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Artykuły w czasopismach na temat "Asymptotic equivalents"
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Bhattacharyya, Jishnu, i David Mattingly. "Universal horizons in maximally symmetric spaces". International Journal of Modern Physics D 23, nr 13 (listopad 2014): 1443005. http://dx.doi.org/10.1142/s0218271814430056.
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Universal horizons in Hořava–Lifshitz gravity and Einstein-æther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared (IR) solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four-dimensional static and spherically symmetric universal horizon solutions with maximally symmetric asymptotics — the equivalents of the Schwarzschild, Schwarzschild–de Sitter or Schwarzschild–anti-de Sitter spacetimes. Additionally, we derive the associated first laws for the universal horizon solutions. Finally, we prove that independent of asymptotic boundary conditions, any spherically symmetric solution in Hořava–Lifshitz gravity with a universal horizon is also a solution of Einstein-æther theory, thereby broadening and complementing the known equivalence region of the solution spaces.
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SPEICHER, ROLAND, i CARLOS VARGAS. "FREE DETERMINISTIC EQUIVALENTS, RECTANGULAR RANDOM MATRIX MODELS, AND OPERATOR-VALUED FREE PROBABILITY THEORY". Random Matrices: Theory and Applications 01, nr 02 (kwiecień 2012): 1150008. http://dx.doi.org/10.1142/s2010326311500080.
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Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators satisfying certain freeness relations. We comment on the relation between our free deterministic equivalent and deterministic equivalents considered in the engineering literature. We do not only consider the case of square matrices, but also show how rectangular matrices can be treated. Furthermore, we emphasize how operator-valued free probability techniques can be used to solve our free deterministic equivalents. As an illustration of our methods we show how the free deterministic equivalent of a random matrix model from [6] can be treated and we thus recover in a conceptual way the results from [6]. On a technical level, we generalize a result from scalar-valued free probability, by showing that randomly rotated deterministic matrices of different sizes are asymptotically free from deterministic rectangular matrices, with amalgamation over a certain algebra of projections. In Appendix A, we show how estimates for differences between Cauchy transforms can be extended from a neighborhood of infinity to a region close to the real axis. This is of some relevance if one wants to compare the original random matrix problem with its free deterministic equivalent.
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Li, Jian, Yong Liu i Weiping Wang. "High-Dimensional Analysis for Generalized Nonlinear Regression: From Asymptotics to Algorithm". Proceedings of the AAAI Conference on Artificial Intelligence 38, nr 12 (24.03.2024): 13500–13508. http://dx.doi.org/10.1609/aaai.v38i12.29253.
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Overparameterization often leads to benign overfitting, where deep neural networks can be trained to overfit the training data but still generalize well on unseen data. However, it lacks a generalized asymptotic framework for nonlinear regressions and connections to conventional complexity notions. In this paper, we propose a generalized high-dimensional analysis for nonlinear regression models, including various nonlinear feature mapping methods and subsampling. Specifically, we first provide an implicit regularization parameter and asymptotic equivalents related to a classical complexity notion, i.e., effective dimension. We then present a high-dimensional analysis for nonlinear ridge regression and extend it to ridgeless regression in the under-parameterized and over-parameterized regimes, respectively. We find that the limiting risks decrease with the effective dimension. Motivated by these theoretical findings, we propose an algorithm, namely RFRed, to improve generalization ability. Finally, we validate our theoretical findings and the proposed algorithm through several experiments.
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Pham, Kim, Agnès Maurel i Jean-Jacques Marigo. "Revisiting imperfect interface laws for two-dimensional elastodynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, nr 2245 (styczeń 2021): 20200519. http://dx.doi.org/10.1098/rspa.2020.0519.
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We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.
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van Oosterom, A., i G. J. H. Uijen. "The Relationship Between the MAXABS and the RMS Error". Methods of Information in Medicine 27, nr 04 (październik 1988): 161–66. http://dx.doi.org/10.1055/s-0038-1635540.
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SummaryResults from mathematical statistics are applied to the analysis of the ratio R between the element having the highest magnitude MAXABS in a sample of size η taken from a Gaussian distribution and the standard deviation RMS of the same sample. Numerically computed . probability density functions of MAXABS are shown for several values of n. For large values of η these density functions are compared with analytical expressions for their asymptotic equivalents. The expectation and variance of MAXABS and RMS are derived and tabulated for different values of n.These results are applied to the analysis of the residual error resulting from an orthogonal expansion of recorded body surface potentials.
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Ammar, Hajer, Ahmed E. Kholif, Manel Missaoui, Halimeh Zoabi, Soha Ghzayel, Mario de Haro-Martí, Izabelle Auxiliadora Molina de Almeida Teixeira i in. "Seasonal Variation in Chemical Composition, Ruminal Fermentation, and Biological Characteristics of Paulownia shan tong: In Vitro Potential Use by Sheep and Goats". Fermentation 9, nr 3 (23.02.2023): 210. http://dx.doi.org/10.3390/fermentation9030210.
