Search results for: bagasse paper

Authors: Reza Shakoori

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This paper presents a structural correction of Arabic and Persian strokes using manipulation of their chain codes in order to improve the rate and performance of Persian and Arabic handwritten word recognition systems. It collects pure and effective features to represent a character with one consolidated feature vector and reduces variations in order to decrease the number of training samples and increase the chance of successful classification. Our results also show that how the proposed approaches can simplify classification and consequently recognition by reducing variations and possible noises on the chain code by keeping orientation of characters and their backbone structures.

Keywords: Arabic, chain code normalization, OCR systems, image processing

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Authors: M. Kamel El-Sayed

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The process of determining the degree of membership for an element to an uncertain concept has been found in many ways, using equivalence and symmetry relations in information systems. In the case of similarity, these methods did not take into account the degree of symmetry between elements. In this paper, we use a new definition for finding the membership based on the degree of symmetry. We provide an example to clarify the suggested methods and compare it with previous methods. This method opens the door to more accurate decisions in information systems.

Keywords: information system, uncertain concept, membership function, similarity relation, degree of similarity

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Authors: Adil Ishag

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Diglossia emerges in a situation where two distinctive varieties of a language are used alongside within a certain community. In this case, one is considered as a high or standard variety and the second one as a low or colloquial variety. Arabic is an extreme example of a highly diglossic language. This diglossity is due to the fact that Arabic is one of the most spoken languages and spread over 22 Countries in two continents as a mother tongue, and it is also widely spoken in many other Islamic countries as a second language or simply the language of Quran. The geographical variation between the countries where the language is spoken and the duality of the classical Arabic and daily spoken dialects in the Arab world on the other hand; makes the Arabic language one of the most diglossic languages. This paper tries to investigate this phenomena and its relation to learning Arabic as a first and second language.

Keywords: Arabic language, diglossia, first and second language, language learning

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Authors: Julius Oluwayomi Oluwadamilare, Michael Olutayo Olatunji

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In the African traditional societies, women have always played the role of a teacher, albeit informally. This is evident in the upbringing of their babies. As mothers, they also serve as the first teachers to teach their wards lessons through day-to-day activities. Furthermore, women always play the role of a musician during naming ceremonies, in the singing of lullabies, during initiation rites of adolescent boys and girls into adulthood, and in preparing their children especially daughters (and sons) for marriage. They also perform this role during religious and cultural activities, chieftaincy title/coronation ceremonies, singing of dirges during funeral ceremonies, and so forth. This traditional role of the African/Nigerian women puts them at a vantage point to contribute maximally to the teaching and learning of music at every level of education. The need for more women in the field of music education in Nigeria cannot be overemphasized. Today, gender equality is a major discourse in most countries of the world, Nigeria inclusive. Statistical data in the field of education and music education reveal the high ratio of male teachers/lecturers over their female counterparts in Nigerian tertiary institutions. The percentage is put at 80% Male and a distant 20% Female! This paper, therefore, examines feminine gender in Nigerian music education by tracing the involvement of women in musical practice from the pre-colonial to the post-colonial periods. The study employed both primary and secondary sources of data collection. The primary source included interviews conducted with 19 music lecturers from 8 purposively selected tertiary institutions from 4 geo-political zones of Nigeria. In addition, observation method was employed in the selected institutions. The results show, inter alia, that though there is a remarkable improvement in the rate of admission of female students into the music programme of Nigerian tertiary institutions, there is still an imbalance in the job placement in these institutions especially in the Colleges of Education which is the main focus of this research. Religious and socio-cultural factors are highly traceable to this development. This paper recommends the need for more female music teachers to be employed in the Nigerian tertiary institutions in line with the provisions stated in the Millennium Development Goals (MDGs) of the Federal Republic of Nigeria.

Keywords: gender, education, music, women

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Authors: Riaz Dhai

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The inherent differences between Islamic and conventional finance have given rise to a debate on whether conventional accounting standards provide sufficient disclosure in the annual financial statements of Islamic financial institutions (IFI). This issue has become more pronounced due to the rapid growth of IFIs over the last decade. This paper seeks to collate the literature surrounding this debate as well as summarise the key macro and micro level financial reporting differences between conventional and Islamic accounting. Based on these findings we propose some important areas of future research in this emerging field.

