Search results for: fixed point

Authors: Kamel Al-Khaled

Abstract:

A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Safeer Hussain Khan, H. Fukhar-ud-Din

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The concept of quasi-contractive type operators was given by Berinde and extended by Imoru and Olatinwo. They named this new type as contractive-like operators. On the other hand, Xu and Noo introduced a three-step-one-mappings iterative process which can be seen as a generalization of Mann and Ishikawa iterative processes. Approximating common fixed points has its own importance as it has a direct link with minimization problem. Motivated by this, in this paper, we first extend the iterative process of Xu and Noor to the case of three-step-three-mappings and then prove a strong convergence result using contractive-like operators for this iterative process. In general, this generalizes corresponding results using Mann, Ishikawa and Xu-Noor iterative processes with quasi-contractive type operators. It is to be pointed out that our results can also be proved with iterative process involving error terms.

Keywords: contractive-like operator, iterative process, common fixed point, strong convergence

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Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong

Abstract:

This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.

Keywords: asymptotically quasi-nonexpansive nonself-mapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space

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Authors: Xiaolai Zhang, Haitao Zhang, Qiwen Sun, Weixin Qian, Weiyong Ying

Abstract:

High temperature Fischer-Tropsch synthesis process use fixed fluidized bed as a reactor. In order to understand the flow behavior in the fluidized bed better, the research of how the radial velocity affect the entire flow field is necessary. Laser Doppler Velocimetry (LDV) was used to study the radial velocity distribution along the diameter direction of the cross-section of the particle in a fixed fluidized bed. The velocity in the cross-section is fluctuating within a small range. The direction of the speed is a random phenomenon. In addition to r/R is 1, the axial velocity are more than 6 times of the radial velocity, the radial velocity has little impact on the axial velocity in a fixed fluidized bed.

Keywords: Fischer-Tropsch synthesis, Fixed fluidized bed, LDV, Velocity

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Karim S. Hassan, Hisham M. Hamed, Yassmine A. Fahmy, Ahmed F. Shalash

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The mismatch between in-phase and quadrature signals in Orthogonal frequency division multiplexing (OFDM) systems, such as DVB-T2, results in a severe degradation in performance. Several general solutions have been proposed in the past, but these are largely computationally intensive, leading to complex implementations. In this paper, we propose a relatively simple iterative solution, which provides good results in relatively few iterations, using fixed precision arithmetic. An additional advantage is that complex digital blocks, such as dividers and square root, are not required. Thus, the proposed solution may be implemented in relatively simple hardware.

Keywords: OFDM, DVB-T2, I/Q imbalance, I/Q mismatch, iterative method, fixed point, reduced complexity

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Authors: Adel Bouchakhchoukha, Hakim Akeb

Abstract:

In this work, we propose a hybrid heuristic in order to solve the Team Orienteering Problem (TOP). Given a set of points (or customers), each with associated score (profit or benefit), and a team that has a fixed number of members, the problem to solve is to visit a subset of points in order to maximize the total collected score. Each member performs a tour starting at the start point, visiting distinct customers and the tour terminates at the arrival point. In addition, each point is visited at most once, and the total time in each tour cannot be greater than a given value. The proposed heuristic combines beam search and a local optimization strategy. The algorithm was tested on several sets of instances and encouraging results were obtained.

Keywords: team orienteering problem, vehicle routing, beam search, local search

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Authors: Mohammad Ali Alavidoost, Hossein Bozorgian

Abstract:

Criterion-referenced tests (CRTs) are designed to measure student performance against a fixed set of predetermined criteria or learning standards. The reliability of such tests cannot be based on internal reliability. Threshold loss agreement is one way to calculate the reliability of CRTs. However, the selection of master and non-master in such agreement is determined by the threshold point. The problem is if the threshold point witnesses a minute change, the selection of master and non-master may have a drastic change, leading to the change in reliability results. Therefore, in this study, the Fuzzy logic approach is employed as a remedial procedure for data analysis to obviate the threshold point problem. Forty-one Iranian students were selected; the participants were all between 20 and 30 years old. A quantitative approach was used to address the research questions. In doing so, a quasi-experimental design was utilized since the selection of the participants was not randomized. Based on the Fuzzy logic approach, the threshold point would be more stable during the analysis, resulting in rather constant reliability results and more precise assessment.

