Relevant bibliographies by topics / Lie symmetry method

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

Academic literature on the topic 'Lie symmetry method'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Lie symmetry method"

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Ji, Lina, and Rui Wang. "Conditional Lie-Bäcklund Symmetries and Differential Constraints of Radially Symmetric Nonlinear Convection-Diffusion Equations with Source." Entropy 22, no. 8 (August 8, 2020): 873. http://dx.doi.org/10.3390/e22080873.

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A conditional Lie-Bäcklund symmetry method and differential constraint method are developed to study the radially symmetric nonlinear convection-diffusion equations with source. The equations and the admitted conditional Lie-Bäcklund symmetries (differential constraints) are identified. As a consequence, symmetry reductions to two-dimensional dynamical systems of the resulting equations are derived due to the compatibility of the original equation and the additional differential constraint corresponding to the invariant surface equation of the admitted conditional Lie-Bäcklund symmetry.
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YU, JUN, and HANWEI HU. "FINITE SYMMETRY GROUP AND COHERENT SOLITON SOLUTIONS FOR THE BROER–KAUP–KUPERSHMIDT SYSTEM." International Journal of Bifurcation and Chaos 23, no. 09 (September 2013): 1350156. http://dx.doi.org/10.1142/s0218127413501563.

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A modified CK direct method is generalized to find finite symmetry groups of nonlinear mathematical physics systems. For the (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, both the Lie point symmetry and the non-Lie symmetry groups are obtained by this method. While using the traditional Lie approach, one can only find the Lie symmetry groups. Furthermore, abundant localized structures of the BKK equation are also obtained from the non-Lie symmetry group.
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Wang, Zhenli, Liangji Sun, Rui Hua, Lihua Zhang, and Haifeng Wang. "Lie Symmetry Analysis, Particular Solutions and Conservation Laws of Benjiamin Ono Equation." Symmetry 14, no. 7 (June 25, 2022): 1315. http://dx.doi.org/10.3390/sym14071315.

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In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships between new solutions and old solutions, two kinds of ODEs as symmetry reductions are obtained. Making use of the power series method, the exact power series solution of the Benjiamin Ono equation has been derived. We also give the conservation laws of Benjiamin Ono equation by means of Ibragimovs new conservation Theorem.
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Chen, Yong, and Xiaorui Hu. "Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation." Zeitschrift für Naturforschung A 64, no. 1-2 (February 1, 2009): 8–14. http://dx.doi.org/10.1515/zna-2009-1-202.

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The classical symmetry method and the modified Clarkson and Kruskal (C-K) method are used to obtain the Lie symmetry group of a nonisospectral Kadomtsev-Petviashvili (KP) equation. It is shown that the Lie symmetry group obtained via the traditional Lie approach is only a special case of the symmetry groups obtained by the modified C-K method. The discrete group analysis is given to show the relations between the discrete group and parameters in the ansatz. Furthermore, the expressions of the exact finite transformation of the Lie groups via the modified C-K method are much simpler than those obtained via the standard approach.
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Bilige, Sudao, and Yanqing Han. "Symmetry reduction and numerical solution of a nonlinear boundary value problem in fluid mechanics." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 3 (March 5, 2018): 518–31. http://dx.doi.org/10.1108/hff-08-2016-0304.

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Purpose The purpose of this paper is to study the applications of Lie symmetry method on the boundary value problem (BVP) for nonlinear partial differential equations (PDEs) in fluid mechanics. Design/methodology/approach The authors solved a BVP for nonlinear PDEs in fluid mechanics based on the effective combination of the symmetry, homotopy perturbation and Runge–Kutta methods. Findings First, the multi-parameter symmetry of the given BVP for nonlinear PDEs is determined based on differential characteristic set algorithm. Second, BVP for nonlinear PDEs is reduced to an initial value problem of the original differential equation by using the symmetry method. Finally, the approximate and numerical solutions of the initial value problem of the original differential equations are obtained using the homotopy perturbation and Runge–Kutta methods, respectively. By comparing the numerical solutions with the approximate solutions, the study verified that the approximate solutions converge to the numerical solutions. Originality/value The application of the Lie symmetry method in the BVP for nonlinear PDEs in fluid mechanics is an excellent and new topic for further research. In this paper, the authors solved BVP for nonlinear PDEs by using the Lie symmetry method. The study considered that the boundary conditions are the arbitrary functions Bi(x)(i = 1,2,3,4), which are determined according to the invariance of the boundary conditions under a multi-parameter Lie group of transformations. It is different from others’ research. In addition, this investigation will also effectively popularize the range of application and advance the efficiency of the Lie symmetry method.
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Zhang, Bo, and Hengchun Hu. "Similarity Reduction and Exact Solutions of a Boussinesq-like Equation." Zeitschrift für Naturforschung A 73, no. 4 (March 28, 2018): 357–62. http://dx.doi.org/10.1515/zna-2017-0442.

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AbstractThe similarity reduction and similarity solutions of a Boussinesq-like equation are obtained by means of Clarkson and Kruskal (CK) direct method. By using Lie symmetry method, we also obtain the similarity reduction and group invariant solutions of the model. Further, we compare the results obtained by the CK direct method and Lie symmetry method, and we demonstrate the connection of the two methods.
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Tian, Yi, and Kang-Le Wang. "Polynomial characteristic method an easy approach to lie symmetry." Thermal Science 24, no. 4 (2020): 2629–35. http://dx.doi.org/10.2298/tsci2004629t.

