Relevant bibliographies by topics / Expansion de Taylor

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
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  5. Conference papers
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Academic literature on the topic 'Expansion de Taylor'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Expansion de Taylor"

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Kitahara, Kazuaki, and Taka Aki Okuno. "A Note on Two Point Taylor Expansion III." International Journal of Modeling and Optimization 4, no. 4 (August 2014): 287–91. http://dx.doi.org/10.7763/ijmo.2014.v4.387.

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Grünwald, Eva, Ydalia Delgado Mercado, and Christof Gattringer. "Taylor and fugacity expansion for the effective ℤ3 spin model of QCD at finite density." International Journal of Modern Physics A 29, no. 32 (December 30, 2014): 1450198. http://dx.doi.org/10.1142/s0217751x1450198x.

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Different series expansions in the chemical potential μ are studied and compared for an effective theory of QCD which has a flux representation where the complex action is overcome. In particular we consider fugacity series, Taylor expansion and a modified Taylor expansion and compare the outcome of these series to the reference results from a Monte Carlo simulation in the flux representation where arbitrary μ is accessible. It is shown that for most parameter values the fugacity expansion gives the best approximation to the data from the flux simulation, followed by our newly proposed modified Taylor expansion. For the conventional Taylor expansion we find that the results coincide with the flux data only for very small μ.
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Shimomura, Tetsu, and Yoshihiro Mizuta. "Taylor expansion of Riesz potentials." Hiroshima Mathematical Journal 25, no. 3 (1995): 595–621. http://dx.doi.org/10.32917/hmj/1206127635.

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Stanković, B. "Taylor Expansion for Generalized Functions." Journal of Mathematical Analysis and Applications 203, no. 1 (October 1996): 31–37. http://dx.doi.org/10.1006/jmaa.1996.0365.

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Chu, M. S., T. H. Jensen, and P. M. Bellan. "General Taylor configuration expansion revisited." Physics of Plasmas 6, no. 5 (May 1999): 1495–99. http://dx.doi.org/10.1063/1.873401.

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Kulchitski, O. Yu, and D. F. Kuznetsov. "The unified Taylor-Ito expansion." Journal of Mathematical Sciences 99, no. 2 (April 2000): 1130–40. http://dx.doi.org/10.1007/bf02673635.

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Gerritzen, L. "Taylor expansion of noncommutative polynomials." Archiv der Mathematik 71, no. 4 (October 1, 1998): 279–90. http://dx.doi.org/10.1007/s000130050265.

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Chouquet, Jules. "Taylor Expansion, Finiteness and Strategies." Electronic Notes in Theoretical Computer Science 347 (November 2019): 65–85. http://dx.doi.org/10.1016/j.entcs.2019.09.005.

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Hong. "Approximation of a Warship Passive Sonar Signal Using Taylor Expansion." Journal Of The Acoustical Society Of Korea 33, no. 4 (2014): 232. http://dx.doi.org/10.7776/ask.2014.33.4.232.

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Stanković, B. "Asymptotic Taylor expansion for Fourier hyperfunctions." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 453, no. 1960 (May 8, 1997): 913–18. http://dx.doi.org/10.1098/rspa.1997.0050.

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Dissertations / Theses on the topic "Expansion de Taylor"

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Dula, Mark, Eunice Mogusu, Sheryl Strasser, Ying Liu, and Shimin Zheng. "Median and Mode Approximation for Skewed Unimodal Continuous Distributions using Taylor Series Expansion." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etsu-works/112.

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Background: Measures of central tendency are one of the foundational concepts of statistics, with the most commonly used measures being mean, median, and mode. While these are all very simple to calculate when data conform to a unimodal symmetric distribution, either discrete or continuous, measures of central tendency are more challenging to calculate for data distributed asymmetrically. There is a gap in the current statistical literature on computing median and mode for most skewed unimodal continuous distributions. For example, for a standardized normal distribution, mean, median, and mode are all equal to 0. The mean, median, and mode are all equal to each other. For a more general normal distribution, the mode and median are still equal to the mean. Unfortunately, the mean is highly affected by extreme values. If the distribution is skewed either positively or negatively, the mean is pulled in the direction of the skew; however, the median and mode are more robust statistics and are not pulled as far as the mean. The traditional response is to provide an estimate of the median and mode as current methodological approaches are limited in determining their exact value once the mean is pulled away. Methods: The purpose of this study is to test a new statistical method, utilizing the first order and second order partial derivatives in Taylor series expansion, for approximating the median and mode of skewed unimodal continuous distributions. Specifically, to compute the approximated mode, the first order derivatives of the sum of the first three terms in the Taylor series expansion is set to zero and then the equation is solved to find the unknown. To compute the approximated median, the integration from negative infinity to the median is set to be one half and then the equation is solved for the median. Finally, to evaluate the accuracy of our derived formulae for computing the mode and median of the skewed unimodal continuous distributions, simulation study will be conducted with respect to skew normal distributions, skew t-distributions, skew exponential distributions, and others, with various parameters. Conclusions: The potential of this study may have a great impact on the advancement of current central tendency measurement, the gold standard used in public health and social science research. The study may answer an important question concerning the precision of median and mode estimates for skewed unimodal continuous distributions of data. If this method proves to be an accurate approximation of the median and mode, then it should become the method of choice when measures of central tendency are required.
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Guillot, Jérémie. "Optimization techniques for high level synthesis and pre-compilation based on Taylor expansion diagrams." Lorient, 2009. http://www.theses.fr/2009LORIS121.

