Search results for: weakly solving

Authors: Mariya V. Yanyukina, Michael A. Bolotov

Abstract:

Assembling accuracy is the degree of accordance between the actual values of the parameters obtained during assembly, and the values specified in the assembly drawings and technical specifications. However, the assembling accuracy depends not only on the quality of the production process but also on the correctness of the assembly process. Therefore, preliminary calculations of assembly stages are carried out to verify the correspondence of real geometric parameters to their acceptable values. In the aviation industry, most calculations involve interacting dimensional chains. This greatly complicates the task. Solving such problems requires a special approach. The purpose of this article is to carry out the problem of improving the technology of assembly of aviation units by use of computer calculations. One of the actual examples of the assembly unit, in which there is an interacting dimensional chain, is the turbine wheel of gas turbine engine. Dimensional chain of turbine wheel is formed by geometric parameters of disk and set of blades. The interaction of the dimensional chain consists in the formation of two chains. The first chain is formed by the dimensions that determine the location of the grooves for the installation of the blades, and the dimensions of the blade roots. The second dimensional chain is formed by the dimensions of the airfoil shroud platform. The interaction of the dimensional chain of the turbine wheel is the interdependence of the first and second chains by means of power circuits formed by a plurality of middle parts of the turbine blades. The timeliness of the calculation of the dimensional chain of the turbine wheel is the need to improve the technology of assembly of this unit. The task at hand contains geometric and mathematical components; therefore, its solution can be implemented following the algorithm: 1) research and analysis of production errors by geometric parameters; 2) development of a parametric model in the CAD system; 3) creation of set of CAD-models of details taking into account actual or generalized distributions of errors of geometrical parameters; 4) calculation model in the CAE-system, loading of various combinations of models of parts; 5) the accumulation of statistics and analysis. The main task is to pre-simulate the assembly process by calculating the interacting dimensional chains. The article describes the approach to the solution from the point of view of mathematical statistics, implemented in the software package Matlab. Within the framework of the study, there are data on the measurement of the components of the turbine wheel-blades and disks, as a result of which it is expected that the assembly process of the unit will be optimized by solving dimensional chains.

Keywords: accuracy, assembly, interacting dimension chains, turbine

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Authors: Midhun Paul, T. Radha Ramanan

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The objective of this work is to present a state-of-the-art literature review highlighting the challenges in the research of the scheduling of assembly job shop problem and providing an insight on how the future directions of the research would be. The number of work has been substantial that it requires a review to enable one to understand the origin of the research and how it is getting evolved. This review paper presents a comprehensive review of the literature dealing with various studies carried on assembly job shop scheduling. The review details the evolution of the AJS from the perspective of other scheduling problems and also presents a classification scheme. The work also identifies the potential directions for future research, which we believe to be worthwhile considering.

Keywords: assembly job shop, future directions, manufacturing, scheduling

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Authors: Qianying Sun, Abdelhadi Kassiba, Guorong Li

