Search results for: q numbers of metric space

Authors: Hosein Shokoohmand, Mohamad Esmaeil Jomeh

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The present thesis studies the effect of different factors such as frequency of oscillatory flow, change in constant wall heat flux and two-phase current state, on heat transfer in a pipe in presence of porous medium. In this experimental study is conducted for Reynolds numbers in a range of Re=850 to Re=10000 and oscillatory frequencies of 5, 20, 10, 30 and 40 Hz with constant heat flux of 585 w/m2 and 819 w/m2. The results indicate that increase in oscillation frequency in higher frequencies for heat flux of 585 w/m2 leads to an increase in heat transfer; however, in the rest of tests it results in a heat transfer decrease. Increasing Reynolds number in a pulsation mist flow causes an increase in average Nusselt number values. The effect of oscillation frequencies in a pulsation mist flow for different Reynolds numbers has revealed different results, in a way that for some Reynolds numbers an increase of frequency has led to a heat transfer decrease.

Keywords: Reynolds numbers, frequency of oscillatory flow, constant heat flux, mist flow

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Authors: Taehan Lee

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We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: integer programming, multicommodity network design, routing, shortest path

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Authors: Wan-I Chen, Tsung-I Pai

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Future the society aging of population will create the social problem has not had the good mechanism solution in the Asian country, especially in Taiwan. In the future ten year the people in Taiwan must facing the condition which is localization aging social problem. In this situation, how to use the spatial in eco way to development space use to solve the old age spatial demand is the way which might develop in the future Taiwan society. Over the next 10 years, taking care of the aging people will become part of the social problem of aging phenomenon. The research concentrate in the feasibility of spatial substitution, secondary use of spatial might solve out of spatial problem for aging people. In order to prove the space usable, the research required to review the project with the support system and infill system for space experiment, by using network grid way. That defined community level of space elements location relationship, make new definitions of space and return to cooperation. Research to innovation in the the appraisal space causes the possibility, by spatial replacement way solution on spatial insufficient suitable condition. To evaluation community spatial by using the support system and infill system in order to see possibilities of use in replacement inner space and modular architecture into housing. The study is discovering the solution on the Eco way to develop space use to figure out the old age spatial demand.

Keywords: sustainable use, space conversion, integration, replacement


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Authors: Labiba Zerari Bourafa, Djebar Mohamed Reda, Berrebah Houria, Khadri Sihem, Chiheb Linda

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The study of the effect of metal dust (pollutants) was performed on higher plant white beans Phaseolus vulgaris; the experience took place in cellular toxicology laboratory (in vitro culture). The seeds of the bean Phaseolus vulgaris are cultured in a metal contaminated dust medium (a single treatment by different increasing doses), at a rate of 10 seeds per box, for 10 days. The measurement of morpho-metric parameters is performed during the first 96 hours that follow the germination; while the dosage of the proline, the protein content and histological sections are formed on the tenth day (240 h). All morpho-metric and biochemical parameters measured were highly disturbed by metal dust; histological sections confirm this disurbance.

Keywords: conductive fabrics, metal dust, osmoticums, roots, Phaseolus vulgaris

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Authors: Arthur Baraov

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Nearly all rocket and spacecraft propulsion concepts in existence today can be linked one way or the other to one of the two ancient warfare devices: the gun and the sling. Chemical, thermoelectric, ion, nuclear thermal and electromagnetic rocket engines – all fall into the first group which, for obvious reasons, can be categorized as “hot” space propulsion concepts. Space elevator, orbital tower, rolling satellite, orbital skyhook, tether propulsion and gravitational assist – are examples of the second category which lends itself for the title “cold” space propulsion concepts. The “hot” space propulsion concepts skyrocketed – literally and figuratively – from the naïve ideas of Jules Verne to the manned missions to the Moon. On the other hand, with the notable exception of gravitational assist, hardly any of the “cold” space propulsion concepts made any progress in terms of practical application. Why is that? This article aims to show that the right answer to this question has the potential comparable by its implications and practical consequences to that of transition from Jules Verne’s stillborn and impractical conceptions of space flight to cogent and highly fertile ideas of Konstantin Tsiolkovsky and Yuri Kondratyuk.