Keywords: criterion-referenced tests, threshold loss agreement, threshold point, fuzzy logic approach

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Authors: Fayssal Amrane, Azeddine Chaiba

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In this paper, type-2 fuzzy logic control (T2FLC) and neuro-fuzzy control (NFC) for a doubly fed induction generator (DFIG) based on direct power control (DPC) with a fixed switching frequency is proposed for wind generation application. First, a mathematical model of the doubly-fed induction generator implemented in d-q reference frame is achieved. Then, a DPC algorithm approach for controlling active and reactive power of DFIG via fixed switching frequency is incorporated using PID. The performance of T2FLC and NFC, which is based on the DPC algorithm, are investigated and compared to those obtained from the PID controller. Finally, simulation results demonstrate that the NFC is more robust, superior dynamic performance for wind power generation system applications.

Keywords: doubly fed induction generator (DFIG), direct power control (DPC), neuro-fuzzy control (NFC), maximum power point tracking (MPPT), space vector modulation (SVM), type 2 fuzzy logic control (T2FLC)

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Authors: Omar Eldenali, Ahmed M. Bufares

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There are primarily two types of Unmanned Aerial Vehicle (UAVs), namely, multirotor and fixed wing. Each type has its own advantages. This study introduces a design of a fixed wing vertical take-off and landing (VTOL) UAV. The design is classified as ready-to-fly (RTF) fixed wing UAV. This means that the UAV is capable of not only taking off, landing, or hovering like a multirotor aircraft but also cruising like a fixed wing UAV. In this study, the conceptual design of 15 kg takeoff weight twin-tail boom configuration FW-VTOL plane is carried out, the initial sizing of the plane is conducted, and both the horizontal and vertical tail configurations are estimated. Moreover, the power required for each stage of flight is determined. Finally, the stability analysis of the plane based on this design is performed, the results shows that this design based on the suggested flight mission is stable and can be utilized.

Keywords: FW-VTOL, initial sizing, constrain analysis, stability

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Authors: M. Khouil, N. Saber, M. Mestari

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This study aimed to propose, a different architecture of a Path Planning using the NECMOP. where several nonlinear objective functions must be optimized in a conflicting situation. The ability to detect and avoid collision is very important for mobile intelligent machines. However, many artificial vision systems are not yet able to quickly and cheaply extract the wealth information. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons linear and threshold logic, which simplified the actual implementation of all the networks proposed. This article represents a comprehensive algorithm that determine through the AMAXNET network a measure (a mini-maximum point) in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: path planning, collision detection, convex polyhedron, neural network

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Authors: A. Aarabzadeh, R. Hizaji

Abstract:

Reinforced Concrete (RC) deep beams are a special type of beams due to their geometry, boundary conditions, and behavior compared to ordinary shallow beams. For example, assumption of a linear strain-stress distribution in the cross section is not valid. Little study has been dedicated to fixed-end RC deep beams. Also, most experimental studies are carried out on simply supported deep beams. Regarding recent tendency for application of deep beams, possibility of using fixed-ended deep beams has been widely increased in structures. Therefore, it seems necessary to investigate the aforementioned structural element in more details. In addition to experimental investigation of a concrete deep beam under cyclic load, different failure mechanisms of fixed-ended deep beams under this type of loading have been evaluated in the present study. The results show that failure mechanisms of deep beams under cyclic loads are quite different from monotonic loads.

Keywords: deep beam, cyclic load, reinforced concrete, fixed-ended

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Authors: Shoeb Ahmed Adeel, Vivek Paul, K. Prajwal, Michael Fenelon

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Techniques have been used to tether and stabilize a multi-rotor MAV but carrying out the same process to a fixed wing MAV is a novel method which can be utilized in order to reduce damage occurring to the fixed wing MAVs while conducting flight test trials and PID tuning. A few sensors and on board controller is required to carry out this experiment in horizontal and vertical plane of the vehicle. Here we will be discussing issues such as sensitivity of the air vehicle, endurance and external load of the string acting on the vehicle.

