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Articles 6991 - 7020 of 7991

Full-Text Articles in Physical Sciences and Mathematics

A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu Jan 2003

A Parametrization Approach For Solving The Hamilton-Jacobi-Equation And Application To The A2 Toda Lattice, Mohammad Dikko Aliyu

LSU Master's Theses

Hamilton-Jacobi (HJ)-theory is an extension of Lagrangian mechanics and concerns itself with a directed search for a coordinate transformation in which the equations of motion can be easily integrated. The equations of motion of a given mechanical system can often be simplified considerably by a suitable transformation of variables such that all the new position and momemtum coordinates are constants. A particular type of transformation is chosen in such a way that the new equations of motion retain the same form as in the former coordinates; such a transformation is called canonical or contact and can greatly simplify the solution …

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Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory Jan 2003

Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory

LSU Master's Theses

The mathematical study of stock price modeling using Brownian motion and stochastic calculus is a relatively new field. The randomness of financial markets, geometric brownian motions, martingale theory, Ito's lemma, enlarged filtrations, and Girsanov's theorem provided the motivation for a simple characterization of the concepts of stock price modeling. This work presents the theory of stochastic calculus and its use in the financial market. The problems on which we focus are the models of an investor's portfolio of stocks with and without the possibility of insider trading, opportunities for fair pricing of an option, enlarged filtrations, consumptions, and admissibility. This …

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Thesis Digest: Mathematical Interpretation Of Political Power And The Arkansas State Government, Andrew King Jan 2003

Thesis Digest: Mathematical Interpretation Of Political Power And The Arkansas State Government, Andrew King

Inquiry: The University of Arkansas Undergraduate Research Journal

On the whole, political power can he very difficult to quantify. A person may be powerful due to his or her personal charm, wealth, fame, credibility, or influential connections. Political bodies do not account for these qualities when creating voting procedures; they only assign voting rules to specific positions. For example, most would say that in the United States government that a Senator is more powerful than a Representative, but less powerful than the President, without knowing any way to quantify or verify those differences. Since the 1950's, mathematicians and political scientists have attempted to create mathematical models that partially …

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Simulation Of Dynamic Electrochemical Processes, John Cassidy Jan 2003

Simulation Of Dynamic Electrochemical Processes, John Cassidy

Articles

This work is designed to introduce electrochemists in a tutorial manner to the basics of modeling of electrochemical systems based primarily on diffusion equations. There is an introduction to analytical and numerical methods with examples taken from typical electrochemical experiments. The Laplace transform is used to derive the Cottrell equation and chronopotentiometry. The response of an electrode to a Gaussian concentration profile is detailed. Laplace’s equation is solved for a simple cell to determine the potential distribution. Discrete methods are employed to calculate the current time behavior following a potential step using the explicit finite difference method. Cyclic voltammetry is …

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On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue Jan 2003

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

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On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb Jan 2003

On The Geometry And Topology Of Moduli Spaces Of Multi-Polygonal Linkages, Michael Edward Holcomb

LSU Doctoral Dissertations

The geometric, topological, and symplectic properties of moduli spaces (spaces of configurations modulo rotations and translations) of polygonal linkages have been studied by Kapovich, Millson, and Kamiyama, et. al. One can form a polygonal linkage by taking two free linkages and identifying initial and terminal vertices. This can be generalized so that one takes three free linkages and identifies initial and terminal vertices. Then one obtains a linkage which contains multiple polygons, any two of which have shared edges. The geometric and topological properties of moduli spaces of these multi-polygonal linkages are studied. These spaces turn out to be compact …

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A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat Jan 2003

A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat

Mathematics and Statistics Faculty Publications and Presentations

A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.

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A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan Jan 2003

A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the ux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners for the lowest order case of the Raviart-Thomas method have been constructed previously by exploiting its connection with a nonconforming method, our approach is different, in that we use a new variational characterization of the Lagrange multiplier equation. This allows us to …

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A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu Jan 2003

