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Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal
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作者 Mahendra Acharya Khomendra Bhandari +2 位作者 Sandesh Dhakal Aasish Giri Prabin Kafle 《International Journal of Geosciences》 CAS 2024年第5期416-432,共17页
The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have diff... The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%. 展开更多
关键词 Finite Element approach Limit Equilibrium method SLOPE Factor of Safety
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On the Approaching Domain Obtained by Finite Element Method
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作者 邹青松 李永海 《Northeastern Mathematical Journal》 CSCD 2002年第3期273-282,共10页
The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the a... The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the approaching domain. 展开更多
关键词 nonconforming isoparametric finite element method approaching do-main DIFFEOMORPHISM
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Exploration of the Impact Mechanism of Government Credibility Based on Variable Screening Method
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作者 Jiajun Wu Yuxiang Ma +2 位作者 Helin Zou Chun Zhang Ran Yan 《Journal of Data Analysis and Information Processing》 2024年第3期479-494,共16页
Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. ... Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. In recent years, researchers’ research on government credibility has mostly focused on exploring theories and mechanisms, with little empirical research on this topic. This article intends to apply variable selection models in the field of social statistics to the issue of government credibility, in order to achieve empirical research on government credibility and explore its core influencing factors from a statistical perspective. Specifically, this article intends to use four regression-analysis-based methods and three random-forest-based methods to study the influencing factors of government credibility in various provinces in China, and compare the performance of these seven variable selection methods in different dimensions. The research results show that there are certain differences in simplicity, accuracy, and variable importance ranking among different variable selection methods, which present different importance in the study of government credibility issues. This study provides a methodological reference for variable selection models in the field of social science research, and also offers a multidimensional comparative perspective for analyzing the influencing factors of government credibility. 展开更多
关键词 Government Credibility Variable Selection Models Social Statistics Regression Based approach method Based on Random Forest
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Teaching Method for Comprehensive English Integration of Grammar-translation Method and Communicative Approach
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作者 黎荣华 《海外英语》 2011年第9X期49-50,共2页
Comprehensive English is a very basic and important course for English majors,according to the features of the text-book A New English Course,teachers should adopt the integration of grammar translation method and com... Comprehensive English is a very basic and important course for English majors,according to the features of the text-book A New English Course,teachers should adopt the integration of grammar translation method and communicative approach to improve students' linguistic competence and communicative competence. 展开更多
关键词 comprehensive English INTEGRATION GRAMMAR TRANSLATION method COMMUNICATIVE approach
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A Possible Approach to Introduce Word Memorizing Methods into College English Teaching
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作者 李姝 《海外英语》 2011年第8X期4-5,共2页
Words acquisition should be the most decisive and basic part, though modern English education does not take enough attention, especially in college English teaching. A recent survey on the Internet reveals that colleg... Words acquisition should be the most decisive and basic part, though modern English education does not take enough attention, especially in college English teaching. A recent survey on the Internet reveals that college students are worrying about their words power very much, eager to find an efficient and effective way. Hence, various modes of word memorizing methods are collected and a brief classification and remark are available. By an overall analysis of those methods, a new approach compromised by different kinds of methods turns out. This new approach completely abides by the philosophy of pragmatism, and every idea with practical use will be introduced to it, e.g. psychology of language and so on. 展开更多
关键词 COLLEGE English teaching MEMORIZING methods PRAGMATISM effective approach new ideas
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Consideration on Vocational Students' Participation in Class:With Special Reference to Task-based Approach and Traditional Method
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作者 董晓霞 《海外英语》 2011年第4X期111-113,共3页
