Yuan, Ke-Hai; Bentler, Peter M.
2002-01-01
Examined the asymptotic distributions of three reliability coefficient estimates: (1) sample coefficient alpha; (2) reliability estimate of a composite score following factor analysis; and (3) maximal reliability of a linear combination of item scores after factor analysis. Findings show that normal theory based asymptotic distributions for these…
Sub-Coulomb 3He transfer and its use to extract three-particle asymptotic normalization coefficients
Avila, M. L.; Baby, L. T.; Belarge, J.; Keeley, N.; Kemper, K. W.; Koshchiy, E.; Kuchera, A. N.; Rogachev, G. V.; Rusek, K.; Santiago-Gonzalez, D.
2018-01-01
Data for the 13C(6Li,t )16O reaction, obtained in inverse kinematics at a 13C incident energy of 7.72 MeV, are presented. A distorted wave Born approximation (DWBA) analysis was used to extract spectroscopic factors and asymptotic normalization coefficients (ANCs) for the 〈" close="〉6Li∣3He +3H 〉">16O∣13C +3He overlaps, subject to the assumption of a fixed factors and ANCs as a function of various inputs to the DWBA calculations was explored. The extracted ANCs were found to vary as a cubic function of the radius of the potential well binding the transferred 3He to the 13C core while the spectroscopic factors varied as a quartic function of the radius. The ANC values could be determined to within a factor of two for this system.
Jones, Jeff A; Waller, Niels G
2015-06-01
Yuan and Chan (Psychometrika, 76, 670-690, 2011) recently showed how to compute the covariance matrix of standardized regression coefficients from covariances. In this paper, we describe a method for computing this covariance matrix from correlations. Next, we describe an asymptotic distribution-free (ADF; Browne in British Journal of Mathematical and Statistical Psychology, 37, 62-83, 1984) method for computing the covariance matrix of standardized regression coefficients. We show that the ADF method works well with nonnormal data in moderate-to-large samples using both simulated and real-data examples. R code (R Development Core Team, 2012) is available from the authors or through the Psychometrika online repository for supplementary materials.
Avila, M L; Koshchiy, E; Baby, L T; Belarge, J; Kemper, K W; Kuchera, A N; Mukhamedzhanov, A M; Santiago-Gonzalez, D; Uberseder, E
2014-01-01
Background. The $^{12}$C($\\alpha,\\gamma$)$^{16}$O reaction plays a fundamental role in astrophysics because its cross section near 300 keV in c.m. determines the $^{12}$C/$^{16}$O ratio at the end of the helium burning stage of stellar evolution. The astrophysically desired accuracy of better than 10\\% has not been achieved. Cascade $\\gamma$ transitions through the excited states of $^{16}$O are contributing to the uncertainty. Purpose. To measure the Asymptotic Normalization Coefficients (ANCs) for the 0$^+$ (6.05 MeV) and 3$^-$ (6.13 MeV) excited states in $^{16}$O and provide constraints on the cross section for the corresponding cascade transitions. Method. The ANCs were measured using the $\\alpha$-transfer reaction $^{12}$C($^6$Li,$d$)$^{16}$O performed at sub-Coulomb energies for both the entrance and exit channels. Results. The ANCs for the 0$^+$(6.05 MeV), 3$^-$(6.13 MeV), 2$^+$(6.92 MeV) and 1$^-$(7.12 MeV) states in $^{16}$O have been measured. The contribution of the 0$^+$ and 3$^-$ cascade transit...
Quantum local asymptotic normality and other questions of quantum statistics
Kahn, Jonas
2008-01-01
This thesis is entitled Quantum Local Asymptotic Normality and other questions of Quantum Statistics ,. Quantum statistics are statistics on quantum objects. In classical statistics, we usually start from the data. Indeed, if we want to predict the weather, and can measure the wind or the
Asymptotically Distribution-Free (ADF) Interval Estimation of Coefficient Alpha
Maydeu-Olivares, Alberto; Coffman, Donna L.; Hartmann, Wolfgang M.
2007-01-01
The point estimate of sample coefficient alpha may provide a misleading impression of the reliability of the test score. Because sample coefficient alpha is consistently biased downward, it is more likely to yield a misleading impression of poor reliability. The magnitude of the bias is greatest precisely when the variability of sample alpha is…
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
Directory of Open Access Journals (Sweden)
Eleni Bisognin
2008-03-01
Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
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.
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.
Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients
Energy Technology Data Exchange (ETDEWEB)
Zielinski, Lech [Universite Paris 7 (D. Diderot), Institut de Mathematiques de Paris-Jussieu UMR9994 (France)
1999-09-15
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.
A simple approximation to the bivariate normal distribution with large correlation coefficient
Albers, Willem/Wim; Kallenberg, W.C.M.
1994-01-01
The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the
A Review on asymptotic normality of sums of associated random ...
African Journals Online (AJOL)
Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research elds in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic ...
Orlov, Yu. V.; Irgaziev, B. F.; Nabi, Jameel-Un
2017-08-01
A new algorithm for the asymptotic nuclear coefficients calculation, which we call the Δ method, is proved and developed. This method was proposed by Ramírez Suárez and Sparenberg (arXiv:1602.04082.) but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function Kl(k2) is actually defined by the Coulomb term. One of the resulting effects is a wrong description of the energy behavior of the elastic scattering phase shift δl reproduced from the fitted total effective-range function Kl(k2) . This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this Δ method to calculate the pole position values and the ANC. We apply it to the vertices 4He+12C ↔16O and 3He+4He↔7Be . The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the 16O bound final states as well as to the 7Be.
Asymptotic normality of non-parametric estimator for the FGT poverty ...
African Journals Online (AJOL)
Abstract. In this paper, we study the kernel estimator of Foster, Greer and Thorbecke class of measures when the poverty aversion parameter is strictly between zero and one, as a generalization of the work of Dia (2009). We solved an open problem arising in mentioned paper. The asymptotic normality of the estimator is ...
A note on asymptotic normality in the thermodynamic limit at low densities
DEFF Research Database (Denmark)
Jensen, J.L.
1991-01-01
We consider a continuous statistical mechanical system with a pair interaction in a region λ tending to infinity. For low densities asymptotic normality of the canonical statistic is proved, both in the grand canonical ensemble and in the canonical ensemble. The results are illustrated through...
Chen, Chunhang; 陳, 春航
1995-01-01
The smoothing parameters in the Holt-Winters seasonal forecasting method are often estimated by minimizing the mean square error of one-step forecasts using the sample. In this note we show that such an estimator holds asymptotic normality for some stochastic processes.
Confidence bounds for normal and lognormal distribution coefficients of variation
Steve Verrill
2003-01-01
This paper compares the so-called exact approach for obtaining confidence intervals on normal distribution coefficients of variation to approximate methods. Approximate approaches were found to perform less well than the exact approach for large coefficients of variation and small sample sizes. Web-based computer programs are described for calculating confidence...
Consistency rates and asymptotic normality of the high risk conditional for functional data
Directory of Open Access Journals (Sweden)
Rabhi Abbes
2016-08-01
Full Text Available The maximum of the conditional hazard function is a parameter of great importance in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates of the first derivative of the conditional hazard function, we establish uniform convergence properties and asymptotic normality of an estimate of the maximum in the context of independence data.
Consistency rates and asymptotic normality of the high risk conditional for functional data
Directory of Open Access Journals (Sweden)
Rabhi Abbes
2015-12-01
Full Text Available The maximum of the conditional hazard function is a parameter of great importance in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates of the first derivative of the conditional hazard function, we establish uniform convergence properties and asymptotic normality of an estimate of the maximum in the context of independence data.
Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps
Faure, Frédéric; Weich, Tobias
2017-10-01
We consider a R -extension of one dimensional uniformly expanding open dynamical systems and prove a new explicit estimate for the asymptotic spectral gap. To get these results, we use a new application of a "global normal form" for the dynamical system, a "semiclassical expression beyond the Ehrenfest time" that expresses the transfer operator at large time as a sum over rank one operators (each is associated to one orbit). In this paper we establish the validity of the so-called "diagonal approximation" up to twice the local Ehrenfest time.
Directory of Open Access Journals (Sweden)
Budiarso Budiarso
2010-10-01
Full Text Available In this study, the limiting maximum drag reduction asymptote for the moment coefficient of an enclosed rotating disk with fine spiral grooves in turbulent flow region were obtained analytically. Analysis which were based on an assumption for a simple parabolic velocity distribution of turbulent pipe flow to represent relative tangential velocity, was carried out using momentum integral equations of the boundary layer. For a certain K- parameter the moment coefficient results agree well with experimental results for maximum drag reduction in an enclosed rotating disk with fine spiral grooves and drag reduction ratio approximately was 15 %. Additionally, the experimental results for drag reduction on a rotating disk can be explained well with the analytical results.
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)
Normal-stress coefficients and rod climbing in colloidal dispersions
Farage, T. F. F.; Reinhardt, J.; Brader, J. M.
2013-10-01
We calculate tractable microscopic expressions for the low-shear normal-stress coefficients of colloidal dispersions. Although restricted to the low rate regime, the presented formulas are valid for all volume fractions below the glass transition and for any interaction potential. Numerical results are presented for a system of colloids interacting via a hard-core attractive Yukawa potential, for which we explore the interplay between attraction strength and volume fraction. We show that the normal-stress coefficients exhibit nontrivial features close to the critical point and at high volume fractions in the vicinity of the reentrant glass transition. Finally, we exploit our formulas to make predictions about rod-climbing effects in attractive colloidal dispersions.
Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Schneider, C.; Wißbrock, F.
2017-08-01
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η = mc2/mb2 ∼ 1 / 10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N = 2 , 4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3). We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Energy Technology Data Exchange (ETDEWEB)
Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); IHES, Bures-sur-Yvette (France)
2017-05-15
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m{sup 2}{sub c}/m{sup 2}{sub b}∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A{sup (3)}{sub gq}. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A{sub gg}. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Ramírez Suárez, O. L.; Sparenberg, J.-M.
2017-09-01
We introduce a simplified effective-range function for charged nuclei, related to the modified K matrix but differing from it in several respects. Negative-energy zeros of this function correspond to bound states. Positive-energy zeros correspond to resonances and "echo poles" appearing in elastic-scattering phase-shifts, while its poles correspond to multiple-of-π phase shifts. Padé expansions of this function allow one to parametrize phase shifts on large energy ranges and to calculate resonance and bound-state properties in a very simple way, independently of any potential model. The method is first tested on a d -wave 12C+α potential model. It is shown to lead to a correct estimate of the subthreshold-bound-state asymptotic normalization constant (ANC) starting from the elastic-scattering phase shifts only. Next, the 12C+α experimental p -wave and d -wave phase shifts are analyzed. For the d wave, the relatively large error bars on the phase shifts do not allow one to improve the ANC estimate with respect to existing methods. For the p wave, a value agreeing with the 12C(6Li,d )16O transfer-reaction measurement and with the recent remeasurement of the 16Nβ -delayed α decay is obtained, with improved accuracy. However, the method displays two difficulties: the results are sensitive to the Padé-expansion order and the simplest fits correspond to an imaginary ANC, i.e., to a negative-energy "echo pole," the physical meaning of which is still debatable.
Confidence bounds and hypothesis tests for normal distribution coefficients of variation
Steve Verrill; Richard A. Johnson
2007-01-01
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.
Silvennoinen, Annestiina; Terasvirta, Timo
2017-01-01
A new multivariate volatility model that belongs to the family of conditional correlation GARCH models is introduced. The GARCH equations of this model contain a multiplicative deterministic component to describe long-run movements in volatility and, in addition, the correlations are deterministically time-varying. Parameters of the model are estimated jointly using maximum likelihood. Consistency and asymptotic normality of maximum likelihood estimators is proved. Numerical aspects of the es...
Energy Technology Data Exchange (ETDEWEB)
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Bierenbaum, I. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Klein, S. [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany); Wissbrock, F. [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Linz (Austria); IHES, Bures-sur-Yvette (France)
2014-09-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bierenbaum, I. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Klein, S. [RWTH Aachen Univ. (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2014-03-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given both in Mellin-N space and z-space.
Null distribution of multiple correlation coefficient under mixture normal model
Directory of Open Access Journals (Sweden)
Hydar Ali
2002-01-01
correlation coefficient, R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of 1−R2 and inverse Mellin transform have been used to derive the density of R2.
Null distribution of multiple correlation coefficient under mixture normal model
Ali, Hydar; Nagar, Daya K.
2002-01-01
The multiple correlation coefficient is used in a large variety of statistical tests and regression problems. In this article, we derive the null distribution of the square of the sample multiple correlation coefficient, R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of 1−R2 and inverse Mellin transform have been used to derive the density of R2.
2015-01-01
The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk. PMID:26421617
DEFF Research Database (Denmark)
Silvennoinen, Annestiina; Terasvirta, Timo
A new multivariate volatility model that belongs to the family of conditional correlation GARCH models is introduced. The GARCH equations of this model contain a multiplicative deterministic component to describe long-run movements in volatility and, in addition, the correlations are deterministi......A new multivariate volatility model that belongs to the family of conditional correlation GARCH models is introduced. The GARCH equations of this model contain a multiplicative deterministic component to describe long-run movements in volatility and, in addition, the correlations...... are deterministically time-varying. Parameters of the model are estimated jointly using maximum likelihood. Consistency and asymptotic normality of maximum likelihood estimators is proved. Numerical aspects of the estimation algorithm are discussed. A bivariate empirical example is provided....
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 ...... Mathematics....
Normal tolerances calculation taking into account deviations of external actions coefficients
Directory of Open Access Journals (Sweden)
Shilo G. N.
2009-02-01
Full Text Available Peculiarities of ellipsoidal tolerance regions forming under given deviations of external actions coefficients are being considered. Methods of tolerances assignment under the normal distribution law of key parameters and external factors coefficients have been developed. Mapping method is being used.
Energy Technology Data Exchange (ETDEWEB)
Zielinski, Lech [Universite du Littoral, LMPA (France)], E-mail: lech.zielinski@lmpa.univ-littoral.fr
2002-06-15
Let A=A{sub 0}+v(x) where A{sub 0} is a second-order uniformly elliptic self-adjoint operator in R{sup d} and v is a real valued polynomially growing potential. Assuming that v and the coefficients of A{sub 0} are Hoelder continuous, we study the asymptotic behaviour of the counting function N(A,{lambda}) ({lambda}{sup {yields}}{infinity}) with the remainder estimates depending on the regularity hypotheses. Our strongest regularity hypotheses involve Lipschitz continuity and give the remainder estimate N(A,{lambda})O({l_brace}{lambda}{r_brace}{sup -{mu}}), where {mu} may take an arbitrary value strictly smaller than the best possible value known in the smooth case. In particular, our results are obtained without any hypothesis on critical points of the potential.
Comparison of RNFL thickness and RPE-normalized RNFL attenuation coefficient for glaucoma diagnosis
Vermeer, K. A.; van der Schoot, J.; Lemij, H. G.; de Boer, J. F.
2013-03-01
Recently, a method to determine the retinal nerve fiber layer (RNFL) attenuation coefficient, based on normalization on the retinal pigment epithelium, was introduced. In contrast to conventional RNFL thickness measures, this novel measure represents a scattering property of the RNFL tissue. In this paper, we compare the RNFL thickness and the RNFL attenuation coefficient on 10 normal and 8 glaucomatous eyes by analyzing the correlation coefficient and the receiver operator curves (ROCs). The thickness and attenuation coefficient showed moderate correlation (r=0.82). Smaller correlation coefficients were found within normal (r=0.55) and glaucomatous (r=0.48) eyes. The full separation between normal and glaucomatous eyes based on the RNFL attenuation coefficient yielded an area under the ROC (AROC) of 1.0. The AROC for the RNFL thickness was 0.9875. No statistically significant difference between the two measures was found by comparing the AROC. RNFL attenuation coefficients may thus replace current RNFL thickness measurements or be combined with it to improve glaucoma diagnosis.
Litniewski, Marek; Gorecki, Jerzy
2011-06-28
We have performed intensive computer simulations of the irreversible annihilation reaction: A + A → C + C and of the trapping reaction: A + B → C + B for a variety of three-dimensional fluids composed of identical spherical particles. We have found a significant difference in the asymptotic behavior of the rate coefficients for these reactions. Both the rate coefficients converge to the same value with time t going to infinity but the convergence rate is different: the O(t(-1/2)) term for the annihilation reaction is higher than the corresponding term for the trapping reaction. The simulation results suggest that ratio of the terms is a universal quantity with the value equal to 2 or slightly above. A model for the annihilation reaction based on the superposition approximation predicts the difference in the O(t(-1/2)) terms, but overestimates the value for the annihilation reaction by about 30%. We have also performed simulations for the dimerization process: A + A → E, where E stands for a dimer. The dimerization decreases the reaction rate due to the decrease in the diffusion constant for A. The effect is successfully predicted by a simple model.
Quantitative RNFL attenuation coefficient measurements by RPE-normalized OCT data
Vermeer, K. A.; van der Schoot, J.; Lemij, H. G.; de Boer, J. F.
2012-03-01
We demonstrate significantly different scattering coefficients of the retinal nerve fiber layer (RNFL) between normal and glaucoma subjects. In clinical care, SD-OCT is routinely used to assess the RNFL thickness for glaucoma management. In this way, the full OCT data set is conveniently reduced to an easy to interpret output, matching results from older (non- OCT) instruments. However, OCT provides more data, such as the signal strength itself, which is due to backscattering in the retinal layers. For quantitative analysis, this signal should be normalized to adjust for local differences in the intensity of the beam that reaches the retina. In this paper, we introduce a model that relates the OCT signal to the attenuation coefficient of the tissue. The average RNFL signal (within an A-line) was then normalized based on the observed RPE signal, resulting in normalized RNFL attenuation coefficient maps. These maps showed local defects matching those found in thickness data. The average (normalized) RNFL attenuation coefficient of a fixed band around the optic nerve head was significantly lower in glaucomatous eyes than in normal eyes (3.0mm-1 vs. 4.9mm-1, P<0.01, Mann-Whitney test).
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.
Sandberg, Mattias
2015-01-07
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.
Abou, B.; Néron de Surgy, G.; Wesfreid, J. E.
1997-08-01
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. Nous avons calculé la relation de dispersion des ondes de surface dans une couche de ferrofluide d'épaisseur et de viscosité quelconques, soumise à un champ magnétique normal à sa surface (instabilité de pics de Rosensweig). Cette relation montre que le champ magnétique critique et le vecteur d'onde critique de l'instabilité dépendent de l'épaisseur de la couche de fluide. La relation de dispersion a été simplifiée pour quatre régimes asymptotiques: couche épaisse ou mince et comportement visqueux ou inertiel. Nous avons calculé les valeurs critiques de l'instabilité dans ces quatre cas. Nous montrons qu'un paramètre typique du ferrofluide permet de savoir dans quel régime, visqueux ou inertiel, se situe le ferrofluide près du seuil de l'instabilité.
Peters, C. (Principal Investigator)
1980-01-01
A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.
Optical measurement of isolated canine lung filtration coefficients at normal hematocrits.
Klaesner, J W; Pou, N A; Parker, R E; Finney, C; Roselli, R J
1997-12-01
In this study, lung filtration coefficient (Kfc) values were measured in eight isolated canine lung preparations at normal hematocrit values using three methods: gravimetric, blood-corrected gravimetric, and optical. The lungs were kept in zone 3 conditions and subjected to an average venous pressure increase of 10.24 +/- 0.27 (SE) cmH2O. The resulting Kfc (ml . min-1 . cmH2O-1 . 100 g dry lung wt-1) measured with the gravimetric technique was 0.420 +/- 0.017, which was statistically different from the Kfc measured by the blood-corrected gravimetric method (0.273 +/- 0.018) or the product of the reflection coefficient (sigmaf) and Kfc measured optically (0. 272 +/- 0.018). The optical method involved the use of a Cellco filter cartridge to separate red blood cells from plasma, which allowed measurement of the concentration of the tracer in plasma at normal hematocrits (34 +/- 1.5). The permeability-surface area product was measured using radioactive multiple indicator-dilution methods before, during, and after venous pressure elevations. Results showed that the surface area of the lung did not change significantly during the measurement of Kfc. These studies suggest that sigmafKfc can be measured optically at normal hematocrits, that this measurement is not influenced by blood volume changes that occur during the measurement, and that the optical sigmafKfc agrees with the Kfc obtained via the blood-corrected gravimetric method.
DEFF Research Database (Denmark)
Franco, Antonio; Trapp, Stefan
2008-01-01
calculated by the software ACD/Labs®. The Henderson-Hasselbalch equation was applied to calculate dissociation. Regressions were developed to predict separately for the neutral and the ionic molecule species the distribution coefficient (Kd) normalized to organic carbon (KOC) from log KOW and pKa. The log...... was highly correlated to log KOW. For bases, a nonlinear regression was developed, too. The new regression equations are applicable in the whole pKa range of acids, bases, and amphoters and are useful in particular for relatively strong bases and amphoters, for which no predictive methods specifically have...
Efficient Estimation in Heteroscedastic Varying Coefficient Models
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Chuanhua Wei
2015-07-01
Full Text Available This paper considers statistical inference for the heteroscedastic varying coefficient model. We propose an efficient estimator for coefficient functions that is more efficient than the conventional local-linear estimator. We establish asymptotic normality for the proposed estimator and conduct some simulation to illustrate the performance of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Dranishnikov, A N [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2000-12-31
In this paper we study the similarity between local topology and its global analogue, so-called asymptotic topology. In the asymptotic case, the notions of dimension, cohomological dimension, and absolute extensor are introduced and some basic facts about them are proved. The Higson corona functor establishing a connection between macro- and micro-topology is considered. A relationship between problems of general asymptotic topology and the Novikov conjecture on higher signatures is discussed. Some new results concerning the Novikov conjecture and other related conjectures are presented.
Energy Technology Data Exchange (ETDEWEB)
Tsili, A.C., E-mail: a_tsili@yahoo.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece); Argyropoulou, M.I., E-mail: margyrop@cc.uoi.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece); Tzarouchi, L., E-mail: ltzar@cc.uoi.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece); Dalkalitsis, N., E-mail: ndalkal@cc.uoi.gr [Department of Obstetrics and Gynaecology, University Hospital of Ioannina (Greece); Koliopoulos, G., E-mail: georgekoliopoulos@yahoo.com [Department of Obstetrics and Gynaecology, University Hospital of Ioannina (Greece); Paraskevaidis, E., E-mail: eparaske@cc.uoi.gr [Department of Obstetrics and Gynaecology, University Hospital of Ioannina (Greece); Tsampoulas, K., E-mail: ctsampou@uoi.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece)
2012-08-15
Objectives: To assess the apparent diffusion coefficient (ADC) changes of the normal uterine zones among reproductive women during the menstrual cycle. Methods: The study included 101 women of reproductive age, each with regular cycle and normal endometrium/myometrium, as proved on histopathology or MR imaging examination. Diffusion-weighted (DW) imaging was performed along the axial plane, using a single shot, multi-slice spin-echo planar diffusion pulse sequence and b-values of 0 and 800 s/mm{sup 2}. The mean and standard deviation of the ADC values of normal endometrium/myometrium were calculated for menstrual, proliferative and secretory phase. Analysis of variance followed by the least significant difference test was used for statistical analysis. Results: The ADC values of the endometrium were different in the three phases of the menstrual cycle (menstrual phase: 1.25 {+-} 0.27; proliferative phase: 1.39 {+-} 0.20; secretory phase: 1.50 {+-} 0.18) (F: 9.64, p: 0.00). Statistical significant difference was observed among all groups (p < 0.05). The ADC values of the normal myometrium were different in the three phases of the menstrual cycle (menstrual phase: 1.91 {+-} 0.35; proliferative phase: 1.72 {+-} 0.27; secretory phase: 1.87 {+-} 0.28) (F: 3.60, p: 0.03). Statistical significant difference was observed between menstrual and proliferative phase and between proliferative and secretory phase (p < 0.05). No significant difference was noted between menstrual and secretory phase (p > 0.05). Conclusions: A wide variation of ADC values of normal endometrium and myometrium is observed during different phases of the menstrual cycle.
Tao, Kai; Grand, Stephen P.; Niu, Fenglin
2017-09-01
In seismic full-waveform inversion (FWI), the choice of misfit function determines what information in data is used and ultimately affects the resolution of the inverted images of the Earth's structure. Misfit functions based on traveltime have been successfully applied in global and regional tomographic studies. However, wave propagation through the upper mantle results in multiple phases arriving at a given receiver in a narrow time interval resulting in complicated waveforms that evolve with distance. To extract waveform information as well as traveltime, we use a misfit function based on the normalized correlation coefficient (CC). This misfit function is able to capture the waveform complexities in both phase and relative amplitude within the measurement window. It is also insensitive to absolute amplitude differences between modeled and recorded data, which avoids problems due to uncertainties in source magnitude, radiation pattern, receiver site effects or even miscalibrated instruments. These features make the misfit function based on normalized CC a good candidate to achieve high-resolution images of complex geological structures when interfering phases coexist in the measurement window, such as triplication waveforms. From synthetic tests, we show the advantages of this misfit function over the cross-correlation traveltime misfit function. Preliminary inversion of data from an earthquake in Northeast China images a sharper and stronger amplitude slab stagnant in the middle of the transition zone than FWI of cross-correlation traveltime.