Keywords: MAV, PID tuning, tethered flight, UAV

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Nishita Jaiswal, Apoorv Mohan Satpute

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The increasing demand for efficient, cost-effective motor control systems in the automotive industry has driven the need for advanced, highly optimized control algorithms. Field-Oriented Control (FOC) has established itself as the leading approach for motor control, offering precise and dynamic regulation of torque, speed, and position. However, as energy efficiency becomes more critical in modern applications, implementing FOC on low-power, cost-sensitive microcontrollers pose significant challenges due to the limited availability of computational and hardware resources. Currently, most solutions rely on high-performance 32-bit microcontrollers or Application-Specific Integrated Circuits (ASICs) equipped with Floating Point Units (FPUs) and Hardware Accelerated Units (HAUs). These advanced platforms enable rapid computation and simplify the execution of complex control algorithms like FOC. However, these benefits come at the expense of higher costs, increased power consumption, and added system complexity. These drawbacks limit their suitability for embedded systems with strict power and budget constraints, where achieving energy and execution efficiency without compromising performance is essential. In this paper, we present an alternative approach that utilizes optimized data representation and computation techniques on a 16-bit microcontroller without FPUs or HAUs. By carefully optimizing data point formats and employing fixed-point arithmetic, we demonstrate how the precision and computational efficiency required for FOC can be maintained in resource-constrained environments. This approach eliminates the overhead performance associated with floating-point operations and hardware acceleration, providing a more practical solution in terms of cost, scalability and improved execution time efficiency, allowing faster response in motor control applications. Furthermore, it enhances system design flexibility, making it particularly well-suited for applications that demand stringent control over power consumption and costs.

Keywords: field-oriented control, fixed-point arithmetic, floating point unit, hardware accelerator unit, motor control systems

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Authors: Meng Wu

Abstract:

Unmanned aerial vehicle (UAV) landing technology is a common task that is required to be fulfilled by fly robots. In this paper, the crazyflie2.0 is located by ultra-wideband (UWB) localization system that contains 4 UWB anchors. Another UWB anchor is introduced and installed on a stationary platform. One cost function is designed to find the minimum distance between crazyflie2.0 and the anchor installed on the stationary platform. The coordinates of the anchor are unknown in advance, and the goal of the cost function is to define the location of the anchor, which can be considered as an optimal landing point. When the cost function reaches the minimum value, the corresponding coordinates of the UWB anchor fixed on the stationary platform can be calculated and defined as the landing point. The simulation shows the effectiveness of the method in this paper.

Keywords: UAV landing, UWB localization system, UWB anchor, cost function, stationary platform

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Authors: Jun Li, Wenze Wang, Zhanggui Hu, Yongwei Zhu, Dunwen Zuo

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Non-water based fixed abrasive polishing was adopted to manufacture LBO crystal for nano precision surface quality because of its deliquescent. Ethyl alcohol was selected as the non-water based slurry solvent and ethanediamine, lactic acid, hydrogen peroxide were add in the slurry as a chemical additive, respectively. Effect of different additives with non-water based slurry on material removal rate, surface topography, microscopic appearances and surface roughness were investigated in fixed abrasive polishing of LBO crystal. The results show the best surface quality of LBO crystal with surface roughness Sa 8.2 nm and small damages was obtained by non-water based slurry with lactic acid. Non-water based fixed abrasive polishing can achieve nano precision surface quality of LBO crystal with high material removal.

Keywords: non-water based slurry, LBO crystal, fixed abrasive polishing, surface roughness

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Authors: Mitsuyoshi Tomiya, Kentaro Kawamura, Shoichi Sakamoto

Abstract:

In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space.

Keywords: chaotic billiard, Poincaré section, scar, wave packet

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Authors: Rupu Yang, Cong Toan Tran, Assaad Zoughaib

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The work provides an iterative nonlinear programming method to synthesize a heat exchanger network by manipulating the trade-offs between the heat load of process heat exchangers (HEs) and utilities. We consider for the synthesis problem two cases, the first one without fixed cost for HEs, and the second one with fixed cost. For the no fixed cost problem, the nonlinear programming (NLP) model with all the potential HEs is optimized to obtain the global optimum. For the case with fixed cost, the NLP model is iterated through adding/removing HEs. The method was applied in five case studies and illustrated quite well effectiveness. Among which, the approach reaches the lowest TAC (2,904,026$/year) compared with the best record for the famous Aromatic plants problem. It also locates a slightly better design than records in literature for a 10 streams case without fixed cost with only 1/9 computational time. Moreover, compared to the traditional mixed-integer nonlinear programming approach, the iterative NLP method opens a possibility to consider constraints (such as controllability or dynamic performances) that require knowing the structure of the network to be calculated.

