Search results for: Space flat

Authors: Sedrak Vardanyan

Abstract:

The investigation of the vibrational character of magnetic cylindrical shells placed in an axial magnetic field has important practical applications. In this work, we study the vibrational behaviour of such a cylindrical shell by making use of the so-called exact space treatment, which does not assume any hypothesis. We discuss the effects of several practically important boundary conditions on the vibrations of the described setup. We find that, for some cases of boundary conditions, e.g. clamped, simply supported or peripherally earthed, as well as for some values of the wave numbers, the vibrational frequencies of the shell are approximately zero. The theoretical and numerical exploration of this fact confirms that the vibrations are absent or attenuate very rapidly. For all the considered cases, the imaginary part of the frequencies is negative, which implies stability for the vibrational process.

Keywords: Free vibrations, magnetic cylindrical shells, exact space treatment, bending vibrational frequencies.

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Authors: A.K.M. Khaled Ahsan Talukder, Taibun Nessa, Kaushik Roy

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The weight constrained shortest path problem (WCSPP) is one of most several known basic problems in combinatorial optimization. Because of its importance in many areas of applications such as computer science, engineering and operations research, many researchers have extensively studied the WCSPP. This paper mainly concentrates on the reduction of total search space for finding WCSP using some existing Genetic Algorithm (GA). For this purpose, some controlled schemes of genetic operators are adopted on list chromosome representation. This approach gives a near optimum solution with smaller elapsed generation than classical GA technique. From further analysis on the matter, a new generalized schema theorem is also developed from the philosophy of Holland-s theorem.

Keywords: Genetic Algorithm, Evolutionary Optimization, Multi Objective Optimization, Non-linear Schema Theorem, WCSPP.

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Authors: Alessandro Bevilacqua, Alessandro Gherardi, Filippo Piccinini

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Image mosaicing is a technique that permits to enlarge the field of view of a camera. For instance, it is employed to achieve panoramas with common cameras or even in scientific applications, to achieve the image of a whole culture in microscopical imaging. Usually, a mosaic of cell cultures is achieved through using automated microscopes. However, this is often performed in batch, through CPU intensive minimization algorithms. In addition, live stem cells are studied in phase contrast, showing a low contrast that cannot be improved further. We present a method to study the flat field from live stem cells images even in case of 100% confluence, this permitting to build accurate mosaics on-line using high performance algorithms.

Keywords: Microscopy, image mosaicing, stem cells.

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Authors: Sameerah Jamal, Abdul Hamid Kara, Ashfaque H. Bokhari

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Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.

Keywords: Bianchi metric, conservation laws, Milne metric, symmetries.

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Authors: Gong Jie, Yu Qianxu, Liu Min, Shan Weiwei

Abstract:

The design of methods of the 20 K large dimension cold shield used for infrared radiation demarcating in space environment simulation test were introduced in this paper. The cold shield were cooled by five G-M cryocoolers , and the dimension of the cold shield is the largest in our country.Cold shield installation and distribution and compensator for contraction on cooling were introduced detailedly. The temperature distribution and cool-down time of cold shield surface were also calculated and analysed in this paper. The design of cold shield resolves the difficulty of compensator for contraction on cooling successfully. Test results show that the actual technical performance indicators of cold shield met and exceeded the design requirements.

Keywords: cold shield, G-M cryocooler，infrared radiometer demarcating, satellite, space environment simulation equipments

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Authors: Baki Koyuncu, Mehmet Güzel

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The kinematics of manipulators is a central problem in the automatic control of robot manipulators. Theoretical background for the analysis of the 5 Dof Lynx-6 educational Robot Arm kinematics is presented in this paper. The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. The Denavit-Harbenterg (D-H) model of representation is used to model robot links and joints in this study. Both forward and inverse kinematics solutions for this educational manipulator are presented, An effective method is suggested to decrease multiple solutions in inverse kinematics. A visual software package, named MSG, is also developed for testing Motional Characteristics of the Lynx-6 Robot arm. The kinematics solutions of the software package were found to be identical with the robot arm-s physical motional behaviors.

Keywords: Lynx 6, robot arm, forward kinematics, inverse kinematics, software, DH parameters, 5 DOF , SSC-32 , simulator.

