Search results for: Mathematical morphology.

Authors: E. K.Appiah, G. M'boungui, A. A. Jimoh, J. L. Munda, A.S.O. Ogunjuyigbe

Abstract:

The operational behavior of a six-phase squirrel cage induction machine with faulted stator terminals is presented in this paper. The study is carried out using the derived mathematical model of the machine in the arbitrary reference frame. Tests are conducted on a 1 kW experimental machine. Steady-state and dynamic performance are analyzed for the machine unloaded and loaded conditions. The results shows that with one of the stator phases experiencing either an open- circuit or short circuit fault the machine still produces starting torque, albeit the running performance is significantly derated.

Keywords: Performance, fault conditions, six-phase induction machine.

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Authors: Wei Dong, Guo-Ying Gu, Xiangyang Zhu, Han Ding

Abstract:

This paper presents preliminary results on modeling and control of a quadrotor UAV. With aerodynamic concepts, a mathematical model is firstly proposed to describe the dynamics of the quadrotor UAV. Parameters of this model are identified by experiments with Matlab Identify Toolbox. A group of PID controllers are then designed based on the developed model. To verify the developed model and controllers, simulations and experiments for altitude control, position control and trajectory tracking are carried out. The results show that the quadrotor UAV well follows the referenced commands, which clearly demonstrates the effectiveness of the proposed approach.

Keywords: Quadrotor UAV, Modeling, Control, Aerodynamics, System Identification.

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Authors: Débora N. Zambrano, Marina O. Gosatti, Leandro M. Dufou, Daniel A. Serrano, M. Mónica Guraya, Soledad Perez-Catán

Abstract:

Nanoporous g-Al₂O₃ samples were synthesized via a sol-gel technique, introducing changes in the Yoldas´ method. The aim of the work was to achieve an effective control of the nanostructure properties and morphology of the final g-Al₂O₃. The influence of the reagent temperature during the hydrolysis was evaluated in case of water at 5 ºC and 98 ºC, and alkoxide at -18 ºC and room temperature. Sol-gel transitions were performed at 120 ºC and room temperature. All g-Al₂O₃ samples were characterized by X-ray diffraction, nitrogen adsorption and thermal analysis. Our results showed that temperature of both water and alkoxide has not much influence on the nanostructure of the final g-Al₂O₃, thus giving a structure very similar to that of samples obtained by the reference method as long as the reaction temperature above 75 ºC is reached soon enough. XRD characterization showed diffraction patterns corresponding to g-Al₂O₃ for all samples. Also BET specific area values (253-280 m²/g) were similar to those obtained by Yoldas’s original method. The temperature of the sol-gel transition does not affect the resulting sample structure, and crystalline boehmite particles were identified in all dried gels. We analyzed the reproducibility of the samples’ structure by preparing different samples under identical conditions; we found that performing the sol-gel transition at 120 ºC favors the production of more reproducible samples and also reduces significantly the time of the sol-gel reaction.

Keywords: Nanostructure alumina, boehmite, sol-gel technique, N2 adsorption/desorption isotherm, pore size distribution, BET area.

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Authors: Wah Wah Aung, Cho Cho San

Abstract:

The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.

Keywords: boundary conditions, conservation laws, finite difference Schemes, traffic flow.

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Authors: R. Kongnuy, P. Pongsumpun

Abstract:

Dengue, a disease found in most tropical and subtropical areas of the world. It has become the most common arboviral disease of humans. This disease is caused by any of four serotypes of dengue virus (DEN1-DEN4). In many endemic countries, the average age of getting dengue infection is shifting upwards, dengue in pregnancy and infancy are likely to be encountered more frequently. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the pregnant, infant human and the vector populations. The stability of each equilibrium point is given. The epidemic dynamic is discussed. Moreover, the numerical results are shown for difference values of dengue antibody.

Keywords: Dengue antibody, infant, pregnant human, mathematical model.

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Authors: Hassan E. A. Ibrahim, Mohamed F. Serag

Abstract:

In this paper, Novel method, Particle Swarm Optimization (PSO) algorithm, based technique is proposed to estimate and analyze the steady state performance of self-excited induction generator (SEIG). In this novel method the tedious job of deriving the complex coefficients of a polynomial equation and solving it, as in previous methods, is not required. By comparing the simulation results obtained by the proposed method with those obtained by the well known mathematical methods, a good agreement between these results is obtained. The comparison validates the effectiveness of the proposed technique.

Keywords: Evolution theory, MATLAB, optimization, PSO, SEIG.

