Indirect Techniques in Nuclear Astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
Energy Technology Data Exchange (ETDEWEB)
Mukhamedzhanov, A.M. [Cyclotron Institute, Texas A and M University, College Station, TX, 77843 (United States); Blokhintsev, L.D. [Institute of Nuclear Physics, Moscow State University, Moscow (Russian Federation); Brown, S. [Florida State University, Tallahassee, FL (United States)] (and others)
2007-05-01
We address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique to determine the astrophysical factor for the {sup 13}C({alpha}, n){sup 16}O reaction which is one of the neutron generators for the s processes in AGB stars. The TH method is a unique indirect technique allowing one to measure astrophysical S factors for rearrangement reactions down to astrophysically relevant energies. We derive equations connecting the cross sections for the binary direct and resonant reactions determined from the indirect TH reactions to direct cross sections measurements.
Indirect techniques in nuclear astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
Mukhamedzhanov, A M; Brown, B A; Burjan, V; Cherubini, S; Gagliardi, C A; Irgaziev, B F; Kroha, V; Nunes, F M; Pirlepesov, F; Pizzone, R G; Romano, S; Spitaleri, C; Tang, X D; Trache, L; Tribble, R E; Tumino, A
2005-01-01
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reac...
Asymptotic Normalization Coefficient of 27P→26Si+p and Radius of 27P Halo
Institute of Scientific and Technical Information of China (English)
GUO Bing; LI Zhi-Hong; LIU Wei-Ping; BAI Xi-Xiang
2006-01-01
The asymptotic normalization coefficient of the virtual decay 27P→26Si+p is extracted to be 1840±240 fm-1 from the peripheral 26Mg(d,p)27Mg reaction using charge symmetry of mirror pair,for the first time.It is then used to derive the rms radius of the valence proton in the ground state of 27P.We obtain the rms radius 1/2=4.57±0.36 fm,significantly larger than the matter radius of 27P.The probability of the valence proton outside the matter radius of 27P is found to be 73%.The present work supports the conclusion that the 27P ground state has a proton halo structure.
Indirect techniques in nuclear astrophysics. Asymptotic normalization coefficient and trojan horse
Energy Technology Data Exchange (ETDEWEB)
Mukhamedzhanov, A.M.; Gagliardi, C.A.; Pirlepesov, F.; Trache, L.; Tribble, R.E. [Texas A and M University, Cyclotron Institute, College Station, TX (United States); Blokhintsev, L.D. [Moscow State University, Institute of Nuclear Physics, Moscow (Russian Federation); Brown, B.A.; Nunes, F.M. [Michigan State University, N.S.C.L. and Department of Physics and Astronomy, East Lansing, MI (United States); Burjan, V.; Kroha, V. [Nuclear Physics Institute of Czech Academy of Sciences, Prague-Rez (Czech Republic); Cherubini, S.; Pizzone, R.G.; Romano, S.; Spitaleri, C.; Tumino, A. [DMFCI, Universita di Catania, Catania, Italy and INFN, Laboratori Nazionali del Sud, Catania (Italy); Irgaziev, B.F. [National University, Physics Department, Tashkent (Uzbekistan); Tang, X.D. [Argonne National Laboratory, Physics Division, Argonne, IL (United States)
2006-03-15
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysically relevant energies. We explain why there is no Coulomb barrier in the sub-process amplitudes extracted from the TH reaction. The expressions for the TH amplitude for direct and resonant cases are presented. (orig.)
Extraction of the rms Radii of 13C from Asymptotic Normalization Coefficients
Institute of Scientific and Technical Information of China (English)
林承键; 刘祖华; 张焕乔; 吴岳伟; 杨峰; 阮明
2001-01-01
The asymptotic normalization coefficients (ANCs) for three bound states of 13C (12 C+n) are extracted from the angular distributions of 12C(d,p) reactions at E1ab = 11.8MeV. With these ANCs, the calculated root-meansquare (rms) radii of these three states agree with our previous results. The ANCs are 1.93±0.17, 1.84±0.16and 0.149±0.012fm-1/2, and the rms radii 〈r2〉1/2 are 3.39±0.31, 5.04±0.75 and 3.68±0.40fm for the ground state, the first and third excitation states, respectively. Further analyses show that the first excitation state with D1=50.3% is a true neutron halo state, while the third excitation state with D1=25.2% is a neutron skin state.
Asymptotic properties of order statistics correlation coefficient in the normal cases
Xu, W; Chang, C.; Hung, YS; Fung, PCW
2008-01-01
We have previously proposed a novel order statistics correlation coefficient (OSCC), which possesses some desirable advantages when measuring linear and monotone nonlinear associations between two signals. However, the understanding of this new coefficient is far from complete. A lot of theoretical questions, such as the expressions of its distribution and moments, remain to be addressed. Motivated by this unsatisfactory situation, in this paper we prove that for samples drawn from bivariate ...
Institute of Scientific and Technical Information of China (English)
GUO Bing; LI Zhi-Hong; LIU Wei-Ping; BAI Xi-Xiang
2007-01-01
The asymptotic normalization coefficients (ANCs) for the virtual decay 17O→16O+n are derived from the angular distributions of the 16O(d, p)17O reaction leading to the ground and first excited states of 17O, respectively, using the distorted wave Born approximation and the adiabatic wave approximation. The ANCs of 17F are then extracted according to charge symmetry of mirror nuclei and used to calculate the astrophysical S-factors of 16O(p,γ)17F leading to the first two states of 17F. The present results are in good agreement with those from the direct measurement. This provides a test of this indirect method to determine direct astrophysical S-factors of(p, γ) reaction. In addition, the S-factors at zero energy for the direct captures to the ground and first excited states of 17F are presented, without the uncertainty associated with the extrapolation from higher energies in direct measurement.
Institute of Scientific and Technical Information of China (English)
GUO Bing; LI Zhi-Hong
2007-01-01
@@ The angular distribution of the 13C(d,p)14C reaction is reanalysed using the Johnson-Soper approach. The squared asymptotic normalization coefficient (ANC) of virtual decay 14C → 13C + n is then derived to be 21.4 ±5.0 fm-1.
Institute of Scientific and Technical Information of China (English)
WU Kai-Su; CHEN Yong-Shou; LIU Zu-Hua; LIN Cheng-Jian; ZHANG Huan-Qiao
2003-01-01
The cross section of the direct neutron capture reaction 12C(n,7)13C(l/2+) is calculated with the asymptotic normalization coefficient method. The result is in good agreement with a recent experiment at low energy. An enormous enhancement of cross section is found for this direct neutron capture in which a p-wave neutron is captured into an 2?i/2 orbit with neutron halo. The possible effect of the neutron halo structure presented in this reaction on the s-process in astrophysics is discussed in general.
Asymptotics of loop quantum gravity fusion coefficients
Energy Technology Data Exchange (ETDEWEB)
Alesci, Emanuele; Bianchi, Eugenio; Magliaro, Elena; Perini, Claudio, E-mail: alesci@fis.uniroma3.i, E-mail: e.bianchi@sns.i, E-mail: elena.magliaro@gmail.co, E-mail: claude.perin@libero.i [Centre de Physique Theorique de Luminy , case 907, F-13288 Marseille (France)
2010-05-07
The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in loop quantum gravity. In this paper we give a simple analytic formula of the Engle-Pereira-Rovelli-Livine fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into SU(2){sub L} x SU(2){sub R} semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.
Institute of Scientific and Technical Information of China (English)
吕士钦; 卢准炜; 张日权
2008-01-01
变系数模型已获得了广泛的应用,半变系数模型是变系数模型的有效推广,本文给出半变系数模型在线性约束条件下的PLS估计,并证明了常系数和函数系数估计的渐近正态性.%Semivarying coefficient models are efficient generalization of the varying-coefficient regression models which have extremely wide applied.In recent years,many approaches are developed to estimate the unknown parameters and the coefficient functions.Based on the ideals of Fan and Huang (2005),the constrained profile least squares estimation on semivarying coefficient models under linear constraints is developed in this paper.Asymptotic normalities of the estimation on parametric component and nonparametric component are investigated.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
王启华; 荆炳义
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Asymptotic results for bifurcating random coefficient autoregressive processes
Blandin, Vassili
2012-01-01
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
Negative normal restitution coefficient for nanocluster collisions
Brilliantov, Nikolai V
2010-01-01
The oblique impact of nanoclusters is studied by means of Molecular Dynamics simulation. Using the standard definition of the normal restitution coefficient $e$ we observe a surprising result, that $e$ becomes negative for large incident angles. We show that this effect may be attributed to the reorientation of the contact plane during collisions, which affects $e$. We propose a modified definition of the normal restitution coefficient $\\Tilde{e}$. This, in contrast to the standard definition, characterizes exclusively the normal motion and is always positive. We develop a simple theoretical model of an oblique impact, which explains the observed behavior of the restitution coefficients and agrees well with the numerical data.
ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC REGRESSION MODEL
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The following heteroscedastic regression model Yi = g(xi) + σiei (1 ≤ i ≤ n) is considered, where it is assumed that σ2i = f(ui), the design points (xi, ui) are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.
Molzon, Raymond; Pinelis, Iosif
2009-01-01
Pearson's is the most common correlation statistic, used mainly in parametric settings. Most common among nonparametric correlation statistics are Spearman's and Kendall's. We show that for bivariate normal i.i.d. samples the pairwise asymptotic relative efficiency between these three statistics depends monotonically on the population correlation coefficient. This monotonicity is a corollary to a stronger result. The proofs rely on the use of l'Hospital-type rules for monotonicity patterns.
Institute of Scientific and Technical Information of China (English)
Li-qun Cao; De-chao Zhu; Jian-Lan Luo
2002-01-01
In this paper, we will discuss the asymptotic behaviour for a class of hyper bolic -parabolic type equation with highly oscillatory coefficients arising from the strong-transient heat and mass transfer problems of composite media. A complete multiscale asymptotic expansion and its rigorous verification will be reported.
Statistical Tests for the Reciprocal of a Normal Mean with a Known Coefficient of Variation
Directory of Open Access Journals (Sweden)
Wararit Panichkitkosolkul
2015-01-01
Full Text Available An asymptotic test and an approximate test for the reciprocal of a normal mean with a known coefficient of variation were proposed in this paper. The asymptotic test was based on the expectation and variance of the estimator of the reciprocal of a normal mean. The approximate test used the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the two statistical tests. Simulation results showed that the two proposed tests performed well in terms of empirical type I errors and power. Nevertheless, the approximate test was easier to compute than the asymptotic test.
Energy Technology Data Exchange (ETDEWEB)
McCleskey, M; Mukhamedzhanov, A M; Trache, L; Tribble, R E; Banu, A; Eremenko, V; Goldberg, V Z; Lui, Y W; McCleskey, E; Roeder, B T; Spiridon, A; Carstoiu, F; Burjan, V; Hons, Z; Thompson, I J
2014-04-17
The ^{14}C + n <--> ^{15}C system has been used as a test case in the evaluation of a new method to determine spectroscopic factors that uses the asymptotic normalization coefficient (ANC). The method proved to be unsuccessful for this case. As part of this experimental program, the ANCs for the ^{15}C ground state and first excited state were determined using a heavy-ion neutron transfer reaction as well as the inverse kinematics (d,p) reaction, measured at the Texas A&M Cyclotron Institute. The ANCs were used to evaluate the astrophysical direct neutron capture rate on ^{14}C, which was then compared with the most recent direct measurement and found to be in good agreement. A study of the ^{15}C SF via its mirror nucleus ^{15}F and a new insight into deuteron stripping theory are also presented.
Asymptotic Behavior of a Competition-Diffusion System with Variable Coefficients and Time Delays
Miguel Uh Zapata; Eric Avila Vales; Angel G. Estrella
2008-01-01
A class of time-delay reaction-diffusion systems with variable coefficients which arise from the model of two competing ecological species is discussed. An asymptotic global attractor is established in terms of the variable coefficients, independent of the time delays and the effect of diffusion by the upper-lower solutions and iteration method.
Zhang, Zhengjun; Qi, Yongcheng; Ma, Xiwen
2011-01-01
This paper first proves that the sample based Pearson’s product-moment correlation coefficient and the quotient correlation coefficient are asymptotically independent, which is a very important property as it shows that these two correlation coefficients measure completely different dependencies between two random variables, and they can be very useful if they are simultaneously applied to data analysis. Motivated from this fact, the paper introduces a new way of combining these two sample ba...
Asymptotic Normality of LS Estimate in Simple Linear EV Regression Model
Institute of Scientific and Technical Information of China (English)
Jixue LIU
2006-01-01
Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model.In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.
Lq-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues
Directory of Open Access Journals (Sweden)
Vladimir Kozlov
2006-01-01
Full Text Available We consider eigenvalues of elliptic boundary value problems, written in variational form, when the leading coefficients are perturbed by terms which are small in some integral sense. We obtain asymptotic formulae. The main specific of these formulae is that the leading term is different from that in the corresponding formulae when the perturbation is small in L∞-norm.
Tian, Jianxiang; Mulero, A
2016-01-01
Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the t...
Asymptotic behavior of elliptic boundary-value problems with some small coefficients
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Senoussi Guesmia
2008-04-01
Full Text Available The aim of this paper is to analyze the asymptotic behavior of the solutions to elliptic boundary-value problems where some coefficients become negligible on a cylindrical part of the domain. We show that the dimension of the space can be reduced and find estimates of the rate of convergence. Some applications to elliptic boundary-value problems on domains becoming unbounded are also considered.
Rubao Ma; Weichao Xu; Yun Zhang; Zhongfu Ye
2014-01-01
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means ...
ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS-IN-VARIABLES MODEL
Institute of Scientific and Technical Information of China (English)
ZHANG Sanguo; CHEN Xiru
2003-01-01
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
Asymptotic normality of the size of the giant component in a random hypergraph
Bollobas, Bela
2011-01-01
Recently, we adapted random walk arguments based on work of Nachmias and Peres, Martin-L\\"of, Karp and Aldous to give a simple proof of the asymptotic normality of the size of the giant component in the random graph $G(n,p)$ above the phase transition. Here we show that the same method applies to the analogous model of random $k$-uniform hypergraphs, establishing asymptotic normality throughout the (sparse) supercritical regime. Previously, asymptotic normality was known only towards the two ends of this regime.
Directory of Open Access Journals (Sweden)
Wararit Panichkitkosolkul
2010-01-01
Full Text Available A new asymptotic confidence interval constructed by using a confidence intervalfor the Poisson mean is proposed for the coefficient of variation of the Poisson distribution.The following confidence intervals are considered: McKay’s confidence interval, Vangel’sconfidence interval and the proposed confidence interval. Using Monte Carlo simulations,the coverage probabilities and expected lengths of these confidence intervals are compared.Simulation results show that all scenarios of the new asymptotic confidence interval havedesired minimum coverage probabilities of 0.95 and 0.90. In addition, the newly proposedconfidence interval is better than the existing ones in terms of coverage probability andexpected length for all sample sizes and parameter values considered in this paper.
Improved Estimators of the Mean of a Normal Distribution with a Known Coefficient of Variation
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Wuttichai Srisodaphol
2012-01-01
Full Text Available This paper is to find the estimators of the mean θ for a normal distribution with mean θ and variance aθ2, a>0, θ>0. These estimators are proposed when the coefficient of variation is known. A mean square error (MSE is a criterion to evaluate the estimators. The results show that the proposed estimators have preference for asymptotic comparisons. Moreover, the estimator based on jackknife technique has preference over others proposed estimators with some simulations studies.
Consistent and asymptotically normal PLS estimators for linear structural equations
Dijkstra, Theo; Henseler, Jorg
2015-01-01
A vital extension to partial least squares (PLS) path modeling is introduced: consistency. While maintaining all the strengths of PLS, the consistent version provides two key improvements. Path coefficients, parameters of simultaneous equations, construct correlations, and indicator loadings are est
ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS
Institute of Scientific and Technical Information of China (English)
YUE LI; CHEN XIRU
2005-01-01
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
Consistent and asymptotically normal PLS estimators for linear structural equations
Dijkstra, Theo K.; Henseler, J.
2015-01-01
A vital extension to partial least squares (PLS) path modeling is introduced: consistency. While maintaining all the strengths of PLS, the consistent version provides two key improvements. Path coefficients, parameters of simultaneous equations, construct correlations, and indicator loadings are estimated consistently. The global goodness-of-fit of the structural model can also now be assessed, which makes PLS suitable for confirmatory research. A Monte Carlo simulation illustrates the new ap...
Czabarka, Eva; Johnson, Virginia; Kupczok, Anne; Szekely, Laszlo A
2011-01-01
P.L. Erdos and L.A. Szekely [Adv. Appl. Math. 10(1989), 488-496] gave a bijection between rooted semilabeled trees and set partitions. L.H. Harper's results [Ann. Math. Stat. 38(1967), 410-414] on the asymptotic normality of the Stirling numbers of the second kind translates into asymptotic normality of rooted semilabeled trees with given number of vertices, when the number of internal vertices varies. The Erdos-Szekely bijection specializes to a bijection between phylogenetic trees and set partitions with classes of size \\geq 2. We consider modified Stirling numbers of the second kind that enumerate partitions of a fixed set into a given number of classes of size \\geq 2, and obtain their asymptotic normality as the number of classes varies. The Erdos- Szekely bijection translates this result into the asymptotic normality of the number of phylogenetic trees with given number of vertices, when the number of leaves varies. We also obtain asymptotic normality of the number of phylogenetic trees with given number...
Uniform Asymptotic Normality of the Matrix-variate Beta-distribution
Institute of Scientific and Technical Information of China (English)
Kai Can LI; He TANG
2012-01-01
With the upper bound of Kullback-Leibler distance between a matrix variate Beta-distribution and a normal distribution,this paper gives the conditions under which a matrix-variate Betadistribution will approach uniformly and asymptotically a normal distribution.
Asymptotics of Bonferroni for Dependent Normal Test Statistics.
Proschan, Michael A; Shaw, Pamela A
2011-07-01
The Bonferroni adjustment is sometimes used to control the familywise error rate (FWE) when the number of comparisons is huge. In genome wide association studies, researchers compare cases to controls with respect to thousands of single nucleotide polymorphisms. It has been claimed that the Bonferroni adjustment is only slightly conservative if the comparisons are nearly independent. We show that the veracity of this claim depends on how one defines "nearly." Specifically, if the test statistics' pairwise correlations converge to 0 as the number of tests tend to ∞, the conservatism of the Bonferroni procedure depends on their rate of convergence. The type I error rate of Bonferroni can tend to 0 or 1 - exp(-α) ≈ α, depending on that rate. We show using elementary probability theory what happens to the distribution of the number of errors when using Bonferroni, as the number of dependent normal test statistics gets large. We also use the limiting behavior of Bonferroni to shed light on properties of other commonly used test statistics.
An asymptotically normal G-estimate for the Anderson-Fisher discriminant function
Energy Technology Data Exchange (ETDEWEB)
Girko, V.L.; Pavlenko, T.V. [Kiev State Univ. (Ukraine)
1994-06-05
Conditions under which a G-estimate of the Anderson-Fisher discriminant function is asymptotically normal are investigated. This estimate decreases by an order of magnitude the quantity of observations needed for a given level of accuracy on the part of an estimate and is thus of significant interest for practical applications. 3 refs.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model
Institute of Scientific and Technical Information of China (English)
Yuan YUAN; Andrew J.MAJDA
2011-01-01
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Recently, techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. The probability distribution functions (PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models. Asymptotic Gaussian lower bounds are also established under suitable hypotheses.
Coefficient of restitution of sports balls: A normal drop test
International Nuclear Information System (INIS)
Dynamic behaviour of bodies during impact is investigated through impact experiment, the simplest being a normal drop test. Normally, a drop test impact experiment involves measurement of kinematic data; this includes measurement of incident and rebound velocity in order to calculate a coefficient of restitution (COR). A high speed video camera is employed for measuring the kinematic data where speed is calculated from displacement of the bodies. Alternatively, sensors can be employed to measure speeds, especially for a normal impact where there is no spin of the bodies. This paper compares experimental coefficients of restitution (COR) for various sports balls, namely golf, table tennis, hockey and cricket. The energy loss in term of measured COR and effects of target plate are discussed in relation to the material and construction of these sports balls.
Directory of Open Access Journals (Sweden)
Yang Zu
2015-07-01
Full Text Available This paper studies the asymptotic normality for the kernel deconvolution estimator when the noise distribution is logarithmic chi-square; both identical and independently distributed observations and strong mixing observations are considered. The dependent case of the result is applied to obtain the pointwise asymptotic distribution of the deconvolution volatility density estimator in discrete-time stochastic volatility models.
Local asymptotic normality in {\\delta}-neighborhoods of standard generalized Pareto processes
Aulbach, Stefan
2011-01-01
De Haan and Pereira (2006) provided models for spatial extremes in the case of stationarity, which depend on just one parameter {\\beta} > 0 measuring tail dependence, and they proposed different estimators for this parameter. This framework was supplemented in Falk (2011) by establishing local asymptotic normality (LAN) of a corresponding point process of exceedances above a high multivariate threshold, yielding in particular asymptotic efficient estimators. The estimators investigated in these papers are based on a finite set of points t1,...,td, at which observations are taken. We generalize this approach in the context of functional extreme value theory (EVT). This more general framework allows estimation over some spatial parameter space, i.e., the finite set of points t1,...,td is replaced by t in [a,b]. In particular, we derive efficient estimators of {\\beta} based on those processes in a sample of iid processes in C[0,1] which exceed a given threshold function.
Bitencourt, Ana Carla P; Littlejohn, Robert G; Anderson, Roger; Aquilanti, Vincenzo
2014-01-01
The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.
Maximal admissible faces and asymptotic bounds for the normal surface solution space
Burton, Benjamin A
2010-01-01
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system. To achieve these results we examine the layout of admissible points within these polytopes. We show that these points correspond to well-behaved substructures of the face lattice, and we study properties of the corresponding "admissible faces". Key lemmata include upper bounds on the number of maximal admissible faces of each dimension, and a bijection between the maximal admissible faces in the two coordinate systems mentioned above.
Yuan, Ke-Hai; Guarnaccia, Charles A.; Hayslip, Bert, Jr.
2003-01-01
Studied the sample coefficient alpha for each of the five subscales of the Hopkins Symptom Checklist (HSL; L. Derogaitis and others, 1974) in a sample of 419 adults. Findings show that the normal-theory-based distribution has a systematic bias in describing the behavior of the sample coefficient alpha. (SLD)
Asymptotic behavior of a delay predator-prey system with stage structure and variable coefficients
Directory of Open Access Journals (Sweden)
Javier A. Hernandez-Pinzon
2008-10-01
Full Text Available In this paper, we establish a global attractor for a Lotka-Volterra type reaction-diffusion predator-prey model with stage structure for the predator, delay due to maturity and variable coefficients. This attractor is found by the method of upper and lower solutions and is given in terms of bounds for the coefficients.
A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index
Directory of Open Access Journals (Sweden)
Jose Olmo
2015-08-01
Full Text Available The extremal index (θ is the key parameter for extending extreme value theory results from i.i.d. to stationary sequences. One important property of this parameter is that its inverse determines the degree of clustering in the extremes. This article introduces a novel interpretation of the extremal index as a limiting probability characterized by two Poisson processes and a simple family of estimators derived from this new characterization. Unlike most estimators for θ in the literature, this estimator is consistent, asymptotically normal and very stable across partitions of the sample. Further, we show in an extensive simulation study that this estimator outperforms in finite samples the logs, blocks and runs estimation methods. Finally, we apply this new estimator to test for clustering of extremes in monthly time series of unemployment growth and inflation rates and conclude that runs of large unemployment rates are more prolonged than periods of high inflation.
An Asymptotic Normal Procedure With Censorship%终检渐近正态法
Institute of Scientific and Technical Information of China (English)
赵长华; 杨兵
2015-01-01
目的：：基于经典渐近正态法，提出一种用于两生存率检验所需样本量的测定的终检渐近正态法。方法：该方法是终检样本的实际样本量随终检概率和时间衰减形成的有效样本量。结果：它具有还原性，摆脱了指数分布的假设，与两生存率检验相匹配；其观测功效和预定功效吻合；相比之下，终检非中心法略显保守， Lachin-Foulkes法对于生存率检验显得功效不足。结论：这种方法适于慢性病临床研究，以检出早、中、晚期疗效差别。%Objective An asymptotic normal procedure with censorship is proposed for determining the sample size required in the test on two survival rates. Methods The procedure is derived from its classical counterpart on the basis of that the real size of censored samples declines with the censoring probability and the time. Results It is re-ducible, free from the assumption of exponential distributions, and matched with the test on two survival rates. The observed power coincides with the prescribed power. By contrast, the non -central procedure with censorship is slightly conservative and the Lachin-Foulkes procedure has the power usually not adequate for the test on two sur-vival rates. Conclusion The procedure is appropriate with planning clinical studies of chronic diseases for detecting early, middle, or late treatment-control difference.
Estimator and tests for common coefficients of variation in normal distributions
Forkman, Johannes
2009-01-01
Inference for the coefficient of variation in normal distributions is considered. An explicit estimator of a coefficient of variation that is shared by several populations with normal distributions is proposed. Methods for making confidence intervals and statistical tests, based on McKay's approximation for the coefficient of variation, are provided. Exact expressions for the first two moments of McKay's approximation are given. An approximate F-test for equality of a coefficient of variation...
Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun
2014-12-01
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The generalized linear model(GLM) based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator(MLE) ^βn are proved.
Institute of Scientific and Technical Information of China (English)
王德辉
2007-01-01
This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1) coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement,even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximatioh of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.