Wang, H J; Pui, M H; Guo, Y; Li, S R; Liu, M J; Guan, J; Zhang, X L; Feng, Y
2014-07-01
To compare the efficacy of apparent diffusion coefficient (ADC) and normalized ADC (nADC) for estimating the histological grade of vesical urothelial carcinoma and to identify an optimal reference for nADC calculation. Thirty patients with histologically confirmed vesical urothelial carcinomas underwent preoperative diffusion-weighted magnetic resonance imaging (DW-MRI) of the pelvis. nADC of the tumour was calculated as ADC (tumour)/ADC (reference) using urine in the bladder lumen, and the obturator internus and gluteus maximus muscles as reference. Receiver operating characteristic (ROC) curves were constructed and compared to identify an optimal reference for nADC calculation. Both ADC and nADC of low-grade tumours (1.112 ± 0.159 × 10(-3) mm(2)/s, 0.403 ± 0.047 × 10(-3) mm(2)/s) were significantly (p obturator internus (0.960) and gluteus maximus (0.945). nADC is superior to ADC for estimating the histological grade of bladder carcinoma using urine in the bladder lumen as an optimal reference for nADC calculation. Copyright © 2014 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.
Bernard, Simon; Marrelec, Guillaume; Laugier, Pascal; Grimal, Quentin
2015-06-01
Resonant ultrasound spectroscopy is an experimental technique for measuring the stiffness of anisotropic solid materials. The free vibration resonant frequencies of a specimen are measured and the stiffness coefficients of the material adjusted to minimize the difference between experimental and predicted frequencies. An issue of this inverse approach is that the measured frequencies are not easily paired with their predicted counterpart, leading to ambiguities in the definition of the objective function. In the past, this issue has been overcome through trial-and-error methods requiring the experimentalist to find the correct pairing, or through involved experimental methods measuring the shapes of the normal vibration modes in addition to their frequencies. The purpose of this work is to show, through a Bayesian formulation, that the inverse problem can be solved automatically and without requiring additions to the usual experimental setup. The pairing of measured and predicted frequencies is considered unknown, and the joint posterior probability distribution of pairing and stiffness is sampled using Markov chain Monte Carlo. The method is illustrated on two published data sets. The first set includes the exact pairing, allowing validation of the method. The second application deals with attenuative materials, for which many predicted modes cannot be observed, further complicating the inverse problem. In that case, introduction of prior information through Bayesian formulation reduces ambiguities.
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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.
Burgers, Phillip; Alexander, David E
2012-01-01
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.
First-principles binary diffusion coefficients for H, H2, and four normal alkanes + N2
Jasper, Ahren W.; Kamarchik, Eugene; Miller, James A.; Klippenstein, Stephen J.
2014-09-01
Collision integrals related to binary (dilute gas) diffusion are calculated classically for six species colliding with N2. The most detailed calculations make no assumptions regarding the complexity of the potential energy surface, and the resulting classical collision integrals are in excellent agreement with previous semiclassical results for H + N2 and H2 + N2 and with recent experimental results for CnH2n+2 + N2, n = 2-4. The detailed classical results are used to test the accuracy of three simplifying assumptions typically made when calculating collision integrals: (1) approximating the intermolecular potential as isotropic, (2) neglecting the internal structure of the colliders (i.e., neglecting inelasticity), and (3) employing unphysical R-12 repulsive interactions. The effect of anisotropy is found to be negligible for H + N2 and H2 + N2 (in agreement with previous quantum mechanical and semiclassical results for systems involving atomic and diatomic species) but is more significant for larger species at low temperatures. For example, the neglect of anisotropy decreases the diffusion coefficient for butane + N2 by 15% at 300 K. The neglect of inelasticity, in contrast, introduces only very small errors. Approximating the repulsive wall as an unphysical R-12 interaction is a significant source of error at all temperatures for the weakly interacting systems H + N2 and H2 + N2, with errors as large as 40%. For the normal alkanes in N2, which feature stronger interactions, the 12/6 Lennard-Jones approximation is found to be accurate, particularly at temperatures above ˜700 K where it predicts the full-dimensional result to within 5% (although with somewhat different temperature dependence). Overall, the typical practical approach of assuming isotropic 12/6 Lennard-Jones interactions is confirmed to be suitable for combustion applications except for weakly interacting systems, such as H + N2. For these systems, anisotropy and inelasticity can safely be
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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.
Kiessling, Michael Karl-Heinz
2017-10-01
Let z\\in C, let σ ^2>0 be a variance, and for N\\in N define the integrals E_N^{}(z;σ ) := {1/σ } \\int _R\\ (x^2+z^2) e^{-{1/2σ^2 x^2}}{√{2π }}/dx \\quad if N=1, {1/σ } \\int _{R^N} \\prod \\prod \\limits _{1≤ k1. These are expected values of the polynomials P_N^{}(z)=\\prod _{1≤ n≤ N}(X_n^2+z^2) whose 2 N zeros ± i X_k^{}_{k=1,\\ldots ,N} are generated by N identically distributed multi-variate mean-zero normal random variables {X_k}N_{k=1} with co-variance {Cov}_N^{}(X_k,X_l)=(1+σ ^2-1/N)δ _{k,l}+σ ^2-1/N(1-δ _{k,l}). The E_N^{}(z;σ ) are polynomials in z^2, explicitly computable for arbitrary N, yet a list of the first three E_N^{}(z;σ ) shows that the expressions become unwieldy already for moderate N—unless σ = 1, in which case E_N^{}(z;1) = (1+z^2)^N for all z\\in C and N\\in N. (Incidentally, commonly available computer algebra evaluates the integrals E_N^{}(z;σ ) only for N up to a dozen, due to memory constraints). Asymptotic evaluations are needed for the large- N regime. For general complex z these have traditionally been limited to analytic expansion techniques; several rigorous results are proved for complex z near 0. Yet if z\\in R one can also compute this "infinite-degree" limit with the help of the familiar relative entropy principle for probability measures; a rigorous proof of this fact is supplied. Computer algebra-generated evidence is presented in support of a conjecture that a generalization of the relative entropy principle to signed or complex measures governs the N→ ∞ asymptotics of the regime iz\\in R. Potential generalizations, in particular to point vortex ensembles and the prescribed Gauss curvature problem, and to random matrix ensembles, are emphasized.
Effects of poroelastic coefficients on normal vibration modes in vocal-fold tissues.
Tao, Chao; Liu, Xiaojun
2011-02-01
The vocal-fold tissue is treated as a transversally isotropic fluid-saturated porous material. Effects of poroelastic coefficients on eigenfrequencies and eigenmodes of the vocal-fold vibration are investigated using the Ritz method. The study demonstrates that the often-used elastic model is only a particular case of the poroelastic model with an infinite fluid-solid mass coupling parameter. The elastic model may be considered appropriate for the vocal-fold tissue when the absolute value of the fluid-solid mass coupling parameter is larger than 10(5) kg/m(3). Otherwise, the poroelastic model may be more accurate. The degree of compressibility of the vocal tissue can also been described by the poroelastic coefficients. Finally, it is revealed that the liquid and solid components in a poroelastic model could have different modal shapes when the coupling between them is weak. The mode decoupling could cause desynchronization and irregular vibration of the folds.
de Bernard, Simon; Marrelec, Guillaume; Laugier, Pascal; GRIMAL, Quentin
2015-01-01
International audience; Resonant ultrasound spectroscopy is an experimental technique for measuring the stiffness of anisotropic solid materials. The free vibration resonant frequencies of a specimen are measured and the stiffness coefficients of the material adjusted to minimize the difference between experimental and predicted frequencies. An issue of this inverse approach is that the measured frequencies are not easily paired with their predicted counterpart, leading to ambiguities in the ...
Algebraic polynomials with random coefficients
Directory of Open Access Journals (Sweden)
K. Farahmand
2002-01-01
Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.
Kawel, Nadine; Nacif, Marcelo; Santini, Francesco; Liu, Songtao; Bremerich, Jens; Arai, Andrew E; Bluemke, David A
2012-09-01
To evaluate the influence of contrast agents with different relaxivity on the partition coefficient (λ) and timing of equilibration using a modified Look-Locker inversion recovery (MOLLI) sequence in cardiac magnetic resonance imaging (MRI). MOLLI was acquired in 20 healthy subjects (1.5T) at the mid-ventricular short axis precontrast and 5, 10, 20, 25, and 30 minutes after administration of a bolus of 0.15 mmol/kg gadobenate dimeglumine (Gd-BOPTA) (n = 10) or gadopentetate dimeglumine (Gd-DTPA) (n = 10). T1 times were measured in myocardium and blood pool. λ was approximated by ΔR1(myocardium) /ΔR1(blood) . Values for Gd-BOPTA and Gd-DTPA were compared. Interobserver agreement was evaluated (intraclass correlation coefficient [ICC]). T1 times of myocardium and blood pool (P < 0.001) and λ (0.42 ± 0.03 and 0.47 ± 0.04, respectively, P < 0.001; excluding 5 minutes for Gd-BOPTA) were significantly lower for Gd-BOPTA than Gd-DTPA. The λ((Gd-DTPA)) showed no significant variation between 5 and 30 minutes. The λ((Gd-BOPTA)) values were significantly lower at 5 minutes compared to other times (0.38 vs. 0.42; P < 0.05). Interobserver agreement for λ values was excellent with Gd-BOPTA (ICC = 0.818) and good for Gd-DTPA (ICC = 0.631). The λ((Gd-BOPTA)) values were significantly lower compared to λ((Gd-DTPA)) at the same administered dose. Using Gd-BOPTA, the equilibrium between myocardium and blood pool was not achieved at 5 minutes postcontrast. Copyright © 2012 Wiley Periodicals, Inc.
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.
Imaoka, Haruna; Kinugawa, Kenichi
2017-03-01
Thermal conductivity, shear viscosity, and bulk viscosity of normal liquid 4He at 1.7-4.0 K are calculated using path integral centroid molecular dynamics (CMD) simulations. The calculated thermal conductivity and shear viscosity above lambda transition temperature are on the same order of magnitude as experimental values, while the agreement of shear viscosity is better. Above 2.3 K the CMD well reproduces the temperature dependences of isochoric shear viscosity and of the time integral of the energy current and off-diagonal stress tensor correlation functions. The calculated bulk viscosity, not known in experiments, is several times larger than shear viscosity.
Niu, Gang; Yu, Xuewen; Yang, Jian; Wang, Rong; Zhang, Shaojuan; Guo, Youmin
2011-01-01
The aim of the present study was to compare the relationship of morphologically defined non-bulging/herniated, bulging and herniated intervertebral lumbar discs with quantitative apparent diffusion coefficient (ADC). Thirty-two healthy volunteers and 28 patients with back pain or sciatica were examined by MRI. All intervertebral lumbar discs from L1 to S1 were classified according to morphological abnormality and degenerated grades. The ADC values of nucleus pulposus (NP) were measured and recorded. The significant differences about mean ADC values of NP were found between non-bulging/herniated discs and bulging discs as well as herniated discs (P herniated discs (P > 0.05). Moreover, statistically significant relationship was found in the mean ADC values of NP between “non-bulging/herniated and non-degenerated discs” and “non-bulging/herniated degenerated discs” as well as herniated discs (P disc level revealed an inverse correlation (r = -0.18). The ADC map of the NP is a potentially useful tool for the quantitative assessment of componential and molecular alterations accompanied with lumbar disc abnormalities. PMID:23554690
Esmailpour, Ayoub; Taghiyari, Hamid Reza; Zolfaghari, Habib
2017-06-01
Effects of impregnation with silver nano-suspension as well as heat-treatment on sound absorption coefficients (AC) were studied in tangential direction of five different solid woods based on their importance. AC was measured at two frequencies of 250 and 500 Hz. A 400 ppm nanosuspension was used for the impregnation; silver nanoparticles had a size range of 30-80 nm. Based on the obtained results, the species reacted significantly different in absorbing sound at the two frequencies. Impregnation with nano-suspension substantially decreased AC at the lower frequency of 250 Hz; it did not show any particular trend when AC was measured at the frequency of 500 Hz. Heat treatment significantly increased AC at the frequency of 250 Hz. ACs of mulberry tended to be similar at the two frequencies; in the other four species though, ACs were significantly different. High significant correlations were found in the hardwoods between the ACs measured at the two frequencies.
Zhu, Jie; Zhang, Jie; Gao, Jia-Yin; Li, Jin-Ning; Yang, Da-Wei; Chen, Min; Zhou, Cheng; Yang, Zheng-Han
2017-01-01
Apparent diffusion coefficient (ADC) measurement in diffusion-weighted imaging (DWI) has been reported to be a helpful biomarker for detection and characterization of lesion. In view of the importance of ADC measurement reproducibility, the aim of this study was to probe the variability of the healthy hepatic ADC values measured at 3 MR scanners from different vendors and with different field strengths, and to investigate the reproducibility of normalized ADC (nADC) value with the spleen as the reference organ. Thirty enrolled healthy volunteers received DWI with GE 1.5T, Siemens 1.5T, and Philips 3.0T magnetic resonance (MR) systems on liver and spleen (session 1) and were imaged again after 10 to 14 days using only GE 1.5T MR and Philips 3.0T MR systems (session 2). Interscan agreement and reproducibility of ADC measurements of liver and the calculated nADC values (ADCliver/ADCspleen) were statistically evaluated between 2 sessions. In session 1, ADC and nADC values of liver were evaluated for the scanner-related variability by 2-way analysis of variance and intraclass correlation coefficients (ICCs). Coefficients of variation (CVs) of ADCs and nADCs of liver were calculated for both 1.5 and 3.0-T MR system. Interscan agreement and reproducibility of ADC measurements of liver and related nADCs between 2 sessions were found to be satisfactory with ICC values of 0.773 to 0.905. In session 1, the liver nADCs obtained from different scanners were consistent (P = 0.112) without any significant difference in multiple comparison (P = 0.117 to >0.99) by using 2-way analysis of variance with post-hoc analysis of Bonferroni method, although the liver ADCs varied significantly (P < 0.001). nADCs measured by 3 scanners were in good interscanner agreements with ICCs of 0.685 to 0.776. The mean CV of nADCs of both 1.5T MR scanners (9.6%) was similar to that of 3.0T MR scanner (8.9%). ADCs measured at 3 MR scanners with different field strengths and vendors could
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Mohd Zamri Jusoh
2013-06-01
Full Text Available The Direct Piercing Carved Wood Panel (DPCWP installed in Masjid Abidin, Kuala Terengganu, is one example that carries much aesthetic and artistic value. The use of DPCWP in earlier mosques was envisaged to improve the intelligibility of indoor speech because the perforated panels allow some of the sound energy to pass through. In this paper, the normal incidence sound absorption coefficient of DPCWP with Daun Sireh motif, which is a form of floral pattern, is discussed. The Daun Sireh motif was chosen and investigated for 30%, 35%, 40%, and 45% perforation ratios. The simulations were conducted using BEASY Acoustic Software based on the boundary element method. The simulation results were compared with measurements obtained by using the sound intensity technique. An accompanying discussion on both the numerical and the measurement tendencies of the sound absorption characteristics of the DPCWP is provided. The results show that the DPCWP with Daun Sireh motif can act as a good sound absorber.
Hirosawa, Kunikazu; Takashima, Kazuhiro; Nakagawa, Hiroshi; Kon, Makoto; Yamamoto, Aki; Lauriks, Walter
2009-12-01
Three different techniques for evaluating the absorption coefficient of sound absorbing materials in free field conditions are discussed. One technique measures the acoustic impedance at one point nearby a specimen, the other two techniques evaluate the impedance from the transfer function of two sound pressures and two particle velocities at two points. These are called "PU-method," "PP-method," and "UU-method," respectively. An iterative algorithm to estimate the acoustic impedance of the locally reactive specimen in the spherical wave field is also applied. First, the effect of receiver positions, specimen areas, and source heights to the measured normal absorption coefficient is investigated by the boundary element method. According to these investigations, the PU-method is most stable against the effect of specimen area, and the UU-method is easily affected by that effect. Closer source to the specimen distance is advantageous for the signal to noise ratio of these measurement techniques, but correction for the effect of the spherical wave field has to be applied. As a finding, the iterative algorithm works for all of three techniques. Finally, the PU-method is applied experimentally with a pressure-velocity sensor and a loudspeaker in a hemi-anechoic room. As a result, the calculated results have been verified.
Baron, Paul; Dorrius, Monique D.; Kappert, Peter; Oudkerk, Matthijs; Sijens, Paul E.
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
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....
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.
Leipus, Remigijus; Philippe, Anne; Pilipauskaitė, Vytautė; Surgailis, Donatas
2015-01-01
We discuss nonparametric estimation of the distribution function $G(x)$ of the autoregressive coefficient $a \\in (-1,1)$ from a panel of $N$ random-coefficient AR(1) data, each of length $n$, by the empirical distribution function of lag 1 sample autocorrelations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established under some regularity conditions on $G(x)$ as $N$ and $n$ increase to ...
Azarov, AV; Ochkin, VN
2004-01-01
The electric characteristics of the cathode layer of a normal glow discharge are discussed. The value of the normal current density and its dependence on the discharge parameters are modeled within a one-dimensional drift approximation with a local ionization. The dependence of the coefficient of
Candra, Henry; Yuwono, Mitchell; Chai, Rifai; Nguyen, Hung T; Su, Steven
2017-07-01
Recognizing emotion from EEG signals is a complicated task that requires complex features and a substantial number of EEG channels. Simple algorithms to analyse the feature and reduce the EEG channel number will give an indispensable advantages. Therefore, this study explores a combination of wavelet entropy and average wavelet coefficient (WEAVE) as a potential EEG-emotion feature to classify valence and arousal emotions with the advantage of the ability to identify the occurrence of a pattern while at the same time identify the shape of a pattern in EEG emotion signal. The complexity of the feature was reduced using the Normalized Mutual Information (NMI) method to obtain a reduced number of channels. Classification with the WEAVE feature achieved 76.8% accuracy for valence and 74.3% for arousal emotion, respectively. The analysis with NMI shows that the WEAVE feature has linear characteristics and offers possibilities to reduce the EEG channels to a certain number. Further analysis also reveals that detection of valence emotion with reduced EEG channels has a different combination of EEG channels compared to arousal emotion.
Estimating varying coefficients for partial differential equation models.
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2017-09-01
Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.
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
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.
Asymptotic prime partitions of integers
Bartel, Johann; Bhaduri, R. K.; Brack, Matthias; Murthy, M. V. N.
2017-05-01
In this paper, we discuss P (n ) , the number of ways a given integer n may be written as a sum of primes. In particular, an asymptotic form Pas(n ) valid for n →∞ is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime partitions in number theory, is constructed. Next, the density of states is obtained using the saddle-point method for Laplace inversion of the partition function in the limit of large n . This gives directly the asymptotic number of prime partitions Pas(n ) . The leading term in the asymptotic expression grows exponentially as √{n /ln(n ) } and agrees with previous estimates. We calculate the next-to-leading-order term in the exponent, proportional to ln[ln(n )]/ln(n ) , and we show that an earlier result in the literature for its coefficient is incorrect. Furthermore, we also calculate the next higher-order correction, proportional to 1 /ln(n ) and given in Eq. (43), which so far has not been available in the literature. Finally, we compare our analytical results with the exact numerical values of P (n ) up to n ˜8 ×106 . For the highest values, the remaining error between the exact P (n ) and our Pas(n ) is only about half of that obtained with the leading-order approximation. But we also show that, unlike for other types of partitions, the asymptotic limit for the prime partitions is still quite far from being reached even for n ˜107 .
Numerical algorithms for uniform Airy-type asymptotic expansions
N.M. Temme (Nico)
1997-01-01
textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing
ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2017-11-01
Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
Block Empirical Likelihood for Longitudinal Single-Index Varying-Coefficient Model
Directory of Open Access Journals (Sweden)
Yunquan Song
2013-01-01
Full Text Available In this paper, we consider a single-index varying-coefficient model with application to longitudinal data. In order to accommodate the within-group correlation, we apply the block empirical likelihood procedure to longitudinal single-index varying-coefficient model, and prove a nonparametric version of Wilks’ theorem which can be used to construct the block empirical likelihood confidence region with asymptotically correct coverage probability for the parametric component. In comparison with normal approximations, the proposed method does not require a consistent estimator for the asymptotic covariance matrix, making it easier to conduct inference for the model's parametric component. Simulations demonstrate how the proposed method works.
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
Zhou, Q.; Leydesdorff, L.
2016-01-01
We prove that Ochiai similarity of the co-occurrence matrix is equal to cosine similarity in the underlying occurrence matrix. Neither the cosine nor the Pearson correlation should be used for the normalization of co-occurrence matrices because the similarity is then normalized twice, and therefore
National Research Council Canada - National Science Library
McDonald, Elizabeth S; Schopp, Jennifer G; Peacock, Sue; DeMartini, Wendy B; DeMartini, Wendy D; Rahbar, Habib; Lehman, Constance D; Partridge, Savannah C
2014-01-01
...) values of normal breast fibroglandular tissue on diffusion-weighted imaging (DWI) at 3 T. The retrospective study included 103 women with negative bilateral findings on 3-T breast MRI examinations...
Optimal asymptotic cloning machines
Chiribella, Giulio; Yang, Yuxiang
2014-06-01
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic cloners enjoy a universality property, consisting in the fact that scaling of their fidelity does not depend on the specific details of the input states, but only on the number of free parameters needed to specify them.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
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...
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.
An efficient locally asymptotic parametric test in nonlinear ...
African Journals Online (AJOL)
Abstract. In this paper we deal with a locally asymptotic stringent test for a general class of nonlinear time series heteroscedastic models. Based on the local asymptotic normality (LAN) property of these models, we propose a scoretyp test statistic for testing hypotheses on the parameters appearing in the mean and variance ...
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.
Quadratic maps without asymptotic measure
Hofbauer, Franz; Keller, Gerhard
1990-02-01
An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences.
Scheven, U. M.; Harris, R.; Johns, M. L.
2008-12-01
The experimental characterization of voidspaces in porous media generally includes measurements of volume averaged scalar properties such as porosity, dispersivity, or the hydrodynamic radius rh = V/S, where V and S are the volume and surface area of the pore space respectively. Displacement encoding NMR experiments have made significant contributions to this characterization. It is clear, however, that NMR derived dispersivities in packed beds—the one random porous system for which there exist canonical but incompatible theoretical predictions with few or no adjustable parameters—can be affected by the same experimental complications which have substantially contributed to the puzzling scatter in published dispersion results based on elution experiments. Notable among these are macroscopic flow heterogeneities near walls, and inhomogeneous flow injection. Using the first three cumulants we delineate a transition from a pre-asymptotic to a quasi-asymptotic dispersion regime and determine the true dispersivity of the random pack of spheres.
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Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex,Falmer Campus, Brighton, BN1 9QH (United Kingdom); Sannino, Francesco [CP-Origins & the Danish Institute for Advanced Study Danish IAS, University of Southern Denmark,Campusvej 55, DK-5230 Odense (Denmark)
2014-12-31
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 fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
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...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed....
Asymptotically flat multiblack lenses
Tomizawa, Shinya; Okuda, Taika
2017-03-01
We present an asymptotically flat and stationary multiblack lens solution with biaxisymmetry of U (1 )×U (1 ) as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of L (n ,1 )=S3/Zn as well as a sphere S3. Moreover, we show that, in contrast to the higher-dimensional Majumdar-Papapetrou multiblack hole and multi-Breckenridge-Myers-Peet-Vafa (BMPV) black hole spacetime, the metric is smooth on each horizon even if the horizon topology is spherical.
Asymptotic structures of cardinals
Directory of Open Access Journals (Sweden)
Oleksandr Petrenko
2014-07-01
Full Text Available A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.
Ho, Pei-Ming
2017-04-01
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.