Keywords: propulsion, rocket, rollet, spacecraft

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Authors: Raliatu Mohammed Kashim

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The study investigated primary school teachers conceptual and procedural knowledge of rational numbers to determine how it effects on pupil’s achievement on rational number. Specifically, primary school teachers’ level of conceptual and procedural knowledge about rational number and its effects on their pupils understanding of rational number in primary school was explored. The study was carried out in Bauchi state of Nigeria, Using a multistage design. The first stage was a descriptive design. The second stage involves a pre-test post-test only quasi experiment design. The population of the study comprises of six mathematics teachers holding the Nigerian Certificate in Education (NCE) teaching primary six and their two hundred and ten pupils in intact class. Two instrument namely Conceptual and Procedural knowledge Test (CPKT) and Rational number Achievement Test (RAT) were used for data collection. Data collected was analyzed using ANCOVA and Scheffe’s Test. The result revealed a significant differences between pupils taught by teachers with high conceptual and procedural knowledge and those target by teachers with low conceptual and procedural knowledge.

Keywords: conceptual knowledge, procedural knowledge, rational numbers, multistage design

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Authors: Shabadini Sampath, Jinglang Feng

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With huge kinetic energy, space debris poses a major threat to astronauts’ space activities and spacecraft in orbit if a collision happens. The active removal of space debris is required in order to avoid frequent collisions that would occur. In addition, the amount of space debris will increase uncontrollably, posing a threat to the safety of the entire space system. But the safe and reliable removal of large-scale space debris has been a huge challenge to date. While capturing and deorbiting space debris, the space manipulator has to achieve high control precision. However, due to uncertainties and unknown disturbances, there is difficulty in coordinating the control of the space manipulator. To address this challenge, this paper focuses on developing a robust and intelligent control algorithm that controls joint movement and restricts it on the sliding manifold by reducing uncertainties. A neural network adaptive sliding mode controller (NNASMC) is applied with the objective of finding the control law such that the joint motions of the space manipulator follow the given trajectory. A computed torque control (CTC) is an effective motion control strategy that is used in this paper for computing space manipulator arm torque to generate the required motion. Based on the Lyapunov stability theorem, the proposed intelligent controller NNASMC and CTC guarantees the robustness and global asymptotic stability of the closed-loop control system. Finally, the controllers used in the paper are modeled and simulated using MATLAB Simulink. The results are presented to prove the effectiveness of the proposed controller approach.

Keywords: GNC, active removal of space debris, AI controllers, MatLabSimulink

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Authors: Xiyue Wen

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With the rapid development of the city, old communities in the city are facing a series of problems. On one hand, aging facilities, obsolete spatial patterns, aging populations arouse in the aging of the community. On the other hand, public space is reduced and is taking up by cars parking or facilities setting, which lead to the collapse of traditional life in the old communities. That is to say, modern amenities haven’t helped to reform the old community, but have leading to tedious and inefficient, when it is not accommodated in the traditional space. Exploring a way is imminent to the east the contradiction between modern living facilities and spatial patterns of traditional. We select a typical site-GeDa Community in Xi’an, built in 70-80s，and carry out a concept calling 'Raising Landscape', which enables a convenient and efficient space for parking, as well as a high-quality yard for activities. In addition, the design implements low cost, simple construction, resident participation, so that it can be spread in the same texture of urban space.

Keywords: old communities, renewal strategy, raising landscape, public space, parking space

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Authors: M. Saeed, A. Shahidzadeh

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Interaction between teachers and learners requires applying a set of samples (examples) which helps to create coordination between the goals and methods. The main result and achievement and application of samples (examples) are that they can bring the teacher and learner to a shared understanding of the concept. mathematical concepts, and also one of the challenging issues in the discussion of the function is to find the collision points of functions of and, regarding that the example space of teachers is different in this issue, this paper aims to present an example space including several problems of the secondary school with the help of intuition and drawing various graphs of functions of and for more familiarity of teachers.

Keywords: inverse function, educational example, Mathematic example, example space

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Authors: U. Yerlikaya, R. T. Balkan

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In this research, a method is developed to obtain high-dimensional configuration space for path planning problems. In typical cases, the path planning problems are solved directly in the 3-dimensional (D) workspace. However, this method is inefficient in handling the robots with various geometrical and mechanical restrictions. To overcome these difficulties, path planning may be formalized and solved in a new space which is called configuration space. The number of dimensions of the configuration space comes from the degree of freedoms of the system of interest. The method can be applied in two ways. In the first way, the point clouds of all the bodies of the system and interaction of them are used. The second way is performed via using the clearance function of simulation software where the minimum distances between surfaces of bodies are simultaneously measured. A double-turret system is held in the scope of this study. The 4-D configuration space of a double-turret system is obtained in these two ways. As a result, the difference between these two methods is around 1%, depending on the density of the point cloud. The disparity between the two forms steadily decreases as the point cloud density increases. At the end of the study, in order to verify 4-D configuration space obtained, 4-D path planning problem was realized as 2-D + 2-D and a sample path planning is carried out with using A* algorithm. Then, the accuracy of the configuration space is proved using the obtained paths on the simulation model of the double-turret system.