Asymptotic normality of the size of the giant component via a random walk
Bollobas, Bela
2010-01-01
In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of $G(n,p)$ above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp's exploration process, obtaining a simple proof of a weak form of this result. Here we use slightly different martingale arguments to obtain the full result of Pittel and Wormald with little extra work.
Fujikoshi, Yasunori; Shimizu, Ryoichi
1989-01-01
This paper deals with the distribution of $\\mathbf{X} = \\sum^{1/2}\\mathbf{Z}$, where $\\mathbf{Z}: p \\times 1$ is distributed as $N_p(0, I_p), \\sum$ is a positive definite random matrix and $\\mathbf{Z}$ and $\\sum$ are independent. Assuming that $\\sum = I_p + BB'$, we obtain an asymptotic expansion of the distribution function of $\\mathbf{X}$ and its error bound, which is useful in the situation where $\\sum$ tends to $I_p$. A stronger version of the expansion is also given. The results are appl...
Energy Technology Data Exchange (ETDEWEB)
Gurdal, G.; Beausang, C. W.; Brenner, D. S.; Ai, H.; Casten, R. F.; Crider, B.; Heinz, A.; Williams, E.; Hartley, D. J.; Carpenter, M. P.; Hecht, A. A.; Janssens, R. V. F.; Lauritsen, T.; Lister, C. J.; Raabe, R.; Seweryniak, D.; Zhu, S.; Saladin, J. X.; Physics; Yale Univ.; Clark Univ.; Univ. of Richmond; United States Naval Academy; Univ. of Maryland; Univ. of Pittsburgh
2008-01-01
Internal conversion coefficients have been measured for transitions in both normal deformed and triaxial strongly deformed bands in {sup 167}Lu using the Gammasphere and ICE Ball spectrometers. The results for all in-band transitions are consistent with E2 multipolarity. Upper limits are determined for the internal conversion coefficients for linking transitions between TSD Band 2 and TSD Band 1, the n{sub w} = 1 and n{sub w} = 0 wobbling bands, respectively.
Institute of Scientific and Technical Information of China (English)
SONG Weixing; CHENG Ping
2002-01-01
In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.
Institute of Scientific and Technical Information of China (English)
SONGWeixing; CHENGPing
2002-01-01
In the distribution family with common support and the one side truncated distribution family,Bickle,I.A.Ibragimov and R.Z.Hasminskii proved two important convolution theorems.As to the two-side truncated case,we also proved a convolution theorem,which plays an extraordinary role in the efficency theory.In this paper,we will study another kind of two-side truncated distribution family,and prove a convolution result with normal form.On the basis of this convolution result,a new kind of efficiency concept is given;meanwhile,we will show that MLE is an efficient estimate in this distribution family.
On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Künsch, Hans R.
1994-01-01
We consider point processes defined through a pairwise interaction potential and admitting a two-dimensional sufficient statistic. It is shown that the pseudo maximum likelihood estimate can be stochastically normed so that the limiting distribution is a standard normal distribution. This result...... is true irrespectively of the possible existence of phase transitions. The work here is an extension of the work Guyon and Künsch (1992, Lecture Notes in Statist., 74, Springer, New York) and is based on viewing a point process interchangeably as a lattice field. © 1994 The Institute of Statistical...
Calculation of Coefficients of Simplest Normal Forms of Hopf and Generalized Hopf Bifurcations
Institute of Scientific and Technical Information of China (English)
TIAN Ruilan; ZHANG Qichang; HE Xuejun
2007-01-01
The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling and an inner product were introduced in the space of homogeneous poiynomials. Theorems were established for the explicit expression of the simplest normal forms in terms of the coefficients of both the conventional normal forms of Hopf and generalized Hopf bifurcation systems. A symbolic manipulation was designed to perform the calculation of the coefficients of the simplest normal forms using Mathematica. The original ordinary differential equation was required in the input and the simplest normal form could be obtained as the output. Finally, the simplest normal forms of 6-dimensional generalized Hopf singularity of type 2 and 5-dimensional Hopf bifurcation system were discussed by executing the program. The output showed that the 5th- and 9th-order terms remained in 6-dimensional generalized Hopf singularity of type 2 and the 3rd- and 5th-order terms remained in 5-dimensional Hopf bifurcation system.
Institute of Scientific and Technical Information of China (English)
Jinhong YOU; CHEN Min; Gemai CHEN
2004-01-01
Consider a semiparametric regression model with linear time series errors Yκ = x′κβ + g(tκ) + εκ,1 ≤ k ≤ n, where Yκ's are responses, xκ= (xκ1,xκ2,…,xκp)′and tκ ∈ T( ) R are fixed design points, β = (β1,β2,…… ,βp)′ is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εκ is a linear process given by εκ = ∑∞j=0 ψjeκ-j, ψ0 = 1, where ∑∞j=0 |ψj| ＜∞, and ej, j = 0,±1,±2,…, are I.I.d, random variables. In this paper we establish the asymptotic normality of the least squares estimator ofβ, a smooth estimator of g(·), and estimators of the autocovariance and autocorrelation functions of the linear process εκ.
Directory of Open Access Journals (Sweden)
Wararit Panichkitkosolkul
2013-01-01
Full Text Available This paper presents three confidence intervals for the coefficient of variation in a normal distribution with a known population mean. One of the proposed confidence intervals is based on the normal approximation. The other proposed confidence intervals are the shortest-length confidence interval and the equal-tailed confidence interval. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. Simulation results have shown that all three proposed confidence intervals perform well in terms of coverage probability and expected length.
Energy Technology Data Exchange (ETDEWEB)
Naganawa, Shinji; Sato, Chiho; Ishigaki, Takeo [Nagoya University School of Medicine, Department of Radiology, Nagoya (Japan); Kumada, Hisashi; Miura, Shunichi [Toyohashi Municipal hospital, Department of Radiology, Toyohashi, Aich (Japan); Takizawa, Osamu [Siemens-Asahi Medical Technologies Ltd, Tokyo (Japan)
2005-01-01
A relation between apparent diffusion coefficient (ADC) values and tumor cellular density has been reported. The purpose of this study was to measure the ADC values of cervical cancers in the uterus and compare them with those of normal cervical tissues, and to test whether ADC could differentiate between normal and malignant cervical tissues in the uterus. Twelve consecutive female patients with cervical cancer of the uterus and ten female patients with other pelvic abnormalities were included in this study. ADC was measured at 1.5 T with b-factors of 0, 300 and 600 s/mm{sup 2} using single-shot echo-planar diffusion-weighted imaging and a parallel imaging technique. The mean ADC value of cervical cancer lesions was 1.09{+-}0.20 x 10{sup -3} mm{sup 2}/s, and that of normal cervix tissue was 1.79{+-}0.24 x 10{sup -3} mm{sup 2}/s (P<0.0001). In nine patients treated by chemotherapy and/or radiation therapy, the mean ADC value of the cervical cancer lesion increased significantly after therapy (P<0.001). The present study showed, with a small number of patients, that ADC measurement has a potential ability to differentiate between normal and cancerous tissue in the uterine cervix. Further study is necessary to determine the accuracy of ADC measurement in monitoring the treatment response. (orig.)
Apparent diffusion coefficient values of normal testis and variations with age
Directory of Open Access Journals (Sweden)
Athina C Tsili
2014-06-01
Full Text Available The usefulness of diffusion-weighted magnetic resonance imaging (DWI in the evaluation of scrotal pathology has recently been reported. A standard reference of normal testicular apparent diffusion coefficient (ADC values and their variations with age is necessary when interpreting normal testicular anatomy and pathology. We evaluated 147 normal testes using DWI, including 71 testes from 53 men aged 20-39 years (group 1, 67 testes from 42 men aged 40-69 years (group 2 and nine testes from six men older than 70 years (group 3. DWI was performed along the axial plane, using a single shot, multislice spin-echo planar diffusion pulse sequence and b-values of 0 and 900 s mm−2 . The mean and standard deviation of the ADC values of normal testicular parenchyma were calculated for each age group separately. Analysis of variance (ANOVA followed by post hoc analysis (Dunnett T3 was used for statistical purposes. The ADC values (× 10−3 mm 2 s−1 of normal testicular tissue were different among age groups (group 1: 1.08 ± 0.13; group 2: 1.15 ± 0.15 and group 3: 1.31 ± 0.22. ANOVA revealed differences in mean ADC among age groups (F = 11.391, P < 0.001. Post hoc analysis showed differences between groups 1 and 2 (P = 0.008 and between groups 1 and 3 (P = 0.043, but not between groups 2 and 3 (P = 0.197. Our findings suggest that ADC values of normal testicular tissue increase with advancing age.
International Nuclear Information System (INIS)
We compute the 3-loop fermion-loop corrections to the asymptotic heavy flavor Wilson coefficients of the structure function F2(x,Q2) and of Transversity in the asymptotic region Q2 >>m2∝Ci Nf TF2 and first contributions ∝Ci TF2, with i=F,A. The computation is based on a factorization theorem of the massive Wilson coefficients into massive operator matrix elements and the massless Wilson coefficients. Our method is based on direct integration, avoiding the integration-by-parts technique, which is advantageous due to the compactness of the intermediate and final results. We also obtain the corresponding contributions to the 3-loop anomalous dimensions and confirm results in the literature.
Abou, B; Wesfreid, J E; Abou, Berengere; Surgy, Gilles Neron de; Wesfreid, Jose-Eduardo
1997-01-01
We have calculated the general dispersion relationship for surface waves on a ferrofluid layer of any thickness and viscosity, under the influence of a uniform vertical magnetic field. The amplification of these waves can induce an instability called peaks instability (Rosensweig instability). The expression of the dispersion relationship requires that the critical magnetic field and the critical wavenumber of the instability depend on the thickness of the ferrofluid layer. The dispersion relationship has been simplified into four asymptotic regimes: thick or thin layer and viscous or inertial behaviour. The corresponding critical values are presented. We show that a typical parameter of the ferrofluid enables one to know in which regime, viscous or inertial, the ferrofluid will be near the onset of instability.
Directory of Open Access Journals (Sweden)
Phillip Burgers
Full Text Available For a century, researchers have used the standard lift coefficient C(L to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S, compared against the total kinetic energy required for generating said lift, ½v(2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.
Skákala, Jozef
2012-01-01
We analyze the largely accepted formulas for the asymptotic quasi-normal frequencies of the non-extremal Reissner-Nordström black hole, (for the electromagnetic-gravitational/scalar perturbations). We focus on the question of whether the gap in the spacing in the imaginary part of the QNM frequencies has a well defined limit as n goes to infinity and if so, what is the value of the limit. The existence and the value of this limit has a crucial importance from the point of view of the currently popular Maggiore's conjecture, which represents a way of connecting the asymptotic behavior of the quasi-normal frequencies to the black hole thermodynamics. With the help of previous results and insights we will prove that the gap in the imaginary part of the frequencies does not converge to any limit, unless one puts specific constraints on the ratio of the two surface gravities related to the two spacetime horizons. Specifically the constraints are that the ratio of the surface gravities must be rational and such that it is given by two relatively prime integers n ± whose product is an even number. If the constraints are fulfilled the limit of the sequence is still not guaranteed to exist, but if it exists its value is given as the lowest common multiplier of the two surface gravities. At the end of the paper we discuss the possible implications of our results.
Directory of Open Access Journals (Sweden)
Aditya Kumar
2013-01-01
Full Text Available The influence of applied normal load and roughness on the tribological behavior between the indenter and sample surface during nanoindentation-based scratching has been experimentally investigated by using different surfaces (fused silica and diamond-like carbon featuring various degrees of roughness. At a sufficiently low applied normal load, wherein the contact is elastic, the friction coefficient is constant. However, at increased normal loads the contact involves plastic deformation and the friction coefficient increases with increasing normal load. The critical load range for a transition from predominantly elastic to plastic contact, between the indenter and sample surface, increases with increasing size of indenter and decreases with roughness. Distinct differences between the present experimental results and the existing theoretical models/predictions are discussed.
Asymptotics of bivariate generating functions with algebraic singularities
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
DEFF Research Database (Denmark)
Franco, Antonio; Trapp, Stefan
2008-01-01
The sorption of organic electrolytes to soil was investigated. A dataset consisting of 164 electrolytes, composed of 93 acids, 65 bases, and six amphoters, was collected from literature and databases. The partition coefficient log KOW of the neutral molecule and the dissociation constant pKa were...
On Asymptotically Orthonormal Sequences
Fricain, Emmanuel; Rupam, Rishika
2016-01-01
An asymptotically orthonormal sequence is a sequence which is 'nearly' orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized reproducing kernels of model spaces and de Branges Rovnyak spaces.
Werner, Charles L.; Wegmueller, Urs; Small, David L.; Rosen, Paul A.
1994-01-01
Terrain slopes, which can be measured with Synthetic Aperture Radar (SAR) interferometry either from a height map or from the interferometric phase gradient, were used to calculate the local incidence angle and the correct pixel area. Both are required for correct thematic interpretation of SAR data. The interferometric correlation depends on the pixel area projected on a plane perpendicular to the look vector and requires correction for slope effects. Methods for normalization of the backscatter and interferometric correlation for ERS-1 SAR are presented.
Directory of Open Access Journals (Sweden)
Ömer Kavaklıoğlu
2011-01-01
Full Text Available We have presented a derivation of the asymptotic equations for transverse magnetic multiple scattering coefficients of an infinite grating of penetrable circular cylinders for obliquely incident plane electromagnetic waves. We have first deducted an “Ansatz” delineating the asymptotic behavior of the transverse magnetic multiple scattering coefficients associated with the most generalized condition of oblique incidence (Kavaklıoğlu, 2000 by exploiting Schlömilch series corresponding to the special circumstance that the grating spacing is much smaller than the wavelength of the incident electromagnetic radiation. The validity of the asymptotic equations for the aforementioned scattering coefficients has been verified by collating them with the Twersky's asymptotic equations at normal incidence. Besides, we have deduced the consequences that the asymptotic forms of the equations at oblique incidence acquired in this paper reduce to Twersky's asymptotic forms at normal incidence by expanding the generalized scattering coefficients at oblique incidence into an asymptotic series as a function of the ratio of the cylinder radius to the grating spacing.
Powell, Douglas A; Anderson, Lucy M; Cheng, Robert Y S; Alvord, W Gregory
2002-10-01
Chen, Dougherty, and Bittner [Y. Chen, E. R. Dougherty, and M. L. Bittner, J. Biomed. Opt. 2(4), 364-374 (1997)] provided the derivation of a probability density function (PDF) for a signal ratio from a DNA microarray. This PDF is potentially useful for testing whether a pair of signals from the same gene has a common mean. The derivation of the PDF assumes the normality of all signal distributions and a common coefficient of variation (CV) for all signals within a microarray. The testing procedure requires the calculation of a common confidence interval for a microarray, based on a maximum likelihood estimator of the "common" CV, and the determination of whether or not a ratio for a particular gene falls within this interval. This study used Monte Carlo techniques and demonstrated that the procedure is robust to violations of normality and also to constancy in the coefficients of variation. A closer examination of the dynamics of the procedure found that the robustness was the result of offsetting effects. The size of the confidence interval was increased as a result of higher estimates of the common CV, as the actual CV pattern became heterogeneous. This effect mitigated the inflation in the size of the ratio as a result of increasing CV heterogeneity. These findings suggest that the Chen-Dougherty-Bittner procedure may be used even if underlying assumptions do not hold.
Dettmann, Carl P.
2002-01-01
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the...
Baron, Paul; Dorrius, Monique D.; Kappert, Peter; Oudkerk, Matthijs; Sijens, Paul E.
2010-01-01
The influence of microperfusion and fat suppression technique on the apparent diffusion coefficient (ADC) values obtained with diffusion weighted imaging (DWI) of normal fibroglandular breast tissue was investigated. Seven volunteers (14 breasts) were scanned using diffusion weighting factors (b val
Doughty, M J; Fonn, D; Trang Nguyen, K
1993-09-01
In endothelial morphometry, uncertainty exists concerning how many cells should be measured. A study was undertaken to calculate mean cell area and coefficient of variation (COV) of cell areas using different numbers of cells from photo-slitlamp pictures and published micrographs. Groups of 65, 95, or 165 tesselated cells were measured and area and COV values calculated in progressive sets of 5 cells; each pair of values was compared to that obtained using all cells in each group. The results show that, for both normal (homomegethous) and irregular (polymegethous) endothelia, even cell counts as low as 50 cells can usually provide average cell area values that are within 1 to 2% of the values estimated from larger groups of cells. A similar reliability was observed for estimates of COV for normal endothelia. However, for polymegethous endothelia, even with 100 cells analyzed, the estimates of COV generally only approached a +/- 4% reliability. This uncertainty in COV estimates should be considered in both comparative studies and in regression analyses of COV changes over time or other variables.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean and...
Studies on Partition Coefficient and its Normalization%划分系数与归一化型的比较研究
Institute of Scientific and Technical Information of China (English)
吴成茂; 李彦; 范九伦
2001-01-01
对J.C.Bezdek提出的划分系数，基于样本最大分类信息的改进划分系数，以及二者的归一化形式的分类性能进行了实验分析，结果表明，归一化处理的分类性能有明显提高。%In this paper,classification performances of J.C.Bezdek's partition coefficient,improved partition coefficient based on maximum classification information and two kinds of normalized partition coefficients are experimented and analyzed ,the conclusion shows that classification performance of two kinds of normalized partition coefficient is improved markedly.
International Nuclear Information System (INIS)
Highlights: → Some concrete were determined photon radiation absorbent for 0.663 keV. → It was concluded that barite was effective. → As known, colemanite was good absorbent to prevent for neutron transmission. → As a neutron absorbent, colemanite would be preferred to normal aggregate. - Abstract: Accurate measurements have been made to determine radiation transmission of concretes produced with barite, colemanite and normal aggregate by using beam transmission method for 0.663 MeV γ-rays energy of 137Cs radioactive isotopes by using NaI(Tl) scintillation detector. Linear and mass attenuation coefficients of thirteen heavy- and four normal-weight concretes were calculated. It was determined that the linear attenuation coefficient (μ, cm-1) decreased with colemanite concentration and increased with barite concentration in both type of the concretes. Mass attenuation coefficient values of our concretes were compared with the values proposed by the United States National Institute of Standards and Technology (NIST).
Confidence Intervals for the Coefficient of Variation for the Normal Distribution%正态分布变差系数的置信区间
Institute of Scientific and Technical Information of China (English)
孙祝岭
2009-01-01
A problem of the estimation of the coefficient of variation for the normal distribution was discussed. A new pivotal variable to construct the classical confidence intervals for the coefficient of variation was given. And precision confidence intervals for the coefficient of variation of the normal distribution with a simple expression were also obtained.%研究正态分布的变差系数估计问题.提出了一个新的枢轴量来构造变差系数的经典置信区间,给出了正态分布变差系数的具有简单表达式的精确置信区间.
Efficient Quantile Estimation for Functional-Coefficient Partially Linear Regression Models
Institute of Scientific and Technical Information of China (English)
Zhangong ZHOU; Rong JIANG; Weimin QIAN
2011-01-01
The quantile estimation methods are proposed for functional-coefficient partially linear regression (FCPLR) model by combining nonparametric and functional-coefficient regression (FCR) model.The local linear scheme and the integrated method are used to obtain local quantile estimators of all unknown functions in the FCPLR model.These resulting estimators are asymptotically normal,but each of them has big variance.To reduce variances of these quantile estimators,the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions,and their asymptotic normalities are derived.Two simulated examples are carried out to illustrate the proposed estimation methodology.
EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES
Institute of Scientific and Technical Information of China (English)
Zhang Riquan; Li Guoying
2008-01-01
In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different co-efficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.
Institute of Scientific and Technical Information of China (English)
孙婷; 凌能祥
2015-01-01
In this paper ,the asymptotic property of modified kernel regression estimation for functional stationary ergodic data is researched w hen the explanatory variable X has functional characteristic and the response variable Y is a scalar in real‐value space R .Specifically ,the modified kernel estimation of the regression function r(x) is constructed by using the classic Nadaraya‐Watson estimator .Under certain conditions ,the asymptotic normality of modified kernel regression estimation for functional stationary ergodic data is established by applying the martingale difference central limit theorem , which extends the α‐mixing data to the functional stationary ergodic data .%文章基于解释变量 X具有函数特征而响应变量Y 取值于实数空间R的条件下，研究了基于平稳遍历函数型数据改良核回归估计的渐近性质。利用经典的N‐W核估计的方法构造了回归函数 r（x）的改良核估计，在一定的条件下，应用鞅差中心极限定理建立了基于平稳遍历函数型数据改良核回归估计的渐近正态性，从而推广了现有文献中的相关结果。
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Institute of Scientific and Technical Information of China (English)
陈桂景; Sa,AKME
2000-01-01
This paper presents the large properties of‘regression quantiles' in linear models, establishing the strong consistency and asymptotic normality in similar form,modifying and extending the results about minimum l1 - norm estimates in linear models obtained by Chen, X.R., et al. (1990,1992).The results in this paper improve the corresponding results obtained by Koenker & Bassett(1978),Gutenburnner & Jure cková(1992),Jure cková & Prochazka(1994),and so on.%论证了线性模型中回归分位点估计量的强相合性及渐近正态性等大样本性质，这些结果推广了陈希孺等(1990，1992)的有关定理，改进了Koenker与Basstee(1978)，Gutenburnner与Jureckova(1992)，以及Jureckovo与Prochazka(1994)等人的有关成果。
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Wang, Bo; Goodpaster, Aaron M; Kennedy, Michael A
2013-10-15
A primary goal of metabonomics research is biomarker discovery for human diseases based on differences in metabolic profiles between healthy and diseased patient populations. One of the most significant challenges in biomarker discovery is validation, which implicitly depends on the coefficient of variation (CV) associated with the measurement technique. This paper investigates how the CV of metabolite resonances measured by nuclear magnetic resonance spectroscopy (NMR) depends on signal-to-noise ratio (SNR) and normalization method. CVs were calculated for NMR resonance peaks in a series of NMR spectra of five synthetic urine samples collected over an eight-month period. An inverse correlation was detected between SNR and CV for all normalization methods. Small peaks with SNR150, which typically had smaller CVs (5-10%). The inverse relationship between CV and SNR roughly obeyed a log10 dependence. Quotient normalization (QN) tended to produce smaller CVs for smaller peaks, but larger CVs for the strongest peaks in the data, compared to no normalization, normalization to total intensity (NTI) or normalization to an internal standard (NIS). Consequently, quotient normalization appears optimal for validating low concentration metabolites. NTI or NIS appear superior to QN for samples that have very small variation in total signal intensity. While the inverse relationship between CV and log10(SNR) did not strictly hold for all metabolites, weaker concentration metabolites will likely require more rigorous validation as potential biomarkers since they tend to have poorer reproducibility.
Comparison of Spearman's rho and Kendall's tau in Normal and Contaminated Normal Models
Xu, Weichao; Hung, Y S; Zou, Yuexian
2010-01-01
This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact analytical formulae of the variance of SR and the covariance between SR and KT are obtained based on the Childs's reduction formula for the quadrivariate normal positive orthant probabilities. Close form expressions with respect to the expectations of SR and KT are established under the bivariate contaminated normal models. The bias, mean square error (MSE) and asymptotic relative efficiency (ARE) of the three estimators based on SR and KT to the Pearson's product moment correlation coefficient (PPMCC) are investigated in both the normal and contaminated normal models. Theoretical and simulation results suggest that, contrary to the opinion of equivalence between SR and KT in some literature, the behaviors of SR and KT are strikingly different in the aspects of bias effect, variance, mean square error, and asymptotic...
Kobryn, A E; Tokarchuk, M V
1999-01-01
An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilibrium statistical operator. On the basis of this equation the normal solutions and transport coefficients such as bulk kappa and shear eta viscosities, thermal conductivity lambda, mutual diffusion D^{\\alpha\\beta} and thermal diffusion D_T^\\alpha have been obtained for a binary mixture in the first approximation using the Chapman-Enskog method. Numerical calculations of all transport coefficients for mixtures Ar-Kr, Ar-Xe, Kr-Xe with different concentrations of compounds have been evaluated for the cases of absence and presence of long-range Coulomb interactions. The results are compared with those obtained from other theories and experiment.
Asymptotic Solutions of Serial Radial Fuel Shuffling
Directory of Open Access Journals (Sweden)
Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
Energy Technology Data Exchange (ETDEWEB)
Fornasa, Francesca; Montemezzi, Stefania [Dept. of Radiology, San Bonifacio Hospital, Verona (Italy)], e-mail: francescafornasa@libero.it
2012-06-15
Background: Diffusion-weighted magnetic resonance imaging (DWI) is increasingly used in the diagnosis of endometrial disease. No complete knowledge, however, exists yet of the influence of physiology on the endometrial apparent diffusion coefficient (ADC) values on which DWI is based. Purpose: To establish whether the ADC values measured with DWI in the endometrium of healthy reproductive-aged women significantly vary from the early proliferative to the periovulatory phase of the menstrual cycle and between the fundus and the isthmus of the uterus. Material and Methods: In 17 women the endometrial ADC values measured on the fifth menstrual day, both at the fundus and at the isthmus of the uterus, were compared to the values obtained on the 14th day before the subsequent cycle. In 81 women (menstrual day: fifth through 21st) the endometrial ADC values measured at the fundus were compared to the values obtained at the isthmus of the uterus. All examinations were performed with a 1.5 T magnet (b values: 0 and 800 mm/s{sup 2}). The results were analyzed by means of Student's t-test per paired data. Results: The endometrial ADC values measured on the fifth day of the menstrual cycle were lower than those obtained in the periovulatory phase both at the fundus (mean 0.923 vs. 1.256 x 10{sup -}3 mm{sup 2}/s) and at the isthmus (mean 1.297 vs. 1.529 x 10{sup -}3 mm{sup 2}/s) of the uterus. The endometrial ADC values measured at the fundus of the uterus were lower than those obtained at the isthmus (mean 1.132 vs. 1.420 x 10{sup -}3 mm{sup 2}/s) through the menstrual cycle. All these differences were highly significant (P < 0.001) at statistical analysis. Conclusion: Physiological variations occurring in endometrial ADC values of healthy women should be considered by the radiologists when interpreting DWI examinations in patients with endometrial disease.