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ZnO with wurtzite structure is a well-known semiconducting oxide (SCO), being applied in thermoelectric devices, varistors, gas sensors, transparent electrodes, solar cells, liquid crystal displays, piezoelectric and electro-optical devices. Intrinsically, ZnO is weakly n-type SCO due to native defects (Znⱼ, Vₒ). However, the substitutional doping by metallic elements as (Al, Ti) gives rise to a high n-type conductivity ensured by donor centers. Under CO+N₂ sintering atmosphere, Schottky barriers of ZnO ceramics will be suppressed by lowering the concentration of acceptors at grain boundaries and then inducing a large increase in the Hall mobility, thereby increasing the conductivity. The presented work concerns ZnO based ceramics, which are fabricated with doping by TiO₂ (0.50mol%), Al₂O₃ (0.25mol%) and MgO (1.00mol%) and sintering in different atmospheres (Air (A), N₂ (N), CO+N₂(C)). We obtained uniform, dense ceramics with ZnO as the main phase and Zn₂TiO₄ spinel as a secondary and minor phase. An important increase of the conductivity was shown for the samples A, N, and C which were sintered under different atmospheres. The highest conductivity (σ = 1.52×10⁵ S·m⁻¹) was obtained under the reducing atmosphere (CO). The role of doping was investigated with the aim to identify the local environment and valence states of the doping elements. Thus, Electron paramagnetic spectroscopy (EPR) determines the concentration of defects and the effects of charge carriers in ZnO ceramics as a function of the sintering atmospheres. The relation between conductivity and defects concentration shows the opposite behavior between these parameters suggesting that defects act as traps for charge carriers. For Al ions, nuclear magnetic resonance (NMR) technique was used to identify the involved local coordination of these ions. Beyond the six and forth coordinated Al, an additional NMR signature of ZnO based TCO requires analysis taking into account the grain boundaries and the conductivity through the Knight shift effects. From the thermal evolution of the conductivity as a function of the sintering atmosphere, we succeed in defining the conditions to realize ZnO based TCO ceramics with an important thermal coefficient of resistance (TCR) which is promising for electrical safety of devices.

Keywords: ceramics, conductivity, defects, TCO, ZnO

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Authors: Yelbek B. Utepov, Assel S. Tulebekova, Alizhan B. Kazkeyev

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Maturity sensors are used to determine concrete strength by the non-destructive method. The method of placement of the maturity sensors determines their number required for a certain frame of a monolithic building. Previous studies weakly describe this aspect, giving only logical assumptions. This paper proposes a cheap prototype of an embedded wireless sensor for monitoring concrete structures, as well as an alternative strategy for placing sensors based on the transitional boundaries of the temperature distribution of concrete curing, which were determined by building a heat map of the temperature distribution, where unknown values are calculated by the method of inverse distance weighing. The developed prototype can simultaneously measure temperature and relative humidity over a smartphone-controlled time interval. It implements a maturity method to assess the in-situ strength of concrete, which is considered an alternative to the traditional shock impulse and compression testing method used in Kazakhstan. The prototype was tested in laboratory and field conditions. The tests were aimed at studying the effect of internal and external temperature and relative humidity on concrete's strength gain. Based on an experimentally poured concrete slab with randomly integrated maturity sensors, it was determined that the transition boundaries form elliptical forms. Temperature distribution over the largest diameter of the ellipses was plotted, resulting in correct and inverted parabolas. As a result, the distance between the closest opposite crossing points of the parabolas is accepted as the maximum permissible step for setting the maturity sensors. The proposed placement strategy can be applied to sensors that measure various continuous phenomena such as relative humidity. Prototype testing has also revealed Bluetooth inconvenience due to weak signal and inability to access multiple prototypes simultaneously. For this reason, further prototype upgrades are planned in future work.

Keywords: heat map, placement strategy, temperature and relative humidity, wireless embedded sensor

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Authors: Sai Siddharth S., Prasanna Kumar G. M., Alagarsamy R.

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This research introduces an alternative approach to urban road maintenance by utilizing Blended Wing Body (BWB) design and Vertical Takeoff and Landing (VTOL) drones. The integration of this aerospace innovation, combining blended wing efficiency with VTOL maneuverability, aims to optimize fuel consumption and explore versatile applications in solving urban problems. A few problems are discussed along with optimization of the design and comparative study with other drone configurations.