Keywords: Islamic financial institutions, financial reporting, critical analysis, conventional accounting standards

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Authors: John E. Foley, Martin Miele, Raul Fonda, Jon Jacobson

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This paper presents development and implementation of new and innovative data collection and analysis methodologies based on deployment of total field magnetometer arrays. Our research has focused on the development of a vertically-integrated suite of platforms all utilizing common data acquisition, data processing and analysis tools. These survey platforms include low-altitude helicopters and ground-based vehicles, including robots, for terrestrial mapping applications. For marine settings the sensor arrays are deployed from either a hydrodynamic bottom-following wing towed from a surface vessel or from a towed floating platform for shallow-water settings. Additionally, sensor arrays are deployed from tethered remotely operated vehicles (ROVs) for underwater settings where high maneuverability is required. While the primary application of these systems is the detection and mapping of unexploded ordnance (UXO), these system are also used for various infrastructure mapping and geologic investigations. For each application, success is driven by the integration of magnetometer arrays, accurate geo-positioning, system noise mitigation, and stable deployment of the system in appropriate proximity of expected targets or features. Each of the systems collects geo-registered data compatible with a web-enabled data management system providing immediate access of data and meta-data for remote processing, analysis and delivery of results. This approach allows highly sophisticated magnetic processing methods, including classification based on dipole modeling and remanent magnetization, to be efficiently applied to many projects. This paper also briefly describes the initial development of magnetometer-based detection systems deployed from low-altitude helicopter platforms and the subsequent successful transition of this technology to the marine environment. Additionally, we present examples from a range of terrestrial and marine settings as well as ongoing research efforts related to sensor miniaturization for unmanned aerial vehicle (UAV) magnetic field mapping applications.

Keywords: dipole modeling, magnetometer mapping systems, sub-surface infrastructure mapping, unexploded ordnance detection

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Authors: Madaki Umar Yusuf, Mohd Rizam B. Abubakar

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The survival censored data with incomplete covariate data is a common occurrence in many studies in which the outcome is survival time. With model when the missing covariates are categorical, a useful technique for obtaining parameter estimates is the EM by the method of weights. The survival outcome for the class of generalized linear model is applied and this method requires the estimation of the parameters of the distribution of the covariates. In this paper, we propose some clinical trials with ve covariates, four of which have some missing values which clearly show that they were fully censored data.

Keywords: EM algorithm, incomplete categorical covariates, ignorable missing data, missing at random (MAR), Weibull Distribution

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Authors: Arshia Khan, Hans-Dietrich Haasis

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Different tools of the supply chain should be managed very efficiently in mass customization. In the automobile industry, there are different strategies to manage these tools. We need to investigate which strategies among the different ones are successful and which are not. There is lack in literature regarding such analysis. Keeping this in view, the purpose of this paper is to construct a framework and model which can help to analyze the supply chain of mass customized automobiles quantitatively for future studies. Furthermore, we will also consider that which type of data can be used for the suggested model and where it can be taken from. Such framework can help to bring insight for future analysis.

Keywords: mass customization, supply chain, inventory, distribution, automobile industry

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Authors: Imèn Khanchouch, Malika Charrad, Mohamed Limam

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The interpretation of the quality of clusters and the determination of the optimal number of clusters is still a crucial problem in clustering. We focus in this paper on multi-SOM clustering method which overcomes the problem of extracting the number of clusters from the SOM map through the use of a clustering validity index. We then tested multi-SOM using real and artificial data sets with different evaluation criteria not used previously such as Davies Bouldin index, Dunn index and silhouette index. The developed multi-SOM algorithm is compared to k-means and Birch methods. Results show that it is more efficient than classical clustering methods.

