Search results for: discrete logarithm

Authors: R. Latif, W. Jenkal, A. Toumanari, A. Hatim

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This paper presents an efficient method of electrocardiogram signal denoising based on a hybrid approach. Two techniques are brought together to create an efficient denoising process. The first is an Adaptive Dual Threshold Filter (ADTF) and the second is the Discrete Wavelet Transform (DWT). The presented approach is based on three steps of denoising, the DWT decomposition, the ADTF step and the highest peaks correction step. This paper presents some application of the approach on some electrocardiogram signals of the MIT-BIH database. The results of these applications are promising compared to other recently published techniques.

Keywords: hybrid technique, ADTF, DWT, thresholding, ECG signal

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Authors: Yao Cheng, Weihua Zhang

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Although the measured vibration signal contains rich information on machine health conditions, the white noise interferences and the discrete harmonic coming from blade, shaft and mash make the fault diagnosis of rolling element bearings difficult. In order to overcome the interferences of useless signals, a new fault diagnosis method combining Complete Ensemble Empirical Mode Decomposition with adaptive noise (CEEMDAN) and Multipoint Optimal Minimum Entropy Deconvolution (MOMED) is proposed for the fault diagnosis of high-speed train bearings. Firstly, the CEEMDAN technique is applied to adaptively decompose the raw vibration signal into a series of finite intrinsic mode functions (IMFs) and a residue. Compared with Ensemble Empirical Mode Decomposition (EEMD), the CEEMDAN can provide an exact reconstruction of the original signal and a better spectral separation of the modes, which improves the accuracy of fault diagnosis. An effective sensitivity index based on the Pearson's correlation coefficients between IMFs and raw signal is adopted to select sensitive IMFs that contain bearing fault information. The composite signal of the sensitive IMFs is applied to further analysis of fault identification. Next, for propose of identifying the fault information precisely, the MOMED is utilized to enhance the periodic impulses in composite signal. As a non-iterative method, the MOMED has better deconvolution performance than the classical deconvolution methods such Minimum Entropy Deconvolution (MED) and Maximum Correlated Kurtosis Deconvolution (MCKD). Third, the envelope spectrum analysis is applied to detect the existence of bearing fault. The simulated bearing fault signals with white noise and discrete harmonic interferences are used to validate the effectiveness of the proposed method. Finally, the superiorities of the proposed method are further demonstrated by high-speed train bearing fault datasets measured from test rig. The analysis results indicate that the proposed method has strong practicability.

Keywords: bearing, complete ensemble empirical mode decomposition with adaptive noise, fault diagnosis, multipoint optimal minimum entropy deconvolution

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Authors: Amaia Martinez Martinez, Martin Turek, Carlos Ventura, Jay Drew

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This study aims to assess the seismic performance of arch and dome structural systems made from easy to assemble precast blocks of recycled concrete. These systems have been developed by Lock Block Ltd. Company from Vancouver, Canada, as an extension of their currently used retaining wall system. The characterization of the seismic behavior of these structures is performed by a combination of experimental static and dynamic testing, and analytical modeling. For the experimental testing, several tilt tests, as well as a program of shake table testing were undertaken using small scale arch models. A suite of earthquakes with different characteristics from important past events are chosen and scaled properly for the dynamic testing. Shake table testing applying the ground motions in just one direction (in the weak direction of the arch) and in the three directions were conducted and compared. The models were tested with increasing intensity until collapse occurred; which determines the failure level for each earthquake. Since the failure intensity varied with type of earthquake, a sensitivity analysis of the different parameters was performed, being impulses the dominant factor. For all cases, the arches exhibited the typical four-hinge failure mechanism, which was also shown in the analytical model. Experimental testing was also performed reinforcing the arches using a steel band over the structures anchored at both ends of the arch. The models were tested with different pretension levels. The bands were instrumented with strain gauges to measure the force produced by the shaking. These forces were used to develop engineering guidelines for the design of the reinforcement needed for these systems. In addition, an analytical discrete element model was created using 3DEC software. The blocks were designed as rigid blocks, assigning all the properties to the joints including also the contribution of the interlocking shear key between blocks. The model is calibrated to the experimental static tests and validated with the obtained results from the dynamic tests. Then the model can be used to scale up the results to the full scale structure and expanding it to different configurations and boundary conditions.