Keywords: heat exchanger network, synthesis, NLP, optimization

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Authors: So-Ra Jeon, Chan Byon

Abstract:

This study investigates the heat transfer characteristics of aluminum foam heat sink and pin fin heat sink subjected to an impinging air jet under a fixed pumping power condition as well as fixed flow rate condition. The effects of dimensionless pumping power or the Reynolds number and the impinging distance ratio on the Nusselt number are considered. The result shows that the effect of the impinging distance on the Nusselt number is negligible under a fixed pumping power condition, while the Nusselt number increases with decreasing the impinging distance under a fixed pumping power condition. A correlation for the pressure drop is obtained as a function of the flow rate and the impinging distance ratio. And correlations for the stagnation Nusselt number of the impinging jet are developed as a function of the pumping power. The aluminum foam heat sinks did not show higher thermal performance compared to a conventional pin fin heat sink under a fixed pumping power condition.

Keywords: aluminum foam, heat sinks, impinging jet, pumping power

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Authors: Umar Yusuf Batsari

Abstract:

Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

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Authors: M. Chafi, S. Akazdam, C. Asrir, L. Sebbahi, B. Gourich, N. Barka, M. Essahli

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Fixed bed adsorption has become a frequently used industrial application in wastewater treatment processes. Various low cost adsorbents have been studied for their applicability in treatment of different types of effluents. In this work, the intention of the study was to explore the efficacy and feasibility for azo dye, Acid Orange 7 (AO7) adsorption onto fixed bed column of NaOH Treated eggshell (TES). The effect of various parameters like flow rate, initial dye concentration, and bed height were exploited in this study. The studies confirmed that the breakthrough curves were dependent on flow rate, initial dye concentration solution of AO7 and bed depth. The Thomas, Yoon–Nelson, and Adams and Bohart models were analysed to evaluate the column adsorption performance. The adsorption capacity, rate constant and correlation coefficient associated to each model for column adsorption was calculated and mentioned. The column experimental data were fitted well with Thomas model with coefficients of correlation R2 ≥0.93 at different conditions but the Yoon–Nelson, BDST and Bohart–Adams model (R2=0.911), predicted poor performance of fixed-bed column. The (TES) was shown to be suitable adsorbent for adsorption of AO7 using fixed-bed adsorption column.

Keywords: adsorption models, acid orange 7, bed depth, breakthrough, dye adsorption, fixed-bed column, treated eggshell

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Authors: Jae Moon Lee

Abstract:

In general, algorithms to find continuous k-nearest neighbors have been researched on the location based services, monitoring periodically the moving objects such as vehicles and mobile phone. Those researches assume the environment that the number of query points is much less than that of moving objects and the query points are not moved but fixed. In gaming environments, this problem is when computing the next movement considering the neighbors such as flocking, crowd and robot simulations. In this case, every moving object becomes a query point so that the number of query point is same to that of moving objects and the query points are also moving. In this paper, we analyze the performance of the existing algorithms focused on location based services how they operate under gaming environments.

Keywords: flocking behavior, heterogeneous agents, similarity, simulation

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Authors: Pratyush Agnihotri

Abstract:

This paper presents a comprehensive overview of the conceptual design process for a fixed-wing vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV). Fixed-wing VTOL UAVs combine the advantages of rotary-wing aircraft, such as vertical take-off and landing capabilities, with the efficiency and speed of fixed-wing flight. The primary objective of this study is to explore the aerodynamic design principles that optimize performance parameters, including range, endurance, and stability while maintaining the VTOL capability. The design process involves selecting appropriate airfoils, optimizing wing configurations, and integrating propulsion systems suitable for both hovering and forward flight. Analytical methods are employed to evaluate aerodynamic performance, with a focus on lift-to-drag ratio, power requirements, and control strategies. The results highlight the challenges and trade-offs inherent in designing such hybrid aircraft, particularly in balancing the conflicting requirements of VTOL and fixed-wing flight. This study contributes to the development of efficient, versatile UAVs capable of operating in diverse environments.