Keywords: clustering, SOM, multi-SOM, DB index, Dunn index, silhouette index

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Authors: Max Filipe Goncalves, Alessandra Concilio, Rodrigo Shimada

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The waste frying oil is highly pollutant when disposed incorrectly in the environment. Is necessary search of the Reverse Logistics to identify how can be structure to return the waste like this to productive chain and to be used in the new process. In this context, the objective of this paper is to analyze the perspective of the waste frying oil in São Paulo, and its dimensions in the production of biodiesel. Subjacent factors such as the agents, motivators and legal aspects were analyzed to demonstrate it. Then, the SWOT matrix was built with the aspects observed and the forces, weaknesses, opportunities and threats of the reverse logistic chain in São Paulo.

Keywords: biodiesel, perspective, reverse logistic, WFO

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Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb

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The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.

Keywords: DCF, PCF, throughput, NS2

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Authors: Andrey V. Timofeev

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The paper presents new results concerning selection of optimal information fusion formula for ensembles of C-OTDR channels. The goal of information fusion is to create an integral classificator designed for effective classification of seismoacoustic target events. The LPBoost (LP-β and LP-B variants), the Multiple Kernel Learning, and Weighing of Inversely as Lipschitz Constants (WILC) approaches were compared. The WILC is a brand new approach to optimal fusion of Lipschitz Classifiers Ensembles. Results of practical usage are presented.

Keywords: Lipschitz Classifier, classifiers ensembles, LPBoost, C-OTDR systems

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Authors: Fabiano Araujo Soares, Sauro Emerick Salomoni, Joao Paulo Lima da Silva, Igor Luiz Moura, Adson Ferreira da Rocha

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This paper presents a tool developed in the Matlab platform. It was developed to simplify the analysis of surface electromyography signals (S-EMG) in a way accessible to users that are not familiarized with signal processing procedures. The tool receives data by commands in window fields and generates results as graphics and excel tables. The underlying math of each S-EMG estimator is presented. Setup window and result graphics are presented. The tool was presented to four non-engineer users and all of them managed to appropriately use it after a 5 minutes instruction period.

Keywords: S-EMG estimators, electromyography, surface electromyography, ARV, RMS, MDF, MNF, CV

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Authors: Hajara Abdulkarim Aliyu, Abdulbasid Ismail Isa

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This research paper studies electrohydraulic system for its role in position and motion control system and develops as mathematical model describing the behaviour of the system. The research further proposes Fuzzy logic and conventional PID controllers in order to achieve both accurate positioning of the payload and overall improvement of the system performance. The simulation result shows Fuzzy logic controller has a superior tracking performance and high disturbance rejection efficiency for its shorter settling time, less overshoot, smaller values of integral of absolute and deviation errors over the conventional PID controller at all the testing conditions.

Keywords: electrohydraulic, fuzzy logic, modelling, NZ-PID

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Authors: Leila Keshavarz Afshar, Hedieh Sajedi

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Estimation of biological brain age from MR images is a topic that has been much addressed in recent years due to the importance it attaches to early diagnosis of diseases such as Alzheimer's. In this paper, we use a 3D Convolutional Neural Network (CNN) to provide a method for estimating the biological age of the brain. The 3D-CNN model is trained by MRI data that has been normalized. In addition, to reduce computation while saving overall performance, some effectual slices are selected for age estimation. By this method, the biological age of individuals using selected normalized data was estimated with Mean Absolute Error (MAE) of 4.82 years.

Keywords: brain age estimation, biological age, 3D-CNN, deep learning, T1-weighted image, SPM, preprocessing, MRI, canny, gray matter

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Authors: Jian Cao

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This paper describes a novel watermarking technique which we call the random direction embedding (RDE) watermarking. Unlike traditional watermarking techniques, the watermark energy after the RDE embedding does not focus on a fixed direction, leading to the security against the traditional unauthorized watermark removal attack. In addition, the experimental results show that when compared with the existing secure watermarking, namely natural watermarking (NW), the RDE watermarking gains significant improvement in terms of robustness. In fact, the security of the RDE watermarking is not at the cost of low robustness, and it can even achieve more robust than the traditional spread spectrum watermarking, which has been shown to be very insecure.