Liapunov structure and asymptotic expressions of linear differential systems
Institute of Scientific and Technical Information of China (English)
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
Institute of Scientific and Technical Information of China (English)
李成好; 汪超; 凌能祥
2012-01-01
文章研究了基于平稳α-混合左删失数据下密度函数一阶、二阶导数的核估计及众数核估计,在一定的条件下获得了导数核估计量的强一致收敛性、收敛速度及众数核估计量的渐近正态性；同时给出了众数估计的置信区间,最后,通过数据模拟显示了主要结论的合理性.%The kernel estimator of the first and second derivative of density function and the kernel mode estimators under left-truncated and stationary a-mixing sequence are studied. The strong uniform convergence and convergence rate of kernel estimator of the first and second derivative of density function are got, and the asymptotic normality of the kernel mode estimators under left-truncated and stationary a-mixing sequence is also obtained under certain conditions. Then the confidence interval of the mode estimator is presented. The numerical simulation demonstrates the rationality of the main conclusions in this paper.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
Asymptotic normality of randomly truncated stochastic algorithms
Lelong, Jérôme
2010-01-01
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
Asymptotic Fitness Distribution in the Bak-Sneppen Model of Biological Evolution with Four Species
Schlemm, Eckhard
2012-08-01
We suggest a new method to compute the asymptotic fitness distribution in the Bak-Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.
Asymptotic fitness distribution in the Bak-Sneppen model of biological evolution with four species
Schlemm, Eckhard
2012-01-01
We suggest a new method to compute the asymptotic fitness distribution in the Bak-Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.
Asymptotic Theory of Cepstral Random Fields
McElroy, Tucker S
2011-01-01
Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. Given the importance of this topic, there has been substantial research devoted to this area. However, in spite of the tremendous research to date, outside the engineering literature, the cepstral random field model remains largely underdeveloped. We provide a comprehensive treatment of the asymptotic theory for cepstral random field models. In particular, we provide recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the necessary autocovariance matrix. Additionally, we establish asymptotic consistency results for Bayesian, maximum likelihood, and quasi-maximum likelihood estimation. Further, in both the maximum and quasi-maximum likelihood frameworks we derive the asymptotic distribution of our estimator. The theoretical results are presented gen...
Quasi-extended asymptotic functions
International Nuclear Information System (INIS)
The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example
On the Asymptotic Accuracy of Efron's Bootstrap
Singh, Kesar
1981-01-01
In the non-lattice case it is shown that the bootstrap approximation of the distribution of the standardized sample mean is asymptotically more accurate than approximation by the limiting normal distribution. The exact convergence rate of the bootstrap approximation of the distributions of sample quantiles is obtained. A few other convergence rates regarding the bootstrap method are also studied.
On the Asymptotic Distribution of Signal Fraction
Volobouev, Igor
2016-01-01
Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.
Zero bias transformation and asymptotic expansions
Jiao, Ying
2012-01-01
Let W be a sum of independent random variables. We apply the zero bias transformation to deduce recursive asymptotic expansions for $\\mathbb {E}[h(W)]$ in terms of normal expectations, or of Poisson expectations for integer-valued random variables. We also discuss the estimates of remaining errors.
Puschnigg, Michael
1996-01-01
The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.
Rayne, Sierra; Forest, Kaya
2009-11-01
Organic carbon-normalized soil and sediment-water partitioning coefficients (K(oc)) were estimated for all C(1) through C(8) perfluoroalkyl carboxylic (PFCA) and sulfonic (PFSA) acid congeners. The limited experimental K(oc) data set for the straight chain C(7) through C(10) PFCAs and C(8) and C(10) PFSAs was correlated to SPARC and ALOGPS computationally estimated octanol-water partitioning/distribution constants and used to predict K(oc) values for both branched and linear C(1) through C(8) isomers. Branched and linear congeners in this homologue range are generally expected to have K(oc) values > 1, leading to their accumulation in organic matter on sediments and soils, retardation during ground and pore water flow, and the preferential association with dissolved organic matter in aquatic systems. Both increasing perfluoroalkyl chain length and linearity increase K(oc) values with substantial intra- and inter-homologue variation and interhomologue mixing. Variability in K(oc) values among the PFCA and PFSA congeners will likely lead to an enrichment of more linear and longer-chain isomers in organic matter fractions, resulting in aqueous phases fractionated towards shorter-chain branched congeners. The expected magnitude of fractionation will require inclusion in source apportionment models and risk assessments. A comparison of representative established quantitative structure property relationships for estimating K(oc) values from octanol-water partitioning constants suggests that these equilibrium partitioning frameworks may be applicable towards modeling PFCA and PFSA environmental fate processes. PMID:20183495
Kondo, M; Hirano, T; Okamura, Y
1989-05-01
The purpose of this study was to determine if there is a change in autonomic nerve function during the menstrual cycle. The subjects were 20 females (average age 26.1 years +/- 4.6) with a normal menstrual cycle. The coefficient of variation of R-R intervals (CV R.R) was measured to investigate autonomic function in the menstrual, follicular, ovulatory, luteal, and premenstrual phases. Average CV R-R for all phases was 5.2 +/- 1.9%. And the CV R-R tended to be lower in those in their 30s than in those in their 20s. And no noticeable difference was seen in the CV R-R among the 5 phases of the menstrual cycle. On the other hand, the CV R-R of 11 females with premenstrual syndrome was low in the ovulatory, luteal and premenstrual phases. These results, which provide basic data for clinical use, suggest the following. (1) The age of subjects should be taken into consideration. (2) Changes in the CV R-R during the menstrual cycle are negligible. (3) However, in those showing symptoms associated with the menstrual cycle such as premenstrual syndrome, changes during the menstrual cycle should be taken into account. At the same time psychological changes in the subjects were evaluated by the following tests: Cornell Medical Index, Taylor's manifest anxiety scale, and Zung's self-rating depression scale. The results of these tests did not vary significantly during the menstrual cycle.
Jones, D S
1997-01-01
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy
tuoc, Trinh Khanh
2010-01-01
The Virk asymptote is shown to be similar in nature to the Karman buffer layer profile and does not represent a new log-law with a modified mixing-length. It is simply part of the wall layer velocity profile but is extended because of the increase in wall layer thickness in drag reduction flows. The friction factors at the maximum drag reduction asymptote correspond to velocity profiles consisting of a wall layer and a law of the wake sub-region. Maximum drag reduction results in the suppression of the law of the wake and full relaminarisation of the flow.
Guttmann, Anthony J.
2016-10-01
Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mechanics or enumerative combinatorics, we show that the method of differential approximants performs surprisingly well in predicting (approximately) subsequent coefficients. These can then be used by the ratio method to obtain improved estimates of critical parameters. In favourable cases, given only the first 20 coefficients, the next 100 coefficients are predicted with useful accuracy. More surprisingly, this is also the case when the method of differential approximants does not do a useful job in estimating the critical parameters, such as those cases in which one has stretched exponential asymptotic behaviour. Nevertheless, the coefficients are predicted with surprising accuracy. As one consequence, significant computer time can be saved in enumeration problems where several runs would normally be made, modulo different primes, and the coefficients constructed from their values modulo different primes. Another is in the checking of newly calculated coefficients. We believe that this concept of approximate series extension opens up a whole new chapter in the method of series analysis.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Andrić, Filip; Šegan, Sandra; Dramićanin, Aleksandra; Majstorović, Helena; Milojković-Opsenica, Dušanka
2016-08-01
Soil-water partition coefficient normalized to the organic carbon content (KOC) is one of the crucial properties influencing the fate of organic compounds in the environment. Chromatographic methods are well established alternative for direct sorption techniques used for KOC determination. The present work proposes reversed-phase thin-layer chromatography (RP-TLC) as a simpler, yet equally accurate method as officially recommended HPLC technique. Several TLC systems were studied including octadecyl-(RP18) and cyano-(CN) modified silica layers in combination with methanol-water and acetonitrile-water mixtures as mobile phases. In total 50 compounds of different molecular shape, size, and various ability to establish specific interactions were selected (phenols, beznodiazepines, triazine herbicides, and polyaromatic hydrocarbons). Calibration set of 29 compounds with known logKOC values determined by sorption experiments was used to build simple univariate calibrations, Principal Component Regression (PCR) and Partial Least Squares (PLS) models between logKOC and TLC retention parameters. Models exhibit good statistical performance, indicating that CN-layers contribute better to logKOC modeling than RP18-silica. The most promising TLC methods, officially recommended HPLC method, and four in silico estimation approaches have been compared by non-parametric Sum of Ranking Differences approach (SRD). The best estimations of logKOC values were achieved by simple univariate calibration of TLC retention data involving CN-silica layers and moderate content of methanol (40-50%v/v). They were ranked far well compared to the officially recommended HPLC method which was ranked in the middle. The worst estimates have been obtained from in silico computations based on octanol-water partition coefficient. Linear Solvation Energy Relationship study revealed that increased polarity of CN-layers over RP18 in combination with methanol-water mixtures is the key to better modeling of
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
Asymptotic distributions in the projection pursuit based canonical correlation analysis
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.
Optimistic Agents are Asymptotically Optimal
Sunehag, Peter; Hutter, Marcus
2012-01-01
We use optimism to introduce generic asymptotically optimal reinforcement learning agents. They achieve, with an arbitrary finite or compact class of environments, asymptotically optimal behavior. Furthermore, in the finite deterministic case we provide finite error bounds.
Institute of Scientific and Technical Information of China (English)
Tao Hu; Heng-jian Cui; Xing-wei Tong
2009-01-01
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a gen-eralization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estima-tor for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.
ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL
Institute of Scientific and Technical Information of China (English)
CUI Hengjian
2005-01-01
This paper addresses estimation and its asymptotics of mean transformation θ = E[h(X)] of a random variable X based on n iid. Observations from errors-in-variables model Y = X + v, where v is a measurement error with a known distribution and h(.) is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
Asymptotic Flatness in Rainbow Gravity
Hackett, Jonathan
2005-01-01
A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Institute of Scientific and Technical Information of China (English)
Xuemei HU; Feng LIU; Zhizhong WANG
2009-01-01
The authors propose a V_(N,P) test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V_(N,P) test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power.
Asymptotic admissibility of priors and elliptic differential equations
Hartigan, J A
2010-01-01
We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Asymptotic sampling distribution of inverse coeﬃcient of variation and its applications: revisited
Directory of Open Access Journals (Sweden)
Ahmed N. Albatineh
2013-12-01
Full Text Available Sharma and Krishna (1994 derived mathematically an appealing asymptotic confidence interval for the population signal-to-noise ratio (SNR. In this paper, an evaluation of the performance of this interval using monte carlo simulations using randomly generated data from normal, log-normal, $\\chi^2$, Gamma, and Weibull distributions three of which are discussed in Sharma and Krishna (1994. Simulations revealed that its performance, as measured by coverage probability, is totally dependent on the amount of noise introduced. A proposal for using ranked set sampling (RSS instead of simple random sampling (SRS improved its performance. It is recommended against using this confidence interval for data from a log-normal distribution. Moreover, this interval performs poorly in all other distributions unless the SNR is around one.Keywords: Signal-to-noise ratio, coefficient of variation, sampling distribution, confidence interval, ranked set sample, simple random sample.
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Enumerative and asymptotic analysis of a moduli space
Readdy, Margaret A
2010-01-01
We focus on combinatorial aspects of the Hilbert series of the cohomology ring of the moduli space of stable pointed curves of genus zero. We show its graded Hilbert series satisfies an integral operator identity. This is used to give asymptotic behavior, and in some cases, exact values, of the coefficients themselves. We then study the total dimension, that is, the sum of the coefficients of the Hilbert series. Its asymptotic behavior involves the Lambert W function, which has applications to classical tree enumeration, signal processing and fluid mechanics.
Asymptotics of thermal spectral functions
Caron-Huot, S
2009-01-01
We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...
Regular Variation and Smile Asymptotics
Benaim, Shalom; Friz, Peter
2006-01-01
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Research on temperature profiles of honeycomb regenerator with asymptotic analysis
Institute of Scientific and Technical Information of China (English)
AI Yuan-fang; MEI Chi; HUANG Guo-dong; JIANG Shao-jian; CHEN Hong-rong
2006-01-01
An asymptotic semi-analytical method for heat transfer in counter-flow honeycomb regenerator is proposed. By introducing a combined heat-transfer coefficient between the gas and solid phase, a heat transfer model is built based on the thin-walled assumption. The dimensionless thermal equation is deduced by considering solid heat conduction along the passage length. The asymptotic analysis is used for the small parameter of heat conduction term in equation. The first order asymptotic solution to temperature distribution under weak solid heat conduction is achieved after Laplace transformation through the multiple scales method and the symbolic manipulation function in MATLAB. Semi-analytical solutions agree with tests and finite-difference numerical results. It is proved possible for the asymptotic analysis to improve the effectiveness, economics and precision of thermal research on regenerator.
New Inference Procedures for Semiparametric Varying-Coefficient Partially Linear Cox Models
Directory of Open Access Journals (Sweden)
Yunbei Ma
2014-01-01
Full Text Available In biomedical research, one major objective is to identify risk factors and study their risk impacts, as this identification can help clinicians to both properly make a decision and increase efficiency of treatments and resource allocation. A two-step penalized-based procedure is proposed to select linear regression coefficients for linear components and to identify significant nonparametric varying-coefficient functions for semiparametric varying-coefficient partially linear Cox models. It is shown that the penalized-based resulting estimators of the linear regression coefficients are asymptotically normal and have oracle properties, and the resulting estimators of the varying-coefficient functions have optimal convergence rates. A simulation study and an empirical example are presented for illustration.
Estimation of Semi-Varying Coefficient Model with Surrogate Data and Validation Sampling
Institute of Scientific and Technical Information of China (English)
Ya-zhao L(U); Ri-quan ZHANG; Zhen-sheng HUANG
2013-01-01
In this paper,we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error.With the help of validation sampling,we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption.We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate.Data-driven bandwidth selection methods are also discussed.Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Asymptotic behavior of generalized functions
Pilipović, Stevan; Vindas, Jasson
2012-01-01
The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach — of Estrada, Kanwal and Vindas — is related to moment asymptotic expansions of generalized functions and the Ces'aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by...
The Asymptotics of Stable Sausages in the Plane
Rosen, Jay
1992-01-01
In this paper we develop an asymptotic expansion for the $\\varepsilon$-neighborhood of the symmetric stable process of order $\\beta, 1 < \\beta < 2$. Our expansion is in powers of $\\varepsilon^{2-\\beta}$ with the $n$th coefficient related to $n$-fold self-intersections of our stable process.
Assessing reproducibility by the within-subject coefficient of variation with random effects models.
Quan, H; Shih, W J
1996-12-01
In this paper we consider the use of within-subject coefficient of variation (WCV) for assessing the reproducibility or reliability of a measurement. Application to assessing reproducibility of biochemical markers for measuring bone turnover is described and the comparison with intraclass correlation is discussed. Both maximum likelihood and moment confidence intervals of WCV are obtained through their corresponding asymptotic distributions. Normal and log-normal cases are considered. In general, WCV is preferred when the measurement scale bears intrinsic meaning and is not subject to arbitrary shifting. The intraclass correlation may be preferred when a fixed population of subjects can be well identified.
Zhang, Hao; Han, Hao; Wang, Jing; Ma, Jianhua; Liu, Yan; Moore, William; Liang, Zhengrong
2014-01-01
Purpose: Repeated computed tomography (CT) scans are required for some clinical applications such as image-guided interventions. To optimize radiation dose utility, a normal-dose scan is often first performed to set up reference, followed by a series of low-dose scans for intervention. One common strategy to achieve the low-dose scan is to lower the x-ray tube current and exposure time (mAs) or tube voltage (kVp) setting in the scanning protocol, but the resulted image quality by the conventi...
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Asymptotic algebra of quantum electrodynamics
Herdegen, Andrzej
2004-01-01
The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.
Conformal Phase Diagram of Complete Asymptotically Free Theories
Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Exponential asymptotics and gravity waves
Chapman, S. J.; Vanden-Broeck, J.
2006-01-01
The problem of irrotational inviscid incompressible free-surface flow is examined in the limit of small Froude number. Since this is a singular perturbation, singularities in the flow field (or its analytic continuation) such as stagnation points, or corners in submerged objects or on rough beds, lead to a divergent asymptotic expansion, with associated Stokes lines. Recent techniques in exponential asymptotics are employed to observe the switching on of exponentially small gravity waves acro...
International Nuclear Information System (INIS)
Purpose: To prospectively investigate the effect on signal intensity (SI) of healthy breast parenchyma on magnetic resonance mammography (MRM) when doubling the contrast dose from 0.1 to 0.2 mmol/kg bodyweight. Materials and methods: Informed consent and institutional review board approval were obtained. Twenty-five healthy female volunteers (median age: 24 years (range: 21-37 years) and median bodyweight: 65 kg (51-80 kg)) completed two dynamic MRM examinations on a 0.6 T open scanner. The inter-examination time was 24 h (23.5-25 h). The following sequences were applied: axial T2W TSE and an axial dynamic T1W FFED, with a total of seven frames. At day 1, an i.v. gadolinium (Gd) bolus injection of 0.1 mmol/kg bodyweight (Omniscan) (low) was administered. On day 2, the contrast dose was increased to 0.2 mmol/kg (high). Injection rate was 2 mL/s (day 1) and 4 mL/s (day 2). Any use of estrogen containing oral contraceptives (ECOC) was recorded. Post-processing with automated subtraction, manually traced ROI (region of interest) and recording of the SI was performed. A random coefficient model was applied. Results: We found an SI increase of 24.2% and 40% following the low and high dose, respectively (P < 0.0001); corresponding to a 65% (95% CI: 37-99%) SI increase, indicating a moderate saturation. Although not statistically significant (P = 0.06), the results indicated a tendency, towards lower maximal SI in the breast parenchyma of ECOC users compared to non-ECOC users. Conclusion: We conclude that the contrast dose can be increased from 0.1 to 0.2 mmol/kg bodyweight, if a better contrast/noise relation is desired but increasing the contrast dose above 0.2 mmol/kg bodyweight is not likely to improve the enhancement substantially due to the moderate saturation observed. Further research is needed to determine the impact of ECOC on the relative enhancement ratio, and further studies are needed to determine if a possible use of ECOC should be considered a compromising
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
1/R expansion for H2 : Analyticity, summability, and asymptotics
Energy Technology Data Exchange (ETDEWEB)
Graffi, S.; Grecchi, V.; Harrell E.M. II; Silverstone, H.J.
1985-12-01
It is proved that the 1/R expansion for H2 is divergent and Borel summable to a complex eigenvalue of a non-self-adjoint operator, which has the same 1/R expansion. The Borel sum is related to the H2 system as follows: its real part agrees with the eigenvalue doublet asymptotically to all orders, and its imaginary part determines the asymptotics of the 1/R expansion coefficients via a dispersion relation. A rigorous estimate of the leading behavior of the imaginary part is obtained, and as a consequence the approximate formula of Brezin and Zinn-Justin relating the square of the eigenvalue gap to the asymptotics of the 1/R expansion is put on a rigorous basis.
Detailed ultraviolet asymptotics for AdS scalar field perturbations
Evnin, Oleg
2016-01-01
We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Asymptotics for restricted integer compositions
Malandro, Martin E
2011-01-01
We study the compositions of an integer n where the part sizes of the compositions are restricted to lie in a finite set. We obtain asymptotic formulas for the number of such compositions, the total and average number of parts among all such compositions, and the total and average number of times a particular part size appears among all such compositions. Several of our asymptotics have the additional property that their absolute errors---not just their percentage errors---go to 0 as n goes to infinity. Along the way we also obtain recurrences and generating functions for calculating several of these quantities. Our asymptotic formulas come from the meromorphic analysis of our generating functions. Our results also apply to questions about certain kinds of tilings and rhythm patterns.
Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation
Institute of Scientific and Technical Information of China (English)
Li-ping Zhu; Li-xing Zhu
2006-01-01
To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.
Ruin problems and tail asymptotics
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...... by an underlying Harris recurrent Markov process some asymptotic results for the ruin probability are derived. Finally, a paper, which is separate in content from the rest of the thesis, treats a RESTART problem in the situation, where failures occur with decreasing intensity....
Asymptotic freedom for nonrelativistic confinement
International Nuclear Information System (INIS)
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle nonrelativistic confining potential model. In this model, asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given, and explicit examples are given for the case of a harmonic oscillator
Asymptotic risks of Viterbi segmentation
Kuljus, Kristi
2010-01-01
We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation.
Comment on Asymptotically Safe Inflation
Tye, S -H Henry
2010-01-01
We comment on Weinberg's interesting analysis of asymptotically safe inflation (arXiv:0911.3165). We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization groupflow away from the fixed point towards the infrared region that reproduces the Newton's constant and today's cosmological constant. We follow this RG flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine tuning is necessary to get enough efolds of infflation in the asymptotically safe inflationary scenario.
Asymptotic distributions for a class of generalized $L$-statistics
Borovskikh, Yuri V; 10.3150/09-BEJ240
2010-01-01
We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$-statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$-statistics.
Second virial coefficients of dipolar hard spheres
Philipse, A.P.; Kuipers, B.W.M.
2010-01-01
An asymptotic formula is reported for the second virial coefficient B2 of a dipolar hard-sphere (DHS) fluid, in zero external field, for strongly coupled dipolar interactions. This simple formula, together with the one for the weak-coupling B2, provides an accurate prediction of the second virial co
Cube Root Asymptotics: Maximal Scores and Irregular Histograms
Moss, Jonas
2015-01-01
Estimators with cube root asymptotics are typically the result of M-estimation with non-smooth objective functions. Aside from being inefficient, they are hard to calculate, have intractable limiting distributions, and are unamenable to the bootstrap. Manski's maximum score estimator and irregular histograms receive special attention. We investigate the geometry, algorithmics and robustness properties of Manski's maximum score estimator, a semiparametric estimator of the coefficients in the b...
Asymptotic expansions of Jacobi functions
International Nuclear Information System (INIS)
The author presents an asymptotic expansion of the Jacobi polynomials which is based on the fact, that these polynomials are special hypergeometric functions. He uses an integral representation of these functions and expands the integrand in a power series. He derives explicit error bounds on this expansion. (HSI)
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the...
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces
Daudé, Thierry; Kamran, Niky; Nicoleau, Francois
2015-12-01
In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists of the complete separability of the Hamilton-Jacobi equations for the geodesic flow. An important related consequence is the fact that the stationary wave equation can be separated into a system of radial and angular ODEs. The full scattering matrix at fixed energy associated to a scalar wave equation on asymptotically hyperbolic Liouville surfaces can be thus simplified by considering its restrictions onto the generalized harmonics corresponding to the angular separated ODE. The resulting partial scattering matrices consists in a countable set of 2 × 2 matrices whose coefficients are the so called transmission and reflection coefficients. It is shown that the reflection coefficients are nothing but generalized Weyl-Titchmarsh (WT) functions for the radial ODE in which the generalized angular momentum is seen as the spectral parameter. Using the complex angular momentum method and recent results on 1D inverse problem from generalized WT functions, we show that the knowledge of the reflection operators at a fixed non-zero energy is enough to determine uniquely the metric of the asymptotically hyperbolic Liouville surface under consideration.
Reducing component estimation for varying coefficient models with longitudinal data
Institute of Scientific and Technical Information of China (English)
2008-01-01
Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice.
Harvey, Danielle J; Weng, Qian; Beckett, Laurel A
2010-06-15
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented.
On Asymptotically Efficient Estimation in Semiparametric Models
Schick, Anton
1986-01-01
A general method for the construction of asymptotically efficient estimates in semiparametric models is presented. It improves and modifies Bickel's (1982) construction of adaptive estimates and obtains asymptotically efficient estimates under conditions weaker than those in Bickel.
Uniform asymptotics for the full moment conjecture of the Riemann zeta function
Hiary, Ghaith A
2011-01-01
Conrey, Farmer, Keating, Rubinstein, and Snaith recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjecture states that the $2k$-th absolute moment of zeta on the critical line is asymptotically given by a certain $2k$-fold residue integral. This residue integral can be expressed as a polynomial of degree $k^2$, whose coefficients are given in exact form by elaborate and complicated formulas. In this article, uniform asymptotics for roughly the first $k$ coefficients of the moment polynomial are derived. Numerical data to support our asymptotic formula are presented. An application to bounding the maximal size of the zeta function is considered.
Asymptotic expansions of integral means and applications to the ratio of gamma functions
ELEZOVIĆ, NEVEN; Vukšić, Lenka
2013-01-01
Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form $B(A(x))=C(x)$, where $B$ and $C$ have known asymptotic expansions. The results are illustrated by calculation of some important integral means connected with gamma and digamma functions.