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This study was conducted to determine the seasonal variation (two seasonal harvests during winter and spring) in some chemical and biochemical characteristics of Paulownia shan tong leaves. To achieve this, we analyzed the chemical composition in terms of dry matter (DM), organic matter (OM), crude protein (CP), cell-wall content (neutral detergent fiber (NDF)), acid detergent fiber (ADF), acid detergent lignin (ADL), and lipids. The phenolic compounds (PC) and antioxidant activity (AA) of the leaves were also determined. In vitro gas production (GP) and nutrient degradability were evaluated using two ruminal-content donors (sheep and goats). Higher (p < 0.05) antioxidant activities were observed in the winter harvest of P. shan tong, while higher concentrations of OM (90.5%), lipids (3.02%), NDF (69.7%), ADF (54.8%), ADL (35.4%), total flavonoids (0.45 mg catechin equivalents/mg DM), and total phenolics (2.52 mg gallic acid equivalents/mg DM) were observed in the spring harvest. Higher asymptotic GP and rate of GP (p < 0.05) were observed when the leaves were incubated with rumen liquor of goats compared to sheep; however, higher (p < 0.05) lag time of GP and half-time of GP were observed with rumen liquor from sheep. Moreover, higher asymptotic GP, rate of GP, and half-time of GP were observed with the winter harvest of P. shan tong. Higher (p < 0.001) metabolizable energy, OM degradability, and microbial protein supplies were obtained when the leaves were incubated with rumen fluids from goats and from the winter harvest of P. shan tong compared to the spring harvest. In conclusion, based on the chemical composition and the kinetics of in vitro gas production, P. shan tong leaves seem to be characterized by a good nutritive value and could be considered as an alternative feed resource for ruminants.
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Deltas, George. "Asymptotic and small sample analysis of the stochastic properties and certainty equivalents of winning bids in independent private values auctions $\!$". Economic Theory 23, nr 4 (1.05.2004): 715–38. http://dx.doi.org/10.1007/s00199-003-0390-3.
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Hou, Xiang-Dong. "Asymptotic numbers of non-equivalent codes in three notions of equivalence". Linear and Multilinear Algebra 57, nr 2 (marzec 2009): 111–22. http://dx.doi.org/10.1080/03081080701539023.
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Planas, Jaime, Manuel Elices i Gonzalo Ruiz. "The equivalent elastic crack: 2. X-Y equivalences and asymptotic analysis". International Journal of Fracture 61, nr 3 (czerwiec 1993): 231–46. http://dx.doi.org/10.1007/bf00036342.
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Bassino, Frédérique, Cyril Nicaud i Pascal Weil. "Statistics of subgroups of the modular group". International Journal of Algebra and Computation 31, nr 08 (12.10.2021): 1691–751. http://dx.doi.org/10.1142/s0218196721500624.
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We count the finitely generated subgroups of the modular group [Formula: see text]. More precisely, each such subgroup [Formula: see text] can be represented by its Stallings graph [Formula: see text], we consider the number of vertices of [Formula: see text] to be the size of [Formula: see text] and we count the subgroups of size [Formula: see text]. Since an index [Formula: see text] subgroup has size [Formula: see text], our results generalize the known results on the enumeration of the finite index subgroups of [Formula: see text]. We give asymptotic equivalents for the number of finitely generated subgroups of [Formula: see text], as well as of the number of finite index subgroups, free subgroups and free finite index subgroups. We also give the expected value of the isomorphism type of a size [Formula: see text] subgroup and prove a large deviation statement concerning this value. Similar results are proved for finite index and for free subgroups. Finally, we show how to efficiently generate uniformly at random a size [Formula: see text] subgroup (respectively, finite index subgroup, free subgroup) of [Formula: see text].
Rozprawy doktorskie na temat "Asymptotic equivalents"
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Mert, Raziye. "Qualitative Behavior Of Solutions Of Dynamic Equations On Time Scales". Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611528/index.pdf.
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In this thesis, the asymptotic behavior and oscillation of solutions of dynamic equations on time scales are studied.
In the first part of the thesis, asymptotic equivalence and asymptotic equilibrium of dynamic systems are investigated. Sufficient conditions are established for the asymptotic equivalence of linear systems and linear and quasilinear systems, respectively, and for the asymptotic equilibrium of quasilinear systems by unifying and extending some known results for differential systems and difference systems to dynamic systems on arbitrary time scales. In particular, for the asymptotic equivalence of differential systems, the well-known theorems of Levinson and Yakubovich are improved and the well-known theorem of Wintner for the asymptotic equilibrium of linear differential systems is generalized to arbitrary time scales. Some of our results for asymptotic equilibrium are new even for difference systems. In the second part, the oscillation of solutions of a particular class of second order nonlinear delay dynamic equations and, more generally, two-dimensional nonlinear dynamic systems, including delay-dynamic systems, are discussed. Necessary and sufficient conditions are derived for the oscillation of solutions of nonlinear delay dynamic equations by extending some continuous results. Specifically, the classical theorems of Atkinson and Belohorec are generalized. Sufficient conditions are established for the oscillation of solutions of nonlinear dynamic systems by unifying and extending the corresponding continuous and discrete results. Particularly, the oscillation criteria of Atkinson, Belohorec, Waltman, and Hooker and Patula are generalized.
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Dahmen, Wolfgang, Helmut Harbrecht i Reinhold Schneider. "Compression Techniques for Boundary Integral Equations - Optimal Complexity Estimates". Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600464.
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In this paper matrix compression techniques in the
context of wavelet Galerkin schemes for boundary
integral equations are developed and analyzed that
exhibit optimal complexity in the following sense.
The fully discrete scheme produces approximate
solutions within discretization error accuracy
offered by the underlying Galerkin method at a
computational expense that is proven to stay
proportional to the number of unknowns.
Key issues are the second compression, that
reduces the near field complexity significantly,
and an additional a-posteriori compression.
The latter one is based on a general result
concerning an optimal work balance, that applies,
in particular, to the quadrature used to compute
the compressed stiffness matrix with sufficient
accuracy in linear time. The theoretical results
are illustrated by a 3D example on a nontrivial
domain.