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.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
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O' Flynn, Elizabeth A.M.; Morgan, Veronica A.; Giles, Sharon L. [Cancer Research UK and ESPSRC Cancer Imaging Centre, Clinical Magnetic Resonance Group, Surrey (United Kingdom); deSouza, Nandita M. [Royal Marsden NHS Foundation Trust, Clinical Magnetic Resonance Group, Institute of Cancer Research, Surrey (United Kingdom)
2012-07-15
To establish the reproducibility of apparent diffusion coefficient (ADC) measurements in normal fibroglandular breast tissue and to assess variation in ADC values with phase of the menstrual cycle and menopausal status. Thirty-one volunteers (13 premenopausal, 18 postmenopausal) underwent magnetic resonance twice (interval 11-22 days) using diffusion-weighted MRI. ADC{sub total} and a perfusion-insensitive ADC{sub high} (omitting b = 0) were calculated. Reproducibility and inter-observer variability of mean ADC values were assessed. The difference in mean ADC values between the two phases of the menstrual cycle and the postmenopausal breast were evaluated. ADC{sub total} and ADC{sub high} showed good reproducibility (r% = 17.6, 22.4). ADC{sub high} showed very good inter-observer agreement (kappa = 0.83). The intraclass correlation coefficients (ICC) were 0.93 and 0.91. Mean ADC values were significantly lower in the postmenopausal breast (ADC{sub total} 1.46 {+-} 0.3 x 10{sup -3} mm{sup 2}/s, ADC{sub high} 1.33 {+-} 0.3 x 10{sup -3} mm{sup 2}/s) compared with the premenopausal breast (ADC{sub total} 1.84 {+-} 0.26 x 10{sup -3} mm{sup 2}/s, ADC{sub high} 1.77 {+-} 0.26 x 10{sup -3} mm{sup 2}/s; both P < 0.001). No significant difference was seen in ADC values in relation to menstrual cycle (ADC{sub total} P = 0.2, ADC{sub high} P = 0.24) or between postmenopausal women taking or not taking oestrogen supplements (ADC{sub total} P = 0.6, ADC{sub high} P = 0.46). ADC values in fibroglandular breast tissue are reproducible. Lower ADC values within the postmenopausal breast may reduce diffusion-weighted contrast and have implications for accurately detecting tumours. (orig.)
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 ...
Asymptotic independence for unimodal densities
Balkema, G.; Nolde, N.
2010-01-01
Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (DFs). DFs are rarely available in an explicit form, especially in the multivariate case. Often
Asymptotic Safety, Fractals, and Cosmology
Reuter, Martin; Saueressig, Frank
These lecture notes introduce the basic ideas of the asymptotic safety approach to quantum Einstein gravity (QEG). In particular they provide the background for recent work on the possibly multi-fractal structure of the QEG space-times. Implications of asymptotic safety for the cosmology of the early Universe are also discussed.
Essentially asymptotically stable homoclinic networks
Driesse, R.; Homburg, A.J.
2009-01-01
Melbourne [An example of a nonasymptotically stable attractor, Nonlinearity 4(3) (1991), pp. 835-844] discusses an example of a robust heteroclinic network that is not asymptotically stable but which has the strong attracting property called essential asymptotic stability. We establish that this
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 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...... 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...
Andrić, Filip; Šegan, Sandra; Dramićanin, Aleksandra; Majstorović, Helena; Milojković-Opsenica, Dušanka
2016-08-05
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
Frequency-dependent seismic reflection coefficient for discriminating gas reservoirs
Xu, Duo; Wang, Yanghua; Gan, Qigan; Tang, Jianming
2011-12-01
The asymptotic equation of wave propagation in fluid-saturated porous media is available for calculating the normal reflection coefficient within a seismic frequency band. This frequency-dependent reflection coefficient is expressed in terms of a dimensionless parameter ɛ, which is the product of the reservoir fluid mobility (i.e. inverse viscosity), fluid density and the frequency of the signal. In this paper, we apply this expression to the Xinchang gas field, China, where reservoirs are in super-tight sands with very low permeability. We demonstrate that the variation in the reflection coefficient at a gas-water contact as a transition zone within a sand formation is observable within the seismic frequency band. Then, we conduct seismic inversion to generate attributes which first indicate the existence of fluid (either gas or water), and then discriminate a gas reservoir from a water reservoir.
Barral, M; Soyer, P; Ben Hassen, W; Gayat, E; Aout, M; Chiaradia, M; Rahmouni, A; Luciani, A
2013-04-01
To evaluate reproducibility and variations in apparent diffusion coefficient (ADC) measurement in normal pancreatic parenchyma at 1.5- and 3.0-Tesla and determine if differences may exist between the four pancreatic segments. Diffusion-weighted MR imaging of the pancreas was performed at 1.5-Tesla in 20 patients and at 3.0-Tesla in other 20 patients strictly matched for gender and age using the same b values (0, 400 and 800s/mm(2)). Two independent observers placed regions of interest within the four pancreatic segments to measure ADC at both fields. Intra- and inter-observer agreement in ADC measurement was assessed using Bland-Altman analysis and comparison between ADC values obtained at both fields using non-parametrical tests. There were no significant differences in ADC between repeated measurements and between ADC obtained at 1.5-Tesla and those at 3.0-Tesla. The 95% limits of intra-observer agreement between ADC were 2.3%-22.7% at 1.5-Tesla and 1%-24.2% at 3.0-Tesla and those for inter-observer agreement between 1.9%-14% at 1.5-Tesla and 8%-25% at 3.0-Tesla. ADC values were similar in all pancreatic segments at 3.0-T whereas the tail had lower ADC at 1.5-Tesla. ADC measurement conveys high degrees of intra- and inter-observer reproducibility. ADC have homogeneous distribution among the four pancreatic segments at 3.0-Tesla. Copyright © 2012 Éditions françaises de radiologie. Published by Elsevier Masson SAS. All rights reserved.
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.
Asymptotic Expansions and Bootstrapping Distributions for Dependent Variables: A Martingale Approach
Mykland, Per Aslak
1992-01-01
The paper develops a one-step triangular array asymptotic expansion for continuous martingales which are asymptotically normal. Mixing conditions are not required, but the quadratic variations of the martingales must satisfy a law of large numbers and a central limit type condition. From this result we derive expansions for the distributions of estimators in asymptotically ergodic differential equation models, and also for the bootstrapping estimators of these distributions.
On the asymptotic behavior of the Durbin-Watson statistic for ARX processes in adaptive tracking
Bercu, Bernard; Portier, Bruno; Vazquez, V.
2012-01-01
International audience; A wide literature is available on the asymptotic behavior of the Durbin-Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin-Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin Watson statistic for ARX models in adaptive tracking. On the one hand, we show the almost sure convergence as well as the asymptotic normality of the ...
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...
Top mass from asymptotic safety
Eichhorn, Astrid; Held, Aaron
2018-02-01
We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately 170GeV is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of Mt,pole ≈ 171GeV.
Integrable theories that are asymptotically CFT
Evans, J M; Jonathan M Evans; Timothy J Hollowood
1995-01-01
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...
Asymptotic vacua with higher derivatives
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Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Asymptotic inference for jump diffusions with state-dependent intensity
Becheri, Gaia; Drost, Feico; Werker, Bas
2016-01-01
We establish the local asymptotic normality property for a class of ergodic parametric jump-diffusion processes with state-dependent intensity and known volatility function sampled at high frequency. We prove that the inference problem about the drift and jump parameters is adaptive with respect to
A note on properties of iterative procedures of asymptotic evidence
Paardekooper, H.C.H.; Steens, H.B.A.; Van der Hoek, G.
1989-01-01
The theoretical results obtained by Dzhaparidze (1983) are based on a theorem dealing with the asymptotically normality of an estimator which is the result of a Newton-like iteration method. The paper establishes a new theorem that supports the use of a more robust BFGS Quasi Newton method with
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...
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...
Naturalness of asymptotically safe Higgs
DEFF Research Database (Denmark)
Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro
2017-01-01
that the scalars can be lighter than Λ. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around Λ ~ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful...
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...
Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems
Dipierro, Serena; Maggi, Francesco; Valdinoci, Enrico
2017-10-01
We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels |z|^{-n-s}, with s\\in (0,1) and n the dimension of the ambient space. The fractional Young's law (contact angle condition) predicted by these models coincides, in the limit as s→ 1^-, with the classical Young's law determined by the Gauss free energy. Here we refine this asymptotics by showing that, for s close to 1, the fractional contact angle is always smaller than its classical counterpart when the relative adhesion coefficient σ is negative, and larger if σ is positive. In addition, we address the asymptotics of the fractional Young's law in the limit case s→ 0^+ of interaction kernels with heavy tails. Interestingly, near s=0, the dependence of the contact angle from the relative adhesion coefficient becomes linear.
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... considerable effect on the final estimations of the method, in particular on the coefficient of variation of the estimated failure probability. Based on these observations, a simple optimization algorithm is proposed which distributes the support points so that the coefficient of variation of the method...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...
Asymptotic ray theory of linear viscoelastic media
Nechtschein, Stephane
The Asymptotic Ray Theory (ART) has become a frequently used technique for the numerical modeling of seismic wave propagation in complex geological models. This theory was originally developed for elastic structures with the ray amplitude computation performed in the time domain. ART is now extended to linear viscoelastic media, the linear theory of viscoelasticity being used to simulate the dispersive properties peculiar to anelastic materials. This extension of ART is based on the introduction of a frequency dependent amplitude term having the same properties as in the elastic case and on a frequency dependent complex phase function. Consequently the ray amplitude computation is now performed in the frequency domain, the final solution being obtained by carrying out an Inverse Fourier Transform. Since ART is used, the boundary conditions for the kinematic and dynamic properties of the waves only have to be satisfied locally. This results in a much simpler Snell's Law for linear viscoelastic media, which in fact turns out to be of the same form as for the elastic case. No complex angle is involved. Furthermore the rays, the ray parameters, the geometrical spreading are all real values implying that the direction of the attenuation vector is always along the ray. The reflection and transmission coefficients were therefore rederived. These viscoelastic ART coefficients behave differently from those obtained with the Plane Wave method. Their amplitude and phase curves are always close to those computed for perfectly elastic media and they smoothly approach the elastic reflection/transmission coefficients when the quality factors increase to infinity. These same ART coefficients also display some non-physical results depending on the choice of the quality factors. This last feature might be useful to determine whether or not the two media making up the interface can be regarded as linear viscoelastic. Finally the results obtained from synthetic seismogram computations
Asymptotic symmetries and electromagnetic memory
Pasterski, Sabrina
2017-09-01
Recent investigations into asymptotic symmetries of gauge theory and gravity have illuminated connections between gauge field zero-mode sectors, the corresponding soft factors, and their classically observable counterparts — so called "memories". Namely, low frequency emissions in momentum space correspond to long time integrations of the corre-sponding radiation in position space. Memory effect observables constructed in this manner are non-vanishing in typical scattering processes, which has implications for the asymptotic symmetry group. Here we complete this triad for the case of large U(1) gauge symmetries at null infinity. In particular, we show that the previously studied electromagnetic memory effect, whereby the passage of electromagnetic radiation produces a net velocity kick for test charges in a distant detector, is the position space observable corresponding to th Weinberg soft photon pole in momentum space scattering amplitudes.
Root Asymptotics of Spectral Polynomials
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B. Shapiro
2007-01-01
Full Text Available We have been studying the asymptotic energy distribution of the algebraic part of the spectrum of the one-dimensional sextic anharmonic oscillator. We review some (both old and recent results on the multiparameter spectral problem and show that our problem ranks among the degenerate cases of Heine-Stieltjes spectral problem, and we derive the density of the corresponding probability measure.
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.
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
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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.
Asymptotics of the filtration problem for suspension in porous media
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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.
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
Numerical Relativity and Asymptotic Flatness
Deadman, E.; Stewart, J. M.
2009-01-01
It is highly plausible that the region of space-time far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al. (1962), Sachs (1962) and Newman & Unti (1962), rely on careful, clever, a-priori choices of chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap...
On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model
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Attila Dénes
2016-09-01
Full Text Available We make more realistic our model [Nonlinear Anal. 73(2010, 650-659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka-Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original non-autonomous system "rolls up"' onto a cycle of the limiting Lotka-Volterra equation as $t\\to\\infty$, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.
Energy Technology Data Exchange (ETDEWEB)
Marklund, Mette [Parker Institute: Imaging Unit, Frederiksberg Hospital (Denmark)], E-mail: mm@frh.regionh.dk; Christensen, Robin [Parker Institute: Musculoskeletal Statistics Unit, Frederiksberg Hospital (Denmark)], E-mail: robin.christensen@frh.regionh.dk; Torp-Pedersen, Soren [Parker Institute: Imaging Unit, Frederiksberg Hospital (Denmark)], E-mail: stp@frh.regionh.dk; Thomsen, Carsten [Department of Radiology, Rigshospitalet, University of Copenhagen (Denmark)], E-mail: carsten.thomsen@rh.regionh.dk; Nolsoe, Christian P. [Department of Radiology, Koge Hospital (Denmark)], E-mail: cnolsoe@dadlnet.dk
2009-01-15
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
On the asymptotic expansion of the Bergman kernel
Seto, Shoo
Let (L, h) → (M, o) be a polarized Kahler manifold. We define the Bergman kernel for H0(M, Lk), holomorphic sections of the high tensor powers of the line bundle L. In this thesis, we will study the asymptotic expansion of the Bergman kernel. We will consider the on-diagonal, near-diagonal and far off-diagonal, using L2 estimates to show the existence of the asymptotic expansion and computation of the coefficients for the on and near-diagonal case, and a heat kernel approach to show the exponential decay of the off-diagonal of the Bergman kernel for noncompact manifolds assuming only a lower bound on Ricci curvature and C2 regularity of the metric.
Ultraviolet asymptotics of glueball propagators
Bochicchio, Marco; Muscinelli, Samuele P.
2013-08-01
We point out that perturbation theory in conjunction with the renormalization group ( RG) puts a severe constraint on the structure of the large- N non-perturbative glueball propagators in SU( N) pure Y M, in QCD and in = 1 SU SY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure Y M and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large- N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large- N limit of Y M . We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/large- N Gauge Theory correspondence satisfies the constraint, actually as expected, since the gravity side of the correspondence is in fact strongly coupled in the ultraviolet. On the contrary, the Topological Field Theory satisfies the constraint that follows by the asymptotic freedom.
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 Waveform Evaluation (AWE) Technique for Frequency Domain Electromagnetic Analysis
Cockrell, C. R.; Beck, F. B.
1996-01-01
The Asymptotic Waveform Evaluation (AWE) technique is applied to a generalized frequency domain electromagnetic problem. Most of the frequency domain techniques in computational electromagnetics result in a matrix equation, which is solved at a single frequency. In the AWE technique, the Taylor series expansion around that frequency is applied to the matrix equation. The coefficients of the Taylor's series are obtained in terms of the frequency derivatives of the matrices evaluated at the expansion frequency. The coefficients hence obtained will be used to predict the frequency response of the system over a frequency range. The detailed derivation of the coefficients (called 'moments') is given along with an illustration for electric field integral equation (or Method of Moments) technique. The radar cross section (RCS) frequency response of a square plate is presented using the AWE technique and is compared with the exact solution at various frequencies.
Asymptotic Normality of Poly-T Densities with Bayesian Applications.
1987-10-01
01003 P.O. Box 16268 Alexandria, VA 22302-0268 Mr. Brad Sympson Navy Personnel R&D Center Dr. H. Wallace Sinaiko San Diego, CA 92152-6800 Manpower...Vale Assessment Systems Corp. Dr. Rand R. Wilcox 2233 University Avenue University of Southern Suite 310 California St. Paul, MN 55114 Department of
Stable Parameter Estimation for Autoregressive Equations with Random Coefficients
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V. B. Goryainov
2014-01-01
Full Text Available In recent yearsthere has been a growing interest in non-linear time series models. They are more flexible than traditional linear models and allow more adequate description of real data. Among these models a autoregressive model with random coefficients plays an important role. It is widely used in various fields of science and technology, for example, in physics, biology, economics and finance. The model parameters are the mean values of autoregressive coefficients. Their evaluation is the main task of model identification. The basic method of estimation is still the least squares method, which gives good results for Gaussian time series, but it is quite sensitive to even small disturbancesin the assumption of Gaussian observations. In this paper we propose estimates, which generalize the least squares estimate in the sense that the quadratic objective function is replaced by an arbitrary convex and even function. Reasonable choice of objective function allows you to keep the benefits of the least squares estimate and eliminate its shortcomings. In particular, you can make it so that they will be almost as effective as the least squares estimate in the Gaussian case, but almost never loose in accuracy with small deviations of the probability distribution of the observations from the Gaussian distribution.The main result is the proof of consistency and asymptotic normality of the proposed estimates in the particular case of the one-parameter model describing the stationary process with finite variance. Another important result is the finding of the asymptotic relative efficiency of the proposed estimates in relation to the least squares estimate. This allows you to compare the two estimates, depending on the probability distribution of innovation process and of autoregressive coefficients. The results can be used to identify an autoregressive process, especially with nonGaussian nature, and/or of autoregressive processes observed with gross
Asymptotic dimension of relatively hyperbolic groups
Osin, D. V.
2004-01-01
Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\\{H_1, ..., H_m\\} $. We prove that if each of the subgroups $H_1, ..., H_m$ has finite asymptotic dimension, then asymptotic dimension of $G$ is also finite.
Asymptotically informative prior for Bayesian analysis
Yuan, A.; de Gooijer, J.G.
2011-01-01
In classical Bayesian inference the prior is treated as fixed, it is asymptotically negligible, thus any information contained in the prior is ignored from the asymptotic first order result. However, in practice often an informative prior is summarized from previous similar or the same kind of
Term structure modeling and asymptotic long rate
Yao, Y.
1999-01-01
This paper examines the dynamics of the asymptotic long rate in three classes of term structure models. It shows that, in a frictionless and arbitrage-free market, the asymptotic long rate is a non-decreasing process. This gives an alternative proof of the same result of Dybvig et al. (Dybvig, P.H.,
Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case
Zeng, Cheng; Liang, Shan; Su, Yingying
2013-01-01
Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractional-order hold (FROH) circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling period $T$ tends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH. Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the...
Structure and asymptotic theory for nonlinear models with GARCH errors
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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.
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....
Asymptotic behavior of solutions to a degenerate quasilinear parabolic equation with a gradient term
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Huilai Li
2015-12-01
Full Text Available This article concerns the asymptotic behavior of solutions to the Cauchy problem of a degenerate quasilinear parabolic equations with a gradient term. A blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at infinity.
Asymptotic methods for wave and quantum problems
Karasev, M V
2003-01-01
The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper "Quantization and Intrinsic Dynamics" a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approxi
An effect size index for comparing two independent alpha coefficients.
Liu, Hsin-Yun; Weng, Li-Jen
2009-05-01
Since Cronbach proposed the alpha coefficient in 1951, researchers have contributed to the derivation of its sampling distribution and the testing of related statistical hypotheses. Yet, there has been no research on effect size index relevant to coefficient alpha to our knowledge. Considering the importance of effect size in understanding quantitative research findings, we therefore developed an effect size index Delta for the comparison of two independent alphas with equal test length based on the asymptotic distribution of (1/2)ln(1 - alphahat) under the assumptions of normality and compound symmetry. Simulations indicated that the index was applicable when the sample size was at least 100. The robustness of the derived index when the required assumptions were violated was also explored. It is suggested that the index should be applicable in most cases of unequal test lengths and could be extended to non-normally distributed component scores. Moreover, a small simulation was conducted to explore the behaviour of Delta with correlated errors, a frequently studied situation violating the assumption of compound symmetry. The proposed index was found to be robust unless a large number of highly correlated errors were present in the data.
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Ashok Sahai
2016-02-01
Full Text Available This paper addresses the issue of finding the most efficient estimator of the normal population mean when the population “Coefficient of Variation (C. V.” is ‘Rather-Very-Large’ though unknown, using a small sample (sample-size ≤ 30. The paper proposes an “Efficient Iterative Estimation Algorithm exploiting sample “C. V.” for an efficient Normal Mean estimation”. The MSEs of the estimators per this strategy have very intricate algebraic expression depending on the unknown values of population parameters, and hence are not amenable to an analytical study determining the extent of gain in their relative efficiencies with respect to the Usual Unbiased Estimator (sample mean ~ Say ‘UUE’. Nevertheless, we examine these relative efficiencies of our estimators with respect to the Usual Unbiased Estimator, by means of an illustrative simulation empirical study. MATLAB 7.7.0.471 (R2008b is used in programming this illustrative ‘Simulated Empirical Numerical Study’.DOI: 10.15181/csat.v4i1.1091
A quantum kinematics for asymptotically flat spacetimes
Campiglia, Miguel
2014-01-01
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports, in addition to the usual LQG operators, the action of `background exponential operators' which are connection dependent operators labelled by `background' $su(2)$ electric fields. KS states have, in addition to the LQG state label corresponding to 1 dimensional excitations of the triad, a label corresponding to a `background' electric field which describes 3 dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields which label the {\\em states} and the background electric fields which label the {\\em operators}. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We...
The Asymptotic Approach to the Twin Paradox
National Research Council Canada - National Science Library
Spiridon Dumitru
2008-01-01
The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant...
The Asymptotic Approach to the Twin Paradox
National Research Council Canada - National Science Library
Dumitru S
2008-01-01
The argument of twins’ asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant...
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...
Ghosh, Prasenjit; Tang, Xueying; Ghosh, Malay; Chakrabarti, Arijit
2013-01-01
Consider the problem of simultaneous testing for the means of independent normal observations. In this paper, we study some asymptotic optimality properties of certain multiple testing rules induced by a general class of one-group shrinkage priors in a Bayesian decision theoretic framework, where the overall loss is taken as the number of misclassified hypotheses. We assume a two-groups normal mixture model for the data and consider the asymptotic framework adopted in Bogdan et al. (2011) who...
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.
On the Folded Normal Distribution
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Michail Tsagris
2014-02-01
Full Text Available The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the parameters are obtained using the asymptotic theory and bootstrap method. The coverage of the confidence intervals is also examined.
Directory of Open Access Journals (Sweden)
G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
Directory of Open Access Journals (Sweden)
Dong Robert Xin
2017-02-01
Full Text Available We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ \\ {0,1}. The cases of other elliptic curves are either the same or trivial. Two proofs depending on elliptic functions’ special properties and Abelian differentials’ Taylor expansions are discussed, respectively. For a holomorphic family of hyperelliptic nodal or cuspidal curves and their Jacobians, we announce our results on the Bergman kernel asymptotics near various singularities. For genus-two curves particularly, asymptotic formulas with precise coefficients involving the complex structure information are written down explicitly.
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 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.
Exact Asymptotics of Bivariate Scale Mixture Distributions
Hashorva, Enkelejd
2009-01-01
Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \\in (0,1] as x tends infintiy assuming that R has distribution function in the Gumbel max-domain of attraction and (U_1,U_2) has a specific tail behaviour around some absorbing point. As a special case of our results we retrieve the exact asymptotic behaviour ...
Asymptotic stability of a catalyst particle
DEFF Research Database (Denmark)
Wedel, Stig; Michelsen, Michael L.; Villadsen, John
1977-01-01
The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...
Asymptotically flat spacetimes with BMS3 symmetry
Compère, Geoffrey; Fiorucci, Adrien
2017-10-01
We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy of the BMS group at both null infinities and spatial infinity. The BMS phase space obeys a notion of holographic causality and can be parametrized by boundary null fields. This automatically leads to the antipodal identification of bulk fields between past and future null infinity in the absence of a global conical defect.
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaël
2017-06-23
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
Fuel Temperature Coefficient of Reactivity
Energy Technology Data Exchange (ETDEWEB)
Loewe, W.E.
2001-07-31
A method for measuring the fuel temperature coefficient of reactivity in a heterogeneous nuclear reactor is presented. The method, which is used during normal operation, requires that calibrated control rods be oscillated in a special way at a high reactor power level. The value of the fuel temperature coefficient of reactivity is found from the measured flux responses to these oscillations. Application of the method in a Savannah River reactor charged with natural uranium is discussed.
Estimates of the Sampling Distribution of Scalability Coefficient H
Van Onna, Marieke J. H.
2004-01-01
Coefficient "H" is used as an index of scalability in nonparametric item response theory (NIRT). It indicates the degree to which a set of items rank orders examinees. Theoretical sampling distributions, however, have only been derived asymptotically and only under restrictive conditions. Bootstrap methods offer an alternative possibility to…
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then
The Asymptotic Expansion Method via Symbolic Computation
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Juan F. Navarro
2012-01-01
Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
Asymptotically periodic solutions of Volterra integral equations
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Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Term structure extrapolation and asymptotic forward rates
de Kort, J.; Vellekoop, M.H.
2015-01-01
We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the
Asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Lovrekovic, Iva
2017-11-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for nontrivial boundary conditions is five dimensional and it leads to global geon solution with nonvanishing charges.
The Asymptotic Approach to the Twin Paradox
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Dumitru S.
2008-04-01
Full Text Available The argument of twins’ asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.
The Asymptotic Approach to the Twin Paradox
Directory of Open Access Journals (Sweden)
Dumitru S.
2008-04-01
Full Text Available The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.
Fixed Point Theorems for Asymptotically Contractive Multimappings
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M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
Asymptotic symmetries, holography and topological hair
Mishra, Rashmish K.; Sundrum, Raman
2018-01-01
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons
Bercu, Bernard; Proia, Frédéric
2013-01-01
International audience; The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator asso...
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard
2015-01-01
The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p–y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained...... shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates...... an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation....
Directory of Open Access Journals (Sweden)
Fulvio Crisciani
1991-05-01
Full Text Available Sufficient conditions for the linear asymptotic stability of large scale wind-driven oceanic flows are derived in the presence of arbitrary longitude-shaped perturbations. Criteria work when both bottom dissipation and lateral diffusion of relative vorticity are simultaneously present. The stability is controlled by the maximum of the shear of the basic flow and by the maximum of its meridional derivative and involves the dissipation-diffusion coefficients.