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Directory of Open Access Journals (Sweden)
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Xiu Kan; Huisheng Shu; Yan Che
2012-01-01
The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t)+β(t)Xt)dt+σ(t)dWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Asymptotic analysis and numerical modeling of mass transport in tubular structures
Cardone, G; Sirakov, Y
2009-01-01
In the paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the diffusion-convection equation set in the thin structure. An asymptotic expansion of solution is constructed. This expansion is used further for justification of an asymptotic domain decomposition strategy essentially reducing the memory and the time of the code. A numerical solution obtained by this strategy is compared to the numerical solution obtained by a direct FEM computation.
Exact and asymptotic results for insurance risk models with surplus-dependent premiums
Albrecher, Hansjörg; Palmowski, Zbigniew; Regensburger, Georg; Rosenkranz, Markus
2011-01-01
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cram\\'er-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.
Testing Serial Correlation in Semiparametric Varying-Coefficient Partially Linear EV Models
Institute of Scientific and Technical Information of China (English)
Xue-mei Hu; Zhi-zhong Wang; Feng Liu
2008-01-01
This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = Xτβ + Zτα(T) + ε,ξ = X + η with the identifying condition E[(ε,ητ)τ] = 0, Cov[(ε,ητ)τ] = σ2Iρ+1. The estimators of interested regression parameters β, and the model error variance σ2, as well as the nonparametric components α(T), are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α(T) achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.
Mel'nikov, A. V.
1996-10-01
Contents Introduction Chapter I. Basic notions and results from contemporary martingale theory §1.1. General notions of the martingale theory §1.2. Convergence (a.s.) of semimartingales. The strong law of large numbers and the law of the iterated logarithm Chapter II. Stochastic differential equations driven by semimartingales §2.1. Basic notions and results of the theory of stochastic differential equations driven by semimartingales §2.2. The method of monotone approximations. Existence of strong solutions of stochastic equations with non-smooth coefficients §2.3. Linear stochastic equations. Properties of stochastic exponentials §2.4. Linear stochastic equations. Applications to models of the financial market Chapter III. Procedures of stochastic approximation as solutions of stochastic differential equations driven by semimartingales §3.1. Formulation of the problem. A general model and its relation to the classical one §3.2. A general description of the approach to the procedures of stochastic approximation. Convergence (a.s.) and asymptotic normality §3.3. The Gaussian model of stochastic approximation. Averaged procedures and their effectiveness Chapter IV. Statistical estimation in regression models with martingale noises §4.1. The formulation of the problem and classical regression models §4.2. Asymptotic properties of MLS-estimators. Strong consistency, asymptotic normality, the law of the iterated logarithm §4.3. Regression models with deterministic regressors §4.4. Sequential MLS-estimators with guaranteed accuracy and sequential statistical inferences Bibliography
Motion Parallax is Asymptotic to Binocular Disparity
Stroyan, Keith
2010-01-01
Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.
Hydrodynamics, resurgence and trans-asymptotics
Basar, Gokce
2015-01-01
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...
Asymptotic safety goes on shell
International Nuclear Information System (INIS)
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters. (paper)
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Exponential asymptotics and capillary waves
Chapman, S. J.; Vanden-Broeck, J.
2002-01-01
Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The amplitude of these waves is determined, and the implications are considered for many quite general flows....
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...... degrees of freedom of these theories to next-to-next-to-leading order in the coupling constants....
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R; Ishibashi, Akihiro; Wald, Robert M
2015-01-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\\ge4$. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, $\\mathcal{E}$. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ...
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
Institute of Scientific and Technical Information of China (English)
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Test and asymptotic normality for mixed bivariate measure
Directory of Open Access Journals (Sweden)
Rachid Sabre
2013-05-01
Full Text Available Consider a pair of random variables whose joint probability measure is the sum of an absolutely continuous measure, a discrete measure and a finite number of absolutely continuous measures on some lines called jum lines. The central limit theorem of the densities estimates is studied and its rate of convergence is given. A statistical test is developed to locate the jump points. An application on real data was conducted.
Asymptotics of the filtration problem for suspension in porous media
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure
Kalamkarov, Alexander L.; Andrianov, Igor V.; Pacheco, Pedro M. C. L.; Savi, Marcelo A.; Starushenko, Galina A.
2016-08-01
The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Conformal symmetries of gravity from asymptotic methods: further developments
Lambert, Pierre-Henry
2014-01-01
In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in $d$ dimensions with and without a cosmological constant. The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions. The second part of this thesis contains the original contributions. Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure...
Sieve M-estimation for semiparametric varying-coefficient partially linear regression model
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method.
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotic black hole quasinormal frequencies
Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a new derivation of the quasinormal frequencies of Schwarzschild black holes in d greater than or equal to 4 and Reissner-Nordstrom black holes in d = 4, in the limit of infinite damping. For Schwarzschild in d greater than or equal to 4 we find that the asymptotic real part is THawkinglog(3) for scalar perturbations and for some gravitational perturbations; this confirms a result previously obtained by other means in the case d = 4. For Reissner-Nordstrom in d = 4 w...
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
The maximum drag reduction asymptote
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re < 100. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
The maximum drag reduction asymptote
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic black hole quasinormal frequencies
Motl, L; Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a simple derivation of the quasinormal frequencies of Schwarzschild black holes in d>=4 and non-extremal Reissner-Nordstrom black holes in d=4, in the limit of infinite damping. For Schwarzschild in d=4 the asymptotic real part of the frequency is (T_Hawking)log(1+2cos(pi.j)), where j is the spin of the perturbation; this confirms a result previously obtained by other means. For Schwarzschild in d>4 we find that the asymptotic real part is (T_Hawking)log(3) for scalar perturbations. For non-extremal Reissner-Nordstrom in d=4 we find a specific but generally aperiodic behavior for the quasinormal frequencies, both for scalar perturbations and for axial electromagnetic-gravitational perturbations; there is nevertheless a hint that the value (T_Hawking)log(2) may be special in this case. The formulae are obtained by studying the monodromy of the perturbation analytically continued to the complex plane.
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
Asymptotic properties of the C-Metric
Sladek, Pavel
2010-01-01
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.
Asymptotically Plane Wave Spacetimes and their Actions
Witt, Julian Le; Ross, Simon F.
2008-01-01
We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff condi...
Asymptotic independence and a network traffic model
Maulik, Krishanu; Resnick, Sidney; Rootzén, Holger
2002-01-01
The usual concept of asymptotic independence, as discussed in the context of extreme value theory, requires the distribution of the coordinatewise sample maxima under suitable centering and scaling to converge to a product measure. However, this definition is too broad to conclude anything interesting about the tail behavior of the product of two random variables that are asymptotically independent. Here we introduce a new concept of asymptotic independence which allows u...
Asymptotics of near unit roots (in Russian)
Stanislav Anatolyev; Nikolay Gospodinov
2012-01-01
Sometimes the conventional asymptotic theory yields that the limiting distribution changes discontinuously, or that the asymptotic distribution does not approximate accurately the actual finite-sample distribution. In such situations one finds useful an asymptotic tool of drifting parameterizations where certain parameters are allowed to depend explicitly on the sample size. It proves useful, among other things, for impulse response analysis and forecasting of strongly dependent processes at ...
Asymptotic conservation laws in field theory
Anderson, Ian M.; Torre, Charles G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation...
Estimating beta-mixing coefficients via histograms
McDonald, Daniel J; Schervish, Mark
2011-01-01
The literature on statistical learning for time series often assumes asymptotic independence or "mixing" of data sources. Beta-mixing has long been important in establishing the central limit theorem and invariance principle for stochastic processes; recent work has identified it as crucial to extending results from empirical processes and statistical learning theory to dependent data, with quantitative risk bounds involving the actual beta coefficients. There is, however, presently no way to actually estimate those coefficients from data; while general functional forms are known for some common classes of processes (Markov processes, ARMA models, etc.), specific coefficients are generally beyond calculation. We present an l1-risk consistent estimator for the beta-mixing coefficients, based on a single stationary sample path. Since mixing coefficients involve infinite-order dependence, we use an order-d Markov approximation. We prove high-probability concentration results for the Markov approximation and show...
A new approach to bootstrap inference in functional coefficient models
Herwartz, Helmut; Xu, Fang
2007-01-01
We introduce a new, factor based bootstrap approach which is robust under heteroskedastic error terms for inference in functional coefficient models. Modeling the functional coefficient parametrically, the bootstrap approximation of an F statistic is shown to hold asymptotically. In simulation studies with both parametric and nonparametric functional coefficients, factor based bootstrap inference outperforms the wild bootstrap and pairs bootstrap approach according to its size features. Apply...
Numerical Asymptotic Solutions Of Differential Equations
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
Why are tensor field theories asymptotically free?
Rivasseau, Vincent
2015-01-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop.
Ultraviolet asymptotics and singular dynamics of AdS perturbations
Craps, Ben; Vanhoof, Joris
2015-01-01
Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order 1/epsilon^2. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive rel...
Asymptotic behaviour of pion-pion total cross-sections
International Nuclear Information System (INIS)
We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log2 s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π+π−, π±π0 and π0π0 scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours Nc and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-Nc QCD and we show that it is possible to make an Ansatz for the isospin I=1 and I=0 spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-Nc counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σπ±π0total(s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-Nc Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp-bar scattering total cross sections
Efficient estimation of price adjustment coefficients
Lyhagen, Johan
1999-01-01
The price adjustment coefficient model of Amihud and Mendelson (1987) is shown to be suitable for estimation by the Kalman filter. A techique that, under some commonly used conditions, is asymptotically efficient. By Monte Carlo simulations it is shown that both bias and mean squared error are much smaler compared to the estimator proposed by Damodaran and Lim (1991) and Damodaran (1993). A test for the adeqacy of the model is also proposed. Using data from four minor, the nordic countries ex...
Asymptotic-preserving Boltzmann model equations for binary gas mixture
Liu, Sha; Liang, Yihua
2016-02-01
An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations.
Renormalization constants and asymptotic behaviour in quantum electrodynamics
International Nuclear Information System (INIS)
Using dimensional regularization a field theory contains at least one parameter less than the dimension of a mass. The Callan-Symanzik equations for the renormalization constants then become soluble entirely in terms of the coefficient functions. Explicit expressions are obtained for all the renormalization constants in Quantum Electrodynamics. At nonexceptional momenta the infrared behaviour and the three leading terms in the asymptotic expansion of any Greens function are controlled by the Callan-Symanzik equations. For the propagators the three leading terms are computed explicitly in terms of functions of α only. The gauge dependence of the electron propagator in momentum space is solved explicitly in all orders of perturbation theory. (Auth.)
Robust and bias-corrected estimation of the coefficient of tail dependence
DEFF Research Database (Denmark)
Dutang, C.; Goegebeur, Y.; Guillou, A.
2014-01-01
We introduce a robust and asymptotically unbiased estimator for the coefficient of tail dependence in multivariate extreme value statistics. The estimator is obtained by fitting a second order model to the data by means of the minimum density power divergence criterion. The asymptotic properties...
Asymptotically flat and regular Cauchy data
Dain, S
2002-01-01
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
8. Asymptotically Flat and Regular Cauchy Data
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
An asymptotic model of the F layer
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Partially linear varying coefficient models stratified by a functional covariate
Maity, Arnab
2012-10-01
We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.
Partially Linear Varying Coefficient Models Stratified by a Functional Covariate.
Maity, Arnab; Huang, Jianhua Z
2012-10-01
We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...... convergence of the postbuckling coefficients. (C) 1998 John Wiley & Sons, Ltd....
Long-range asymptotic expansion of the diagonal Born–Oppenheimer correction
International Nuclear Information System (INIS)
Graphical abstract: We derived formulas for coefficients A6, A8, A10 determining long-range asymptotic behavior of the adiabatic correction to the potential energy. The formulas were used to compute the coefficients for hydrogen molecule and helium dimers. Abstract: Formulas for the coefficients A6, A8, and A10 determining the long-range asymptotic behavior Ead(R)∼-A6R-6-A8R-8-A10R-10 of the diagonal Born–Oppenheimer (adiabatic) correction Ead(R) to the potential energy of a diatomic molecule are derived using two standard definitions of Ead(R). The first one is based on the explicit separation of the center-of-mass and rotational coordinates from the total Hamiltonian of a system, while the second definition uses the Born–Handy expression in a laboratory system of coordinates. Expressions for the asymptotic coefficients resulting from both definitions are proved to be equivalent. The obtained formulas are used to compute the asymptotics of the adiabatic correction for the ground state of the hydrogen molecule and for the helium dimer in the lowest quintet and singlet states. In the latter case basis sets up to 8-tuple zeta quality were used to adequately account for the electron correlation effects.
Institute of Scientific and Technical Information of China (English)
王金良; 周笠
2003-01-01
In this paper,our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior.In case the coefficients are periodic,we give some sufficient conditions for the existence and uniqueness of periodic solution.Furthermore,we also study the effect of time-delay on the solution.
Determination Permeability Coefficient from Piezocone
Directory of Open Access Journals (Sweden)
Qiang Wang
2014-01-01
Full Text Available The permeability coefficient of soil profile is one of the problems concerned by engineers, and the determination of permeability coefficient method mainly relies on the laboratory permeability test and field pumping test, but these tests are time-consuming and inefficient, and especially the permeability coefficient of soil under the condition of partial drainage was difficult to determine; in this paper, the modern digital CPTU technology was used. Dimensional permeability KT was defined by using the dimensionless normalized cone tip resistance Qt, friction factor Fr, and pore pressure ratio Bq, these parameters enable plots of Bq-Qt, Fr-Qt, Bq-Fr to be contoured KT and hence for permeability coefficient. The relationship has been applied to Nanjing 4th Yangtze river bridge, and compared with laboratory penetration test. The results indicate that the method can accurately determine the permeability coefficient of soil under partial drainage condition and provide the theoretical basis for engineering application.
On spectral properties of the fourth order differential operator with singular coefficients
Man'ko, Stepan
2010-01-01
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of differential operators with smooth coefficients approximating the singular coefficients is studied. We explore how behavior of eigenvalues and eigenfunctions is influenced by singular coefficients. The limit operator is constructed and is shown to depend on a type of approximation of singular coefficients.
An asymptotic model of seismic reflection from a permeable layer
Energy Technology Data Exchange (ETDEWEB)
Silin, D.; Goloshubin, G.
2009-10-15
Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot's model of poroelasticity. A review of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and Darcy's law suggests an alternative new physical interpretation of some coefficients of the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and at-tribute analysis.
Adaptive Control of a Two-Item Inventory Model with Unknown Demand Rate Coefficients
Ahmad M. Alshamrani
2012-01-01
This paper considers a multiitem inventory model with unknown demand rate coefficients. An adaptive control approach with a nonlinear feedback is applied to track the output of the system toward the inventory goal level. The Lyapunov technique is used to prove the asymptotic stability of the adaptive controlled system. Also, the updating rules of the unknown demand rate coefficients are derived from the conditions of the asymptotic stability of the perturbed system. The linear stability analy...
Asymptotic Safety, Emergence and Minimal Length
Percacci, R
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Asymptotic Likelihood Distribution for Correlated & Constrained Systems
Agarwal, Ujjwal
2016-01-01
It describes my work as summer student at CERN. The report discusses the asymptotic distribution of the likelihood ratio for total no. of parameters being h and 2 out of these being are constrained and correlated.
EMC effect: asymptotic freedom with nuclear targets
International Nuclear Information System (INIS)
General features of the EMC effect are discussed within the framework of quantum chromodynamics as expressed via the operator product expansion and asymptotic freedom. These techniques are reviewed with emphasis on the target dependence. 22 references
A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
Kraus, Per
2016-01-01
Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT. This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy's formula for the high energy density of states. The derivation uses certain asymptotic properties of one-point conformal blocks on the torus. Our asymptotic formula matches a dual AdS_3 computation of one point functions in a black hole background. This is evidence that the BTZ black hole geometry emerges upon course-graining over a suitable family of heavy microstates.
Complete WKB asymptotics of high frequency vibrations in a stiff problem
Babych, N
2008-01-01
Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter epsilon and vanishes as epsilon tends to zero on a subinterval, we prove the existence of low and high frequency resonance vibrations. The low frequency vibrations admit the power series expansions on epsilon but this method is not applicable to the description of high frequency vibrations. However, the nonclassical asymptotics on epsilon of the high frequency vibrations were constructed using the WKB method.
Jarroudi, Mustapha El; 10.1093/imamat/66.6.567
2010-01-01
We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $\\epsilon$-periodically distributed fibers of size $r_{\\epsilon}$, with $0 < r_{\\epsilon} < \\epsilon$, filled in with some different elastic material, when this small parameter $\\epsilon$ goes to 0. The case of small deformations and small strains is considered. We exhibit a critical size of the fibers and a critical link between the radius of the fibers and the size of the Lam\\'e coefficients of the reinforcing elastic material. Epi-convergence arguments are used in order to prove this asymptotic behaviour. The proof is essentially based on the construction of appropriate test-functions.
Precise Asymptotics for Lévy Processes
Institute of Scientific and Technical Information of China (English)
Zhi Shui HU; Chun SU
2007-01-01
Let {X(t), t ≥ 0} be a Lévy process with EX(1)=0 and EX2(1)＜∞. In this paper, we shall give two precise asymptotic theorems for {X(t), t≥0}. By the way, we prove the corresponding conclusions for strictly stable processes and a general precise asymptotic proposition for sums of i.i.d.random variables.
The trouble with asymptotically safe inflation
Fang, Chao
2013-01-01
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
Asymptotic representation theorems for poverty indices
Lo, Gane Samb; Sall, Serigne Touba
2010-01-01
We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotics of the bulk of poverty indices and issues in poverty analysis. Our representation results uniformly hold on a large collection of poverty indices. They enable the continuous measure of poverty with longitudinal data.
Dirichlet eigenvalues of asymptotically flat triangles
Ourmières-Bonafos, Thomas
2015-01-01
This paper is devoted to the study of the eigenpairs of the Dirichlet Laplacian on a family of triangles where two vertices are fixed and the altitude associated with the third vertex goes to zero. We investigate the dependence of the eigenvalues on this altitude. For the first eigenvalues and eigenfunctions, we obtain an asymptotic expansion at any order at the scale cube root of this altitude due to the influence of the Airy operator. Asymptotic expansions of the eigenpairs are provided, ex...
Asymptotically hyperbolic black holes in Horava gravity
Janiszewski, Stefan
2014-01-01
Solutions of Hořava gravity that are asymptotically Lifshitz are explored. General near boundary expansions allow the calculation of the mass of these spacetimes via a Hamiltonian method. Both analytic and numeric solutions are studied which exhibit a causal boundary called the universal horizon, and are therefore black holes of the theory. The thermodynamics of an asymptotically Anti-de Sitter Hořava black hole are verified.
Loop Quantum Gravity and Asymptotically Flat Spaces
Arnsdorf, Matthias
2000-01-01
After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be interpreted as describing fluctuations around fiducial fixed backgrounds. When the backgr...
AGB [asymptotic giant branch]: Star evolution
International Nuclear Information System (INIS)
Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs
Asymptotic and Exact Expansions of Heat Traces
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Michał, E-mail: michal@eckstein.pl [Jagiellonian University, Faculty of Physics, Astronomy and Applied Computer Science (Poland); Zając, Artur, E-mail: artur.zajac@uj.edu.pl [Jagiellonian University, Faculty of Mathematics and Computer Science (Poland)
2015-12-15
We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.
General smile asymptotics with bounded maturity
Francesco Caravenna; Jacopo Corbetta
2014-01-01
We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [Math. Finance 19 (2009), 1-12]. We present applications to popular models, including Carr-Wu finite moment logstable model, Merton's jump diffusion ...
Time-harmonic Maxwell equations with asymptotically linear polarization
Qin, Dongdong; Tang, Xianhua
2016-06-01
This paper is concerned with the following time-harmonic semilinear Maxwell equation: nabla× (nabla× u)+λ u=f(x,u), &in Ω ν × u=0, &on partialΩ, where {Ωsubset {R}3} is a bounded, convex domain and {ν : partial Ωto {R}3} is the exterior normal. Motivated by recent work of Bartsch and Mederski and based on some observations and new techniques, we study above equation by developing the generalized Nehari manifold method. Particularly, existence of ground-state solutions of Nehari-Pankov type for the equation is established with asymptotically linear nonlinearity.
On the asymptotic distribution of an alternative measure of kurtosis
Directory of Open Access Journals (Sweden)
Kagba Suaray
2015-08-01
Full Text Available Pearson defined the fourth standardized moment of a symmetric distribution as its kurtosis. There has been much discussion in the literature concerning both the meaning of kurtosis, as well as the effectiveness of the classical sample kurtosis as a reliable measure of peakedness and tail weight. In this paper, we consider an alternative measure, developed by Crow and Siddiqui, used to describe kurtosis. Its value is calculated for a number of common distributions, and a derivation of its asymptotic distribution is given. Simulations follow, which reveal an interesting connection to the literature on the ratio of normal random variables.
Yarmukhamedov, R
2016-01-01
Asymptotic expressions for the radial and full wave functions of a three{body bound halo nuclear system with two charged particles in relative coordinates are obtained in explicit form, when the relative distance between two particles tends to infinity. The obtained asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (pn?) wave functions for the halo ($E^*=3.562$ MeV, $J^{\\pi}=0^+$, $T=1$) state of $^6$Li derived by D. Baye within the Lagrange-mesh method for two forms of the $\\alpha N$ -potential. The agreement between the calculated wave function and the asymptotic formula is excellent for distances up to 30 fm. Information about the values of the three-body asymptotic normalization functions is extracted. It is shown that the extracted values of the three-body asymptotic normalization function are sensitive to the form of the $\\alpha N$ -potential. The mirror symmetry is revealed for the three-body asymptotic normalization functions derived for the isobaric ($^6$He, $^...
Institute of Scientific and Technical Information of China (English)
杨运俊; 郭献忠; 高凌云; 郭翔; 付军; 陈伟建
2013-01-01
Objective To investigate the variability and trends of apparent diffusion coefficient (ADC) of different brain segments in normal middle- aged and aged Han adults. Methods Thirty Han normal adult subjects aged 40~70 without positive cerebral symptoms were divided into 3 age groups (40~49, 50~59, 60~70). Plain scan and diffusion weighted imaging (DWI) were performed by 3.0T MR in al subjects. The images were transferred to ADW 4.3 workstations for post- processing. Regions of interest were placed covering grey and white matter of frontal lobe, putamen, thalamus and cerebel um. The relationship of ADC value with different ages and cerebral regions was analyzed. Results The cerebral tissues of different location had differ-ent values in the same age group. The highest ADC value was detected in gray matter of the frontal lobe, fol owed by putamen, white matter of frontal lobe and the thalamus, and the lowest one was in cerebel um. There was no significant difference in ADCs between two sides of the same cerebral parts of different regions.(P>0.05).Although there was no significant difference in ADCs between grey and white matter of frontal lobe, putamen, thalamus and cerebel um of different age groups, the ADC value of the same region tended to increase with age. The changes of ADC value in subjects aged 40~60 presented a much slower rate and an upshift tendency was observed in subjects aged>60. Conclusion The ADC value of the same region in middle- aged and elderly people tended to increase with the age, particularly in subjects aged>60 years.%目的：探讨40～70岁年龄段正常汉族人颅脑各区域磁共振表观弥散系数（ADC）变化特点，建立正常中老年人群颅脑ADC值变化趋势的基准。方法选择30例无阳性颅脑病征的正常汉族受试者，按年龄段分为3组，使用GE Medical System 3.0 T超导磁共振扫描仪进行头部平扫及弥散加权成像，测量额叶灰质、白质、壳核、丘脑及小脑感兴趣区
Extracting OPE coefficient of Konishi at four loops
Gonçalves, Vasco
2016-01-01
We compute in this short note the OPE coefficient of two 20' operators and the Konishi. We use the OPE decomposition of a four point function of four 20' operators and the method of asymptotic expansions to compute the integrals at the order that it is needed.
Kartuzova, Olga; Kassemi, Mohammad
2015-01-01
A CFD model for simulating the self-pressurization of a large scale liquid hydrogen storage tank is utilized in this paper to model the MHTB self-pressurization experiment. The kinetics-based Schrage equation is used to account for the evaporative and condensi ng interfacial mass flows in this model. The effect of the accommodation coefficient for calculating the interfacial mass transfer rate on the tank pressure during tank selfpressurization is studied. The values of the accommodation coefficient which were considered in this study vary from 1.0e-3 to 1.0e-1 for the explicit VOF model and from 1.0e-4 to 1.0e-3 for the implicit VOF model. The ullage pressure evolutions are compared against experimental data. A CFD model for controlling pressure in cryogenic storage tanks by spraying cold liquid into the ullage is also presented. The Euler-Lagrange approach is utilized for tracking the spray droplets and for modeling the interaction between the droplets and the continuous phase (ullage). The spray model is coupled with the VOF model by performing particle tracking in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. Droplet-ullage heat and mass transfer are modeled. The flow, temperature, and interfacial mass flux, as well as droplets trajectories, size distribution and temperatures predicted by the model are presented. The ul lage pressure and vapor temperature evolutions are compared with experimental data obtained from the MHTB spray bar mixing experiment. The effect of the accommodation coefficient for calculating the interfacial and droplet mass transfer rates on the tank pressure during mixing of the vapor using spray is studied. The values used for the accommodation coefficient at the interface vary from 1.0e-5 to 1.0e-2. The droplet accommodation coefficient values vary from 2.0e-6 to 1.0e-4.
Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models
Haddar, Houssem; Jiang, Zixian
2015-11-01
Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and it is therefore important that they are identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layer’s small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. A standard iterative inversion algorithm is then applied to the asymptotic models to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and showing the benefits of the inversion procedure are provided.
Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials
Directory of Open Access Journals (Sweden)
Xin Wang
2014-01-01
Full Text Available An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.
Index-free Heat Kernel Coefficients
De van Ven, A E M
1998-01-01
Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the first time. For a flat space with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as required for the fourth coefficient. These results are obtained by directly solving the relevant recursion relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our procedure is thus noncovariant, but we show that for any coefficient the `gauged' respectively `curved' version is found from the corresponding `non-gauged' respectively `flat' coefficient by making some simple covariant substitutions. These substitutions being understood, the coefficients retain their `flat' form and size. In this sense the fift...
Sinharay, Sandip
2015-01-01
The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice✩
Harvey, Danielle J.; Weng, Qian; Beckett, Laurel A.
2010-01-01
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented. PMID:20436940
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
Asymptotic analysis of outwardly propagating spherical flames
Institute of Scientific and Technical Information of China (English)
Yun-Chao Wu; Zheng Chen
2012-01-01
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Asymptotic Behaviour of Pion--Pion Total Cross--Sections
Greynat, David; Vulvert, Grégory
2014-01-01
We derive a sum rule which shows an inconsistency between the Lukaszuk-Martin coefficient of the Froissart-Martin bound and well known properties of $\\pi\\pi$ amplitudes in QCD. We next compute the total cross sections for $\\pi^+ \\pi^-$, $\\pi^{\\pm} \\pi^0$ and $\\pi^0 \\pi^0$ scattering within the framework of the constituent chiral quark model (C$\\chi$QM) in the limit of a large number of colours $\\mathrm{N_c}$ and discuss their asymptotic behaviours. The same $\\pi\\pi$ cross sections are also discussed within the general framework of Large-$\\mathrm{N_c}$ QCD and we show that it is possible to make an Ansatz for the isospin $I=1$ and $I=0$ spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-$\\mathrm{N_c}$ counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the $\\sigma_{\\pi^{\\pm}\\pi^0}^{\\rm total}(s)$ cross section predicted by the C...
Asymptotic Regime in N Random Interacting Species
Fiasconaro, A; Valenti, D
2005-01-01
The asymptotic regime of a complex ecosystem with N random interacting species and in the presence of an external multiplicative noise is analyzed. We find the role of the external noise on the long time probability distribution of the i_th density species, the extinction of species and the local field acting on the i_th population. We analyze in detail the transient dynamics of this field and the cavity field, which is the field acting on the i_th species when this is absent. We find that the presence or the absence of some population give different asymptotic distributions of these fields.
Asymptotic Methods for Solitary Solutions and Compactons
Directory of Open Access Journals (Sweden)
Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
Institute of Scientific and Technical Information of China (English)
冯涛; 王晶; 刘斌; 李楠; 尹亦阳
2012-01-01
Foam material is widely used in mechanical noise control engineering.With two travelling wave in opposite direction as the port parameter,an experimental identification method of the transfer matrix for the foam material was researched,and the method for calculating the transfer matrix of multilayer foam from single layer foam was studied as well to obtain a method for calculating the absorption coefficient of the multilayer foam under rigid backlining.Then the measurement and calculation method was validated through test and the relationship between the thickness of the foam and the absorption coefficient was researched preliminarily,which results imply that the transfer matrix is the inherent acoustical attribute of the foam material which does not change with the change of the acoustical boundary condition, thus the absorption coefficient of the multilayer foam can be calculated from the transfer matrix of the single layer foam.%泡沫材料在机械噪声控制工程中应用广泛.以方向相反的两列行波为端口参量,研究泡沫材料传递矩阵的实验辨识方法,研究由一层材料得到多层材料传递矩阵的计算方法,形成刚性背衬下多层泡沫材料吸声系数的计算方法.通过实验对测量计算方法进行验证,对材料厚度与吸声系数的关系进行了初步研究.研究结果表明:传递矩阵是材料本身固有的声学属性,不随其声学边界条件的改变而改变,以一层泡沫材料的传递矩阵参数为基础,通过计算可得到多层泡沫材料的吸声系数.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Graphite friction coefficient for various conditions
Institute of Scientific and Technical Information of China (English)
2001-01-01
The friction coefficient the graphite used in the Tsinghua University 10MW High Tem-perature Gas-Cooled Reactor was analyzed for various conditions. The variation of the graphitefriction coefficient was measured for various sliding velocities, sliding distances, normal loads, en-vironments and temperatures. A scanning elector microscope (SEM) was used to analyze the fric-tion surfaces.
On the micropolar flow in a circular pipe: the effects of the viscosity coefficients
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper considers the stationary flow of incompressible micropolar fluid through a thin cylindrical pipe governed by the pressure drop between pipe's ends. Its goal is to investigate the influence of the viscosity coefficients on the effective flow. Depending on the magnitude of viscosity coefficients with respect to the pipe's thickness, it derives different asymptotic models and discusses their properties.
Calculation of anisotropic few-group constants in asymptotic cells: the code ANICELL
International Nuclear Information System (INIS)
The theoretical background of the ANICELL computer program together with a user's manual is presented. ANICELL is a nuclear reactor neutron transport code which solves the traditional asymptotic and the so-called tilted flux transport problems in one-dimensional cylindrical geometry using linearly anisotropic scattering. The method of solution used is the first flight collision probability technique. Few-group constants including radial and axial diffusion coefficients for the cell are also prepared by the program. (author)
Light rays in static spacetimes with critical asymptotic behavior: A variational approach
Directory of Open Access Journals (Sweden)
Valeria Luisi
2006-09-01
Full Text Available Let $mathcal{M}=mathcal{M}_{0}imes mathbb{R}$ be a Lorentzian manifold equipped with the static metric $langle cdot ,cdot angle _{z}=langle cdot ,cdot angle -eta (xdt^{2}$. The aim of this paper is investigating the existence of lightlike geodesics joining a point $z_{0}=(x_{0},t_{0}$ to a line $gamma ={ x_{1}} imes mathbb{R}$ when coefficient $eta $ has a quadratic asymptotic behavior by means of a variational approach.
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, Nico
2000-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range including the classical integral domain.
Lectures on renormalization and asymptotic safety
International Nuclear Information System (INIS)
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method
Eigenvalue asymptotics for Dirac-Bessel operators
Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.
2016-06-01
In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac-Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.
Large degree asymptotics of generalized Bessel polynomials
López, J.L.; Temme, N.M.
2011-01-01
Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in t
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, N.M.
1999-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu
Heavy axion in asymptotically safe QCD
Kobakhidze, Archil
2016-01-01
Assuming QCD exhibits an interacting fixed-point behaviour in the ultraviolet regime, I argue that the axion can be substantially heavier than in the conventional case of asymptotically free QCD due to the enhanced contribution of small size instantons to its mass.
Asymptotic theory of relativistic, magnetized jets.
Lyubarsky, Yuri
2011-01-01
The structure of a relativistically hot, strongly magnetized jet is investigated at large distances from the source. Asymptotic equations are derived describing collimation and acceleration of the externally confined jet. Conditions are found for the transformation of the thermal energy into the fluid kinetic energy or into the Poynting flux. Simple scalings are presented for the jet collimation angle and Lorentz factors. PMID:21405769
Asymptotic analysis of the Forward Search
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made...
THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS
Institute of Scientific and Technical Information of China (English)
Chungou Zhang; Quane Wang
2007-01-01
In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.
Exponential asymptotics of the Voigt functions
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
Infrared studies of asymptotic giant branch stars
International Nuclear Information System (INIS)
In this thesis studies are presented of asymptotic giant branch stars, which are thought to be an important link in the evolution of the galaxy. The studies were performed on the basis of data collected by the IRAS, the infrared astronomical satelite. 233 refs.; 33 figs.; 16 tabs
Asymptotic theory of integrated conditional moment tests
Bierens, H.J.; Ploberger, W.
1995-01-01
In this paper we derive the asymptotic distribution of the test statistic of a generalized version of the integrated conditional moment (ICM) test of Bierens (1982, 1984), under a class of Vn-local alternatives, where n is the sample size. The generalized version involved includes neural network tes
An asymptotically optimal nonparametric adaptive controller
Institute of Scientific and Technical Information of China (English)
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
Liu, Cheng-shi
2016-01-01
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the same time, the mathematical foundation of the method is simple and the logic of the method is very clear, therefore, it is very easy in practice. As application, we obtain the uniform valid asymptotic solutions to some problems including vector field, boundary layer and boundary value problems of nonlinear wave equations. Moreover, we discuss the normal form theory and reduction equations of dynamical systems. Furthermore, by combining the topological deformation and the RG method, a modified method namely the homotopy r...
The asymptotic D-state to S-state ratio of triton
Indian Academy of Sciences (India)
Hossen Sadeghi; Reza Pourimani; Hassan Khalili
2013-11-01
At low energies, an effective field theory (EFT) with only contact interactions as well as three-body forces allow a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behaviour. Triton as a three-body system, based on the EFT have been previously shown to provide representative binding energies, charge radii, S-wave scattering amplitude and asymptotic normalization constants for the 3H bound state system. Herein, EFT predictions of the asymptotic D-state to S-state ratio of triton are calculated to more fully evaluate the adequacy of the EFT model. Manifestly model-independent calculations can be carried out to high orders, leading to high precision.
Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
Craps, Ben; Jai-akson, Puttarak; Vanhoof, Joris
2015-01-01
Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated....
Asymptotic expansion of the wavelet transform with error term
R. S. Pathak; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Institute of Scientific and Technical Information of China (English)
FENG Jie; XU WenCheng; LI ShuXian; LIU SongHao
2008-01-01
Based on the constant coefficients of Ginzburg-Landau equation that considers the influence of the doped fiber retarded time on the evolution of self-similar pulse, the parabolic asymptotic self-similar solutions were obtained by the symmetry reduc-tion algorithm.The parabolic asymptotic amplitude function, phase function, strict linear chirp function and the effective temporal pulse width of self-similar pulse are given in this paper.And these theoretical results are consistent with the numerical simulations.
On Large Scale Inductive Dimension of Asymptotic Resemblance Spaces
Kalantari, Sh.; Honari, B.
2014-01-01
We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class contains the class of all geodesic metric spaces and all finitely generated groups. This leads to an answer for a question asked by E. Shchepin concerning the relation between the asymptotic inductive dimension and the asymptotic dimensiongrad, for r-convex m...
EXACT SAMPLING DISTRIBUTION OF SAMPLE COEFFICIENT OF VARIATION
Dr.G.S.David Sam Jayakumar; A.Sulthan
2015-01-01
This paper proposes the sampling distribution of sample coefficient of variation from the normal population. We have derived the relationship between the sample coefficient of variation, standard normal and chi-square variate. We have derived density function of the sample coefficient of variation in terms of the confluent hyper-geometric distribution. Moreover, the first two moments of the distribution are derived and we have proved that the sample coefficient of variation (cv...
Wave Reflection Coefficient Spectrum
Institute of Scientific and Technical Information of China (English)
俞聿修; 邵利民; 柳淑学
2003-01-01
The wave reflection coefficient frequency spectrum and directional spectrum for concrete face slope breakwaters and rubble mound breakwaters are investigated through physical model tests in the present study. The reflection coefficients of oblique irregular waves are analyzed by the Modified Two-Point Method (MTPM) proposed by the authors. The results show that the wave reflection coefficient decreases with increasing wave frequency and incident angle or decreasing structure slope. The reflection coefficient frequency spectrum and its variation with Iribarren number are given in this paper. The paper also suggests an empirical 3-dimensional reflection coefficient spectrum, i.e. reflection coefficient directional spectrum, which can be used to illustrate quantitatively the variation of reflection coefficient with the incident angle and the Iribarren number for oblique irregular waves.
Generalized Asymptotic Pointwise Contractions and Nonexpansive Mappings Involving Orbits
Directory of Open Access Journals (Sweden)
Nicolae Adriana
2010-01-01
Full Text Available We give fixed point results for classes of mappings that generalize pointwise contractions, asymptotic contractions, asymptotic pointwise contractions, and nonexpansive and asymptotic nonexpansive mappings. We consider the case of metric spaces and, in particular, CAT spaces. We also study the well-posedness of these fixed point problems.
Componentwise Asymptotic Stability of Continuous-Time Interval Systems
Institute of Scientific and Technical Information of China (English)
赵胜民; 唐万生; 李光泉; 李文秀
2003-01-01
A special type of asymptotic (exponential) stability, namely componentwise asymptotic (exponential) stability for the continuous-time interval system is investigated. A set-valued map that represents the constraint of the state of the system is defined. And, by applying the viability theory of differential equation, sufficient and necessary conditions for the componentwise asymptotical (exponential) stability of this kind of systems are given.
Supersymmetric 3D gravity with torsion: asymptotic symmetries
Cvetkovic, B.; Blagojevic, M
2007-01-01
We study the structure of asymptotic symmetries in N=1+1 supersymmetric extension of three-dimensional gravity with torsion. Using a natural generalization of the bosonic anti-de Sitter asymptotic conditions, we show that the asymptotic Poisson bracket algebra of the canonical generators has the form of two independent super-Virasoro algebras with different central charges.
Asymptotic symmetries in 3d gravity with torsion
Blagojevic, M; Vasilic, M.
2003-01-01
We study the nature of asymptotic symmetries in topological 3d gravity with torsion. After introducing the concept of asymptotically anti-de Sitter configuration, we find that the canonical realization of the asymptotic symmetry is characterized by the Virasoro algebra with classical central charge, the value of which is the same as in general relativity: c=3l/2G.
Asymptotic estimates and compactness of expanding gradient Ricci solitons
Deruelle, Alix
2014-01-01
We first investigate the asymptotics of conical expanding gradient Ricci solitons by proving sharp decay rates to the asymptotic cone both in the generic and the asymptotically Ricci flat case. We then establish a compactness theorem concerning nonnegatively curved expanding gradient Ricci solitons.
Fields Institute International Symposium on Asymptotic Methods in Stochastics
Kulik, Rafal; Haye, Mohamedou; Szyszkowicz, Barbara; Zhao, Yiqiang
2015-01-01
This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Pólya distribution and its asymptotics in nucleation theory
Dubrovskii, V. G.
2014-02-01
A model of condensation-decay rate constants that are linear with respect to the number of monomers in the nucleus is considered. In a particular case of stable growth, this model leads to an exact solution of discrete kinetic equations of the theory of heterogeneous nucleation in the form of the Pólya distribution function. An asymptotic solution in the region of large nucleus sizes that satisfies the normalization condition and provides correct mean nucleus size has been found. It is shown that, in terms of the logarithmic invariant size, the obtained distribution has a universal time-independent form. The obtained solution, being more general than the double-exponent distribution used previously, describes both Gaussian and asymmetric distributions depending on the rate constant of condensation on a bare core. The obtained results are useful for modeling processes in some systems, in particular, the growth of linear chains, two-dimensional clusters, and filamentary nanocrystals.
Asymptotic expansions for large closed and loss queueing networks
Directory of Open Access Journals (Sweden)
Kogan Yaakov
2002-01-01
Full Text Available Loss and closed queueing network models have long been of interest to telephone and computer engineers and becoming increasingly important as models of data transmission networks. This paper describes a uniform approach that has been developed during the last decade for asymptotic analysis of large capacity networks with product form of the stationary probability distribution. Such a distribution has an explicit form up to the normalization constant, or the partition function. The approach is based on representing the partition function as a contour integral in complex space and evaluating the integral using the saddle point method and theory of residues. This paper provides an introduction to the area and a review of recent work.
Asymptotic dynamics of three-dimensional gravity
Donnay, Laura
2016-01-01
These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\\mathbb R)\\times SL(2,\\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime.
The Asymptotic Safety Scenario in Quantum Gravity
Directory of Open Access Journals (Sweden)
Niedermaier Max
2006-12-01
Full Text Available The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
Asymptotically Honest Confidence Regions for High Dimensional
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
While variable selection and oracle inequalities for the estimation and prediction error have received considerable attention in the literature on high-dimensional models, very little work has been done in the area of testing and construction of confidence bands in high-dimensional models. However......, in a recent paper van de Geer et al. (2014) showed how the Lasso can be desparsified in order to create asymptotically honest (uniform) confidence band. In this paper we consider the conservative Lasso which penalizes more correctly than the Lasso and hence has a lower estimation error. In particular, we...... of the asymptotic covariance matrix of an increasing number of parameters which is robust against conditional heteroskedasticity. To our knowledge we are the first to do so. Next, we show that our confidence bands are honest over sparse high-dimensional sub vectors of the parameter space and that they contract...
Asymptotically Lifshitz brane-world black holes
International Nuclear Information System (INIS)
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: ► Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. ► Studying the thermodynamical behavior of asymptotically Lifshitz black holes. ► Showing that the entropy imposes the critical exponent z to be bounded from above. ► Discussing the phase transition for different spatial topologies.
Asymptotically Lifshitz Brane-World Black Holes
Ranjbar, Arash; Shahidi, Shahab
2012-01-01
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We show that although the Lifshitz space-time cannot be considered as a vacuum solution of the RSII brane-world, the asymptotically Lifshitz solution can. We then study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the condition on the positivity of entropy imposes an upper bound on the critical exponent $z$. This maximum value of $z$ corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed.
Asymptotically anti-de Sitter Proca Stars
Duarte, Miguel
2016-01-01
We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully non-linear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in $5$ dimensions.
Variational Asymptotic Micromechanics Modeling of Composite Materials
Tang, Tian
2008-01-01
The issue of accurately determining the effective properties of composite materials has received the attention of numerous researchers in the last few decades and continues to be in the forefront of material research. Micromechanics models have been proven to be very useful tools for design and analysis of composite materials. In the present work, a versatile micromechanics modeling framework, namely, the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), has been invented a...
Lattice Quantum Gravity and Asymptotic Safety
Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.
2016-01-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we identify the target symmetry as the Hamiltonian canonical symmetry, which is closely related to, but n...
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan; Pawlowski, Jan M.
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christia...
Asymptotic completeness in QED. Pt. 1
International Nuclear Information System (INIS)
Projection operators onto the asymptotic scattering states are defined in the space of quasilocal states of QED in a Gupta-Bleuler formulation. They are obtained as weak limits for t → ±∞ of expressions formed with interacting fields, in close analogy to the LSZ expressions known from field theories without infrared problems. It is shown that these limits exist in perturbative QED and are equal to the identity. (orig.)
Asymptotic completeness in QED. Pt. 2
International Nuclear Information System (INIS)
Physical states and fields in QED are defined as limits in the sense of Wightman functions of states and composite fields of the Gupta-Bleuler formalism. A formulation of asymptotic completeness proposed in an earlier publication for the Gupta-Bleuler case is transferred to the physical state space and shown to be valid in perturbation theory. An application to the calculation of inclusive cross sections is discussed. (orig.)
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Asymptotics of high order noise corrections
Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre
1999-01-01
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.
Asymptotic elastic energy in simple metals
International Nuclear Information System (INIS)
The asymptotic form of the elastic binding energy ΔEsup(as)(R) between two Mg atoms in Al is expressed as a product of a lattice Green function and the dipole force tensor P. The quantity P is obtained by a nearly free electron model in which the impurity effect is introduced by a screened Ashcroft pseudopotential characterized by an excess charge ΔZ and a core radius rsub(j). (author)
On DIS Wilson coefficients in N=4 super Yang–Mills theory
International Nuclear Information System (INIS)
In this Letter we evaluate Wilson coefficients for “deep inelastic scattering” (DIS) in N=4 SYM theory at NLO in perturbation theory, using as a probe an R-symmetry conserved current. They exhibit uniform transcendentality and coincide with the piece of highest transcendentality in the corresponding QCD Wilson coefficients. We extract from the QCD result a NNLO prediction for the N=4 SYM Wilson coefficient, and comment on the features of its Regge limit asymptotics
The Asymptotic Regime of High Density QCD
Gay-Ducati, M B
2000-01-01
We discuss the distinct approaches for high density QCD (hdQCD) in the asymptotic regime of large values of parton density. We derive the AGL equation for running coupling constant and obtain the asymptotic solution, demonstrating that the property of partial saturation of the solution of the AGL equation is not modified by the running of the coupling constant. We show that in this kinematical regime, the solution of the AGL equation coincides with the solution of an evolution equation, obtained recently using the McLerran-Venugopalan approach. Using the asymptotic behavior of the gluon distribution we calculate the $F_2$ structure function assuming first that the leading twist relation between these two quantities is valid and second that this relation is modified by the higher twist terms associated to the unitarity corrections. In the first case we obtain that the corresponding $F_2$ structure function is linearly proportional to $ln s$, which agrees with the results obtained recently by Kovchegov using a ...
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
Asymptotics of the instantons of Painleve I
Garoufalidis, Stavros; Kapaev, Andrei; Marino, Marcos
2010-01-01
The 0-instanton solution of Painlev\\'e I is a sequence $(u_{n,0})$ of complex numbers which appears universally in many enumerative problems in algebraic geometry, graph theory, matrix models and 2-dimensional quantum gravity. The asymptotics of the 0-instanton $(u_{n,0})$ for large $n$ were obtained by the third author using the Riemann-Hilbert approach. For $k=0,1,2,...$, the $k$-instanton solution of Painlev\\'e I is a doubly-indexed sequence $(u_{n,k})$ of complex numbers that satisfies an explicit quadratic non-linear recursion relation. The goal of the paper is three-fold: (a) to compute the asymptotics of the 1-instanton sequence $(u_{n,1})$ to all orders in $1/n$ by using the Riemann-Hilbert method, (b) to present formulas for the asymptotics of $(u_{n,k})$ for fixed $k$ and to all orders in $1/n$ using resurgent analysis, and (c) to confirm numerically the predictions of resurgent analysis. We point out that the instanton solutions display a new type of Stokes behavior, induced from the tritronqu\\'ee ...
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. no reference of conformal rescaling nor conformal spacetime is made, at least not explicitly. By investigating the Schwarzschild-de Sitter spacetime in spherical coordinates, we subsequently stipulate the fall-offs of the null tetrad and spin coefficients for asymptotically de Sitter spacetimes such that the terms which would give rise to the Bondi mass-loss due to energy carried by gravitational radiation (i.e. involving $\\sigma^o$) must be non-zero. After solving the vacuum Newman-Penrose equations asymptotically, we obtain the Bondi mass-loss formula by integrating the Bianchi identity involving $D'\\Psi_2$ over a compact 2-surface on $\\mathcal{I}$. Whilst our original intention was to study asymptotically de Sitter spacetimes, the use of spherical coordinates implies that this readily applies for $\\Lambd...
Institute of Scientific and Technical Information of China (English)
Rogerio Luiz Quintino de OLIVEIRA JUNIOR
2013-01-01
In this paper, we study the large time behavior of solutions of the parabolic semilinear equation∂tu−div(a(x)∇u)=−|u|αu in (0,∞) × RN , whereα>0 is constant and a ∈ C1b(RN) is a symmetric periodic matrix satisfying some ellipticity assumptions. Considering an integrable initial data u0 andα∈(2/N, 3/N), we prove that the large time behavior of solutions is given by the solution U (t, x) of the homogenized linear problem∂tU −div(ah∇U ) = 0, U (0) = Cδ, where ah is the homogenized matrix of a(x), C is a positive constant and δ is the Dirac measure at 0.
Directory of Open Access Journals (Sweden)
Elkum Nasser
2006-05-01
Full Text Available Abstract Background In this paper we propose the use of the within-subject coefficient of variation as an index of a measurement's reliability. For continuous variables and based on its maximum likelihood estimation we derive a variance-stabilizing transformation and discuss confidence interval construction within the framework of a one-way random effects model. We investigate sample size requirements for the within-subject coefficient of variation for continuous and binary variables. Methods We investigate the validity of the approximate normal confidence interval by Monte Carlo simulations. In designing a reliability study, a crucial issue is the balance between the number of subjects to be recruited and the number of repeated measurements per subject. We discuss efficiency of estimation and cost considerations for the optimal allocation of the sample resources. The approach is illustrated by an example on Magnetic Resonance Imaging (MRI. We also discuss the issue of sample size estimation for dichotomous responses with two examples. Results For the continuous variable we found that the variance stabilizing transformation improves the asymptotic coverage probabilities on the within-subject coefficient of variation for the continuous variable. The maximum like estimation and sample size estimation based on pre-specified width of confidence interval are novel contribution to the literature for the binary variable. Conclusion Using the sample size formulas, we hope to help clinical epidemiologists and practicing statisticians to efficiently design reliability studies using the within-subject coefficient of variation, whether the variable of interest is continuous or binary.
Ghosh, Saugata
2008-01-01
We derive bulk asymptotics of skew-orthogonal polynomials (sop) $\\pi^{\\bt}_{m}$, $\\beta=1$, 4, defined w.r.t. the weight $\\exp(-2NV(x))$, $V (x)=gx^4/4+tx^2/2$, $g>0$ and $t 0$, such that $\\epsilon\\leq (m/N)\\leq \\lambda_{\\rm cr}-\\epsilon$, where $\\lambda_{\\rm cr}$ is the critical value which separates sop with two cuts from those with one cut. Simultaneously we derive asymptotics for the recursive coefficients of skew-orthogonal polynomials. The proof is based on obtaining a finite term recur...
Institute of Scientific and Technical Information of China (English)
Hossain O. Yakhlef; Francisco Marcellán
2002-01-01
Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of Ln(Ω)Ln(Ω)-1 and Φn(z;Ω)Φn(z;Ω)-1 where Ω(z) = Ω(z) + zδ(z - w); |w| ＞ 1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, Ln ( @ ) means the leading coefficient of the orthonormal matrix polynomials Φn(z; @ ).Finally, we deduce the asymptotic behavior of Φn (w;Ω)Φn (w;Ω) * in the case when M=I.