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Erdozain, Aralar. "Méthodes de Réduction de Modèles pour l'Inversion Rapide de Mesures de Résistivité en Forage". Thesis, Pau, 2016. http://www.theses.fr/2016PAUU3029/document.
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Les mesures de résistivité en forage sont communément utilisées pour obtenirune meilleure caractérisation du sous-sol. L’utilisation d’un tube métallique pourcouvrir le puits complique énormément les simulations numériques pour lepotentiel électrique à cause de la faible épaisseur du tube et de sa conductivitéélevée par rapport à celle des formations du sous-sol. Dans ce travail, motivé pardes configurations réalistes, le tube est modélisé par une couche mincecylindrique d’épaisseur uniforme et la résistivité du tube est proportionnelle aucube de son épaisseur.Dans cette thèse, on se concentre sur ce problème pour obtenir des Conditionsde transmission (ITCs) approchées pour le potentiel électrique à travers le tubemétallique. Pour ce faire, on considère dans une première approche, un modèle2D en coordonnées cartésiennes, puis on résout le problème 3D axisymétriquequi est considéré dans la majorité des simulations de mesures de résistivité enforage à travers un tube. On considère d’abord le cas statique (fréquence nulle),puis on obtient des ITCs pour des fréquences non-nulles, lesquelles sontimportantes pour comprendre certains phénomènes physiques, comme les effetsDelaware et Groningen. Ensuite, on analyse les modèles en prouvant desrésultats de stabilité et convergence, et on évalue la performance numérique deces modèles en utilisant la méthode des éléments finis. Enfin, on construit dessolutions semi-analytiques pour ces modèles, lesquelles nous fournissent unemanière plus efficace d’évaluer nos modèles approchés par rapport aux solutionsnumériques (éléments finis)Through-casing borehole resistivity measurements are commonly acquired inorder to characterize the Earth’s subsurface. The use of a casing surrounding theborehole highly complicates numerical simulations of the electric potential due toits thinness and a large contrast between casing conductivity and surroundingrock formation conductivity. In this work, we model the casing as a thin cylindricallayer of uniform thickness. Motivated by realistic scenarios, we realize that theconductivity of the case is typically proportional to its thickness to the power ofminus three.In this Ph.D. Dissertation, we focus on the above problem to derive ImpedanceTransmission Conditions (ITCs) in order to replace the metallic casing. To do so,we start by considering a 2D model in Cartesian coordinates that serves as aninitial approximation to solve the more realistic 3D axi-symmetric model (usingcylindrical coordinates) considered in most realistic through casing boreholesimulations. We start by considering the static (zero frequency) case, and we alsoderive ITCs for nonzero frequencies, which are important to understand certainphysical phenomena occurring in through casing borehole measurements,namely, the so called Delaware and Groningen effects. Then, we analyze thesemodels by proving stability and convergence results, and we asses the numericalperformance of these models by employing a Finite Element Method. Finally, wederive semi-analytical solutions for such models, which provide a more efficientway of evaluating our approximate models as in comparison with full numericalsolutions
Las medidas de resistividad en perforaciones a traves de tubos se utilizan demanera común para obtener una mejor caracterización del subsuelo de la tierra.El uso de un tubo que cubre el pozo complica enormemente las simulacionesnuméricas debido a su finura y al gran contraste entre la conductividad del tuboy la de las formaciones rocosas. En este trabajo, modelizamos el tubo como unamembrana cilíndrica fina de grosor uniforme. Basándonos en configuracionesrealistas, consideramos que la conductividad del tubo es proporcional a su grosora la potencia de menos tres.En esta tesis doctoral, nos concentramos en el problema anterior para obtenercodiciones de transmisión de impedancia (ITCs) que sirvan para reemplazar eltubo metálico. Para ello, empezamos por considerar un modelo 2D encoordenadas cartesianas, que sirve como una primera aproximación pararesolver el problema 3D con simetría axial (empleando coordenadas cilíndricas)considerado en la mayoría de las simulaciones realistas de perforaciones contubos. Empezamos por considerar el caso estático (frecuencia nula), y más tardeobtenemos ITCs para frecuencias no nulas, las cuales son importantes paraentender ciertos fenómenos físicos que ocurren al obtener medidas deresistividad en pozos a través de tubos, como por ejemplo, los efectos deDelaware y Groningen. Después, analizamos estos modelos demostrandoresultados de estabilidad y convergencia, y evaluamos el rendimiento numéricode estos modelos empleando el método de elementos finitos. Por último,obetnemos soluciones semi-analíticas para dichos modelos, las cualesproporcionan una manera más eficiente de evaluar las soluciones a nuestrosmodelos aproximados en comparación con soluciones puramente numéricas
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Holtz, Sebastian. "High-frequency statistics for Gaussian processes from a Le Cam perspective". Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21123.
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Diese Arbeit untersucht Inferenz für Streuungsparameter bedingter Gaußprozesse anhand diskreter verrauschter Beobachtungen in einem Hochfrequenz-Setting. Unser Ziel dabei ist es, eine asymptotische Charakterisierung von effizienter Schätzung in einem allgemeine Gaußschen Rahmen zu finden.
Für ein parametrisches Fundamentalmodell wird ein Hájek-Le Cam-Faltungssatz hergeleitet, welcher eine exakte asymptotische untere Schranke für Schätzmethoden liefert. Dazu passende obere Schranken werden konstruiert und die Bedeutung des Satzes wird verdeutlicht anhand zahlreicher Beispiele wie der (fraktionellen) Brownschen Bewegung, dem Ornstein-Uhlenbeck-Prozess oder integrierten Prozessen. Die Herleitung der Effizienzresultate basiert auf asymptotischen Äquivalenzen und kann für verschiedene Verallgemeinerungen des parametrischen Fundamentalmodells verwendet werden.