Keywords: arch, discrete element model, seismic assessment, shake-table testing

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Authors: Nirmal Yadav, Tanuja Srivastava

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Shannon theory is an exact method to recover a band limited signals from its sampled values in discrete implementation, using sinc interpolators. But sinc based results are not much satisfactory for band-limited calculations so that convolution with window function, having compact support, has been introduced. Convolution Backprojection algorithm with window function is an approximation algorithm. In this paper, the error has been calculated, arises due to this approximation nature of reconstruction algorithm. This result will be defined for fan beam projection data which is more faster than parallel beam projection.

Keywords: computed tomography, convolution backprojection, radon transform, fan beam

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Authors: Tomasz Komornicki

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The primary aim of the presentation is to try to model border traffic and, at the same time to explain on which economic variables the intensity of border traffic depended in the long term. For this purpose, long series of traffic data on the Polish borders were used. Models were estimated for three variants of explanatory variables: a) for total arrivals and departures (total movement of Poles and foreigners), b) for arrivals and departures of Poles, and c) for arrivals and departures of foreigners. Each of the defined explanatory variables in the models appeared as the logarithm of the natural number of persons. Data from 1994-2017 were used for modeling (for internal Schengen borders for the years 1994-2007). Information on the number of people arriving in and leaving Poland was collected for a total of 303 border crossings. On the basis of the analyses carried out, it was found that one of the main factors determining border traffic is generally differences in the level of economic development (GDP) and the condition of the economy (level of unemployment) and the degree of border permeability. Also statistically significant for border traffic are differences in the prices of goods (fuels, tobacco, and alcohol products) and services (mainly basic ones, e.g., hairdressing services). Such a relationship exists mainly on the eastern border (border traffic determined largely by differences in the prices of goods) and on the border with Germany (in the first analysed period, border traffic was determined mainly by the prices of goods, later - after Poland's accession to the EU and the Schengen area - also by the prices of services). The models also confirmed differences in the set of factors shaping the volume and structure of border traffic on the Polish borders resulting from general geopolitical conditions, with the year 2007 being an important caesura, after which the classical population mobility factors became visible. The results obtained were additionally related to changes in traffic that occurred as a result of the CPOVID-19 pandemic and as a result of the Russian aggression against Ukraine.

Keywords: border, modal structure, transport, Ukraine

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Authors: Natasha Sharma, Kulbhushan Agnihotri

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Cellular Automata are discrete dynamical systems which are based on local character and spatial disparateness of the spreading process. These factors are generally neglected by traditional models based on differential equations for epidemic spread. The aim of this work is to introduce an SEIR model based on cellular automata on graphs to imitate epidemic spreading. Distinctively, it is an SEIR-type model where the population is divided into susceptible, exposed, infected and recovered individuals. The results obtained from simulations are in accordance with the spreading behavior of a real time epidemics.

Keywords: cellular automata, epidemic spread, graph, susceptible

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Authors: Thierry Ganomanana, Dominique Hervé, Solo Randriamahaleo

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Management of Malagasy renewable natural re-sources allows, in the case of forest, the mobilization of several actors with norms and/or territory. The interaction in this socio-ecosystem is represented by a graph of two different relationships in which most of action chains, from individual activities under the continuous of forest dynamic and discrete interventions by institutional, are also studied. The fuzzy set theory is adapted to graduate the elements of the set Illegal Activities in the space of sanction’s institution by his severity and in the space of degradation of forest by his extent.