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Cette thèse adresse la problématique de l'optimisation automatique des spécifications dans le flot de conception des circuits intégrés. Par l'utilisation d'un formalisme canonique (basé sur les Taylors Expansion Diagram) et la reconnaissance de motifs particuliers dans le graphe, les optimisations issues de ces travaux permettent d'améliorer les résultats générés par les outils de synthèse de haut niveau sans connaissance à priori de l'application à implémenter
This thesis addresses the design productivity gap problem in design automation by emp]oying a canonical representation, called Taylor Expansion Diagram. TED is a graphical representation based on Taylor series decomposition of the data-flow computation. Optimizations and high-level transformations developed in this thesis are based on transformations and pattern recognition applied to the TED representation. The results of su ch transformations are the optimized data-flow graphs, which provide input to standard, HLS too]s for final architectural synthesis. Such optimizations cannot be achieved by traditional architectural and high-level synthesis tools or compiJers available today
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Liljas, Erik. "Stochastic Differential Equations : and the numerical schemes used to solve them." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-86799.

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This thesis explains the theoretical background of stochastic differential equations in one dimension. We also show how to solve such differential equations using strong It o-Taylor expansion schemes over large time grids. We also attempt to solve a problem regarding a specific approximation of a stochastic integral for which there is no explicit solution. This approximation, which utilizes the distribution of this particular stochastic integral, gives the wrong order of convergence when performing a grid convergence study. We use numerical integration of the stochastic integral as an alternative approximation, which is correct with regards to convergence.
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García, Monera María. "r-critical points and Taylor expansion of the exponential map, for smooth immersions in Rk+n." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/50935.