Keywords: design optimization, CFD, CAD, VTOL, blended wing body

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Ahmad Khoirul Umam

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This paper investigates the role of vested interests and its impacts on anti-corruption agenda in Indonesia following the collapse of authoritarian regime in 1998. A pervasive and rampant corruption has been believed as the main cause of the state economy’s fragility. Hence, anti-corruption measures were implemented by applying democratization and market liberalization since the establishment of a consolidated democracy which go hand in hand with a liberal market economy is convinced to be an efficacious prescription for effective anti-corruption. The reform movement has also mandated the establishment of the independent, neutral and professional special anti-corruption agency namely Corruption Eradication Commission (KPK) to more intensify the fight against the systemic corruption. This paper will examine whether these anti-corruption measures have been effective to combat corruption, and investigate to what extend have the anti-corruption efforts, especially those conducted by KPK, been impeded by the emergence of a nexus of vested interests as the side-effect of democratization and market liberalization. Based on interviews with key stakeholders from KPK, other law enforcement agencies, government, prominent scholars, journalists and NGOs in Indonesia, it is found that since the overthrow of Soeharto, anti-corruption movement in the country have become more active and serious. After gradually winning the hearth of people, KPK successfully touched the untouchable corruption perpetrators who were previously protected by political immunity, legal protection and bureaucratic barriers. However, these changes have not necessarily reduced systemic and structural corruption practices. Ironically, intensive and devastating counterattacks were frequently posed by the alignment of business actors, elites of political parties, government, and also law enforcement agencies by hijacking state’s instruments to make KPK deflated, powerless, and surrender. This paper concludes that attempts of democratization, market liberalization and the establishment of anti-corruption agency may have helped Indonesia to reduce corruption. However, it is still difficult to imply that such anti-corruption measures have fostered the more effective anti-corruption works in the newly democratized and weakly regulated liberal economic system.

Keywords: vested interests, democratization, market liberalization, anti-corruption, Indonesia

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Authors: Mitat Uysal

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A new met heuristic optimization algorithm called as Migrating Birds Optimization is used for curve fitting by rational cubic Bezier Curves. This requires solving a complicated multivariate optimization problem. In this study, the solution of this optimization problem is achieved by Migrating Birds Optimization algorithm that is a powerful met heuristic nature-inspired algorithm well appropriate for optimization. The results of this study show that the proposed method performs very well and being able to fit the data points to cubic Bezier Curves with a high degree of accuracy.

Keywords: algorithms, Bezier curves, heuristic optimization, migrating birds optimization

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Authors: Sourabh Joshi, Geetinder Kaur, Sarabjit Kaur, Gulwatanpreet Singh, Geetika Mannan

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In this paper, we have use an algorithm that able to obtain an optimal solution to travelling salesman problem from a huge search space, quickly. This algorithm is based upon the ant colony optimization technique and employees roulette wheel selection mechanism. To illustrate it more clearly, a program has been implemented which is based upon this algorithm, that presents the changing process of route iteration in a more intuitive way. In the event, we had find the optimal path between hundred cities and also calculate the distance between two cities.

Keywords: ant colony, optimization, travelling salesman problem, roulette wheel selection

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

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Elliptic curve discrete logarithm problem (ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard's rho method to evaluate the security of ECDLP on Barreto-Naehrig (BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard's rho method, BN curve, Montgomery multiplication

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Rumeysa Terzioglu

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Social entrepreneurship is not only a new concept but also an engaging factor of development that utilizes opportunities in economic and social areas for women. Social entrepreneurs have experience in determining and solving social problems with community participation. Social entrepreneurship is a consequence of individual social and economic initiatives contributing to women’s social and economic development against poverty. Women’s empowerment is an essential point for development. Türkiye has been developing an alternative empowerment model for women affected by the national development plan. Social entrepreneurship is an alternative model of social and economic empowerment of women’s status in Türkiye.

Keywords: social entrepreneurship, women, women empowerment, development

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

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This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: bus scheduling problem, decision support system, genetic algorithm, shortest path

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Boris Melnikov, Ye Zhang, Dmitrii Chaikovskii

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This study explores the pseudo-geometric version of the extensively researched Traveling Salesman Problem (TSP), proposing a novel generalization of existing algorithms which are traditionally confined to the geometric version. By adapting the "onion husk" method and introducing auxiliary algorithms, this research fills a notable gap in the existing literature. Through computational experiments using randomly generated data, several metrics were analyzed to validate the proposed approach's efficacy. Preliminary results align with expected outcomes, indicating a promising advancement in TSP solutions.