Keywords: fuzzy set, graph, institution, renewable resource, system

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Authors: A. F. Momin, D. V. Khakhar

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Granular materials consist of particulate particles found in nature and various industries that, due to gravity flow, behave macroscopically like liquids. A fundamental industrial unit operation is a hopper with inclined walls or a converging channel in which material flows downward under gravity and exits the storage bin through the bottom outlet. The simplest form of the flow corresponds to a wedge-shaped, quasi-two-dimensional geometry with smooth walls and radially directed gravitational force toward the apex of the wedge. These flows were examined using the Mohr-Coulomb criterion in the classic work of Savage (1965), while Ravi Prakash and Rao used the critical state theory (1988). The smooth-wall radial gravity (SWRG) wedge-shaped hopper is simulated using the discrete element method (DEM) to test existing theories. DEM simulations involve the solution of Newton's equations, taking particle-particle interactions into account to compute stress and velocity fields for the flow in the SWRG system. Our computational results are consistent with the predictions of Savage (1965) and Ravi Prakash and Rao (1988), except for the region near the exit, where both viscous and frictional effects are present. To further comprehend this behaviour, a parametric analysis is carried out to analyze the rheology of wedge-shaped hoppers by varying the orifice diameter, wedge angle, friction coefficient, and stiffness. The conclusion is that velocity increases as the flow rate increases but decreases as the wedge angle and friction coefficient increase. We observed no substantial changes in velocity due to varying stiffness. It is anticipated that stresses at the exit result from the transfer of momentum during particle collisions; for this reason, relationships between viscosity and shear rate are shown, and all data are collapsed into a single curve. In addition, it is demonstrated that viscosity and volume fraction exhibit power law correlations with the inertial number and that all the data collapse into a single curve. A continuum model for determining granular flows is presented using empirical correlations.

Keywords: discrete element method, gravity flow, smooth-wall, wedge-shaped hoppers

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Authors: Prudhvinath Reddy Ankireddy, Narasimha Mangadoddy

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Spiral concentrators are commonly used in various industries, including mineral and coal processing, to efficiently separate materials based on their density and size. In these concentrators, a mixture of solid particles and fluid (usually water) is introduced as feed at the top of a spiral channel. As the mixture flows down the spiral, centrifugal and gravitational forces act on the particles, causing them to stratify based on their density and size. Spiral flows exhibit complex fluid dynamics, and interactions involve multiple phases and components in the process. Understanding the behavior of these phases within the spiral concentrator is crucial for achieving efficient separation. An experimental bi-component particle interaction study is conducted in this work utilizing magnetite (heavier density) and silica (lighter density) with different proportions processed in the spiral concentrator. The observation separation reveals that denser particles accumulate towards the inner region of the spiral trough, while a significant concentration of lighter particles are found close to the outer edge. The 5th turn of the spiral trough is partitioned into five zones to achieve a comprehensive distribution analysis of bicomponent particle segregation. Samples are then gathered from these individual streams using an in-house sample collector, and subsequent analysis is conducted to assess component segregation. Along the trough, there was a decline in the concentration of coarser particles, accompanied by an increase in the concentration of lighter particles. The segregation pattern indicates that the heavier coarse component accumulates in the inner zone, whereas the lighter fine component collects in the outer zone. The middle zone primarily consists of heavier fine particles and lighter coarse particles. The zone-wise results reveal that there is a significant fraction of segregation occurs in inner and middle zones. Finer magnetite and silica particles predominantly accumulate in outer zones with the smallest fraction of segregation. Additionally, numerical simulations are also carried out using the computational fluid dynamics (CFD) model based on the volume of fluid (VOF) approach incorporating the RSM turbulence model. The discrete phase model (DPM) is employed for particle tracking, thereby understanding the particle segregation of magnetite and silica along the spiral trough.