Long-range asymptotic expansion of the diagonal Born-Oppenheimer correction
Przybytek, Michał; Jeziorski, Bogumił
2012-06-01
Formulas for the coefficients A6, A8, and A10 determining the long-range asymptotic behavior Ead(R)˜-A6R-6-A8R-8-A10R-10 of the diagonal Born-Oppenheimer (adiabatic) correction Ead(R) to the potential energy of a diatomic molecule are derived using two standard definitions of Ead(R). The first one is based on the explicit separation of the center-of-mass and rotational coordinates from the total Hamiltonian of a system, while the second definition uses the Born-Handy expression in a laboratory system of coordinates. Expressions for the asymptotic coefficients resulting from both definitions are proved to be equivalent. The obtained formulas are used to compute the asymptotics of the adiabatic correction for the ground state of the hydrogen molecule and for the helium dimer in the lowest quintet and singlet states. In the latter case basis sets up to 8-tuple zeta quality were used to adequately account for the electron correlation effects.
IS THE SAMPLE COEFFICIENT OF VARIATION A GOOD ESTIMATOR FOR THE POPULATION COEFFICIENT OF VARIATION?
Mahmoudvand, Rahim; Hassani, Hossein; Wilson, Rob
2007-01-01
In this paper, we obtain bounds for the population coefficient of variation (CV) in Bernoulli, Discrete Uniform, Normal and Exponential distributions. We also show that the sample coefficient of variation (cv) is not an accurate estimator of the population CV in the above indicated distributions. Finally we provide some suggestions based on the Maximum Likelihood Estimation to improve the population CV estimate.
Forward-smooth high-order uniform Aharonov–Bohm asymptotics
Berry, M. V.
2016-07-01
The Aharonov–Bohm (AB) function, describing a plane wave scattered by a flux line, is expanded asymptotically in a Fresnel-integral based series whose terms are smooth in the forward direction and uniformly valid in angle and flux. Successive approximations are valid for large distance r from the flux (or short wavelength) but are accurate even within one wavelength of it. Coefficients of all the terms are exhibited explicitly for the forward direction, enabling the high-order asymptotics to be understood in detail. The series is factorally divergent, with optimal truncation error exponentially small in r. Systematic resummation gives further exponential improvement. Terms of the series satisfy a resurgence relation: the high orders are related to the low orders. Discontinuities in the backward direction get smaller order by order, with systematic cancellation by successive terms. The relation to an earlier scheme based on the Cornu spiral is discussed.
Asymptotics for a generalization of Hermite polynomials
Alfaro, M; Peña, A; Rezola, M L
2009-01-01
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler--Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.
Large Degree Asymptotics of Generalized Bessel Polynomials
López, J. L.; Temme, Nico
2011-01-01
Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\\pm i/n$ are derived, and a new expansion in terms of modified Bessel fu...
Taming perturbative divergences in asymptotically safe gravity
Energy Technology Data Exchange (ETDEWEB)
Benedetti, Dario, E-mail: dbenedetti@perimeterinstitute.c [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada); Machado, Pedro F., E-mail: p.f.machado@uu.n [Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank, E-mail: Frank.Saueressig@cea.f [Institut de Physique Theorique, CEA Saclay, F-91191 Gif-Sur-Yvette Cedex (France); CNRS URA 2306, F-91191 Gif-Sur-Yvette Cedex (France)
2010-01-01
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.
BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
Liu Yue; Wang Zhengping
2007-01-01
This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N ＞ 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).
Homogenization and asymptotics for small transaction costs
Soner, H Mete
2012-01-01
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.
The ADM mass of asymptotically flat hypersurfaces
de Lima, Levi Lopes
2011-01-01
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.
Asymptotic behaviour of exclusive processes in QCD
International Nuclear Information System (INIS)
The main ideas, methods and results in the investigation of the asymptotic behaviour of exclusive processes are reviewed. We discuss power behaviour and its dependence on hadron quantum numbers, logarithmic corrections and properties of nonperturbative hadronic wave functions. Applications to meson and baryon form factors, strong, electromagnetic and weak decays of heavy mesons, elastic scattering, threshold behaviour of inclusive structure functions, etc., are described. Comparison of theoretical predictions with experimental data is made whenever possible. The review may be of interest to theoreticians, experimentalists and students specializing in elementary particle physics. The experts in this field can also find new results (nonleading logarithms, higher twist processes, novel applications, etc.). (orig.)
Asymptotic curved interface models in piezoelectric composites
Serpilli, Michele
2016-10-01
We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.
The rate of convergence of some asymptotically chi-square distributed statistics by Stein's method
Gaunt, Robert E.; Reinert, Gesine
2016-01-01
We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and establish some simple sufficient conditions for convergence rates of order $n^{-1}$ for smooth test functions. These general bounds are applied to Friedman's statistic for comparing $r$ treatments across $n$ trials and the family of power divergence statistics fo...
Dujardin, G. M.
2009-08-12
This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.
Transport Coefficients of Fluids
Eu, Byung Chan
2006-01-01
Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium.
Directory of Open Access Journals (Sweden)
Uğur YALÇIN
2004-02-01
Full Text Available In this study, quasi-optical scattering of finite source electromagnetic waves from a dielectric coated cylindrical surface is analysed with Physical Optics (PO approach. A linear electrical current source is chosen as the finite source. Reflection coefficient of the cylindrical surface is derived by using Geometrical Theory of Diffraction (GTD. Then, with the help of this coefficient, fields scattered from the surface are obtained. These field expressions are used in PO approach and surface scattering integral is determined. Evaluating this integral asymptotically, fields reflected from the surface and surface divergence coefficient are calculated. Finally, results obtained in this study are evaluated numerically and effects of the surface impedance to scattered fields are analysed. The time factor is taken as j te? in this study.
Asymptotic behaviour of electro-$\\Lambda$ spacetimes
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\\Lambda=0$. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with the Bondi mass-loss formula in any un...
Asymptotically Lifshitz brane-world black holes
Energy Technology Data Exchange (ETDEWEB)
Ranjbar, Arash, E-mail: a_ranjbar@sbu.ac.ir; Sepangi, Hamid Reza, E-mail: hr-sepangi@sbu.ac.ir; Shahidi, Shahab, E-mail: s_shahidi@sbu.ac.ir
2012-12-15
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: Black-Right-Pointing-Pointer Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. Black-Right-Pointing-Pointer Studying the thermodynamical behavior of asymptotically Lifshitz black holes. Black-Right-Pointing-Pointer Showing that the entropy imposes the critical exponent z to be bounded from above. Black-Right-Pointing-Pointer Discussing the phase transition for different spatial topologies.
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M.; Flachi, Antonino; Lemos, José P. S.
2016-06-01
There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti-de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti-de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M; Lemos, José P S
2016-01-01
There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to...
Lattice Quantum Gravity and Asymptotic Safety
Laiho, J; Coumbe, D; Du, D; Neelakanta, J T
2016-01-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we identify the target symmetry as the Hamiltonian canonical symmetry, which is closely related to, but not identical to, four-dimensional diffeomorphism invariance. After introducing and fine-tuning a non-trivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3/2, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue tha...
Numerical integration of asymptotic solutions of ordinary differential equations
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Asymptotic analysis of the Nörlund and Stirling polynomials
Directory of Open Access Journals (Sweden)
Mark Daniel Ward
2012-04-01
Full Text Available We provide a full asymptotic analysis of the N{\\"o}rlund polynomials and Stirling polynomials. We give a general asymptotic expansion---to any desired degree of accuracy---when the parameter is not an integer. We use singularity analysis, Hankel contours, and transfer theory. This investigation was motivated by a need for such a complete asymptotic description, with parameter 1/2, during this author's recent solution of Wilf's 3rd (previously Unsolved Problem.
Singularities in asymptotically anti-de Sitter spacetimes
Ishibashi, Akihiro; Maeda, Kengo
2012-01-01
We consider singularity theorems in asymptotically anti-de Sitter (AdS) spacetimes. In the first part, we discuss the global methods used to show geodesic incompleteness and see that when the conditions imposed in Hawking and Penrose's singularity theorem are satisfied, a singularity must appear in asymptotically AdS spacetime. The recent observations of turbulent instability of asymptotically AdS spacetimes indicate that AdS spacetimes are generically singular even if a closed trapped surfac...
Asymptotic parameterization in inverse limit spaces of dendrites
Hamilton, Brent
2012-01-01
In this paper, we study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point is periodic. Using symbolic dynamics, sufficient conditions for two rays in the inverse limit space to have asymptotic parameterizations are given. Being a topological invariant, the classification of asymptotic parameterizations would be a useful tool when d...
ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT
Institute of Scientific and Technical Information of China (English)
A.Eisinberg; G.Franzè; N.Salerno
2001-01-01
Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
The Frictional Coefficient of Bovine Knee Articular Cartilage
Institute of Scientific and Technical Information of China (English)
Qian Shan-hua; Ge Shi-rong; Wang Qing-liang
2006-01-01
The normal displacement of articular cartilage was measured under load and in sliding, and the coefficient of friction during sliding was measured using a UMT-2 Multi-Specimen Test System. The maximum normal displacement under load and the start-up frictional coefficient have similar tendency of variation with loading time. The sliding speed does not significantly influence the frictional coefficient of articular cartilage.
On the asymptotic methods for nuclear collective models
Gheorghe, A. C.; Raduta, A. A.
2009-01-01
Contractions of orthogonal groups to Euclidean groups are applied to analytic descriptions of nuclear quantum phase transitions. The semiclassical asymptotic of multipole collective Hamiltonians are also investigated.
Asymptotic stability of Riemann waves for conservation laws
Chen, G.-Q.; Frid, H.; Marta
We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in L∞ . Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.
ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS
Institute of Scientific and Technical Information of China (English)
ZHU Xiao-feng; LI Xiu-chun
2006-01-01
Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds are discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
Institute of Scientific and Technical Information of China (English)
WU Lei
2009-01-01
@@ Recently, Feng et al. claimed that "they have found the asymptotic self-similar parabolic solutions in gain medium of the normal GVD", where the evolution of optical pulses is governed by the following Ginzburg-Landau equation (GLE):[1
Narski Jacek; Negulescu Claudia; Maldarella Dario; Degond Pierre; Deluzet Fabrice; Parisot Martin
2011-01-01
International audience In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, ellip-tic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed in this ...
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Asymptotic Behavior of a Viscous Liquid-Gas Model with Mass-Dependent Viscosity and Vacuum
liu, Qingqing
2011-01-01
In this paper, we consider two classes of free boundary value problems of a viscous two-phase liquid-gas model relevant to the flow in wells and pipelines with mass-dependent viscosity coefficient. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. We obtain the asymptotic behavior and decay rates of the mass functions $n(x,t)$,\\$m(x,t)$ when the initial masses are assumed to be connected to vacuum both discontinuously and continuously, which improves the corresponding result about Navier-Stokes equations in \\cite{Zhu}.
Asymptotic behavior of a viscous liquid-gas model with mass-dependent viscosity and vacuum
Liu, Qingqing; Zhu, Changjiang
In this paper, we consider two classes of free boundary value problems of a viscous two-phase liquid-gas model relevant to the flow in wells and pipelines with mass-dependent viscosity coefficient. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. We obtain the asymptotic behavior and decay rates of the mass functions n(x,t), m(x,t) when the initial masses are assumed to be connected to vacuum both discontinuously and continuously, which improves the corresponding result about Navier-Stokes equations in Zhu (2010) [23].
Asymptotic Behavior of a Viscous Liquid-Gas Model with Mass-Dependent Viscosity and Vacuum
Liu, Qingqing; Zhu, Changjiang
2011-01-01
In this paper, we consider two classes of free boundary value problems of a viscous two-phase liquid-gas model relevant to the flow in wells and pipelines with mass-dependent viscosity coefficient. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. We obtain the asymptotic behavior and decay rates of the mass functions $n(x,t)$,\\$m(x,t)$ when the initial masses are assumed to be connected to vacuum both discontinuously and continuously, which improve...
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
Asymptotically thermal responses for smoothly switched detectors
Fewster, Christopher J; Louko, Jorma
2015-01-01
Thermal phenomena in quantum field theory can be detected with the aid of particle detectors coupled to quantum fields along stationary worldlines, by testing whether the response of such a detector satisfies the detailed balance version of the KMS condition at a constant temperature. This relation holds when the interaction between the field and the detector has infinite time duration. Operationally, however, detectors interact with fields for a finite amount of time, controlled by a switching function of compact support, and the KMS detailed balance condition cannot hold exactly for finite time interactions at arbitrarily large detector energy gap. In this large energy gap regime, we show that, for an adiabatically switched Rindler detector, the Unruh temperature emerges asymptotically after the detector and the field have interacted for a time that is polynomially long in the large energy. We comment on the significance of the adiabaticity assumption in this result.
Loop Quantum Gravity and Asymptotically Flat Spaces
Arnsdorf, Matthias
2002-12-01
Remarkable progress has been made in the field of non-perturbative (loop) quantum gravity in the last decade or so and it is now a rigorously defined kinematical theory (c.f. [5] for a review and references). We are now at the stage where physical applications of loop quantum gravity can be studied and used to provide checks for the consistency of the quantisation programme. Equally, old fundamental problems of canonical quantum gravity such as the problem of time or the interpretation of quantum cosmology need to be reevaluated seriously. These issues can be addressed most profitably in the asymptotically flat sector of quantum gravity. Indeed, it is likely that we should obtain a quantum theory for this special case even if it is not possible to quantise full general relativity. The purpose of this summary is to advertise the extension of loop quantum gravity to this sector that was developed in [1]...
The asymptotic safety scenario in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Saueressig, Frank [Institute of Physics, University of Mainz, D-55099 Mainz (Germany)
2011-07-01
Asymptotic safety offers the possibility that gravity constitutes a consistent and predictive quantum field theory within Wilsons generalized framework of renormalization. The key ingredient of this scenario is a non-trivial fixed point of the gravitational renormalization group flow which governs the UV behavior of the theory. The fixed point itself thereby guarantees the absence of unphysical UV divergences while its associated finite-dimensional UV-critical surface ensures the predictivity of the resulting quantum theory. This talk summarizes the evidence for the existence of such a fixed point, which emerged from the flow equation for the effective average action, the gravitational beta-functions in 2+{epsilon} dimensions, the 2-Killing vector reduction of the gravitational path-integral and lattice simulations. Possible phenomenological consequences are discussed in detail.
Modeling of nanoplastic by asymptotic homogenization method
Institute of Scientific and Technical Information of China (English)
张为民; 何伟; 李亚; 张平; 张淳源
2008-01-01
The so-called nanoplastic is a new simple name for the polymer/layered silicate nanocomposite,which possesses excellent properties.The asymptotic homogenization method(AHM) was applied to determine numerically the effective elastic modulus of a two-phase nanoplastic with different particle aspect ratios,different ratios of elastic modulus of the effective particle to that of the matrix and different volume fractions.A simple representative volume element was proposed,which is assumed that the effective particles are uniform well-aligned and perfectly bonded in an isotropic matrix and have periodic structure.Some different theoretical models and the experimental results were compared.The numerical results are good in agreement with the experimental results.
Chiral fermions in asymptotically safe quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2016-05-15
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)
Asymptotic theory of quantum statistical inference
Hayashi, Masahito
Part I: Hypothesis Testing: Introduction to Part I -- Strong Converse and Stein's lemma in quantum hypothesis testing/Tomohiro Ogawa and Hiroshi Nagaoka -- The proper formula for relative entropy and its asymptotics in quantum probability/Fumio Hiai and Dénes Petz -- Strong Converse theorems in Quantum Information Theory/Hiroshi Nagaoka -- Asymptotics of quantum relative entropy from a representation theoretical viewpoint/Masahito Hayashi -- Quantum birthday problems: geometrical aspects of Quantum Random Coding/Akio Fujiwara -- Part II: Quantum Cramèr-Rao Bound in Mixed States Model: Introduction to Part II -- A new approach to Cramèr-Rao Bounds for quantum state estimation/Hiroshi Nagaoka -- On Fisher information of Quantum Statistical Models/Hiroshi Nagaoka -- On the parameter estimation problem for Quantum Statistical Models/Hiroshi Nagaoka -- A generalization of the simultaneous diagonalization of Hermitian matrices and its relation to Quantum Estimation Theory/Hiroshi Nagaoka -- A linear programming approach to Attainable Cramèr-Rao Type Bounds/Masahito Hayashi -- Statistical model with measurement degree of freedom and quantum physics/Masahito Hayashi and Keiji Matsumoto -- Asymptotic Quantum Theory for the Thermal States Family/Masahito Hayashi -- State estimation for large ensembles/Richard D. Gill and Serge Massar -- Part III: Quantum Cramèr-Rao Bound in Pure States Model: Introduction to Part III-- Quantum Fisher Metric and estimation for Pure State Models/Akio Fujiwara and Hiroshi Nagaoka -- Geometry of Quantum Estimation Theory/Akio Fujiwara -- An estimation theoretical characterization of coherent states/Akio Fujiwara and Hiroshi Nagaoka -- A geometrical approach to Quantum Estimation Theory/Keiji Matsumoto -- Part IV: Group symmetric approach to Pure States Model: Introduction to Part IV -- Optimal extraction of information from finite quantum ensembles/Serge Massar and Sandu Popescu -- Asymptotic Estimation Theory for a Finite-Dimensional Pure
Quantum defect theory and asymptotic methods
International Nuclear Information System (INIS)
It is shown that quantum defect theory provides a basis for the development of various analytical methods for the examination of electron-ion collision phenomena, including di-electronic recombination. Its use in conjuction with ab initio calculations is shown to be restricted by problems which arise from the presence of long-range non-Coulomb potentials. Empirical fitting to some formulae can be efficient in the use of computer time but extravagant in the use of person time. Calculations at a large number of energy points which make no use of analytical formulae for resonance structures may be made less extravagant in computer time by the development of more efficient asymptotic methods. (U.K.)
Chiral fermions in asymptotically safe quantum gravity
Meibohm, J.; Pawlowski, J. M.
2016-05-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
Vortex shedding by matched asymptotic vortex method
Guo, Xinjun; Mandre, Shreyas
2014-11-01
An extension of the Kutta condition, using matched asymptotic expansion applied to the Navier-Stokes equations, is presented for flow past a smooth body at high Reynolds number. The goal is to study the influence of unsteady fluid dynamical effects like leading edge vortex, unsteady boundary layer separation, etc. In order to capture accurately the location and strength of vortex shedding, the simplified Navier-Stokes equations in the form of boundary layer approximation are solved in the thin inner region close to the solid body. In the outer region far from the structure, the vortex methods are applied, which significantly reduces the computational cost compared to CFD in the whole domain. With this method, the flow past an airfoil with two degrees of freedom, pitching and heaving, is investigated.
Asymptotic Behavior of Excitable Cellular Automata
Durrett, R; Durrett, Richard; Griffeath, David
1993-01-01
Abstract: We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, the "shape" of its neighbor set, threshold value for contact updating, and number of possible states per site. GHM and CCA are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Earlier work by Fisch, Gravner, and Griffeath studied the ergodic behavior of these excitable cellular automata on Z^2, and identified two distinct (but closely-related) elaborate phase portraits as the parameters vary. In particular, they noted the emergence of asymptotic phase diagrams (and Euclidean dynamics) in a well-defined threshold-range scaling limit. In this study we present several rigorous results and som...
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Entropy Production during Asymptotically Safe Inflation
Directory of Open Access Journals (Sweden)
Martin Reuter
2011-01-01
Full Text Available The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.
Traversable asymptotically flat wormholes in Rastall gravity
Moradpour, H
2016-01-01
Having introduced the Rastall gravitational theory, and by virtue of the fact that this theory has two unknown parameters, we take the Newtonian limit to define a new parameter for Rastall gravitational theory; a useful dimensionless parameter for simplifying calculations in the Rastall framework. Equipped with basics of the theory, we study the properties of traversable asymptotically flat wormholes in Rastall framework. Then, we investigate the possibility of supporting such geometries by a source with the same state parameter as that of the baryonic matters. Our survey indicates that the parameters of Rastall theory affect the wormhole parameters. It also shows the weak energy condition is violated for all of the studied cases. We then come to investigate the possibility of supporting such geometries by a source of negative energy density and the same state parameter as that of dark energy. Such dark energy-like sources have positive radial and transverse pressures.
Black holes in Asymptotically Safe Gravity
Saueressig, Frank; D'Odorico, Giulio; Vidotto, Francesca
2015-01-01
Black holes are among the most fascinating objects populating our universe. Their characteristic features, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. In this note we observe that the renormalization group improved Schwarzschild black holes constructed by Bonanno and Reuter within Weinberg's asymptotic safety program constitute a prototypical example of a Hayward geometry used to model non-singular black holes within quantum gravity phenomenology. Moreover, they share many features of a Planck star: their effective geometry naturally incorporates the one-loop corrections found in the effective field theory framework, their Kretschmann scalar is bounded, and the black hole singularity is replaced by a regular de Sitter patch. The role of the cosmological constant in the renormalization group improvement process is briefly discussed.
Institute of Scientific and Technical Information of China (English)
徐美荣; 时宝
2004-01-01
In this paper, we first consider differential equations with several delays inthe neutral term of the form d/dt[y(t)+∑j=1L piy(t-ki)-∑j=1Mrjy(t-Pj)]+q(t)y(t-r)=0 for t∈R+,(1*) study various cases of coefficients in the neutral term and obtain the asymptotic behavior for nonoscillatory solution of (1") under some hypotheses. Moreover,we consider reaction-diffusion differential equations with several delays in the neutral term of the form α/αt[u(t,x)+∑i=1L piu(t-ki,x)-∑j=1M rju(t-Pj,x)]+q(t,x)u(t-r,x)=a2△u(t,x)for (t,x)∈R+ ×Ω. We also study various cases of coefficients in the neutral term and obtain the asymptotic behavior for nonoscillatory solutionun of (2*)under some hypotheses.
DEFF Research Database (Denmark)
Hubalek, Friedrich; Posedel, Petra
We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressi......We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit...... expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function approach for a bivariate model, that is not a diffusion, but admits jumps. We do not use ergodicity arguments. We assume that both, logarithmic returns and instantaneous variance are observed on a...... discrete grid of fixed width, and the observation horizon tends to infinity. This anaysis is a starting point and benchmark for further developments concerning optimal martingale estimating functions, and for theoretical and empirical investigations, that replace the (actually unobserved) variance process...
Khirevich, Siarhei; Höltzel, Alexandra; Tallarek, Ulrich
2011-06-28
We study the time and length scales of hydrodynamic dispersion in confined monodisperse sphere packings as a function of the conduit geometry. By a modified Jodrey-Tory algorithm, we generated packings at a bed porosity (interstitial void fraction) of ε=0.40 in conduits with circular, rectangular, or semicircular cross section of area 100πd(p)(2) (where d(p) is the sphere diameter) and dimensions of about 20d(p) (cylinder diameter) by 6553.6d(p) (length), 25d(p) by 12.5d(p) (rectangle sides) by 8192d(p) or 14.1d(p) (radius of semicircle) by 8192d(p), respectively. The fluid-flow velocity field in the generated packings was calculated by the lattice Boltzmann method for Péclet numbers of up to 500, and convective-diffusive mass transport of 4×10(6) inert tracers was modelled with a random-walk particle-tracking technique. We present lateral porosity and velocity distributions for all packings and monitor the time evolution of longitudinal dispersion up to the asymptotic (long-time) limit. The characteristic length scales for asymptotic behaviour are explained from the symmetry of each conduit's velocity field. Finally, we quantify the influence of the confinement and of a specific conduit geometry on the velocity dependence of the asymptotic dispersion coefficients. PMID:21576163
Rook numbers and the normal ordering problem
Varvak, Anna
2004-01-01
For an element $w$ in the Weyl algebra generated by $D$ and $U$ with relation $DU=UD+1$, the normally ordered form is $w=\\sum c_{i,j}U^iD^j$. We demonstrate that the normal order coefficients $c_{i,j}$ of a word $w$ are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients $c_{i,j}$. We calculate the Weyl binomial coefficients: normal order coefficients of the element ...
Tiemann, Eberhard; Pachomow, Evgenij; Riehle, Fritz; Sterr, Uwe
2015-01-01
We present calculations of the Zeeman effect of narrow photoassociation lines of $^{40}$Ca near the $^3$P$_1$ + $^1$S$_0$ asymptote. Using a coupled-channel model we find a nonlinear Zeeman effect that even at low fields of a few mT amounts to several kHz. With this model we analyze previous measurements and give corrected long range dispersion coefficients of the $^3\\Pi_{u}$ and $^3\\Sigma^+ _{u}$ states.
Schlemm, Eckhard
2015-01-01
The Bak--Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness...
A new coefficient of concordance with applications to biosignal analysis
Xu, Weichao; Chen, Zhaoguo; Liu, Wenqing
2015-12-01
In this paper we propose a novel concordance coefficients called Order Statistics Concordance Coefficients based on order statistics and Pearson's Product Moment Correlation Coefficient. For comparison, we also construct other three similar index based on Average Pearson's Product Moment Correlation Coefficient, Kendall's Concordance Coefficients, Average Kendall's tau. We propose Multivariate Normal Model to estimate the correlation coefficient, Linear Model and Nonlinear Model to model the linear and nonlinear association between multichannel signals, And we also apply the concordance coefficients to biosignal analysis developed a new organizational index for quantifying organization of AF. Statistical evidences suggest that (a) Order Statistics Concordance Coefficients have better robust than other three index; (b) capable of distinguishing fibrillatory rhythms from nonfibrillatory rhythms, such as Atiral flutter; (c) can reflect the effectiveness of adenosine, a drug commonly used during electrophysiological procedures; and (d) perform better than other three concordance coefficients.