Keywords: optimization problems, traveling salesman problem, heuristic algorithms, “onion husk” algorithm, pseudo-geometric version

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Authors: Amritpal Singh Nafria, Rohit Sharma, Md. Shami Ansari

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Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion.

Keywords: velocity-time graph, fundamental equations, additional equations, requisite conditions, importance and educational benefits

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Authors: Engin Metin Kaplan, Kemal Yaman

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In this study, the crash of a medium heavy vehicle onto a designed Road blocker (vehicle barrier) is studied numerically. Structural integrity of the Road blocker is studied by nonlinear dynamic methods under the loading conditions which are defined in the standards. NASTRAN® and LS-DYNA® which are commercial software are used to solve the problem. Outer geometry determination, alignment of the inner part and material properties of the road blocker are studied linearly to yield design parameters. Best design parameters are determined to achieve the most structurally optimized road blocker. Strain and stress values of the vehicle barrier are obtained by solving the partial differential equations.

Keywords: vehicle barrier, truck collision, road blocker, crash analysis

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Authors: Giulia Magi Meconi, Nicholas Ballard, José M. Asua, Ronen Zangi

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Experimental and computational studies are combined to elucidate the adsorption proprieties of ionic and nonionic surfactants on hydrophobic polymer surface such us poly(styrene). To present these two types of surfactants, sodium dodecyl sulfate and poly(ethylene glycol)-block-poly(ethylene), commonly utilized in emulsion polymerization, are chosen. By applying quartz crystal microbalance with dissipation monitoring it is found that, at low surfactant concentrations, it is easier to desorb (as measured by rate) ionic surfactants than nonionic surfactants. From molecular dynamics simulations, the effective, attractive force of these nonionic surfactants to the surface increases with the decrease of their concentration, whereas, the ionic surfactant exhibits mildly the opposite trend. The contrasting behavior of ionic and nonionic surfactants critically relies on two observations obtained from the simulations. The first is that there is a large degree of interweavement between head and tails groups in the adsorbed layer formed by the nonionic surfactant (PEO/PE systems). The second is that water molecules penetrate this layer. In the disordered layer, these nonionic surfactants generate at the surface, only oxygens of the head groups present at the interface with the water phase or oxygens next to the penetrating waters can form hydrogen bonds. Oxygens inside this layer lose this favorable energy, with a magnitude that increases with the surfactants density at the interface. This reduced stability of the surfactants diminishes their driving force for adsorption. All that is shown to be in accordance with experimental results on the dynamics of surfactants desorption. Ionic surfactants assemble into an ordered structure and the attraction to the surface was even slightly augmented at higher surfactant concentration, in agreement with the experimentally determined adsorption isotherm. The reason these two types of surfactants behave differently is because the ionic surfactant has a small head group that is strongly hydrophilic, whereas the head groups of the nonionic surfactants are large and only weakly attracted to water.

Keywords: emulsion polymerization process, molecular dynamics simulations, polymer surface, surfactants adsorption

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Authors: Chonlawit Yuwajitaa, Suttipong Pruangkab

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Existing situation on labour use, health management and problems, and ancillary work done along with buffalo farming in Thailand was studied, There were 52 farms had been interviewed during August to September 2014. The study revealed that 100 percent of labor use was family labors themselves and all of farmers reared their buffaloes and grew rice simultaneously. The farmers valued veterinary service and advice as the most important problem (40.40%) and buffalo farming health problems was found 7.69% of dystocia, retain placenta and abortion. The major problem that should be taken into account was officials involved and buffalo farming should be continually promoted by government sectors to help solving economic problems as a whole.