Keywords: spiral concentrator, bi-component particle segregation, computational fluid dynamics, discrete phase model

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Authors: Wilson Enríquez, Daniel Cardenas

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This article proposes a filter bank format combined with the mathematical tool called polyphase decomposition and the discrete Fourier transform (DFT) with the purpose of improving the performance of the fifth-generation communication systems (5G). We started with a review of the literature and the study of the filter bank theory and its combination with DFT in order to improve the performance of wireless communications since it reduces the computational complexity of these communication systems. With the proposed technique, several experiments were carried out in order to evaluate the structures in 5G systems. Finally, the results are presented in graphical form in terms of bit error rate against the ratio bit energy/noise power spectral density (BER vs. Eb / No).

Keywords: multi-carrier system (5G), filter bank, polyphase decomposition, FIR equalizer

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Authors: Sadam Alwadi

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Outlier values become a problem that frequently occurs in the data observation or recording process. Thus, the need for data imputation has become an essential matter. In this work, it will make use of the methods described in the prior work to detect the outlier values based on a collection of stock market data. In order to implement the detection and find some solutions that maybe helpful for investors, real closed price data were obtained from the Amman Stock Exchange (ASE). Tukey and Maximum Overlapping Discrete Wavelet Transform (MODWT) methods will be used to impute the detect the outlier values.

Keywords: outlier values, imputation, stock market data, detecting, estimation

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Authors: Hachmi Ben Ameur, Jean Luc Prigent

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We propose an extension of the CPPI method, which is based on conditional floors. In this framework, we examine in particular the TIPP and margin based strategies. These methods allow keeping part of the past gains and protecting the portfolio value against future high drawdowns of the financial market. However, as for the standard CPPI method, the investor can benefit from potential market rises. To control the risk of such strategies, we introduce both Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures. For each of these criteria, we show that the conditional floor must be higher than a lower bound. We illustrate these results, for a quite general ARCH type model, including the EGARCH (1,1) as a special case.

Keywords: CPPI, conditional floor, ARCH, VaR, expected ehortfall

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh Kumar Pandey

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A discrete time fractional orderdifferentiator has been modeled for estimating the fractional order derivatives of contaminated signal. The proposed approach is based on Chebyshev’s polynomials. We use the Riemann-Liouville fractional order derivative definition for designing the fractional order SG differentiator. In first step we calculate the window weight corresponding to the required fractional order. Then signal is convoluted with this calculated window’s weight for finding the fractional order derivatives of signals. Several signals are considered for evaluating the accuracy of the proposed method.

Keywords: fractional order derivative, chebyshev polynomials, signals, S-G differentiator

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Authors: Riddhi Jangid, Gajendra Pratap Singh

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Petri nets, a formalized modeling language that was introduced back around 50-60 years, have been widely used for modeling discrete event dynamic systems and simulating their behavior. Reachability analysis of Petri nets gives many insights into a modeled system. This idea leads us to study the reachability technique and use it in the reachability problem in the state space of reachable markings. With the same concept, Crisp Boolean Petri nets were defined in which the marking vectors that are boolean are distinct in the reachability analysis of the nets. We generalize the concept and define ‘Crisp’ Petri nets that generate the marking vectors exactly once in their reachability-based analysis, not necessarily Boolean.