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

中智学为何诞生? 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借此对学科正式 命名并引入中国。 科学是真理吗? 比如, 当今信息科学的突出问题之一就是知识表达、知识处理及知识交流中的逻辑单一性: 不是真就是假, 从而不 能面对任何矛盾和冲突。由此, 人工智能、计算机网络、数据库、信息工程, 乃至电子商务、电子政务多多少少在走死 胡同。从表面上看, 它是模糊数学或协调逻辑的问题, 而从本质上看, 它属于结构性问题, 涉及到对哲学、逻辑学、集 合论、概率论、认知科学、信息科学基本概念以及众多相关领域的重新认识、重新塑造问题。 众所周知, 我国学习西方, 只图表面, 而不注重科学的内在结构, 不懂科学的概念和原理中也有基础设施 (换句话 说, 就是基础设施的基础设施), 从而建不起高楼大厦, 更谈不上科学上的自主, 从而形成盲目跟从西方的弊病。 科学, 这个被认为是永恒的真理, 其本质上没有半点永恒, 相反, 它时刻处于新老交替、新陈代谢、自我否定、自 我淘汰的动态之中——即使存在什么永恒的真理, 也终究会被后人推翻。科学实际上是一种战争, 而中智学正是关于它 的战略战术的科学。 当今世界上高深的科学莫过于爱因斯坦的相对论, 然而一切的一切, 都是建立在恒定光速的基础上——它正 在被现代的人们推翻!

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Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang Jan 2003

Equations Of Parametric Surfaces With Base Points Via Syzygies, Haohao Wang

LSU Doctoral Dissertations

Suppose $S$ is a parametrized surface in complex projective 3-space $mathbf{P}^3$ given as the image of $phi: mathbf{P}^1 imes mathbf{P}^1 o mathbf{P}^3$. The implicitization problem is to compute an implicit equation $F=0$ of $S$ using the parametrization $phi$. An algorithm using syzygies exists for computing $F$ if $phi$ has no base points, i.e. $phi$ is everywhere defined. This work is an extension of this algorithm to the case of a surface with multiple base points of total multiplicity k. We accomplish this in three chapters. In Chapter 2, we develop the concept and properties of Castelnuovo-Mumford regularity in biprojective spaces. …

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The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris Jan 2003

The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris

LSU Doctoral Dissertations

In this work, we study the structure of the Kauffman bracket skein module of the quaternionic manifold over the field of rational functions. We begin with a brief survey of manifolds whose Kauffman bracket skein modules are known, and proceed in Chapter 2 by recalling the facts from Temperley-Lieb recoupling theory that we use in the proofs. In Chapter 3, using recoupling theory and with Mathematica's assistance, we index an infinite presentation of the skein module, and conjecture that it is five-dimensional. In Chapter 4, using a new set of relations, we prove that the skein module is indeed spanned …

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Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek Jan 2003

Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek

Articles and Preprints

We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analyzing, step by step, the action of homogeneous transformations on the homogeneous part of the same degree of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and a dual canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms (resp., their dual canonical forms) coincide. We give an explicit construction of transformations bringing …

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On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue Dec 2002

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

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A Comparison Of Semi-Analytical And Numerical Solutions For The Microwave Heating Of A Lossy Material In A Three-Dimensional Waveguide, Prof. Tim Marchant Dec 2002

A Comparison Of Semi-Analytical And Numerical Solutions For The Microwave Heating Of A Lossy Material In A Three-Dimensional Waveguide, Prof. Tim Marchant

Tim Marchant

The microwave heating of a three-dimensional block in an infinitely long rectangular waveguide propagating the TE10 mode is considered. The electrical conductivity (the dielectric loss) is assumed to be a function of temperature, and modelled by the Arrhenius law. A coupled set of equations is obtained that describes the electromagnetic fields and the temperature distribution in the block. The numerical solutions of this problem are obtained by two methods, the well known FD-TD scheme and a frequency domain method which makes the further assumption that a single TE10 mode exists in the waveguide and material. The results show that an …

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Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He Dec 2002

Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He

Tian-Xiao He

In this paper, we apply a boundary-type quadrature technique to derive a type of boundary element scheme, which is used to solve the boundary-value problems of partial differential equations.Numerical examples for solving the exterior boundary-value problem of Helmholtz equation by using the spline approximation and the spline wavelet approximation are given.

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Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek Dec 2002

Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We study the feedback group action on two-inputs non-linear control systems. We follow an approach proposed by Kang and Krener which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes that obtained in the single-input case. We also give homogeneous m-invariants of the action of the group of homogeneous transformations on the homogeneous systems of the same degree. We illustrate our results by analyzing the normal form and invariants of homogeneous systems of degree two.