Keywords: fixed wing, hybrid, VTOL, UAV

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Authors: Lazhar mouloud, Chemat Zoubida, Ouhoumna Faiza

Abstract:

The main objective of this study, concerns the modeling of breakthrough curves obtained in the adsorption column of malachite green into alginate-encapsulated aluminium pillared clay in fixed bed according to various operating parameters such as the initial concentration, the feed rate and the height fixed bed, applying mathematical models namely: the model of Bohart and Adams, Wolborska, Bed Depth Service Time, Clark and Yoon-Nelson. These models allow us to express the different parameters controlling the performance of the dynamic adsorption system. The results have shown that all models were found suitable for describing the whole or a definite part of the dynamic behavior of the column with respect to the flow rate, the inlet dye concentration and the height of fixed bed.

Keywords: adsorption column, malachite green, pillared clays, alginate, modeling, mathematic models, encapsulation.

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Authors: A. Benmerkhi, A. Bounouioua, M. Bouchemat, T. Bouchemat

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In this paper, we present a numerical optical properties of a triangular periodic lattice of elliptical air holes. We report the influence of the ratio (semi-major axis length of elliptical hole to the filling ratio) on the photonic band gap. Then by using the finite difference time domain (FDTD) algorithm, the resonant wavelength of the point defect microcavities in a two-dimensional photonic crystal (PC) shifts towards the low wavelengths with significantly increased filing ratio. It can be noted that the Q factor is gradually changed to higher when the filling ratio increases. It is due to an increase in reflectivity of the PC mirror. Also we theoretically investigate the H1 cavity, where the value of semi-major axis (Rx) of the six holes surrounding the cavity are fixed at 0.5a and the Rx of the two edge air holes are fixed at the optimum value of 0.52a. The highest Q factor of 4.1359 × 10⁶ is achieved at the resonant mode located at λ = 1.4970 µm.

Keywords: photonic crystal, microcavity, filling ratio, elliptical holes

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Authors: Y. L. Sun, L. Shao, Y. Zhao, H. X. Zhou, W. Z. Lu, J. Li, D. W. Zuo

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This study introduces an ice fixed-abrasive polishing (IFAP) technology. Using silica solution IFAP pad and Al2O3 IFAP pad, orthogonal tests were performed on polishing high-definition display panel glass, respectively. The results show that the polishing efficiency and effect polished with silica solution IFAP pad are better than those polished with Al2O3 IFAP pad. The optimized silica solution IFAP parameters are: polishing pressure 0.1MPa, polishing time 40min, table velocity 80r/min, and the ratio of accelerator and slurry 1:10. Finally, the IFAP mechanism was studied and it suggests by complicated analysis that IFAP is comprehensive effect of mechanical removal and microchemical reaction, combined with fixed abrasive polishing and free abrasive polishing.

Keywords: ice fixed-abrasive polishing, high-definition display panel glass, material removal rate, surface roughness

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Authors: Wenhao Lan, Ning Li, Qiang Tong

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To improve the registration accuracy of a source point cloud and template point cloud when the initial relative deflection angle is too large, a PointNetLK algorithm combined with an oriented bounding box (PointNetLK-OBB) is proposed. In this algorithm, the OBB of a 3D point cloud is used to represent the macro feature of source and template point clouds. Under the guidance of the iterative closest point algorithm, the OBB of the source and template point clouds is aligned, and a mirror symmetry effect is produced between them. According to the fitting degree of the source and template point clouds, the mirror symmetry plane is detected, and the optimal rotation and translation of the source point cloud is obtained to complete the 3D point cloud registration task. To verify the effectiveness of the proposed algorithm, a comparative experiment was performed using the publicly available ModelNet40 dataset. The experimental results demonstrate that, compared with PointNetLK, PointNetLK-OBB improves the registration accuracy of the source and template point clouds when the initial relative deflection angle is too large, and the sensitivity of the initial relative position between the source point cloud and template point cloud is reduced. The primary contribution of this paper is the use of PointNetLK to avoid the non-convex problem of traditional point cloud registration and leveraging the regularity of the OBB to avoid the local optimization problem in the PointNetLK context.

Keywords: mirror symmetry, oriented bounding box, point cloud registration, PointNetLK-OBB

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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