Keywords: marking vector, n-vector, Petri nets, reachability

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Authors: Takashi Mitsuishi

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Fuzzy logic has gained acceptance in the recent years in the fields of social sciences and humanities such as psychology and linguistics because it can manage the fuzziness of words and human subjectivity in a logical manner. However, the major field of application of the fuzzy logic is control engineering as it is a part of the set theory and mathematical logic. Mamdani method, which is the most popular technique for approximate reasoning in the field of fuzzy control, is one of the ways to numerically represent the control afforded by human language and sensitivity and has been applied in various practical control plants. Fuzzy logic has been gradually developing as an artificial intelligence in different applications such as neural networks, expert systems, and operations research. The objects of inference vary for different application fields. Some of these include time, angle, color, symptom and medical condition whose fuzzy membership function is a periodic function. In the defuzzification stage, the domain of the membership function should be unique to obtain uniqueness its defuzzified value. However, if the domain of the periodic membership function is determined as unique, an unintuitive defuzzified value may be obtained as the inference result using the center of gravity method. Therefore, the authors propose a method of circular-polar-coordinates transformation and defuzzification of the periodic membership functions in this study. The transformation to circular polar coordinates simplifies the domain of the periodic membership function. Defuzzified value in circular polar coordinates is an argument. Furthermore, it is required that the argument is calculated from a closed plane figure which is a periodic membership function on the circular polar coordinates. If the closed plane figure is continuous with the continuity of the membership function, a significant amount of computation is required. Therefore, to simplify the practice example and significantly reduce the computational complexity, we have discretized the continuous interval and the membership function in this study. In this study, the following three methods are proposed to decide the argument from the discrete polygon which the continuous plane figure is transformed into. The first method provides an argument of a straight line passing through the origin and through the coordinate of the arithmetic mean of each coordinate of the polygon (physical center of gravity). The second one provides an argument of a straight line passing through the origin and the coordinate of the geometric center of gravity of the polygon. The third one provides an argument of a straight line passing through the origin bisecting the perimeter of the polygon (or the closed continuous plane figure).

Keywords: defuzzification, fuzzy membership function, periodic function, polar coordinates transformation

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Authors: Karthiyayini J., Arpita Chowdary Vantipalli, Darshana Sailu Tanti, Malvika Ravi Kudari, Krtin Kannan

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This paper is propelled from the generally existing undertaking of the smart water quality management, which addresses an IoT (Internet of things) based brilliant water quality observing (SWQM) framework which we call it AquaSwach that guides in the ceaseless estimation of water conditions dependent on five actual boundaries i.e., temperature, pH, electric conductivity and turbidity properties and water virtue estimation each time you drink water. Six sensors relate to Arduino-Mega in a discrete way to detect the water parameters. Extracted data from the sensors are transmitted to a desktop application developed in the NET platform and compared with the WHO (World Health Organization) standard values.

Keywords: AquaSwach, IoT, WHO, water quality

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The paper is focused on the operational model for transport the single wagon consignments on railway network by using two different models of train formation. The paper gives an overview of possibilities of improving the quality of transport services. Paper deals with two models used in problematic of train formatting - time continuously and time discrete. By applying these models in practice, the transport company can guarantee a higher quality of service and expect increasing of transport performance. The models are also applicable into others transport networks. The models supplement a theoretical problem of train formation by new ways of looking to affecting the organization of wagon flows.

Keywords: train formation, wagon flows, marshalling yard, railway technology

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Authors: Tassadit Tabouche

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Water sprays pattern, and water droplets size (different droplets diameter) are a key factors in the success of the suppression by water spray. The effects of the two important factors are investigated in this study. However, the fire extinguishing mechanism in such devices is not well understood due to the complexity of the physical and chemical interactions between water spray and fire plume. in this study, 3D, unsteady, two phase flow CFD simulation approach is introduced to provide a quantitative analysis of the complex interactions occurring between water spray and fire plume. Lagrangian Discrete Phase Model (DPM) was used for water droplets and a global one-step reaction mechanism in combustion model was used for fire plume.

Keywords: droplets, water spray, water droplets size, 3D

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Authors: Aouaouche Elmaouhab, Hassina Beggar

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Solving multi-objective discrete optimization applications has always been limited by the resources of one machine: By computing power or by memory, most often both. To speed up the calculations, the grid computing represents a primary solution for the treatment of these applications through the parallelization of these resolution methods. In this work, we are interested in the study of some methods for solving multiple objective integer linear programming problem based on Branch-and-Bound and the study of grid computing technology. This study allowed us to propose an implementation of the method of Abbas and Al on the grid by reducing the execution time. To enhance our contribution, the main results are presented.