Als eine solche Erweiterung betrachten wir das Schätzen der quadrierten Kovariation eines stetigen Martingals anhand verrauschter asynchroner Beobachtungen, welches ein fundamentales Schätzproblem in der Öknometrie ist. Für dieses Modell erhalten wir einen semi-parametrischen Faltungssatz, welcher bisherige Resultate im Sinne von Multidimensionalität, Asynchronität und Annahmen verallgemeinert.
Basierend auf den vorhergehenden Herleitungen entwickeln wir einen statistischen Test für den Hurst-Parameter einer fraktionellen Brownschen Bewegung. Ein Score- und ein Likelihood-Quotienten-Test werden implementiert sowie analysiert und erste empirische Eindrücke vermittelt.This work studies inference on scaling parameters of a conditionally Gaussian process under discrete noisy observations in a high-frequency regime. Our aim is to find an asymptotic characterisation of efficient estimation for a general Gaussian framework. For a parametric basic case model a Hájek-Le Cam convolution theorem is derived, yielding an exact asymptotic lower bound for estimators. Matching upper bounds are constructed and the importance of the theorem is illustrated by various examples of interest such as the (fractional) Brownian motion, the Ornstein-Uhlenbeck process or integrated processes. The derivation of the efficiency result is based on asymptotic equivalences and can be employed for several generalisations of the parametric basic case model. As such an extension we consider estimation of the quadratic covariation of a continuous martingale from noisy asynchronous observations, which is a fundamental estimation problem in econometrics. For this model, a semi-parametric convolution theorem is obtained which generalises existing results in terms of multidimensionality, asynchronicity and assumptions. Based on the previous derivations, we develop statistical tests on the Hurst parameter of a fractional Brownian motion. A score test and a likelihood ratio type test are implemented as well as analysed and first empirical impressions are given.
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Andersson, Björn. "Contributions to Kernel Equating". Doctoral thesis, Uppsala universitet, Statistiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-234618.
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The statistical practice of equating is needed when scores on different versions of the same standardized test are to be compared. This thesis constitutes four contributions to the observed-score equating framework kernel equating. Paper I introduces the open source R package kequate which enables the equating of observed scores using the kernel method of test equating in all common equating designs. The package is designed for ease of use and integrates well with other packages. The equating methods non-equivalent groups with covariates and item response theory observed-score kernel equating are currently not available in any other software package. In paper II an alternative bandwidth selection method for the kernel method of test equating is proposed. The new method is designed for usage with non-smooth data such as when using the observed data directly, without pre-smoothing. In previously used bandwidth selection methods, the variability from the bandwidth selection was disregarded when calculating the asymptotic standard errors. Here, the bandwidth selection is accounted for and updated asymptotic standard error derivations are provided. Item response theory observed-score kernel equating for the non-equivalent groups with anchor test design is introduced in paper III. Multivariate observed-score kernel equating functions are defined and their asymptotic covariance matrices are derived. An empirical example in the form of a standardized achievement test is used and the item response theory methods are compared to previously used log-linear methods. In paper IV, Wald tests for equating differences in item response theory observed-score kernel equating are conducted using the results from paper III. Simulations are performed to evaluate the empirical significance level and power under different settings, showing that the Wald test is more powerful than the Hommel multiple hypothesis testing method. Data from a psychometric licensure test and a standardized achievement test are used to exemplify the hypothesis testing procedure. The results show that using the Wald test can provide different conclusions to using the Hommel procedure.
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Dabo, Issa-Mbenard. "Applications de la théorie des matrices aléatoires en grandes dimensions et des probabilités libres en apprentissage statistique par réseaux de neurones". Electronic Thesis or Diss., Bordeaux, 2025. http://www.theses.fr/2025BORD0021.
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Le fonctionnement des algorithmes d’apprentissage automatique repose grandement sur la structure des données qu’ils doivent utiliser. La majorité des travaux de recherche en apprentissage automatique se concentre sur l’étude de données homogènes, souvent modélisées par des variables aléatoires indépendantes et identiquement distribuées. Pourtant, les données apparaissant en pratique sont souvent hétérogènes. Nous proposons dans cette thèse de considérer des données hétérogènes en les dotant d’un profil de variance. Cette notion, issue de la théorie des matrices aléatoires, nous permet notamment d’étudier des données issues de modèles de mélanges. Nous nous intéressons plus particulièrement à la problématique de la régression ridge à travers deux modèles : la régression ridge linéaire (linear ridge model) et la régression ridge à caractéristiques aléatoires (random feature ridge model). Nous étudions dans cette thèse la performance de ces deux modèles dans le cadre de la grande dimension, c’est-à-dire lorsque la taille de l’échantillon d’entraînement et la dimension des données tendent vers l’infini avec des vitesses comparables. Dans cet objectif, nous proposons des équivalents asymptotiques de l’erreur d’entraînement et de l’erreur de test relatives aux modèles d’intérêt. L’obtention de ces équivalents repose grandement sur l’étude spectrale issue de la théorie des matrices aléatoires, des probabilités libres et de la théorie des trafics. En effet, la mesure de la performance de nombreux modèles d’apprentissage dépend de la distribution des valeurs propres de matrices aléatoires. De plus, ces résultats nous ont permis d’observer des phénomènes spécifiques à la grande dimension, comme le phénomène de la double descente. Notre étude théorique s’accompagne d’expériences numériques illustrant la précision des équivalents asymptotiques que nous fournissonsThe functioning of machine learning algorithms relies heavily on the structure of the data they are given to study. Most research work in machine learning focuses on the study of homogeneous data, often modeled by independent and identically distributed random variables. However, data encountered in practice are often heterogeneous. In this thesis, we propose to consider heterogeneous data by endowing them with a variance profile. This notion, derived from random matrix theory, allows us in particular to study data arising from mixture models. We are particularly interested in the problem of ridge regression through two models: the linear ridge model and the random feature ridge model. In this thesis, we study the performance of these two models in the high-dimensional regime, i.e., when the size of the training sample and the dimension of the data tend to infinity at comparable rates. To this end, we propose asymptotic equivalents for the training error and the test error associated with the models of interest. The derivation of these equivalents relies heavily on spectral analysis from random matrix theory, free probability theory, and traffic theory. Indeed, the performance measurement of many learning models depends on the distribution of the eigenvalues of random matrices. Moreover, these results enabled us to observe phenomena specific to the high-dimensional regime, such as the double descent phenomenon. Our theoretical study is accompanied by numerical experiments illustrating the accuracy of the asymptotic equivalents we provide
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Powell, Kevin James. "Topics in Analytic Number Theory". BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.