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Along the approach to Lie symmetry, it is always needed to solve an over-determined system, which is difficult and complex if not impossible. Here we suggest a new polynomial characteristic method combined with Lie algorithm to complete symmetry classification for a class of perturbed equations. A differential polynomial characteristic set algorithm is proposed to decompose the determining equations into a series of equations easy to be solved.
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Zhang, Lihua, Gangwei Wang, Qianqian Zhao, and Lingshu Wang. "Lie Symmetries and Conservation Laws of Fokas–Lenells Equation and Two Coupled Fokas–Lenells Equations by the Symmetry/Adjoint Symmetry Pair Method." Symmetry 14, no. 2 (January 26, 2022): 238. http://dx.doi.org/10.3390/sym14020238.

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The Fokas–Lenells equation and its multi-component coupled forms have attracted the attention of many mathematical physicists. The Fokas–Lenells equation and two coupled Fokas–Lenells equations are investigated from the perspective of Lie symmetries and conservation laws. The three systems have been turned into real multi-component coupled systems by appropriate transformations. By procedures of symmetry analysis, Lie symmetries of the three real systems are obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair method, which depends on Lie symmetries and adjoint symmetries. The relationships between the multiplier and the adjoint symmetry are investigated.
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Yang, Huizhang, Wei Liu, and Yunmei Zhao. "Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation." Complexity 2020 (October 24, 2020): 1–8. http://dx.doi.org/10.1155/2020/3465860.

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In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.
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Jadaun, Vishakha, and Sachin Kumar. "Symmetry analysis and invariant solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili equation." International Journal of Geometric Methods in Modern Physics 15, no. 08 (June 22, 2018): 1850125. http://dx.doi.org/10.1142/s0219887818501256.

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Based on Lie symmetry analysis, we study nonlinear waves in fluid mechanics with strong spatial dispersion. The similarity reductions and exact solutions are obtained based on the optimal system and power series method. We obtain the infinitesimal generators, commutator table of Lie algebra, symmetry group and similarity reductions for the [Formula: see text]-dimensional Kadomtsev–Petviashvili equation. For different Lie algebra, Lie symmetry method reduces Kadomtsev–Petviashvili equation into various ordinary differential equations (ODEs). Some of the solutions of [Formula: see text]-dimensional Kadomtsev–Petviashvili equation are of the forms — traveling waves, Weierstrass’s elliptic and Zeta functions and exponential functions.
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Dissertations / Theses on the topic "Lie symmetry method"

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Mehraban, Arash. "Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1736.

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In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish this task, the non-classical method is utilized to find the infinitesimal generator and the invariant surface condition for the subgroup where the solutions for the desired PDE exist. Using the infinitesimal generator and the invariant surface condition, we reduce the PDE to a mildly nonlinear ordinary differential equation that could be explored numerically or perhaps solved in closed form.
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DE, VECCHI FRANCESCO CARLO. "LIE SYMMETRY ANALYSIS AND GEOMETRICAL METHODS FOR FINITE AND INFINITE DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/565457.

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The main aim of the thesis is a systematic application (via suitable generalizations) of Lie symmetry analysis, or more generally, of the various geometric techniques for differential equations, to the study of finite and infinite dimensional stochastic differential equations (SDEs). The work can be divided in three main parts. In the first part a new geometric approach to finite dimensional SDEs driven by a multidimensional Brownian motion is proposed, which is based on a new notion of random transformations of a stochastic process called stochastic transformations. After having studied the probabilistic and geometric properties of stochastic transformations, we provide a useful generalization of the well-known results of reduction and reconstruction of symmetric ODEs to the stochastic setting. We give many applications of previous results to some interesting SDEs among which the two dimensional Brownian motion, the Kolmogorov-Pearson equation, a generalized Langevin equation and the SABR model. Finally, using the previous theorems, we propose a symmetry-adapted numerical scheme whose effectiveness is verified through both theoretical estimates and numerical simulations. The second part contains an extension of the results obtained in the first part to finite dimensional SDEs driven by a general semimartingale taking values in a Lie group. In order to provide such an extension we use the notion of geometrical SDEs introduced by Serge Choen, and we introduce some new notions of stochastic invariance for semimartingales called gauge and time symmetries of a semimartingale. Using these mathematical tools we generalize the notion of stochastic transformations in this setting and we propose the natural definition of symmetry based on this group of transformations. The formulated theory allows us to analyze in detail an important class of SDEs with possible relevant applications to iterated random maps theory. In the third part we take advantage of the geometry of the infinite jets bundle to develop a convenient algorithm for the explicit determination of finite dimensional solutions to stochastic partial differential equations (SPDEs). In this setting we are able to propose a generalization of Frobenius theorem in the infinite jet bundles setting, which, exploiting the classical notion of characteristics of a PDE, allows us to find some sufficient conditions for the existence of finite dimensional solutions to an SPDE and then to explicitly reduce the SPDE to a finite dimensional SDE. Our techniques permits to individuate new finite dimensional solutions to interesting SPDEs among which the proportional volatility equation in Heath-Jarrow-Morton framework, a stochastic perturbation of Hunter-Saxton equation and a filtering problem related to affine type processes.
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Granström, Frida. "Symmetry methods and some nonlinear differential equations : Background and illustrative examples." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-48020.