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Authors: Idil Kanter Otcu

Abstract:

Nowadays, due to the growing problems of energy supply and the drastic reduction of natural non-renewable resources, the development of new applications in the energy sector and steps towards greater efficiency in energy consumption are required. Since buildings account for a large share of energy consumption, increasing the structural density of buildings causes an increase in energy consumption. This increase in energy consumption means that energy efficiency approaches to building design and the integration of new systems using emerging technologies become necessary in order to curb this consumption. As new systems for productive usage of generated energy are developed, buildings that require less energy to operate, with rational use of resources, need to be developed. One solution for reducing the energy requirements of buildings is through landscape planning, design and application. Requirements such as heating, cooling and lighting can be met with lower energy consumption through planting design, which can help to achieve more efficient and rational use of resources. Within this context, rather than a planting design which considers only the ecological and aesthetic features of plants, these considerations should also extend to spatial organization whereby the relationship between the site and open spaces in the context of climatic elements and planting designs are taken into account. In this way, the planting design can serve an additional purpose. In this study, a landscape design which takes into consideration location, local climate morphology and solar angle will be illustrated on a sample building project.

Keywords: Energy efficiency, landscape design, plant design, xeriscape landscape.

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Authors: Roengruen P., Tipsuwanporn V., Puawade P., Numsomran A.

Abstract:

Smith Predictor control is theoretically a good solution to the problem of controlling the time delay systems. However, it seldom gets use because it is almost impossible to find out a precise mathematical model of the practical system and very sensitive to uncertain system with variable time-delay. In this paper is concerned with a design method of smith predictor for temperature control system by Coefficient Diagram Method (CDM). The simulation results show that the control system with smith predictor design by CDM is stable and robust whilst giving the desired time domain system performance.

Keywords: CDM, Smith Predictor, temperature process

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Authors: Xun Ge, Jinjin Li, Ying Ge

Abstract:

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

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

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Authors: Noor Zuhaira Abd Aziz, Rahmah Mohamed, Mohd Muizz Fahimi M.

Abstract:

Rice husk and kenaf filled with calcium carbonate (CaCO3) and high density polyethylene (HDPE) composite were prepared separately using twin-screw extruder at 50rpm. Different filler loading up to 30 parts of rice husk particulate and kenaf fiber were mixed with the fixed 30% amount of CaCO3 mineral filler to produce rice husk/CaCO3/HDPE and kenaf/CaCO3/HDPE hybrid composites. In this study, the effects of natural fiber for both rice husk and kenaf in CaCO3/HDPE composite on physical, mechanical and morphology properties were investigated. Field Emission Scanning Microscope (FeSEM) was used to investigate the impact fracture surfaces of the hybrid composite. The property analyses showed that water absorption increased with the presence of kenaf and rice husk fillers. Natural fibers in composite significantly influence water absorption properties due to natural characters of fibers which contain cellulose, hemicellulose and lignin structures. The result showed that 10% of additional natural fibers into hybrid composite had caused decreased flexural strength, however additional of high natural fiber (>10%) filler loading has proved to increase its flexural strength.

Keywords: Hybrid composites, Water absorption, Mechanical properties.

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Authors: M. Ahmad, M. Gourgand, C. Caux

Abstract:

The Resource-Constrained Project Scheduling Problem (RCPSP) is concerned with single-item or small batch production where limited resources have to be allocated to dependent activities over time. Over the past few decades, a lot of work has been made with the use of optimal solution procedures for this basic problem type and its extensions. Brucker and Knust[1] discuss, how timetabling problems can be modeled as a RCPSP. Authors discuss high school timetabling and university course timetabling problem as an example. We have formulated two mathematical formulations of course timetabling problem in a new way which are the prototype of single-mode RCPSP. Our focus is to show, how course timetabling problem can be transformed into RCPSP. We solve this transformation model with genetic algorithm.

Keywords: Course Timetabling, Integer programming, Combinatorial optimizations

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Authors: Kezia Amanda Kurniadi, Emre Islamoglu, Kwangyeol Ryu

Abstract:

As there has been a recognizable transition in automotive industry from mass production to mass customization, automobile manufacturers and their suppliers have been seeking ways for more flexible and efficient processes. Eventually, modular production is currently being applied to manage the changing orders of the industry. In this paper, two different modular assembly line concepts were studied: conveyor line and box assembly line. Mathematical model for two assembly line concepts were developed and their production line efficiency were compared as a performance measure to improve their assembly line balancing.