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The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 completely. Dr. Baker corrected my work for k=4 and proved the result for k=5. He then generalized our work into the paper as it now stands. We also discussed and both contributed to parts of section 3 on bounds for exponential sums. The second part represents my own work guided by my advisor. I study the zeros of derivatives of Dirichlet L-functions. The first theorem gives an analog for a result of Speiser on the zeros of ζ'(s). He proved that RH is equivalent to the hypothesis that ζ'(s) has no zeros with real part strictly between 0 and ½. The last two theorems discuss zero-free regions to the left and right for L^{(k)}(s,χ).
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Mattesi, Vanessa. "Propagation des ondes dans un domaine comportant des petites hétérogénéités : modélisation asymptotique et calcul numérique". Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3026/document.
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Dans cette thèse, nous nous intéressons à la modélisation mathématique des hétérogénéités de longueurs caractéristiques beaucoup plus petites que la longueur d'ondes. La thèse consiste en deux parties. La partie théorique est dédiée à l'obtention d'un développement asymptotique raccordé: la solution est décrite à l'aide d'un développement de champ proche au voisinage de l'obstacle et par un développement de champ lointain hors de ce voisinage. Le développement de champ lointain met en jeu des solutions singulières de l'équation des ondes tandis que le champ proche lui est régi par un modèle quasi-statique. Ces deux développements sont alors raccordés dans une zone intermédiaire dite de raccord. Nous obtenons alors des estimations d'erreurs permettant de rendre rigoureux ce développement asymptotique formel. La deuxième partie est numérique. Elle décrit à la fois la méthode de Galerkine discontinue, une méthode de raffinement de maillage espace-temps et propose une discrétisation des modèles asymptotiques obtenues précédemment. Elle est illustrée par un certain nombre de tests numériquesIn this thesis, we focus our attention on the modeling of heterogeneities which are smaller than the wavelength. The document is decomposed into two parts : a theoretical one and a numerical one. In the first part, we derive a matched asymptotic expansion composed of a far-field expansion and a near-field expansion. The terms of the far-field expansion are singular solutions of the wave equation whereas the terms of the near-field expansion satisfy quasistatic problems. These expansions are matched in an intermediate region. We justify mathematically this theory by proving error estimates. In the second part, we describe the Discontinuous Galerkin method, a local time stepping method and the implementation of the matched asymptotic method. Numerical simulations illustrate these results
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Penny, Melissa. "Mathematical modelling of dye-sensitised solar cells". Queensland University of Technology, 2006. http://eprints.qut.edu.au/16270/.
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This thesis presents a mathematical model of the nanoporous anode within a dyesensitised solar cell (DSC). The main purpose of this work is to investigate interfacial charge transfer and charge transport within the porous anode of the DSC under both illuminated and non-illuminated conditions. Within the porous anode we consider many of the charge transfer reactions associated with the electrolyte species, adsorbed dye molecules and semiconductor electrons at the semiconductor-dye- electrolyte interface. Each reaction at this interface is modelled explicitly via an electrochemical equation, resulting in an interfacial model that consists of a coupled system of non-linear algebraic equations. We develop a general model framework for charge transfer at the semiconductor-dye-electrolyte interface and simplify this framework to produce a model based on the available interfacial kinetic data. We account for the charge transport mechanisms within the porous semiconductor and the electrolyte filled pores that constitute the anode of the DSC, through a one- dimensional model developed under steady-state conditions. The governing transport equations account for the diffusion and migration of charge species within the porous anode. The transport model consists of a coupled system of non-linear differential equations, and is coupled to the interfacial model via reaction terms within the mass-flux balance equations. An equivalent circuit model is developed to account for those components of the DSC not explicitly included in the mathematical model of the anode. To obtain solutions for our DSC mathematical model we develop code in FORTRAN for the numerical simulation of the governing equations. We additionally employ regular perturbation analysis to obtain analytic approximations to the solutions of the interfacial charge transfer model. These approximations facilitate a reduction in computation time for the coupled mathematical model with no significant loss of accuracy. To obtain predictions of the current generated by the cell we source kinetic and transport parameter values from the literature and from experimental measurements associated with the DSC commissioned for this study. The model solutions we obtain with these values correspond very favourably with experimental data measured from standard DSC configurations consisting of titanium dioxide porous films with iodide/triiodide redox couples within the electrolyte. The mathematical model within this thesis enables thorough investigation of the interfacial reactions and charge transport within the DSC.We investigate the effects of modified cell configurations on the efficiency of the cell by varying associated parameter values in our model. We find, given our model and the DSC configuration investigated, that the efficiency of the DSC is improved with increasing electron diffusion, decreasing internal resistances and with decreasing dark current. We conclude that transport within the electrolyte, as described by the model, appears to have no limiting effect on the current predicted by the model until large positive voltages. Additionally, we observe that the ultrafast injection from the excited dye molecules limits the interfacial reactions that affect the DSC current.
