Relevant bibliographies by topics / Arithmetical rank

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Arithmetical rank'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Arithmetical rank"

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Katsabekis, Anargyros. "Arithmetical rank of binomial ideals." Archiv der Mathematik 109, no. 4 (August 3, 2017): 323–34. http://dx.doi.org/10.1007/s00013-017-1071-y.

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Thoma, A. "On the binomial arithmetical rank." Archiv der Mathematik 74, no. 1 (January 2000): 22–25. http://dx.doi.org/10.1007/pl00000405.

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Kimura, Kyouko, Naoki Terai, and Ken-ichi Yoshida. "Arithmetical rank of squarefree monomial ideals of small arithmetic degree." Journal of Algebraic Combinatorics 29, no. 3 (May 29, 2008): 389–404. http://dx.doi.org/10.1007/s10801-008-0142-3.

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Kimura, Kyouko, and Paolo Mantero. "Arithmetical rank of strings and cycles." Journal of Commutative Algebra 9, no. 1 (March 2017): 89–106. http://dx.doi.org/10.1216/jca-2017-9-1-89.

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Eto, Kazufumi. "Binomial arithmetical rank of lattice ideals." manuscripta mathematica 109, no. 4 (December 1, 2002): 455–63. http://dx.doi.org/10.1007/s00229-002-0317-5.

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Lyubeznik, Gennady. "On the arithmetical rank of monomial ideals." Journal of Algebra 112, no. 1 (January 1988): 86–89. http://dx.doi.org/10.1016/0021-8693(88)90133-0.

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Mohammadi, Fatemeh, and Dariush Kiani. "On the Arithmetical Rank of the Edge Ideals of Some Graphs." Algebra Colloquium 19, spec01 (October 31, 2012): 797–806. http://dx.doi.org/10.1142/s1005386712000685.

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In this paper, we compute the projective dimension of the edge ideals of graphs consisting of some cycles and lines which are joint in a common vertex. Moreover, we show that for such graphs, the arithmetical rank equals the projective dimension. As an application, we can compute the arithmetical rank for some homogenous monomial ideals.
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Varbaro, Matteo. "On the arithmetical rank of certain segre embeddings." Transactions of the American Mathematical Society 364, no. 10 (October 1, 2012): 5091–109. http://dx.doi.org/10.1090/s0002-9947-2012-05435-3.

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Katsabekis, Anargyros. "Arithmetical rank of toric ideals associated to graphs." Proceedings of the American Mathematical Society 138, no. 09 (September 1, 2010): 3111. http://dx.doi.org/10.1090/s0002-9939-2010-10335-0.

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Kimura, Kyouko, and Naoki Terai. "Binomial arithmetical rank of edge ideals of forests." Proceedings of the American Mathematical Society 141, no. 6 (January 2, 2013): 1925–32. http://dx.doi.org/10.1090/s0002-9939-2013-11473-5.

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Dissertations / Theses on the topic "Arithmetical rank"

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Costa, Diego Alves da. "Cohomologia Local: noções básicas e aplicações." Universidade Federal de Sergipe, 2017. https://ri.ufs.br/handle/riufs/5805.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The purpose of this dissertation is to introduce the notion of local cohomology as well as some of its applications. Initially, we performed a brief review on the main homological tools used in this work, such as: homology of a complex, isomorphism of complexes, injective resolutions, derived functors, etc. Next, we detail properties of the injective modules in the context of Noetherian rings. Finally, we present di erent ways of de ning local cohomology and we show how this notion is used to investigate the arithmetical rank of an ideal.
O objetivo dessa dissertação é introduzir a noção de cohomologia local bem como algumas de suas aplicações. Inicialmente, realizamos um breve apanhado sobre as principais noções homológicas utilizadas no trabalho, tais como: homologia de um complexo, isomorfismo de complexos, resoluções injetivas, funtores derivados, etc. Em seguida, detalhamos propriedades dos módulos injetivos no contexto dos anéis Noetherianos. Finalmente, apresentamos formas variadas de definir cohomologia local e mostramos como essa noção é utilizada para investigar o posto aritmético de um ideal.
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Pichon, Grégoire. "On the use of low-rank arithmetic to reduce the complexity of parallel sparse linear solvers based on direct factorization techniques." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0249/document.