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Differential equations, in particular the nonlinear ones, are commonly used in formulating most of the fundamental laws of nature as well as many technological problems, among others. This makes the need for methods in finding closed form solutions to such equations all-important. In this thesis we study Lie symmetry methods for some nonlinear ordinary differential equations (ODE). The study focuses on identifying and using the underlying symmetries of the given first order nonlinear ordinary differential equation. An extension of the method to higher order ODE is also discussed. Several illustrative examples are presented.
Differentialekvationer, framförallt icke-linjära, används ofta vid formulering av fundamentala naturlagar liksom många tekniska problem. Därmed finns det ett stort behov av metoder där det går att hitta lösningar i sluten form till sådana ekvationer. I det här arbetet studerar vi Lie symmetrimetoder för några icke-linjära ordinära differentialekvationer (ODE). Studien fokuserar på att identifiera och använda de underliggande symmetrierna av den givna första ordningens icke-linjära ordinära differentialekvationen. En utvidgning av metoden till högre ordningens ODE diskuteras också. Ett flertal illustrativa exempel presenteras.
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Altafini, Claudio. "Geometric control methods for nonlinear systems and robotic applications." Doctoral thesis, Stockholm : Tekniska högsk, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3151.

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Семеген, Богдан Васильович, and Bohdan Semehen. "Метод підвищення криптостійкості симетричних алгоритмів шифрування." Master's thesis, Тернопільський національний технічний університет імені Івана Пулюя, 2021. http://elartu.tntu.edu.ua/handle/lib/36750.

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Мета цієї роботи полягає у розробці методу для підвищення криптостійксті симетричних алгоритмів шифрування та програмній його реалізації. У кваліфікаційній роботі проаналізовано симетричні алгоритми шифрування, що дало змогу визначити слабкі сторони їхнього застосування. Описано основні методи криптоаналізу, які можуть зробити шифри уразливими і становити загрозу розкриття відкритого тексту. Також було розглянуто способи генерації перестановок та створено новий алгоритм генерації унікальної перестановки. В роботі було розроблено метод підвищення криптостійкості на основі генерації унікальних перестановок, для кожного блоку даних, за допомогою згенерованого псевдовипадкового числа. Створено програмне забезпечення в якому реалізовано даний метод.
The aim of the work is to develop an algorithm to increase the cryptographic strength of symmetric encryption algorithms and its implementation Symmetric encryption algorithms were analyzed in the thesis, which allowed to identify the weaknesses of their application. The main methods of cryptanalysis that can make ciphers vulnerable and threaten the disclosure of plaintext are described. In the thesis a method was developed to increase cryptosecurity based on the generation of unique permutations for each block of data using the generated pseudo-random number. The software in which this method is implemented was created.
ВСТУП ...8 РОЗДІЛ 1. АНАЛІТИЧНА ЧАСТИНА ...10 1.1 Аналіз існуючих алгоритмів шифрування та їх поділ за типами ...10 1.2 Типи атак на алгоритми шифрування і їх перелік ...16 1.3 Види аналізу криптостійкості алгоритмів шифрування...19 1.4 Висновки до розділу 1...21 РОЗДІЛ 2. МАТЕМАТИЧНИЙ ОПИС СИМЕТРИЧНИХ АЛГОРИТМІВ ШИФРУВАННЯ ДАНИХ ТА МЕТОДУ ПІДВИЩЕННЯ ЇХ КРИПТОСТІЙКОСТІ ...23 2.1 Аналіз та математичний опис алгоритму шифрування TEA як прикладу нестійких шифрів ...23 2.2 Генерація унікальних перестановок ...28 2.2 Розробка алгоритму посилення криптостійкості симетричних алгоритмів шифрування даних ...33 2.3 Висновки до розділу 2...41 РОЗДІЛ 3. ПРОГРАМНА РЕАЛІЗАЦІЯ СИСТЕМИ ШИФРУВАННЯ ...42 3.1 Опис середовища розробки PureBasic ...42 3.2 Опис коду програмного забезпечення ...46 3.3 Результати тестування ...53 3.4 Висновки до розділу 3...59 РОЗДІЛ 4. ОХОРОНА ПРАЦІ ТА БЕЗПЕКА В НАДЗВИЧАЙНИХ СИТУАЦІЯХ ...61 4.1. Охорона праці ...61 4.2. Функціональні заходи у сфері державного регулювання та контролю захисту населення і територій. ...63 4.3. Висновки до розділу 4...66 ВИСНОВКИ .... 677 СПИСОК ЛІТЕРАТУРИ ...68 Додаток А ...72 Додаток Б ...76
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Khojayori, Farahnoz N. "Floral symmetry genes elucidate the development and evolution of oil-bee pollinated flowers of Malpighiaceae and Krameriaceae." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5585.

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Specialization on insect and animal pollinators is thought to be the driving force for the evolution of floral traits. Specifically in the New World (NW), the oil-bee pollination syndrome has led to the convergence of floral characters in two distantly related families of core eudicots, Malpighiaceae and Krameriaceae. Both families display a flag-like structure that establishes a zygomorphic flower and floral oil rewards in epithelial elaiophores. These traits work concomitantly to attract and reward female oil-bees that help fertilize these flowers and in return receive oils. The underlying genetics of floral zygomorphy were studied in several clades of core eudicots, which implicated CYCLOIDEA2-(CYC2-)like genes of the TCP gene family to play a role in the establishment and maintenance of this trait. In Malpighiaceae, previous work demonstrated that two CYC2-like genes, CYC2A and CYC2B, are expressed during development correlated with establishing zygomorphy in flowers of NW Malpighiaceae. In this thesis work, I investigated the underlying developmental and genetic basis for the establishment of non-homologous and yet functionally similar traits in the oil-bee pollinated flowers of Malpighiaceae and Krameriaceae. In Chapter 1, I investigated the modification of a conserved CYC2 genetic program in the Old World (OW) acridocarpoids of Malpighiaceae following a major biogeographic disjunction. And in Chapter 2, I studied the floral ontogeny and genetic basis of floral zygomorphy development in Krameria lanceolata Torrey of Krameriaceae. This thesis work sheds light on the significance of the interdisciplinary study of floral symmetry evolution through comparative pollination ecology, development, and genetics.
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Yeh, Po-Kai, and 葉柏開. "Application of Lie Symmetry Analysis and Method of Generating Integrals of Motion to Third Order Emden-Fowler Equations." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/79023777230158728006.