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[EN] Classically, the study of the contact with hyperplanes and hyperspheres has been realized by using the family of height and distance squared functions. On the first part of the thesis, we analyze the Taylor expansion of the exponential map up to order three of a submanifold $M$ immersed in $\r n.$ Our main goal is to show its usefulness for the description of special contacts of the submanifolds with geometrical models. As we analyze the contacts of high order, the complexity of the calculations increases. In this work, through the Taylor expansion of the exponential map, we characterize the geometry of order higher than $3$ in terms of invariants of the immersion, so that the effective computations in specific cases become more affordable. It allows also to get new geometric insights. On the second part of the thesis, we introduce the concept of critical point of a smooth map between submanifolds. If we consider a differentiable $k$-dimensional manifold $M$ immersed in $\r{k+n},$ we know that its focal set can also be interpreted as the image of the critical points of the {\it normal map} $\nu(m,u): NM\to \r{k+n}$ defined by $\nu(m,u)=\pi_N(m,u)+ u,$ for $m\in M$ and $u\in N_mM,$ where $\pi_N:NM\to M$ denotes the normal bundle. In the same way, the parabolic set of a differential submanifold is given through the analysis of the singularities of the height functions over the submanifold. If we consider a differentiable $k$-dimensional manifold $M$ immersed in $\r{k+n},$ we know that its parabolic set can also be interpreted as the image of the critical points of the {\it generalized Gauss map} $\psi(m,u): NM\to \r{k+n}$ defined by $\psi(m,u)= u,$ for $u\in N_mM.$ Finally, we characterize the asymptotic directions as the tangent set of a $k$-dimensional manifold $M$ immersed in $\r{k+n}$ throughout the study of the singularities of the tangent map $\Omega(m,y): TM\to \r{k+n}$ defined by $\Omega(m,y)=\pi(m,y)+y,$ for $y\in T_mM,$ where $\pi:TM\to M$ denotes the tangent bundle. We describe first the focal set and its geometrical relation to the Veronese of curvature for $k$-dimensional immersions in $\r{k+n}.$ Then we define the $r$-critical points of a differential map $f:H \to K$ between two differential manifolds and characterize the $2$ and $3$-critical points of the normal map and generalized Gauss map. The number of these critical points at $m\in M$ may depend on the degeneration of the curvature ellipse and we calculate those numbers in the particular case that $M$ is an immersed surface in $\r{4}$ for the normal map and $\r{5}$ for the generalized Gauss map.
[ES] En general, el estudio del contacto con hiperplanos e hiperesferas se ha llevado a cabo usando la familia de funciones altura y la función distancia al cuadrado. En la primera parte de la tesis analizamos el desarrollo de Taylor de la aplicación exponencial hasta orden 3 de una subvariedad $M$ inmersa en $\r n.$ Nuestro principal objetivo es mostrar su utilidad en el estudio de contactos especiales de subvariedades con modelos geométricos. A medida que analizamos los contactos de orden mayor, la complejidad de las cuentas aumenta. En este trabajo, a través del desarrollo de Taylor de la aplicación exponencial, caracterizamos la geometría de orden mayor que $3$ en términos de invariantes geométricos de la inmersión, por lo que el trabajo con las cuentas en casos especiales se convierte en más manejable. Esto nos permite también obtener nuevos resultados geométricos. En la segunda parte de la tesis se introduce el concepto de punto crítico de una aplicación regular entre subvariedades. Si consideramos una variedad diferenciable $M$ de dimensión $k$ e inmersa en $\r{k+n},$ sabemos que su conjunto focal puede ser interpretado como la imagen de los puntos críticos de la {\it aplicación normal} $\nu(m,u): NM\to \r{k+n}$ definida por $\nu(m,u)=\pi_N(m,u)+ u,$ para $m\in M$ y $u\in N_mM,$ donde $\pi_N:NM\to M$ denota el fibrado normal. De la misma manera, el conjunto parabólico de una subvariedad diferencial viene dado por el análisis de las singularidades de la función altura sobre la subvariedad. Si consideramos una subvariedad $M$ de dimensión $k$ e inmersa en $\r{k+n},$ sabemos que su conjunto parabólico puede ser interpretado como la imagen de los puntos críticos de la {\it aplicación generalizada de Gauss} $\psi(m,u): NM\to \r{k+n}$ definida por $\psi(m,u)= u,$ donde $u\in N_mM.$ Finalmente, caracterizamos las direcciones asintóticas como el conjunto de direcciones del tangente de una subvariedad $M$ de dimensión $k$ e inmersa en $\r{k+n}$ a través del estudio de las singularidades de la aplicación tangente $\Omega(m,y): TM\to \r{k+n}$ definida por $\Omega(m,y)=\pi(m,y)+y,$ para $y\in T_mM,$ donde $\pi:TM\to M$ denota el fibrado tangente. Describimos primero el conjunto focal y su relación geométrica con la Veronese de curvatura para una variedad $k$ dimensional inmersa en $\r{k+n}.$ Entonces, definimos los puntos $r$-críticos de una aplicación $f:H \to K$ entre dos subvariedades y caracterizamos los puntos $2$ y $3$ críticos de la aplicación normal y la aplicación generalizada de Gauss. El número de estos puntos críticos en $m\in M$ depende de la degeneración de la elipse de curvatura y calculamos ese número en el caso particular de una superficie inmersa en $\r{4}$ para la aplicación normal y $\r{5}$ para la aplicación generalizada de Gauss.
[CAT] En general, l'estudi del contacte amb hiperplans i hiperesferes s'ha dut a terme utilitzant la família de funcions altura i la funció distància al quadrat. A la primera part de la tesi analitzem el desenvolupament de Taylor de l'aplicació exponencial fins a ordre 3 d'una subvarietat $M$ immersa en $\r n.$ El nostre principal objectiu és mostrar la seua utilitat en l'estudi de contactes especials de subvarietats amb models geomètrics. A mesura que analitzem els contactes d'ordre major, la complexitat dels comptes augmenta. En aquest treball, a través del desenvolupament de Taylor de l'aplicació exponencial, caracteritzem la geometria d'ordre major que $ 3 $ en termes d'invariants geomètrics de la immersió, de manera que el treball amb els comptes en casos especials es converteix en més manejable. Això ens permet també obtenir nous resultats geomètrics. A la segona part de la tesi s'introdueix el concepte de punt crític d'una aplicació regular entre subvarietats. Si considerem una varietat diferenciable $ M $ de dimensió $ k $ i immersa en $ \r {k + n}, $ sabem que el seu conjunt focal pot ser interpretat com la imatge dels punts crítics de la {\it aplicació normal} $ \nu (m, u): NM \to \r {k + n} $ definida per $ \nu (m, u) = \pi_N (m, u) + o, $ per $ m \in M $ i $ u \in N_mM, $ on $ \pi_N: NM \to M $ denota el fibrat normal. De la mateixa manera, el conjunt parabòlic d'una subvarietat diferencial ve donat per l'anàlisi de les singularitats de la funció altura sobre la subvarietat. Si considerem una subvarietat $ M $ de dimensió $ k $ i immersa en $ \r {k + n}, $ sabem que el seu conjunt parabòlic pot ser interpretat com la imatge dels punts crítics de la {\it aplicació generalitzada de Gauss} $ \psi (m, u): NM \to \r{k + n} $ definida per $ \psi (m, u) = u, $ on $ u \in N_mM. $ Finalment, caracteritzem les direccions asimptòtiques com el conjunt de direccions del tangent d'una subvarietat $ M $ de dimensió $ k $ i immersa en $ \r{k + n} $ a través de l'estudi de les singularitats de l'aplicació tangent $ \Omega (m, y): TM \to \r {k + n} $ definida per $ \Omega (m, y) = \pi (m, y) + y, $ per $ y \in T_mM, $ on $ \pi: TM \to M $ denota el fibrat tangent. Descrivim primer el conjunt focal i la seva relació geomètrica amb la Veronese de curvatura per a una varietat $ k $ dimensional immersa en $ \r{k + n}. $ Llavors, definim els punts $ r $-crítics d'una aplicació $ f: H \to K $ entre dues subvarietats i caracteritzem els punts $ 2 $ i $ 3 $ crítics de l'aplicació normal i l'aplicació generalitzada de Gauss. El nombre d'aquests punts crítics en $ m \in M $ depèn de la degeneració de l'el·lipse de curvatura i calculem aquest nombre en el cas particular d'una superfície immersa en $ \r{4} $ per a l'aplicació normal i $ \r{5} $ per a l'aplicació generalitzada de Gauss.
García Monera, M. (2015). r-critical points and Taylor expansion of the exponential map, for smooth immersions in Rk+n [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/50935
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Kratky, Joseph J. "SERIES EXPANSION FOR SEMI-SPDES WITH REMARKS ON HYPERBOLIC SPDES ON THE LATTICE." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310614464.