Keywords: A* algorithm, autonomous turrets, high-dimensional C-space, manifold C-space, point clouds

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Authors: Engin Eyceyurt, Josko Zec

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The current and future cellular mobile communication networks generate enormous amounts of data. Networks have become extremely complex with extensive space of parameters, features and counters. These networks are unmanageable with legacy methods and an enhanced design and optimization approach is necessary that is increasingly reliant on machine learning. This paper proposes that machine learning as a viable approach for uplink throughput prediction. LTE radio metric, such as Reference Signal Received Power (RSRP), Reference Signal Received Quality (RSRQ), and Signal to Noise Ratio (SNR) are used to train models to estimate expected uplink throughput. The prediction accuracy with high determination coefficient of 91.2% is obtained from measurements collected with a simple smartphone application.

Keywords: drive test, LTE, machine learning, uplink throughput prediction

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Authors: Nicholas Freer

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Rhythmic complexity in progressive metal is a developing area of analysis, particularly the interpretation of hyper-metric time spans as hierarchically significant rhythmic units of compositional organisation (Pieslak 2007, Charupakorn 2012, Capuzzo 2018, Calder 2018, Lucas 2018, Hannan 2020). This paper adds to this developing area by considering the relationships between the concepts of tactus, metric imposition, polymeter and rhythmic parallax in the Meshuggah composition “Do Not Look Down”. By considering an architectonic rhythmic framework within “Do Not Look Down” as the controlling organisation mechanism, an exploration of the interaction between distinct rhythmic layers and the composition’s formal segmentation and harmony (as riffs), reveals a pervasive structural misalignment between these elements. By exhibiting how Meshuggah’s manipulations of rhythmic complexities deliberately blur structural boundaries, creating misalignments in a flat approach to temporal partitioning (Nieto 2014), rhythmic characteristics of Meshuggah and the genre of Djent are exposed.

Keywords: hypermeter, rhythmic parallax, meshuggah, temporal partitioning

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Authors: Muhammad Feteha

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The socio-political Middle East scene has radically changed over the last decade, and one major contributor to this change was the Egyptian revolution of 2011. The massive impact of this revolution that originally started as a small protest in the Tahrir square has attracted more scholars to study the public space in Egypt, where it has become a necessity in order to understand and improve the socio-political conditions. The status of public space in Egypt has been deteriorating due to many reasons, including privatization and neglect. This paper studies one of the major problems of the contemporary public space in Cairo, which is the lack of identity. This takes place through a comparative analysis between selected case studies from both medieval and contemporary Cairo. The theoretical framework upon which the analysis is based views public space as a ‘container of social action’ and a ‘product of spatial practice’. Through the ‘deciphering of space’, differences in the socio-political role, symbolism, and identity of public spaces between both eras are shown. The paper aims to extract some lessons from public space in medieval Cairo, which was truly the ‘centerpiece of the public realm’ and a ‘fundamental expressions’ of the unique trans-dynastic architectural identity of Cairo. In addition, it suggests some strategies to revive the Cairene identity of public space instead of constructing new ones to be only ‘utilitarian spaces used for circulation’ and lack any identity.

Keywords: architectural identity, Cairene public space, Islamic architectural history, production of space

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Authors: U. M. Swamy

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A compact Hausdorff and totally disconnected topological space are known as Boolean space in view of the stone duality between Boolean algebras and such topological spaces. A sheaf over X is a triple (S, p, X) where S and X are topological spaces and p is a local homeomorphism of S onto X (that is, for each element s in S, there exist open sets U and G containing s and p(s) in S and X respectively such that the restriction of p to U is a homeomorphism of U onto G). Here we mainly concern on sheaves over Boolean spaces. From a given sheaf over a Boolean space, we obtain an algebraic structure in such a way that there is a one-to-one correspondence between these algebraic structures and sheaves over Boolean spaces.