Keywords: multi-objective optimization, integer linear programming, grid computing, parallel computing

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Authors: Vassilis C. Moulianitis, Evgenios Scourboutis, Ilias Katsanis, Paraskevas Papanikos, Nikolas Zacharopoulos

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This paper presents the conceptual design of an automated biomethane potential measurement system. First, the design specifications for the BMP system and the basic components of the system will be presented. Three concepts that meet the design specifications will be presented. The basic characteristics of each concept will be analyzed in detail. The concepts will be evaluated using a set of design criteria that includes flexibility, cost, size, complexity, aesthetics, and accessibility in order to determine the best solution. The evaluation will be based on the discrete Choquet integral.

Keywords: automated biomethane test, conceptual mechatronics design, concept evaluation, Choquet integral

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Authors: V. Kumar, K. Jha

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The present study is done to explore design modifications of the vortex finder, as it has a significant effect on the cyclone separator performance. It is evident that modifications of the vortex finder improve the performance of the cyclone separator significantly. The study conducted strives to improve the overall performance of cyclone separators by utilizing a converging-diverging (CD) vortex finder instead of the traditional uniform diameter vortex finders. The velocity and pressure fields inside a Stairmand cyclone separator with body diameter 0.29m and vortex finder diameter 0.1305m are calculated. The commercial software, Ansys Fluent v14.0 is used to simulate the flow field in a uniform diameter cyclone and six cyclones modified with CD vortex finders. Reynolds stress model is used to simulate the effects of turbulence on the fluid and particulate phases, discrete phase model is used to calculate the particle trajectories. The performance of the modified vortex finders is compared with the traditional vortex finder. The effects of the lengths of the converging and diverging sections, the throat diameter and the end diameters of the convergent divergent section are also studied to achieve enhanced performance. The pressure and velocity fields inside the vortex finder are presented by means of contour plots and velocity vectors and changes in the flow pattern due to variation of the geometrical variables are also analysed. Results indicate that a convergent-divergent vortex finder is capable of decreasing the pressure drop than that achieved through a uniform diameter vortex finder. It is also observed that the end diameters of the CD vortex finder, the throat diameter and the length of the diverging part of the vortex finder have a significant impact on the cyclone separator performance. Increase in the lower diameter of the vortex finder by 66% results in 11.5% decrease in the dimensionless pressure drop (Euler number) with 5.8% decrease in separation efficiency. Whereas 50% decrease in the throat diameter gives 5.9% increase in the Euler number with 10.2% increase in the separation efficiency and increasing the length of the diverging part gives 10.28% increase in the Euler number with 5.74% increase in the separation efficiency. Increasing the upper diameter of the CD vortex finder is seen to produce an adverse effect on the performance as it increases the pressure drop significantly and decreases the separation efficiency. Increase in length of the converging is not seen to affect the performance significantly. From the present study, it is concluded that convergent-divergent vortex finders can be used in place of uniform diameter vortex finders to achieve a better cyclone separator performance.

Keywords: convergent-divergent vortex finder, cyclone separator, discrete phase modeling, Reynolds stress model

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Authors: Joshua W. Edefo, Shafiul Azam, Murray D. Smith