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碩士
國立嘉義大學
應用數學系研究所
95
In this thesis, we use Lie symmetry analysis and the method of generating integrals of motion to find the general solutions or the first integrals of the third order Emden-Fowler equations. We also reduce some of the equations to lower order ODEs, through the method of canonical coordinates and the method of differential invariants.
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Lamothe, Vincent. "Analyse de groupe d’un modèle de la plasticité idéale planaire et sur les solutions en termes d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre." Thèse, 2013. http://hdl.handle.net/1866/10343.

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Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie admissibles selon la force choisie est effectuée. Pour chaque type de force, les champs de vecteurs sont présentés. L’algèbre ayant la dimension la plus élevée possible a été obtenues en considérant les forces monogéniques et elle a été classifiée en classes de conjugaison. La méthode de réduction par symétrie est appliquée pour obtenir des solutions explicites et implicites de plusieurs types parmi lesquelles certaines s’expriment en termes d’une ou deux fonctions arbitraires d’une variable et d’autres en termes de fonctions elliptiques de Jacobi. Plusieurs solutions sont interprétées physiquement pour en déduire la forme de filières d’extrusion réalisables. Dans la seconde partie, on s’intéresse aux solutions s’exprimant en fonction d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre. La méthode des caractéristiques généralisées ainsi qu’une méthode basée sur les symétries conditionnelles pour les invariants de Riemann sont étendues pour être applicables à des systèmes dans leurs régions elliptiques. Leur applicabilité est démontrée par des exemples de la plasticité idéale non-stationnaire pour un flot irrotationnel ainsi que les équations de la mécanique des fluides. Une nouvelle approche basée sur l’introduction de matrices de rotation satisfaisant certaines conditions algébriques est développée. Elle est applicable directement à des systèmes non-homogènes et non-autonomes sans avoir besoin de transformations préalables. Son efficacité est illustrée par des exemples comprenant un système qui régit l’interaction non-linéaire d’ondes et de particules. La solution générale est construite de façon explicite.
The objects under consideration in this thesis are systems of first-order quasilinear equations. In the first part of the thesis, a study is made of an ideal plasticity model from the point of view of the classical Lie point symmetry group. Planar flows are investigated in both the stationary and non-stationary cases. Two new vector fields are obtained. They complete the Lie algebra of the stationary case, and the subalgebras are classified into conjugacy classes under the action of the group. In the non-stationary case, a classification of the Lie algebras admissible under the chosen force is performed. For each type of force, the vector fields are presented. For monogenic forces, the algebra is of the highest possible dimension. Its classification into conjugacy classes is made. The symmetry reduction method is used to obtain explicit and implicit solutions of several types. Some of them can be expressed in terms of one or two arbitrary functions of one variable. Others can be expressed in terms of Jacobi elliptic functions. Many solutions are interpreted physically in order to determine the shape of realistic extrusion dies. In the second part of the thesis, we examine solutions expressed in terms of Riemann invariants for first-order quasilinear systems. The generalized method of characteristics, along with a method based on conditional symmetries for Riemann invariants are extended so as to be applicable to systems in their elliptic regions. The applicability of the methods is illustrated by examples such as non-stationary ideal plasticity for an irrotational flow as well as fluid mechanics equations. A new approach is developed, based on the introduction of rotation matrices which satisfy certain algebraic conditions. It is directly applicable to non-homogeneous and non-autonomous systems. Its efficiency is illustrated by examples which include a system governing the non-linear superposition of waves and particles. The general solution is constructed in explicit form.
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Khosravian, Alireza. "State Estimation for Systems on Lie Groups with Nonideal Measurements." Phd thesis, 2016. http://hdl.handle.net/1885/109348.

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This thesis considers the state estimation problem for invariant systems on Lie groups with inputs in its associated Lie algebra and outputs in homogeneous spaces of the Lie group. A particular focus of this thesis is the development of state estimation methodologies for systems with nonideal measurements, especially systems with additive input measurement bias, output measurement delay, and sampled outputs. The main contribution of the thesis is to effectively employ the symmetries of the system dynamics and to benefit from the Lie group structure of the underlying state space in order to design robust state estimators that are computationally simple and are ideal for embedded applications in robotic systems. We address the input measurement bias problem by proposing a novel nonlinear observer to adaptively eliminate the input measurement bias. Despite the nonlinear and non-autonomous nature of the resulting error dynamics and the complexity of the underlying state space, the proposed observer exhibits asymptotic/exponential convergence of the state and bias estimation errors to zero. To tackle the output measurement delay problem, we propose novel dynamic predictors used in an observer-predictor arrangement. The observer provides estimates of the delayed state using the delayed output measurements and the predictor takes those estimates, compensates for the delay, and provides predictions of the current state. Separately, we propose output predictors employed in a predictor-observer arrangement to address the problem of sampled output measurements. The output predictors take the sampled measurements and provide continuous predictions of the current outputs. Feeding the predicted outputs into the observer yields estimates of the current state. Both methods rely on the invariance of the underlying system dynamics to recursively provide predictions with low computation requirements. We demonstrate applications of the theory with examples of attitude, velocity, and position estimation on SO(3) and SE(3). A key contribution of this thesis is the development of C++ libraries in an embedded implementation as well as experimental verification of the developed theory with real flight tests using model UAVs.
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Коробка, Назар Петрович, and Nazar Petrovych Korobka. "Дослідження сучасних методів блочного симетричного шифрування інформації в автоматизованих банківських системах." Bachelor's thesis, 2021. http://elartu.tntu.edu.ua/handle/lib/35365.