Keywords: Boolean algebra, Boolean space, sheaf, stone duality

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Authors: Dong Wei, Wu Jinxiu

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As China's urban construction enters a new phase of 'stock optimization,' the key point of urban development has shifted to the development and reuse of existing public space. However, cities still face a series of challenges, such as the shortage of space quantity and insufficient space quality, which indirectly affect urban vitality. A review of the vitality of urban public space will significantly contribute to optimizing the quality of the urban built environment. It firstly analyses the research hotspots of urban vitality at home and abroad, based on a semi-systematic literature review. Then this paper summarizes the theoretical definitions of the vitality of urban public space and sorts out the influencing factors from the perspectives of society, environment, and users. Lastly, the paper concludes with the mainstream quantitative and evaluation methods, such as linear evaluation and integrated evaluation. This paper renders a multi-theoretical perspective to understand the characteristics and evaluation system of the vitality of public space, which helps to acknowledge the dynamic relationship between users, urban environment, and vitality. It also looks forward to providing optimal design strategies for constructing a vigorous public space in future cities.

Keywords: public space, quantification of vitality, spatial vitality, urban vitality

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Authors: Patik Joslin Kenfack, Polyakov Vladimir Mikhailovich

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Machine Learning (ML) systems are trained using human generated data that could be biased by implicitly containing racist, sexist, or discriminating data. ML models learn those biases or even amplify them. Recent research in work on has begun to consider issues of fairness. The concept of fairness is extended to recommendation. A recommender system will be considered fair if it doesn’t under rank items of protected group (gender, race, demographic...). Several metrics for evaluating fairness concerns in recommendation systems have been proposed, which take pairs of items as ‘instances’ in fairness evaluation. It doesn’t take in account the fact that the fairness should be evaluated across a list of items. The paper explores a probabilistic approach that generalize pairwise metric by using a list k (listwise) of items as ‘instances’ in fairness evaluation, parametrized by k. We also explore new regularization method based on this metric to improve fairness ranking during model training.

Keywords: Fairness, Recommender System, Ranking, Listwise Approach

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Authors: Semeh Ben Salem, Sami Naouali, Moetez Sallami

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The increasing amount of collected data has limited the performance of the current analyzing algorithms. Thus, developing new cost-effective algorithms in terms of complexity, scalability, and accuracy raised significant interests. In this paper, a modified effective k-means based algorithm is developed and experimented. The new algorithm aims to reduce the computational load without significantly affecting the quality of the clusterings. The algorithm uses the City Block distance and a new stop criterion to guarantee the convergence. Conducted experiments on a real data set show its high performance when compared with the original k-means version.

Keywords: pattern recognition, global terrorism database, Manhattan distance, k-means clustering, terrorism data analysis

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Authors: Jonathan R. Olsen, Natalie Nicholls, Jenna Panter, Hannah Burnett, Michael Tornow, Richard Mitchell

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The 20-minute neighborhood is a policy priority for governments worldwide and a key feature of this policy is providing access to natural space within 800 meters of home. The study aims were to (1) examine the association between distance to nearest natural space and frequent use over time and (2) examine whether frequent use and changes in use were patterned by income and housing tenure over time. Bi-annual Scottish Household Survey data were obtained for 2013 to 2019 (n:42128 aged 16+). Adults were asked the walking distance to their nearest natural space, the frequency of visits to this space and their housing tenure, as well as age, sex and income. We examined the association between distance from home of nearest natural space, housing tenure, and the likelihood of frequent natural space use (visited once a week or more). Two-way interaction terms were further applied to explore variation in the association between tenure and frequent natural space use over time. We found that 87% of respondents lived within 10 minute walk of a natural space, meeting the policy specification for a 20-minute neighbourhood. Greater proximity to natural space was associated with increased use; individuals living a 6 to 10 minute walk and over 10 minute walk were respectively 53% and 78% less likely to report frequent natural space use than those living within a 5 minute walk. Housing tenure was an important predictor of frequent natural space use; private renters and homeowners were more likely to report frequent natural space use than social renters. Our findings provide evidence that proximity to natural space is a strong predictor of frequent use. Our study provides important evidence that time-based access measures alone do not consider deep-rooted socioeconomic variation in use of Natural space. Policy makers should ensure a nuanced lens is applied to operationalising and monitoring the 20-minute neighbourhood to safeguard against exacerbating existing inequalities.

Keywords: natural space, housing, inequalities, 20-minute neighbourhood, urban design

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Authors: Khodijah Salimah

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Game Space Program is the program design and development game for therapy the autistic child who had problems with sensory processing and integration. This program is the basic for game space to expand treatment therapy in many areas to help autistic's ability to think through visual perception. This problem can be treated with sensory experience and integration with visual experience to learn how to think and how to learn with visual perception. This perception can be accommodated through an understanding of visual thinking received from sensory exist in game space as virtual healthcare facilities are adjusted based on the sensory needs of children with autism. This paper aims to analyze the potential of virtual visual thinking for treatment autism with the game space program.