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Authors: Ferenc Kovács, Gábor Hosszú

Abstract:

The paper presents an advanced control system for tennis ball throwing machines to improve their accuracy according to the ball impact points. A further advantage of the system is the much easier calibration process involving the intelligent solution of the automatic adjustment of the stroking parameters according to the ball elasticity, the self-calibration, the use of the safety margin at very flat strokes and the possibility to placing the machine to any position of the half court. The system applies mathematical methods to determine the exact ball trajectories and special approximating processes to access all points on the aimed half court.

Keywords: Control system, robot programming, robot control, sports equipment, throwing machine.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Surinder Singh, Adish Bindal

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The effects of the pumping wavelength and their power on the gain flattening of a fiber Raman amplifier (FRA) are investigated. The multi-wavelength pumping scheme is utilized to achieve gain flatness in FRA. It is proposed that gain flatness becomes better with increase in number of pumping wavelengths applied. We have achieved flat gain with 0.27 dB fluctuation in a spectral range of 1475-1600 nm for a Raman fiber length of 10 km by using six pumps with wavelengths with in the 1385-1495 nm interval. The effect of multi-wavelength pumping scheme on gain saturation in FRA is also studied. It is proposed that gain saturation condition gets improved by using this scheme and this scheme is more useful for higher spans of Raman fiber length.

Keywords: FRA, gain, pumping, WDM.

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Authors: Jun-Yong Lee, Hyoung-Gook Kim

Abstract:

In this paper, we propose a smart music player that combines the musical genre classification and the spatial audio processing. The musical genre is classified based on content analysis of the musical segment detected from the audio stream. In parallel with the classification, the spatial audio quality is achieved by adding an artificial reverberation in a virtual acoustic space to the input mono sound. Thereafter, the spatial sound is boosted with the given frequency gains based on the musical genre when played back. Experiments measured the accuracy of detecting the musical segment from the audio stream and its musical genre classification. A listening test was performed based on the virtual acoustic space based spatial audio processing.

Keywords: Automatic equalization, genre classification, music segment detection, spatial audio processing.

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Authors: Vatasta Koul, Ayush Gupta, Vaibhav Sharma, Rajesh Yadav

Abstract:

Today we are unmarking the secrets of the universe by exploring different stars and planets and most of the space exploration is done by unmanned space robots. In addition to our planet Earth, there are pieces of evidence that show other astronomical objects in our solar system such as Venus, Mars, Saturn’s moon Titan and Uranus support the flight of fixed wing air vehicles. In this paper, we take forward the concept of presence of large rounded tubercles along the leading edge of a wing and use it as a passive flow control device that will help in improving its aerodynamic performance and maneuverability. Furthermore, in this research, aerodynamic measurements and performance analysis of wavy leading tubercles on the fixed wings at 5-degree angle of attack are carried out after determination of the flow conditions on the selected planetary bodies. Wavelength and amplitude for the sinusoidal modifications on the leading edge are analyzed and simulations are carried out for three-dimensional NACA 0012 airfoil maintaining unity AR (Aspect Ratio). Tubercles have consistently demonstrated the ability to delay and decrease the severity of stall as per the studies were done in the Earth’s atmosphere. Implementing the same design on the leading edges of Micro-Air Vehicles (MAVs) and UAVs could make these aircrafts more stable over a greater range of angles of attack in different planetary environments of our solar system.

Keywords: Amplitude, NACA0012, tubercles, unmanned space robots.

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Authors: L. Pina, M. Mika, R. Havlikova, M. Landova, L. Sveda, R. Hudec, V. Marsikova, A. Inneman

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We developed a non-contact method for the in-situ monitoring of the thermal forming of glass and Si foils to optimize the manufacture of mirrors for high-resolution space x-ray telescopes. Their construction requires precise and light-weight segmented optics with angular resolution better than 5 arcsec. We used 75x25 mm Desag D263 glass foils 0.75 mm thick and 0.6 mm thick Si foils. The glass foils were shaped by free slumping on a frame at viscosities in the range of 109.3-1012 dPa·s, the Si foils by forced slumping above 1000°C. Using a Nikon D80 digital camera, we took snapshots of a foil-s shape every 5 min during its isothermal heat treatment. The obtained results we can use for computer simulations. By comparing the measured and simulated data, we can more precisely define material properties of the foils and optimize the forming technology.