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Introduction: In April 2022, the Welsh Government introduced the six goals for urgent and emergency care programs. One of these goals was to provide access to clinically safe alternatives, leading to the establishment of the Same Day Emergency Care (SDEC) program. The SDEC initiative aims to offer viable options that maintain patient safety while avoiding unnecessary hospital stays. The aim of the study is to determine the duration of patient stay in SDEC and compare it with that of Emergency department (ED) stay to ascertain if one of the objectives of SDEC is achieved. Methods: Patient stays and attendance datasets were constructed from Withybush SDEC and ED patient records. These records were provided by Hywel Dda University Health Board Informatics. Some hypothetical pathways were identified, notably SDEC visits involving a single attendance and ED visits then immediately transferred to SDEC. Descriptive statistics were used to summarise the data, and hypothesis tests for mean differences used the student t-test. Propensity scoring was employed to match a set of ED patient stays to SDEC patient stays which were then used to determine the average treatment effect (ATE) to compare durations of stay in SDEC with ED. Regression methods were used to model the natural logarithm of the duration of SDEC attendance, and the level of statistical significance was set to 0.05. Results: SDEC visits involving a single attendance (170 of 384; 44.3%) is the most frequently observed pathway with patient length of stay at 256 minutes (95%CI 237.4 - 275.1). The next most frequently observed pathway of patient stay was SDEC attendance after presenting to ED (80 of 384; 20.8%) and gave the length of stay of 440 minutes (95%CI 351.6 - 529.2). Time spent in this pathway significantly increased by 184 minutes (95%CI 118.0 - 250.2, support for no difference p<0.001) compared to the most seen pathway. When SDEC data were compared with ED, the estimate for the ATE from SDEC single attendance was -272 minutes (95%CI -334.1 - -210.5; p<0.001), while that of ED then SDEC pathway was -50.6 min (95%CI -182.7-81.5; p=0.453). Conclusion: When patients are admitted to SDEC and successfully discharged, their stays are significantly shorter, approximately 4.5 hours, compared to patients who spend their entire stay in the Emergency Department. That difference vanishes when the patient stay includes a period spent previously in ED before transfer to SDEC.

Keywords: attendance, emergency-department, patient-stay, same-day-emergency-care

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Authors: I. Khutsishvili, G. Sirbiladze, B. Ghvaberidze

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This work proposes a fuzzy methodology to support the investment decisions. While choosing among competitive investment projects, the methodology makes ranking of projects using the new aggregation OWA operator – AsPOWA, presented in the environment of possibility uncertainty. For numerical evaluation of the weighting vector associated with the AsPOWA operator the mathematical programming problem is constructed. On the basis of the AsPOWA operator the projects’ group ranking maximum criteria is constructed. The methodology also allows making the most profitable investments into several of the project using the method developed by the authors for discrete possibilistic bicriteria problems. The article provides an example of the investment decision-making that explains the work of the proposed methodology.

Keywords: expert evaluations, investment decision making, OWA operator, possibility uncertainty

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Authors: Andrey Davydov, Konstantin Sveshnikov, Yulia Voronina

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There is now a lot of interest to the non-perturbative QED-effects, caused by diving of discrete levels into the negative continuum in the supercritical static or adiabatically slowly varying Coulomb fields, that are created by the localized extended sources with Z > Z_cr. Such effects have attracted a considerable amount of theoretical and experimental activity, since in 3+1 QED for Z > Z_cr,1 ≈ 170 a non-perturbative reconstruction of the vacuum state is predicted, which should be accompanied by a number of nontrivial effects, including the vacuum positron emission. Similar in essence effects should be expected also in both 2+1 D (planar graphene-based hetero-structures) and 1+1 D (one-dimensional ‘hydrogen ion’). This report is devoted to the study of such essentially non-perturbative vacuum effects for the supercritical Dirac-Coulomb systems in 1+1D and 2+1D, with the main attention drawn to the vacuum polarization energy. Although the most of works considers the vacuum charge density as the main polarization observable, vacuum energy turns out to be not less informative and in many respects complementary to the vacuum density. Moreover, the main non-perturbative effects, which appear in vacuum polarization for supercritical fields due to the levels diving into the lower continuum, show up in the behavior of vacuum energy even more clear, demonstrating explicitly their possible role in the supercritical region. Both in 1+1D and 2+1D, we explore firstly the renormalized vacuum density in the supercritical region using the Wichmann-Kroll method. Thereafter, taking into account the results for the vacuum density, we formulate the renormalization procedure for the vacuum energy. To evaluate the latter explicitly, an original technique, based on a special combination of analytical methods, computer algebra tools and numerical calculations, is applied. It is shown that, for a wide range of the external source parameters (the charge Z and size R), in the supercritical region the renormalized vacuum energy could significantly deviate from the perturbative quadratic growth up to pronouncedly decreasing behavior with jumps by (-2 x mc^2), which occur each time, when the next discrete level dives into the negative continuum. In the considered range of variation of Z and R, the vacuum energy behaves like ~ -Z^2/R in 1+1D and ~ -Z^3/R in 2+1D, exceeding deeply negative values. Such behavior confirms the assumption of the neutral vacuum transmutation into the charged one, and thereby of the spontaneous positron emission, accompanying the emergence of the next vacuum shell due to the total charge conservation. To the end, we also note that the methods, developed for the vacuum energy evaluation in 2+1 D, with minimal complements could be carried over to the three-dimensional case, where the vacuum energy is expected to be ~ -Z^4/R and so could be competitive with the classical electrostatic energy of the Coulomb source.