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La résolution de systèmes linéaires creux est un problème qui apparaît dans de nombreuses applications scientifiques, et les solveurs creux sont une étape coûteuse pour ces applications ainsi que pour des solveurs plus avancés comme les solveurs hybrides direct-itératif. Pour ces raisons, optimiser la performance de ces solveurs pour les architectures modernes est un problème critique. Cependant, les contraintes mémoire et le temps de résolution limitent l’utilisation de ce type de solveur pour des problèmes de très grande taille. Pour les approches concurrentes, par exemple les méthodes itératives, des préconditionneurs garantissant une bonne convergence pour un large ensemble de problèmes sont toujours inexistants. Dans la première partie de cette thèse, nous présentons deux approches exploitant la compression Block Low-Rank (BLR) pour réduire la consommation mémoire et/ou le temps de résolution d’un solveur creux. Ce format de compression à plat, sans hiérarchie, permet de tirer profit du caractère low-rank des blocs apparaissant dans la factorisation de systèmes linéaires creux. La solution proposée peut être utilisée soit en tant que solveur direct avec une précision réduite, soit comme un préconditionneur très robuste. La première approche, appelée Minimal Memory, illustre le meilleur gain mémoire atteignable avec la compression BLR, alors que la seconde approche, appelée Just-In-Time, est dédiée à la réduction du nombre d’opérations, et donc du temps de résolution. Dans la seconde partie, nous présentons une stratégie de reordering qui augmente la granularité des blocs pour tirer davantage profit de la localité dans l’utilisation d’architectures multi-coeurs et pour fournir de tâches plus volumineuses aux GPUs. Cette stratégie s’appuie sur la factorisation symbolique par blocs pour raffiner la numérotation produite par des outils de partitionnement comme Metis ou Scotch, et ne modifie pas le nombre d’opérations nécessaires à la résolution du problème. A partir de cette approche, nous proposons dans la troisième partie de ce manuscrit une technique de clustering low-rank qui a pour objectif de former des clusters d’inconnues au sein d’un séparateur. Nous démontrons notamment les intérêts d’une telle approche par rapport aux techniques de clustering classiquement utilisées. Ces deux stratégies ont été développées pour le format à plat BLR, mais sont également une première étape pour le passage à un format hiérarchique. Dans la dernière partie de cette thèse, nous nous intéressons à une modification de la technique de dissection emboîtée afin d’aligner les séparateurs par rapport à leur père pour obtenir des structures de données plus régulières
Solving sparse linear systems is a problem that arises in many scientific applications, and sparse direct solvers are a time consuming and key kernel for those applications and for more advanced solvers such as hybrid direct-iterative solvers. For those reasons, optimizing their performance on modern architectures is critical. However, memory requirements and time-to-solution limit the use of direct methods for very large matrices. For other approaches, such as iterative methods, general black-box preconditioners that can ensure fast convergence for a wide range of problems are still missing. In the first part of this thesis, we present two approaches using a Block Low-Rank (BLR) compression technique to reduce the memory footprint and/or the time-to-solution of a supernodal sparse direct solver. This flat, non-hierarchical, compression method allows to take advantage of the low-rank property of the blocks appearing during the factorization of sparse linear systems. The proposed solver can be used either as a direct solver at a lower precision or as a very robust preconditioner. The first approach, called Minimal Memory, illustrates the maximum memory gain that can be obtained with the BLR compression method, while the second approach, called Just-In-Time, mainly focuses on reducing the computational complexity and thus the time-to-solution. In the second part, we present a reordering strategy that increases the block granularity to better take advantage of the locality for multicores and provide larger tasks to GPUs. This strategy relies on the block-symbolic factorization to refine the ordering produced by tools such as Metis or Scotch, but it does not impact the number of operations required to solve the problem. From this approach, we propose in the third part of this manuscript a new low-rank clustering technique that is designed to cluster unknowns within a separator to obtain the BLR partition, and demonstrate its assets with respect to widely used clustering strategies. Both reordering and clustering where designed for the flat BLR representation but are also a first step to move to hierarchical formats. We investigate in the last part of this thesis a modified nested dissection strategy that aligns separators with respect to their father to obtain more regular data structure
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Wortman, Kevin. "Quasi-isometric rigidity of higher rank S-arithmetic lattices /." 2003. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3088799.

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Chen, Yi-Fan, and 陳翊帆. "The arithmetical ranks of some types of ideals overpolynomial rings via local cohomology." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/74675546773137013909.