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Кваліфікаційна робота присвячена аналізу методів блочного симетричного шифрування в автоматизованих банківських системах і підвищення криптографічної стійкості алгоритмів блочного симетричного перетворення інформації на підґрунті динамічно керованих криптографічних примітивів Розроблено динамічно керованих блоків нелінійних замін, дослідження їх криптографічних властивостей виконані з використанням математичного апарату булевих функцій, методів кореляційного і спектрального аналізу. Розроблено алгоритму блочного симетричного криптографічного перетворення інформації з динамічно керованими примітивами і дослідження криптографічної стійкості проведені з використанням методів теорії захисту інформації. Досліджено криптостійкість алгоритму проведено з використанням теорії імовірності та математичної статистики, теорії захисту інформації.
The qualification thesis is devoted to analysis of methods of the block symmetric enciphering in computer-aided bank systems and an increase of cryptographic firmness of algorithms of sectional symmetric transformation of information on the basis of the dynamically guided cryptographic primitives. Development of the dynamically guided blocks of nonlinear replacements, research of their cryptographic properties executed with the use of mathematical vehicle of boolean functions, methods of cross-correlation and spectral analysis is conducted. Development of algorithm of block symmetric cryptographic transformation of information with the dynamically guided primitives and research of cryptographic firmness is conducted with the use of the methods of the theory of information security. Criptofirmness of algorithm is researched with the use of probability theory and mathematical statistics, the theory of information security.
ВСТУП .... 8 РОЗДІЛ 1 ЗАХИСТ ІНФОРМАЦІЇ В СУЧАСНИХ УМОВАХ ІНФОРМАЦІЙНОГО СУЛЬСПІЛЬСТВА .. 10 1.1. Концептуальні питання створення, функціонування, розвитку та використання Національної системи конфіденційного зв’язку .. 10 1.2 Побудова моделей атак на внутрішньо-платіжну банківську систему ..13 1.2.1 Аналіз сучасних загроз інформації банківської системи.... 13 1.2.2 Побудова моделі реалізації загроз безпеки ВПБС .. 16 1.2.3 Побудова загальної структури підсистеми безпеки інформаційної безпеки ВПБС ... 17 1.2.4 Побудова математичної моделі пасивних атак на ВПБС ... 20 1.2.5 Побудова моделі активних атак на ВПБС із блокуванням передачі інформації ... 21 1.2.6 Побудова моделі активних атак на ВПБС із внесенням перешкод .... 22 1.2.7 Побудова моделі активних атак “маскарад” на ВПБС ...23 1.3. Аналіз сучасних послуг та механізмів захисту інформації та визначення основних напрямків захисту ВПБС ....26 1.4. Висновки за першим розділом ...31 РОЗДІЛ 2 РОЗРОБКА АЛГОРИТМУ БЛОЧНОГО СИМЕТРИЧНОГО КРИПТОГРАФІЧНОГО ПЕРЕТВОРЕННЯ ІНФОРМАЦІЇ З ДИНАМІЧНО КЕРОВАНИМИ ПРИМІТИВАМИ (ALGORITHM OF DYNAMIC ENCRYPTION – ADE) ... 32 2.1 Обґрунтування конструкції та структурної схеми алгоритму блочного симетричного криптографічного перетворення інформації з динамічно керованими примітивами ...32 2.2 Специфікація складених компонентів шифру, стан, ключ шифру та кількість раундів ... 38 2.3 Дослідження раундових перетворень із динамічно керованими криптопримітивами ... 41 2.3.1 Дослідження динамічно керованого нелінійного перетворення Subbyte ..... 41 2.3.2 Дослідження динамічно керованого лінійного перетворення Shiftrows .... 48 2.3.3 Дослідження динамічно керованого лінійного перетворення Mixcolumn ... 50 2.3.4 Дослідження динамічно керованого лінійного перетворення Addroundkey ....58 2.4 Обґрунтування процедури формування та розширення ключів ...59 2.5 Висновки за другим розділом ... 60 РОЗДІЛ 3 РОЗРОБЛЕННЯ ПРАКТИЧНИХ РЕКОМЕНДАЦІЙ З РЕАЛІЗАЦІЇ КРИПТОАЛГОРИТМА ADE І ЕКСПЕРИМЕНТАЛЬНІ ДОСЛІДЖЕННЯ ЙОГО ПРОДУКТИВНОСТІ ... 61 3.1 Розроблення практичних рекомендацій з реалізації розробленого криптоалгоритму ... 61 3.1.1 Розроблення практичних рекомендацій з реалізації розробленого криптоалгоритма на 32-х бітних процесорах ..61 3.1.2 Розроблення практичних рекомендацій реалізації інверсного шифру розробленого криптоалгоритму ... 64 3.1.3 Розробка інтерфейсу програми ADE .. 68 3.2 Дослідження статистичної безпеки алгоритму ADE.... 70 3.2.1 Методика дослідження статистичної безпеки алгоритму ADE .. 70 3.2.2 Результати дослідження статистичної безпеки алгоритмів ADE і AES.. 74 3.3 Розроблення пропозицій застосування ADE в банківських системах ... 76 3.4. Висновки за третім розділом ... 84 4 БЕЗПЕКА ЖИТТЄДІЯЛЬНОСТІ, ОСНОВИ ХОРОНИ ПРАЦІ .. 85 4.1 Естетичне оформлення та ергономічне дослідження робочого місця оператора ... 85 4.2 Вимоги до режимів праці і відпочинку при роботі з ВДТ ... 86 ВИСНОВКИ ...90 СПИСОК ЛІТЕРАТУРНИХ ДЖЕРЕЛ ...94 ДОДАТКИ 102
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Books on the topic "Lie symmetry method"

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1943-, Bluman George W., ed. Symmetry and integration methods for differential equations. New York: Springer, 2002.