Keywords: Glass, in-situ monitoring, silicone, thermal forming, x-ray telescope

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Authors: Hyeon-Seong Kim, Sang-Mi Park, Seul-Gi Kim, Seon-Ju Han, Leen-Seok Kang

Abstract:

The use of BIM, including 4D CAD system, in a construction project is gradually increasing. Since the building construction works repeatedly in the vertical space, it is relatively easy to confirm the interference effect when applying the BIM, but the interference effect for the civil engineering project is relatively small because the civil works perform non-repetitive processes in the horizontal space. For this reason, it is desirable to apply BIM to the construction phase when applying BIM to the civil engineering project, and the most active BIM tool applied to the construction phase is the 4D CAD function for the schedule management. This paper proposes the application procedure of BIM by the construction phase of civil engineering project and a linear 4D CAD construction methodology suitable for the civil engineering project in which linear work is performed.

Keywords: BIM, 4D CAD, Horizontal work area, Linear simulation, VR.

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Authors: Werner Sandmann, Verena Wolf

Abstract:

Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.

Keywords: Computational Modeling, Biological Networks, Stochastic Models, Markov Chains, Transition Class Models.

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Authors: Pavel Y. Tabakov, Kevin Duffy

Abstract:

The present study presents a new approach to automatic data clustering and classification problems in large and complex databases and, at the same time, derives specific types of explicit rules describing each cluster. The method works well in both sparse and dense multidimensional data spaces. The members of the data space can be of the same nature or represent different classes. A number of N-dimensional ellipsoids are used for enclosing the data clouds. Due to the geometry of an ellipsoid and its free rotation in space the detection of clusters becomes very efficient. The method is based on genetic algorithms that are used for the optimization of location, orientation and geometric characteristics of the hyper-ellipsoids. The proposed approach can serve as a basis for the development of general knowledge systems for discovering hidden knowledge and unexpected patterns and rules in various large databases.

Keywords: Classification, clustering, data minig, genetic algorithms.

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Authors: K. Al-Heuseen, M. R. Hashim

Abstract:

The current-voltage (I-V) characteristics of Pd/n-GaN Schottky barrier were studied at temperatures over room temperature (300-470K). The values of ideality factor (n), zero-bias barrier height (φB0), flat barrier height (φBF) and series resistance (Rs) obtained from I-V-T measurements were found to be strongly temperature dependent while (φBo) increase, (n), (φBF) and (Rs) decrease with increasing temperature. The apparent Richardson constant was found to be 2.1x10-9 Acm-2K-2 and mean barrier height of 0.19 eV. After barrier height inhomogeneities correction, by assuming a Gaussian distribution (GD) of the barrier heights, the Richardson constant and the mean barrier height were obtained as 23 Acm-2K-2 and 1.78eV, respectively. The corrected Richardson constant was very closer to theoretical value of 26 Acm-2K-2. 

Keywords: Electrical properties, Gaussian distribution, Pd-GaN Schottky diodes, thermionic emission.

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Authors: M. Mika, L. Pina, M. Landova, L. Sveda, R. Havlikova, V. Marsikova, R. Hudec, A. Inneman

Abstract:

Future astronomical projects on large space x-ray imaging telescopes require novel substrates and technologies for the construction of their reflecting mirrors. The mirrors must be lightweight and precisely shaped to achieve large collecting area with high angular resolution. The new materials and technologies must be cost-effective. Currently, the most promising materials are glass or silicon foils. We focused on precise shaping these foils by thermal forming process. We studied free and forced slumping in the temperature region of hot plastic deformation and compared the shapes obtained by the different slumping processes. We measured the shapes and the surface quality of the foils. In the experiments, we varied both heat-treatment temperature and time following our experiment design. The obtained data and relations we can use for modeling and optimizing the thermal forming procedure.

Keywords: Glass, silicon, thermal forming, x-ray

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Authors: V. Kahya, A. Birinci, R. Erdol

Abstract:

A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.

Keywords: Frictionless contact, Initial separation, Orthotropicmaterial, Singular integral equation.

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Authors: Viet-Hung Truong, Seung-Eock Kim

Abstract:

This paper presents a robust software package for practical advanced analysis of space steel framed structures. The pre- and post-processors of the presented software package are coded in the C++ programming language while the solver is written by using the FORTRAN programming language. A user-friendly graphical interface of the presented software is developed to facilitate the modeling process and result interpretation of the problem. The solver employs the stability functions for capturing the second-order effects to minimize modeling and computational time. Both the plastic-hinge and fiber-hinge beam-column elements are available in the presented software. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations.