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碩士
國立中正大學
應用數學研究所
99
In this thesis, I will compute the arithmetical ranks of some types of ideals in polynomial rings. I will use the Non-Vanishing theorem in local cohomology to obtain the lower bound of arithmetical ranks and use a lemma get an upper bound of arithmetical ranks of some types of ideals in polynomial rings.
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Books on the topic "Arithmetical rank"

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Abbes, Ahmed, Michel Gros, and Takeshi Tsuji. Almost étale coverings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691170282.003.0005.

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This chapter explains Faltings' theory of almost étale extensions, a tool that has become essential in many questions in arithmetic geometry, even beyond p-adic Hodge theory. It begins with a brief historical overview of almost étale extensions, noting how Faltings developed the “almost purity theorem” and proved the Hodge–Tate decomposition of the étale cohomology of a proper smooth variety. The chapter proceeds by discussing almost isomorphisms, almost finitely generated projective modules, trace, rank and determinant, almost flat modules and almost faithfully flat modules, almost étale coverings, almost faithfully flat descent, and liftings. Finally, it describes group cohomology of discrete A–G-modules and Galois cohomology.
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Book chapters on the topic "Arithmetical rank"

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Penkov, Ivan, and Alexander S. Tikhomirov. "Rank-2 Vector Bundles on ind-Grassmannians." In Algebra, Arithmetic, and Geometry, 555–72. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4747-6_18.

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Goss, David. "Sign Normalized Rank 1 Drinfeld Modules." In Basic Structures of Function Field Arithmetic, 193–233. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-61480-4_7.

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Alamélou, Quentin, Olivier Blazy, Stéphane Cauchie, and Philippe Gaborit. "A Practical Group Signature Scheme Based on Rank Metric." In Arithmetic of Finite Fields, 258–75. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-55227-9_18.

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Grasedyck, Lars, and Christian Löbbert. "Parallel Algorithms for Low Rank Tensor Arithmetic." In Advances in Mechanics and Mathematics, 271–82. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02487-1_16.

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Graber, Tom, Joseph Harris, Barry Mazur, and Jason Starr. "Jumps in Mordell-Weil Rank and Arithmetic Surjectivity." In Progress in Mathematics, 141–47. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8170-8_9.

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Kelly, Tyler L. "Picard Ranks of K3 Surfaces of BHK Type." In Calabi-Yau Varieties: Arithmetic, Geometry and Physics, 45–63. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2830-9_2.

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Ish-Shalom, Oren, Shachar Itzhaky, Noam Rinetzky, and Sharon Shoham. "Run-time Complexity Bounds Using Squeezers." In Programming Languages and Systems, 320–47. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_12.

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AbstractDetermining upper bounds on the time complexity of a program is a fundamental problem with a variety of applications, such as performance debugging, resource certification, and compile-time optimizations. Automated techniques for cost analysis excel at bounding the resource complexity of programs that use integer values and linear arithmetic. Unfortunately, they fall short when execution traces become more involved, esp. when data dependencies may affect the termination conditions of loops. In such cases, state-of-the-art analyzers have shown to produce loose bounds, or even no bound at all.We propose a novel technique that generalizes the common notion of recurrence relations based on ranking functions. Existing methods usually unfold one loop iteration, and examine the resulting relations between variables. These relations assist in establishing a recurrence that bounds the number of loop iterations. We propose a different approach, where we derive recurrences by comparing whole traces with whole traces of a lower rank, avoiding the need to analyze the complexity of intermediate states. We offer a set of global properties, defined with respect to whole traces, that facilitate such a comparison, and show that these properties can be checked efficiently using a handful of local conditions. To this end, we adapt state squeezers, an induction mechanism previously used for verifying safety properties. We demonstrate that this technique encompasses the reasoning power of bounded unfolding, and more. We present some seemingly innocuous, yet intricate, examples where previous tools based on cost relations and control flow analysis fail to solve, and that our squeezer-powered approach succeeds.
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"Higher rank theory." In Function Field Arithmetic, 205–35. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562388_0006.

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Sharma, Jyoti. "Research Outcome of Faculty Members of Library and Information Science in North Indian Universities." In Advances in Library and Information Science, 350–63. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-8437-7.ch016.

