Search results for: bounded base

Authors: Sima Hassankhali, Ildar Sadeqi

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In the theory of Pareto efficient points, the existence of a bounded base for a cone K of a normed space X is so important. In this article, we study the geometric structure of a nonzero closed convex cone K with a bounded base. For this aim, we study the structure of the polar cone K# of K. Furthermore, we obtain a necessary and sufficient condition for a nonempty closed convex set C so that its recession cone C∞ has a bounded base.

Keywords: solid cones, recession cones, polar cones, bounded base

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Authors: Min Kyung An

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In this paper, we study the data collection problem in Wireless Sensor Networks (WSNs) adopting the two interference models: The graph model and the more realistic physical interference model known as Signal-to-Interference-Noise-Ratio (SINR). The main issue of the problem is to compute schedules with the minimum number of timeslots, that is, to compute the minimum latency schedules, such that data from every node can be collected without any collision or interference to a sink node. While existing works studied the problem with unit-sized and unbounded-sized message models, we investigate the problem with the bounded-sized message model, and introduce a constant factor approximation algorithm. To the best known of our knowledge, our result is the first result of the data collection problem with bounded-sized model in both interference models.

Keywords: data collection, collision-free, interference-free, physical interference model, SINR, approximation, bounded-sized message model, wireless sensor networks

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Authors: Abdullah Ali H. Ahmadini, Firoz Ahmad, Intekhab Alam

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Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work.

Keywords: varying parameters, geometric programming problem, bounded solution method, system reliability optimization

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Authors: Henni Mansour Abdelwaheb

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This study discusses the design of a bounded position/force feedback controller developed to ensure position and force tracking for bilateral teleoperation arms operating with variable delay, and actuator saturation. Also, an adaptive robust Radial Basis Function (RBF) neural network is used to estimate the environment torque. The parameters of the environment torque are then sent from the slave site to the master site as a non-power signal to avoid passivity problems. Moreover, a nonlinear function is applied to each controller term as a smooth saturation function, providing a bounded control signal and preserving the system’s actuators. Lastly, the Lyapunov approach demonstrates the global stability of the controlled system, and numerical experiment results further confirm the validity of the presented strategy.

Keywords: teleoperation manipulators system, time-varying delay, actuator saturation, adaptive robust rbf neural network approximation, uncertainties

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Authors: A. Bhandari, S. Mukherjee

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Two frames in a Hilbert space are called woven or weaving if all possible merge combinations between them generate frames of the Hilbert space with uniform frame bounds. Weaving frames are powerful tools in wireless sensor networks which require distributed data processing. Considering the practical applications, this article deals with finite woven frames. We provide methods of constructing finite woven frames, in particular, bounded linear operators are used to construct woven frames from a given frame. Several examples are discussed. We also introduce the notion of woven frame sequences and characterize them through the concepts of gaps and angles between spaces.

Keywords: frames, woven frames, gap, angle

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Authors: Chinh Phuong Do

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Dynamic analysis of slope under seismic condition requires the elimination of spurious reflection at the bounded domain. This paper studies the performances of wave transmitting boundaries, including the standard viscous boundary and the viscoelastic boundary to the material point method (MPM) framework. First, analytical derivations of these non-reflecting conditions particularly to the implicit MPM are presented. Then, a number of benchmark and geotechnical examples will be shown. Overall, the results agree well with analytical solutions, indicating the ability to accurately simulate the radiation at the bounded domain.

Keywords: dynamic analysis, implicit, MPM, non-reflecting boundary

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

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This paper deals with a stabilization problem for multi-agent systems, when all agents in a multi-agent system receive the same broadcasting control signal and the controller can measure not each agent output but the sum of all agent outputs. It is analytically shown that when the sum of all agent outputs is bounded with a certain broadcasting controller for a given reference, each agent output is separately bounded:stabilization of the sum of agent outputs always results in the stability of every agent output. A numerical example is presented to illustrate our theoretic findings in this paper.