Asymptotics of eigenfunctions for Sturm-Liouville problem in difference equations
Bas, Erdal; Ozarslan, Ramazan
2016-06-01
In this study, Sturm-Liouville problem with variable coefficient, potential function q (n), for difference equation is considered. The representation of solutions is obtained by variation of parameters method for two different initial value problems and trigonometric solutions are found by means of complex characteristic roots. It is proved that these results hold the equation by using summation by parts method. Two estimations of asymptotic expansion of the solutions are established.
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 approximations for non-integer order derivatives of monomials
Aşiru, Muniru A.
2015-02-01
In this note, we develop new, simple and very accurate asymptotic approximations for non-integer order derivatives of monomial functions by using the more accurate asymptotic approximations for large factorials that have recently appeared in the literature.
Parallelism, uniqueness, and large-sample asymptotics for the Dantzig selector.
Dicker, Lee; Lin, Xihong
2013-03-01
The Dantzig selector (Candès and Tao, 2007) is a popular ℓ1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to parallelism and, when satisfied, ensures the uniqueness of Dantzig selector estimators. The condition holds with probability 1, if the predictors are drawn from a continuous distribution. We discuss the necessity of this condition for uniqueness and also provide a closely related condition which ensures uniqueness of lasso estimators (Tibshirani, 1996). Large sample asymptotics for the Dantzig selector, i.e. almost sure convergence and the asymptotic distribution, follow directly from our uniqueness results and a continuity argument. The limiting distribution of the Dantzig selector is generally non-normal. Though our asymptotic results require that the number of predictors is fixed (similar to (Knight and Fu, 2000)), our uniqueness results are valid for an arbitrary number of predictors and observations.
Estimation and asymptotic inference in the first order AR-ARCH model
DEFF Research Database (Denmark)
Lange, Theis; Rahbek, Anders; Jensen, Søren Tolver
2011-01-01
This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of individu...... for the QMLE to be asymptotically normal. Finally, geometric ergodicity for AR-ARCH processes is shown to hold under mild and classic conditions on the AR and ARCH processes.......This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of individual...
Asymptotic modelling of a thermopiezoelastic anisotropic smart plate
Long, Yufei
Motivated by the requirement of modelling for space flexible reflectors as well as other applications of plate structures in engineering, a general anisotropic laminated thin plate model and a monoclinic Reissner-Mindlin plate model with thermal deformation, two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structure helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. For the zeroth-order approximation, the asymptotically correct expression of energy is derived into the form of energetic equation in classical laminated plate theory, which will be enough to predict the behavior of plate structures as thin as a space flexible reflector. A through-the-thickness strain field can be expressed in terms of material constants and two-dimensional membrane and bending strains, while the transverse normal and shear stresses are not predictable yet. In the first-order approximation, the warping functions are further disturbed into a high order and an asymptotically correct energy expression with derivatives of the two-dimensional strains is acquired. For the convenience of practical use, the expression is transformed into a Reissner-Mindlin form with optimization implemented to minimize the error. Transverse stresses and strains are recovered using the in-plane strain variables. Several numerical examples of different laminations and shapes are studied with the help of analytical solutions or shell elements in finite element codes. The constitutive relation is
Ke, Zijun; Zhang, Zhiyong Johnny
2017-09-12
Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such as the 1/T approximation method and the Bartlett's formula method may fail in finite samples and are vulnerable to non-normality. Resampling techniques such as the moving block bootstrap and the surrogate data method are competitive alternatives. In this study, we use a Monte Carlo simulation study and a real data example to compare asymptotic methods with the aforementioned resampling techniques. For each resampling technique, we consider both the percentile method and the bias-corrected and accelerated method for interval construction. Simulation results show that the surrogate data method with percentile intervals yields better performance than the other methods. An R package pautocorr is used to carry out tests evaluated in this study. © 2017 The British Psychological Society.
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....
Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model
Scarfone, Leonard M.
2010-05-01
The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D 3 occurring in periodic intervals over the range of 0
Asymptotic Behavior of Certain Integrodifferential Equations
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Said Grace
2016-01-01
Full Text Available This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: atx′t′=e(t+∫ct(t-sα-1k(t,sf(s,x(sds, c>1, 0<α<1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.
Kink fluctuation asymptotics and zero modes
Energy Technology Data Exchange (ETDEWEB)
Izquierdo, A.A. [Universidad de Salamanca, Departamento de Matematica Aplicada and IUFFyM, Salamanca (Spain); Guilarte, J.M. [Universidad de Salamanca, Departamento de Fisica Fundamental and IUFFyM, Salamanca (Spain)
2012-10-15
In this paper we propose a refinement of the heat-kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero-energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat-kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat-kernel expansion. (orig.)
Theorems for asymptotic safety of gauge theories
Bond, Andrew D.; Litim, Daniel F.
2017-06-01
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 emphasised. 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.
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.
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...
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
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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.
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.
Directory of Open Access Journals (Sweden)
J. Kalas
2012-01-01
Full Text Available The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for $t$ approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.
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 ...... of the estimator are investigated. The efficiency of our methodology is illustrated on a small simulation study and by a real dataset from the actuarial context. (C) 2014 Elsevier B.V. All rights reserved....
Asymptotic Representations of Quantum Affine Superalgebras
Zhang, Huafeng
2017-08-01
We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.
Asymptotically safe inflation from quadratic gravity
Bonanno, Alfio
2015-01-01
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type $R^{2-\\theta/2}$ in the effective Lagrangian, where $\\theta>0$ is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data puts important constraints on the strenght of this new type of couplings.
Discrete dispersion models and their Tweedie asymptotics
DEFF Research Database (Denmark)
Jørgensen, Bent; Kokonendji, Célestin C.
2016-01-01
in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models......-Tweedie asymptotic framework where Poisson-Tweedie models appear as dilation limits. This unifies many discrete convergence results and leads to Poisson and Hermite convergence results, similar to the law of large numbers and the central limit theorem, respectively. The dilation operator also leads to a duality...
Lectures on the asymptotic theory of ideals
Rees, D
1988-01-01
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work
Asymptotic granularity reduction and its application
Su, Shenghui; Lü, Shuwang; Fan, Xiubin
2011-01-01
It is well known that the inverse function of y = x with the derivative y' = 1 is x = y, the inverse function of y = c with the derivative y' = 0 is inexistent, and so on. Hence, on the assumption that the noninvertibility of the univariate increasing function y = f(x) with x > 0 is in direct proportion to the growth rate reflected by its derivative, the authors put forward a method of comparing difficulties in inverting two functions on a continuous or discrete interval called asymptotic gra...
On the Asymptotics of Takeuchi Numbers
Prellberg, Thomas
2000-01-01
I present an asymptotic formula for the Takeuchi numbers $T_n$. In particular, I give compelling numerical evidence and present a heuristic argument showing that $$T_n\\sim C_T B_n\\exp{1\\over2}{W(n)}^2$$as $n$ tends to infinity, where $B_n$ are the Bell numbers, W(n) is Lambert's $W$ function, and $C_T=2.239...$ is a constant. Moreover, I show that the method presented here can be generalized to derive conjectures for related problems.
Dynamics and Asymptotics of Brane-Worlds
Antoniadis, I.; Cotsakis, S.; Klaoudatou, I.
2015-01-01
The self-tuning mechanism aims to provide a way to address the cosmological constant problem by guarantying the existence of flat brane solutions independently of the brane tension value. In recent work we have studied the asymptotics of different models of brane-worlds, and here we highlight certain interesting behaviors we have encountered in our search for appropriate conditions to avoid finite-distance singularities in flat brane solutions. Finding such conditions offers a framework within which the self-tuning mechanism could be realized.
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
Asymptotic accuracy of two-class discrimination
Energy Technology Data Exchange (ETDEWEB)
Ho, T.K.; Baird, H.S. [AT& T Bell Laboratories, Murray Hill, NJ (United States)
1994-12-31
Poor quality-e.g. sparse or unrepresentative-training data is widely suspected to be one cause of disappointing accuracy of isolated-character classification in modern OCR machines. We conjecture that, for many trainable classification techniques, it is in fact the dominant factor affecting accuracy. To test this, we have carried out a study of the asymptotic accuracy of three dissimilar classifiers on a difficult two-character recognition problem. We state this problem precisely in terms of high-quality prototype images and an explicit model of the distribution of image defects. So stated, the problem can be represented as a stochastic source of an indefinitely long sequence of simulated images labeled with ground truth. Using this sequence, we were able to train all three classifiers to high and statistically indistinguishable asymptotic accuracies (99.9%). This result suggests that the quality of training data was the dominant factor affecting accuracy. The speed of convergence during training, as well as time/space trade-offs during recognition, differed among the classifiers.
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.
Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case
Directory of Open Access Journals (Sweden)
Cheng Zeng
2013-01-01
Full Text Available Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractional-order hold (FROH circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH. Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the limiting zeros for the sampled-data system with FROH is also given as power series with respect to a sampling period up to the third-order term. And, further, the corresponding stability conditions of the sampling zeros are discussed for fast sampling rates. The ideas of the paper here provide a more accurate approximation for asymptotic zeros, and certain known achievements on asymptotic behavior of limiting zeros are shown to be particular cases of the results presented.
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...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
An asymptotic solution of large-$N$ $QCD$
Bochicchio, Marco
2014-01-01
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-poin...
Soft pion theorem, asymptotic symmetry and new memory effect
Hamada, Yuta; Sugishita, Sotaro
2017-11-01
It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the S-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
Viscous asymptotically flat Reissner-Nordström black branes
Energy Technology Data Exchange (ETDEWEB)
Gath, Jakob; Pedersen, Andreas Vigand [Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2014-03-12
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.
Viscous asymptotically flat Reissner-Nordström black branes
Gath, Jakob; Pedersen, Andreas Vigand
2014-03-01
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.
Angot, Philippe; Goyeau, Benoît; Ochoa-Tapia, J. Alberto
2017-06-01
We develop asymptotic modeling for two- or three-dimensional viscous fluid flow and convective transfer at the interface between a fluid and a porous layer. The asymptotic model is based on the fact that the thickness d of the interfacial transition region Ωfp of the one-domain representation is very small compared to the macroscopic length scale L . The analysis leads to an equivalent two-domain representation where transport phenomena in the transition layer of the one-domain approach are represented by algebraic jump boundary conditions at a fictive dividing interface Σ between the homogeneous fluid and porous regions. These jump conditions are thus stated up to first-order in O (d /L ) with d /L ≪1 . The originality and relevance of this asymptotic model lies in its general and multidimensional character. Indeed, it is shown that all the jump interface conditions derived for the commonly used 1D-shear flow are recovered by taking the tangential component of the asymptotic model. In that case, the comparison between the present model and the different models available in the literature gives explicit expressions of the effective jump coefficients and their associated scaling. In addition for multi-dimensional flows, the general asymptotic model yields the different components of the jump conditions including a new specific equation for the cross-flow pressure jump on Σ .
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.
The asymptotic complexity of merging networks
DEFF Research Database (Denmark)
Miltersen, Peter Bro; Paterson, Mike; Tarui, Jun
1996-01-01
Let M(m,n) be the minimum number of comparatorsneeded in a comparator network that merges m elements x1≤x2≤&cdots;≤xm and n elements y1≤y2≤&cdots;≤yn , where n≥m . Batcher's odd-even merge yields the following upper bound: Mm,n≤1 2m+nlog 2m+on; in particular, Mn,n≤nlog 2n+On. We prove the following...... lower bound that matches the upper bound above asymptotically as n≥m→∞: Mm,n≥1 2m+nlog 2m-Om; in particular, Mn,n≥nlog 2n-On. Our proof technique extends to give similarily tight lower bounds for the size of monotone Boolean circuits for merging, and for the size of switching networks capable...... of realizing the set of permutations that arise from merging....
Asymptotic freedom beyond the leading order
Buras, Andrzej J; Ross, D A; Sachrajda, Christopher T C
1977-01-01
The authors make a quantitative analysis of the full G/sup 2/ interaction corrections to the leading Q/sup 2/ dependence of nu W/sub 2/ at x>or=0.4, as given by an asymptotically free gauge theory. It turns out that due to partial cancellations between various contributions the g/sup 2/ corrections are small. The best fit with the SLAC ep data after including the g/sup 2/ corrections is almost identical to that without these corrections, the only effect being a change in Lambda , the one free parameter, which sets the scale of the theory. On the other hand the effect of including target mass corrections is to improve the agreement of the prediction for nu W/sub 2//sup ep/ with data for large values of x. (20 refs).
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
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...
Traversable asymptotically flat wormholes in Rastall gravity
Moradpour, H.; Sadeghnezhad, N.; Hendi, S. H.
2017-12-01
There are some gravitational theories in which the ordinary energy-momentum conservation law is not valid in the curved spacetime. Rastall gravity is one of the known theories in this regard which includes a non-minimal coupling between geometry and matter fields. Equipped with the basis of such theory, we study the properties of traversable wormholes with flat asymptotes. We investigate the possibility of exact solutions by a source with the baryonic matter state parameter. Our survey indicates that Rastall theory has considerable effects on the wormhole characteristics. In addition, we study various case studies and show that the weak energy condition may be met for some solutions. We also give a discussion regarding to traversability of such wormhole geometry with phantom sources.
Correlation at low temperature;2, Asymptotics
Bach, V
2003-01-01
The present paper is a continuation of our paper [Bach-Moller mp_arc 02-215] where the truncated two-point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature, under a weak coupling assumption. In this paper we compute the asymptotics of the correlation function as the temperature goes to zero. This paper thus extends [Bach-Jecko-Sjostrand, mp_arc 98-552] in two directions: The Hamiltonian function is allowed to have several local minima other than a unique global minimum, and we do not require translation invariance of the Hamiltonian function. We are in particular able to handle spin systems on a general lattice.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
Asymptotic properties of restricted naming games
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
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...
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...... 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...... at the optimal rate. All our results are valid in high-dimensional models. Our simulations reveal that the desparsified conservative Lasso estimates the parameters much more precisely than the desparsified Lasso, has much better size properties and produces confidence bands with markedly superior coverage rates....
Lattice quantum gravity and asymptotic safety
Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.
2017-09-01
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 argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial 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 that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.
Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics.
Demler, Olga V; Pencina, Michael J; Cook, Nancy R; D'Agostino, Ralph B
2017-09-20
The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
Chen, Hua; Chen, Kun
2013-07-01
The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by Tm the mth coalescent time, when m + 1 lineages coalesce into m lineages, and An(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, An(t), and the coalescence times, Tm, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n - An(t) follows a Poisson distribution, and as m → n, $$n\\left(n-1\\right){T}_{m}/2N\\left(0\\right)$$ follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference.
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. 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 asymptotic of the bulk of poverty indices and issues in poverty ...
Asymptotic size determines species abundance in the marine size spectrum
DEFF Research Database (Denmark)
Andersen, Ken Haste; Beyer, Jan
2006-01-01
The majority of higher organisms in the marine environment display indeterminate growth; that is, they continue to grow throughout their life, limited by an asymptotic size. We derive the abundance of species as a function of their asymptotic size. The derivation is based on size-spectrum theory...
Asymptotic behaviour of solutions of a nonlinear transport equation
C.J. van Duijn (Hans); M.A. Peletier (Mark)
1996-01-01
textabstractWe investigate the asymptotic behaviour of solutions of the convection- diffusion equation $$ b(u)_t + divleft( u q - n u right) = 0 qquad hbox{for r = |x| > e quadhbox{andquad t>0, $$ where $q=l/r, er $, $l>0$. The asymptotic limits that we consider are $ttoinfty$ and $e downto0$. We
Comparison of the asymptotic stability properties for two multirate strategies
V. Savcenco (Valeriu)
2007-01-01
textabstractThis paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use
Journal Afrika Statistika ISSN 0852-0305 Asymptotic representation ...
African Journals Online (AJOL)
Abstract. 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 asymptotic of the bulk of poverty indices and issues in poverty ...
On oscillation and asymptotic behaviour of solutions of forced first ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 111; Issue 3. On Oscillation and Asymptotic Behaviour of Solutions of Forced First Order Neutral Differential Equations. N Parhi R N Rath. Volume 111 Issue 3 August 2001 pp ... Keywords. Oscillation; nonoscillation; neutral equations; asymptotic behaviour.
Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
Cha, Ye Sle; Sakovich, Anna
2016-01-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
Asymptotic distribution of products of sums of independent random ...
Indian Academy of Sciences (India)
453007 Henan, China. E-mail: bigduckwyl@163.com; duhongxia24@gmail.com. MS received 7 April 2012; revised 10 October 2012. Abstract. In the paper we consider the asymptotic distribution of products of weighted sums of independent random variables. Keywords. Asymptotic distribution; products of sums. 1.
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.
An asymptotic solution of large-N QCD
Bochicchio, Marco
2014-11-01
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.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Numerical and asymptotic aspects of parabolic cylinder functions
N.M. Temme (Nico)
2000-01-01
textabstractSeveral 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
Asymptotic behavior of a system of linear fractional difference equations
Directory of Open Access Journals (Sweden)
Nurkanović M
2005-01-01
Full Text Available We investigate the global asymptotic behavior of solutions of the system of difference equations , , , where the parameters , , , and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. We obtain some asymptotic results for the positive equilibrium of this system.
Oliveira, José J.
2017-10-01
In this paper, we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.
Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation
Directory of Open Access Journals (Sweden)
Philippe Dumas
2007-01-01
Full Text Available We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using tools from probability theory, and from analytic number theory. We derive a Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system. The method is applicable to a wide class of sequences rational with respect to a numeration system essentially under the condition that they admit a linear representation with nonnegative coefficients.
Sharma, J. N.; Sharma, P. K.; Rana, S. K.
2011-01-01
In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.
Directory of Open Access Journals (Sweden)
R. Kenna
2014-09-01
Full Text Available We analyze the resistance between two nodes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M x N cobweb network with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.
Asymptotic expansions and the possibilities to drop the hypotheses in the prandtl problem
Georgievskii, D. V.
2009-02-01
The plane problem on the quasistatic compression of a thin perfectly plastic layer between undeformable rough plates (the Prandtl problem) has a well-known analytic solution at all points sufficiently far from the midsection and endpoints of the layer. Both the static and the kinematic component of this solution were obtained on the basis of the Prandtl hypothesis [1] stating that the tangential stress is linear along the layer thickness and is maximal in absolute value on the plate surfaces. (If the plates are perfectly rough, then this maximum value coincides with the shear yield stress.) The Prandtl hypothesis was widely confirmed in experiments carried out after the paper [1] had been published. At the same time, it is natural to ask whether one can construct a classical solution of this problem without imposing any static or kinematic hypotheses on the unknown variables and whether there exist any other mathematical solutions in which these hypotheses do not hold and which themselves are not observed in experiments. In the present paper, we use asymptotic analysis with a natural small geometric parameter and uniquely determine an exact solution (in the sense of finiteness of the number of terms in the asymptotic expansion), which coincides with the Prandtl solution generalized to the case of an arbitrary roughness coefficient of the plates. We rigorously show that such asymptotics cannot hold near the layer midsection, where we construct another, internal asymptotic expansion. In the abovementioned sense, the solution corresponding to the internal expansion is also exact and models the compression of a thin vertical strip in the middle of the layer. We realize two possible versions of matching of the two expansions in the cross-section whose distance from the midsection is equal to the layer thickness.
Asymptotic behavior of local dipolar fields in thin films
Energy Technology Data Exchange (ETDEWEB)
Bowden, G.J., E-mail: gjb@phys.soton.ac.uk [School of Physics and Astronomy, University of Southampton, SO17 1BJ (United Kingdom); Stenning, G.B.G., E-mail: Gerrit.vanderlaan@diamond.ac.uk [Magnetic Spectroscopy Group, Diamond Light Source, Didcot OX11 0DE (United Kingdom); Laan, G. van der, E-mail: gavin.stenning@stfc.ac.uk [ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Didcot OX11 0QX (United Kingdom)
2016-10-15
A simple method, based on layer by layer direct summation, is used to determine the local dipolar fields in uniformly magnetized thin films. The results show that the dipolar constants converge ~1/m where the number of spins in a square film is given by (2m+1){sup 2}. Dipolar field results for sc, bcc, fcc, and hexagonal lattices are presented and discussed. The results can be used to calculate local dipolar fields in films with either ferromagnetic, antiferromagnetic, spiral, exponential decay behavior, provided the magnetic order only changes normal to the film. Differences between the atomistic (local fields) and macroscopic fields (Maxwellian) are also examined. For the latter, the macro B-field inside the film is uniform and falls to zero sharply outside, in accord with Maxwell boundary conditions. In contrast, the local field for the atomistic point dipole model is highly non-linear inside and falls to zero at about three lattice spacing outside the film. Finally, it is argued that the continuum field B (used by the micromagnetic community) and the local field B{sub loc}(r) (used by the FMR community) will lead to differing values for the overall demagnetization energy. - Highlights: • Point-dipolar fields in uniformly magnetized thin films are characterized by just three numbers. • Maxwell's boundary condition is partially violated in the point-dipole approximation. • Asymptotic values of point dipolar fields in circular monolayers scale as π/r.
Coefficient estimates of negative powers and inverse coefficients for ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 127; Issue 3. Coefficient estimates of negative powers and inverse coefficients for certain starlike functions. MD FIROZ ALI A ... Keywords. Univalent; starlike; meromorphic functions; subordination; coefficient bounds; inverse coefficient bounds ...
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.
Asymptotic Behaviour of the QED Perturbation Series
Directory of Open Access Journals (Sweden)
Idrish Huet
2017-01-01
Full Text Available I will summarize the present state of a long-term effort to obtain information on the large-order asymptotic behaviour of the QED perturbation series through the effective action. Starting with the constant-field case, I will discuss the Euler-Heisenberg Lagrangian in various dimensions and up to the three-loop level. This Lagrangian holds the information on the N-photon amplitudes in the low-energy limit, and combining it with Spinor helicity methods explicit all-N results can be obtained at the one-loop and, for the “all +” amplitudes, also at the two-loop level. For the imaginary part of the Euler-Heisenberg Lagrangian, an all-loop formula has been conjectured independently by Affleck, Alvarez, and Manton for Scalar QED and by Lebedev and Ritus for Spinor QED. This formula can be related through a Borel dispersion relation to the leading large-N behaviour of the N-photon amplitudes. It is analytic in the fine structure constant, which is puzzling and suggests a diagrammatic investigation of the large-N limit in perturbation theory. Preliminary results of such a study for the 1+1 dimensional case throw doubt on the validity of the conjecture.
Solvable Optimal Velocity Models and Asymptotic Trajectory
Nakanishi, K; Igarashi, Y; Bando, M
1996-01-01
In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic traj...
Numerical Simulations of Asymptotically AdS Spacetimes
Bantilan, Hans
In this dissertation, we introduce a numerical scheme to construct asymptotically anti-de Sitter spacetimes with Lorentzian signature, focusing on cases that preserve five-dimensional axisymmetry. We study the field theories that are dual to these spacetimes by appealing to the AdS/CFT correspondence in the regime where the gravity dual is completely described by Einstein gravity. The numerical scheme is based on generalized harmonic evolution, and we begin by obtaining initial data defined on some Cauchy hypersurface. For the study described in this dissertation, we use a scalar field to source deviations from pure AdS5, and obtain data that correspond to highly deformed black holes. We evolve this initial data forward in time, and follow the subsequent ringdown. What is novel about this study is that the initial horizon geometry cannot be considered a small perturbation of the final static horizon, and hence we are probing an initial non-linear phase of the evolution of the bulk spacetime. On the boundary, we find that the dual CFT stress tensor behaves like that of a thermalized N = 4 SYM fluid. We find that the equation of state of this fluid is consistent with conformal invariance, and that its transport coefficients match those previously calculated for an N = 4 SYM fluid via holographic methods. Modulo a brief transient that is numerical in nature, this matching appears to hold from the initial time onwards. We transform these solutions computed in global AdS onto a Minkowski piece of the boundary, and examine the temperature of the corresponding fluid flows. Under this transformation, the spatial profile of temperature at the initial time resembles a Lorentz-flattened pancake centered at the origin of Minkowski space. By interpreting the direction along which the data is flattened as the beam-line direction, our initial data can be thought of as approximating a head-on heavy ion collision at its moment of impact.
Asymptotic distribution of zeros of polynomials satisfying difference equations
Krasovsky, I. V.
2003-01-01
We propose a way to find the asymptotic distribution of zeros of orthogonal polynomials pn(x) satisfying a difference equation of the formB(x)pn(x+[delta])-C(x,n)pn(x)+D(x)pn(x-[delta])=0.We calculate the asymptotic distribution of zeros and asymptotics of extreme zeros of the Meixner and Meixner-Pollaczek polynomials. The distribution of zeros of Meixner polynomials shows some delicate features. We indicate the relation of our technique to the approach based on the Nevai-Dehesa-Ullman distribution.
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.
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.