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Semeraro, Emanuele. "Experimental investigation on hydrodynamic phenomena associated with a sudden gas expansion in a narrow channel." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066516/document.

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La vaporisation rapide du sodium liquide surchauffé est supposée être à l’origine des arrêts automatiques pour réactivité négative du réacteur Phénix.Un dispositif expérimental a été mis en œuvre pour reproduire la détente d'un gaz pressurisé, repoussant un liquide dans un canal de section rectangulaire très allongée.L’interface qui sépare les deux fluides, initialement plate, ondule du fait d'instabilités de Rayleigh-Taylor dont le caractère 2D est garanti par le rapport d'aspect de la section du canal. L’aire interfaciale augmente d'un facteur 50.L’expansion du gaz peut être divisée en deux phases principales : une phase dite « de Rayleigh-Taylor » (linéaire et non-linéaire) et une phase dite « à multi-structures » (transitionnelle et chaotique). La première est caractérisée par la dynamique de l'interface et l’aire interfaciale qui en résulte est proportionnelle à l’amplitude des ondulations. La deuxième est influencée par le comportement des structures liquides, dispersées dans la matrice gazeuse et l’aire interfaciale est alors proportionnelle au nombre de structures.La distribution de fraction volumique suggère un modèle d’écoulement composé de trois régions : une région où la frontière des bulles est clairement définie et régulière, une région compartimentée par des membranes liquides issues des frontières des bulles, une région diphasique formée de la queue de ces structures. L’analyse de sensibilité à la tension superficielle confirme que plus la tension est faible, plus les interfaces sont instables. Les ondes sont plus prononcées et plus de structures sont produites, ce qui conduit à une majoration du taux de production de l’aire interfaciale
The sharp vaporization of superheated liquid sodium is investigated. It is suspected to be at the origin of the automatic shutdown for negative reactivity, occurred in the Phénix reactor at the end of the eighties.An experimental apparatus has been designed and operated to reproduce the expansion of overpressurized air, superposed to water in a narrow vertical rectangular section channel.When expansion begins, the initial flat interface separating the two fluids becomes corrugated under the development of two-dimensional Rayleigh-Taylor instabilities. The interface area increases significantly and becomes even 50 times larger than the initial value. Since the channel is very narrow, instabilities along the channel depth do not develop.The gas expansion in a narrow channel can be divided into two main phases: Rayleigh-Taylor (linear and non-linear) and multi-structures (transition and chaotic) phases. The former is characterized by the dynamic of corrugated profile and the interface area results proportional to the amplitude of corrugation The latter is influenced by the behavior of the liquid structures dispersed in gas matrix and the interface area is mainly proportional to the number of liquid structures.The distribution of volume fraction suggests a model of channel flow consisting of three regions: the regular profile of peaks, the spike region and the structures tails. The analysis of sensibility to surface tension confirms that, with a lower surface tension, the fluids configuration is more unstable. The interface corrugations are more pronounced and more structures are produced, leading to a higher increment of the interface area
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Volkmer, Toni. "Taylor and rank-1 lattice based nonequispaced fast Fourier transform." Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-106489.