Keywords: broadcasting control, multi-agent system, transfer function, stabilization

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Authors: Young-Min Ko, Seung-Jun Yu, Chang-Bin Ha, Hyoung-Kyu Song

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In a wireless communication system, the failure of base station can result in a communication disruption in the cell. This paper proposes a way to deal with the failure of base station in a wireless communication system based on OFDM. Cooperative communication of the adjacent base stations can be a solution of the problem. High performance is obtained by the configuration of transmission signals which is applied CDD scheme in the cooperative communication. The Cooperative scheme can be a effective solution in case of the particular situation.

Keywords: base station, CDD, OFDM, diversity gain, MIMO

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Authors: A. Nazeri, R. Ziaie Moayed, H. Ghiasinejad

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The present research has been performed to investigate the effect of base course application on load-settlement characteristics of sandy subgrade using plate load test. The main parameter investigated in this study was the subgrade reaction coefficient. The model tests were conducted in a 1.35 m long, 1 m wide, and 1 m deep steel test box of Imam Khomeini International University (IKIU Calibration Chamber). The base courses used in this research were in three different thicknesses of 15 cm, 20 cm, and 30 cm. The test results indicated that in the case of using base course over loose sandy subgrade, the values of subgrade reaction coefficient can be increased from 7  to 132 , 224 , and 396  in presence of 15 cm, 20 cm, and 30 cm base course, respectively.

Keywords: modulus of subgrade reaction, plate load test, base course, sandy subgrade

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Authors: Firoz Alam Faroque, Ankur Neog

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Earthquake causes significant loss of lives and severe damage to infrastructure. Base isolator is one of the most suitable solutions to make a building earthquake resistant. Base isolation consists of installing an isolator along with the steel plates covered with pads of strong material like steel, rubber, etc. In our study, we have used lead rubber bearing (LRB). The basic idea of seismic isolation is based on the reduction of the earthquake-induced inertia forces by shifting the fundamental period of the structure out of dangerous resonance range, and concentration of the deformation and energy dissipation demands at the isolation and energy dissipation systems, which are designed for this purpose. In this paper, RC frame buildings have been modeled and analyzed by response spectrum method using ETABS software. The LRB used in the model is designed as per uniform building code (UBC) 97. It is found that time period for the base isolated structures are higher than that of the fixed base structure and the value of base shear significantly reduces in the case of base-isolated buildings. It has also been found that buildings with vertical irregularities give better performance as compared to building with plan irregularities using base isolators.

Keywords: base isolation, base shear, irregularities in buildings, lead rubber bearing (LRB)

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: Joseph Ignagni, Rebecca Deen

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In this study, the decision making of the Justices of the United States Supreme Court will be considered in terms of constrained maximization and cognitive-cybernetic theory. This paper will integrate research in such fields as law, psychology, political science, economics and decision-making theory. It will be argued that due to its heavy workload, the Supreme Court may be forced to make decisions in a boundedly rational manner. The ideas and theory put forward here will be considered in the area of the Court’s decisions involving religion. Therefore, the cases involving the U.S. Constitution’s Free Exercise Clause and Establishment Clause will be analyzed.

Keywords: bounded rationality, cognitive-cybernetic, US supreme court, religion

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Authors: Kailas S. Jagtap, Karthik Sundarraj, Nirmal Kumar, S. Rajnarasimha, Prakash S. Kulkarni

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The issue of turbulence base streams and the drag related to it have been of important attention for rockets, missiles, and aircraft. Different techniques are used for base drag reduction. This paper presents the numerical study of numerous drag reduction technique. The base drag or afterbody drag of bluff bodies can be reduced easily using locked vortex drag reduction technique. For bluff bodies having a cylindrical shape, the base drag is much larger compared to streamlined bodies. For such bodies using splitter plates, the vortex can be trapped between the base and the plate, which results in smooth flow. Splitter plate with round and curved corner shapes has influence in drag reduction. In this paper, the comparison is done between single splitter plate as different positions and with the bluff body. Base drag for the speed of 30m/s can be reduced about 20% to 30% by using single splitter plate as compared to the bluff body.