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Detectability Of Excitatory Versus Inhibitory Drive In An Integrate-And-Fire-Or-Burst Thalamocortical Relay Neuron Model, Gregory D. Smith, S. M. Sherman Dec 2002

Detectability Of Excitatory Versus Inhibitory Drive In An Integrate-And-Fire-Or-Burst Thalamocortical Relay Neuron Model, Gregory D. Smith, S. M. Sherman

Arts & Sciences Articles

Although inhibitory inputs are often viewed as equal but opposite to excitatory inputs, excitatory inputs may alter the firing of postsynaptic cells more effectively than inhibitory inputs. This is because spike cancellation produced by an inhibitory input requires coincidence in time, whereas an excitatory input can add spikes with less temporal constraint. To test for such potential differences, especially in the context of the function of thalamocortical (TC) relay nuclei, we used a stochastic “integrate-and-fire-or-burst” TC neuron model to quantify the detectability of excitatory and inhibitory drive in the presence and absence of the low-threshold Ca 2+ current, IT, and …

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Resolvability In Graphs, Varaporn Saenpholphat Dec 2002

Resolvability In Graphs, Varaporn Saenpholphat

Dissertations

The distance d (u, v ) between two vertices u and v in a connected graph G is the length of a shortest u - v path in G . For an ordered set W = { w1 , w2 , [Special characters omitted.] &cdots; , wk } of vertices in G and a vertex v of G , the code of v with respect to W is the k -vector cW (v ) = (d ( v, w1 ),d (v, w 2 ), [Special characters omitted.] &cdots; , d …

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Asymptotic Solitons For A Higher-Order Modified Korteweg–De Vries Equation, T. Marchant Oct 2002

Asymptotic Solitons For A Higher-Order Modified Korteweg–De Vries Equation, T. Marchant

Tim Marchant

Solitary wave interaction for a higher-order modified Korteweg–de Vries (mKdV) equation is examined. The higher-order mKdV equation can be asymptotically transformed to the mKdV equation, if the higher-order coefficients satisfy a certain algebraic relationship. The transformation is used to derive the higher-order two-soliton solution and it is shown that the interaction is asymptotically elastic. Moreover, the higher-order phase shifts are derived using the asymptotic theory. Numerical simulations of the interaction of two higher-order solitary waves are also performed. Two examples are considered, one satisfies the algebraic relationship derived from the asymptotic theory, and the other does not. For the example …

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An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan Oct 2002

An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …

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Fixed Point And Two-Cycles Of The Discrete Logarithm, Joshua Holden Oct 2002

Fixed Point And Two-Cycles Of The Discrete Logarithm, Joshua Holden

Mathematical Sciences Technical Reports (MSTR)

We explore some questions related to one of Brizolis: does every prime p have a pair (g, h) such that h is a fixed point for the discrete logarithm with base g? We extend this question to ask about not only fixed points but also two-cycles. Campbell and Pomerance have not only answered the fixed point question for sufficiently large p but have also rigorously estimated the number of such pairs given certain conditions on g and h. We attempt to give heuristics for similar estimates given other conditions on g and h and also in the case …

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A Review Of Selected Works On Crack Indentification, Kurt M. Bryan Oct 2002

A Review Of Selected Works On Crack Indentification, Kurt M. Bryan

Mathematical Sciences Technical Reports (MSTR)

We give a short survey of some of the results obtained within the last 10 years or so concerning crack identification using impedance imaging techniques. We touch upon uniqueness results, continuous dependence results, and computational algorithms.

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Pattern Recognition For Electric Power System Protection, Yong Sheng Oct 2002

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …

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A Mathematical Model Of Bacterial Aerotaxis, Borbala Mazzag, Alex Mogilner Sep 2002

A Mathematical Model Of Bacterial Aerotaxis, Borbala Mazzag, Alex Mogilner

Borbala Mazzag

No abstract provided.

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Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah Sep 2002

Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of locating and describing an internal point defect in a one­ dimensional rod W by controlling the heat inputs and measuring the subsequent temperatures at the boundary of W. We use a variation of the forward heat equation to model heat flow through W, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.

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Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela Sep 2002

Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela

Mathematical Sciences Technical Reports (MSTR)

We examine the problem of Identifying both the location and constitutive law governing electrical current flow across a one-dimensional linear crack in a two dimensional region when the crack only partially blocks the flow of current. We develop a a constructive numerical procedure for solving the inverse problem and provide computational examples.

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Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell Sep 2002

Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …

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A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga Sep 2002

A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga

Mathematics Research Reports

Superconvergence of order O(h1+rho), for some rho is greater than 0, is established for gradients recovered using Polynomial Preserving Recovery technique when the mesh is mildly structured. Consequently this technique can be used in building a posteriori error estimator that is asymptotically exact.

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Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty Sep 2002

Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty

Mathematics and Statistics Faculty Publications

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

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The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt Sep 2002

The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt

All HMC Faculty Publications and Research

We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.

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