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The nonequispaced fast Fourier transform (NFFT) allows the fast approximate evaluation of trigonometric polynomials with frequencies supported on full box-shaped grids at arbitrary sampling nodes. Due to the curse of dimensionality, the total number of frequencies and thus, the total arithmetic complexity can already be very large for small refinements at medium dimensions. In this paper, we present an approach for the fast approximate evaluation of trigonometric polynomials with frequencies supported on an arbitrary subset of the full grid at arbitrary sampling nodes, which is based on Taylor expansion and rank-1 lattice methods. For the special case of symmetric hyperbolic cross index sets in frequency domain, we present error estimates and numerical results.
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Matchie, Lydienne. "Cubature methods and applications to option pricing." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5374.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: In this thesis, higher order numerical methods for weak approximation of solutions of stochastic differential equations (SDEs) are presented. They are motivated by option pricing problems in finance where the price of a given option can be written as the expectation of a functional of a diffusion process. Numerical methods of order at most one have been the most used so far and higher order methods have been difficult to perform because of the unknown density of iterated integrals of the d-dimensional Brownian motion present in the stochastic Taylor expansion. In 2001, Kusuoka constructed a higher order approximation scheme based on Malliavin calculus. The iterated stochastic integrals are replaced by a family of finitely-valued random variables whose moments up to a certain fixed order are equivalent to moments of iterated Stratonovich integrals of Brownian motion. This method has been shown to outperform the traditional Euler-Maruyama method. In 2004, this method was refined by Lyons and Victoir into Cubature on Wiener space. Lyons and Victoir extended the classical cubature method for approximating integrals in finite dimension to approximating integrals in infinite dimensional Wiener space. Since then, many authors have intensively applied these ideas and the topic is today an active domain of research. Our work is essentially based on the recently developed higher order schemes based on ideas of the Kusuoka approximation and Lyons-Victoir “Cubature on Wiener space” and mostly applied to option pricing. These are the Ninomiya-Victoir (N-V) and Ninomiya- Ninomiya (N-N) approximation schemes. It should be stressed here that many other applications of these schemes have been developed among which is the Alfonsi scheme for the CIR process and the decomposition method presented by Kohatsu and Tanaka for jump driven SDEs. After sketching the main ideas of numerical approximation methods in Chapter 1 , we start Chapter 2 by setting up some essential terminologies and definitions. A discussion on the stochastic Taylor expansion based on iterated Stratonovich integrals is presented, we close this chapter by illustrating this expansion with the Euler-Maruyama approximation scheme. Chapter 3 contains the main ideas of Kusuoka approximation scheme, we concentrate on the implementation of the algorithm. This scheme is applied to the pricing of an Asian call option and numerical results are presented. We start Chapter 4 by taking a look at the classical cubature formulas after which we propose in a simple way the general ideas of “Cubature on Wiener space” also known as the Lyons-Victoir approximation scheme. This is an extension of the classical cubature method. The aim of this scheme is to construct cubature formulas for approximating integrals defined on Wiener space and consequently, to develop higher order numerical schemes. It is based on the stochastic Stratonovich expansion and can be viewed as an extension of the Kusuoka scheme. Applying the ideas of the Kusuoka and Lyons-Victoir approximation schemes, Ninomiya- Victoir and Ninomiya-Ninomiya developed new numerical schemes of order 2, where they transformed the problem of solving SDE into a problem of solving ordinary differential equations (ODEs). In Chapter 5 , we begin by a general presentation of the N-V algorithm. We then apply this algorithm to the pricing of an Asian call option and we also consider the optimal portfolio strategies problem introduced by Fukaya. The implementation and numerical simulation of the algorithm for these problems are performed. We find that the N-V algorithm performs significantly faster than the traditional Euler-Maruyama method. Finally, the N-N approximation method is introduced. The idea behind this scheme is to construct an ODE-valued random variable whose average approximates the solution of a given SDE. The Runge-Kutta method for ODEs is then applied to the ODE drawn from the random variable and a linear operator is constructed. We derive the general expression for the constructed operator and apply the algorithm to the pricing of an Asian call option under the Heston volatility model.
AFRIKAANSE OPSOMMING: In hierdie proefskrif, word ’n hoërorde numeriese metode vir die swak benadering van oplossings tot stogastiese differensiaalvergelykings (SDV) aangebied. Die motivering vir hierdie werk word gegee deur ’n probleem in finansies, naamlik om opsiepryse vas te stel, waar die prys van ’n gegewe opsie beskryf kan word as die verwagte waarde van ’n funksionaal van ’n diffusie proses. Numeriese metodes van orde, op die meeste een, is tot dus ver in algemene gebruik. Dit is moelik om hoërorde metodes toe te pas as gevolg van die onbekende digtheid van herhaalde integrale van d-dimensionele Brown-beweging teenwoordig in die stogastiese Taylor ontwikkeling. In 2001 het Kusuoka ’n hoërorde benaderings skema gekonstrueer wat gebaseer is op Malliavin calculus. Die herhaalde stogastiese integrale word vervang deur ’n familie van stogastiese veranderlikes met eindige waardes, wat se momente tot ’n sekere vaste orde bestaan. Dit is al gedemonstreer dat hierdie metode die tradisionele Euler-Maruyama metode oortref. In 2004 is hierdie metode verfyn deur Lyons en Victoir na volumeberekening op Wiener ruimtes. Lyons en Victoir het uitgebrei op die klassieke volumeberekening metode om integrale te benader in eindige dimensie na die benadering van integrale in oneindige dimensionele Wiener ruimte. Sedertdien het menige outeurs dié idees intensief toegepas en is die onderwerp vandag ’n aktiewe navorsings gebied. Ons werk is hoofsaaklik gebaseer op die onlangse ontwikkelling van hoërorde skemas, wat op hul beurt gebaseer is op die idees van Kusuoka benadering en Lyons-Victoir "Volumeberekening op Wiener ruimte". Die werk word veral toegepas op die prysvastelling van opsies, naamlik Ninomiya-Victoir en Ninomiya-Ninomiya benaderings skemas. Dit moet hier beklemtoon word dat baie ander toepassings van hierdie skemas al ontwikkel is, onder meer die Alfonsi skema vir die CIR proses en die ontbinding metode wat voorgestel is deur Kohatsu en Tanaka vir sprong aangedrewe SDVs. Na ’n skets van die hoof idees agter metodes van numeriese benadering in Hoofstuk 1 , begin Hoofstuk 2 met die neersetting van noodsaaklike terminologie en definisies. ’n Diskussie oor die stogastiese Taylor ontwikkeling, gebaseer op herhaalde Stratonovich integrale word uiteengeset, waarna die hoofstuk afsluit met ’n illustrasie van dié ontwikkeling met die Euler-Maruyama benaderings skema. Hoofstuk 3 bevat die hoofgedagtes agter die Kusuoka benaderings skema, waar daar ook op die implementering van die algoritme gekonsentreer word. Hierdie skema is van toepassing op die prysvastelling van ’n Asiatiese call-opsie, numeriese resultate word ook aangebied. Ons begin Hoofstuk 4 deur te kyk na klassieke volumeberekenings formules waarna ons op ’n eenvoudige wyse die algemene idees van "Volumeberekening op Wiener ruimtes", ook bekend as die Lyons-Victoir benaderings skema, as ’n uitbreiding van die klassieke volumeberekening metode gebruik. Die doel van hierdie skema is om volumeberekening formules op te stel vir benaderings integrale wat gedefinieer is op Wiener ruimtes en gevolglik, hoërorde numeriese skemas te ontwikkel. Dit is gebaseer op die stogastiese Stratonovich ontwikkeling en kan beskou word as ’n ontwikkeling van die Kusuoka skema. Deur Kusuoka en Lyon-Victoir se idees oor benaderings skemas toe te pas, het Ninomiya-Victoir en Ninomiya- Ninomiya nuwe numeriese skemas van orde 2 ontwikkel, waar hulle die probleem omgeskakel het van een waar SDVs opgelos moet word, na een waar gewone differensiaalvergelykings (GDV) opgelos moet word. Hierdie twee skemas word in Hoofstuk 5 uiteengeset. Alhoewel die benaderings soortgelyk is, is daar ’n beduidende verskil in die algoritmes self. Hierdie hoofstuk begin met ’n algemene uiteensetting van die Ninomiya-Victoir algoritme waar ’n arbitrêre vaste tyd horison, T, gebruik word. Dié word toegepas op opsieprysvastelling en optimale portefeulje strategie probleme. Verder word numeriese simulasies uitgevoer, die prestasie van die Ninomiya-Victoir algoritme was bestudeer en vergelyk met die Euler-Maruyama metode. Ons maak die opmerking dat die Ninomiya-Victoir algoritme aansienlik vinniger is. Die belangrikste resultaat van die Ninomiya-Ninomiya benaderings skema word ook voorgestel. Deur die idee van ’n Lie algebra te gebruik, het Ninomiya en Ninomiya ’n stogastiese veranderlike met GDV-waardes gekonstrueer wat se gemiddeld die oplossing van ’n gegewe SDV benader. Die Runge-Kutta metode vir GDVs word dan toegepas op die GDV wat getrek is uit die stogastiese veranderlike en ’n lineêre operator gekonstrueer. ’n Veralgemeende uitdrukking vir die gekonstrueerde operator is afgelei en die algoritme is toegepas op die prysvasstelling van ’n Asiatiese opsie onder die Heston onbestendigheids model.
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Adolfsson, David, and Tom Claesson. "Estimation methods for Asian Quanto Basket options." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-160920.