This paper covers an experimental study on vocational students' participation in the class under task-based approach and traditional grammar-translation teaching method.As vocational colleges in China have develop... This paper covers an experimental study on vocational students' participation in the class under task-based approach and traditional grammar-translation teaching method.As vocational colleges in China have developed rapidly,teachers are still exploring and experimenting with different teaching approaches in order to find the suitable one(s).Using the theory of task-based approach,the grammartranslation method,the author conducts an experiment by recording.The following key issue has been addressed and some conclusive results have been made.The paper intends to find an answer to the following question:Under which teaching approach can students participate in the class more actively? Based on the above research work,the following result has been reached:Task-based approach can promote students' mastering of vocabulary and grammar,and students participate in the class more actively.The author would like to share her experiences with others in pedagogical studies of teaching vocational college students English. 展开更多
关键词 TASK-BASED approach grammar-translation method students’participation
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On the Reforms of the College English Teaching—More Advantages of the Communicative Approach over the Grammar-Translation Method
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作者 于贺 《海外英语》 2012年第24期140-142,共3页
With the world globalization, China's communication with other countries has become more frequent. It is in great demand that a large number of college graduates who not only master their major but also do well in... With the world globalization, China's communication with other countries has become more frequent. It is in great demand that a large number of college graduates who not only master their major but also do well in communication in English with English speakers. However, such graduates are scare because the backward teaching method-the Grammar-Traditional Method, cannot meet what the contemporary Chinese society demands. The reforms of the college English teaching are urgent and necessary. This paper first explores the major problems existing in the college English teaching. Furthermore, it introduces the basic theory of the Communicative Approach and analyzes its advantages in college English teaching. 展开更多
关键词 the COMMUNICATIVE approach the Grammar-Translation
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One Step Positive Approach for Sheet Metal Forming Simulation Based on Quasi-conjugate-gradient Method 被引量:3
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作者 NA Jingxin CHEN Wei 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2013年第4期730-736,共7页
In one step inverse finite element approach, an initial blank shape is normally predicted from the final deformed shape. The final deformed shape needs to be trimmed into a final part after stamping, the trimmed area,... In one step inverse finite element approach, an initial blank shape is normally predicted from the final deformed shape. The final deformed shape needs to be trimmed into a final part after stamping, the trimmed area, therefore, needs to be compensated manually before using one step inverse approach, which causes low efficiency and in consistency with the real situation. To solve this problem, one step positive approach is proposed to simulate the sheet metal stamping process. Firstly the spatial initial solution of one step positive method is preliminarily obtained by using the mapping relationship and area coordinates, then based on the deformation theory the iterative solving is carried out in three-dimensional coordinate system by using quasi-conjugate-gradient method. During iterative process the contact judgment method is introduced to ensure that the nodes on the spatial initial solution are not separated from die surface. The predicted results of sheet metal forming process that include the shape and thickness of the stamped part can be obtained after the iterative solving process. The validity of the proposed approach is verified by comparing the predicted results obtained through the proposed approach with those obtained through the module of one step inverse approach in Autoform and the real stamped part. In one step positive method, the stamped shape of regular sheet can be calculated fast and effectively. During the iterative solution, the quasi-conjugate-gradient method is proposed to take the place of solving system of equations, and it can improve the stability and precision of the algorithm. 展开更多
关键词 positive approach deformation theory quasi-conjugate-gradient method
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A Simple Weighted Integration Method for Calculating Surface Tension Force to Suppress Parasitic Flow in the Level Set Approach 被引量:5
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作者 王剑峰 杨超 毛在砂 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2006年第6期740-746,共7页
Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved met... Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved method for calculating the surface tension based on the level set approach is proposed, in which the contribution of not only the center node but also the rest area of a control volume to the calculation of surface tension is considered in a balanced manner. The weighted integration method (WIM) is more consistent with the concept of a banded interface in the level set method. It is applied to the temporal evolution of a two-dimensional neutrally buoyant liquid drop and a buoyancy driven deformable bubble in an immiscible fluid for the validation of WIM. The results show that the parasitic flows are evidently suppressed by the weighted integration method. The weight factors for WIM in 3-D cases are also suggested. 展开更多
关键词 PARASITIC flow WEIGHTED integration method SURFACE tension level set approach numerical simulation
