Ivorian telecom operators. Therefore, the corporate social and environmental responsibilities of these telecommunication companies can no longer be overlooked. This paper assesses the sustainability of the three Ivorian telecommunication network operators by applying a combination of commonly used sustainability management indexes. These tools are streamlined and adapted to the relatively young and developing digital network of Cote D’Ivoire. We trust that this article will push the respective CEOs to make sustainability a top strategic priority and understand the substantial potential returns in terms of saving, new products, and new clients while improving their corporate image. In addition, good sustainability management can increase their stakeholders.

Keywords: sustainability of telecom operators, sustainability management index, carbon footprint, digital communications

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Authors: Ruchi, A. M. Acu, Purshottam N. Agrawal

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The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of 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, Peetre’s K-functional, Lipschitz class, mixed modulus of smoothness

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Authors: Iveta Eimontaite, Sarah R. Fletcher, Michele Surico, Alfio Minissale, Fabio F. Abba

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Industry 4.0 offers possibilities for increased production volumes and greater efficiency whilst at the same time presenting new opportunities and challenges for the human workforce. Exoskeletons have been used in healthcare and are now starting to be adopted in manufacturing. The potential benefits of reducing fatigue and physical strain are attractive prospects of the technology for industry; however, the novelty of exoskeletons and surrounding ethical issues raise concerns amongst the stakeholders. The current case study investigated the introduction of an upper body exoskeleton designed to support posture but not increase physical strength in a factory over three time points: before the exoskeleton was introduced, and one and two months post-introduction once operators had experienced working with it. The main focus was to evaluate changes in operators' workload, situation awareness, technology self-efficacy, and physical discomfort following the introduction of the exoskeleton. After using the exoskeleton over two months, operators reported a decrease in temporal demand and an increase in performance of the NASA TLX instrument. Furthermore, over the second month, operators' self-reported technology self-efficacy scores increased, but at the same time, their situation awareness decreased. Interestingly, operators' physical discomfort after using the exoskeleton for two months increased from not uncomfortable to quite uncomfortable in the shoulder, arm, and middle back regions. The results suggest that self-perceived task efficiency improved; however, increased discomfort and decreased situation awareness scores indicate that two months might not be long enough for the exoskeleton to be integrated into operators’ mental body schema. The paper will discuss further implications and suggestions for exoskeleton introduction to manufacturing environments.

Keywords: exoskeleton, manufacturing, mental workload, physical discomfort, situation awareness, technology self-efficacy

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Authors: Ashis Pradhan, Mohan P. Pradhan

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Pattern Matching is useful for recognizing character in a digital image. OCR is one such technique which reads character from a digital image and recognizes them. Line segmentation is initially used for identifying character in an image and later refined by morphological operations like binarization, erosion, thinning, etc. The work discusses a recognition technique that defines a set of morphological operators based on its orientation in a character. These operators are further categorized into groups having similar shape but different orientation for efficient utilization of memory. Finally the characters are recognized in accordance with the occurrence of frequency in hierarchy of significant pattern of those morphological operators and by comparing them with the existing database of each character.

Keywords: binary image, morphological patterns, frequency count, priority, reduction data set and recognition

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Authors: J. E. Jung, J. M. Yang, J. W. Kim

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The railway market across the world has been standardized with the globalization strategy of Europe. On the other hand, the Korean urban railway system is operated by 10 operators which have established their standards and independently managed BOMs. When operators manage different BOMs, lack of system compatibility prevents them from sharing information and hinders work linkage and efficiency. Europe launched a large-scale railway project in 1993 when the European Union went into effect. In particular, the recent standardization efforts of the EU-funded MODTRAIN project are similar to the approach of the urban rail system standardization research that is underway in Korea. This paper looks into the BOMs of Koran urban rail transit operators and suggests the standard BOM for the rail transit system in Korea by reviewing rail vehicle technologies and the MODTRAIN project of Europe. The standard BOM is structured up to the key device level or module level, and it allows vehicle manufacturers and component manufacturers to manage their lower-level BOMs and share them with each other and with operators.

Keywords: BOM, Korean rail, urban rail, standardized

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Authors: Chong-Yang Qiao, Teeravarunyou Sakol

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Current production-oriented factories need maintenance operators to work in shifts monitoring and inspecting complex systems and different equipment in the situation of mechanical breakdown. Augmented reality (AR) is an emerging technology that embeds data into the environment for situation awareness to help maintenance operators make decisions and solve problems. An application was designed to identify the problem of steam generators and inspection centrifugal pumps. The objective of this research was to find the best medium of AR and type of problem solving strategies among analogy, focal object method and mean-ends analysis. Two scenarios of inspecting leakage were temperature and vibration. Two experiments were used in usability evaluation and future innovation, which included decision-making process and problem-solving strategy. This study found that maintenance operators prefer build-in magnifier to zoom the components (55.6%), 3D exploded view to track the problem parts (50%), and line chart to find the alter data or information (61.1%). There is a significant difference in the use of analogy (44.4%), focal objects (38.9%) and mean-ends strategy (16.7%). The marked differences between maintainers and operators are of the application of a problem solving strategy. However, future work should explore multimedia information retrieval which supports maintenance operators for decision-making.

Keywords: augmented reality, situation awareness, decision-making, problem-solving

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Authors: Mohammed Husein Mohammed Rashid

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Let Τ = U |Τ| be a polar decomposition of a bounded linear operator T on a complex Hilbert space with ker U = ker |T|. T is said to be class p-w A(s,t) if (|T*|ᵗ|T|²ˢ|T*|ᵗ )ᵗᵖ/ˢ⁺ᵗ ≥|T*|²ᵗᵖ and |T|²ˢᵖ ≥ (|T|ˢ|T*|²ᵗ|T|ˢ)ˢᵖ/ˢ⁺ᵗ with 0Keywords: class p-w A (s, t), normaloid, isoloid, finite, orthogonality

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Authors: Ahmed Rashad Harb Riad Ismail

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The purpose of this research is to study the potential of Dynamic Pricing if deployed by mobile operators and analyse its effects from both operators and consumers side. Furthermore, to conclude, throughout the research study, the recommended conditions for successful Dynamic Pricing deployment, recommended factors identifying the type of markets where Dynamic Pricing can be effective, and proposal for a Dynamic Pricing stakeholders’ framework were presented. Currently, the mobile telecommunications industry is witnessing a dramatic growth rate in the data consumption, being fostered mainly by higher data speed technology as the 4G LTE and by the smart devices penetration rates. However, operators’ revenue from data services lags behind and is decupled from this data consumption growth. Pricing strategy is a key factor affecting this ecosystem. Since the introduction of the 4G LTE technology will increase the pace of data growth in multiples, consequently, if pricing strategies remain constant, then the revenue and usage gap will grow wider, risking the sustainability of the ecosystem. Therefore, this research study is focused on Dynamic Pricing for 4G LTE data services, researching the drivers, benefits and challenges of 4G LTE Dynamic Pricing and the feasibility of its deployment in practice from different perspectives including operators, regulators, consumers, and telecommunications equipment manufacturers point of views.

Keywords: LTE, dynamic pricing, EPC, research

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