Variation in aerodynamic coefficients with altitude
Shahid, Faiza; Hussain, Mukkarum; Baig, Mirza Mehmood; Haq, Ihtram ul
Precise aerodynamics performance prediction plays key role for a flying vehicle to get its mission completed within desired accuracy. Aerodynamic coefficients for same Mach number can be different at different altitude due to difference in Reynolds number. Prediction of these aerodynamics coefficients can be made through experiments, analytical solution or Computational Fluid Dynamics (CFD). Advancements in computational power have generated the concept of using CFD as a virtual Wind Tunnel (WT), hence aerodynamic performance prediction in present study is based upon CFD (numerical test rig). Simulations at different altitudes for a range of Mach numbers with zero angle of attack are performed to predict axial force coefficient behavior with altitude (Reynolds number). Similar simulations for a fixed Mach number '3' and a range of angle of attacks are also carried out to envisage the variation in normal force and pitching moment coefficients with altitude (Reynolds number). Results clearly depict that the axial force coefficient is a function of altitude (Reynolds number) and increase as altitude increases, especially for subsonic region. Variation in axial force coefficient with altitude (Reynolds number) slightly increases for larger values of angle of attacks. Normal force and pitching moment coefficients do not depend on altitude (Reynolds number) at smaller values of angle of attacks but show slight decrease as altitude increases. Present study suggests that variation of normal force and pitching moment coefficients with altitude can be neglected but the variation of axial force coefficient with altitude should be considered for vehicle fly in dense atmosphere. It is recommended to continue this study to more complex configurations for various Mach numbers with side slip and real gas effects.
Variation in aerodynamic coefficients with altitude
Directory of Open Access Journals (Sweden)
Faiza Shahid
Full Text Available Precise aerodynamics performance prediction plays key role for a flying vehicle to get its mission completed within desired accuracy. Aerodynamic coefficients for same Mach number can be different at different altitude due to difference in Reynolds number. Prediction of these aerodynamics coefficients can be made through experiments, analytical solution or Computational Fluid Dynamics (CFD. Advancements in computational power have generated the concept of using CFD as a virtual Wind Tunnel (WT, hence aerodynamic performance prediction in present study is based upon CFD (numerical test rig. Simulations at different altitudes for a range of Mach numbers with zero angle of attack are performed to predict axial force coefficient behavior with altitude (Reynolds number. Similar simulations for a fixed Mach number â3â and a range of angle of attacks are also carried out to envisage the variation in normal force and pitching moment coefficients with altitude (Reynolds number. Results clearly depict that the axial force coefficient is a function of altitude (Reynolds number and increase as altitude increases, especially for subsonic region. Variation in axial force coefficient with altitude (Reynolds number slightly increases for larger values of angle of attacks. Normal force and pitching moment coefficients do not depend on altitude (Reynolds number at smaller values of angle of attacks but show slight decrease as altitude increases. Present study suggests that variation of normal force and pitching moment coefficients with altitude can be neglected but the variation of axial force coefficient with altitude should be considered for vehicle fly in dense atmosphere. It is recommended to continue this study to more complex configurations for various Mach numbers with side slip and real gas effects. Keywords: Mach number, Reynolds number, Blunt body, Altitude effect, Angle of attacks
An asymptotic model in acoustics: acoustic drift equations.
Vladimirov, Vladimir A; Ilin, Konstantin
2013-11-01
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
Preheating in an asymptotically safe quantum field theory
DEFF Research Database (Denmark)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J....... High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance....... Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e-foldings of the inflationary phase....
Pseudo-random number generator based on asymptotic deterministic randomness
Energy Technology Data Exchange (ETDEWEB)
Wang Kai [Department of Radio Engineering, Southeast University, Nanjing (China)], E-mail: kaiwang@seu.edu.cn; Pei Wenjiang; Xia Haishan [Department of Radio Engineering, Southeast University, Nanjing (China); Cheung Yiuming [Department of Computer Science, Hong Kong Baptist University, Hong Kong (China)
2008-06-09
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.
Radial asymptotics of Lemaitre-Tolman-Bondi dust models
Sussman, Roberto A
2010-01-01
We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular "open" LTB models whose space slices allow for a diverging $\\ell$, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as $\\ell\\to\\infty$. The "asymptotic state" is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By ...
Earthquake Nucleation on Faults With Heterogeneous Frictional Properties, Normal Stress
Ray, Sohom; Viesca, Robert C.
2017-10-01
We examine the development of an instability of fault slip rate. We consider a slip rate and state dependence of fault frictional strength, in which frictional properties and normal stress are functions of position. We pose the problem for a slip rate distribution that diverges quasi-statically within finite time in a self-similar fashion. Scenarios of property variations are considered and the corresponding self-similar solutions found. We focus on variations of coefficients, a and b, respectively, controlling the magnitude of a direct effect on strength due to instantaneous changes in slip rate and of strength evolution due to changes in a state variable. These results readily extend to variations in fault-normal stress, σ, or the characteristic slip distance for state evolution, Dc. We find that heterogeneous properties lead to a finite number of self-similar solutions, located about critical points of the distributions: maxima, minima, and between them. We examine the stability of these solutions and find that only a subset is asymptotically stable, occurring at just one of the critical point types. Such stability implies that during instability development, slip rate and state evolution can be attracted to develop in the manner of the self-similar solution, which is also confirmed by solutions to initial value problems for slip rate and state. A quasi-static slip rate divergence is ultimately limited by inertia, leading to the nucleation of an outward expanding dynamic rupture: asymptotic stability of self-similar solutions then implies preferential sites for earthquake nucleation, which are determined by distribution of frictional properties.
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.
On the generalized asymptotically nonspreading mappings in convex metric spaces
Directory of Open Access Journals (Sweden)
Withun Phuengrattana
2017-04-01
Full Text Available In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0 spaces.
Comparison of the asymptotic stability properties for two multirate strategies
Savcenco, V Valeriu
2007-01-01
textabstractThis paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Some remarks on the relevance of the results for 2 x 2 test problems are presented.
Singularity-free gravitational collapse and asymptotic safety
Torres, Ramón
2014-06-01
A general class of quantum improved stellar models with interiors composed of non-interacting (dust) particles is obtained and analyzed in a framework compatible with asymptotic safety. First, the effective exterior, based on the Quantum Einstein Gravity approach to asymptotic safety is presented and, second, its effective compatible dust interiors are deduced. The resulting stellar models appear to be devoid of shell-focusing singularities.
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
Asymptotics of perturbed soliton for Davey-Stewartson; 2, equation
Gadylshin, R R
1998-01-01
It is shown that, under a small perturbation of lump (soliton) for Davey-Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.
Asymptotic estimation of shift parameter of a quantum state
Holevo, A. S.
2003-01-01
We develop an asymptotic theory of estimation of a shift parameter in a pure quantum state to study the relation between entangled and unentangled covariant estimates in the analytically most transparent way. After recollecting basics of estimation of shift parameter in Sec. 2, we study the structure of the optimal covariant estimate in Sec. 3, showing how entanglement comes into play for several independent trials. In Secs. 4,5 we give the asymptotics of the performance of the optimal covari...
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.
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}.
Time-varying coefficient estimation in SURE models. Application to portfolio management
DEFF Research Database (Denmark)
Casas, Isabel; Ferreira, Eva; Orbe, Susan
This paper provides a detailed analysis of the asymptotic properties of a kernel estimator for a Seemingly Unrelated Regression Equations model with time-varying coefficients (tv-SURE) under very general conditions. Theoretical results together with a simulation study differentiates the cases for...
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.
Afsar, Mohammed; Sescu, Adrian; Sassanis, Vasileios; Bres, Guillaume; Towne, Aaron; Lele, Sanjiva
2016-11-01
The Goldstein-Sescu-Afsar asymptotic theory postulated that the appropriate distinguished limit in which non-parallel mean flow effects introduces a leading order change in the 'propagator' (which is related adjoint linearized Euler Green's function) within Goldstein's acoustic analogy must be when the jet spread rate is the same order as Strouhal number. We analyze the low frequency structure of the acoustic spectrum using Large-eddy simulations of two axi-symmetric jets (heated & unheated) at constant supersonic jet Mach number to obtain the mean flow for the asymptotic theory. This approach provides excellent quantitative agreement for the peak jet noise when the coefficients of the turbulence model are tuned for good agreement with the far-field acoustic data. Our aim in this talk, however, is to show the predictive capability of the asymptotics when the turbulence model in the acoustic analogy is 'exactly' re-constructed by numerically matching the length scale coefficients of an algebraic-exponential model for the 1212-component of the Reynolds stress auto-covariance tensor (1 is streamwise & 2 is radial direction) with LES data at any spatial location and temporal frequency. In this way, all information is obtained from local unsteady flow. We thank Professor Parviz Moin for supporting this work as part of the Center for Turbulence Research Summer Program 2016.
Efficient asymptotic frame selection for binary black hole spacetimes using asymptotic radiation
O'Shaughnessy, R; Healy, J; Meeks, Z; Shoemaker, D
2011-01-01
Previous studies have demonstrated that gravitational radiation reliably encodes information about the natural emission direction of the source (e.g., the orbital plane). In this paper, we demonstrate that these orientations can be efficiently estimated by the principal axes of , an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. Evaluating this average at each time provides the instantaneous emission direction. Further averaging across the entire signal yields an average orientation, closely connected to the angular components of the Fisher matrix. The latter direction is well-suited to data analysis and parameter estimation when the instantaneous emission direction evolves significantly. Finally, in the time domain, the average provides fast, invariant diagnostics of waveform quality.
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.
Application of Normal Family to the Spread Inequality and the Paley ...
African Journals Online (AJOL)
In this paper we derive a Paley type inequality for subharmonic functions of order λ,0 < λ≤½ and describe the asymptotic behaviour of the extremal functions near Pòlya peaks. We also give an alternative proof for the spread inequality using a non-asymptotic method via - a normal family of δ -subharmonic functions.
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.
King, Richard B; Stanford, Kristin M; Jones, Peter C; Bekker, Kent
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631-820 mm snout-vent length in males and from 835-1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation.
Numerical Analysis of Asymptotic Stability of Equilibrium Points
Directory of Open Access Journals (Sweden)
A. A. Vorkel
2017-01-01
Full Text Available The aim of this study is to numerically analyze an asymptotic stability of the equilibrium points of autonomous systems of ordinary differential equations on the basis of the asymptotic stability criterion given in the article and the functional localization method of invariant compact sets. The article formulates the necessary and sufficient conditions for an asymptotic stability in terms of invariant compact sets and positively invariant sets and describes a functional localization method. Presents appropriate localization theorems for invariant compact sets of dynamical systems.To investigate the asymptotic stability is proposed an algorithm for a numerical iteration procedure to construct the localizing bounds for invariant compact sets contained in a given initial set. Application of the asymptotic stability criterion is based on the results of this procedure. The author of the article verifies the conditions of the appropriate theorem and confirms the use of this criterion.The examples of two- and three-dimensional systems of differential equations demonstrate a principle of the iteration procedure. The article also gives an example of the system with a limit cycle and it shows that the developed numerical algorithm and the functional localization method of invariant compact sets can be used to analyze stability of the limit cycles.Thanks to the method described in the article, when analyzing an asymptotic stability of equilibrium points, finding a Lyapunov function and calculating eigenvalues of a matrix of linear approximation are non-essential. Thus, it is possible to avoid labour-intensive work with complex analytical structures.The numerical iteration procedure can be used in systems of different dimensions and makes the presented algorithm of asymptotic stability analysis universal.
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size
King, Richard B.
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID
Spectral asymptotics for nonsmooth singular Green operators
DEFF Research Database (Denmark)
Grubb, Gerd
2014-01-01
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain Ω ⊂ ℝ n , and more generally they appear in the calculus of pseudodifferential boundary problems. In particular, the boundary term in a Krein resolvent formula......) are known. We show that (*) holds when G is a general selfadjoint nonnegative singular Green operator with symbol merely Hölder continuous in x. We also show (*) with t = 2 for the boundary term in the Krein resolvent formula comparing the Dirichlet and a Neumann-type problem for a strongly elliptic...... second-order differential operator (not necessarily selfadjoint) with coefficients in for some q > n....
Max-Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low Complexity Transceivers
Sifaou, Houssem
2016-12-28
This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with M antennas communicates with K single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which M and K grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per- UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.
Energy Technology Data Exchange (ETDEWEB)
Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, School of Mathematical Science, MOELSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Shu, Ruiwen, E-mail: rshu2@math.wisc.edu [Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706 (United States)
2017-04-15
In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.
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.…
Large gauge symmetries and asymptotic states in QED
Energy Technology Data Exchange (ETDEWEB)
Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)
2016-12-19
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
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.
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 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...
Spherical convective dynamos in the rapidly rotating asymptotic regime
Aubert, Julien; Fournier, Alexandre
2016-01-01
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state...
Asymptotic Analysis in MIMO MRT/MRC Systems
Directory of Open Access Journals (Sweden)
Zhou Quan
2006-01-01
Full Text Available Through the analysis of the probability density function of the squared largest singular value of a complex Gaussian matrix at the origin and tail, we obtain two asymptotic results related to the multi-input multi-output (MIMO maximum-ratio-transmission/maximum-ratio-combining (MRT/MRC systems. One is the asymptotic error performance (in terms of SNR in a single-user system, and the other is the asymptotic system capacity (in terms of the number of users in the multiuser scenario when multiuser diversity is exploited. Similar results are also obtained for two other MIMO diversity schemes, space-time block coding and selection combining. Our results reveal a simple connection with system parameters, providing good insights for the design of MIMO diversity systems.
Directory of Open Access Journals (Sweden)
A.N. Safiullina
2016-06-01
Full Text Available The problem of estimating the parameters m and p of the binomial distribution for a sample having the fixed volume n with the help of the method of moments is considered in this paper. Using the delta method, the joint asymptotic normality of the estimates is established and the parameters of the limit distribution are calculated. The moment estimates of the parameters m and p do not have averages and variance. An explanation is offered for the asymptotic normality parameters in terms of characteristics of the accuracy properties of the estimates. On the basis of the data of statistical modelling, the accuracy properties of the estimates by the delta-method and their modifications which do not have initial defects of the estimates (the values of the estimates of p are below zero and those of m are smaller than the greatest value in the sample are explored. An example of estimating the parameters m and p according to the observations of the number of responses in the experiment with nervous synapse (m is the number of vesicles with acetylcholine in the vicinity of the synapse, p is the probability of acetylcholine release by each vesicle is provided.
Vacuum energy in asymptotically flat 2+1 gravity
Directory of Open Access Journals (Sweden)
Olivera Miskovic
2017-04-01
Full Text Available We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré 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.
Vacuum energy in asymptotically flat 2 + 1 gravity
Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj
2017-04-01
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincaré 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.
Vacuum energy in asymptotically flat 2 + 1 gravity
Energy Technology Data Exchange (ETDEWEB)
Miskovic, Olivera, E-mail: olivera.miskovic@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago (Chile); Roy, Debraj, E-mail: roy.debraj@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)
2017-04-10
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré 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.
Asymptotic shape of solutions to nonlinear eigenvalue problems
Directory of Open Access Journals (Sweden)
Tetsutaro Shibata
2005-03-01
Full Text Available We consider the nonlinear eigenvalue problem $$ -u''(t = f(lambda, u(t, quad u mbox{greater than} 0, quad u(0 = u(1 = 0, $$ where $lambda > 0$ is a parameter. It is known that under some conditions on $f(lambda, u$, the shape of the solutions associated with $lambda$ is almost `box' when $lambda gg 1$. The purpose of this paper is to study precisely the asymptotic shape of the solutions as $lambda o infty$ from a standpoint of $L^1$-framework. To do this, we establish the asymptotic formulas for $L^1$-norm of the solutions as $lambda o infty$.
Asymptotic solutions of diffusion models for risk reserves
Directory of Open Access Journals (Sweden)
S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
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
Global Asymptotic Stability for Linear Fractional Difference Equation
Directory of Open Access Journals (Sweden)
A. Brett
2014-01-01
Full Text Available Consider the difference equation xn+1=(α+∑i=0kaixn-i/(β+∑i=0kbixn-i, n=0,1,…, where all parameters α,β,ai,bi, i=0,1,…,k, and the initial conditions xi, i∈{-k,…,0} are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.
An asymptotic observer-based monitoring scheme for a class of plug flow reactors.
Aguilar-Garnica, Efrén; García-Sandoval, Juan Paulo; Aceves-Lara, César Arturo; Escalante, Froylán Mario E
2012-01-01
In this paper a monitoring tool is designed for a class of plug flow reactors whose mathematical model is described by a set of first-order partial differential equations with different coefficients in the convective terms. The infinite dimensional structure of such a tool is derived according to the methodology established in the design of the well-known asymptotic observer. As a consequence, it preserves the robustness of the aforementioned observer against the lack of information of the nonlinear terms involved in the model. The original structure of the estimator is then represented as a couple of integral equations by means of the method of characteristics and its behaviour is analyzed through simulation experiments. These simulations show that the mean square observation error is 0.58 when the proposed observer is implemented in a solid-waste anaerobic digestion process to estimate the evolution of biomass concentration.
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.
A note on the Fisher information matrix for the skew-generalized-normal model
Arellano-Valle, Reinaldo B.; Gómez, Héctor W.; Salinas, Hugo S.
2013-01-01
In this paper, the exact form of the Fisher information matrix for the skew-generalized normal (SGN) distribution is determined. The existence of singularity problems of this matrix for the skew-normal and normal particular cases is investigated. Special attention is given to the asymptotic properties of the MLEs under the skew-normality hypothesis. Peer Reviewed
Deformation limits on two-parameter fracture mechanics in terms of higher order asymptotics
Crane, D. L.; Anderson, T. L.
1994-09-01
This report addresses the limitations of two-parameter fracture mechanics. We performed an asymptotic analysis of the general power series representation of the crack tip stress potential in an elastic plastic material that obeys a Ramberg-Osgood constitutive law. Expansion of the power series over a substantial number of terms yields. only three independent coefficients for low. and medium-hardening materials. The first independent The second and third independent coefficients, K2 and K4 are a function of geometry and loading level. A two-parameter theory implies that the crack tip stress fields have two degrees of freedom, but the asymptotic analysis implies that three parameters are required to characterize near-tip conditions. Thus two-parameter fracture theory is a valid engineering model only when there is an approximately unique relationship between K2 and K4. We performed elastic-plastic finite element analyses on several geometries and evaluated K2 and K4 as a function of deformation level. A reference,two-parameter solution (which gives a unique relation between K2 and K4) was provided by the modified boundary layer (MBL) geometry. Results indicate that the near tip stresses in all but the deeply cracked SENT (a/W-.5.O.9) and SENT (a/W-0.9) lend themselves to a two-parameter characterization. However, the deeply cracked SENT and SENT specimens maintain a high level of constraint to relatively large deformation levels. Thus single-parameter fracture mechanics is fairly robust for these high constraint geometries, but two-parameter theory is of little value when constraint loss eventually occurs.
Relaxing the parity conditions of asymptotically flat gravity
Compère, G.; Dehouck, F.
2011-01-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm
High energy asymptotics of the scattering amplitude for the ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
High energy asymptotics of the scattering amplitude for the. Schrödinger equation. D YAFAEV. Department of Mathematics, University Rennes-1, Campus Beaulieu, 35042 Rennes,. France. Abstract. We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy.
Asymptotics of sums of lognormal random variables with Gaussian copula
DEFF Research Database (Denmark)
Asmussen, Søren; Rojas-Nandayapa, Leonardo
2008-01-01
Let (Y1, ..., Yn) have a joint n-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let Xi = eYi, Sn = X1 + ⋯ + Xn. The asymptotics of P (Sn > x) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In part...
Chemical Analysis of Asymptotic Giant Branch Stars in M62
Lapenna, E.; Mucciarelli, A.; Ferraro, F. R.; Origlia, L.; Lanzoni, B.; Massari, D.; Dalessandro, E.
2015-01-01
We have collected UVES-FLAMES high-resolution spectra for a sample of 6 asymptotic giant branch (AGB) and 13 red giant branch (RGB) stars in the Galactic globular cluster (GC) M62 (NGC 6266). Here we present the detailed abundance analysis of iron, titanium, and light elements (O, Na, Mg, and Al).
Precise asymptotics for complete moment convergence in Hilbert ...
Indian Academy of Sciences (India)
... Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 122; Issue 1. Precise Asymptotics for Complete Moment Convergence in Hilbert Spaces. Keang Fu Juan Chen. Volume 122 Issue 1 February 2012 ...
Exact overflow asymptotics for queues with many Gaussian inputs
Debicki, Krzysztof; Mandjes, M.R.H.
2003-01-01
In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
Abstract. In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute ...
Asymptotic linear estimation of the quantile function of a location ...
African Journals Online (AJOL)
Specific results are discussed for the ABLUE of Qξ for the location-scale exponential and double exponential distributions. As a further application of the exponential results, we discuss the asymptotically best optimal spacings for the location-scale logistic distribution. Keywords: Quantiles; Order statistics; Optimal spacing; ...
The Asymptotic Solution for the Steady Variable-Viscosity Free ...
African Journals Online (AJOL)
Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...
Asymptotic stability results for retarded differential systems | Igobi ...
African Journals Online (AJOL)
The transcendental character of the polynomial equation of the retarded differential system makes it difficult to express its solution explicitly. This has cause a set back in the asymptotic stability analysis of the system solutions. Various acceptable mathematical techniques have been used to address the issue. In this paper ...
Hardy-Weinberg law: asymptotic approach to a generalized form.
Stark, A E
1976-09-17
The equilibrium frequencies of a generalized Hardy-Weinberg law are approached at a geometric rate under assortative mating, irrespective of the initial genotypic frequencies. The asymptotic form is similar to that of Wright, and the pattern of assortative mating is based on deviations from the mean genotypic value.
Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
Saeidi Shahram
2010-01-01
Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in ...
Asymptotic estimates of viscoelastic Green's functions near the wavefront
Hanyga, Andrzej
2014-01-01
Asymptotic behavior of viscoelastic Green's functions near the wavefront is expressed in terms of a causal function $g(t)$ defined in \\cite{SerHanJMP} in connection with the Kramers-Kronig dispersion relations. Viscoelastic Green's functions exhibit a discontinuity at the wavefront if $g(0) < \\infty$. Estimates of continuous and discontinuous viscoelastic Green's functions near the wavefront are obtained.
Uniqueness and asymptotic stability properties of the critical solution ...
African Journals Online (AJOL)
In this research, the Volterra prey/predator model system is modified by introducing time-lag functions f (t - h) into the state parameters to account for the ... The asymptotic stability properties of the critical solution are investigated using the quadratic matrix equation and symmetric linear matrix inequality test. Results obtained ...
Asymptotics and Numerics for Laminar Flow over Finite Flat Plate
Dijkstra, D.; Kuerten, J.G.M.; Kaper, Hans G.; Garbey, Mare; Pieper, Gail W.
1992-01-01
A compilation of theoretical results from the literature on the finite flat-plate flow at zero incidence is presented. This includes the Blasius solution, the Triple Deck at the trailing edge, asymptotics in the wake, and properties near the edges of the plate. In addition, new formulas for skin
Asymptotic-bound-state model for Feshbach resonances
Tiecke, T.G.; Goosen, M.R.; Walraven, J.T.M.; Kokkelmans, S.J.J.M.F.
2010-01-01
We present an asymptotic-bound-state model which can be used to accurately describe all Feshbach resonance positions and widths in a two-body system. With this model we determine the coupled bound states of a particular two-body system. The model is based on analytic properties of the two-body
Parabolic cyclinder functions : examples of error bounds for asymptotic expansions
R. Vidunas; N.M. Temme (Nico)
2002-01-01
textabstractSeveral asymptotic expansions of parabolic cylinder functions are discussedand error bounds for remainders in the expansions are presented. Inparticular Poincaré-type expansions for large values of the argument$z$ and uniform expansions for large values of the parameter areconsidered.
Precise asymptotics for complete moment convergence in Hilbert ...
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 122, No. 1, February 2012, pp. 87–97. c Indian Academy of Sciences. Precise asymptotics for complete moment convergence in Hilbert spaces ... School of Statistics and Mathematics, Zhejiang Gongshang University, .... Now we start to introduce some Propositions, and the proof of our main result is based.
Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes
Caldeira Costa, R.N.
2012-01-01
In this work we elaborate on an extension of the AdS/CFT framework to a sub-class of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family
From A to Z: Asymptotic expansions by van Zwet
Albers, Willem/Wim; de Gunst, Mathisca; Klaasen, Chris; van der Vaart, Aad
2001-01-01
Refinements of first order asymptotic results axe reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and [/-statistics. After these special classes, the question about a general second
From A to Z: asymptotic expansions by van Zwet
Albers, Willem/Wim; de Gunst, M.C.M.; Klaassen, C.A.J.; van der Vaart, A.W.
2001-01-01
Refinements of first order asymptotic results are reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and U-statistics. After these special classes, the question about a general second
Tail asymptotics for dependent subexponential diﬀerences
DEFF Research Database (Denmark)
Albrecher, H; Asmussen, Søren; Kortschak, D.