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A Simple Weighted Integration Method for Calculating Surface Tension Force to Suppress Parasitic Flow in the Level Set Approach 被引量:1
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作者 王剑峰 杨超 毛在砂 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2006年第6X期740-746,共7页
Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved met... Parasitic flows may occur in the numerical simulation of incompressible multiphase flow due to errors in the calculation of surface tension terms, specifically for the curvature and unit normal vector. An improved method for calculating the surface tension based on the level set approach is proposed, in which the contribution of not only the center node but also the rest area of a control volume to the calculation of surface tension is considered in a balanced manner. The weighted integration method (WIM) is more consistent with the concept of a banded in- terface in the level set method. It is applied to the temporal evolution of a two-dimensional neutrally buoyant liquid drop and a buoyancy driven deformable bubble in an immiscible fluid for the validation of WIM. The results show that the parasitic flows are evidently suppressed by the weighted integration method. The weight factors for WIM in 3-D cases are also suggested. 展开更多
关键词 PARASITIC FLOW WEIGHTED integration method SURFACE tension level set approach numerical simulation
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Equivalence of Ratio and Residual Approaches in the Homotopy Analysis Method and Some Applications in Nonlinear Science and Engineering 被引量:1
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作者 Mustafa Turkyilmazoglu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2019年第7期63-81,共19页
A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications.It was shown in the latter through various comparative physical mode... A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications.It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual(squared)error.A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the traditional residual approach,especially regarding the root-finding problems via the homotopy analysis method.Examples are provided to further justify this.Moreover,it is conjectured that every nonlinear differential equation can be considered as a root-finding problem by plugging a parameter in it from a physical viewpoint.Two examples from the boundary and initial and value problems are provided to verify this assertion.Hence,besides the advantages as deciphered in the previous publications,the feasibility of the ratio approach over the traditional residual approach is made clearer in this paper. 展开更多
关键词 HOMOTOPY analysis method convergence control parameter OPTIMUM value RATIO approach RESIDUAL approach
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A Hybrid Unit Commitment Approach Incorporating Modified Priority List with Charged System Search Methods 被引量:1
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作者 Yuan-Kang Wu Chih-Cheng Huang +1 位作者 Chun-Liang Lin Shih-Ming Chang 《Smart Grid and Renewable Energy》 2017年第6期178-194,共17页
This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems... This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL);however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods. 展开更多
关键词 A HYBRID Unit COMMITMENT approach Incorporating MODIFIED Priority List with CHARGED SYSTEM Search methods
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Critical Approach to Methods of Glacier Reconstruction in High Asia and Discussion of the Probability of a Qinghai-Xizang (Tibetan) Inland Ice 被引量:1
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作者 Matthias Kuhle 《Journal of Mountain Science》 SCIE CSCD 2007年第2期91-123,共33页
This overview discusses old and new results as to the controversy on the past glacier extension in High Asia, which has been debated for 35 years now. This paper makes an attempt to come closer to a solution. H.v. Wis... This overview discusses old and new results as to the controversy on the past glacier extension in High Asia, which has been debated for 35 years now. This paper makes an attempt to come closer to a solution. H.v. Wissmann's interpretation (1959) of a small-scale glaciation contrasts with M. Kuhle's reconstruction (1974) of a large-scale glaciation with a 2.4 million km2 extended Qinghai-Xizang (Tibetan) inland glaciation and a Himalaya-Karakorum icestream network. Both opinions find support but also contradiction in the International and Chinese literature (Academia Sinica). The solution of this question is of supraregional importance because of the subtropical position of the concerned areas. In case of large albedo-intensive ice surfaces, a global cooling would be the energetical consequence and, furthermore, a breakdown of the summer monsoon. The current and interglacial heat-low above the very effective heating panel of the Qinghai-Xizang (Tibetan) Plateau exceeding 4000 m, which gives rise to this monsoon circulation, would be replaced by the cold-high of an inland ice. In addition, the plate-tectonically created Pleistocene history of the uplift of High Asia — should the occasion arise up to beyond the snowline (ELA) —would attain a paleoclimatically great, perhaps global importance. In case of a heavy superimposed ice load, the question would come up as to the glacio-isostatic interruption of this primary uplift. The production of the loesses sedimentated in NE-China and their very probable glacial genesis as well as an eustatic lowering of the sea-level by 5 to 7 m in the maximum case of glaciation are immediately tied up with the question of glaciation we want to discuss. Not the least, the problems of biotopes of the sanctuary-centres of flora and fauna, i.e., interglacial re-settlement, are also dependent on it. On the basis of this Quaternary- geomorphological-glaciological connection, future contributions are requested on the past glaciation, the current and glacial permafrost table and periglacial development, the history of uplift, and the development of Ice Age lakes and loess, but also on the development of vegetation and fauna in High Asia. 展开更多