Keywords: robustness, spread spectrum watermarking, watermarking security, random direction embedding (RDE)

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Authors: Ana Elvira Ojanguren Lopez, Javier Martin Arista

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The aims of this paper are to present the automatisation procedure adopted in the implementation of a parallel corpus of Old English, as well as, to assess the progress of automatisation with respect to tagging, annotation, and lemmatisation. The corpus consists of an aligned parallel text with word-for-word comparison Old English-English that provides the Old English segment with inflectional form tagging (gloss, lemma, category, and inflection) and lemma annotation (spelling, meaning, inflectional class, paradigm, word-formation and secondary sources). This parallel corpus is intended to fill a gap in the field of Old English, in which no parallel and/or lemmatised corpora are available, while the average amount of corpus annotation is low. With this background, this presentation has two main parts. The first part, which focuses on tagging and annotation, selects the layouts and fields of lexical databases that are relevant for these tasks. Most information used for the annotation of the corpus can be retrieved from the lexical and morphological database Nerthus and the database of secondary sources Freya. These are the sources of linguistic and metalinguistic information that will be used for the annotation of the lemmas of the corpus, including morphological and semantic aspects as well as the references to the secondary sources that deal with the lemmas in question. Although substantially adapted and re-interpreted, the lemmatised part of these databases draws on the standard dictionaries of Old English, including The Student's Dictionary of Anglo-Saxon, An Anglo-Saxon Dictionary, and A Concise Anglo-Saxon Dictionary. The second part of this paper deals with lemmatisation. It presents the lemmatiser Norna, which has been implemented on Filemaker software. It is based on a concordance and an index to the Dictionary of Old English Corpus, which comprises around three thousand texts and three million words. In its present state, the lemmatiser Norna can assign lemma to around 80% of textual forms on an automatic basis, by searching the index and the concordance for prefixes, stems and inflectional endings. The conclusions of this presentation insist on the limits of the automatisation of dictionary-based annotation in a parallel corpus. While the tagging and annotation are largely automatic even at the present stage, the automatisation of alignment is pending for future research. Lemmatisation and morphological tagging are expected to be fully automatic in the near future, once the database of secondary sources Freya and the lemmatiser Norna have been completed.

Keywords: corpus linguistics, historical linguistics, old English, parallel corpus

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Authors: Guenther Schuh, Michael Riesener, Frederic Diels

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Nowadays, manufacturing companies are faced with the challenge of meeting heterogeneous customer requirements in short product life cycles with a variety of product functions. So far, some of the functional requirements remain unknown until late stages of the product development. A way to handle these uncertainties is the highly iterative product development (HIP) approach. By structuring the development project as a highly iterative process, this method provides customer oriented and marketable products. There are first approaches for combined, hybrid models comprising deterministic-normative methods like the Stage-Gate process and empirical-adaptive development methods like SCRUM on a project management level. However, almost unconsidered is the question, which development scopes can preferably be realized with either empirical-adaptive or deterministic-normative approaches. In this context, a development scope constitutes a self-contained section of the overall development objective. Therefore, this paper focuses on a methodology that deals with the uncertainty of requirements within the early development stages and the corresponding selection of the most appropriate development approach. For this purpose, internal influencing factors like a company’s technology ability, the prototype manufacturability and the potential solution space as well as external factors like the market accuracy, relevance and volatility will be analyzed and combined into an Agile-Indicator. The Agile-Indicator is derived in three steps. First of all, it is necessary to rate each internal and external factor in terms of the importance for the overall development task. Secondly, each requirement has to be evaluated for every single internal and external factor appropriate to their suitability for empirical-adaptive development. Finally, the total sums of internal and external side are composed in the Agile-Indicator. Thus, the Agile-Indicator constitutes a company-specific and application-related criterion, on which the allocation of empirical-adaptive and deterministic-normative development scopes can be made. In a last step, this indicator will be used for a specific clustering of development scopes by application of the fuzzy c-means (FCM) clustering algorithm. The FCM-method determines sub-clusters within functional clusters based on the empirical-adaptive environmental impact of the Agile-Indicator. By means of the methodology presented in this paper, it is possible to classify requirements, which are uncertainly carried out by the market, into empirical-adaptive or deterministic-normative development scopes.

