Search results for: exact space treatment

Authors: Bhupendra C. S. Chauhan, P. S. Bisht, O. P. S. Negi

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According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient, divergence and curl in seven dimension. It is shown that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We have tried to write all the vector inequalities and formulas in terms of seven dimensions and it is shown that same formulas loose their meaning in seven dimensions due to non-associativity of octonions. The vector formulas are retained only if we put certain restrictions on octonions and split octonions.

Keywords: Octonions, Vector Space and seven dimensions

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Authors: M. M. M. Jaradat, M. K. Al-Qeyyam

Abstract:

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

Keywords: Cycle space, minimum cycle basis, wreath product.

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Authors: R. Uthayakumar, D. Easwaramoorthy

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This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.

Keywords: Fractal Analysis, Fixed Point, Contraction, Iterated Function System, Intuitionistic Fuzzy Metric Space.

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Authors: Hemanth KumarA.R, Sudhakara G., Satyanarayana B.S.

Abstract:

The Cluster Dimension of a network is defined as, which is the minimum cardinality of a subset S of the set of nodes having the property that for any two distinct nodes x and y, there exist the node Si, s2 (need not be distinct) in S such that ld(x,s1) — d(y, s1)1 > 1 and d(x,s2) < d(x,$) for all s E S — {s2}. In this paper, strictly non overlap¬ping clusters are constructed. The concept of LandMarks for Unique Addressing and Clustering (LMUAC) routing scheme is developed. With the help of LMUAC routing scheme, It is shown that path length (upper bound)PLN,d < PLD, Maximum memory space requirement for the networkMSLmuAc(Az) < MSEmuAc < MSH3L < MSric and Maximum Link utilization factor MLLMUAC(i=3) < MLLMUAC(z03) < M Lc

Keywords: Metric dimension, Cluster dimension, Cluster.

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Authors: Iosif-Viorel Onut, Bin Zhu, Ali A. Ghorbani

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We propose a novel graphical technique (SVision) for intrusion detection, which pictures the network as a community of hosts independently roaming in a 3D space defined by the set of services that they use. The aim of SVision is to graphically cluster the hosts into normal and abnormal ones, highlighting only the ones that are considered as a threat to the network. Our experimental results using DARPA 1999 and 2000 intrusion detection and evaluation datasets show the proposed technique as a good candidate for the detection of various threats of the network such as vertical and horizontal scanning, Denial of Service (DoS), and Distributed DoS (DDoS) attacks.

Keywords: Anomaly Visualization, Network Security, Intrusion Detection.

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Authors: V. Thamizh Arasan, G. Dhivya

Abstract:

Traffic Density provides an indication of the level of service being provided to the road users. Hence, there is a need to study the traffic flow characteristics with specific reference to density in detail. When the length and speed of the vehicles in a traffic stream vary significantly, the concept of occupancy, rather than density, is more appropriate to describe traffic concentration. When the concept of occupancy is applied to heterogeneous traffic condition, it is necessary to consider the area of the road space and the area of the vehicles as the bases. Hence, a new concept named, 'area-occupancy' is proposed here. It has been found that the estimated area-occupancy gives consistent values irrespective of change in traffic composition.

Keywords: Density Measurement, Heterogeneity, Occupancy, Traffic Flow.

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Authors: A.R.Rizulla, F.S.Tashimova, A.R. Massalimova, A.K.Mynbayeva, G.S.Abdiraiymova

Abstract:

The importance of happiness understanding research is caused by cardinal changes experiences in system of people values in the post-Soviet countries territory. «The time of changes», which characterized with destruction of old values and not creativeness of new, stimulating experiences by the person of existential vacuum. The given research is actual not only in connection with sense formation, but also in connection with necessity creatively to adapt in integrative space. According to numerous works [1,2,3], we define happiness as the peak experience connected with satisfaction correlated system of needs, dependent on style of subject's coping behavior.

Keywords: Coping behavior, happiness, overcoming, psychological defense.