关键词 approach methods inland ice glacier reconstruction High Asia Qinghai-Xizang (Tibetan)
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Pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential using Nikiforov-Uvarov method and supersymmetric quantum mechanics approach 被引量:1
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作者 Wen-Li Chen I B Okon 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第5期107-112,共6页
Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential in... Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number. 展开更多
关键词 Dirac equation modified Rosen-Morse potential Nikiforov-Uvarov method supersymmetric quantum mechanics approach
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Quantitative comparison of cranial approaches in the anatomy laboratory: A neuronavigation based research method 被引量:1
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作者 Francesco Doglietto Jimmy Qiu +7 位作者 Mayoorendra Ravichandiran Ivan Radovanovic Francesco Belotti Anne Agur Gelareh Zadeh Marco Maria Fontanella Walter Kucharczyk Fred Gentili 《World Journal of Methodology》 2017年第4期139-147,共9页
AIMTo describe the development and validation of a novel neuronavigation-based method, which allows the quan-tification of the anatomical features that define anapproach, as well as real-time visualization of the surg... AIMTo describe the development and validation of a novel neuronavigation-based method, which allows the quan-tification of the anatomical features that define anapproach, as well as real-time visualization of the surgicapyramid. METHODSThe method was initially developed with commercially-available hardware for coordinate collection (a digitizerand a frameless navigation system) and software forvolume rendering; dedicated neuronavigation software (ApproachViewer, part of GTx-UHN) was then developed. The accuracy of measurements and the possibility of volumetric rendering of surgical approaches simulated in a phantom were compared among three different methods and commercially-available radiological software. In the anatomy laboratory, ApproachViewer was applied to the comparative quantitative analysis of multiple neurosurgical approaches and was used by many surgeons who were untrained for the research method.RESULTSThe accuracy of ApproachViewer is comparable to com-mercially-available radiological software. In the anatomy laboratory, the method appears versatile. The system can be easily used after brief training. ApproachViewer allows for real-time evaluation and comparison of surgical approaches, as well as post-dissection analyses of collected data. The accuracy of the method depends on the navigation registration: with a 1-2 mm registration error, it is adequate for evaluation and comparison of most neurosurgical approaches.CONCLUSIONThis new research method and software allows semi-automated visualization, quantifcation, and comparison of neurosurgical approaches in the anatomy laboratory. 展开更多
关键词 Anatomical study COMPARISON Neurosurgical approach Quantifcation Research method 3D rendering
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Indirect-approach method for specified-end points seismic ray tracing in three dimen-sional inhomogeneous media
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作者 徐朝繁 张先康 +3 位作者 杨健 杨卓欣 邓宏钊 宋松岩 《Acta Seismologica Sinica(English Edition)》 EI CSCD 1998年第3期56-63,共8页
Generally speaking, the factors of both medium and tectonic that give rise to heterogeneity of the earth crust and mantle structures should be taken into account simultaneously in three dimensional seismic ray tracin... Generally speaking, the factors of both medium and tectonic that give rise to heterogeneity of the earth crust and mantle structures should be taken into account simultaneously in three dimensional seismic ray tracing. In this paper, the three dimensional structure models are constructed with the model similar to generation system in computer aid design and manufacturing (CAD/CAM). Based on the algorithm proposed by Cerveny et al . for complete seismic ray tracing in complex three dimensional structures, a new technique called the indirect approach method for two point seismic ray tracing in three dimensional laterally heterogeneous media has been put forward, and its numerical computing examples were given. 展开更多
关键词 3 D ray tracing CRUST mantle structure indirect approach method
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Airfoil design optimization based on lattice Boltzmann method and adjoint approach
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作者 Xiaowei LI Liang FANG Yan PENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第6期891-904,共14页