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The chapter aims to ascertain the ranks of 10 universities on the basis of participative index (PAI), average publications per faculty member (APPFM), and combined arithmetic mean (CAM). The data used for the present study was obtained by an online questionnaire. However, detailed information regarding their research output was collected directly from them. A total of 971 publications were published by LIS faculty till 31st December 2014. The results found that the position of some universities goes up and the position of some universities fall down when evaluated on different parameters. PU has the 2nd rank as per PAI but on the basis of other two parameters (i.e., on the basis of APPFM and CAM, it has 1st rank whereas BHU has the 1st rank as per PAI, but on the basis of APPFM it has 4th rank, and on the basis of CAM, it has the 3rd rank).
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"Free Profinite Groups of Infinite Rank." In Field Arithmetic, 591–631. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26949-5_25.

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Conference papers on the topic "Arithmetical rank"

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Raz, Ran. "Tensor-rank and lower bounds for arithmetic formulas." In the 42nd ACM symposium. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1806689.1806780.

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Karimian, Pourya, and Masoud Ardakani. "Rank deficient decoding for arithmetic subspace network coding." In 2016 International Conference for Students on Applied Engineering (ICSAE). IEEE, 2016. http://dx.doi.org/10.1109/icsae.2016.7810225.

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Naldi, Simone. "Solving Rank-Constrained Semidefinite Programs in Exact Arithmetic." In ISSAC '16: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2930889.2930925.

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Chia, Nai-Hui, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, and Chunhao Wang. "Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning." In STOC '20: 52nd Annual ACM SIGACT Symposium on Theory of Computing. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3357713.3384314.

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Li, Rijie, Liwei Liu, Lixiang Guo, Dakui Feng, and Xianzhou Wang. "Numerical Simulation of Hydrodynamic Performance of Multi-Hull Catamaran With 3DOF Motion." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77241.

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This paper presents CFD to study the hydrodynamic performance for the high-speed, multi-hull Catamaran advancing in calm water. It uses inhouse computational fluid dynamics (CFD) code to solve RANS equation coupled with six degrees of freedom solid body motion equations. RANS equations are solved by finite difference method and PISO arithmetic. Computations have been made using structured grid with overset technology. Turbulence models used the anisotropic two equations Shear Stress Transport (SST) k-ω model. Single phase level set was used for free surface simulation. A good agreement on the resistance prediction between CFD and experimental fluid dynamics (EFD) has been observed (on the resistance prediction of about 4.0%). Differences between CFD and EFD have been seen for the 3 degrees of freedom (3DOF) motion, whereas larger discrepancy is observed for the sinkage and trim estimation (about 8.0%).
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Zhang, Heng, Hang Zhang, Xuanshu Chen, Hao Liu, and Xianzhou Wang. "Scale Effect Studies on Hydrodynamic Performance for DTMB 5415 Using CFD." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77331.

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Making CFD with the capability of predicting ship scale design performance, rather than relying on scale model tests will help reduce design costs and provide a greater opportunity to develop more energy efficient ship designs. The key objective of this paper is to perform a fully nonlinear unsteady RANS simulation to predict the ship motions and resistance of a full scale DTMB 5415 ship model. The analyses are performed at design speeds, at a certain Fr number, using in-house computational fluid dynamics (CFD) to solve RANS equation coupled with six degrees of freedom (6DOF) solid body motion equations. RANS equations are solved by finite difference method and PISO arithmetic. Computations have been made using structured grid with overset technology. Simulation results shown that the total resistance coefficient in calm water at service speed is predicted by 2.36% error compared to the related towing tank results. The ship resistance for different scale demonstrated that the current in-house CFD model could predict the resistance in a reasonable range of the EFD data. The comparison of flow field for wave pattern for different scale model were analyzed and discussed.
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Cheng, Harry H., Xudong Hu, and Bin Lin. "Design and Implementation of High-Level Numerical Analysis Functions Based on Computational Arrays for Applications in Engineering." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/cie-14674.

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Abstract This paper presents the design and implementation of high-level numerical analysis functions in CH, a superset of C language developed for the convenience of scientific and engineering computations. In CH, complex number is treated as a built-in data type, so that the syntaxes of complex arithmetic, relational operations, and built-in mathematical functions are the same as those for real numbers. The variable number of arguments is used in the built-in mathematical functions to simplify the computation of different branches of multi-valued complex functions. The computational arrays are introduced to handle the arrays in the numerical computations. Passing arrays of variable length by arrays of deferred-shape and arrays of assumed-shape to functions are discussed. These methods allow the arrays to be passed with their rank, dimensions and data types. A list of high-level numerical functions and two examples of the applications in the scientific and engineering are given in the paper.
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Mazurkin, Peter Matveevich, and Yana Oltgovna Georgieva. "WAVELET ANALYSIS OF HEIGHT AT POINTS OF THE CHANNEL OF A SMALL RIVER FROM THE MOUTH ON SPACE IMAGES." In GEOLINKS International Conference. SAIMA Consult Ltd, 2020. http://dx.doi.org/10.32008/geolinks2020/b1/v2/31.