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Authors: Ravi Kiran Pothamsetty, Radha Rani Ghosh, Baby Paul Thaliath

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Radiation therapy has undergone many advancements and evloved from 2D to 3D. Recently, with rapid pace of drug discoveries, cutting edge technology, and clinical trials has made innovative advancements in computer technology and treatment planning and upgraded to intensity modulated radiotherapy (IMRT) which delivers in homogenous dose to tumor and normal tissues. The present study was a hospital-based experience comparing two different conformal radiotherapy techniques for brain tumors. This analytical study design has been conducted at Regional Cancer Centre, India from January 2014 to January 2015. Ten patients have been selected after inclusion and exclusion criteria. All the patients were treated on Artiste Siemens Linac Accelerator. The tolerance level for maximum dose was 6.0 Gyfor lenses and 54.0 Gy for brain stem, optic chiasm and optical nerves as per RTOG criteria. Mean and standard deviation values of PTV98%, PTV 95% and PTV 2% in IMRT were 93.16±2.9, 95.01±3.4 and 103.1±1.1 respectively; for 3DCRT were 91.4±4.7, 94.17±2.6 and 102.7±0.39 respectively. PTV max dose (%) in IMRT and 3D-CRT were 104.7±0.96 and 103.9±1.0 respectively. Maximum dose to the tumor can be delivered with IMRT with acceptable toxicity limits. Variables such as expertise, location of tumor, patient condition, and TPS influence the outcome of the treatment.

Keywords: IMRT, 3D CRT, Brain, tumors, OARs, RTOG.

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Authors: Mohammad Reza Kangavari, Samira Ghandchi, Manak Golpour

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Question answering (QA) aims at retrieving precise information from a large collection of documents. Most of the Question Answering systems composed of three main modules: question processing, document processing and answer processing. Question processing module plays an important role in QA systems to reformulate questions. Moreover answer processing module is an emerging topic in QA systems, where these systems are often required to rank and validate candidate answers. These techniques aiming at finding short and precise answers are often based on the semantic relations and co-occurrence keywords. This paper discussed about a new model for question answering which improved two main modules, question processing and answer processing which both affect on the evaluation of the system operations. There are two important components which are the bases of the question processing. First component is question classification that specifies types of question and answer. Second one is reformulation which converts the user's question into an understandable question by QA system in a specific domain. The objective of an Answer Validation task is thus to judge the correctness of an answer returned by a QA system, according to the text snippet given to support it. For validating answers we apply candidate answer filtering, candidate answer ranking and also it has a final validation section by user voting. Also this paper described new architecture of question and answer processing modules with modeling, implementing and evaluating the system. The system differs from most question answering systems in its answer validation model. This module makes it more suitable to find exact answer. Results show that, from total 50 asked questions, evaluation of the model, show 92% improving the decision of the system.

Keywords: Answer processing, answer validation, classification, question answering, query reformulation.

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Authors: Kazuki Sonoda, Masahiro Hori

Abstract:

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

Keywords: Concept Labeling, Ontology, Thesaurus, VocabularyProblem

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Authors: Safae El Alaoui, Mohamed Ouzahra

Abstract:

In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.

Keywords: Exponential stabilization, unbounded operator, Desch-Schappacher, Miyadera-Voigt operator.

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Authors: T.C. Manjunath,

Abstract:

This paper features the trajectory planning design of a indigenously developed 4-Axis SCARA robot which is used for doing successful robotic manipulation task in the laboratory. Once, a trajectory is being designed and given as input to the robot, the robot's gripper tip moves along that specified trajectory. Trajectories have to be designed in the work space only. The main idea of this paper is to design a continuous path trajectory model for the indigenously developed SCARA robot arm during its maneuvering from one point to another point (during pick and place operations) in a workspace avoiding all the obstacles in its path of motion.

Keywords: SCARA, Trajectory, Planning.

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Authors: Maria Diogo, Patrícia Diogo

Abstract:

The stone is a constituent part of the geological structure of the Territory, introducing himself as a subject that has always interconnected human and environment in the development of a discourse of meanings and symbols that reflect elements realized in different cultures and experiences. This action meant that the first settlements and their areas of influence gained importance in the field of humanization and spatial organization of the territory, not only for the appropriation that its inhabitants did, but mainly because the community regardless of their economic or social condition, used it as living space and cultural integration. These factors become decisive in the characterization of the landscape area in the northwest of Portugal, because the stone is a material that appears not only in the natural landscape, but is also a strong element in humanized landscape, becoming this relation the main characterization of the study area.

Keywords: Landscape, Men, Stone, Territory.

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Authors: Xijian Wang

Abstract:

This paper is concerned with the numerical minimization of energy functionals in BV ( ) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.