We present a new aerodynamic design method based on the lattice Boltzmann method (LBM) and the adjoint approach. The flow field and the adjoint equation are numerically simulated by the GILBM (generalized form of i... We present a new aerodynamic design method based on the lattice Boltzmann method (LBM) and the adjoint approach. The flow field and the adjoint equation are numerically simulated by the GILBM (generalized form of interpolation supplemented LBM) on non-uniform meshes. The first-order approximation for the equilibrium dis- tribution function on the boundary is proposed to diminish the singularity of boundary conditions. Further, a new treatment of the solid boundary in the LBM is described par- ticularly for the airfoil optimization design problem. For a given objective function, the adjoint equation and its boundary conditions are derived analytically. The feasibility and accuracy of the new approach have been perfectly validated by the design optimization of NACA0012 airfoil. 展开更多
关键词 lattice Boltzmann method (LBM) adjoint approach boundary treatment aerodynamic design optimization
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Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle
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作者 Jui-Hsiang Kao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2016年第7期59-73,共15页
In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integra... In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly. 展开更多
关键词 STEP approach method Time domain Radiated WAVES Multiple frequencies BOUNDARY integral equation NEUMANN BOUNDARY condition
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Impact of central venous port implantation method and access choice on outcomes 被引量:1
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作者 Ayhan Erdemir Huseyin Kemal Rasa 《World Journal of Clinical Cases》 SCIE 2023年第1期116-126,共11页
BACKGROUND Although the number of patients who need central venous ports for permanent vascular access is increasing,there is still no“gold standard”for the implantation technique.AIM To identify the implantation te... BACKGROUND Although the number of patients who need central venous ports for permanent vascular access is increasing,there is still no“gold standard”for the implantation technique.AIM To identify the implantation technique that should be favored.METHODS Two hundred central venous port-implanted patients in a tertiary hospital were retrospectively evaluated.Patients were assigned into two groups according to the access method.The first group comprised patients whose jugular veins were used,and the second group comprised patients whose subclavian veins were used.Groups were evaluated regarding age,sex,application side,primary diagnosis,active follow-up period in the hospital,chemotherapy agents administered,number of complications,and the Clavien-Dindo severity score.The distribution of the variables was tested with the Kolmogorov-Smirnov test and the Mann-Whitney U test.Theχ^(2) test was used to analyze the variables.RESULTS There was no statistically significant difference between the groups regarding age,sex,side,number of chemotherapy drugs,and duration of port usage(P>0.05).Only 2 patients in group 1 had complications,whereas in group 2 we observed 19 patients with complications(P<0.05).No port occlusion was found in group 1,but the catheters of 4 patients were occluded in group 2.One port was infected in group 1 compared to three infected ports in group 2.Two port ruptures,two pneumothorax,one revision due to a mechanical problem,one tachyarrhythmia during implantation,and four suture line problems were also recorded in group 2 patients.We also showed that it would be sufficient to evaluate and wash ports once every 2 mo.CONCLUSION Our results robustly confirm that the jugular vein route is safer than the subclavian vein approach for central venous port implantation. 展开更多
关键词 Permanent vascular access Central venous ports Central venous port implantation methods Jugular vein route Subclavian vein approach Impact of implantation method on outcomes
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Approach to Riemann Hypothesis by Combined Commensurable Step Function Approximation with Bonnet Method
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作者 Alfred Wünsche 《Advances in Pure Mathematics》 2020年第5期201-228,共28页
To the Riemann hypothesis, we investigate first the approximation by step-wise Omega functions Ω(u) with commensurable step lengths u0 concerning their zeros in corresponding Xi functions Ξ(z). They are periodically... To the Riemann hypothesis, we investigate first the approximation by step-wise Omega functions Ω(u) with commensurable step lengths u0 concerning their zeros in corresponding Xi functions Ξ(z). They are periodically on the y-axis with period proportional to inverse step length u0. It is found that they possess additional zeros off the imaginary y-axis and additionally on this axis and vanish in the limiting case u0 → 0 in complex infinity. There remain then only the “genuine” zeros for Xi functions to continuous Omega functions which we call “analytic zeros” and which lie on the imaginary axis. After a short repetition of the Second mean-value (or Bonnet) approach to the problem and the derivation of operational identities for Trigonometric functions we give in Section 8 a proof for the position of these genuine “analytic” zeros on the imaginary axis by construction of a contradiction for the case off the imaginary axis. In Section 10, we show by a few examples that monotonically decreasing of the Omega functions is only a sufficient condition for the mentioned property of the positions of zeros on the imaginary axis but not a necessary one. 展开更多
关键词 RIEMANN Zeta FUNCTION RIEMANN Xi FUNCTION Second Mean-Value approach (Bonnet method) Chebyshev Polynomials BESSEL Functions
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