Keywords: autism, game space program, sensory, virtual healthcare facilities, visual perception

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Authors: Wei Yan, Wei Dong

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Facing the understanding problem of update and preservation of urban history space under background of rapid Chinese urbanization, so at first there is a need to dig the philosophic principles of “antithesis” and “unification” which are contained in the traditional Chinese literature known as “antithesis” and do the job of planning translation by personal understanding in order to form understanding and value systems of dialectical urban history space under the foundation of “antithesis”. Then we could put forward a “context” concept for urban history space under the foregoing basis. After that, we will take the update and preservation of Ningbo Tianyi Pavilion’s historical district as an example to discuss problems related to understanding of urban history area under the basis of Chinese tradition culture, improvement of value system, construction of urban trait space and Chinese “localization” of planning theory.

Keywords: antithesis, traditional values, city renewal and conservation, the “context” of city history space

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Authors: Biswanath Gupta, Raju Kd

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Space law is the new entry in the basket of international law in the latter half of the 20th Century. In the last hundred and fifty years, courts and scholars developed a consensus that, the custom is an important source of international law. Article 38(1) (b) of the statute of the International Court of Justice recognized international custom as a source of international law. State practices and usages have a greater role to play in formulating customary international law. This paper examines those state practices which can be qualified to become international customary law. Since, 1979 (after Moon Treaty) no hard law have been developed in the area of space exploration. It tries to link between state practices and custom in space exploration and development of customary international law in space activities. The paper uses doctrinal method of legal research for examining the current questions of international law. The paper explores different international legal documents such as General Assembly Resolutions, Treaty principles, working papers of UN, cases relating to customary international law and writing of jurists relating to space law and customary international law. It is argued that, principles such as common heritage of mankind, non-military zone, sovereign equality, nuclear weapon free zone and protection of outer space environment, etc. developed state practices among the international community which can be qualified to become international customary law.

Keywords: customary international law, state practice, space law, treaty

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Authors: Neda Mozaffari

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This study represents an investigation into the poetics of space within Annie Ernaux's autobiographical work La honte, highlighting the intricate interplay among space, the individual, and society. The research aims to dissect the spatial dimension of the town Yvetot, the referential locale of the author's childhood, drawing upon the frameworks of geocriticism and geopoetics. Our analysis exposes a profound dialectical tension fundamentally predicated on the binaries of "interior/exterior" and "here/there," emphasizing how space and its occupants may reciprocally influence each other. This endeavor aspires to attribute meaning to space in Ernaux's writing in La honte and to forge a connection between spatial elements and the author's autobiographical perspective, heavily imprinted by social dynamics. Ernaux's approach fluctuates between certain binaries that segment space according to the collective perception of social hierarchy, thus unveiling the author's preoccupation with social distancing. Consequently, space transforms into a structured milieu that transfers fear and insecurity to the child, where spatial and architectural segregation further cements class divisions in terms of the language employed by its inhabitants. Ernaux's depiction of space serves both as a repository of collective memory and an instrument of social distinction, where her autobiographical perception echoes within a collective geography marked by class determinism and culture.

Keywords: geocriticism, literary study, social class, social space, spatial analysis

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Authors: Matthieu-P. Schapranow

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Recruitment of participants for clinical trials requires the screening of a big number of potential candidates, i.e. the testing for trial-specific inclusion and exclusion criteria, which is a time-consuming and complex task. Today, a significant amount of time is spent on identification of adequate trial participants as their selection may affect the overall study results. We introduce a unique patient eligibility metric, which allows systematic ranking and classification of candidates based on trial-specific filter criteria. Our web application enables real-time analysis of patient data and assessment of candidates using freely definable inclusion and exclusion criteria. As a result, the overall time required for identifying eligible candidates is tremendously reduced whilst additional degrees of freedom for evaluating the relevance of individual candidates are introduced by our contribution.