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Jürgen, Fuchs. Symmetries, lie algebras and representations: A graduate course for physicists. Cambridge, U.K: Cambridge University Press, 1997.

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Jürgen, Fuchs. Symmetries, lie algebras and representations: A graduate course for physicists. Cambridge: Cambridge University Press, 2003.

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Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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Advanced Symmetry Method Differential Equations (Applied Mathematical Sciences). Springer, 2007.

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Rouvière, François. Symmetric Spaces and the Kashiwara-Vergne Method. Springer London, Limited, 2014.

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Rouvière, François. Symmetric Spaces and the Kashiwara-Vergne Method. Springer, 2014.

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Fuchs, Jürgen, and Christoph Schweigert. Symmetries, Lie Algebras and Representations: A Graduate Course for Physicists (Cambridge Monographs on Mathematical Physics). Cambridge University Press, 1997.

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Book chapters on the topic "Lie symmetry method"

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Mishra, Shivam Kumar. "Soliton Solutions of (2+1)-Dimensional Modified Calogero-Bogoyavlenskii-Schiff (mCBS) Equation by Using Lie Symmetry Method." In Lecture Notes in Electrical Engineering, 203–19. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1824-7_13.

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Baldeaux, Jan, and Eckhard Platen. "Lie Symmetry Group Methods." In Functionals of Multidimensional Diffusions with Applications to Finance, 101–40. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00747-2_4.

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Baldeaux, Jan, and Eckhard Platen. "Transition Densities via Lie Symmetry Methods." In Functionals of Multidimensional Diffusions with Applications to Finance, 141–59. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00747-2_5.

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Qadir, Asghar, and Fazal M. Mahomed. "Complex Methods for Lie Symmetry Analysis." In Nonlinear Physical Science, 125–51. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4683-6_4.

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Vassilev, Vassil M., Petar A. Djondjorov, and Ivaïlo M. Mladenov. "Lie Group Analysis of the Willmore and Membrane Shape Equations." In Similarity and Symmetry Methods, 365–76. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08296-7_7.

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Rouvière, François. "The Kashiwara-Vergne Method for Lie Groups." In Symmetric Spaces and the Kashiwara-Vergne Method, 1–49. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09773-2_1.

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Johansson, Arne V., Björn Lindgren, and Jens M. Österlund. "Experimental Tests of Mean Velocity Distribution Laws Derived by Lie Group Symmetry Methods in Turbulent Boundary Layers." In IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, 257–64. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-007-0997-3_45.

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Matelski, Sławomir. "Secure Human Identification Protocol with Human-Computable Passwords." In Information Security Practice and Experience, 452–67. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-21280-2_25.

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AbstractIn this paper we present a new method of secure human-computer identification, which remains safe also in untrusted systems and environments. This method allows the elimination of any supplementary gadgets/devices or theft-sensitive biometric data used by the Multi-Factor Authentication (MFA), and using only one secret as a universal private key for all obtainable online accounts. However, the features of this solution make it best suited for use by the Authentication Authority with the Single-Sign-On (SSO) method of identity and access management, rather than for individual services. Such a key is used by our innovative challenge-response protocol to generate One-Time-Password, e.g., 6-digit OTP, could be calculated by a human in only 12 s, also offline on paper documents with an acceptable level of security required for post-quantum symmetric cyphers, thanks to the hard lattice problem with noise introduced by our new method, which we call Learning with Options (LWO). The secret has the form of an outline like a kind of handwritten autograph, designed in invisible ink on the mapping grid. The password generation process requires following such an invisible contour on the challenge matrix created randomly by the verifier and reading values from secret fields to easily calculate each digit of OTP.
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Hartisch, Michael, Christian Reintjes, Tobias Marx, and Ulf Lorenz. "Robust Topology Optimization of Truss-Like Space Structures." In Lecture Notes in Mechanical Engineering, 296–306. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77256-7_23.

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AbstractDue to the additional design freedom and manufacturing possibilities of additive manufacturing compared to traditional manufacturing, topology optimization via mathematical optimization gained importance in the initial design of complex high-strength lattice structures. We consider robust topology optimization of truss-like space structures with multiple loading scenarios. A typical dimensioning method is to identify and examine a suspected worst-case scenario using experience and component-specific information and to incorporate a factor of safety to hedge against uncertainty. We present a quantified programming model that allows us to specify expected scenarios without having explicit knowledge about worst-case scenarios, as the resulting optimal structure must withstand all specified scenarios individually. This leads to less human misconduct, higher efficiency and, thus, to cost and time savings in the design process. We present three-dimensional space trusses with minimal volume that are stable for up to 100 loading scenarios. Additionally, the effect of demanding a symmetric structure and explicitly limiting the diameter of truss members in the model is discussed.
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Borrelli, Arianna. "The Great Yogurt Project: Models and Symmetry Principles in Early Particle Physics." In Model and Mathematics: From the 19th to the 21st Century, 221–54. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97833-4_6.