Keywords: finite element method, discontinuous Galerkin method, total variation minimization, inpainting

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

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In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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Authors: T. M. Agbede, A. O. Adekiya

Abstract:

Field experiments were conducted during 2013, 2014 and 2015 cropping seasons at Rufus Giwa Polytechnic, Owo, Ondo State, southwest Nigeria. The objective of the investigation was to determine the effect of Cocoa Pod Ash (CPA) and Poultry Manure (PM) applied solely and their combined form, as sources of fertilizers on soil properties, leaf nutrient composition, growth and yield of yam. Three soil amendments: CPA, PM (sole forms), CPA and PM (mixture), were applied at 20 t ha^-1 with an inorganic fertilizer (NPK 15-15-15) at 400 kg ha^-1 as a reference and a natural soil fertility, NSF (control). The five treatments were arranged in a randomized complete block design with three replications. The test soil was slightly acidic, low in organic carbon (OC), N, P, K, Ca and Mg. Results showed that soil amendments significantly increased (p = 0.05) tuber weights and growth of yam, soil and leaf N, P, K, Ca and Mg, soil pH and OC concentrations compared with the NSF (control). The mixture of CPA+PM treatment increased tuber weights of yam by 36%, compared with inorganic fertilizer (NPK) and 19%, compared with PM alone. Sole PM increased tuber weight of yam by 15%, compared with NPK. Sole or mixed forms of soil amendments showed remarkable improvement in soil physical properties, nutrient availability, compared with NPK and the NSF (control). Integrated application of CPA at 10 t ha^-1 + PM at 10 t ha^-1 was the most effective treatment in improving soil physical properties, increasing nutrient availability and yam performance than sole application of any of the fertilizer materials.

Keywords: Cocoa pod ash, leaf nutrient composition, poultry manure, soil properties, yam.

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Authors: Yilun Shang

Abstract:

We study a long-range percolation model in the hierarchical lattice ΩN of order N where probability of connection between two nodes separated by distance k is of the form min{αβ−k, 1}, α ≥ 0 and β > 0. The parameter α is the percolation parameter, while β describes the long-range nature of the model. The ΩN is an example of so called ultrametric space, which has remarkable qualitative difference between Euclidean-type lattices. In this paper, we characterize the sizes of large clusters for this model along the line of some prior work. The proof involves a stationary embedding of ΩN into Z. The phase diagram of this long-range percolation is well understood.

Keywords: percolation, component, hierarchical lattice, phase transition.

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Authors: Akbar Seraly, Kazbek Primbetov, Gulmira Abdiraiymova, Gulnapis Abdikerova

Abstract:

the article analyzes the development prospects of education system in Kazakhstan. Education is among key sources of culture and social mobility. Modern education must become civic which means availability of high quality education to all people irrespective of their racial, ethnic, religious, social, gender and any other differences. Socially focused nature of modernization of Kazakhstan-s society is predicated upon formation of a civic education model in the future. Kazakhstan-s education system undergoes intensive reforms first of all intended to achieve international education standards and integration into the global educational and information space.

Keywords: Education system, Kazakhstan , Modernization

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Authors: J. Daba, J. Dubois

Abstract:

In this work, we improve a previously developed segmentation scheme aimed at extracting edge information from speckled images using a maximum likelihood edge detector. The scheme was based on finding a threshold for the probability density function of a new kernel defined as the arithmetic mean-to-geometric mean ratio field over a circular neighborhood set and, in a general context, is founded on a likelihood random field model (LRFM). The segmentation algorithm was applied to discriminated speckle areas obtained using simple elliptic discriminant functions based on measures of the signal-to-noise ratio with fractional order moments. A rigorous stochastic analysis was used to derive an exact expression for the cumulative density function of the probability density function of the random field. Based on this, an accurate probability of error was derived and the performance of the scheme was analysed. The improved segmentation scheme performed well for both simulated and real images and showed superior results to those previously obtained using the original LRFM scheme and standard edge detection methods. In particular, the false alarm probability was markedly lower than that of the original LRFM method with oversegmentation artifacts virtually eliminated. The importance of this work lies in the development of a stochastic-based segmentation, allowing an accurate quantification of the probability of false detection. Non visual quantification and misclassification in medical ultrasound speckled images is relatively new and is of interest to clinicians.

Keywords: Discriminant function, false alarm, segmentation, signal-to-noise ratio, skewness, speckle.