Keywords: Line Efficiency, Box assembly line, Conventional conveyor line

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Authors: Wenbin Zhang, Hantian Wu, Jian Tang

Abstract:

An artificial neural network is a mathematical model inspired by biological neural networks. There are several kinds of neural networks and they are widely used in many areas, such as: prediction, detection, and classification. Meanwhile, in day to day life, people always have to make many difficult decisions. For example, the coach of a soccer club has to decide which offensive player to be selected to play in a certain game. This work describes a novel Neural Network using a combination of the General Regression Neural Network and the Probabilistic Neural Networks to help a soccer coach make an informed decision.

Keywords: General Regression Neural Network, Probabilistic Neural Networks, Neural function.

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Authors: Fahad Alsharari, Mohd Salmi Md Noorani

Abstract:

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, x will be in the Motzkin subshift 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, a new direct method of calculating the topological entropy of the Motzkin shift is given without any measure theoretical discussion.

Keywords: Motzkin shift, topological entropy.

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Authors: Sobir T. Navruzov

Abstract:

The problem of complex use of water resources in Central Asia by taking into consideration the sovereignty of the states and increasing demand on use of water for economic aspects are considered. Complex program with appropriate mathematical software intended for calculation of possible variants of using the Amudarya up-stream water resources according to satisfaction of incompatible requirements of the national economics in irrigation and energy generation is proposed.

Keywords: water resources, national economics, irrigation, transboundry, energy generation, optimal solution, program complex, up-stream, down-stream, compensating services.

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Authors: M. Mousavi-Daramoroudi, H. Yousefnia, F. Abbasi-Davani, S. Zolghadri

Abstract:

In this study, ¹⁷⁷Lu-DOTATOC was prepared under optimized conditions (radiochemical purity: > 99%, radionuclidic purity: > 99%). The percentage of injected dose per gram (%ID/g) was calculated for organs up to 168 h post injection. Compartmental model was applied to mathematical description of the drug behaviour in tissue at different times. The biodistribution data showed the significant excretion of the radioactivity from the kidneys. The adrenal and pancreas, as major expression sites for somatostatin receptor (SSTR), had significant uptake. A pharmacokinetic model of ¹⁷⁷Lu-DOTATOC was presented by compartmental analysis which demonstrates the behavior of the complex.

Keywords: Biodistribution, compartmental modeling, 177Lu, octreotide.

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Authors: Volodymyr Chegel

Abstract:

The computer modeling is carried out for parameter of sensitivity of optoelectronic chemical and biosensors, using phenomena of surface plasmon resonance (SPR). The physical model of SPR-sensor-s is described with (or without) of modifications of sensitive gold film surface by a dielectric layer. The variants of increasing of sensitivity for SPR-biosensors, constructed on the principle gold – dielectric – biomolecular layer are considered. Two methods of mathematical treatment of SPR-curve are compared – traditional, with estimation of sensor-s response as shift of the SPRcurve minimum and proposed, for system with dielectric layer, using calculating of the derivative in the point of SPR-curve half-width.

Keywords: Surface Plasmon Resonance, modeling, sensitivity, biosensor

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Authors: Ibrahim A. Al-Muhaisen, Mohammad N. Al Ymemeni

Abstract:

Ozone (O3) is considered as one of the most phytotoxic pollutants with deleterious effects on living and non living components of Ecosystems. It reduces growth and yield of many crops as well as alters the physiology and crop quality. The present study described series of experiments to investigate the effects of ambient O3 at different locations with different ambient levels of O3 depending on proximity to pollutant source and ranged between 17 ppb/h in control experiment to 112 ppb/h in industrial area respectively. The ambient levels in other three locations (King Saud University botanical garden, King Fahd Rd, and Almanakh Garden) were 61,61,77 ppb/h respectively. Tow legume crops species (vicia vaba L ; and Pisum sativum) differ in their phenology and sensitivity were used. The results showed a significant negative effect to ozone on morphology, number of injured leaves, growth and productivity with a difference in the degree of response depending on the plant type. Visia Faba showed sensitivity to ozone to number and leaf area and the degree of injury leaves 3, pisum sativum show higher sensitivity for the gas for degree of injury 1,The relative growth rate and seed weight, it turns out there is no significant difference between the two plants in plant height and number of seeds.

Keywords: Ozone, Legume crops, growth and production, Resistance, Riyadh city.