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Penny, Melissa. "Mathematical modelling of dye-sensitised solar cells". Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16270/1/Melissa_Penny_Thesis.pdf.
Pełny tekst źródłaStreszczenie:
This thesis presents a mathematical model of the nanoporous anode within a dyesensitised solar cell (DSC). The main purpose of this work is to investigate interfacial charge transfer and charge transport within the porous anode of the DSC under both illuminated and non-illuminated conditions. Within the porous anode we consider many of the charge transfer reactions associated with the electrolyte species, adsorbed dye molecules and semiconductor electrons at the semiconductor-dye- electrolyte interface. Each reaction at this interface is modelled explicitly via an electrochemical equation, resulting in an interfacial model that consists of a coupled system of non-linear algebraic equations. We develop a general model framework for charge transfer at the semiconductor-dye-electrolyte interface and simplify this framework to produce a model based on the available interfacial kinetic data. We account for the charge transport mechanisms within the porous semiconductor and the electrolyte filled pores that constitute the anode of the DSC, through a one- dimensional model developed under steady-state conditions. The governing transport equations account for the diffusion and migration of charge species within the porous anode. The transport model consists of a coupled system of non-linear differential equations, and is coupled to the interfacial model via reaction terms within the mass-flux balance equations. An equivalent circuit model is developed to account for those components of the DSC not explicitly included in the mathematical
model of the anode. To obtain solutions for our DSC mathematical model we develop code in FORTRAN for the numerical simulation of the governing equations. We additionally employ regular perturbation analysis to obtain analytic approximations to the solutions of the interfacial charge transfer model. These approximations facilitate a reduction in computation time for the coupled mathematical model with no significant loss of accuracy. To obtain predictions of the current generated by the cell we source kinetic and transport parameter values from the literature and from experimental measurements associated with the DSC commissioned for this study. The model solutions we obtain with these values correspond very favourably with experimental data measured from standard DSC configurations consisting of titanium dioxide porous films with iodide/triiodide redox couples within the electrolyte. The mathematical model within this thesis enables thorough investigation of the interfacial reactions and charge transport within the DSC.We investigate the effects of modified cell configurations on the efficiency of the cell by varying associated parameter values in our model. We find, given our model and the DSC configuration investigated, that the efficiency of the DSC is improved with increasing electron diffusion, decreasing internal resistances and with decreasing dark current. We conclude that transport within the electrolyte, as described by the model, appears to have no limiting effect on the current predicted by the model until large positive voltages. Additionally, we observe that the ultrafast injection from the excited dye molecules limits the interfacial reactions that affect the DSC current.
Książki na temat "Asymptotic equivalents"
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Akhmet, Marat. Almost Periodicity, Chaos, and Asymptotic Equivalence. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-20572-0.
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Cheng, Russell. Standard Asymptotic Theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0003.
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This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.
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Horing, Norman J. Morgenstern. Quantum Mechanical Ensemble Averages and Statistical Thermodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0006.
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Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.
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Herrington, William G., Aron Chakera i Christopher A. O’Callaghan. Diabetic renal disease. Redaktorzy Patrick Davey i David Sprigings. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199568741.003.0164.
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Diabetic nephropathy is kidney damage occurring as a result of diabetes mellitus. Overt diabetic nephropathy is defined as proteinuria greater than 0.5 g/day. Diabetic nephropathy has a complicated pathogenesis including glomerular hypertension with hyperfiltration and advanced glycation end products. Poor glycaemic control is associated with progression to microalbuminuria and overt diabetic nephropathy. The lifetime risk is fairly equivalent for type 1 and type 2 diabetes mellitus. Early disease is usually asymptomatic. Hyperglycaemia causes an osmotic diuresis and, thus, diabetes can present with polyuria. Hypertension develops with microalbuminuria; oedema indicates abnormal sodium and water retention and, occasionally, the development of nephrotic syndrome. Patients with diabetes, perhaps due to accompanying cardiac disease, are particularly susceptible to fluid overload and uraemic symptoms. End-stage renal disease can occur as early as when the estimated glomerular filtration rate is 15 ml/min 1.73 m−2.
Części książek na temat "Asymptotic equivalents"
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Shackell, John R. "Zero Equivalence". W Symbolic Asymptotics, 7–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-10176-6_2.
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Akhmet, Marat. "Asymptotic Equivalence of Hybrid Systems". W Nonlinear Systems and Complexity, 323–54. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20572-0_14.
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Akhmet, Marat. "Asymptotic Equivalence and Almost Periodic Solutions". W Nonlinear Systems and Complexity, 309–21. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20572-0_13.
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Marichal, Jean-Luc, i Naïm Zenaïdi. "Asymptotic Analysis". W A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions, 59–89. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95088-0_6.