A coefficient average approximation towards Gutzwiller wavefunction formalism
Liu, Jun; Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2015-06-01
Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.
Coefficient Omega Bootstrap Confidence Intervals: Nonnormal Distributions
Padilla, Miguel A.; Divers, Jasmin
2013-01-01
The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
Directory of Open Access Journals (Sweden)
Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
Asymptotic variance of grey-scale surface area estimators
DEFF Research Database (Denmark)
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...
An asymptotic solution of large-N QCD
Directory of Open Access Journals (Sweden)
Bochicchio Marco
2014-01-01
Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
Asymptotic Hyperstability of Dynamic Systems with Point Delays
Directory of Open Access Journals (Sweden)
M. De la Sen
2005-01-01
Full Text Available It is proved that a linear time-invariant system with internal point delays is asymptotically hyperstable independent of the delays if an associate delay-free system is asymptotically hyperstable and the delayed dynamics are sufficiently small.
Asymptotic behavior of support points for planar curves
Nikonorov, Yu G
2010-01-01
In this paper we prove a universal inequality described the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some (partially known) assertions on the asymptotic of the mean value points for various classical analytic theorems. Some open questions are formulated.
Numerical and asymptotic aspects of parabolic cylinder functions
Temme, N.M.
2000-01-01
Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are
Asymptotic Formula for Quantum Harmonic Oscillator Tunneling Probabilities
Jadczyk, Arkadiusz
2015-10-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Asymptotic formula for quantum harmonic oscillator tunneling probabilities
Jadczyk, Arkadiusz
2015-01-01
Using simple methods of asymptotic analysis it is shown that for a quantum harmonic oscillator in n-th energy eigenstate the probability of tunneling into the classically forbidden region obeys an unexpected but simple asymptotic formula: the leading term is inversely proportional to the cube root of n.
Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
Wei Shi-long; Guo Wei-ping
2015-01-01
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
Einstein-Yang-Mills theory : I. Asymptotic symmetries
Barnich, Glenn
2013-01-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four dimensional asymptotically flat case.
Uniform asymptotic estimates of transition probabilities on combs
Bertacchi, Daniela; Zucca, Fabio
2000-01-01
We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than local limit estimates. Our results also point out the impossibility of getting Jones-type non-Gaussian estimates.
Global asymptotic stability of cellular neural networks with multiple delays
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.
Global asymptotic stability of delay BAM neural networks with impulses
Energy Technology Data Exchange (ETDEWEB)
Lou Xuyang [Research Center of Control Science and Engineering, Southern Yangtze University, 1800 Lihu Road, Wuxi, Jiangsu 214122 (China); Cui Baotong [Research Center of Control Science and Engineering, Southern Yangtze University, 1800 Lihu Road, Wuxi, Jiangsu 214122 (China)]. E-mail: btcui@sohu.com
2006-08-15
The global asymptotic stability of delay bi-directional associative memory neural networks with impulses are studied by constructing suitable Lyapunov functional. Sufficient conditions, which are independent to the delayed quantity, are obtained for the global asymptotic stability of the neural networks. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.
Asymptotic behavior of the number of Eulerian orientations of graphs
Isaev, Mikhail
2011-01-01
We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In addition, we establish some new properties of the Laplacian matrix, as well as an estimate of a conditionality of matrices with the asymptotic diagonal predominance
Asymptotic analysis, Working Note No. 1: Basic concepts and definitions
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universite Claude Bernard Lyon 1, 69 - Villeurbanne (France). Lab. d`Analyse Numerique; Kaper, H.G. [Argonne National Lab., IL (United States)
1993-07-01
In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.
Confidence Intervals for Squared Semipartial Correlation Coefficients: The Effect of Nonnormality
Algina, James; Keselman, H. J.; Penfield, Randall D.
2010-01-01
The increase in the squared multiple correlation coefficient ([delta]R[superscript 2]) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size…
Recent results on the 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, J.; Freitas A. de; Raab, C.; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ablinger, J.; Hasselhuhn, A.; Round, M.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Manteuffel, A. von [Mainz Univ. (Germany). PRISMA Cluster of Excellence; Mainz Univ. (Germany). Inst. fuer Physik
2013-07-15
We report on recent progress in the calculation of the 3-loop massive Wilson coefficients in deep-inelastic scattering at general values of N for neutral and charged current reactions in the asymptotic region Q{sup 2}>>m{sup 2}.
Equation of state for hard sphere fluids offering accurate virial coefficients
Tian, Jianxiang; Gui, Yuanxing; Mulero, A
2016-01-01
The asymptotic expansion method is extended by using currently available accurate values for the first ten virial coefficients for hard sphere fluids. It is then used to yield an equation of state for hard sphere fluids, which accurately represents the currently accepted values for the first sixteen virial coefficients and compressibility factor data in both the stable and the metastable regions of the phase diagram.
Asymptotic performance of the quadratic discriminant function to skewed training samples.
Adebanji, Atinuke; Asamoah-Boaheng, Michael; Osei-Tutu, Olivia
2016-01-01
This study investigates the asymptotic performance of the quadratic discriminant function (QDF) under skewed training samples. The main objective of this study is to evaluate the performance of the QDF under skewed distribution considering different sample size ratios, varying the group centroid separators and the number of variables. Three populations [Formula: see text] with increasing group centroid separator function were considered. A multivariate normal distributed data was simulated with MatLab R2009a. There was an increase in the average error rates of the sample size ratios 1:2:2 and 1:2:3 as the total sample size increased asymptotically in the skewed distribution when the centroid separator increased from 1 to 3. The QDF under the skewed distribution performed better for the sample size ratio 1:1:1 as compared to the other sampling ratios and under centroid separator [Formula: see text]. PMID:27652103
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
Hod, Shahar
2015-01-01
The spheroidal harmonics $S_{lm}(\\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues $\\{A_{lm}(c)\\}$ of these functions have been determined by many authors. However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\\to\\infty$ with a fixed value of $c$, or to the complementary regime $|c|\\to\\infty$ with a fixed value of $m$. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both $m$ and $c$. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit $m\\to\\infty$ and $|c|\\to\\infty$ with a fixed $m/c$ ratio.
Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals
Pan, Chi-Ruei; Chai, Jeng-Da
2013-01-01
Aiming to remedy the incorrect asymptotic behavior of conventional semilocal exchange-correlation (XC) density functionals for finite systems, we propose an asymptotic correction scheme, wherein an exchange density functional whose functional derivative has the correct (-1/r) asymptote can be directly added to any semilocal density functional. In contrast to semilocal approximations, our resulting exchange kernel in reciprocal space exhibits the desirable singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for describing the excitonic effects in non-metallic solids. By applying this scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the properties that are sensitive to the asymptote are significantly improved, while the predictions of the properties that are insensitive to the asymptote remain essentially the same as PBE. Relative to the popular model XC potential scheme, our scheme is sig...
Prestarlike functions with negative coefficients
Directory of Open Access Journals (Sweden)
H. Silverman
1979-01-01
Full Text Available The extreme points for prestarlike functions having negative coefficients are determined. Coefficient, distortion and radii of univalence, starlikeness, and convexity theorems are also obtained.
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
Hale, Nicholas
2014-02-06
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.
QCD Condensates and Holographic Wilson Loops for Asymptotically AdS Spaces
Energy Technology Data Exchange (ETDEWEB)
Quevedo, R. Carcasses [Instituto Balseiro, Centro Atomico Bariloche, 8400 San Carlos de Bariloche (Argentina); CONICET, Rivadavia 1917, 1033 Buenos Aires (Argentina); Goity, Jose L. [Hampton University, Hampton, VA 23668 (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Trinchero, Roberto C. [Instituto Balseiro, Centro Atomico Bariloche, 8400 San Carlos de Bariloche (Argentina); CONICET, Rivadavia 1917, 1033 Buenos Aires (Argentina)
2014-02-01
The minimization of the Nambu-Goto (NG) action for a surface whose contour defines a circular Wilson loop of radius a placed at a finite value of the coordinate orthogonal to the border is considered. This is done for asymptotically AdS spaces. The condensates of dimension n = 2, 4, 6, 8, and 10 are calculated in terms of the coefficients in the expansion in powers of the radius a of the on-shell subtracted NG action for small a->0. The subtraction employed is such that it presents no conflict with conformal invariance in the AdS case and need not introduce an additional infrared scale for the case of confining geometries. It is shown that the UV value of the gluon condensates is universal in the sense that it only depends on the first coefficients of the difference with the AdS case.
Gorenstein Hilbert Coefficients
Khoury, Sabine El
2012-01-01
We prove upper and lower bounds for all the coefficients in the Hilbert Polynomial of a graded Gorenstein algebra $S=R/I$ with a quasi-pure resolution over $R$. The bounds are in terms of the minimal and the maximal shifts in the resolution of $R$ . These bounds are analogous to the bounds for the multiplicity found in \\cite{S} and are stronger than the bounds for the Cohen Macaulay algebras found in \\cite{HZ}.
Asymptotics of Entropy Rate in Special Families of Hidden Markov Chains
Han, Guangyue
2008-01-01
We derive an asymptotic formula for entropy rate of a hidden Markov chain around a "weak Black Hole". We also discuss applications of the asymptotic formula to the asymptotic behaviors of certain channels.
Qualitative and Asymptotic Theory of Detonations
Faria, Luiz
2014-11-09
Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
Extended Analytic Device Optimization Employing Asymptotic Expansion
Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred
2013-01-01
Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.
Asymptotic Orbits in Barred Spiral Galaxies
Harsoula, Maria; Contopoulos, George
2010-01-01
We study the formation of the spiral structure of barred spiral galaxies, using an $N$-body model. The evolution of this $N$-body model in the adiabatic approximation maintains a strong spiral pattern for more than 10 bar rotations. We find that this longevity of the spiral arms is mainly due to the phenomenon of stickiness of chaotic orbits close to the unstable asymptotic manifolds originated from the main unstable periodic orbits, both inside and outside corotation. The stickiness along the manifolds corresponding to different energy levels supports parts of the spiral structure. The loci of the disc velocity minima (where the particles spend most of their time, in the configuration space) reveal the density maxima and therefore the main morphological structures of the system. We study the relation of these loci with those of the apocentres and pericentres at different energy levels. The diffusion of the sticky chaotic orbits outwards is slow and depends on the initial conditions and the corresponding Jaco...
Asymptotic dynamics of inertial particles with memory
Langlois, Gabriel Provencher; Haller, George
2014-01-01
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $\\mathcal O(\\epsilon)$-close to the fluid velocity, where $0<\\epsilon\\ll 1$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of existence and uniqueness of global solutions to the Maxey--Riley equation, a nonlinear system of fractional-order differential equ...
Truly Minimal Unification Asymptotically Strong Panacea ?
Aulakh, Charanjit S
2002-01-01
We propose Susy GUTs have a UV {\\it{attractor}} at $E\\sim \\Lambda_{cU} \\sim 10^{17} GeV $ where gauge symmetries ``confine'' forming singlet condensates at scales $E\\sim\\Lambda_{cU}$. The length $l_U\\sim \\Lambda_{cU}^{-1}$ characterizies the {\\it{size}} of gauge non- singlet particles yielding a picture dual to the Dual Standard model of Vachaspati. This Asymptotic Slavery (AS) fixed point is driven by realistic Fermion Mass(FM) Higgs content which implies AS. This defines a dynamical morphogenetic scenario dependent on the dynamics of UV strong N=1 Susy Gauge-Chiral(SGC) theories. Such systems are already understood in the AF case but ignored in the AS case. Analogy to the AFSGC suggests the perturbative SM gauge group of the Grand Desert confines at GUT scales i.e GUT symmetry is ``non-restored''. Restoration before confinement and self-inconsistency are the two other (less likely) logical possibilities. Truly Minimal (TM) SU(5) and SO(10) models with matter and FM Higgs only are defined; AM (adjoint multip...
Asymptotic dynamics of reflecting spiral waves.
Langham, Jacob; Biktasheva, Irina; Barkley, Dwight
2014-12-01
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as pointlike objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this velocity and may often result in a reflection of the drift trajectory. Such reflections have diverse characteristics and are known to be highly nonspecular in general. In this context we apply the theory of response functions, which via numerically computable integrals, reduces the reaction-diffusion equations governing the whole excitable medium to the dynamics of just the rotation center and rotation phase of a spiral wave. Spiral reflection trajectories are computed by this method for both small- and large-core spiral waves in the Barkley model. Such calculations provide insight into the process of reflection as well as explanations for differences in trajectories across parameters, including the effects of incidence angle and forcing amplitude. Qualitative aspects of these results are preserved far beyond the asymptotic limit of weak boundary effects and slow resonant drift. PMID:25615159
Thermodynamics of Vacuum of Asymptotic Subspace
Bogdanov, A V; Bogdanov, Alexander V.; Gevorkyan, Ashot S.
1997-01-01
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the extended space. This wave functional obeys some stochastic differential equation (SDE). Based on the nonlinear Langevin type SDE of second order, introduced in the functional space R{W(t)}, the variables in original equation are separated. The general measure in the space R{W(t)} of the Fokker-Planck type is obtained and expression for total wave function (wave mixture) of random QRHO is constructed as functional expansion over the stochastic basis set. The pertinent transition matrix S_br is constructed. For Wiener type measure W(t) of functional space the exact representation for ''vacuum-vacuum'' transition probability is obtained. The thermodynamics of vacuum is described in detail for the asymptotic space R1_as. The exact values for Energy, shift and expansion of ground sta...
Long-Time Asymptotics of a Bohmian Scalar Quantum Field in de Sitter Space-Time
Tumulka, Roderich
2015-01-01
We consider a model quantum field theory with a scalar quantum field in de Sitter space-time in a Bohmian version with a field ontology, i.e., an actual field configuration $\\varphi({\\bf x},t)$ guided by a wave function on the space of field configurations. We analyze the asymptotics at late times ($t\\to\\infty$) and provide reason to believe that for more or less any wave function and initial field configuration, every Fourier coefficient $\\varphi_{\\bf k}(t)$ of the field is asymptotically of the form $c_{\\bf k}\\sqrt{1+{\\bf k}^2 \\exp(-2Ht)/H^2}$, where the limiting coefficients $c_{\\bf k}=\\varphi_{\\bf k}(\\infty)$ are independent of $t$ and $H$ is the Hubble constant quantifying the expansion rate of de Sitter space-time. In particular, every field mode $\\varphi_{\\bf k}$ possesses a limit as $t\\to\\infty$ and thus "freezes." This result is relevant to the question whether Boltzmann brains form in the late universe according to this theory, and supports that they do not.
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ22 null limiting distribution.
Asymptotic stability of solitons for the Benjamin-Ono equation
Kenig, C. E.; Martel, Y.
2008-01-01
In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [Martel, Y. and Merle, F.: Asymptotic stability of solitons for subcritical generalized KdV equations. Arch. Ration. Mech. Anal. 157 (2001), 219-254], [Martel, Y. and Merle, F.: Asymptotic stability of solitons of the gKdV equations wit...
Asymptotic Solution of the Theory of Shells Boundary Value Problem
Directory of Open Access Journals (Sweden)
I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Asymptotic failure rate of a continuously monitored system
Energy Technology Data Exchange (ETDEWEB)
Grall, A. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: antoine.grall@utt.fr; Dieulle, L. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: laurence.dieulle@utt.fr; Berenguer, C. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: christophe.berenguer@utt.fr; Roussignol, M. [Laboratoire d' Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, 5 bd Descartes, Champs sur Marne, 77454 Marne la Vallee, Cedex 2 (France)]. E-mail: michel.roussignol@univ-mlv.fr
2006-02-01
This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.
The Truth About Ballistic Coefficients
Courtney, Michael
2007-01-01
The ballistic coefficient of a bullet describes how it slows in flight due to air resistance. This article presents experimental determinations of ballistic coefficients showing that the majority of bullets tested have their previously published ballistic coefficients exaggerated from 5-25% by the bullet manufacturers. These exaggerated ballistic coefficients lead to inaccurate predictions of long range bullet drop, retained energy and wind drift.
Directory of Open Access Journals (Sweden)
Jichul Ryu
2016-04-01
Full Text Available In this study, 52 asymptotic Curve Number (CN regression equations were developed for combinations of representative land covers and hydrologic soil groups. In addition, to overcome the limitations of the original Long-term Hydrologic Impact Assessment (L-THIA model when it is applied to larger watersheds, a watershed-scale L-THIA Asymptotic CN (ACN regression equation model (watershed-scale L-THIA ACN model was developed by integrating the asymptotic CN regressions and various modules for direct runoff/baseflow/channel routing. The watershed-scale L-THIA ACN model was applied to four watersheds in South Korea to evaluate the accuracy of its streamflow prediction. The coefficient of determination (R2 and Nash–Sutcliffe Efficiency (NSE values for observed versus simulated streamflows over intervals of eight days were greater than 0.6 for all four of the watersheds. The watershed-scale L-THIA ACN model, including the asymptotic CN regression equation method, can simulate long-term streamflow sufficiently well with the ten parameters that have been added for the characterization of streamflow.
Asymptotic Properties of Self-Consistent Estimators with Doubly-Censored Data
Institute of Scientific and Technical Information of China (English)
Qi Qing YU; Lin Xiong LI
2001-01-01
The asymptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the assumption that X is observable everywhere in the interval [a, b], where a ＝ inf{x: F(x) ＞ 0} and b ＝ sup{x : F(x) ＜ 1}. Such an assumption does not allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. However, often in practice this assumption is not satisfied. In this manuscript we establish strong uniform consistency, asymptotic normality and asymptotic efficiency of the SCE under a set of assumptions that allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. Finally, we point out a gap in the proofs of the existing results in the literature due to the definition of the SCE.
Absorption spectra and light penetration depth of normal and pathologically altered human skin
Barun, V. V.; Ivanov, A. P.; Volotovskaya, A. V.; Ulashchik, V. S.
2007-05-01
A three-layered skin model (stratum corneum, epidermis, and dermis) and engineering formulas for radiative transfer theory are used to study absorption spectra and light penetration depths of normal and pathologically altered skin. The formulas include small-angle and asymptotic approximations and a layer-addition method. These characteristics are calculated for wavelengths used for low-intensity laser therapy. We examined several pathologies such as vitiligo, edema, erythematosus lupus, and subcutaneous wound, for which the bulk concentrations of melanin and blood vessels or tissue structure (for subcutaneous wound) change compared with normal skin. The penetration depth spectrum is very similar to the inverted blood absorption spectrum. In other words, the depth is minimal at blood absorption maxima. The calculated absorption spectra enable the power and irradiation wavelength providing the required light effect to be selected. Relationships between the penetration depth and the diffuse reflectance coefficient of skin (unambiguously expressed through the absorption coefficient) are analyzed at different wavelengths. This makes it possible to find relationships between the light fields inside and outside the tissue.
ON COEFFICIENT POLYNOMIALS OF CUBIC HERMITE-PAD(E) APPROXIMATIONS TO THE EXPONENTIAL FUNCTION
Institute of Scientific and Technical Information of China (English)
Cheng-de Zheng; Guo-can Wang; Zhi-bin Li
2005-01-01
The polynomials related with cubic Hermite-Pade approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.
Directory of Open Access Journals (Sweden)
Narski Jacek
2011-11-01
Full Text Available In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem addressed in this paper is well suited for the simulation of a plasma in the presence of a magnetic field, whose intensity may vary considerably within the simulation domain.
EXACT SAMPLING DISTRIBUTION OF SAMPLE COEFFICIENT OF VARIATION
Directory of Open Access Journals (Sweden)
Dr.G.S.David Sam Jayakumar
2015-06-01
Full Text Available This paper proposes the sampling distribution of sample coefficient of variation from the normal population. We have derived the relationship between the sample coefficient of variation, standard normal and chi-square variate. We have derived density function of the sample coefficient of variation in terms of the confluent hyper-geometric distribution. Moreover, the first two moments of the distribution are derived and we have proved that the sample coefficient of variation (cv is the biased estimator of the population coefficient of variation (CV. Moreover, the shape of the density function of sample co-efficient of variation is also visualized and the critical points of sample (cv at 5% and 1% level of significance for different sample sizes have also been computed.
ASYMPTOTIC SOLUTION TO NONLINEAR ECOLOGICAL REACTION DIFFUSION SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Nonlinear ecological species group singularly perturbed initial boundary value problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities, the existence and asymptotic behavior of solution to initial boundary value problems are studied.
Asymptotical Properties for Parabolic Systems of Neutral Type
Institute of Scientific and Technical Information of China (English)
CUI Bao-tong; HAN Mao-an
2005-01-01
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
ASYMPTOTICALLY OPTIMAL SUCCESSIVE OVERRELAXATION METHODS FOR SYSTEMS OF LINEAR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zhong-zhi Bai; Xue-bin Chi
2003-01-01
We present a class of asymptotically optimal successive overrelaxation methods forsolving the large sparse system of linear equations. Numerical computations show thatthese new methods are more efficient and robust than the classical successive overrelaxationmethod.
Semilocal density functional theory with correct surface asymptotics
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Spherical Cap Packing Asymptotics and Rank-Extreme Detection
Zhang, Kai
2015-01-01
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors are themselves independently uniformly distributed, we further develop the extreme value distribution limit of the maximal inner product, which characterizes its uncertainty around the bound. As applications of the above asymptotic results, we derive (1) an asymptotic sharp universal uniform bound on the maximal spurious correlation, as well as its uniform convergence in distribution when the explanatory variables are independently Gaussian distributed; and (2) an asymptotic sharp universal bound on the maximum norm of a low-rank elliptically distributed vector, as well as related limiting distributions. With these results, we develop a fast detection method for a low-rank structure in high-dime...
Asymptotic behaviour of the number of the Eulerian circuits
Isaev, Mikhail
2011-01-01
We determine the asymptotic behaviour of the number of the Eulerian circuits in undirected simple graphs with large second eigenvalue of the Laplacian matrix (the algebraic connectivity). We also prove some new properties of the Laplacian matrix.
Asymptotic formula for eigenvalues of one dimensional Dirac system
Ulusoy, Ismail; Penahlı, Etibar
2016-06-01
In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.
Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds
An, Ok Song; Papadimitriou, Ioannis
2016-01-01
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associat...
Global asymptotic stability for a class of nonlinear chemical equations
Anderson, David F.
2007-01-01
We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More specifically, we will consider chemical reaction systems that are weakly reversible, have a deficiency of zero, and are equipped with mass action kinetics. We show that if for each $c \\in \\R_{> 0}^m$ the intersection of the stoichiometric compatibility class $c + S$ ...
Asymptotical stability analysis of linear fractional differential systems
Institute of Scientific and Technical Information of China (English)
LI Chang-pin; ZHAO Zhen-gang
2009-01-01
It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts,electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.
Functional truncations in asymptotic safety for quantum gravity
Dietz, Juergen
2016-01-01
Finite dimensional truncations and the single field approximation have thus far played dominant roles in investigations of asymptotic safety for quantum gravity. This thesis is devoted to exploring asymptotic safety in infinite dimensional, or functional, truncations of the effective action as well as the effects that can be caused by the single field approximation in this context. It begins with a comprehensive analysis of the three existing flow equations of the single field f(R) truncation...
Asymptotic heat transfer model in thin liquid films
Chhay, Marx; Dutykh, Denys; Gisclon, Marguerite; Ruyer-Quil, Christian
2015-01-01
In this article, we present a modelling of heat transfer occuring through a liquid film flowing down a vertical wall. This model is formally derived thanks to asymptotic developpment, by considering the physical ratio of typical length scales of the study. A new Nusselt thermal solution is proposed, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms in the asymptotic model are numerically pointed out. The comparisons are provided again...
Asymptotic optimal designs under long-range dependence error structure
Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly; 10.3150/09-BEJ185
2010-01-01
We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function. Several examples are investigated to illustrate the theory. Finally, the optimal designs are compared with asymptotic optimal designs which were derived by Bickel and Herzberg [Ann. Statist. 7 (1979) 77--95] for regression models with short-range dependent error.
Asymptotics for maximum score method under general conditions
Taisuke Otsu; Myung Hwan Seo
2014-01-01
Abstract. Since Manski's (1975) seminal work, the maximum score method for discrete choice models has been applied to various econometric problems. Kim and Pollard (1990) established the cube root asymptotics for the maximum score estimator. Since then, however, econometricians posed several open questions and conjectures in the course of generalizing the maximum score approach, such as (a) asymptotic distribution of the conditional maximum score estimator for a panel data dynamic discrete ch...
An asymptotically exact theory of smart sandwich shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.
High frequency asymptotics of antenna/structure interactions
Coats, J.
2002-01-01
This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors. We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point. In chapter 5 we review and extend the asymptotic results concerning illuminat...
High-order topological asymptotic expansion for Stokes equations
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Mohamed Abdelwahed
2016-06-01
Full Text Available We use the topological sensitivity analysis method to solve various optimization problems. It consists of studying the asymptotic expansion of the objective function relative to a perturbation of the domain topology. This expansion becomes insufficient in some applications when it is limited to the first order topological derivative. We present a new topological sensitivity analysis for the Stokes equations based on a high order asymptotic expansion. The derived result is valid for different class of shape functions.