Keywords: base drag, bluff body, splitter plate, vortex flow, ANSYS, fluent

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: complex potential, conformal mapping, image well theory, Laplace’s equation, superposition principle

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Authors: J. Omer, H. Haroglu

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Base enlargement in piles was invented to enhance pile resistance in downward loading, but the contribution of an enlarged base to the lateral load resistance of a pile has not been fully exploited or understood. This paper presents a laboratory investigation of the lateral capacity and deformation response of small-scale steel piles with enlarged bases installed in dry sand. Static loading tests were performed on 24 model piles having different base-to-shaft diameter ratios. The piles were installed in a box filled with dry sand, and lateral loads were applied to the pile tops using a pulley system. The test piles had shaft diameters of 20 mm, 16 mm, and 10 mm; base diameters of 900 mm, 700 mm, and 500 mm. As a control, a pile without base enlargement was tested to allow comparisons with the enlarged base piles. Incremental maintained loads were applied until pile failure approached while recording pile head deflections with high-precision dial gauges. The results showed that the lateral capacity increased with an increase in base diameter, albeit by different percentages depending on the shaft diameters and embedment length in the sand. There was always an increase in lateral capacity with increasing embedment length. Also, it was observed that an enlarged pile base had deflected less at a given load when compared to the control pile. Therefore, the research demonstrated the benefits of lateral capacity and stability of enlarging a pile base.

Keywords: pile foundations, enlarged base, lateral loading

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Authors: Man Chul Jeong, Hyoung Jin Lee, Sang Yoon Lee, Ji Hyun Park, Min Wook Chang, In-Seuck Jeung

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This study focus on the drag reduction effect of the base bleed at supersonic flow. Base bleed is the method which bleeds the gas on the tail of the flight vehicle and reduces the base drag, which occupies over 50% of the total drag in any flight speed. Thus base bleed can reduce the total drag significantly, and enhance the total flight range. Drag reduction ratio of the base bleed is strongly related to the mass flow rate of the bleeding gas. Thus selecting appropriate mass flow rate is important. However, since the flight vehicle has various flight speed, same mass flow rate of the base bleed can have different drag reduction effect during the flight. Thus, this study investigates the effect of the drag reduction depending on the flight speed by numerical analysis using STAR-CCM+. The analysis model is 155mm diameter projectile with boat-tailed shape base. Angle of the boat-tail is chosen previously for minimum drag coefficient. Numerical analysis is conducted for Mach 2 and Mach 3, with various mass flow rate, or the injection parameter I, of the bleeding gas and the temperature of the bleeding gas, is fixed to 300K. The results showed that I=0.025 has the minimum drag at Mach 2, and I=0.014 has the minimum drag at Mach 3. Thus as the Mach number is higher, the lower mass flow rate of the base bleed has more effect on drag reduction.

Keywords: base bleed, supersonic, drag reduction, recirculation

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Authors: Vigen Arakelian

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This paper deals with the study of devices for displacement of the mould base of blow-molding machines. The displacement of the mould in the studied case is carried out by a linear actuator, which ensures the descent of the mould base and by extension springs, which return the letter in the initial position. The aim of this paper is to study the inverse dynamics of the device for displacement of the mould base of blow-molding machines and to determine its optimum parameters for higher rate of production. In the other words, it is necessary to solve the inverse dynamic problem to find the equation of motion linking applied forces with displacements. This makes it possible to determine the stiffness coefficient of the spring to turn the mold base back to the initial position for a given time. The obtained results are illustrated by a numerical example. It is shown that applying a spring with stiffness returns the mould base of the blow molding machine into the initial position in 0.1 sec.