Keywords: Advanced analysis, beam-column, fiber-hinge, plastic hinge, steel frame.

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

Abstract:

In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Consistency, Crank-Nicolson scheme, Gerschgorin circle, Lax-Richtmyer theorem, Peclet number, stability.

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Authors: Khine Phyu, Aung Myint Aye

Abstract:

This paper presents results of measurements campaign carried out at a carrier frequency of 24GHz with the help of TPLINK router in indoor line-of-sight (LOS) scenarios. Firstly, the radio wave propagation strategies are analyzed in some rooms with router of point to point Ad hoc network. Then floor attenuation is defined for 3 floors in experimental region. The free space model and dual slope models are modified by considering the influence of corridor conditions on each floor. Using these models, indoor signal attenuation can be estimated in modeling of indoor radio wave propagation. These results and modified models can also be used in planning the networks of future personal communications services.

Keywords: radio wave signal analyzing, LOS radio wavepropagation, indoor radio wave propagation, free space model, tworay model and indoor attenuation.

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Authors: Veronika Antoniou, Rene Carraz, Yiorgos Hadjichristou

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The Green Urban Lab took the form of public installations that were placed at various locations in four cities in Cyprus. These installations - through which a series of events, activities, workshops and research took place - were the main tools in regenerating a series of urban public spaces in Cyprus. The purpose of this project was to identify issues and opportunities related to public space and to offer guidelines on how design and participatory democracy improvements could strengthen civil society, while raising the quality of the urban public scene. Giant inflatable structures were injected in important urban fragments in order to accommodate series of events. The design and playful installation generated a wide community engagement. The fluid presence of the installations acted as a catalyst for social interaction. They were accessed and viewed effortlessly and surprisingly, creating opportunities to rediscover public spaces.

Keywords: Bottom-up initiatives, creativity, public space, social innovation, urban environments.

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Authors: Ishtiaq A. Chaudhry, Zia R. Tahir

Abstract:

Experimental investigation has been carried out towards understanding the complex fluid dynamics involved in the interaction of vortical structures with zero pressure gradient boundary layer. A laminar boundary layer is produced on the flat plate placed in the water flume and the synthetic jet actuator is deployed on top of the plate at a definite distance from the leading edge. The synthetic jet actuator has been designed in such a way that the to and fro motion of the diaphragm is maneuvered at will by varying the operating parameters to produce the typical streamwise vortical structures namely hairpin and tilted vortices. PIV measurements are made on the streamwise plane normal to the plate to evaluate their interaction with the near wall fluid.

Keywords: Boundary layer, synthetic jet actuator, flow separation control, vortical structures.

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Authors: Petru V. Notingher, Stefan Busoi, Laurentiu M. Dumitran, Cristina Stancu, Gabriel Tanasescu, Emanuel Balescu

Abstract:

Degradation of polymeric insulation systems of electrical equipments increases the space charge density and the concentration of electrical dipoles. By consequence, the maximum values and the slopes of absorption/resorption (A/R) currents can change with insulation systems ageing. In this paper, an analysis of the nature of the A/R currents and the importance of their components, especially the polarization current and the current given by the space charge, is presented. The experimental study concerns the A/R currents measurements of plane samples (made from CALMICAGLAS tapes), virgin and thermally accelerated aged. The obtained results show that the ageing process produces an increase of the values and a decrease of shapes of the A/R currents. Finally, the possibility of estimating insulations ageing state and lifetime from A/R currents measurements is discussed.

Keywords: Insulation Systems, Absorption/Resorption Currents, Ageing, Lifetime.

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Authors: Romuald Synak, Wlodzimierz Lipinski, Marcin Pawelczak

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An area-integrating method that uses the technique of total integrated light scatter for evaluating the root mean square height of the surface Sq has been presented in the paper. It is based on the measurement of the scatter power using a flat photodiode integrator rather than an optical sphere or a hemisphere. By this means, one can obtain much less expensive and smaller instruments than traditional ones. Thanks to this, they could find their application for surface control purposes, particularly in small and medium size enterprises. A description of the functioning of the measuring unit as well as the impact caused by different factors on its properties is presented first. Next, results of measurements of the Sq values performed for optical, silicon and metal samples have been shown. It has been also proven that they are in a good agreement with the results obtained using the Ulbricht sphere instrument.