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AbstractAccording to the received view of the development of particle physics, mathematics, and more specifically group theory, provided the key which, between the late 1950s and the early 1960s, allowed scientists to achieve both a deeper physical understanding and an empirically successful modeling of particle phenomena. Indeed, a posteriori it has even been suggested that just by looking at diagrams of observed particle properties (see Fig. 1) one could have recognized in them the structures of specific groups (see Fig. 2). However, a closer look at theoretical practices of the 1950s and early 1960s reveals a tension between the employment of advanced mathematical tools and the “modeling” of observation, if the term “model” is understood as a construction allowing for the fitting and predicting of phenomena. As we shall see, the most empirically successful schemes, such as the “Gell-Mann and Nishijima model” or the “eightfold way”, were mathematically very simple, made no use of group-theoretical notions and for quite a time resisted all attempts to transform them into more refined mathematical constructs. Indeed, the theorists who proposed them had little or no interest in abstract approaches to mathematical practice. On the other hand, there were a number of particle theorists who did care about and employ group-theoretical notions, yet not primarily as tools to fit phenomena, but rather as a guide to uncover the fundamental principles of particle interactions. Moreover, these theorists did not regard all groups as epistemically equivalent, and instead clearly preferred those transformations related to space-time invariances over all others. These authors also often made a distinction between purely descriptive “models” and the “theories” they were (unsuccessfully) trying to build and which in their opinion would provide a deeper understanding of nature. Nonetheless, they expected their “theories”, too, to be empirically successful in describing observation, and thus to also function as “models”. In this sense, like their less mathematically-inclined colleagues, they also saw no clear-cut distinction between “modeling” and “theorizing” particle phenomena. In my paper I will discuss the development of these theoretical practices between the 1950s and the early 1960s as examples of the complex relationship between mathematics and the conceptualization of physical phenomena, arguing that, at least in this case, no general statements are possible on the relationship of mathematics and models. At that time, very different mathematical practices coexisted and the epistemic attitudes of physicists towards theoretical constructs could depend both on the assumptions and goals of the individual authors and on the specific mathematical methods and concepts linked to the constructs.
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Conference papers on the topic "Lie symmetry method"

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Mavuri, Satya P., Simon Watkins, and Jon Watmuff. "A Novel Mirror-Image Technique for Wheel and Ground Simulation in Automotive Wind-Tunnels." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77102.

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A novel method for simulating the relative motions of the wheels and moving ground for road vehicle aerodynamics is presented. The method revisits an old concept where two identical vehicles are used and positioned so that they are mirror images, with the ground being represented by the horizontal plane of symmetry. The method involves double symmetry, where two half models (e.g. a car split down the vertical centerline) contact at the rotating wheel contact patches and the resulting (opened) vehicle halves lie on a reflection plane. This can either be the tunnel floor or the equivalent CFD plane. For some forms of physical testing this offers advantages (such as easy access to wheel cavities and requiring only one vehicle) but sealing the gap between the tunnel floor and the vehicle halves can interfere with the force balance accuracy and problems can arise with time-varying flows crossing the time averaged zero flow boundary. This paper describes the concept and CFD and model-scale EFD evaluations which were found to compare well.
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Reinhardt, Wolf. "Effect of Plane Strain, Plane Stress and Bending on Equivalent Solid Collapse Predictions for Perforated Plates." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1303.

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An equivalent solid based method of predicting the plastic (limit) collapse of perforated plates has been developed in the recent literature. Higher order collapse surfaces with suitable symmetry properties are used for the analysis. The equation for the collapse surface contains a number of constants that are determined by comparison to a Finite Element analysis of an actual perforated periodic cell subject to selected membrane states of stress. Using a typical triangular perforation pattern, the present paper investigates the effect of simplifying assumptions that were made during the periodic cell analysis on the predicted collapse load of the actual cell geometry. For a finite thickness cell subjected to a membrane state of stress, the collapse load is expected to lie between that of the bounding cases of plane stress and generalised plane strain, which are compared here. The connection between the collapse of a cell subjected to a membrane state of stress and a cell of large thickness in bending is established.
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Honda, Tomonori, Fabien Nicaise, and Erik K. Antonsson. "Synthesis of Structural Symmetry Driven by Cost Savings." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85111.

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An engineer presented with a design challenge often creates a symmetric solution. For instance, consider a table (front-back and left-right symmetry), a car (left and right symmetry), a bridge (front-back and left-right symmetry), or the space shuttle (left-right) symmetry. These examples may not be 100% symmetric, but their overriding features are remarkably similar. The reasons for the design of symmetric structures is not always clear. In some cases, like the table, symmetry may be a tradition. Similarly, the symmetry may be for aesthetic reasons. However in automated design algorithms, especially stochastic techniques, the output is often largely asymmetric, One reason for this is that fitness functions are not rewarded for symmetry. A possible resolution to this is to add a reward function for symmetry. Unfortunately, this approach is computationally intractable as well as arbitrary. In this paper a Genetic Algorithm based method is presented that rewards re-use of parts. The method is applied to a simple, idealized situation as well as to real design case. The results show that in some situations, symmetry naturally emerges from the synthesis, but that it does not provide clear performance advantages over asymmetric configurations.
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Muriel, C., J. L. Romero, and A. Ruiz. "Integration methods for equations without enough Lie point symmetries." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125078.

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5

Changizi, M. Amin, Ali Abolfathi, and Ion Stiharu. "MEMS Wind Speed Sensor: Large Deflection of Curved Micro-Cantilever Beam Under Uniform Horizontal Force." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50560.