Keywords: design, mechanisms, dynamics, blow-molding machines

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Authors: Baofeng Pan, Heng Liu

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Because of the high strength and large carrying capacity, the semi-rigid base is widely used in modern road engineering. However, hydrodynamic pressure, which is one of the main factors to cause early damage of semi-rigid base, cannot be avoided in the nature environment when pavement is subjected to some loadings such as the passing vehicles. In order to investigating how moisture-induced-damage of semi-rigid base influenced by hydrodynamic pressure, a new and effective experimental research method is provided in this paper. The results show that: (a) The washing action of high hydrodynamic pressure is the direct cause of strength reducing of road semi-rigid base. (b) The damage of high hydrodynamic pressure mainly occurs at the beginning of the scoring test and with the increasing of testing time the influence reduces. (c) Under the same hydrodynamic pressure, the longer the specimen health age, the stronger ability to resist moisture induced damage.

Keywords: semi-rigid base, hydrodynamic pressure, moisture-induced-damage, experimental research

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Authors: H. Y. Jung, Ju H. Park, S. M. Lee

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A sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The sector bounded nonlinear systems, which have a feedback connection with a linear dynamical system and nonlinearity satisfying certain sector type constraints. Also, the sampled-data control scheme is very useful since it is possible to handle digital controller and increasing research efforts have been devoted to sampled-data control systems with the development of modern high-speed computers. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: sampled-data control, fuel cell, linear matrix inequalities, nonlinear control

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Authors: Shatadru Das, Natarajan Vijayarangan

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In this paper, a system and method for generating and recovering an authorization code has been designed and analyzed. The system creates an authorization code by accepting a base-sentence from a user. Based on the characters present in this base-sentence, the system computes a base-sentence matrix. The system also generates a plurality of patterns. The user can either select the pattern from the multiple patterns suggested by the system or can create his/her own pattern. The system then performs multiplications between the base-sentence matrix and the selected pattern matrix at different stages in the path forward, for obtaining a strong authorization code. In case the user forgets the base sentence, the system has a provision to manage and retrieve 'forgotten authorization code'. This is done by fragmenting the base sentence into different matrices and storing the fragmented matrices into a repository after computing matrix multiplication with a security question-answer approach and with a secret key provided by the user.

Keywords: easy authentication, key retrieval, memorable passwords, strong password generation

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Authors: Daniel Barkley, Jianyi Zhu

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This study investigates base salary differentials and gender equity among university presidents across 427 U.S. colleges and universities. While endowments typically do not directly determine university presidents' base salaries, our analysis reveals a noteworthy pattern: endowments explain more than half of the variance in female university presidents' base salaries, compared to a mere 0.69 percent for males. Moreover, female presidents' base salaries tend to rise much faster than male base salaries with increasing university endowments. This disparate impact of endowments on base salaries implies an endowment threshold for achieving gender pay equity. We develop an analytical model predicting an endowment threshold for achieving gender equality and empirically estimate this equity threshold using data from over 427 institutions. Surprisingly, the fields of science and athletics have emerged as sources of gender-neutral base pay. Both male and female university presidents with STEM backgrounds command higher base salaries than those without such qualifications. Additionally, presidents of universities affiliated with Power 5 conferences consistently receive higher base salaries regardless of gender. Consistent with the theory of human capital accumulation, the duration of the university presidency incrementally raises base salaries for both genders but at a diminishing rate. Curiously, prior administrative leadership experience as a vice president, provost, dean, or department chair does not significantly influence base salaries for either gender. By providing empirical evidence and analytical models predicting an endowment threshold for achieving gender equality in base salaries, the study offers valuable insights for policymakers, university administrators, and other stakeholders. These findings hold crucial policy implications, informing strategies to promote gender equality in executive compensation within higher education institutions.