Keywords: agile, highly iterative development, agile-indicator, product development

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Authors: Huiling Feng, Jihong Liang, Xiaodong Gong, Yongjun Xu

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Recording history is a tradition in ancient China. A record of a dynasty makes a dynastic history; a record of a locality makes a chorography, and a record of a clan makes a genealogy – the three combined together depicts a complete national history of China both macroscopically and microscopically, with genealogy serving as the foundation. Genealogy in ancient China traces back to a family tree or pedigrees in the early and medieval historical times. After Song Dynasty, the civilian society gradually emerged, and the Emperor had to allow people from the same clan to live together and hold the ancestor worship activities, thence compilation of genealogy became popular in the society. Since then, genealogies, regarded as important as ancestor and religious temples in a traditional villages even today, have played a primary role in identification of a clan and maintain local social order. Chinese genealogies are rich in their documentary materials. Take the Genealogy of Wu Clan in Gaoqian as an example. Gaoqian is a small village in Xianju County of Zhejiang Province. The Genealogy of Wu Clan in Gaoqian is composed of a whole set of materials from Foreword to Family Trees, Family Rules, Family Rituals, Family Graces and Glories, Ode to An ancestor’s Portrait, Manual for the Ancestor Temple, documents for great men in the clan, works written by learned men in the clan, the contracts concerning landed property, even notes on tombs and so on. Literally speaking, the genealogy, with detailed information from every aspect recorded in stylistic rules, is indeed the carrier of the entire culture of a clan. However, due to their scarcity in number and difficulties in reading, genealogies seldom fall into the horizons of common people. This paper, focusing on the case of the Genealogy of Wu Clan in the Village of Gaoqian, intends to reproduce a digital Genealogy by use of ICTs, through an in-depth interpretation of the literature and field investigation in Gaoqian Village. Based on this, the paper goes further to explore the general methods in transferring physical genealogies to digital ones and ways in visualizing the clanism culture embedded in the genealogies with a combination of digital technologies such as software in family trees, multimedia narratives, animation design, GIS application and e-book creators.

Keywords: clanism culture, multimedia narratives, genealogy of Wu Clan, GIS

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Authors: Carlo Bianchini, Lorenzo Catena

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The appearance of 3D scanners and then, more recently, of image-based systems that generate point clouds directly from common digital images have deeply affected the survey process in terms of both capturing and 2D/3D modelling. In this context, low cost and mobile systems are increasingly playing a key role and actually paving the way to the democratization of what in the past was the realm of few specialized technicians and expensive equipment. The application of Google Tango on the ancient church of Santa Maria delle Vigne in Pratica di Mare – Rome presented in this paper is one of these examples.

Keywords: the architectural survey, augmented/mixed/virtual reality, Google Tango project, image-based 3D capturing

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Authors: Pruthvi Nath Palleti, Sarmada Madhulika Kone

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Communities are formed based on the commonalities that exist in a set of individuals and when the group comes together on identifying those commonalities and to achieve their common goals. Thus, community planning with its vision to strengthen the community mostly involves with making or remaking of commons, which results in making or remaking of communities. This paper looks into different practices of planning around the world and tried to establish a link between commoning (the act of exercising the rights over commons by commoners) and participatory approach to community planning.

Keywords: commoners, commoning, community, participatory planning, urban local bodies

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Authors: Asha Gupta, Ramandeep Kaur

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The purpose of this paper is to study a class of closed sets, called generalized pre-closed sets with respect to an ideal (briefly Igp-closed sets), which is an extension of generalized pre-closed sets in general topology. Then, by using these sets, the concepts of Igp- compact spaces along with some classes of maps like continuous and closed maps via ideals have been introduced and analogues of some known results for compact spaces, continuous maps and closed maps in general topology have been obtained.