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Authors: J. E. Oti, J. M. Kinuthia, R. Robinson, P. Davies

Abstract:

This work reports the potential of using Palm Kernel (PK) ash and shell as a partial substitute for Portland Cement (PC) and coarse aggregate in the development of mortar and concrete. PK ash and shell are agro-waste materials from palm oil mills, the disposal of PK ash and shell is an environmental problem of concern. The PK ash has pozzolanic properties that enables it as a partial replacement for cement and also plays an important role in the strength and durability of concrete, its use in concrete will alleviate the increasing challenges of scarcity and high cost of cement. In order to investigate the PC replacement potential of PK ash, three types of PK ash were produced at varying temperature (350-750C) and they were used to replace up to 50% PC. The PK shell was used to replace up to 100% coarse aggregate in order to study its aggregate replacement potential. The testing programme included material characterisation, the determination of compressive strength, tensile splitting strength and chemical durability in aggressive sulfatebearing exposure conditions. The 90 day compressive results showed a significant strength gain (up to 26.2 N/mm2). The Portland cement and conventional coarse aggregate has significantly higher influence in the strength gain compared to the equivalent PK ash and PK shell. The chemical durability results demonstrated that after a prolonged period of exposure, significant strength losses in all the concretes were observed. This phenomenon is explained, due to lower change in concrete morphology and inhibition of reaction species and the final disruption of the aggregate cement paste matrix.

Keywords: Sustainability, Concrete, mortar, Palm kernel shell, compressive strength, consistency.

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Authors: J. Ritonja

Abstract:

The biochemical technology has been developing extremely fast since the middle of the last century. The main reason for such development represents a requirement for large production of high-quality biologically manufactured products such as pharmaceuticals, foods, and beverages. The impact of the biochemical industry on the world economy is enormous. The great importance of this industry also results in intensive development in scientific disciplines relevant to the development of biochemical technology. In addition to developments in the fields of biology and chemistry, which enable to understand complex biochemical processes, development in the field of control theory and applications is also very important. In the paper, the control for the biochemical reactor for the milk fermentation was studied. During the fermentation process, the biophysical quantities must be precisely controlled to obtain the high-quality product. To control these quantities, the bioreactor’s stirring drive and/or heating system can be used. Available commercial biochemical reactors are equipped with open loop or conventional linear closed loop control system. Due to the outstanding parameters variations and the partial nonlinearity of the biochemical process, the results obtained with these control systems are not satisfactory. To improve the fermentation process, the self-tuning adaptive control system was proposed. The use of the self-tuning adaptive control is suggested because the parameters’ variations of the studied biochemical process are very slow in most cases. To determine the linearized mathematical model of the fermentation process, the recursive least square identification method was used. Based on the obtained mathematical model the linear quadratic regulator was tuned. The parameters’ identification and the controller’s synthesis are executed on-line and adapt the controller’s parameters to the fermentation process’ dynamics during the operation. The use of the proposed combination represents the original solution for the control of the milk fermentation process. The purpose of the paper is to contribute to the progress of the control systems for the biochemical reactors. The proposed adaptive control system was tested thoroughly. From the obtained results it is obvious that the proposed adaptive control system assures much better following of the reference signal as a conventional linear control system with fixed control parameters.

Keywords: Adaptive control, biochemical reactor, linear quadratic regulator, recursive least square identification.

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Authors: Deepak Kukkar, Inderpreet Kaur, Jagtar Singh, Lalit M Bharadwaj

Abstract:

Polymeric microreactors have emerged as a new generation of carriers that hold tremendous promise in the areas of cancer therapy, controlled delivery of drugs, for removal of pollutants etc. Present work reports a simple and convenient methodology for synthesis of polystyrene and poly caprolactone microreactors. An aqueous suspension of carboxylated (1μm) polystyrene latex particles was mixed with toluene solution followed by freezing with liquid nitrogen. Freezed particles were incubated at -20°C and characterized for formation of voids on the surface of polymer microspheres by Field Emission Scanning Electron Microscope. The hollow particles were then overnight incubated at 40ºC with unfunctionalized quantum dots (QDs) in 5:1 ratio. QDs Encapsulated polystyrene microcapsules were characterized by fluorescence microscopy. Likewise Poly ε-caprolactone microreactors were prepared by micro-volcanic rupture of freeze dried microspheres synthesized using emulsification of polymer with aqueous Poly vinyl alcohol and freezed with liquid nitrogen. Microreactors were examined with Field Emission Scanning Electron Microscope for size and morphology. Current study is an attempt to create hollow polymer particles which can be employed for microencapsulation of nanoparticles and drug molecules.

Keywords: FE-SEM, Microreactors, Microvolcanic rupture, Poly (ε-caprolactone), Polystyrene

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Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we mainly analyze an automated parking system where the storage and retrieval requests are performed by a tower crane. In this parking system, the S/R crane which is located at the middle of the bottom of the cylinder parking area can rotate in both clockwise and counterclockwise and three kinds of movements can be done simultaneously. We develop some mathematical travel time models for the single command cycle under the random storage assignment using the characteristics of this system. Finally, we compare these travel models with discrete case and it is shown that these travel models display a good satisfactory performance.