Keywords: higher education, endowments, base salaries, university presidents

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Authors: Abdulmagid A. Khattabi

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The aim of this research is to study the manner of alumina (Al2O3) particles dispersion with (2-10) mm size in (Al-7%Si-0.45% Mg) base of alloy melt employing of classical casting method. The mechanism of particles diffusions by melt turning and stirring that makes vortexes help the particles entrance in the matrix of base alloy also has been studied. The samples of metallic composites (MMCs) with dispersed particles percentages (4% - 6% - 8% - 10% - 15% and 20%) are prepared. The effect of the particles dispersion on the mechanical properties of produced samples were carried out by tension & hardness tests. It is found that the ultimate tensile strength of the produced composites can be increased by increasing the percentages of alumina particles in the matrix of the base alloy. It becomes (232 Mpa) at (20%) of added particles. The results showed that the average hardness of prepared samples increasing with increases the alumina content. Microstructure study of prepared samples was carried out. The results showed particles location and distribution of it in the matrix of base alloy. The dissolution of Alumina particles into liquid base alloy was clear in some cases.

Keywords: base alloy, matrix, hardness, thermal properties, base metal MMCs

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Authors: Smita Jauhari, Bhupendra Mistry

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Schiff base (E)-2-methyl-N-(tetrazolo[1,5-a]quinolin-4-ylmethylene)aniline (QMA) was synthesized, and its inhibitive effect for mild steel in 1M HCl solution was investigated by weight loss measurement and electrochemical tests.From the weight loss measurements and electrochemical tests, it was observed that the inhibition efficiency increases with the increase in the Schiff base concentration and reaches a maximum at the optimum concentration. This is further confirmed by the decrease in corrosion rate. It is found that the system follows Langmuir adsorption isotherm.

Keywords: Schiff base, acid corrosion, electrochemical impedance spectroscopy, polarization

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Authors: Messai Amel, Badis Zakaria, Benali-Cherif Nourredine, Dominique Luneaub

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We are interested in molecular polymetallic species having high spin and nuclearities in relation to the field of so call single-molecule magnets (SMMs). The goal is to find a way to synthesis metal clusters which may have application in magnetism and nano sciences. With this purpose, we decided to investigate the coordination chemistry of the Schiff base. Along this way we were able to create cubane-like complexes and elaborate new Single Molecule-Magnets. The idea was to use Schiff base ligands and different metals to generate high nuclear complexes. Complexation of Shiff base with copper (II) has been investigated. Tetra nuclear complex with a cubane like core have been synthesized with (Sciff base), with the same base and cobalt (II) we obtain an other single magnetic complex completely different. In this presentation, we report the synthesis, crystal structure and magnetic properties of the tetranuclear compound (Cu4 L4), and the tetranuclear compound. (Co4L4)

Keywords: cluster-assembled materials, magnetic compounds, Sciff base, cupper, cobalt

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Authors: Nur Sulihatimarsyila Abd Wafti, Harrison Lik Nang Lau, Nabilah Kamaliah Mustaffa, Nur Azreena Idris

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The use of biolubricant has gained its popularity over the last decade. Base stock produced using methyl ester and trimethylolethane (TME) can be potentially used for biolubricant production due to its biodegradability, non-toxicity and good thermal stability. The synthesis of biolubricant base stock e.g. triester (TE) via transesterification of palm methyl ester and TME in the presence of sodium methoxide as the catalyst was conducted. Factors influencing the reaction conditions were investigated including reaction time, temperature and pressure. The palm-based biolubricant base stock produced was analysed for its monoester (ME), diester (DE) and TE contents using gas chromatography as well as its lubricating properties such as viscosity, viscosity index, oxidation stability, and density. The resulting base stock containing 90 wt% TE was successfully synthesized.