Keywords: buffalo, labor use, health management, Thailand

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Authors: Jo Rhodes, Peter Lok, Zahra Sadeghinejad

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The aim of this study is to determine the impact of metacognition on top management team members and firm performance based on full team integration. A survey of 1500 small to medium enterprises (SMEs) was initiated and 140 firms were obtained in this study (with response rate of 9%). The result showed that different metacognitive abilities of managers [knowledge and experience] could enhance team decision-making and problem solving, resulting in greater firm performance. This is a significant finding for SMEs because these organisations have small teams with owner leadership and entrepreneurial orientation.

Keywords: metacognition, behavioural integration, top management team (TMT), performance

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Authors: Muhammad Hassan Khalil, Xu Jiadong

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Early detection through screening is the best tool short of a perfect treatment against the malignant tumor inside the breast of a woman. By detecting cancer in its early stages, it can be recognized and treated before it has the opportunity to spread and change into potentially dangerous. Microwave tomography is a new imaging method based on contrast in dielectric properties of materials. The mathematical theory of microwave tomography involves solving an inverse problem for Maxwell’s equations. In this paper, we present designed antenna for breast cancer detection, which will use in microwave tomography configuration.

Keywords: microwave imaging, inverse scattering, breast cancer, malignant tumor detection

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Authors: Afroze Ibrahim Baqapuri, Ilya Trofimov

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Sponsored search is a multi-billion dollar industry and makes up a major source of revenue for search engines (SE). Click-through-rate (CTR) estimation plays a crucial role for ads selection, and greatly affects the SE revenue, advertiser traffic and user experience. We propose a novel architecture of solving CTR prediction problem by combining artificial neural networks (ANN) with decision trees. First, we compare ANN with respect to other popular machine learning models being used for this task. Then we go on to combine ANN with MatrixNet (proprietary implementation of boosted trees) and evaluate the performance of the system as a whole. The results show that our approach provides a significant improvement over existing models.

Keywords: neural networks, sponsored search, web advertisement, click prediction, click-through rate

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Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

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The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, inpainting, parallel projection methods

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Authors: Tom Nakotte, Hongmei Luo

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Lead chalcogenide-based (PbS, PbSe, and PbTe) quantum dots (QDs) were synthesized for the purpose of implementing them in radiation detectors. Pb based materials have long been of interest for gamma and x-ray detection due to its high absorption cross section and Z number. The emphasis of the studies was on exploring how to control charge carrier transport within thin films containing the QDs. The properties of QDs itself can be altered by changing the size, shape, composition, and surface chemistry of the dots, while the properties of carrier transport within QD films are affected by post-deposition treatment of the films. The QDs were synthesized using colloidal synthesis methods and films were grown using multiple film coating techniques, such as spin coating and doctor blading. Current QD radiation detectors are based on the QD acting as fluorophores in a scintillation detector. Here the viability of using QDs in solid-state radiation detectors, for which the incident detectable radiation causes a direct electronic response within the QD film is explored. Achieving high sensitivity and accurate energy quantification in QD radiation detectors requires a large carrier mobility and diffusion lengths in the QD films. Pb chalcogenides-based QDs were synthesized with both traditional oleic acid ligands as well as more weakly binding oleylamine ligands, allowing for in-solution ligand exchange making the deposition of thick films in a single step possible. The PbS and PbSe QDs showed better air stability than PbTe. After precipitation the QDs passivated with the shorter ligand are dispersed in 2,6-difloupyridine resulting in colloidal solutions with concentrations anywhere from 10-100 mg/mL for film processing applications, More concentrated colloidal solutions produce thicker films during spin-coating, while an extremely concentrated solution (100 mg/mL) can be used to produce several micrometer thick films using doctor blading. Film thicknesses of micrometer or even millimeters are needed for radiation detector for high-energy gamma rays, which are of interest for astrophysics or nuclear security, in order to provide sufficient stopping power.

Keywords: colloidal synthesis, lead chalcogenide, radiation detectors, quantum dots

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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