We study the asymptotic behavior of P(X − Y > u) as u → ∞, where X is subexponential and X, Y are positive random variables that may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic...
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
Asymptotic symmetries in de Sitter and inflationary spacetimes
DEFF Research Database (Denmark)
Ferreira, Ricardo J. Z.; Sandora, McCullen; Sloth, Martin S.
2017-01-01
Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state...
Asymptotic Normality of Minimum L1-Norm Estimates in Linear Models
1987-09-01
E*nl(§) (2.13) ’ ,ni(O *nQ (2n1- t = )n) + xni(). (2.14) By (2.7), when a e D and i < n, we have, for large n, Ixni < d_ nIW < ( 2vn )-I (2.15) and...taken at the true parameter point - We shall proceed to show that AI(e0 ) - in probability as T - " Define 1, if y- 1 t 0, otherwise. Since CT = Td < d...2log(l+e 1)hlTCT 2 Here we used the fact that CT Td and 1/3 < d < 1/2. Further T’. 31 Var(A) < (2CT 1 log(l +e-)) 2 E t=l <(2C 1 log( +e 1 2Th2CT
Carpenter, Donald A.
2008-01-01
Confusion exists among database textbooks as to the goal of normalization as well as to which normal form a designer should aspire. This article discusses such discrepancies with the intention of simplifying normalization for both teacher and student. This author's industry and classroom experiences indicate such simplification yields quicker…
Li, Xiaoqi; Jiang, Huabei
2013-02-21
We present a study through extensive simulation that considers the impact of inhomogeneous optical scattering coefficient distribution on recovery of optical absorption coefficient maps using tomographic photoacoustic data collected from media mimicking breast tissue. We found that while the impact of scattering heterogeneities/targets is modest on photoacoustic recovery of optical absorption coefficients, the impact of scattering contrast caused by adipose tissue, a layer of normal tissue along the boundary of the breast, is dramatic on reconstruction of optical absorption coefficients using photoacoustic data-up to 25.8% relative error in recovering the absorption coefficient is estimated in such cases. To overcome this problem, we propose a new method to enhance photoacoustic recovery of the optical absorption coefficient in heterogeneous media by considering inhomogeneous scattering coefficient distribution provided by diffuse optical tomography (DOT). Results from extensive simulations show that photoacoustic recovery of absorption coefficient maps can be improved considerably with a priori scattering information from DOT.
On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability
Directory of Open Access Journals (Sweden)
Işık Mahmut
2017-01-01
Full Text Available In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.
On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability
Işık Mahmut; Akbaş Kübra Elif
2017-01-01
In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.
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 ...
An Asymptotic Approach for the Elastodynamic Problem of a Plate under Impact Loading
Directory of Open Access Journals (Sweden)
Penelope Michalopoulou
2010-01-01
Full Text Available An approach is presented for analyzing the transient elastodynamic problem of a plate under an impact loading. The plate is considered to be in the form of a long strip under plane strain conditions. The loading is taken as a concentrated line force applied normal to the plate surface. It is assumed that this line force is suddenly applied and maintained thereafter (i.e., it is a Heaviside step function of time. Inertia effects are taken into consideration and the problem is treated exactly within the framework of elastodynamic theory. The approach is based on multiple Laplace transforms and on certain asymptotic arguments. In particular, the one-sided Laplace transform is applied to suppress time dependence and the two-sided Laplace transform to suppress the dependence upon a spatial variable (along the extent of the infinite strip. Exact inversions are then followed by invoking the asymptotic Tauber theorem and the Cagniard-deHoop technique. Various extensions of this basic analysis are also discussed.
Rosner, Bernard; Glynn, Robert J
2007-02-10
The Spearman (rho(s)) and Kendall (tau) rank correlation coefficient are routinely used as measures of association between non-normally distributed random variables. However, confidence limits for rho(s) are only available under the assumption of bivariate normality and for tau under the assumption of asymptotic normality of tau. In this paper, we introduce another approach for obtaining confidence limits for rho(s) or tau based on the arcsin transformation of sample probit score correlations. This approach is shown to be applicable for an arbitrary bivariate distribution. The arcsin-based estimators for rho(s) and tau (denoted by rho(s,a), tau(a)) are shown to have asymptotic relative efficiency (ARE) of 9/pi2 compared with the usual estimators rho(s) and tau when rho(s) and tau are, respectively, 0. In some nutritional applications, the Spearman rank correlation between nutrient intake as assessed by a reference instrument versus nutrient intake as assessed by a surrogate instrument is used as a measure of validity of the surrogate instrument. However, if only a single replicate (or a few replicates) are available for the reference instrument, then the estimated Spearman rank correlation will be downwardly biased due to measurement error. In this paper, we use the probit transformation as a tool for specifying an ANOVA-type model for replicate ranked data resulting in a point and interval estimate of a measurement error corrected rank correlation. This extends previous work by Rosner and Willett for obtaining point and interval estimates of measurement error corrected Pearson correlations. 2006 John Wiley & Sons, Ltd.
Directory of Open Access Journals (Sweden)
Javier E. Contreras-Reyes
2016-10-01
Full Text Available Mixture models are in high demand for machine-learning analysis due to their computational tractability, and because they serve as a good approximation for continuous densities. Predominantly, entropy applications have been developed in the context of a mixture of normal densities. In this paper, we consider a novel class of skew-normal mixture models, whose components capture skewness due to their flexibility. We find upper and lower bounds for Shannon and Rényi entropies for this model. Using such a pair of bounds, a confidence interval for the approximate entropy value can be calculated. In addition, an asymptotic expression for Rényi entropy by Stirling’s approximation is given, and upper and lower bounds are reported using multinomial coefficients and some properties and inequalities of L p metric spaces. Simulation studies are then applied to a swordfish (Xiphias gladius Linnaeus length dataset.
Precise asymptotic behavior of solutions to damped simple pendulum equations
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Tetsutaro Shibata
2009-11-01
Full Text Available We consider the simple pendulum equation $$displaylines{ -u''(t + epsilon f(u'(t = lambdasin u(t, quad t in I:=(-1, 1,cr u(t > 0, quad t in I, quad u(pm 1 = 0, }$$ where $0 < epsilon le 1$, $lambda > 0$, and the friction term is either $f(y = pm|y|$ or $f(y = -y$. Note that when $f(y = -y$ and $epsilon = 1$, we have well known original damped simple pendulum equation. To understand the dependance of solutions, to the damped simple pendulum equation with $lambda gg 1$, upon the term $f(u'(t$, we present asymptotic formulas for the maximum norm of the solutions. Also we present an asymptotic formula for the time at which maximum occurs, for the case $f(u = -u$.
Asymptotic analysis of multicell massive MIMO over Rician fading channels
Sanguinetti, Luca
2017-06-20
This work considers the downlink of a multicell massive MIMO system in which L base stations (BSs) of N antennas each communicate with K single-antenna user equipments randomly positioned in the coverage area. Within this setting, we are interested in evaluating the sum rate of the system when MRT and RZF are employed under the assumption that each intracell link forms a MIMO Rician uncorrelated fading channel. The analysis is conducted assuming that N and K grow large with a non-trivial ratio N/K under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, and an arbitrary large scale attenuation. Numerical results are used to validate the asymptotic analysis in the finite system regime and to evaluate the network performance under different settings. The asymptotic results are also instrumental to get insights into the interplay among system parameters.
The asymptotic convergence factor for a polygon under a perturbation
Energy Technology Data Exchange (ETDEWEB)
Li, X. [Georgia Southern Univ., Statesboro, GA (United States)
1994-12-31
Let Ax = b be a large system of linear equations, where A {element_of} C{sup NxN}, nonsingular and b {element_of} C{sup N}. A few iterative methods for solving have recently been presented in the case where A is nonsymmetric. Many of their algorithms consist of two phases: Phase I: estimate the extreme eigenvalues of A; Phase II: construct and apply an iterative method based on the estimates. For convenience, it is rewritten as an equivalent fixed-point form, x = Tx + c. Let {Omega} be a compact set excluding 1 in the complex plane, and let its complement in the extended complex plane be simply connected. The asymptotic convergence factor (ACF) for {Omega}, denoted by {kappa}({Omega}), measures the rate of convergence for the asymptotically optimal semiiterative methods for solving, where {sigma}(T) {contained_in} {Omega}.
Asymptotic Floquet states of non-Markovian systems
Magazzú, Luca; Denisov, Sergey; Hänggi, Peter
2017-10-01
We propose a method to find asymptotic states of a class of periodically modulated open systems which are outside the range of validity of the Floquet theory due to the presence of memory effects. The method is based on a Floquet treatment of the time-local, memoryless dynamics taking place in a minimally enlarged state space where the original system is coupled to auxiliary—typically nonphysical—variables. A projection of the Floquet solution into the physical subspace returns the sought asymptotic state of the system. The spectral gap of the Floquet propagator acting in the enlarged state space can be used to estimate the relaxation time. We illustrate the method with a modulated quantum random walk model.
Upper bound on the Abelian gauge coupling from asymptotic safety
Eichhorn, Astrid; Versteegen, Fleur
2018-01-01
We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.
Higher order corrections to asymptotic-de Sitter inflation
Mohsenzadeh, M.; Yusofi, E.
2017-08-01
Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.
Asymptotically Lifshitz spacetimes with universal horizons in (1 +2 ) dimensions
Basu, Sayandeb; Bhattacharyya, Jishnu; Mattingly, David; Roberson, Matthew
2016-03-01
Hořava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two-derivative Hořava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to z =2 in 1 +2 dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions and show that, unlike the asymptotically anti-de Sitter case, the first law applied to the universal horizon is straightforwardly compatible with a thermodynamic interpretation.
Broer, H.; Hoveijn, I.; Lunter, G.; Vegter, G.
2003-01-01
The Birkhoff normal form procedure is a widely used tool for approximating a Hamiltonian systems by a simpler one. This chapter starts out with an introduction to Hamiltonian mechanics, followed by an explanation of the Birkhoff normal form procedure. Finally we discuss several algorithms for
Non-Tikhonov Asymptotic Properties of Cardiac Excitability
Biktashev, V. N.; Suckley, R.
2004-10-01
Models of electric excitability of cardiac cells can be studied by singular perturbation techniques. To do this one should take into account parameters appearing in equations in nonstandard ways. The physical reason for this is near-perfect switch behavior of ionic current gates. This leads to a definition of excitability different from the currently accepted one. The asymptotic structure revealed by our analysis can be used to devise simplified caricature models, to obtain approximate analytical solutions, and to facilitate numerical simulations.
TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS
DEFF Research Database (Denmark)
Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.
2017-01-01
We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle......, and supplemented with bounds, results on a random number N of terms, and simulation algorithms....
Local asymptotic stability for nonlinear quadratic functional integral equations
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2008-03-01
Full Text Available In the present study, using the characterizations of measures of noncompactness we prove a theorem on the existence and local asymptotic stability of solutions for a quadratic functional integral equation via a fixed point theorem of Darbo. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of abstract result presented in the paper.
Asymptotic behaviour of the Weyl tensor in higher dimensions
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravdová, Alena
2014-01-01
Roč. 90, č. 10 (2014), s. 104011 ISSN 1550-7998 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * asymptotic structure * classical general relativity Subject RIV: BA - General Mathematics Impact factor: 4.643, year: 2014 http://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.104011
Asymptotic behavior of Maxwell fields in higher dimensions
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello
2014-01-01
Roč. 90, č. 12 (2014), s. 124020 ISSN 1550-7998 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * asymptotic structure * classical general relativity Subject RIV: BA - General Mathematics Impact factor: 4.643, year: 2014 http://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.124020
On the accuracy of the asymptotic theory for cylindrical shells
DEFF Research Database (Denmark)
Niordson, Frithiof; Niordson, Christian
1999-01-01
We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this theory for a cylindrical shell with clamped ends with the results of a solution to the three-dimensional problem....... The results are also compared with those of some commonly used engineering shell theories....
On the accuracy of the asymptotic theory for cylindrical shells
DEFF Research Database (Denmark)
Niordson, Frithiof; Niordson, Christian
1999-01-01
We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this shell theory for a cylindrical shell with clamped ends with the results of a solution to the three......-dimensional problem. The results are also compared with those of some commonly used engineering shell theories....
Asymptotics of solutions to semilinear stochastic wave equations
Chow, Pao-Liu
2006-01-01
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution, in mean-square and the almost sure sense, are studied. Then...
Framework for an asymptotically safe standard model via dynamical breaking
Abel, Steven; Sannino, Francesco
2017-09-01
We present a consistent embedding of the matter and gauge content of the Standard Model into an underlying asymptotically safe theory that has a well-determined interacting UV fixed point in the large color/flavor limit. The scales of symmetry breaking are determined by two mass-squared parameters with the breaking of electroweak symmetry being driven radiatively. There are no other free parameters in the theory apart from gauge couplings.
Asymptotic estimation of xi^{(2n)}(1/2)
Coffey, Mark W.
2009-06-01
We verify a very recent conjecture of Farmer and Rhoades on the asymptotic rate of growth of the derivatives of the Riemann xi function at s=1/2 . We give two separate proofs of this result, with the more general method not restricted to s=1/2 . We briefly describe other approaches to our results, give a heuristic argument, and mention supporting numerical evidence.
Gauge hierarchy problem in asymptotically safe gravity - The resurgence mechanism
Wetterich, Christof; Yamada, Masatoshi
2017-07-01
The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a ;resurgence mechanism; where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomalous dimension plays a crucial role for the required ;self-tuned criticality; in the ultraviolet regime beyond the Planck scale.
Solution branches for nonlinear problems with an asymptotic oscillation property
Directory of Open Access Journals (Sweden)
Lin Gong
2015-10-01
Full Text Available In this article we employ an oscillatory condition on the nonlinear term, to prove the existence of a connected component of solutions of a nonlinear problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions to the nonlinear problem for all parameter values in that interval.
Bounds and asymptotics for orthogonal polynomials for varying weights
Levin, Eli
2018-01-01
This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .
Asymptotic analysis of Lévy-driven tandem queues
P.M.D. Lieshout (Pascal); M.R.H. Mandjes (Michel)
2008-01-01
htmlabstractWe analyze tail asymptotics of a two-node tandem queue with spectrally-positive Lévy input. A first focus lies in the tail probabilities of the type ¿(Q 1>¿ x,Q 2>(1¿¿)x), for ¿¿(0,1) and x large, and Q i denoting the steady-state workload in the ith queue. In case of light-tailed input,
Directory of Open Access Journals (Sweden)
Prayag Prasad Mishra
2007-01-01
Full Text Available In this paper sufficient conditions are obtained so that every solution of $$ (y(t- p(ty(t-au'+ Q(tG(y(t-sigma-U(tG(y(t-alpha = f(t $$ tends to zero or to $pm infty$ as $t$ tends to $infty$, where $au ,sigma ,alpha$ are positive real numbers, $p,fin C([0,infty,R,Q,Uin C([0,infty,[0,infty$, and $Gin C(R,R$, $G$ is non decreasing with $xG(x>0$ for $ x eq 0$. The two primary assumptions in this paper are $int_{t_0}^{infty}Q(t=infty$ and $int_{t_0}^{infty}U(t
Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
Modeling broadband poroelastic propagation using an asymptotic approach
Energy Technology Data Exchange (ETDEWEB)
Vasco, Donald W.
2009-05-01
An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.
Sabine absorption coefficients to random incidence absorption coefficients
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2014-01-01
into random incidence absorption coefficients for porous absorbers are investigated. Two optimization-based conversion methods are suggested: the surface impedance estimation for locally reacting absorbers and the flow resistivity estimation for extendedly reacting absorbers. The suggested conversion methods......Absorption coefficients measured by the chamber method are referred to as Sabine absorption coefficients, which sometimes exceed unity due to the finite size of a specimen and non-uniform intensity in the test chamber. In this study, several methods that convert Sabine absorption coefficients...
Directory of Open Access Journals (Sweden)
Justine Yasappan
2013-01-01
Full Text Available Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.
Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series
DEFF Research Database (Denmark)
Davis, Richard A.; Mikosch, Thomas Valentin; Pfaffel, Olivier
2016-01-01
In this paper we give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index α∈(0,4) in...... particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues...... of a non-negative definite matrix. Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix...
Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow
Grooms, Ian G.
This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic
A note on the Fisher information matrix for the skew-generalized-normal model
Arellano-Valle, Reinaldo B.
2013-01-01
In this paper, the exact form of the Fisher information matrix for the skew-generalized normal (SGN) distribution is determined. The existence of singularity problems of this matrix for the skewnormal and normal particular cases is investigated. Special attention is given to the asymptotic properties of the MLEs under the skew-normality hypothesis.
Stochastic modeling of the diffusion coefficient for concrete
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
. A deterministic relationship between the diffusion coefficient and the w/c ratio and the temperature is used for the stochastic modelling. The w/c ratio and the temperature are modelled by log-normally and normally distributed stochastic variables, respectively. It is then shown by Monte Carlo simulation...... that the diffusion coefficient D may be modelled by a normally distributed stochastic variable. The sensitivities of D with regard to the mean values and the standard deviations are evaluated.......In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on a physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficient D is strongly dependent on the w/c ratio and the temperature...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Measuring of heat transfer coefficient
DEFF Research Database (Denmark)
Henningsen, Poul; Lindegren, Maria
Subtask 3.4 Measuring of heat transfer coefficient Subtask 3.4.1 Design and setting up of tests to measure heat transfer coefficient Objective: Complementary testing methods together with the relevant experimental equipment are to be designed by the two partners involved in order to measure...... the heat transfer coefficient for a wide range of interface conditions in hot and warm forging processes. Subtask 3.4.2 Measurement of heat transfer coefficient The objective of subtask 3.4.2 is to determine heat transfer values for different interface conditions reflecting those typically operating in hot...
Imposed quasi-normality in covariance structure analysis
Koning, Ruud H.; Neudecker, H.; Wansbeek, T.
1993-01-01
In the analysis of covariance structures, the distance between an observed covariance matrix S of order k x k and C(6) E(S) is minimized by searching over the 8-space. The criterion leading to a best asymptotically normal (BAN) estimator of 0 is found by minimizing the difference between vecS and
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...
Edgeworth expansions and normalizing transforms for inequality measures
Schluter, C.; van Garderen, K.J.
2009-01-01
Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality
Graph characterization via Ihara coefficients.
Ren, Peng; Wilson, Richard C; Hancock, Edwin R
2011-02-01
The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.
Asymptotics of work distributions in a stochastically driven system
Manikandan, Sreekanth K.; Krishnamurthy, Supriya
2017-12-01
We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82, 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89, 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87, 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16, 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16, 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (β → ∞) limit.
Exploring central opacity and asymptotic scenarios in elastic hadron scattering
Fagundes, D. A.; Menon, M. J.; Silva, P. V. R. G.
2016-02-01
In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio X between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m. energy interval 5 GeV-8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for X, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratio X bar = 0.30 ± 0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for X and physical aspects related to a change of curvature in this quantity at 80-100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.
On selfdual spin-connections and asymptotic safety
Directory of Open Access Journals (Sweden)
U. Harst
2016-02-01
Full Text Available We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein–Cartan gravity without the selfduality condition.
Subexponential loss rate asymptotics for Lévy processes
DEFF Research Database (Denmark)
Andersen, Lars Nørvang
2011-01-01
We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics...... for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula....
Asymptotic Behavior for a Class of Nonclassical Parabolic Equations
Yanjun Zhang; Qiaozhen Ma
2013-01-01
This paper is devoted to the qualitative analysis of a class of nonclassical parabolic equations ut-εΔut-ωΔu+f(u)=g(x) with critical nonlinearity, where ε∈[0,1] and ω>0 are two parameters. Firstly, we establish some uniform decay estimates for the solutions of the problem for g(x)∈H-1(Ω), which are independent of the parameter ε. Secondly, some uniformly (with respect to ε∈[0,1]) asymptotic regularity about the solutions has been established for g(x)∈L2(Ω), which shows that the solutions are ...
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Directory of Open Access Journals (Sweden)
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Asymptotic shape of solutions to the perturbed simple pendulum problems
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Tetsutaro Shibata
2007-05-01
Full Text Available We consider the positive solution of the perturbed simple pendulum problem $$ u''(r + frac{N-1}{r}u'(r - g(u(t + lambda sin u(r = 0, $$ with $0 < r < R$, $ u'(0 = u(R = 0$. To understand well the shape of the solution $u_lambda$ when $lambda gg 1$, we establish the leading and second terms of $Vert u_lambdaVert_q$ ($1 le q < infty$ with the estimate of third term as $lambda o infty$. We also obtain the asymptotic formula for $u_lambda'(R$ as $lambda o infty$.
Asymptotic formulae for likelihood-based tests of new physics
Cowan, Glen; Cranmer, Kyle; Gross, Eilam; Vitells, Ofer
2011-02-01
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.
Asymptotic formulae for likelihood-based tests of new physics
Energy Technology Data Exchange (ETDEWEB)
Cowan, Glen [Royal Holloway, University of London, Physics Department, Egham (United Kingdom); Cranmer, Kyle [New York University, Physics Department, New York, NY (United States); Gross, Eilam; Vitells, Ofer [Weizmann Institute of Science, Rehovot (Israel)
2011-02-15
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the ''Asimov data set'', which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation. (orig.)
Shrinkage singularities of amplitudes and weak interaction cross- section asymptotic
Dolgov, A D; Okun, Lev Borisovich
1972-01-01
The so called shrinkage singularities of amplitudes caused by shrinkage of diffraction peak at asymptotically high energies are discussed given the condition that the amplitude singularities are not stronger than t/sup 2/ ln t (as is case for neutrino pair exchange diagrams) then total cross-section sigma /sub tot/ cannot increase faster at s to infinity than s/sup 1/3/. If shrinkage singularities are absent then sigma /sub tot/ cannot increase as any power of s. All the conclusions are valid, if the dispersion relations with finite number of subtractions exist at t
Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations
Directory of Open Access Journals (Sweden)
Josef Diblík
2011-01-01
Full Text Available A linear Volterra difference equation of the form x(n+1=a(n+b(nx(n+∑i=0nK(n,ix(i, where x:N0→R, a:N0→R, K:N0×N0→R and b:N0→R∖{0} is ω-periodic, is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on ∏j=0ω-1b(j is assumed. The results generalize some of the recent results.
Asymptotic behavior of observables in the asymmetric quantum Rabi model
Semple, J.; Kollar, M.
2018-01-01
The asymmetric quantum Rabi model with broken parity invariance shows spectral degeneracies in the integer case, that is when the asymmetry parameter equals an integer multiple of half the oscillator frequency, thus hinting at a hidden symmetry and accompanying integrability of the model. We study the expectation values of spin observables for each eigenstate and observe characteristic differences between the integer and noninteger cases for the asymptotics in the deep strong coupling regime, which can be understood from a perturbative expansion in the qubit splitting. We also construct a parent Hamiltonian whose exact eigenstates possess the same symmetries as the perturbative eigenstates of the asymmetric quantum Rabi model in the integer case.
Asymptotic Analysis and Spatial Coupling of Counter Braids
Rosnes, Eirik; Amat, Alexandre Graell i
2016-01-01
A counter braid (CB) is a novel counter architecture introduced by Lu et al. in 2007 for per-flow measurements on high-speed links. CBs achieve an asymptotic compression rate (under optimal decoding) that matches the entropy lower bound of the flow size distribution. In this paper, we apply the concept of spatial coupling to CBs to improve their belief propagation (BP) threshold, and analyze the performance of the resulting spatially-coupled CBs (SC-CBs). We introduce an equivalent bipartite ...
Asymptotic geometry in higher products of rank one Hadamard spaces
Link, Gabriele
2013-01-01
Given a product X of locally compact rank one Hadamard spaces, we study asymptotic properties of certain discrete isometry groups. First we give a detailed description of the structure of the geometric limit set and relate it to the limit cone; moreover, we show that the action of the group on a quotient of the regular geometric boundary of X is minimal and proximal. This is completely analogous to the case of Zariski dense discrete subgroups of semi-simple Lie groups acting on the associated...
Asymptotics of Rydberg states for the hydrogen atom
Energy Technology Data Exchange (ETDEWEB)
Thomas, L.E. [Virginia Univ., Charlottesville, VA (United States). Dept. of Mathematics; Villegas-Blas, C. [Universidad Nacional Autonoma de Mexico, Instituto de Matematicas, Unidad Cuernavaca, A. P. 273-3 Admon. 3, Cuernavaca Morelos 62251 (Mexico)
1997-08-01
The asymptotics of Rydberg states, i.e., highly excited bound states of the hydrogen atom Hamiltonian, and various expectations involving these states are investigated. We show that suitable linear combinations of these states, appropriately rescaled and regarded as functions either in momentum space or configuration space, are highly concentrated on classical momentum space or configuration space Kepler orbits respectively, for large quantum numbers. Expectations of momentum space or configuration space functions with respect to these states are related to time-averages of these functions over Kepler orbits. (orig.)