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Authors: Samad Lotfollahzadeh

Abstract:

To evaluate the effect of intramuscular administration of vitamin A in pregnant dairy cows during late stages of pregnancy, on vitamin A status of neonatal calves, a total of 30 cows were randomly selected and divided into three groups; two treatment groups and one control group. Single intramuscular injection of 2000000 IU vitamin A; was carried in 10 dairy cows at 7 months of pregnancy (group 1). In second group of treated animals (10 cows) the injection was performed in 8 months of pregnancy (group 2). Ten pregnant dairy cows were received saline injection as placebo and selected as control group. Blood samples were collected from experimental dairy cows at 7 and 8 months of pregnancy as well as their newborn calves’ pre and after colostrum intake. There was no significant difference between vitamin A and β-carotene concentration of dairy cows of three groups in two last months of pregnancy (P> 0.05). Vitamin A concentration of calves of two treatment groups before and after receiving of colostrum were significantly higher than that in control group (P< 0.05). There was no significant difference between serum concentrations of vitamin A in calves of two treated groups (P> 0.05). β-Carotene concentration of serum samples of dairy cows and neonatal calves of three groups were not significantly different as compared with together. From results of the present study it can be concluded that single injection of vitamin A during at 7 or 8 month of pregnancy can significantly increase level of vitamin A in their colostrum and neonatal calves.

Keywords: Dry cow, Beta-carotene, Newborn calves, Vitamin A.

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Authors: Hai Ming Wong, Kuen Wai Ma, Lavender Yu Xin Yang, Yanqi Yang

Abstract:

Objectives: In recent years, the Faculty of Dentistry of the University of Hong Kong have extended the implementation of 3D electronic models (e-models) into problem-based learning (PBL) of the Bachelor of Dental Surgery (BDS) curriculum, aiming at mutual enhancement of PBL teaching quality and the students’ skills in using e-models. This study focuses on the effectiveness of e-models serving as a tool to enhance the students’ skills and competences in PBL. Methods: The questionnaire surveys are conducted to measure 50 fourth-year BDS students’ attitude change between beginning and end of blended PBL tutorials. The response rate of this survey is 100%. Results: The results of this study show the students’ agreement on enhancement of their learning experience after e-model implementation and their expectation to have more blended PBL courses in the future. The potential of e-models in cultivating students’ self-learning skills reduces their dependence on others, while improving their communication skills to argue about pros and cons of different treatment options. The students’ independent thinking ability and problem solving skills are promoted by e-model implementation, resulting in better decision making in treatment planning. Conclusion: It is important for future dental education curriculum planning to cope with the students’ needs, and offer support in the form of software, hardware and facilitators’ assistance for better e-model implementation.

Keywords: Problem-Based learning, curriculum, dental education, 3-D electronic models.

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Authors: A. Vassila, D. Kalogeropoulos, R. Rawashdeh, N. Hall, N. Rahman, M. Fabian, S. Thulasidharan, H. Parwez

Abstract:

Necrotising scleritis is a severe form of scleritis and poses a significant threat to vision. It can manifest in various systemic autoimmune disorders, systemic vasculitis, or as a consequence of microbial infections. The objective of this study is to present a case of necrotizing scleritis associated with scleroderma, which was further complicated by a secondary Staphylococcus epidermidis infection. This is a retrospective analysis, which examines the medical records of a patient who was hospitalised in the Eye Unit at University Hospital Southampton. A 78-year-old woman presented at the eye casualty department of our unit with a two-week history of progressively worsening pain in her left eye. She received a diagnosis of necrotising scleritis and was admitted to the hospital for further treatment. It was decided to commence a three-day course of intravenous methylprednisolone followed by a tapering regimen of oral steroids. Additionally, a conjunctival swab was taken, and two days later, it revealed the presence of S. epidermidis, indicating a potential secondary infection. Given this finding, she was also prescribed topical (Ofloxacin 0.3% - four times daily) and oral (Ciprofloxacin 750 mg – twice daily) antibiotics. The inflammation and symptoms gradually improved, leading to the patient being scheduled for a scleral graft and applying an amniotic membrane to cover the area of scleral thinning. Rheumatoid arthritis and granulomatosis with polyangiitis are the most commonly identifiable systemic diseases associated with necrotising scleritis. Although association with scleroderma is extremely rare, early identification and treatment are necessary to prevent scleritis-related complications.

Keywords: Scleritis, necrotizing scleritis, scleroderma, autoimmune disease.

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Authors: Patrycja J. Haupt

Abstract:

Today we tend to go back to the past to our root relation to nature. Therefore in search of friendly spaces there are elements of natural environment introduced as elements of spatial composition. Though reinvented through the use of the new substance such as greenery, water etc. made possible by state of the art technologies, still, in principal, they remain the same. As a result, sustainable design, based upon the recognized means of composition in addition to the relation of architecture and urbanism vs. nature introduces a new aesthetical values into architectural and urban space.

Keywords: architectural composition, biodiversity, elements of composition, green architecture, sustainable design, urban composition, water management.