Keywords: ISO 25178 Standard, scatterometry, surface metrology, surface roughness

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Authors: Hossein Mirzaee, Farhad Besharati

Abstract:

Solar sunspot rotation, latitudinal bands are studied based on intelligent computation methods. A combination of image fusion method with together tree decomposition is used to obtain quantitative values about the latitudes of trajectories on sun surface that sunspots rotate around them. Daily solar images taken with SOlar and Heliospheric (SOHO) satellite are fused for each month separately .The result of fused image is decomposed with Quad Tree decomposition method in order to achieve the precise information about latitudes of sunspot trajectories. Such analysis is useful for gathering information about the regions on sun surface and coordinates in space that is more expose to solar geomagnetic storms, tremendous flares and hot plasma gases permeate interplanetary space and help human to serve their technical systems. Here sunspot images in September, November and October in 2001 are used for studying the magnetic behavior of sun.

Keywords: Quad tree decomposition, sunspot image.

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Authors: Yanqun Li, Hong Geng

Abstract:

The occurrence of Wenchuan earthquake in 2008 has led to severe damage to the rural areas of Chengdu city, such as the rupture of the social network, the stagnation of economic production and the rupture of living space. The post-disaster reconstruction has become a sustainable issue. As an important link to maintain the order of rural social development, social network should be an important content of post-disaster reconstruction. Therefore, this paper takes rural reconstruction communities in earthquake-stricken areas of Chengdu as the research object and adopts sociological research methods such as field survey, observation and interview to try to understand the transformation of rural social relations network under the influence of earthquake and its impact on rural space. It has found that rural societies under the earthquake generally experienced three phases: the break of stable social relations, the transition of temporary non-normal state, and the reorganization of social networks. The connotation of phased rural social relations also changed accordingly: turn to a new division of labor on the social orientation, turn to a capital flow and redistribution in new production mode on the capital orientation, and turn to relative decentralization after concentration on the spatial dimension. Along with such changes, rural areas have emerged some social issues such as the alienation of competition in the new industry division, the low social connection, the significant redistribution of capital, and the lack of public space. Based on a comprehensive review of these issues, this paper proposes the corresponding response mechanism. First of all, a reasonable division of labor should be established within the villages to realize diversified commodity supply. Secondly, the villages should adjust the industrial type to promote the equitable participation of capital allocation groups. Finally, external public spaces should be added to strengthen the field of social interaction within the communities.

Keywords: Social relations, social support networks, industrial division, capital allocation, public space.

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Authors: Francesco Caputo, Giuseppe Lamanna, Alessandro Soprano

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This work is focused on the numerical prediction of the fracture resistance of a flat stiffened panel made of the aluminium alloy 2024 T3 under a monotonic traction condition. The performed numerical simulations have been based on the micromechanical Gurson-Tvergaard (GT) model for ductile damage. The applicability of the GT model to this kind of structural problems has been studied and assessed by comparing numerical results, obtained by using the WARP 3D finite element code, with experimental data available in literature. In the sequel a home-made procedure is presented, which aims to increase the residual strength of a cracked stiffened aluminum panel and which is based on the stochastic design improvement (SDI) technique; a whole application example is then given to illustrate the said technique.

Keywords: Residual strength, R-Curve, Gurson model, SDI.

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Authors: H. H. Huynh, J. Meunier, J.Sequeira, M.Daniel

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In this paper, the detection and tracking of face, mouth, hands and medication bottles in the context of medication intake monitoring with a camera is presented. This is aimed at recognizing medication intake for elderly in their home setting to avoid an inappropriate use. Background subtraction is used to isolate moving objects, and then, skin and bottle segmentations are done in the RGB normalized color space. We use a minimum displacement distance criterion to track skin color regions and the R/G ratio to detect the mouth. The color-labeled medication bottles are simply tracked based on the color space distance to their mean color vector. For the recognition of medication intake, we propose a three-level hierarchal approach, which uses activity-patterns to recognize the normal medication intake activity. The proposed method was tested with three persons, with different medication intake scenarios, and gave an overall precision of over 98%.

Keywords: Activity recognition, background subtraction, tracking, medication intake, video surveillance

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: Optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, Implementation, MATLAB.

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