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All financial institutions that provide options to counterparties will in most cases get involved withMonte Carlo simulations. Options with a payoff function that depends on asset’s value at differenttime points over its lifespan are so called path dependent options. This path dependency impli-cates that there exists no parametric solution and the price must hence be estimated, it is hereMonte Carlo methods come into the picture. The problem though with this fundamental optionpricing method is the computational time. Prices fluctuate continuously on the open market withrespect to different risk factors and since it’s impossible to re-evaluate the option for all shifts dueto its computing intensive nature, estimations of the option price must be used. Estimating theprice from known points will of course never produce the same result as a full re-evaluation but anestimation method that produces reliable results and greatly reduces computing time is desirable.This thesis will evaluate different approaches and try to minimize the estimation error with respectto a certain number of risk factors.This is the background for our master thesis at Swedbank. The goal is to create multiple estima-tion methods and compare them to Swedbank’s current estimation model. By doing this we couldpotentially provide Swedbank with improvement ideas regarding some of its option products andrisk measurements. This thesis is primarily based on two estimation methods that estimate optionprices with respect to two variable risk factors, the value of the underlying assets and volatility.The first method is a grid that uses a second order Taylor expansion and the sensitivities delta,gamma and vega. The other method uses a grid of pre-simulated option prices for different shiftsin risk factors. The interpolation technique that is used in this method is calledPiecewise CubicHermiteinterpolation. The methods (or referred to as approaches in the report) are implementedto handle a relative change of 50 percent in the underlying asset’s index value, which is the firstrisk factor. Concerning the second risk factor, volatility, both methods estimate prices for a 50percent relative downward change and an upward change of 400 percent from the initial volatility.Should there emerge even more extreme market conditions both methods use linear extrapolationto estimate a new option price.
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Guo, Longkai. "Numerical investigation of Taylor bubble and development of phase change model." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEI095.