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The purpose of the article is to analyze asymmetric wavelets of changing the coordinate - the local elevation of the Irovka river channel, as well as the influence of local latitude and longitude on it of 290 characteristic points along the river channel from source to mouth. After identifying the general wavelet equation, 12 terms were obtained in the form of asymmetric wavelets with variable amplitude and oscillation period. The first three members gave a correlation coefficient of 0.9993, which is slightly less than for latitude 0.9999, but more than for longitude 0.9991. As a result, all three coordinates have the strongest factorial relation with an adequacy of more than 0.999. All 12 wavelets distribute 95.52% of the points of the channel with a model error of up to 5%. The first term of the error distribution formula at 290 points of the river bed is the Laplace (Mandelbrot, Zipf-Perl, Pareto) law of exponential decline, and the second equation shows the stress excitation of the number of errors according to the biotechnical law. The comparison showed that 25 fractal terms were obtained for latitude, 18 for longitude, and 12 wavelets for altitude. As a result, height as a factor also shows high certainty in the quantization of wave equations. A zero rank in the fractal distribution of 12 wavelets receives an arithmetic mean value. The standard deviation decreases from 12.219 for the arithmetic mean to 1.489, that is, 8.2 times, for the first term. After the 12th wavelet, according to the tri-sigma rule, a spread of 0.3 m is formed, which is much less than the actual measurement error of 0.5 m for height from satellite images.
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Guo, LiXiang, JiaWei Yu, JiaJun Chen, KaiJun Jiang, and DaKui Feng. "Unsteady Viscous CFD Simulations of KCS Behaviour and Performance in Head Seas." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-77330.

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It is critical to be able to estimate a ship’s response to waves, since the added resistance and loss of speed may cause delays or course alterations, with consequent financial repercussions. Traditional methods for the study of ship motions are based on potential flow theory without viscous effects. Results of scaling model are used to predict full-scale of response to waves. Scale effect results in differences between the full-scale prediction and reality. The key objective of this study is to perform a fully nonlinear unsteady RANS simulation to predict the ship motions and added resistance of a full-scale KRISO Container Ship. The analyses are performed at design speeds in head waves, using in house computational fluid dynamics (CFD) to solve RANS equation coupled with two degrees of freedom (2DOF) solid body motion equations including heave and pitch. RANS equations are solved by finite difference method and PISO arithmetic. Computations have used structured grid with overset technology. Simulation results show that the total resistance coefficient in calm water at service speed is predicted by 4 .68% error compared to the related towing tank results. The ship motions demonstrated that the current in house CFD model predicts the heave and pitch transfer functions within a reasonable range of the EFD data, respectively.
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Li, Zhiheng, Jiawei Yu, Dakui Feng, Kaijun Jiang, and Yujie Zhou. "Research on the Improved Body-Force Method Based on Viscous Flow." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95887.

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Abstract The virtual propeller model can achieve the rapid numerical prediction of the ship self-propulsion performance through viscous flow, which used the improved body-force method. The two-dimensional lift coefficient CL and the drag coefficient CD are very important parameters in this method, which are generally obtained by the potential flow methods and cannot incorporate viscous effects. This study will perform a fully nonlinear unsteady RANS (Reynolds Average Navier-Stokes) simulation to get the KP505 open-water characteristics and then divide its blade into several parts to get the lift coefficient CL and the drag coefficient CD on each one. Then fitting by multivariate regression method, the relationship between CL, CD and propeller parameters is obtained. The Unsteady Blade Element Theory (UBET) is coupled with RANS in house CFD code HUST-Ship (Hydrodynamic Unsteady Simulation Technology for Ship) to calculate the flow around the propeller. RANS equations are solved by the finite difference method and PISO arithmetic. have been made using structured grid with overset technology. The results show that comparing with the EFD data, the maximum differences of the result of the improved body-force method are 4.32% and 2.7% for the thrust coefficient and the torque coefficient respectively near the propeller operating point.
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