Keywords: in-memory technology, clinical trials, screening, eligibility metric, data analysis, clustering

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Authors: Kexin Chen

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As an important method of transportation to solve the demand and supply contradiction generated in the rapid urbanization process, urban rail traffic system has been rapidly developed over the past ten years in China. During the rapid development, the space of urban rail Transit has encountered many problems, such as space simplification, sensory experience dullness, and poor regional identification, etc. This paper, focus on the study of the negative space of subway station and spatial softening, by comparing and learning from foreign cases. The article sorts out cases at home and abroad, make a comparative study of the cases, analysis more diversified setting of public art, and sets forth propositions on the domestic type of public art in the space of urban rail transit for reference, then shows the relationship of the spatial attribute in the space of urban rail transit and public art form. In this foundation, it aims to characterize more diverse setting ways for public art; then suggests the three public art forms corresponding properties, such as static presenting mode, dynamic image mode, and spatial softening mode; finds out the method of urban public art to optimize negative space.

Keywords: diversification, negative space, optimization strategy, public art planning

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Authors: Dai Zhimei, Hua Chen

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The exploration of urban spatial evolution is an important part of urban development research. Therefore, the evolutionary modern Yangzhou urban spatial texture was taken as the research object, and Spatial Syntax was used as the main research tool, this paper explored Yangzhou spatial evolution law and its driving factors from the urban street network scale, district scale and street scale. The study has concluded that at the urban scale, Yangzhou urban spatial evolution is the result of a variety of causes, including physical and geographical condition, policy and planning factors, and traffic conditions, and the evolution of space also has an impact on social, economic, environmental and cultural factors. At the district and street scales, changes in space will have a profound influence on the history of the city and the activities of people. At the end of the article, the matters needing attention during the evolution of urban space were summarized.

Keywords: block, space syntax and methodology, street, urban space, Yangzhou

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Authors: Yulong Wang, Yuan Yan Tang, Cuiming Zou, Lina Yang

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This paper presents a novel sparse representation method for robust pattern classification. Generalized orthogonal matching pursuit (GOMP) is a recently proposed efficient sparse representation technique. However, GOMP adopts the mean square error (MSE) criterion and assign the same weights to all measurements, including both severely and slightly corrupted ones. To reduce the limitation, we propose an information-theoretic GOMP (ITGOMP) method by exploiting the correntropy induced metric. The results show that ITGOMP can adaptively assign small weights on severely contaminated measurements and large weights on clean ones, respectively. An ITGOMP based classifier is further developed for robust pattern classification. The experiments on public real datasets demonstrate the efficacy of the proposed approach.

Keywords: correntropy induced metric, matching pursuit, pattern classification, sparse representation

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Authors: Asmaa Sokrat, Aykut Karaman

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Public and private spaces are major components of the morphology of the city. This research aims to study the interactions between public and private domains in terms of urban space in Casablanca. The research focuses on a general vision of a socio-spatial issue. It plans to identify the public, private, and transition (semi-public, semi-private) spaces as the constituent of the urban space. Moreover, the study investigates the link between public and private spaces with the social dimensions. Additionally, the research argues that the public space is a place of social interaction; as a reflection, this interaction is the intersection between urban space and social connectedness. Besides, social interaction can be the key to distinguishing between the public and private spheres. The methodological approach of the research is based on the literature review and field study. The article is targeting a case study on the old Medina of Casablanca, from daily use of the public and private spaces, the urban tissue, and the urban space types. In conclusion, the research exhibits that a public space could influence the privacy of the residents of a local urban area; thus, this privacy is inverted on the social interaction. This social interaction is the link between the urban space and social connectedness. Hence, this equation affects the typology of the private space.

Keywords: public sphere, private sphere, social connectedness, old Medina of Casablanca

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Authors: Usamah Al-Ali

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We explore the effect of expanding space on the exoticity of the matter supporting a traversable Lorentzian wormhole of zero radial tide whose line element is given by ds2 = dt^2 − a^2(t)[ dr^2/(1 − kr2 −b(r)/r)+ r2dΩ^2 in the context of General Relativity. This task is achieved by deriving the Einstein field equations for anisotropic matter field corresponding to the considered cosmological wormhole metric and performing a classification of their solutions on the basis of a variable equations of state (EoS) of the form p = ω(r)ρ. Explicit forms of the shape function b(r) and the scale factor a(t) arising in the classification are utilized to construct the corresponding energy-momentum tensor where the energy conditions for each case is investigated. While the violation of energy conditions is inevitable in case of static wormholes, the classification we performed leads to interesting solutions in which this violation is either reduced or eliminated.

Keywords: general relativity, Einstein field equations, energy conditions, cosmological wormhole

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Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava

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This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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Authors: R. M. Kashim

Abstract:

The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: conceptual knowledge, primary school teachers, procedural knowledge, rational numbers

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