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Le mouvement d'une bulle d'azote de Taylor dans des solutions mixtes glycérol-eau s'élevant à travers différents types d'expansions et de contractions est étudié par une approche numérique. La procédure CFD est basée sur un solveur open-source Basilisk, qui adopte la méthode du volume de fluide (VOF) pour capturer l'interface gaz-liquide. Les résultats des expansions/contractions soudaines sont comparés aux résultats expérimentaux. Les résultats montrent que les simulations sont en bon accord avec les expériences. La vitesse de la bulle augmente dans les expansions soudaines et diminue dans les contractions soudaines. Le modèle de rupture des bulles est observé dans les expansions soudaines avec de grands taux d'expansion, et un modèle de blocage des bulles est observé dans les contractions soudaines avec de petits rapports de contraction. De plus, la contrainte de cisaillement de la paroi, l'épaisseur du film liquide et la pression dans les simulations sont étudiées pour comprendre l'hydrodynamique de la bulle de Taylor montant par expansions/contractions. Le processus transitoire de la bulle de Taylor passant par une expansion/contraction soudaine est ensuite analysé pour trois singularités différentes: graduelle, parabolique convexe et parabolique concave. Une caractéristique unique de la contraction concave parabolique est que la bulle de Taylor passe par la contraction même pour de petits rapports de contraction. De plus, un modèle de changement de phase est développé dans le solveur Basilisk. Afin d'utiliser la méthode VOF géométrique existante dans Basilisk, une méthode VOF géométrique générale en deux étapes est implémentée. Le flux de masse n'est pas calculé dans les cellules interfaciales mais transféré aux cellules voisines autour de l'interface. La condition aux limites de température saturée est imposée à l'interface par une méthode de cellule fantôme. Le modèle de changement de phase est validé par évaporation de gouttelettes avec un taux de transfert de masse constant, le problème de Stefan unidimensionnel, le problème d'aspiration de l'interface et un cas d'ébullition à film plan. Les résultats montrent un bon accord avec les solutions analytiques ou les corrélations
The motion of a nitrogen Taylor bubble in glycerol-water mixed solutions rising through different types of expansions and contractions is investigated by a numerical approach. The CFD procedure is based on an open-source solver Basilisk, which adopts the volume-of-fluid (VOF) method to capture the gas-liquid interface. The results of sudden expansions/contractions are compared with experimental results. The results show that the simulations are in good agreement with experiments. The bubble velocity increases in sudden expansions and decreases in sudden contractions. The bubble break-up pattern is observed in sudden expansions with large expansion ratios, and a bubble blocking pattern is found in sudden contractions with small contraction ratios. In addition, the wall shear stress, the liquid film thickness, and pressure in the simulations are studied to understand the hydrodynamics of the Taylor bubble rising through expansions/contractions. The transient process of the Taylor bubble passing through sudden expansion/contraction is further analyzed for three different singularities: gradual, parabolic convex and parabolic concave. A unique feature in parabolic concave contraction is that the Taylor bubble passes through the contraction even for small contraction ratios. Moreover, a phase change model is developed in the Basilisk solver. In order to use the existed geometric VOF method in Basilisk, a general two-step geometric VOF method is implemented. Mass flux is calculated not in the interfacial cells but transferred to the neighboring cells around the interface. The saturated temperature boundary condition is imposed at the interface by a ghost cell method. The phase change model is validated by droplet evaporation with a constant mass transfer rate, the one-dimensional Stefan problem, the sucking interface problem, and a planar film boiling case. The results show good agreement with analytical solutions or correlations
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Books on the topic "Expansion de Taylor"

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Kloeden, Peter E. Numerical solution of SDE through computer experiments. 2nd ed. Berlin: Springer, 1997.

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Eckhard, Platen, and Schurz Henri, eds. Numerical solution of SDE through computer experiments. Berlin: Springer-Verlag, 1994.

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Lee, Maurice S. Overwhelmed. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691192925.001.0001.

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What happens to literature during an information revolution? How do readers and writers adapt to proliferating data and texts? These questions appear uniquely urgent today in a world of information overload, big data, and the digital humanities. But as this book shows, these concerns are not new—they also mattered in the nineteenth century, as the rapid expansion of print created new relationships between literature and information. Exploring four key areas—reading, searching, counting, and testing—in which nineteenth-century British and American literary practices engaged developing information technologies, the book delves into a diverse range of writings, from canonical works by Samuel Taylor Coleridge, Ralph Waldo Emerson, Charlotte Brontë, Nathaniel Hawthorne, and Charles Dickens to lesser-known texts such as popular adventure novels, standardized literature tests, antiquarian journals, and early statistical literary criticism. In doing so, it presents a new argument: rather than being at odds, as generations of critics have viewed them, literature and information in the nineteenth century were entangled in surprisingly collaborative ways. The book illuminates today's debates about the digital humanities, the crisis in the humanities, and the future of literature.
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Platen, Eckhard, Peter Eris Kloeden, and Henri Schurz. Numerical Solution of SDE Through Computer Experiments (Universitext). Springer, 2003.

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Book chapters on the topic "Expansion de Taylor"

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Duistermaat, J. J., and J. A. C. Kolk. "Taylor Expansion in Several Variables." In Distributions, 59–63. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4675-2_6.