Keywords: ideal, gp-closed sets, gp-closed maps, gp-continuous maps

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Authors: I. Ioannou, I. M. Gitman

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This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: effective properties, homogenization, representative volume element, short fiber reinforced composites

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Authors: Abdeljalil Beniiche

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The limitation with smart contracts is that they cannot access external data that might be required to control the execution of business logic. Oracles can be used to provide external data to smart contracts. An oracle is an interface that delivers data from external data outside the blockchain to a smart contract to consume. Oracle can deliver different types of data depending on the industry and requirements. In this paper, we study and describe the widely used blockchain oracles. Then, we elaborate on his potential role, technical architecture, and design patterns. Finally, we discuss the human oracle and its key role in solving the truth problem by reaching a consensus about a certain inquiry and tasks.

Keywords: blockchain, oracles, oracles design, human oracles

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Authors: M. Ndaw, G. Mendy, S. Ouya

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Risk management in banking sector is a key issue linked to financial system stability and its importance has been elevated by technological developments and emergence of new financial instruments. In this paper, we improve the model previously defined for quantifying internal control impact on banking risks by automatizing the residual criticality estimation step of FMECA. For this, we defined three equations and a maturity coefficient to obtain a mathematical model which is tested on all banking processes and type of risks. The new model allows an optimal assessment of residual criticality and improves the correlation rate that has become 98%.

Keywords: risk, control, banking, FMECA, criticality

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Authors: Lingge Tan, Hongpeng Xu, Jieun Yang, Maarten Hornikx

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Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper provides a type of modular diffuser based on the Sierpinski Triangle of the plane and combines it with fractal theory to expand the effective frequency range. In numerical calculations and full-scale model experiments, the effect of fractal design elements on normal-incidence diffusion coefficients is examined. It is demonstrated the reasonable times of iteration of modules is three, and the coverage density is 58.4% in the design frequency from 125Hz to 4kHz.

Keywords: acoustic diffuser, fractal, Sierpinski-triangle, diffusion coefficient

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Authors: Darshini Mahadevia, Kanika Gounder, Saumya Lathia

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Cities, an outcome of natural growth and migration, are ever-expanding due to urban sprawl. In the Global South, urban areas are experiencing a switch from public transport to private vehicles, coupled with intensified urban agglomeration, leading to frequent longer commutes by automobiles. This increase in travel distance and motorized vehicle kilometres lead to unsustainable cities. To achieve the nationally pledged GHG emission mitigation goal, the government is prioritizing a modal shift to low-carbon transport modes like mass transit and paratransit. Mixed land-use and urban densification are crucial for the economic viability of these projects. Informed by desktop assessment of mobility plans and in-person primary surveys, the paper explores the challenges around urban densification and travel patterns in two Indian cities of contrasting nature- Surat, a metropolitan industrial city with a 5.9 million population and a very compact urban form, and Udaipur, a heritage city attracting large international tourists’ footfall, with limited scope for further densification. Dense, mixed-use urban areas often improve access to basic services and economic opportunities by reducing distances and enabling people who don't own personal vehicles to reach them on foot/ cycle. But residents travelling on different modes end up contributing to similar trip lengths, highlighting the non-uniform distribution of land-uses and lack of planned transport infrastructure in the city and the urban-peri urban networks. Additionally, it is imperative to manage these densities to reduce negative externalities like congestion, air/noise pollution, lack of public spaces, loss of livelihood, etc. The study presents a comparison of the relationship between transport systems with the built form in both cities. The paper concludes with recommendations for managing densities in urban areas along with promoting low-carbon transport choices like improved non-motorized transport and public transport infrastructure and minimizing personal vehicle usage in the Global South.

Keywords: India, low-carbon transport, travel behaviour, trip length, urban densification

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Authors: Safeer Hussain Khan

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In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

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

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Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

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A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift AZ, x is in M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, we find a new method of calculating the topological entropy of the Motzkin shift M(M,N) without any measure theoretical discussion.

Keywords: entropy, Motzkin shift, mathematical model, theory

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Authors: Khidir R. Sharaf, Didar A. Ali

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The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: graph theory, graph spectra, nullity of graphs, statistic

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