Keywords: biolubricant, methyl ester, triester transesterification, lubricating properties

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Authors: Mert Turanli, Hakan Temeltas

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In this paper, we present an adaptive controller for decentralized coordination problem of multiple non-holonomic agents. The performance of the presented Multi-Agent Bounded Gain Forgetting (BGF) Composite Adaptive controller is compared against the tracking error criterion with a Feedback Linearization controller. By using the method, the sensor nodes move and reconfigure themselves in a coordinated way in response to a sensed environment. The multi-agent coordination is achieved through Centroidal Voronoi Tessellations and Coverage Control. Also, a consensus protocol is used for synchronization of the parameter vectors. The two controllers are given with their Lyapunov stability analysis and their stability is verified with simulation results. The simulations are carried out in MATLAB and ROS environments. Better performance is obtained with BGF Adaptive Controller.

Keywords: adaptive control, centroidal voronoi tessellations, composite adaptation, coordination, multi robots

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Authors: Greg Fetzer

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One of the fundamental tensions of creative work is between the need to be passionate and persistent in advancing novel and risky ideas and the need to be flexible, revising, or even abandoning ideas in favor of others. The tension becomes fraught in part because of the attachment that creators have toward their ideas. Idea attachment is defined here as a multifaceted concept referring to affection, passion, and connection toward a target—in this case, one’s projects or ideas. Yet feeling attached can make creators resistant to feedback, making them less flexible and leading them to escalate commitment. Despite a growing understanding of how attachment develops and evolves in response to project changes, feedback, and creative jolts, we still know relatively little about the organizational dynamics that may shape idea attachment. Through a qualitative, inductive study of early-stage R&D scientists in the pharmaceutical industry, this research finds that scientists develop bounded attachment, a mindset that limits emotional attachment to ideas while still fostering engagement in idea development. This research develops a process model of how bounded attachment is developed and enacted across three stages of the creative process, idea generation, idea evaluation, and outcome assessment, as well as the role that organizational practices and professional identity play in shaping this process: these collective practices provided structures to ensure ideas were evaluated in a rational (i.e. non-emotional way) while also providing socioemotional support in the face of setbacks. Together, this process led to continued creative engagement across ideas in a portfolio and helped scientists construct a sense of meaningful work despite a high likelihood (and frequency) of failure.

Keywords: creativity, innovation, organizational practices, qualitative, attachment

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Authors: Alan C. Lin, Ricky N. Joevan

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This paper focuses on developing a system to transfer mold base plates and standard parts faster during the stage of injection mold design. This system not only provides a way to compare the file version, but also it utilizes Siemens NX 10 to isolate the updated information into a single executable file (.dll), and then, the file can be transferred without the need of transferring the whole file. By this way, the system can help the user to download only necessary mold base plates and standard parts, and those parts downloaded are only the updated portions.

Keywords: CAD, injection molding, mold base, data retrieval

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Authors: Mulugeta Fola, Mengistu Ketema, Kumilachew Alamerie

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Watershed provides vast economic benefits within and beyond the management area of interest. But most watersheds in Ethiopia are increasingly facing the threats of degradation due to both natural and man-made causes. To reverse these problems, communities’ participation in sustainable management programs is among the necessary measures. Hence, this study assessed the households’ willingness to pay for watershed management practices through a contingent valuation study approach. Double bounded dichotomous choice with open-ended follow-up format was used to elicit the households’ willingness to pay. Based on data collected from 275 randomly selected households, descriptive statistics results indicated that most households (79.64%) were willing to pay for watershed management practices. A bivariate Probit model was employed to identify determinants of households’ willingness to pay and estimate mean willingness to pay. Its result shows that age, gender, income, livestock size, perception of watershed degradation, social position, and offered bids were important variables affecting willingness to pay for watershed management practices. The study also revealed that the mean willingness to pay for watershed management practices was calculated to be 58.41 Birr and 47.27 Birr per year from the double bounded and open-ended format, respectively. The study revealed that the aggregate welfare gains from watershed management practices were calculated to be 931581.09 Birr and 753909.23 Birr per year from double bounded dichotomous choice and open-ended format, respectively. Therefore, the policymakers should make households to pay for the services of watershed management practices in the study area.

Keywords: bivariate probit model, contingent valuation, watershed management practices, willingness to pay

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Authors: Jixiang Zhang

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A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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