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AbstractThe asymptotic behavior of the gamma function for large values of its argument can be summarized as follows: for any a ≥ 0, we have the following asymptotic equivalences (see Titchmarsh (The Theory of Functions, 2nd edn. Oxford University Press, Oxford, 1939, Section 1.87)) $$\displaystyle \begin{aligned} \Gamma (x+a) ~\sim ~ x^a\,\Gamma (x) \mbox{as }x\to \infty {\,},\end{aligned} $$ Γ ( x + a ) ∼ x a Γ ( x ) as x → ∞ , $$\displaystyle \begin{aligned}\Gamma (x) ~\sim ~ \sqrt {2\pi }{\,}e^{-x}x^{x-\frac {1}{2}} \mbox{as }x\to \infty {\,},\end{aligned} $$ Γ ( x ) ∼ 2 π e − x x x − 1 2 as x → ∞ , $$\displaystyle \begin{aligned}\Gamma (x+1) ~\sim ~ \sqrt {2\pi x}{\,}e^{-x}x^x \mbox{as }x\to \infty {\,}, \end{aligned} $$ Γ ( x + 1 ) ∼ 2 π x e − x x x as x → ∞ , where both formulas (6.2) and (6.3) are known by the name Stirling’s formula.
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Hirai, Hayato. "Equivalence Between Soft Theorem and Asymptotic Symmetry". W Springer Theses, 61–69. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-3045-3_4.
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Molahajloo, Shahla, Luigi Rodino i M. W. Wong. "Metaplectic Equivalence of the Hierarchical Twisted Laplacian". W Pseudo-Differential Operators, Generalized Functions and Asymptotics, 77–84. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0585-8_4.
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Bailey, B. A. "An Asymptotic Equivalence Between Two Frame Perturbation Theorems". W Springer Proceedings in Mathematics, 1–7. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0772-0_1.
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Reinfelds, Andrejs. "Asymptotic Equivalence of Difference Equations in Banach Space". W Springer Proceedings in Mathematics & Statistics, 215–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44140-4_12.
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Bíró, József. "Novel Equivalent Capacity Approximations through Asymptotic Analysis: A Review". W Performance Modelling and Analysis of Heterogeneous Networks, 45–72. New York: River Publishers, 2022. http://dx.doi.org/10.1201/9781003339052-4.
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Cheng, H. K. "Transonic Equivalence Rule: Unresolved Aspects of Asymptotic and CFD Studies". W Symposium Transsonicum III, 179–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83584-1_15.
Pełny tekst źródłaStreszczenia konferencji na temat "Asymptotic equivalents"
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Heeb, Hansruedi. "EMI Simulation Using Retarded Partial Element Equivalent Circuits and Asymptotic Waveform Evaluation". W 11th International Zurich Symposium and Technical Exhibition on Electromagnetic Compatibility, 191–96. IEEE, 1995. https://doi.org/10.23919/emc.1995.10784315.
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Hou, Zhenjie, i Xuchu Dai. "On the Asymptotic Equivalence of Singular Values for Block Circulant and Block Toeplitz Matrices". W 2024 10th International Conference on Computer and Communications (ICCC), 1035–39. IEEE, 2024. https://doi.org/10.1109/iccc62609.2024.10941923.
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Schau, Kyle, i Gopal Gaonkar. "A Framework for Modeling Wind-Farm Wake Turbulence from a Database for Simulation and Analysis". W Vertical Flight Society 71st Annual Forum & Technology Display, 1–20. The Vertical Flight Society, 2015. http://dx.doi.org/10.4050/f-0071-2015-10302.
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This paper presents a mathematical framework for constructing interpretive autospectral models of wind-farm wake turbulence from a database; these models are in closed form, and the database refers to flow velocity points from experimental - wind-tunnel and full-scale, and computational fluid dynamics, investigations. The framework begins with a perturbation series expansion of the autocorrelations for all three velocity components; therein, the first term has a form of the von Karman longitudinal or lateral correlation function. These series are then transformed into equivalent series of autospectra, and the coefficients of the series are evaluated by satisfying the theoretical constraints and fitting a curve on a set of selected autospectral data points. The framework ensures that the developed models and the corresponding autospectral data points have the same time scale, mean square value (energy) and autospectral asymptotic decay according to the Kolmogorov -5/3 law. It is tested against a demanding database of wake turbulence inside a wind farm over a complex terrain, and the developed models are further tested as to their suitability for routine simulation through white-noise-driven filters. Generally, a two-term series is found to be adequate and the filter design is as routine as the currently used procedure for the von Karman models. The framework can be applied to any database, and this model development from a database represents a new and promising research avenue.
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Schau, Kyle, Susan Polsky i Gopal Gaonkar. "Helicopter Downwash Effects on Ship Airwake: Predictions, Modeling from a Database, and Simulation". W Vertical Flight Society 70th Annual Forum & Technology Display, 1–17. The Vertical Flight Society, 2014. http://dx.doi.org/10.4050/f-0070-2014-9582.
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Helicopter downwash impact on ship airwake is addressed from a three-pronged approach: 1.) Predictions of one-point statistics of autospectrum and two-point statistics of cross-spectrum and coherence from a Computational Fluid Dynamics database of flow velocity predictions; 2.) Development of a mathematical framework for extracting interpretive autospectral models in closed form from a database; 3.) Simulation through white-noise-driven filters for the extracted models. The framework begins with an earlier-exercised perturbation series expansion of the autocorrelation for all three velocity components, and the first term of the series has a form of the von Karman longitudinal or lateral correlation function. After transformation into equivalent series of autospectrum, the perturbation coefficients are evaluated by satisfying the theoretical constraints and fitting a curve on a set of selected autospectral data points generated from the database. These constraints ensure that the extracted models and the autospectral data points have the same time scale, intensity, energy, and asymptotic decay according to the Kolmogorov -5/3 law. The framework represents a sensible combination of series expansion, exploitation of a database, and theoretical constraints to provide a foothold on airwake-downwash phenomenon for engineering analysis. The framework's strengths and weaknesses and its advancement over the earlier series-expansion schemes are also included. Downwash increases airwake energy by one order of magnitude, and all of this airwake-downwash energy is concentrated within the bandwidth ( 0 < f (Hz) < 1.6 that affects flight mechanics.