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Micro-cantilever beams are currently employed as sensor in various fields. Of main applications, is using such beams in wind speed sensors. For this purpose, curved out of plane micro-cantilever beams are used. Uniform pressure on such beams causes a large deflection of beam. General mechanics of material theory deals with small deflection and thus cannot be used for explaining this deflection. Although there are a body of works on analysing of large deflection [1], nonlinear deflection, of curved beams [2], yet there is no research on large deflection of curved beam under horizontal uniform distributed force. Theoretically, the wind force is applying horizontally on curved micro-cantilever beam. Here, we neglect the effect of moving weather from beam sides. We first aim how to drive the governed equation. A curved beam does not have a calculable centroid. Also large deflection of beam changes its curvature which would change the centroid of beam consciously. The variation of centroid makes very though calculating the bending moment of each cross section in the beam. To address this issue, an integral equation will be used. The total force will be considered as a single force applied at the centroid. The second challenge is solving the governed nonlinear ordinary differential equation (ODE). Although there are several methods to solve analytically nonlinear ODE, Lie symmetry method, with all its complication, is a general method for this kind of equations. This approach covers all current methods in analytical solving nonlinear ODEs. In this method, an infinitesimal transformation should be calculated. All transformations under one parameter creates a group that called Lie group. A value of parameter which transfers the equation onto itself is called invariant of ODE. One can calculate canonical coordinates ODEs by the invariant. Solving the canonical coordinates ODEs yields to calculating the canonical coordinates. Canonical coordinate are used to reduce the order of nonlinear ODE [3]. By repeating this method one can solve high order ODEs. Our last question is how to do numerical solution of ODE. The possible answer will help to explain the phenomena of deflection clearly and compare the analytical solution with numerical results. Small dimensions of beam, small values of applied force from one side and Young modules value from the other side, will create a stiff ODE. Authors experience in this area shows that the best method to sole these kind of equations is LSODE. This method can be used in Maple. Here, primary calculations show that the governed equation is second order nonlinear ODE and we propose two possible invariants to solve ODE. Overall, the primary numerical solution has shown perfect match with the exact solution.
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Changizi, M. Amin, and Ion Stiharu. "A Complete Parametric Study of Pull-In Voltage by Nonlinear Differential Equation." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37744.

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Micro-cantilever beams are interested structures in MEMS because of their fabrication is very easy and its versatility. The importance of micro-cantilevers beam in MEMS has driven various investigations like static and dynamic performances under different loading such as potential fields. In this research the non-linear differential equation which models dynamics of a micro-cantilever beams vibration subjected to electrostatic field has been studied. The model which has one degree of freedom is used to calculate the pull-in voltage. This model adopted based on different method of calculating stiffness of micro-cantilever beam. The nonlinear ordinary differential equation which used to model the dynamics of the cantilever subjected to electric field close to snap on is highly stiff. Investigation on solving of nonlinear stiff ordinary equation showed that only Lsode algorithm yield to correct solution to the problem. Lsode is equipped with a robust adaptive time step selection mechanism that enables solutions to very stiff problems, as the one under discussion. The best match in the resonant frequency for equivalent stiffness based on four different models was considered. The stiffness model suitable for the best match in deflection is proved to be different from the model that yields. Pull-in voltage under electric field was studied. Pull-in voltage has been investigated from the analytical and numerical perspective. A complete parametric study of structural damping effect on large deflection of micro-cantilever beam was studied was done numerically in this work. Different kind of impulse voltages were considered and effect of them on pulling voltage numerically was studied. A cumbersome mathematical method, Lie symmetry, was used to drive a closed from of time response to step voltage for undamped system and pull in voltage of such system was calculated. Finally, a closed form driven from the nonlinear ODE for calculating pulling voltage was presented.
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Ahasan, Kawkab, and Jong-Hoon Kim. "Study of Angle-of-Attack (AoA) for Airfoil in Deterministic Lateral Displacement (DLD)." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-11708.

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Abstract Deterministic lateral displacement (DLD) is a method of inertial size-based particle separation with potential applications in high throughput sample processing, such as the fractionation of blood or the purification of target species like viral particles or circulating tumor cells. Recently, it has been shown that symmetric airfoils with neutral angle-of-attack (AoA) can be used for high-throughput design of DLD device, due to their mitigation of vortex effects and preservation of flow symmetry under high Reynolds number (Re) conditions. While high-Re operation with symmetric airfoils has been established, the effect of AoA for airfoil on the DLD performance has not been characterized. In this study, we present a high-Re investigation with symmetric airfoil-shaped pillars having positive and negative 15 degree AoA. Both positive and negative AoA configurations yield significant flow anisotropy at higher flow rates. The stronger shift of the critical diameter (Dc) was observed with negative AoA, but not in positive AoA device. The most likely contributor may be the growing anisotropy that develops in the AoA device at higher flow rates. This study shows that high-Re DLD design with airfoil shaped pillars requires significant consideration for pillar orientation to control flow symmetry.
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Lindgren, B., J. Osterlund, and A. Johansson. "Evaluation of scaling laws derived from lie group symmetry methods in turbulent boundary layers." In 40th AIAA Aerospace Sciences Meeting & Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-1103.

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Striebel, Michael, Michael Günther, Francesco Knechtli, and Michele Wandelt. "Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie-Groups." In XXIX International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.139.0049.

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Uvarov, D. V. "Quantum BRST Charge and OSp(1∣8) Superalgebra of Twistor-Like p-branes with Exotic Supersymmetry and Weyl Symmetry." In FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium. AIP, 2005. http://dx.doi.org/10.1063/1.1923336.

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