Asymptotic Theory for the Probability Density Functions in Burgers Turbulence
Weinan, E; Eijnden, Eric Vanden
1999-01-01
A rigorous study is carried out for the randomly forced Burgers equation in the inviscid limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than $|\\xi|^{-3}$. A further argument confirms the prediction of E et al., Phys. Rev. Lett. {\\bf 78}, 1904 (1997), that it should decay as $|\\xi|^{-7/2}$.
Joint Asymptotic Distributions of Smallest and Largest Insurance Claims
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Hansjörg Albrecher
2014-07-01
Full Text Available Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace transforms of the normalised sums of the smallest and largest claims, when the length of the considered time interval tends to infinity. The results crucially depend on the value of the tail index of the claim distribution, as well as on the number of largest claims under consideration.
Asymptotic Limits for Transport in Binary Stochastic Mixtures
Energy Technology Data Exchange (ETDEWEB)
Prinja, A. K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-01
The Karhunen-Loeve stochastic spectral expansion of a random binary mixture of immiscible fluids in planar geometry is used to explore asymptotic limits of radiation transport in such mixtures. Under appropriate scalings of mixing parameters - correlation length, volume fraction, and material cross sections - and employing multiple- scale expansion of the angular flux, previously established atomic mix and diffusion limits are reproduced. When applied to highly contrasting material properties in the small cor- relation length limit, the methodology yields a nonstandard reflective medium transport equation that merits further investigation. Finally, a hybrid closure is proposed that produces both small and large correlation length limits of the closure condition for the material averaged equations.
Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks
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Milan Tuba
2013-01-01
Full Text Available Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully investigated by maximum entropy method application. In this paper we prove a theorem that establishes asymptotic properties of the maximum entropy routing solution. This result, besides being theoretically interesting, can be used to direct initial approximation for iterative optimization algorithms and to speed up their convergence.
Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes
Bantilan, Hans; Figueras, Pau; Kunesch, Markus; Romatschke, Paul
2017-11-01
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of nonspherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.
Asymptotics of weakly collapsing solutions of nonlinear Schroedinger equation
Ovchinnikov, Yu N
2001-01-01
One studied possible types of asymptotic behavior of weakly collapsing solution of the 3-rd nonlinear Schroedinger equation. It is shown that within left brace A, C sub 1 right brace parameter space there are two neighboring lines along which the amplitude of oscillation terms is exponentially small as to C sub 1 parameter. The same lines locates values of left brace A, C sub 1 right brace parameters at which the energy is equal to zero. With increase of C sub 1 parameter the accuracy of numerical determination of points with zero energy drops abruptly
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
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Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
Asymptotically Efficient Identification of Known-Sensor Hidden Markov Models
Mattila, Robert; Rojas, Cristian R.; Krishnamurthy, Vikram; Wahlberg, Bo
2017-12-01
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator (formulated as a convex optimization problem) followed by a single iteration of a Newton-Raphson maximum likelihood estimator. The two-fold contribution of this letter is, firstly, to theoretically show that the proposed estimator is consistent and asymptotically efficient, and secondly, to numerically show that the method is computationally less demanding than conventional methods - in particular for large data sets.
Asymptotic Stability for a Class of Nonlinear Difference Equations
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Chang-you Wang
2010-01-01
Full Text Available We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k/(α+bxn-s+cxn-t, n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a,l,k,s,t are nonnegative integers, r=max{l,k,s,t} and α,a,b,c are positive constants. Moreover, some numerical simulations are given to illustrate our results.
Asymptotic Ergodic Capacity Analysis of Composite Lognormal Shadowed Channels
Ansari, Imran Shafique
2015-05-01
Capacity analysis of composite lognormal (LN) shadowed links, such as Rician-LN, Gamma-LN, and Weibull-LN, is addressed in this work. More specifically, an exact closed-form expression for the moments of the end-to-end signal-to-noise ratio (SNR) of a single composite link transmission system is presented in terms of well- known elementary functions. Capitalizing on these new moments expressions, we present asymptotically tight lower bounds for the ergodic capacity at high SNR. All the presented results are verified via computer-based Monte-Carlo simulations. © 2015 IEEE.
J.W. Klop (Jan Willem); R. de Vrijer
2005-01-01
textabstractIn infinitary orthogonal first-order term rewriting the properties confluence (CR), Uniqueness of Normal forms (UN), Parallel Moves Lemma (PML) have been generalized to their infinitary versions CR-inf, UN-inf, PML-inf, and so on. Several relations between these properties have been
Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.
2016-12-01
Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.
Gravitational geons in asymptotically anti-de Sitter spacetimes
Martinon, Grégoire; Fodor, Gyula; Grandclément, Philippe; Forgács, Peter
2017-06-01
We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.
Asymptotic behavior for a quadratic nonlinear Schrodinger equation
Directory of Open Access Journals (Sweden)
Pavel I. Naumkin
2008-02-01
Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.
Asymptotically simple spacetimes and mass loss due to gravitational waves
Saw, Vee-Liem
The cosmological constant Λ used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of Λ or Λ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on Λ: null infinity ℐ is a spacelike, null, or timelike hypersurface, if Λ > 0, Λ = 0, or Λ 0 in Einstein’s theory of GR. A quantity that depends on the conformal structure of spacetime, especially on the nature of ℐ, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with Λ > 0 has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearization, attempts using a Hamiltonian formulation based on “linearized” asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.
arXiv Naturalness of asymptotically safe Higgs
Pelaggi, Giulio Maria; Strumia, Alessandro; Vigiani, Elena
2017-01-01
We extend the list of theories featuring a rigorous interacting ultraviolet fixed point by constructing the first theory featuring a Higgs-like scalar with gauge, Yukawa and quartic interactions. We show that the theory enters a perturbative asymptotically safe regime at energies above a physical scale $\\Lambda$. We determine the salient properties of the theory and use it as a concrete example to test whether scalars masses unavoidably receive quantum correction of order $\\Lambda$. Having at our dispose a calculable model allowing us to precisely relate the IR and UV of the theory we demonstrate that the scalars can be lighter than $\\Lambda$. Although we do not have an answer to whether the Standard Model hypercharge coupling growth towards a Landau pole at around $\\Lambda \\sim 10^{40}$ GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful, it might also offer an explanation for the unbearable lightness of the Higgs.
Quantum gravity on foliated spacetimes: Asymptotically safe and sound
Biemans, Jorn; Platania, Alessia; Saueressig, Frank
2017-04-01
Asymptotic safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the Arnowitt-Deser-Misner formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed-point characteristic for asymptotic safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the ɛ -expansion around two dimensions, Monte Carlo simulations based on lattice quantum gravity, and the discretized Wheeler-DeWitt equation.
The asymptotic behavior of Buneman instability in dissipative plasma
Rostomyan, Eduard V.
2017-10-01
The problem of time evolution of initial perturbation excited at the development of the Buneman instability (BI) in plasma with dissipation is solved. Developing fields are presented in the form of a wave train with slowly varying amplitude. It is shown that the evolution of the initial pulse in space and time is given by the differential equation of third order. The equation is solved and the expression for the asymptotic pulse shape is obtained. The expression gives the most complete information on the instability: the space-time distribution of the fields, growth rates, velocities of unstable perturbations, the influence of the collisions/dissipation on the instability, its character, (absolute/convective), etc. All these characteristics of the BI are carried out by analyzing the expression for the shape. The obtained results may be applied to any system in which the red-shifted electron stream oscillations resonantly interact with ions. Asymptotic shapes of the BI are presented for various levels of dissipation.
Normality of different orders for Cantor series expansions
Airey, Dylan; Mance, Bill
2017-10-01
Let S \\subseteq {N} have the property that for each k \\in S the set (S - k) \\cap {N} \\setminus S has asymptotic density 0. We prove that there exists a basic sequence Q where the set of numbers Q-normal of all orders in S but not Q-normal of all orders not in S has full Hausdorff dimension. If the function \
Christodorescu, Mihai; Kinder, Johannes; Jha, Somesh; Katzenbeisser, Stefan; Veith, Helmut
2005-01-01
Malware is code designed for a malicious purpose, such as obtaining root privilege on a host. A malware detector identifies malware and thus prevents it from adversely affecting a host. In order to evade detection by malware detectors, malware writers use various obfuscation techniques to transform their malware. There is strong evidence that commercial malware detectors are susceptible to these evasion tactics. In this paper, we describe the design and implementation of a malware normalizer ...
Coulomb-distorted plane wave: Partial wave expansion and asymptotic forms
Hornyak, I.; Kruppa, A. T.
2013-05-01
Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric function 2F2(a, a; a + l + 1, a - l; z) is expressed with the help of confluent hypergeometric functions and the asymptotic expansion of 2F2(a, a; a + l + 1, a - l; z) is simplified.
Test of the second order asymptotic theory with low degree solar gravity modes
Energy Technology Data Exchange (ETDEWEB)
Barry, C.T.; Rosenwald, R.D.; Gu, Y.; Hill, H.A
1988-01-01
Further testing of first and second order asymptotic theory predictions for solar gravity modes is possible with the work of gu and Hill in which the number of classified low-degree gravity mode multiplets was increased from 31 to 53. In an extension of the work where the properties of 31 multiplets were analyzed in the framework of first order asymptotic theory, a new analysis has been performed using the properties of the 53 classified multiplets. The result of this analysis again shows the inadequacy of first order asymptotic theory for describing the eigenfrequency spectrum and clearly demonstrates the necessity of using second order asymptotic theory. 30 refs.
Ground state solutions for asymptotically periodic Schrodinger equations with critical growth
Directory of Open Access Journals (Sweden)
Hui Zhang
2013-10-01
Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
Time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles
Ha, Seung-Yeal; Ko, Dongnam; Zhang, Xiongtao; Zhang, Yinglong
2017-07-01
We study the time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles. For this, we use a coupled hydrodynamic Cucker-Smale system and discuss two frameworks, leading to mono-cluster and bi-cluster flockings asymptotically depending on initial configurations, coupling strengths, and the far-field decay property of communication weights. Under the proposed two frameworks, we show that mono-cluster and bi-cluster flockings emerge asymptotically exponentially fast and algebraically slow, respectively. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system.
Elastohydrodynamic lubrication for line and point contacts asymptotic and numerical approaches
Kudish, Ilya I
2013-01-01
Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches describes a coherent asymptotic approach to the analysis of lubrication problems for heavily loaded line and point contacts. This approach leads to unified asymptotic equations for line and point contacts as well as stable numerical algorithms for the solution of these elastohydrodynamic lubrication (EHL) problems. A Unique Approach to Analyzing Lubrication Problems for Heavily Loaded Line and Point Contacts The book presents a robust combination of asymptotic and numerical techniques to solve EHL p
Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas
Chacon, Luis; Del-Castillo-Negrete, Diego
2012-03-01
Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel Lagrangian Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical formulation, which ensures a consistent numerical discretization temporally and spatially for arbitrary χ/χ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.
Genetic trends in the expected progeny difference of the asymptotic weight of Nelore females
Directory of Open Access Journals (Sweden)
Analía del Valle Garnero
2006-01-01
Full Text Available There are few studies on weight covering the full life cycle of Zebu cattle, and there is no entire growth description or mean growth pattern for animals belonging to this breed. In order to provide such data, 1,158 Nelore females born between 1985 and 1995 were weighed 14,563 times from birth to full growth maturity, in ten herds spread over seven Brazilian states. The Von Bertalanffy, Brody, logistic and Gompertz non-linear models were used to obtain the asymptotic weights (A and the maturation rates (K. The (covariance and breeding value components for A and K were obtained by using the multiple trait derivative free restricted maximum likelihood method under the animal model. Genetic trends were calculated in function of the mean expected progeny differences (EPD for the trait (A or K divided by the number of animals according to their year of birth. The genetic trends of the expected progeny difference with reference to the date of birth of the cows were, on average, -6.5g y-1 for A and 2.0g y-1 for K, close to zero as confirmed by the low (0.0023 to 0.003 coefficient of regression values. The curve parameters are recommended as a selection criterion to reach precocity and avoid adult weight increase in the female herd.
Conn, Vicki S; Zerwic, Julie; Jefferson, Urmeka; Anderson, Cindy M; Killion, Cheryl M; Smith, Carol E; Cohen, Marlene Z; Fahrenwald, Nancy L; Herrick, Linda; Topp, Robert; Benefield, Lazelle E; Loya, Julio
2016-02-01
Getting turned down for grant funding or having a manuscript rejected is an uncomfortable but not unusual occurrence during the course of a nurse researcher's professional life. Rejection can evoke an emotional response akin to the grieving process that can slow or even undermine productivity. Only by "normalizing" rejection, that is, by accepting it as an integral part of the scientific process, can researchers more quickly overcome negative emotions and instead use rejection to refine and advance their scientific programs. This article provides practical advice for coming to emotional terms with rejection and delineates methods for working constructively to address reviewer comments. © The Author(s) 2015.
Approximate reflection coefficients for a thin VTI layer
Hao, Qi
2017-09-18
We present an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer thickness is assumed to be much smaller than the wavelengths of P- and SV-waves inside. The exact reflection and transmission coefficients are derived by the propagator matrix method. In the case of normal incidence, the exact reflection and transmission coefficients are expressed in terms of the impedances of vertically propagating P- and S-waves. For subcritical incidence, the approximate reflection coefficients are expressed in terms of the contrast in the VTI parameters between the layer and the background. Numerical examples are designed to analyze the reflection coefficients at normal and oblique incidence, and investigate the influence of transverse isotropy on the reflection coefficients. Despite giving numerical errors, the approximate formulae are sufficiently simple to qualitatively analyze the variation of the reflection coefficients with the angle of incidence.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Thermodynamical description of stationary, asymptotically flat solutions with conical singularities
Herdeiro, Carlos; Rebelo, Carmen
2010-01-01
We examine the thermodynamical properties of a number of asymptotically flat, stationary (but not static) solutions having conical singularities, with both connected and non-connected event horizons, using the thermodynamical description recently proposed in arXiv:0912.3386 [gr-qc]. The examples considered are the double-Kerr solution, the black ring rotating in either S^2 or S^1 and the black Saturn, where the balance condition is not imposed for the latter two solutions. We show that not only the Bekenstein-Hawking area law is recovered from the thermodynamical description but also the thermodynamical angular momentum is the ADM angular momentum. We also analyse the thermodynamical stability and show that, for all these solutions, either the isothermal moment of inertia or the specific heat at constant angular momentum is negative, at any point in parameter space. Therefore, all these solutions are thermodynamically unstable in the grand canonical ensemble.
Asymptotic analysis of downlink MISO systems over Rician fading channels
Falconet, Hugo
2016-06-24
In this work, we focus on the ergodic sum rate in the downlink of a single-cell large-scale multi-user MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments. A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming N and K grow large with a non trivial ratio and perfect channel state information is available at the base station. Recent results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of the system parameters, the spatial correlation matrix and the Rician factor. Numerical results are used to evaluate the performance gap in the finite system regime under different operating conditions. © 2016 IEEE.
Asymptotic approximation method of force reconstruction: Proof of concept
Sanchez, J.; Benaroya, H.
2017-08-01
An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. An alternative approach is developed that draws upon concepts from control systems theory, the equilibrium analysis of linear dynamical systems with time-dependent inputs, and asymptotic approximation analysis. This paper presents the theoretical development of the proposed method. A simple application of the method is presented to demonstrate the procedure. A more complex application to a continuous system is performed to demonstrate the applicability of the method.
Asymptotic coherence of gluons and of q-bosons
Energy Technology Data Exchange (ETDEWEB)
Nelson, C.A.
1993-12-31
In theoretical physics one of the most important aspects of coherent states is that they can often be simply and reliably used to investigate the quantum coherence and correlation properties of new dynamical, quantum field theories. First, this paper reviews the coherent/degenerate state treatment of the infra-red dynamics of perturbative QCD. This based on the asymptotic behavior of the Hamiltonian operator as {vert_bar}t{vert_bar} {yields} {infinity} in the interaction representation. Second, the paper reviews the usage of q-analogue coherent states {vert_bar}z>{sub q} to deduce coherence and uncertainty properties of the q-analogue quantized radiation field in the {vert_bar}z>{sub q} ``classical limit`` where {vert_bar}z{vert_bar} is large. Third, for future applications, a new ``projector`` definition of the usual coherent states and of the squeezed states is reported.
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
Mellor, G. L.
1972-01-01
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
Asymptotic freedom in the Hamiltonian approach to binding of color
Directory of Open Access Journals (Sweden)
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2017-03-01
We derive asymptotic freedom and the SU(3) Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size) parameter s. The effective Hamiltonians Hs and the (regularized) canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations
Baranwal, Vipul K.; Pandey, Ram K.
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems. PMID:27437484
Sharp asymptotics for Einstein-$\\lambda$-dust flows
Friedrich, Helmut
2016-01-01
We consider the Einstein-dust equations with positive cosmological constant $\\lambda$ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the Einstein-$\\lambda$-dust equations on $S$ contains an open (in terms of suitable Sobolev norms) subset of data that develop into solutions which admit at future time-like infinity a space-like conformal boundary ${\\cal J}^+$ that is $C^{\\infty}$ if the data are of class $C^{\\infty}$ and of correspondingly lower smoothness otherwise. As a particular case follows a strong stability result for FLRW solutions. The solutions can conveniently be characterized in terms of their asymptotic end data induced on ${\\cal J}^+$, only a linear equation must be solved to construct such data. In the case where the energy density $\\hat{\\rho}$ is everywhere positive such data can be constructed without solving any differential equation at all.
Solution of internal erosion equations by asymptotic expansion
Directory of Open Access Journals (Sweden)
Dubujet P.
2012-07-01
Full Text Available One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.
Asymptotic analysis of radiation extinction of stretched premixed flames
Energy Technology Data Exchange (ETDEWEB)
Ju, Y.; Masuya, G. [Tohoku Univ., Sendai (Japan). Dept. of Aeronautics and Space Engineering; Liu, F. [National Research Council, Ottawa, Ontario (Canada). Inst. for Chemical Prpcess and Environmental Technology; Hattori, Yuji [Tohoku Univ., Sendai (Japan). Inst. of Fluid Science; Riechelmann, D. [Ishikawajima-Harima Heavy Industry, Tokyo (Japan). Research Inst.
2000-01-01
The flammability limit, radiation extinction of stretched premixed flame and effect of non-unity Lewis numbers are analyzed by the large-activated-energy asymptotic method. Particular attention is paid to the effect of Lewis number, the upstream and downstream radiation heat losses as well as the non-linearity of radiation. Explicit expressions for the flame temperature, extinction limit and flammability limit are obtained. The C-shaped extinction curve is reproduced. The dependence of radiation heat loss and the Lewis number effect on the stretch rate and flame separation distance is investigated. The effects of fuel Lewis number, oxidizer Lewis number, upstream radiation heat loss and the non-linearity of radiation on the C-shaped extinction curve are also examined. The results demonstrate a significant influence of these parameters on the radiation extinction and flammability limit and provide a good explanation to the experimental results and numerical simulations. (Author)
An introduction to covariant quantum gravity and asymptotic safety
Percacci, Roberto
2017-01-01
This book covers recent developments in the covariant formulation of quantum gravity. Developed in the 1960s by Feynman and DeWitt, by the 1980s this approach seemed to lead nowhere due to perturbative non-renormalizability. The possibility of non-perturbative renormalizability or "asymptotic safety," originally suggested by Weinberg but largely ignored for two decades, was revived towards the end of the century by technical progress in the field of the renormalization group. It is now a very active field of research, providing an alternative to other approaches to quantum gravity. Written by one of the early contributors to this subject, this book provides a gentle introduction to the relevant ideas and calculational techniques. Several explicit calculations gradually bring the reader close to the current frontier of research. The main difficulties and present lines of development are also outlined.
An asymptotic state of the critical ionization velocity phenomenon
Goertz, C. K.; Machida, S.; Smith, R. A.
1985-01-01
The paper considers the problem of how the momentum of ions created by electron impact ionization of neutrals moving at a speed v(0) perpendicular to the magnetic field through a background plasma is coupled to this plasma. It has been found that the plasma accelerates, and the relative velocity between neutrals and plasma decreases. If this decrease is rapid and large enough, the critical ionization velocity (CIV) phenomenon may turn off. Equations for the evolution of plasma density, electron and ion thermal energy, and plasma velocity have been derived. It was found that the CIV process reaches an asymptotic quasi-steady state, in which the ionization rate reaches a constant value which depends on the properties of the surrounding medium and the value of v(0).
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
Stynes, Martin; Zhang, Zhimin
2017-01-01
This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed diffe...
The complex dynamics of products and its asymptotic properties.
Directory of Open Access Journals (Sweden)
Orazio Angelini
Full Text Available We analyse global export data within the Economic Complexity framework. We couple the new economic dimension Complexity, which captures how sophisticated products are, with an index called logPRODY, a measure of the income of the respective exporters. Products' aggregate motion is treated as a 2-dimensional dynamical system in the Complexity-logPRODY plane. We find that this motion can be explained by a quantitative model involving the competition on the markets, that can be mapped as a scalar field on the Complexity-logPRODY plane and acts in a way akin to a potential. This explains the movement of products towards areas of the plane in which the competition is higher. We analyse market composition in more detail, finding that for most products it tends, over time, to a characteristic configuration, which depends on the Complexity of the products. This market configuration, which we called asymptotic, is characterized by higher levels of competition.
Sharp Asymptotics for Einstein-{λ}-Dust Flows
Friedrich, Helmut
2017-03-01
We consider the Einstein-dust equations with positive cosmological constant {λ} on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold {S}. It is shown that the set of standard Cauchy data for the Einstein-{λ}-dust equations on {S} contains an open (in terms of suitable Sobolev norms) subset of data which develop into solutions that admit at future time-like infinity a space-like conformal boundary J^+ that is C^{∞} if the data are of class C^{∞} and of correspondingly lower smoothness otherwise. The class of solutions considered here comprises non-linear perturbations of FLRW solutions as very special cases. It can conveniently be characterized in terms of asymptotic end data induced on J^+. These data must only satisfy a linear differential equation. If the energy density is everywhere positive they can be constructed without solving differential equations at all.
Bulk Viscous Matter-dominated Universes: Asymptotic Properties
Avelino, Arturo; Gonzalez, Tame; Nucamendi, Ulises; Quiros, Israel
2013-01-01
By means of a combined study of the type Ia supernovae test,together with a study of the asymptotic properties in the equivalent phase space -- through the use of the dynamical systems tools -- we demonstrate that the bulk viscous matter-dominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of very particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed...
Asymptotically AdS spacetimes with a timelike Kasner singularity
Energy Technology Data Exchange (ETDEWEB)
Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-21
Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.
Turbomachinery computational fluid dynamics: asymptotes and paradigm shifts.
Dawes, W N
2007-10-15
This paper reviews the development of computational fluid dynamics (CFD) specifically for turbomachinery simulations and with a particular focus on application to problems with complex geometry. The review is structured by considering this development as a series of paradigm shifts, followed by asymptotes. The original S1-S2 blade-blade-throughflow model is briefly described, followed by the development of two-dimensional then three-dimensional blade-blade analysis. This in turn evolved from inviscid to viscous analysis and then from steady to unsteady flow simulations. This development trajectory led over a surprisingly small number of years to an accepted approach-a 'CFD orthodoxy'. A very important current area of intense interest and activity in turbomachinery simulation is in accounting for real geometry effects, not just in the secondary air and turbine cooling systems but also associated with the primary path. The requirements here are threefold: capturing and representing these geometries in a computer model; making rapid design changes to these complex geometries; and managing the very large associated computational models on PC clusters. Accordingly, the challenges in the application of the current CFD orthodoxy to complex geometries are described in some detail. The main aim of this paper is to argue that the current CFD orthodoxy is on a new asymptote and is not in fact suited for application to complex geometries and that a paradigm shift must be sought. In particular, the new paradigm must be geometry centric and inherently parallel without serial bottlenecks. The main contribution of this paper is to describe such a potential paradigm shift, inspired by the animation industry, based on a fundamental shift in perspective from explicit to implicit geometry and then illustrate this with a number of applications to turbomachinery.
Recursive calculation of Hansen coefficients
Branham, Richard L., Jr.
1990-06-01
Hansen coefficients are used in expansions of the elliptic motion. Three methods for calculating the coefficients are studied: Tisserand's method, the Von Zeipel-Andoyer (VZA) method with explicit representation of the polynomials required to compute the Hansen coefficients, and the VZA method with the values of the polynomials calculated recursively. The VZA method with explicit polynomials is by far the most rapid, but the tabulation of the polynomials only extends to 12th order in powers of the eccentricity, and unless one has access to the polynomials in machine-readable form their entry is laborious and error-prone. The recursive calculation of the VZA polynomials, needed to compute the Hansen coefficients, while slower, is faster than the calculation of the Hansen coefficients by Tisserand's method, up to 10th order in the eccentricity and is still relatively efficient for higher orders. The main advantages of the recursive calculation are the simplicity of the program and one's being able to extend the expansions to any order of eccentricity with ease. Because FORTRAN does not implement recursive procedures, this paper used C for all of the calculations. The most important conclusion is recursion's genuine usefulness in scientific computing.