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Bastys, Algirdas, Justas Kranauskas, and Volker Krüger. "Iris Recognition with Taylor Expansion Features." In Handbook of Iris Recognition, 185–209. London: Springer London, 2016. http://dx.doi.org/10.1007/978-1-4471-6784-6_8.

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Bastys, Algirdas, Justas Kranauskas, and Volker Krüger. "Iris Recognition with Taylor Expansion Features." In Handbook of Iris Recognition, 103–27. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4402-1_6.

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Kamerich, Ernic. "Taylor or Laurent expansion and limits." In A Guide to Maple, 107–16. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4419-8556-9_8.

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Tanizaki, Hisashi. "Nonlinear Filters Based on Taylor Series Expansion." In Lecture Notes in Economics and Mathematical Systems, 35–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-22237-9_3.

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Friedlander, Benjamin, and Erik Friedlander. "Time-Frequency Analysis Using Local Taylor Series Expansion." In Recent Developments in Time-Frequency Analysis, 41–49. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2838-5_5.

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Guerrieri, Giulio, Luc Pellissier, and Lorenzo Tortora de Falco. "Proof-Net as Graph, Taylor Expansion as Pullback." In Logic, Language, Information, and Computation, 282–300. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. http://dx.doi.org/10.1007/978-3-662-59533-6_18.

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Hernandez-del-Valle, Gerardo, and Yuemeng Sun. "Optimal Execution of Derivatives: A Taylor Expansion Approach." In Optimization, Control, and Applications of Stochastic Systems, 151–56. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8337-5_9.

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Manzonetto, Giulio, and Michele Pagani. "Böhm’s Theorem for Resource Lambda Calculus through Taylor Expansion." In Lecture Notes in Computer Science, 153–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21691-6_14.

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Morgan, R. V., O. A. Likhachev, and J. W. Jacobs. "Experiments on the Expansion Wave Driven Rayleigh-Taylor Instability." In 29th International Symposium on Shock Waves 2, 1149–54. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16838-8_57.

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Conference papers on the topic "Expansion de Taylor"

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Wilfling, Max, and Christof Gattringer. "A test of fugacity-, Taylor- and improved Taylor-expansion." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0452.

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Gomez-Prado, D., Q. Ren, S. Askar, M. Ciesielski, and E. Boutillon. "Variable ordering for taylor expansion diagrams." In Proceedings. Ninth IEEE International High-Level Design Validation and Test Workshop (IEEE Cat. No.04EX940). IEEE, 2004. http://dx.doi.org/10.1109/hldvt.2004.1431235.

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Yu, Kegen, Y. Jay Guo, and Ian Oppermann. "Modified Taylor Series Expansion Based Positioning Algorithms." In 2008 IEEE Vehicular Technology Conference (VTC 2008-Spring). IEEE, 2008. http://dx.doi.org/10.1109/vetecs.2008.582.

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Ciesielski, M., S. Askar, D. Gomez-Prado, J. Guillot, and E. Boutillon. "Data-Flow Transformations using Taylor Expansion Diagrams." In Design, Automation & Test in Europe Conference. IEEE, 2007. http://dx.doi.org/10.1109/date.2007.364634.

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Wang, Guan-jun, Guang-sheng Ma, Jin-liang Jiao, and Gang Feng. "A new timed taylor expansion diagrams method." In 2006 8th International Conference on Solid-State and Integrated Circuit Technology Proceedings. IEEE, 2006. http://dx.doi.org/10.1109/icsict.2006.306541.

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Liu, Hongbo, Ye Ji, and Xiukun Wang. "Image analysis by analogy with Taylor expansion." In the 20th spring conference. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1037210.1037243.

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Gomez-Prado, Daniel, Dusung Kim, Maciej Ciesielski, and Emmanuel Boutillon. "Retiming arithmetic datapaths using Timed Taylor Expansion Diagrams." In 2010 IEEE International High Level Design Validation and Test Workshop (HLDVT 2010). IEEE, 2010. http://dx.doi.org/10.1109/hldvt.2010.5496664.

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Pagani, Michele, and Christine Tasson. "The Inverse Taylor Expansion Problem in Linear Logic." In 2009 24th Annual IEEE Symposium on Logic In Computer Science (LICS). IEEE, 2009. http://dx.doi.org/10.1109/lics.2009.35.

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Huo, Feng, and Aun-Neow Poo. "Generalized Taylor Series Expansion for Contour Error Compensation." In 4th Asia International Symposium on Mechatronics. Singapore: Research Publishing Services, 2010. http://dx.doi.org/10.3850/978-981-08-7723-1_p131.

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Tsukada, Takeshi, Kazuyuki Asada, and C. H. Luke Ong. "Species, Profunctors and Taylor Expansion Weighted by SMCC." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209157.

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Reports on the topic "Expansion de Taylor"

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Iwashige, Kengo, and Takashi Ikeda. Numerical simulation of stratified shear flow using a higher order Taylor series expansion method. Office of Scientific and Technical Information (OSTI), September 1995. http://dx.doi.org/10.2172/115072.

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