Keywords: non-perturbative QED-effects, one- and two-dimensional Dirac-Coulomb systems, supercritical fields, vacuum polarization

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Authors: Mahboobeh Eghtesad, Reza Mohseni

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We develop methods for detecting a target for orthogonal frequency division multiplexing (OFDM) based radars. As a preliminary step we introduce the target and Gaussian noise models in discrete–time form. Then, resorting to match filter (MF) we derive a detector for two different scenarios: a non-fluctuating target and a Rayleigh fluctuating target. It will be shown that a MF is not suitable for Rayleigh fluctuating targets. In this paper we propose a reduced-complexity method based on fast Fourier transfrom (FFT) for such a situation. The proposed method has better detection performance.

Keywords: constant false alarm rate (CFAR), match filter (MF), fast Fourier transform (FFT), OFDM radars, Rayleigh fluctuating target

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: Joon-Hoon Park

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In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: Masato Sasaki, Masayoshi Yamamoto

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The majority of wireless power transfer (WPT) systems transfer power in a directional manner. This paper describes a discrete exciting voltage control technique for WPT via magnetic resonant coupling with two orthogonal transmitter coils (2D omni-directional WPT system) which can maximize the power transfer efficiency in response to the change of coupling status. The theory allows the equations of the efficiency of the system to be determined at all the rate of the mutual inductance. The calculated results are included to confirm the advantage to one directional WPT system and the validity of the theory and the equations.

Keywords: wireless power transfer, omni-directional, orthogonal, efficiency

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Authors: Neda Lovričević, Đilda Pečarić, Josip Pečarić

Abstract:

The Jensen functional in its discrete form is brought in relation to the Csiszar divergence functional, this time via its monotonicity property. This approach presents a generalization of the previously obtained results that made use of interpolating Jensen-type inequalities. Thus the monotonicity property is integrated with the Zipf-Mandelbrot law and applied to f-divergences for probability distributions that originate from the Csiszar divergence functional: Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance, chi-square divergence, total variation distance. The Zipf-Mandelbrot and the Zipf law are widely used in various scientific fields and interdisciplinary and here the focus is on the aspect of the mathematical inequalities.

Keywords: Jensen functional, monotonicity, Csiszar divergence functional, f-divergences, Zipf-Mandelbrot law

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Authors: Omid Heydarnia, Akbar Allahverdizadeh, Behnam Dadashzadeh, M. R. Sayyed Noorani

Abstract:

Underactuated biped robots control is one of the interesting topics in robotics. The main difficulties are its highly nonlinear dynamics, open-loop instability, and discrete event at the end of the gait. One of the methods to control underactuated systems is the partial feedback linearization, but it is not robust against uncertainties and disturbances that restrict its performance to control biped walking and running. In this paper, fuzzy partial feedback linearization is presented to overcome its drawback. Numerical simulations verify the effectiveness of the proposed method to generate stable and robust biped walking and running gaits.

Keywords: underactuated system, biped robot, fuzzy control, partial feedback linearization

Procedia PDF Downloads 350