Asymptotic solutions of magnetohydrodynamics equations near the derivatives discontinuity lines
International Nuclear Information System (INIS)
Asymptotic solutions of one-dimensional and scalar magnetohydrodynamics equations near the derivatives discontinuity lines have been discussed. The equations of magnetohydrodynamics for the cases of finite and infinite conductivities are formulated and the problem of eigenvalues and eigenvectors is solved. The so called transport equations which describe the behaviour of derivatives in solutions of the quasilinear equations have been used to find the asymptotic solutions of the magnetohydrodynamics equations. (S.B.)
An asymptotically exact theory of functionally graded piezoelectric shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.
Random attractors for asymptotically upper semicompact multivalue random semiflows
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
Asymptotic Solutions of Algebraic Reynolds Stress Model Applied to Rough Bottom Open Channel Flow
Directory of Open Access Journals (Sweden)
Soualmia Amel
2014-05-01
Full Text Available We interpret experimental results on the structure of an open channel flow with a strong transverse variation of the bottom roughness. Knowing the wall parameters, we analyze the behavior of Reynolds stress components by using asymptotic solutions of an algebraic stress model developed in the wall and free surface regions. This analysis allowed us to emphasize effects of secondary flows on the production of turbulence near the wall, and the capability of this model to predict the normal components of the Reynolds tensor in the wall and free surface regions when the turbulent shear stresses are well predicted.
On the asymptotic ergodic capacity of FSO links with generalized pointing error model
Al-Quwaiee, Hessa
2015-09-11
Free-space optical (FSO) communication systems are negatively affected by two physical phenomenon, namely, scintillation due to atmospheric turbulence and pointing errors. To quantize the effect of these two factors on FSO system performance, we need an effective mathematical model for them. Scintillations are typically modeled by the log-normal and Gamma-Gamma distributions for weak and strong turbulence conditions, respectively. In this paper, we propose and study a generalized pointing error model based on the Beckmann distribution. We then derive the asymptotic ergodic capacity of FSO systems under the joint impact of turbulence and generalized pointing error impairments. © 2015 IEEE.
Asymptotics for Hessenberg matrices for the Bergman shift operator on Jordan regions
Saff, Edward B
2012-01-01
Let G be a bounded Jordan domain in the complex plane and consider the infinite upper Hessenberg matrix M associated with the Bergman orthogonal polynomials of G. This matrix represents the Bergman shift operator of G. The main purpose of the paper is to describe and analyze a close relation between M and the Toeplitz matrix with symbol the normalized conformal map of the exterior of the unit circle onto the complement of the closure of G. Our results are based on the strong asymptotics of the Bergman polynomials. As an application, we describe and analyze an algorithm for recovering the shape of G from its area moments.
ON TESTING THE EQUALITY OF K MULTIPLEAND PARTIAL CORRELATION COEFFICIENTS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Coutsourides (1980) derives an ad hoc nuisance parameter removal test for testing the equality of two multiple correlation coefficients of two independent p variate normal populations, under the assumption that a sample of size n is available from each population. He also extends his ad hoc nuisance parameter removal test to the testing of the equality of two multiple correlation matrices. This paper presents likelihood ratio tests for testing the equality of k multiple correlation coefficients, and also k partial correlation coefficients.
A Generalized Definition of the Polychoric Correlation Coefficient
Ekström, Joakim
2011-01-01
The polychoric correlation coefficient is a measure of association for ordinal variables which rests upon an assumption of an underlying joint continuous distribution. More specifically, in Karl Pearson’s original definition an underlying joint normal distribution is assumed. In this article, the definition of the polychoric correlation coefficient is generalized so that it allows for other distributional assumptions than the joint normal distribution. The generalized definition is analogous ...
Generalized multiplicative error models: Asymptotic inference and empirical analysis
Li, Qian
This dissertation consists of two parts. The first part focuses on extended Multiplicative Error Models (MEM) that include two extreme cases for nonnegative series. These extreme cases are common phenomena in high-frequency financial time series. The Location MEM(p,q) model incorporates a location parameter so that the series are required to have positive lower bounds. The estimator for the location parameter turns out to be the minimum of all the observations and is shown to be consistent. The second case captures the nontrivial fraction of zero outcomes feature in a series and combines a so-called Zero-Augmented general F distribution with linear MEM(p,q). Under certain strict stationary and moment conditions, we establish a consistency and asymptotic normality of the semiparametric estimation for these two new models. The second part of this dissertation examines the differences and similarities between trades in the home market and trades in the foreign market of cross-listed stocks. We exploit the multiplicative framework to model trading duration, volume per trade and price volatility for Canadian shares that are cross-listed in the New York Stock Exchange (NYSE) and the Toronto Stock Exchange (TSX). We explore the clustering effect, interaction between trading variables, and the time needed for price equilibrium after a perturbation for each market. The clustering effect is studied through the use of univariate MEM(1,1) on each variable, while the interactions among duration, volume and price volatility are captured by a multivariate system of MEM(p,q). After estimating these models by a standard QMLE procedure, we exploit the Impulse Response function to compute the calendar time for a perturbation in these variables to be absorbed into price variance, and use common statistical tests to identify the difference between the two markets in each aspect. These differences are of considerable interest to traders, stock exchanges and policy makers.
ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE
Institute of Scientific and Technical Information of China (English)
林正炎
2003-01-01
Let {Xn,n> _ 1} be a strictly stationary sequence of random variables,which are either associated or negatively associated,f(·)be their common density.In this paper,the author shows a central limit theorem for a kernel estimate of f(·)under certain regular conditions.
The Number of Same-Sex Marriages in a Perfectly Bisexual Population is Asymptotically Normal
Ekhad, Shalosh B
2011-01-01
Why bother with fully rigorous proofs when one can very quickly get semi-rigorous ones? Yes, yes, we know how to get a "rigorous" proof of the result stated in the title of this article. One way is the boring, human one, citing some heavy guns of theorems that already exist in the literature. We also know how to get a fully rigorous proof automatically, using the methods in this http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/georgy.htm neat article (but it would be a little more complicated, since the probability generating polynomial is not "closed form" but satisfies a second-order recurrence gotten from the Zeilberger algorithm), otherwise the same method would work, alas, it is not yet implemented. Instead, we chose to use the great Maple package http://www.math.rutgers.edu/~zeilberg/tokhniot/HISTABRUT">HISTABRUT(in fact, a very tiny part of it, procedure AlphaSeq), explained in this other http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/histabrut.html">neat article, and get a semi-rig...
The size of coefficients of certain polynomials related to the Goldbach conjecture
Martin, Greg
2010-01-01
Recent work of Borwein, Choi, and the second author examined a collection of polynomials closely related to the Goldbach conjecture: the polynomial $F_N$ is divisible by the $N$th cyclotomic polynomial if and only if there is no representation of $N$ as the sum of two odd primes. The coefficients of these polynomials stabilize, as $N$ grows, to a fixed sequence $a(m)$; they derived upper and lower bounds for $a(m)$, and an asymptotic formula for the summatory function $A(M)$ of the sequence, both under the assumption of a famous conjecture of Hardy and Littlewood. In this article we improve these results: we obtain an asymptotic formula for $a(m)$ under the same assumption, and we establish the asymptotic formula for $A(M)$ unconditionally.
Schlemm, Eckhard
2015-09-01
The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness distribution in larger systems may help pave the way towards a resolution of the question of whether or not, in the limit of infinitely many species, the fitness is asymptotically uniformly distributed on the interval [fc, 1] with fc ≳ 2/3. PMID:26144945
On the Kendall Correlation Coefficient
Stepanov, Alexei
2015-01-01
In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendall rank correlation coefficient and show that the later is free of n. We also prove that in continuous case the Kendall correlation coefficient converges in probability to its expected value. We then propose to consider the expected value of the Kendall rank ...
Universal statistics of the scattering coefficient of chaotic microwave cavities.
Hemmady, Sameer; Zheng, Xing; Antonsen, Thomas M; Ott, Edward; Anlage, Steven M
2005-05-01
We consider the statistics of the scattering coefficient S of a chaotic microwave cavity coupled to a single port. We remove the nonuniversal effects of the coupling from the experimental S data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized scattering coefficient whose probability density function (PDF) is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We compare experimental PDFs of the normalized scattering coefficients with those obtained from random matrix theory (RMT), and find excellent agreement. The results apply to scattering measurements on any wave chaotic system.
The Semiparametric Normal Variance-Mean Mixture Model
DEFF Research Database (Denmark)
Korsholm, Lars
1997-01-01
We discuss the normal vairance-mean mixture model from a semi-parametric point of view, i.e. we let the mixing distribution belong to a non parametric family. The main results are consistency of the non parametric maximum likelihood estimat or in this case, and construction of an asymptotically...
A remark on asymptotic dimension and digital dimension of finite metric spaces
Čatyrko, Vitalij Al´bertovič; Zarichnyi, Michael
2015-01-01
Asymptotic dimension was introduced by M. L. Gromov as an asymptotic analogue of the covering dimension. In the current note, the authors introduce the concept of digital dimension (essentially asymptotic dimension at a particular scale) and investigate the relationship between the asymptotic dimension of a proper metric space and the digital dimension of its finite subspaces. In particular, they show that the asymptotic dimension of a proper metric space is at most ▫$n$▫ exactly when there i...
Critical exponents from cluster coefficients
Rotman, Z.; Eisenberg, E.
2009-09-01
For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal real symmetric matrix Rmn , whose elements converge to two constants. This allows for an effective extrapolation of the equation of state for these models. Due to a nearby (nonphysical) singularity on the negative real z axis, standard methods (e.g., Padé approximants based on the cluster integrals expansion) fail to capture the behavior of these models near the ordering transition, and, in particular, do not detect the critical point. A recent work [E. Eisenberg and A. Baram, Proc. Natl. Acad. Sci. U.S.A. 104, 5755 (2007)] has shown that the critical exponents σ and σ' , characterizing the singularity of the density as a function of the activity, can be exactly calculated if the decay of the R matrix elements to their asymptotic constant follows a 1/n2 law. Here we employ renormalization group (RG) arguments to extend this result and analyze cases for which the asymptotic approach of the R matrix elements toward their limiting value is of a more general form. The relevant asymptotic correction terms (in RG sense) are identified, and we then present a corrected exact formula for the critical exponents. We identify the limits of usage of the formula and demonstrate one physical model, which is beyond its range of validity. The formula is validated numerically and then applied to analyze a number of concrete physical models.
asymptotics for open-loop window flow control
Directory of Open Access Journals (Sweden)
Arthur W. Berger
1994-01-01
Full Text Available An open-loop window flow-control scheme regulates the flow into a system by allowing at most a specified window size W of flow in any interval of length L. The sliding window considers all subintervals of length L, while the jumping window considers consecutive disjoint intervals of length L. To better understand how these window control schemes perform for stationary sources, we describe for a large class of stochastic input processes the asymptotic behavior of the maximum flow in such window intervals over a time interval [0,T] as T and Lget large, with T substantially bigger than L. We use strong approximations to show that when T≫L≫logT an invariance principle holds, so that the asymptotic behavior depends on the stochastic input process only via its rate and asymptotic variability parameters. In considerable generality, the sliding and jumping windows are asymptotically equivalent. We also develop an approximate relation between the two maximum window sizes. We apply the asymptotic results to develop approximations for the means and standard deviations of the two maximum window contents. We apply computer simulation to evaluate and refine these approximations.
Singularities in asymptotically anti-de Sitter spacetimes
Ishibashi, Akihiro
2012-01-01
We consider singularity theorems in asymptotically anti-de Sitter (AdS) spacetimes. In the first part, we discuss the global methods used to show geodesic incompleteness and see that when the conditions imposed in Hawking and Penrose's singularity theorem are satisfied, a singularity must appear in asymptotically AdS spacetime. The recent observations of turbulent instability of asymptotically AdS spacetimes indicate that AdS spacetimes are generically singular even if a closed trapped surface, which is one of the main conditions of the Hawking and Penrose theorem, does not exist in the initial hypersurface. This may lead one to expect to obtain a singularity theorem without imposing the existence of a trapped set in asymptotically AdS spacetimes. This, however, does not appear to be the case. We consider, within the use of global methods, two such attempts and discuss difficulties in eliminating conditions concerning a trapped set from singularity theorems in asymptotically AdS spacetimes. Then in the second...
Sufficient conditions for globally asymptotic self-stability of pressurized water reactors
International Nuclear Information System (INIS)
Highlights: • Self-stability analysis of the PWR is presented through the shifted-ectropy based approach. • Sufficient conditions for the globally asymptotic self-stability are established. • The correctness of the theoretic results are finally verified through numerical simulation. - Abstract: After the Fukushima accident, safe, stable and efficient operation of reactors is very necessary for the development of nuclear power industry. Since pressurized water reactor (PWR) is the mostly widely used fission reactor, the improvement of its operation performance is quite meaningful. Self-stability is the most important dynamic feature of any reactors, and analyzing the self-stability can give the approach of improving the operation performance. With this in mind, the self-stability analysis of the PWR is presented through the shifted-ectropy based approach, and sufficient conditions for the globally asymptotic self-stability in cases of negative, zero and positive coolant temperature feedback coefficient are all established. The correctness of the theoretical results are finally verified through numerical simulation. The results of this paper give the way to not only guaranteeing self-stability through physical and thermal-hydraulic reactor design but also strengthening closed-loop stability and robustness by the means of feedback control
Normal BGG solutions and polynomials
Cap, A; Hammerl, M
2012-01-01
First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include those controlling infinitesimal automorphisms, higher symmetries, and many other widely studied PDE of geometric origin. The machinery of BGG sequences also singles out a subclass of solutions called normal solutions. These correspond to parallel tractor fields and hence to (certain) holonomy reductions of the canonical normal Cartan connection. Using the normal Cartan connection, we define a special class of local frames for any natural vector bundle associated to a parabolic geometry. We then prove that the coefficient functions of any normal solution of a first BGG operator with respect to such a frame are polynomials in the normal coordinates of the parabolic geometry. A bound on the degree of these polynomials in terms of representation theory data is derived. For geometries locally isomorphic to the homogeneous model of ...
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Asymptotic symmetries of QED and Weinberg's soft photon theorem
Campiglia, Miguel
2015-01-01
Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.
Fast evaluation of asymptotic waveforms from gravitational perturbations
Benedict, Alex G; Lau, Stephen R
2012-01-01
In the context of blackhole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user's standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge-Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equa...
Contact mechanics of articular cartilage layers asymptotic models
Argatov, Ivan
2015-01-01
This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...
Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials
Gómez-Ullate, David; Milson, Robert
2012-01-01
The location and asymptotic behaviour for large n of the zeros of exceptional Jacobi and Laguerre polynomials are discussed. The zeros of exceptional polynomials fall into two classes: the regular zeros, which lie in the interval of orthogonality and the exceptional zeros, which lie outside that interval. We show that the regular zeros have two interlacing properties: one is the natural interlacing between consecutive polynomials as a consequence of their Sturm-Liouville character, while the other one shows interlacing between the zeros of exceptional and classical polynomials. A generalization of the classical Heine-Mehler formula is provided for the exceptional polynomials, which allows to derive the asymptotic behaviour of their regular zeros. We also describe the location and the asymptotic behaviour of the exceptional zeros, which converge for large n to fixed values.
Asymptotics of a singularly perturbed GUE partition function
Mezzadri, F
2010-01-01
We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.
Asymptotic completeness and multiparticle structure in field theories
International Nuclear Information System (INIS)
Previous proofs of asymptotic completeness and related results on scattering in field theories are restricted to P(φ)2 models in the 2- and 3-particle regions. In this paper, new cluster expansions that are well adapted to more direct proofs and generalizations of these results are presented. In contrast to previous ones, they are designed to provide direct graphical definitions of general irreducible kernels satisfying structure equations recently proposed and shown to be closely linked with asymptotic completeness and with the multiparticle structure of Green functions and collision amplitudes in general energy regions. The method can be applied as previously to P(φ)2 and can also be extended to theories involving renormalization which are controlled by phase-space analysis. It is here illustrated in detail for the Bethe-Salpeter kernel in φ24, in which case a new proof of its 4-particle decay (which yields asymptotic completeness in the 2-particle region) is given. (orig.)
Holography of 3D Asymptotically Flat Black Holes
Fareghbal, Reza
2014-01-01
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking flat-space limit (zero cosmological constant limit) of New Massive Gravity (NMG). We propose that the dual field theory of the flat-space limit of NMG can be described by a Contracted Conformal Field Theory (CCFT). Using Flat/CCFT correspondence we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. Furthermore, by taking appropriate limit of the Cardy formula in the parent CFT, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.
The unitary conformal field theory behind 2D Asymptotic Safety
Nink, Andreas
2015-01-01
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a...
Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion
Akagi, Goro
2016-07-01
The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for fast diffusion equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy. It is noteworthy that this result can cover non-isolated profiles, e.g., those for thin annular domain cases. The method of proof is based on the Łojasiewicz-Simon inequality, which is usually used to prove the convergence of solutions to prescribed limits, as well as a uniform extinction estimate for solutions to FDE. Besides, local minimizers of an energy functional associated with this issue are characterized. Furthermore, the instability of positive radial asymptotic profiles in thin annular domains is also proved by applying the Łojasiewicz-Simon inequality in a different way.
Consistency of matter models with asymptotically safe quantum gravity
Donà, P; Percacci, Roberto
2014-01-01
We discuss the compatibility of quantum gravity with dynamical matter degrees of freedom. Specifically, we present bounds we obtained in [1] on the allowed number and type of matter fields within asymptotically safe quantum gravity. As a novel result, we show bounds on the allowed number of spin-3/2 (Rarita-Schwinger) fields, e.g., the gravitino. These bounds, obtained within truncated Renormalization Group flows, indicate the compatibility of asymptotic safety with the matter fields of the standard model. Further, they suggest that extensions of the matter content of the standard model are severely restricted in asymptotic safety. This means that searches for new particles at colliders could provide experimental tests for this particular approach to quantum gravity.
Directory of Open Access Journals (Sweden)
H. S. Negi
2011-04-01
Full Text Available An asymptotic analytical radiative transfer (AART theory was used to retrieve snow optical parameters such as extinction coefficient, diffuse exponent, asymptotic flux extinction coefficient (AFEC, snow optical thickness and probability of photon absorption (PPA. This theory was applied to the reflection and transmission data for a temperate snow cover from 400–1000 nm wavelength region, to retrieve AFEC for different types of snow cover (thick, thin, dry, wet, new and old snow. The AFEC values were found at 450 nm wavelength region in the range from 0.06 to 0.22 cm^{−1}, where high values were observed for increased wetness and impurity in snow. A good agreement between AART retrieved and other radiative transfer model retrieved parameter shows that AART theory can work well for different types of snow. The extinction coefficients for temperate snow ranged from 0.5 to 1.0 mm^{−1} and the e-folding depths ranged from 5 to 25 cm. The snow physical characteristics such as grain size and density were also retrieved using derived optical parameters and found in agreement with ground measurements. The main advantages of the proposed AART method are the simple analytical equations that provide a valuable alternative from complex numerical radiative transfer solutions.
High-Frequency Asymptotics for Lipschitz-Killing Curvatures of Excursion Sets on the Sphere
Marinucci, Domenico
2016-01-01
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. We put particular emphasis on the analysis of Euler-Poincar\\'e characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries and anisotropies in Cosmological data.
Scaling of the asymptotic entropy jump in the superadiabatic layers of stellar atmospheres
Magic, Zazralt
2016-01-01
Stellar structure calculations are able to predict precisely the properties of stars during their evolution. However, convection is still modelled by the mixing length theory; therefore, the upper boundary conditions near the optical surface do not agree with asteroseismic observations. We want to improve how the outer boundary conditions are determined in stellar structure calculations. We study realistic 3D stellar atmosphere models to find alternative properties. We find that the asymptotic entropy run of the superadiabatic convective surface layers exhibit a distinct universal stratification when normalised by the entropy minimum and jump. The normalised entropy can be represented by a 5th order polynomial very accurately, and a 3rd order polynomial also yields accurate coefficients. This generic entropy stratification or the solar stratification, when scaled by the entropy jump and minimum, can be used to improve the modelling of superadiabatic surface layers in stellar structure calculations. Furthermor...
Low-frequency asymptotic analysis of seismic reflection from afluid-saturated medium
Energy Technology Data Exchange (ETDEWEB)
Silin, D.B.; Korneev, V.A.; Goloshubin, G.M.; Patzek, T.W.
2004-04-14
Reflection of a seismic wave from a plane interface betweentwo elastic media does not depend on the frequency. If one of the mediais poroelastic and fluid-saturated, then the reflection becomesfrequency-dependent. This paper presents a low-frequency asymptoticformula for the reflection of seismic plane p-wave from a fluid-saturatedporous medium. The obtained asymptotic scaling of the frequency-dependentcomponent of the reflection coefficient shows that it is asymptoticallyproportional to the square root of the product of the reservoir fluidmobility and the frequency of the signal. The dependence of this scalingon the dynamic Darcy's law relaxation time is investigated as well.Derivation of the main equations of the theory of poroelasticity from thedynamic filtration theory reveals that this relaxation time isproportional to Biot's tortuosity parameter.
Bitencourt, A C P; Ragni, M; Anderson, R W; Aquilanti, V
2012-01-01
Increasing interest is being dedicated in the last few years to the issues of exact computations and asymptotics of spin networks. The large-entries regimes (semiclassical limits) occur in many areas of physics and chemistry, and in particular in discretization algorithms of applied quantum mechanics. Here we extend recent work on the basic building block of spin networks, namely the Wigner 6j symbol or Racah coefficient, enlightening the insight gained by exploiting its self-dual properties and studying it as a function of two (discrete) variables. This arises from its original definition as an (orthogonal) angular momentum recoupling matrix. Progress also derives from recognizing its role in the foundation of the modern theory of classical orthogonal polynomials, as extended to include discrete variables. Features of the imaging of various regimes of these orthonormal matrices are made explicit by computational advances -based on traditional and new recurrence relations- which allow an interpretation of the...
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
Institute of Scientific and Technical Information of China (English)
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
Dynamics of loops: asymptotic freedom and quark confinement
International Nuclear Information System (INIS)
New manifestly gauge invariant diagram technique in the loop space is developed. For that purpose a boot-strap ' equation, determining the self-consistent asymptotics, is solved in the framework of the perturbation theory. The boot-strap equation is equivalent to the system including the Bianchi identity and the planar equation accompanied by Euclidean boundary conditions. It is shown that the area law of quark confinement is a self-consistent solution of the boot-strap equation. The frame diagrams constructed by means of certain operator technique reproduce asymptotic freedom in the ultraviolet range
Vacuum energy in asymptotically flat 2+1 gravity
Miskovic, Olivera; Roy, Debraj
2016-01-01
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincare group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Selected asymptotic methods with applications to electromagnetics and antennas
Fikioris, George; Bakas, Odysseas N
2013-01-01
This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffery D [Los Alamos National Laboratory
2009-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
Energy Technology Data Exchange (ETDEWEB)
Densmore, Jeffery D [Los Alamos National Laboratory
2008-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large, We demonstrate the validity of our analysis with a set of numerical examples.
The Asymptotic Limit for the 3D Boussinesq System
Institute of Scientific and Technical Information of China (English)
LI Lin-rui; WANG Ke; HONG Ming-li
2016-01-01
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coeﬃcient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosityν=0 or zero diffusivityη=0) in 2D case separately.
Asymptotic Distribution of the Jump Change-Point Estimator
Institute of Scientific and Technical Information of China (English)
Changchun TAN; Huifang NIU; Baiqi MIAO
2012-01-01
The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent identically distributed random variables with Eεi=0 and Var(εi) ＜ oo,with the help of the slip window method,the asymptotic distribution of the jump change-point estimator (T) is studied under the condition of the local alternative hypothesis.
EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
Counting spanning trees on fractal graphs and their asymptotic complexity
Anema, Jason A.; Tsougkas, Konstantinos
2016-09-01
Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.
Asymptotic heat transfer model in thin liquid films
Chhay, Marx; Gisclon, Marguerite; Ruyer-Quil, Christian
2015-01-01
In this article, we present a modelling of heat transfer occuring through a liquid film flowing down a vertical wall. This model is formally derived thanks to asymptotic developpment, by considering the physical ratio of typical length scales of the study. A new Nusselt thermal solution is proposed, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms in the asymptotic model are numerically pointed out. The comparisons are provided against the resolution of the full Fourier equations in a steady state frame.
Asymptotic dynamics, large gauge transformations and infrared symmetries
Gomez, Cesar
2016-01-01
Infrared finite S matrices enjoy an infinite family of symmetries, namely decoupling of asymptotic soft modes with arbitrary direction. The infrared structure of the theory manifests itself in the form of vacuum degeneracy and in nontrivial asymptotic dynamics. These two ingredients are unified in the infrared finite S matrix symmetries and can be disentangled as soft and hard components of corresponding charges. When these two components are disentangled, the nontrivial role of large gauge transformations becomes manifest. The soft decoupling symmetry of the physical S matrix leads to relations between the corresponding soft/hard decompositions for the in and out states that can encode crucial nontrivial information about the scattering process.
Asymptotic Marginal Tax Rate of Individual Income Tax in China
Institute of Scientific and Technical Information of China (English)
ZHENYA; LIU; WU; YANG; DAVID; DICKINSON
2014-01-01
This paper examines the asymptotic marginal rate of individual income tax which maximizes China’s social welfare through numerical simulation based on the elasticity of China’s labor supply, income distribution and the social objectives of redistribution in accordance with the optimal direct taxation theory. Taking advantage of the optimal direct taxation model with consideration of the income effect, it comes to the conclusion that combined with China’s reality, the asymptotic marginal rate of individual labor income tax in China should be between 35% and 40%.