Keywords: Parking system, travel time model, tower crane.

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Authors: Homa Torabizadeh, Mohaddeseh Mikani

Abstract:

Inulinase from Aspergillus niger was covalently immobilized on magnetic nanoparticles (MNPs/Fe₃O₄) covered with soy protein isolate (SPI/Fe₃O₄) functionalized by bovine serum albumin (BSA) nanoparticles. MNPs are promising enzyme carriers because they separate easily under external magnetic fields and have enhanced immobilized enzyme reusability. As MNPs aggregate simply, surface coating strategy was employed. SPI functionalized by BSA was a suitable candidate for nanomagnetite coating due to its superior biocompatibility and hydrophilicity. Fe₃O₄@SPI-BSA nanoparticles were synthesized as a novel carrier with narrow particle size distribution. Step by step fabrication monitoring of Fe₃O₄@SPI-BSA nanoparticles was performed using field emission scanning electron microscopy and dynamic light scattering. The results illustrated that nanomagnetite with the spherical morphology was well monodispersed with the diameter of about 35 nm. The average size of the SPI-BSA nanoparticles was 80 to 90 nm, and their zeta potential was around −34 mV. Finally, the mean diameter of fabricated Fe₃O₄@SPI-BSA NPs was less than 120 nm. Inulinase enzyme from Aspergillus niger was covalently immobilized through gluteraldehyde on Fe₃O₄@SPI-BSA nanoparticles successfully. Fourier transform infrared spectra and field emission scanning electron microscopy images provided sufficient proof for the enzyme immobilization on the nanoparticles with 80% enzyme loading.

Keywords: High fructose syrup, inulinase immobilization, functionalized magnetic nanoparticles, soy protein isolate.

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Authors: C. Ardil

Abstract:

A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.

Keywords: Integral methods, determination of temperature fields, cooled blades, gas turbines.

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Authors: I. López , J. Garay, R. Carreño, Z. Varga

Abstract:

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. The method is illustrated with a trophic chain of resource – producer – primary consumer type and a numerical example is also presented.

Keywords: Monitoring, observer system, trophic chain

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Authors: A. M. Pashaev, R. A. Sadihov, A. S. Samedov, C. Ardil

Abstract:

A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.

Keywords: Aviation gas turbine, temperature field, cooled blades, numerical modeling.

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

Abstract:

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.

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Authors: Ahmed Amin Mousa, Tamer M. Ismail, M. Abd El Salam

Abstract:

This work presents a robot called Conceptual Robotic Cube, CR-Cube. The robot can be used as an educational tool for children from the age of three. It has a cube shape attached with a camera colours sensor. In addition, it contains four wheels to move smoothly. The researchers prepared a questionnaire to measure the efficiency of the robot. The design and the questionnaire was presented to 11 experts who agreed that the robot is appropriate for learning numbering and colours for preschool children.

Keywords: CR-Cube, robotic cube, conceptual robot, conceptual cube, colour concept, early childhood education.

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Authors: M. Faraji, F. Berroug

Abstract:

A one-dimensional mathematical model was developed in order to analyze and optimize the latent heat storage wall. The governing equations for energy transport were developed by using the enthalpy method and discretized with volume control scheme. The resulting algebraic equations were next solved iteratively by using TDMA algorithm. A series of numerical investigations were conducted in order to examine the effects of the thickness of the PCM layer on the thermal behavior of the proposed heating system. Results are obtained for thermal gain and temperature fluctuation. The charging discharging process was also presented and analyzed.

Keywords: Phase change material, Building, Concrete, Latent heat, Thermal control.

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Authors: Ibtihel Nouira, Asma Ben Abdallah, Ibtissem Kouaja, Mohamed Hèdi Bedoui

Abstract:

The processing of the electrocardiogram (ECG) signal consists essentially in the detection of the characteristic points of signal which are an important tool in the diagnosis of heart diseases. The most suitable are the detection of R waves. In this paper, we present various mathematical tools used for filtering ECG using digital filtering and Discreet Wavelet Transform (DWT) filtering. In addition, this paper will include two main R peak detection methods by applying a windowing process: The first method is based on calculations derived, the second is a time-frequency method based on Dyadic Wavelet Transform DyWT.

Keywords: Derived calculation methods, Electrocardiogram, R peaks, Wavelet Transform.

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