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Authors: Omid Mirmotahari, Yngvar Berg, Mats Hovin

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The problem discussed in this paper involves packing fresh fish fileet of the northern Cod into a standard square container. The fish is first cleaned and split and then collected on a belt ready to be stacked in a container. The aim of our work is to pack the fish into the container with constraints on the amount of overlap allowed for the fileets. The current focus is to design a packing cell that can be real-time and of practical use, while finding the optimal solution to the degree of overlap and minimise the unused space of the container.

Keywords: Facilities Planning and Management, Intelligent Systems, Manufacturing Systems, Operations Research, Production Planning and Control.

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Authors: A. Taqaddas

Abstract:

Magnetic Nanoparticles (MNPs) have great potential to overcome many of the shortcomings of the present diagnostic and therapeutic approaches used in cancer diagnosis and treatment. This Literature review discusses the use of Magnetic Nanoparticles focusing mainly on Iron oxide based MNPs in cancer imaging using MRI.

Keywords: Cancer, Imaging, Magnetic Nanoparticles, MRI.

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Authors: R.L. Sanders, L. McKeown

Abstract:

An international cooperation between educators in Australia and the US has led to a reconceptualization of the teaching of a library science course at Appalachian State University. The pedagogy of Action Learning coupled with a 3D virtual learning environment immerses students in a social constructivist learning space that incorporates and supports interaction and reflection. The intent of this study was to build a bridge between theory and practice by providing students with a tool set that promoted personal and social reflection, and created and scaffolded a community of practice. Besides, action learning is an educational process whereby the fifty graduate students experienced their own actions and experience to improve performance.

Keywords: action learning, action research, reflection, metacognition, virtual worlds

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Authors: Yiannis G. Smirlis

Abstract:

The classification and the prediction of efficiencies in Data Envelopment Analysis (DEA) is an important issue, especially in large scale problems or when new units frequently enter the under-assessment set. In this paper, we contribute to the subject by proposing a grid structure based on interval segmentations of the range of values for the inputs and outputs. Such intervals combined, define hyper-rectangles that partition the space of the problem. This structure, exploited by Interval DEA models and a dominance relation, acts as a DEA pre-processor, enabling the classification and prediction of efficiency scores, without applying any DEA models.

Keywords: Data envelopment analysis, interval DEA, efficiency classification, efficiency prediction.

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Authors: Azam Anaraki Firooz, Ali Reza Mahjoub, Reza Donyaei Ziba

Abstract:

A simple and dexterous in situ method was introduced to load CdS nanocrystals into organofunctionalized mesoporous, which used an ion-exchange method. The products were extensively characterized by combined spectroscopic methods. X- ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) demonstrated both the maintenance of pore symmetry (space group p6mm) of SBA-15 and the presence of CdS nanocrystals with uniform sizes of about 6 - 8 nm inside the functionalized SBA-15 channels. These mesoporous silica-supported CdS composites showed room temperature photoluminescence properties with a blue shift, indicating the quantum size effect of nanocrystalline CdS.

Keywords: Semiconductors, luminescence, mesoporous material, CdS.

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Authors: S. B. Kulkarni, Hasim A. Chikte, V. Murali Mohan

Abstract:

Exact solution of an unsteady MHD flow of elasticoviscous fluid through a porous media in a tube of elliptic cross section under the influence of magnetic field and constant pressure gradient has been obtained in this paper. Initially, the flow is generated by a constant pressure gradient. After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in a tube of elliptical cross section by taking into account of the porosity factor and magnetic parameter of the bounding surface is investigated. The problem is solved in two-stages the first stage is a steady motion in tube under the influence of a constant pressure gradient, the second stage concern with an unsteady motion. The problem is solved employing separation of variables technique. The results are expressed in terms of a non-dimensional porosity parameter, magnetic parameter and elastico-viscosity parameter, which depends on the Non-Newtonian coefficient. The flow parameters are found to be identical with that of Newtonian case as elastic-viscosity parameter, magnetic parameter tends to zero, and porosity tends to infinity. The numerical results were simulated in MATLAB software to analyze the effect of Elastico-viscous parameter, porosity parameter, and magnetic parameter on velocity profile. Boundary conditions were satisfied. It is seen that the effect of elastico-viscosity parameter, porosity parameter and magnetic parameter of the bounding surface has significant effect on the velocity parameter.

Keywords: Elastico-viscous fluid, Porous media, Elliptic cross-section, Magnetic parameter, Numerical Simulation.

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Authors: Xun Ge, Jinjin Li, Ying Ge

Abstract:

Adopting Zakowski-s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximation spaces by logical methods and mathematical methods in computer science. Results of this paper give further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Keywords: Rough set, covering approximation space, granularitywise separation.

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