DEFF Research Database (Denmark)
Madsen, Lars Bojer; Tolstikhin, Oleg I.; Morishita, Toru
2012-01-01
The recently developed weak-field asymptotic theory [ Phys. Rev. A 84 053423 (2011)] is applied to the analysis of tunneling ionization of a molecular ion (H2+), several homonuclear (H2, N2, O2) and heteronuclear (CO, HF) diatomic molecules, and a linear triatomic molecule (CO2) in a static...... Hartree-Fock wave functions for the diatomics, and a Hartree-Fock quantum chemistry wave function for CO2. The structure factors are expanded in terms of standard functions and the associated structure coefficients, allowing the determination of the ionization rate for any orientation of the molecule...... with respect to the field, are tabulated. Our results, which are exact in the weak-field limit for H2+ and, in addition, under the Hartree-Fock approximation for the diatomics, are compared with results from the recent literature....
DEFF Research Database (Denmark)
Madsen, Louise Sofia; Handberg, Charlotte
2018-01-01
semistructured interviews with 9 lymphoma survivors. Interpretive description methodology and social practice theory guided the analytical framework. RESULTS: "Pursuing normality" was an overall finding and was comprised of 2 overarching patterns, "future prospects" and "survivorship care perceptions," both......BACKGROUND: The present study explored the reflections on cancer survivorship care of lymphoma survivors in active treatment. Lymphoma survivors have survivorship care needs, yet their participation in cancer survivorship care programs is still reported as low. OBJECTIVE: The aim of this study...... was to understand the reflections on cancer survivorship care of lymphoma survivors to aid the future planning of cancer survivorship care and overcome barriers to participation. METHODS: Data were generated in a hematological ward during 4 months of ethnographic fieldwork, including participant observation and 46...
DEFF Research Database (Denmark)
Gildberg, Frederik Alkier; Bradley, Stephen K.; Fristed, Peter Billeskov
2012-01-01
Forensic psychiatry is an area of priority for the Danish Government. As the field expands, this calls for increased knowledge about mental health nursing practice, as this is part of the forensic psychiatry treatment offered. However, only sparse research exists in this area. The aim of this study...... was to investigate the characteristics of forensic mental health nursing staff interaction with forensic mental health inpatients and to explore how staff give meaning to these interactions. The project included 32 forensic mental health staff members, with over 307 hours of participant observations, 48 informal...... interviews, and seven semistructured interviews. The findings show that staff interaction is typified by the use of trust and relationship-enabling care, which is characterized by the establishment and maintenance of an informal, trusting relationship through a repeated reconstruction of normality...
Coefficient estimates of negative powers and inverse coefficients for ...
Indian Academy of Sciences (India)
1 an(−λ, f )zn for z ∈ D. (1.4). One of the well-known extremal problems in the theory of univalent functions is to esti- mate the modulus of the Taylor coefficients an(−λ, f ) given by (1.4). This problem has been extensively studied in the literature ...
Harmonic functions with varying coefficients
Directory of Open Access Journals (Sweden)
Jacek Dziok
2016-05-01
Full Text Available Abstract Complex-valued harmonic functions that are univalent and sense preserving in the open unit disk can be written in the form f = h + g ‾ $f=h+\\overline{g}$ , where h and g are analytic. In this paper we investigate some classes of univalent harmonic functions with varying coefficients related to Janowski functions. By using the extreme points theory we obtain necessary and sufficient convolution conditions, coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions. The radii of starlikeness and convexity for these classes are also determined.
Delay-dependent asymptotic stability for neural networks with time-varying delays
Directory of Open Access Journals (Sweden)
Xiaofeng Liao
2006-01-01
ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
Asymptotic description of a test particle around a Schwarzschild black hole
Rosales-Vera, Marco
2018-03-01
In this paper, the movement of a test particle around a Schwarzschild black hole is revisited. Using matched asymptotic expansions, approximate analytical expressions for the orbit of the test particle in the case of large eccentricity are found. The asymptotic solutions are compared with numerical and analytical results.
Asymptotic expansion of unsteady gravity flow of a power-law fluid ...
African Journals Online (AJOL)
We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...
On the tail asymptotics of the area swept under the Brownian storage graph
Arendarczyk, M.; Dȩbicki, K.; Mandjes, M.
2014-01-01
In this paper, the area swept under the workload graph is analyzed: with {Q(t): t≥0} denoting the stationary workload process, the asymptotic behavior of πT(u)(u):=P(∫T(u)0Q(r)dr>u) is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of πT(u)(u) are given for the case
On the asymptotic structure of a Navier-Stokes flow past a rotating body
Kyed, Mads
2014-01-01
Consider a rigid body moving with a prescribed constant non-zero velocity and rotating with a prescribed constant non-zero angular velocity in a three-dimensional Navier-Stokes liquid. The asymptotic structure of a steady-state solution to the corresponding equations of motion is analyzed. In particular, an asymptotic expansion of the corresponding velocity field is obtained.
Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations
Directory of Open Access Journals (Sweden)
Bahman Ghazanfari
2013-08-01
Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
Assessing model fit in latent class analysis when asymptotics do not hold
van Kollenburg, Geert H.; Mulder, Joris; Vermunt, Jeroen K.
2015-01-01
The application of latent class (LC) analysis involves evaluating the LC model using goodness-of-fit statistics. To assess the misfit of a specified model, say with the Pearson chi-squared statistic, a p-value can be obtained using an asymptotic reference distribution. However, asymptotic p-values
Asymptotic Dichotomy in a Class of Odd-Order Nonlinear Differential Equations with Impulses
Directory of Open Access Journals (Sweden)
Kunwen Wen
2013-01-01
Full Text Available We investigate the oscillatory and asymptotic behavior of a class of odd-order nonlinear differential equations with impulses. We obtain criteria that ensure every solution is either oscillatory or (nonoscillatory and zero convergent. We provide several examples to show that impulses play an important role in the asymptotic behaviors of these equations.
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
An asymptotic expansion for product integration applied to Cauchy principal value integrals
Wesseling, P.
1975-01-01
Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic
Irrational "Coefficients" in Renaissance Algebra.
Oaks, Jeffrey A
2017-06-01
Argument From the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply by x, for instance, the result was expressed as the rhetorical equivalent of . The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or "number," of a term was thought of as how many of that term are present, and not as the scalar multiple that we work with today. Then, in sixteenth-century Europe, a few algebraists began to allow for irrational coefficients in their notation. Christoff Rudolff (1525) was the first to admit them in special cases, and subsequently they appear more liberally in Cardano (1539), Scheubel (1550), Bombelli (1572), and others, though most algebraists continued to ban them. We survey this development by examining the texts that show irrational coefficients and those that argue against them. We show that the debate took place entirely in the conceptual context of premodern, "cossic" algebra, and persisted in the sixteenth century independent of the development of the new algebra of Viète, Decartes, and Fermat. This was a formal innovation violating prevailing concepts that we propose could only be introduced because of the growing autonomy of notation from rhetorical text.
Kuznetsov equation with variable coefficients
Indian Academy of Sciences (India)
Travelling wave-like solutions of the Zakharov–Kuznetsov equation with vari- able coefficients are studied using the ... exact solutions of nonlinear partial differential equations. Some of the most impor- tant methods are the ... In general, there is no standard method for solving nonlinear. PDEs and more so for PDEs in 2+1 ...
Robust correlation coefficient based on Qn estimator
Zakaria, Nur Amira; Abdullah, Suhaida; Ahad, Nor Aishah
2017-11-01
This paper presents a new robust correlation coefficient called Qn correlation coefficient. This coefficient is developed as an alternative for classical correlation coefficient as the performance of classical correlation coefficient is nasty under contamination data. This study applied robust scale estimator called Qn because this estimator have high breakdown point. Simulation studies are carried out in determining the performances of the new robust correlation coefficient. Clean and contamination data are generated in assessing the performance of these coefficient. The performances of the Qn correlation coefficient is compared with classical correlation coefficient based on the value of coefficient, average bias and standard error. The outcome of the simulation studies shows that the performance of Qn correlation coefficient is superior compared to the classical and existing robust correlation coefficient.
Static pressure and temperature coefficients of laboratory standard microphones
DEFF Research Database (Denmark)
Rasmussen, Knud
1996-01-01
on an extended lumped parameter representation of the mechanical and acoustical elements of the microphone, assuming the velocity distribution of the diaphragm to follow the zero-order Bessel function. The extension involves the frequency dependency of the dynamic diaphragm mass and stiffness as well as a first......-order approximation of resonances in the back cavity. It was found that each of the coefficients, for a given type of microphone, can be expressed by a single function when the coefficients are normalized by their low-frequency value and the frequency axis normalized by the individual resonance frequency...... of the microphone. The static pressure and temperature coefficients were determined experimentally for about twenty samples of type BK 4160 and BK 4180 microphones. The results agree almost perfectly with the predictions for BK 4160, while some modifications of the lumped parameter values are called for to make...
Determination of Local Barley (Hordeum Vulgare) Crop Coefficient ...
African Journals Online (AJOL)
Furthermore, the major reason for mismanagement of irrigation water in barley fields was not due to use of wrong crop coefficient values but could be due to inadequate irrigation technical skill and knowledge of the farmer. The average economic water productivity (EWP) of barley for the very wet, wet, normal, dry and very ...
Asymptotic theory of evolution and failure of self-sustained detonations
Kasimov, Aslan R.; Stewart, D. Scott
2005-02-01
Based on a general theory of detonation waves with an embedded sonic locus that we have previously developed, we carry out asymptotic analysis of weakly curved slowly varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman-Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed versus curvature (D-κ) curves with multiple turning points. An evolution equation that retains the shock acceleration, skew2dot{D}, namely a skew2dot{D}-D-κ relation is rationally derived which describes the dynamics of pre-existing detonation waves. The solutions of the equation for spherical detonation are shown to reproduce the ignition/failure phenomenon observed in both numerical simulations of blast wave initiation and in experiments. A single-step chemical reaction described by one progress variable is employed, but the kinetics is sufficiently general and is not restricted to Arrhenius form, although most specific calculations are performed for Arrhenius kinetics. As an example, we calculate critical energies of direct initiation for hydrogen-oxygen mixtures and find close agreement with available experimental data.
Labbe, Fernando
2007-04-01
Elbows with a shallow surface cracks in nuclear pressure pipes have been recognized as a major origin of potential catastrophic failures. Crack assessment is normally performed by using the J-integral approach. Although this one-parameter-based approach is useful to predict the ductile crack onset, it depends strongly on specimen geometry or constraint level. When a shallow crack exists (depth crack-to-thickness wall ratio less than 0.2) and/or a fully plastic condition develops around the crack, the J-integral alone does not describe completely the crack-tip stress field. In this paper, we report on the use of a three-term asymptotic expansion, referred to as the J- A 2 methodology, for modeling the elastic-plastic stress field around a three-dimensional shallow surface crack in an elbow subjected to internal pressure and out-of-plane bending. The material, an A 516 Gr. 70 steel, used in the nuclear industry, was modeled with a Ramberg-Osgood power law and flow theory of plasticity. A finite deformation theory was included to account for the highly nonlinear behavior around the crack tip. Numerical finite element results were used to calculate a second fracture parameter A 2 for the J- A 2 methodology. We found that the used three-term asymptotic expansion accurately describes the stress field around the considered three-dimensional shallow surface crack.
Using two coefficients modeling of nonsubsampled Shearlet transform for despeckling
Jafari, Saeed; Ghofrani, Sedigheh
2016-01-01
Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise. Two approaches based on modeling the nonsubsampled Shearlet transform (NSST) coefficients are presented. Two-sided generalized Gamma distribution and normal inverse Gaussian probability density function have been used to model the statistics of NSST coefficients. Bayesian maximum a posteriori estimator is applied to the corrupted NSST coefficients in order to estimate the noise-free NSST coefficients. Finally, experimental results, according to objective and subjective criteria, carried out on both artificially speckled images and the true SAR images, demonstrate that the proposed methods outperform other state of art references via two points of view, speckle noise reduction and image quality preservation.
Asymptotic performance of regularized quadratic discriminant analysis based classifiers
Elkhalil, Khalil
2017-12-13
This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
3D face recognition with asymptotic cones based principal curvatures
Tang, Yinhang
2015-05-01
The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.
Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
Energy Technology Data Exchange (ETDEWEB)
Kofinas, Georgios [Research Group of Geometry, Dynamical Systems and Cosmology,Department of Information and Communication Systems Engineering,University of the Aegean, Karlovassi 83200, Samos (Greece); Zarikas, Vasilios [Department of Electrical Engineering, Theory Division, ATEI of Central Greece,35100 Lamia (Greece); Department of Physics, Aristotle University of Thessaloniki,54124 Thessaloniki (Greece)
2015-10-30
New general spherically symmetric solutions have been derived with a cosmological “constant” Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.
Asymptotic expansions for high-contrast elliptic equations
Calo, Victor M.
2014-03-01
In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
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Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.
Quantum learning: asymptotically optimal classification of qubit states
Guţă, Mădălin; Kotłowski, Wojciech
2010-12-01
Pattern recognition is a central topic in learning theory, with numerous applications such as voice and text recognition, image analysis and computer diagnosis. The statistical setup in classification is the following: we are given an i.i.d. training set (X1, Y1), ... , (Xn, Yn), where Xi represents a feature and Yiin{0, 1} is a label attached to that feature. The underlying joint distribution of (X, Y) is unknown, but we can learn about it from the training set, and we aim at devising low error classifiers f: X→Y used to predict the label of new incoming features. In this paper, we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown mixed qubit states. Given a number of 'training' copies from each of the states, we would like to 'learn' about them by performing a measurement on the training set. The outcome is then used to design measurements for the classification of future systems with unknown labels. We found the asymptotically optimal classification strategy and show that typically it performs strictly better than a plug-in strategy, which consists of estimating the states separately and then discriminating between them using the Helstrom measurement. The figure of merit is given by the excess risk equal to the difference between the probability of error and the probability of error of the optimal measurement for known states. We show that the excess risk scales as n-1 and compute the exact constant of the rate.
Subordinated diffusion and continuous time random walk asymptotics.
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2010-12-01
Anomalous transport is usually described either by models of continuous time random walks (CTRWs) or, otherwise, by fractional Fokker-Planck equations (FFPEs). The asymptotic relation between properly scaled CTRW and fractional diffusion process has been worked out via various approaches widely discussed in literature. Here, we focus on a correspondence between CTRWs and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes. One of them is the Monte Carlo simulation of uncoupled CTRW with a Lévy α-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times. The other is based on a discretized form of a subordinated Langevin equation in which the physical time defined via the number of subsequent steps of motion is itself a random variable. Both approaches are tested for their numerical performance and verified with known analytical solutions for the Green function of a space-time fractional diffusion equation. The comparison demonstrates a trade off between precision of constructed solutions and computational costs. The method based on the subordinated Langevin equation leads to a higher accuracy of results, while the CTRW framework with a Mittag-Leffler distribution of waiting times provides efficiently an approximate fundamental solution to the FFPE and converges to the probability density function of the subordinated process in a long-time limit. © 2010 American Institute of Physics.
Photodetachment cross-section evaluation using asymptotic considerations
Babilotte, Philippe; Vandevraye, Mickael
2017-06-01
Mathematical calculations are given concerning the evaluation of the negative ions photodetachment cross-section σ , into a so-called saturation regime. The interaction between a negative ion particle beam and a laser beam is examined under theoretical aspects. A quantitative criterion S is proposed to define the saturation threshold between the linear and the saturated domains, which are both present in this saturation regime. The asymptotic behaviours extracted at the low and high energy limits are used to determine this threshold quantitative criterion S and to evaluate also the photodetachment cross-section σ . The case of a symmetric gaussian photodetachment laser beam shape is examined according to the proposed formalism, which can be used either for the photo-detachment or photo-ionization processes, and could be potentially used into technological solutions for negative ion neutralisation processes (such as neutral beam injector) in the future fusion energy devices. Estimations onto the errors related to the use of this methodology are given.
Physical renormalization schemes and asymptotic safety in quantum gravity
Falls, Kevin
2017-12-01
The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.
Quasinormal modes of asymptotically flat rotating black holes
Dias, Óscar J. C.; Hartnett, Gavin S.; Santos, Jorge E.
2014-12-01
We study the main properties of general linear perturbations of rotating black holes (BHs) in asymptotically flat higher-dimensional spacetimes. In particular, we determine the quasinormal mode (QNM) spectrum of singly spinning and equal angular momenta Myers-Perry BHs (MP BHs). Emphasis is also given to the timescale of the ultraspinning and bar-mode instabilities in these two families of MP BHs. For the bar-mode instabilities in the singly spinning MP BH, we find excellent agreement with our linear analysis and the nonlinear time evolution of Shibata and Yoshino for d = 6,7 spacetime dimensions. We find that d = 5 singly spinning BHs are linearly stable. In the context of studying general relativity in the large dimension limit, we obtain the QNM spectrum of Schwarzschild BHs and rotating MP BHs for large dimensions. We identify two classes of modes. For large dimensions, we find that in the limit of zero rotation, unstable modes of the MP BHs connect to a class of Schwarzschild QNMs that saturate to finite values.
Bulk viscous matter-dominated Universes: asymptotic properties
Energy Technology Data Exchange (ETDEWEB)
Avelino, Arturo [Departamento de Física, Campus León, Universidad de Guanajuato, León, Guanajuato (Mexico); García-Salcedo, Ricardo [Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada - Legaria del IPN, México D.F. (Mexico); Gonzalez, Tame [Departamento de Ingeniería Civil, División de Ingeniería, Universidad de Guanajuato, Guanajuato (Mexico); Nucamendi, Ulises [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP. 58040 Morelia, Michoacán (Mexico); Quiros, Israel, E-mail: avelino@fisica.ugto.mx, E-mail: rigarcias@ipn.mx, E-mail: tamegc72@gmail.com, E-mail: ulises@ifm.umich.mx, E-mail: iquiros6403@gmail.com [Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Corregidora 500 S.R., Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico)
2013-08-01
By means of a combined use of the type Ia supernovae and H(z) data tests, together with the study of the asymptotic properties in the equivalent phase space — through the use of the dynamical systems tools — we demonstrate that the bulk viscous matter-dominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of unique and very specific initial conditions, i. e., of very unstable particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed. Also, we found that the bulk viscosity is positive just until very late times in the cosmic evolution, around z < 1. For earlier epochs it is negative, been in tension with the local second law of thermodynamics.
Polynomial asymptotic stability of damped stochastic differential equations
Directory of Open Access Journals (Sweden)
John Appleby
2004-08-01
Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.
DEFF Research Database (Denmark)
Jeong, Cheol-Ho; Chang, Ji-ho
2015-01-01
Absorption coefficients measured in reverberation chambers, Sabine absorption coefficients, suffer from two major problems. Firstly, they sometimes exceed unity. Secondly, the reproducibility of the Sabine absorption coefficients is quite poor, meaning that the Sabine absorption coefficients vary...
Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer.
Wedin, Håkan; Cherubini, Stefania; Bottaro, Alessandro
2015-07-01
The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K̂ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K̂=0). This leads to a Reynolds number of approximately Re(c)=54400 for the onset of linearly unstable waves, and close to Re(g)=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Re(c)=796 and Re(g)=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re(-ρ), where the value of ρ depends on the permeability coefficient K̂. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for
A note on asymptotically anti-de Sitter quantum spacetimes in loop quantum gravity
Bodendorfer, Norbert
2015-01-01
A framework conceptually based on the conformal techniques employed to study the structure of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions.
Optimal adaptive normalized matched filter for large antenna arrays
Kammoun, Abla
2016-09-13
This paper focuses on the problem of detecting a target in the presence of a compound Gaussian clutter with unknown statistics. To this end, we focus on the design of the adaptive normalized matched filter (ANMF) detector which uses the regularized Tyler estimator (RTE) built from N-dimensional observations x, · · ·, x in order to estimate the clutter covariance matrix. The choice for the RTE is motivated by its possessing two major attributes: first its resilience to the presence of outliers, and second its regularization parameter that makes it more suitable to handle the scarcity in observations. In order to facilitate the design of the ANMF detector, we consider the regime in which n and N are both large. This allows us to derive closed-form expressions for the asymptotic false alarm and detection probabilities. Based on these expressions, we propose an asymptotically optimal setting for the regularization parameter of the RTE that maximizes the asymptotic detection probability while keeping the asymptotic false alarm probability below a certain threshold. Numerical results are provided in order to illustrate the gain of the proposed detector over a recently proposed setting of the regularization parameter.
Study of transport coefficients of nanodiamond nanofluids
Pryazhnikov, M. I.; Minakov, A. V.; Guzei, D. V.
2017-09-01
Experimental data on the thermal conductivity coefficient and viscosity coefficient of nanodiamond nanofluids are presented. Distilled water and ethylene glycol were used as the base fluid. Dependences of transport coefficients on concentration are obtained. It was shown that the thermal conductivity coefficient increases with increasing nanodiamonds concentration. It was shown that base fluids properties and nanodiamonds concentration affect on the rheology of nanofluids.
Evaluation of Rock Joint Coefficients
Audy, Ondřej; Ficker, Tomáš
2017-10-01
A computer method for evaluation of rock joint coefficients is described and several applications are presented. The method is based on two absolute numerical indicators that are formed by means of the Fourier replicas of rock joint profiles. The first indicator quantifies the vertical depth of profiles and the second indicator classifies wavy character of profiles. The absolute indicators have replaced the formerly used relative indicators that showed some artificial behavior in some cases. This contribution is focused on practical computations testing the functionality of the newly introduced indicators.
Directory of Open Access Journals (Sweden)
Cristinel Mortici
2015-01-01
Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.
Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation
Zakharov, Sergei V.
2015-01-01
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
Directory of Open Access Journals (Sweden)
Vladimir V. Varlamov
1999-01-01
classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.
Directory of Open Access Journals (Sweden)
Xiaolong Qin
2011-01-01
Full Text Available An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.
Holography and Colliding gravitational shock waves in asymptotically AdS5 spacetime.
Chesler, Paul M; Yaffe, Laurence G
2011-01-14
Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.
Holography and Colliding Gravitational Shock Waves in Asymptotically AdS5 Spacetime
Chesler, Paul M.; Yaffe, Laurence G.
2011-01-01
Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.
Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.
Chen, Boshan; Chen, Jiejie
2015-08-01
We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
Directory of Open Access Journals (Sweden)
Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Directory of Open Access Journals (Sweden)
I. V. Samoilenko
2005-01-01
Full Text Available We study the asymptotic expansion for solution of singularly perturbed equation for functional of Markovian evolution in Rd. The view of regular and singular parts of solution is found.
M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractThe paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. This enables checking of internal consistency
An Asymptotic Formula for r-Bell Numbers with Real Arguments
Corcino, Cristina B.; Corcino, Roberto B.
2013-01-01
The r-Bell numbers are generalized using the concept of the Hankel contour. Some properties parallel to those of the ordinary Bell numbers are established. Moreover, an asymptotic approximation for r-Bell numbers with real arguments is obtained.
Directory of Open Access Journals (Sweden)
Maria Crespo
2017-08-01
Full Text Available In this work, we present an asymptotic analysis of a coupled system of two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacteria, called biomass, and a diluted organic contaminant (e.g., nitrates, called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the linearization method to give sufficient conditions for the linear asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.
Globally Asymptotic Stability of Stochastic Nonlinear Systems by the Output Feedback
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Wenwen Cheng
2015-01-01
the traditional mathematical induction method. Indeed, we develop a new method to study the globally asymptotic stability by introducing a series of specific inequalities. Moreover, an example and its simulations are given to illustrate the theoretical result.
Modeling of the long-time asymptotic dynamics of a point-like object
Ribaric, Marijan
2012-01-01
We introduce the first-ever mathematical framework for modeling of the long-time asymptotic behavior of acceleration of such a point-like object whose velocity eventually stops changing after the cessations of the external force. For the small and slowly changing external force we approximate its long-time asymptotic acceleration by a relativistic polynomial in time-derivatives of the external force. Without knowing the equation of motion for such a point-like object, an approximation of this kind enables us to model the long-time asymptotic behavior of its dynamics, and access its long-time asymptotic kinetic constants, which supplement mass and charge. We give various examples.
Stellmach, S; Julien, K; Vasil, G; Cheng, J S; Ribeiro, A; King, E M; Aurnou, J M
2014-01-01
Rapidly rotating Rayleigh-B\\'enard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments and asymptotic modeling. The asymptotic theory is shown to provide a good description of the bulk dynamics at low, but finite Rossby number. However, large deviations from the asymptotically predicted heat transfer scaling are found, with laboratory experiments and DNS consistently yielding much larger Nusselt numbers than expected. These deviations are traced down to dynamically active Ekman boundary layers, which are shown to play an integral part in controlling heat transfer even for Ekman numbers as small as $10^{-7}$. By adding an analytical parameterization of the Ekman transport to simulations using stress-free boundary conditions, we demonstrate that the heat transfer jumps from values broadly compatible with the asymptotic theory to states of strongly increased heat transfer, in good quantitative agreement with no-slip DNS and compatible with the experimental d...