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Pesterev, Alexander V., Lawrence A. Bergman, Chin An Tan, T. C. Tsao i Bingen Yang. "On Equivalence of the Moving Mass and Moving Oscillator Problems". W ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21518.
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Abstract Asymptotic behavior of the solution of the moving oscillator problem is examined for large values of the spring stiffness for the general case of nonzero beam initial conditions. In the limit of infinite spring stiffness, the moving oscillator problem for a simply supported beam is shown to be not equivalent in a strict sense to the moving mass problem; i.e., beam displacements obtained by solving the two problems are the same, but the higher-order derivatives of the two solutions are different. In the general case, the force acting on the beam from the oscillator is shown to contain a high-frequency component, which does not vanish, or even grows, when the spring coefficient tends to infinity. The magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion. For the case of a simply supported beam, the magnitude of the high-frequency force linearly depends on the oscillator eigenfrequency and velocity. The deficiency of the moving mass model is noted in that it fails to predict stresses in the bridge structure. Results of numerical experiments are presented.
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Ghosh, Supratim, i Ji-Woong Lee. "Equivalent conditions for uniform asymptotic consensus among distributed agents". W 2010 American Control Conference (ACC 2010). IEEE, 2010. http://dx.doi.org/10.1109/acc.2010.5530892.
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Fang, Yuan, Xinmin Li i Ling Qiu. "Asymptotic Equivalent Performance of Uplink Massive MIMO Systems with Phase Noise". W 2018 IEEE International Conference on Communications (ICC 2018). IEEE, 2018. http://dx.doi.org/10.1109/icc.2018.8422265.
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Nguyen, Duc Minh, Hiroshi Shirai i Se-Yun Kim. "Uniform Asymptotic Solution for Dielectric Wedge Diffraction Based on Equivalent Currents". W 2021 XXXIVth General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS). IEEE, 2021. http://dx.doi.org/10.23919/ursigass51995.2021.9560354.
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Yoo, Young Geon, i Joon Ho Cho. "Asymptotic Equivalence of SC LMMSE-FDE to Continuous-Time LMMSE Equalizer". W 2007 IEEE Wireless Communications and Networking Conference. IEEE, 2007. http://dx.doi.org/10.1109/wcnc.2007.278.
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Liu, C. T. "Estimating the Initial Crack Size in a Particulate Composite Material: An Analytical and Experimental Approach". W ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/pvp-25202.
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Abstract In this study, a technique to predict the equivalent initial crack size (EICS) in a particulate composite material, containing hard particles embedded in a rubber matrix, was developed using constant strain rate crack propagation test data. The accuracy of the developed technique was determined. In addition, the statistical distribution of the equivalent initial crack size follows the second asymptotic distribution of maximum value.
Raporty organizacyjne na temat "Asymptotic equivalents"
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Petrova, Katerina. On the Validity of Classical and Bayesian DSGE-Based Inference. Federal Reserve Bank of New York, styczeń 2024. http://dx.doi.org/10.59576/sr.1084.
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This paper studies large sample classical and Bayesian inference in a prototypical linear DSGE model and demonstrates that inference on the structural parameters based on a Gaussian likelihood is unaffected by departures from Gaussianity of the structural shocks. This surprising result is due to a cancellation in the asymptotic variance resulting into a generalized information equality for the block corresponding to the structural parameters. The underlying reason for the cancellation is the certainty equivalence property of the linear rational expectation model. The main implication of this result is that classical and Bayesian Gaussian inference achieve a semi-parametric efficiency bound and there is no need for a “sandwich-form” correction of the asymptotic variance of the structural parameters. Consequently, MLE-based confidence intervals and Bayesian credible sets of the deep parameters based on a Gaussian likelihood have correct asymptotic coverage even when the structural shocks are non-Gaussian. On the other hand, inference on the reduced-form parameters characterizing the volatility of the shocks is invalid whenever the structural shocks have a non-Gaussian density and the paper proposes a simple Metropolis-within-Gibbs algorithm that achieves correct large sample inference for the volatility parameters.
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Amengual, Dante, Xinyue Bei, Marine Carrasco i Enrique Sentana. Score-type tests for normal mixtures. CIRANO, styczeń 2023. http://dx.doi.org/10.54932/uxsg1990.
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Testing normality against discrete normal mixtures is complex because some parameters turn increasingly underidentified along alternative ways of approaching the null, others are inequality constrained, and several higher-order derivatives become identically 0. These problems make the maximum of the alternative model log-likelihood function numerically unreliable. We propose score-type tests asymptotically equivalent to the likelihood ratio as the largest of two simple intuitive statistics that only require estimation under the null. One novelty of our approach is that we treat symmetrically both ways of writing the null hypothesis without excluding any region of the parameter space. We derive the asymptotic distribution of our tests under the null and sequences of local alternatives. We also show that their asymptotic distribution is the same whether applied to observations or standardized residuals from heteroskedastic regression models. Finally, we study their power in simulations and apply them to the residuals of Mincer earnings functions.