Relaxing the parity conditions of asymptotically flat gravity
Compère, Geoffrey; Dehouck, François
2011-12-01
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 which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
Relaxing the Parity Conditions of Asymptotically Flat Gravity
Compère, Geoffrey; Dehouck, François
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 counter-term which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincar\\'e transformations as well as supertranslations and logarithmic translations are associated wi...
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
Asymptotic conditions of motion for radiating charged particles
Anderson, James L.
1997-10-01
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein-Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac equations, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey asymptotically in the future of an initial starting time. And furthermore, they do not admit the runaway solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., sourceless) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields appearing in these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, are required for this purpose, nor is there a need for any infinite mass renormalizations such as are required in other derivations since all integrals are over surfaces and thus finite. In addition to being asymptotic, the conditions of motion derived here are also approximate and apply, as do the original EIH equations, only to slowly moving systems. A ``slowness'' parameter ɛ is identified as the ratio of the light travel time across the system divided by a characteristic time, e.g., a period. Use is made of both the method of matched asymptotic expansions and the method of multiple time scales to obtain an asymptotic expansion in ɛ and the expansion is carried to sufficiently high order ɛ7 to obtain the lowest-order radiation reaction terms. The resulting conditions of motion are shown to not allow runaway motions.
GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS
Institute of Scientific and Technical Information of China (English)
ZHOU Dong-ming; CAO Jin-de; ZHANG Li-ming
2005-01-01
Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore, the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
2015-01-01
This article proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and quite general and, in particular, encompasses...
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
Briant, Marc; Guo, Yan
2016-12-01
In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.
Prescribing Transient and Asymptotic Behaviour of LTI Systems with Stochastic Initial Conditions
Dresscher, Martijn; Jayawardhana, Bayu
2017-01-01
This paper considers two different control problems for deterministic systems with stochastic initial conditions where, in addition to the usual asymptotic behavior requirement, we are interested in the transient behavior of the state distribution evolution. For the first one, we study control desig
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
Asymptotic forms for hard and soft edge general $\\beta$ conditional gap probabilities
Forrester, Peter J
2011-01-01
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\\beta$-ensembles. The conditioning is that there are $n$ eigenvalues in the gap, with $n \\ll |t|$, $t$ denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consistent with known asymptotic expansions in the case $n=0$. With this modification made for general $n$, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O$(\\log|t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating $\\beta$ to $4/\\beta$.
Asymptotic forms for hard and soft edge general {beta} conditional gap probabilities
Energy Technology Data Exchange (ETDEWEB)
Forrester, Peter J., E-mail: p.forrester@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Witte, Nicholas S., E-mail: nsw@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2012-06-21
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix {beta}-ensembles. The conditioning is that there are n eigenvalues in the gap, with n Much-Less-Than |t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating {beta} to 4/{beta}.
Asymptotic forms for hard and soft edge general β conditional gap probabilities
Forrester, Peter J.; Witte, Nicholas S.
2012-06-01
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix β-ensembles. The conditioning is that there are n eigenvalues in the gap, with n≪|t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions — which are for the logarithm of the gap probabilities — are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating β to 4/β.
Araneda, Bernardo
2016-01-01
The static region outside the event horizon of an asymptotically anti de Sitter black hole has a conformal timelike boundary $\\mathscr{I}$, the evolution from initial data of linear fields satisfying hyperbolic equations is a well posed problem only after imposing boundary conditions at $\\mathscr{I}$. Boundary conditions preserving the action of the background isometry group on the solution space are limited to the homogeneous Dirichlet, Neumann or Robin types. We study, scalar and Maxwell fields and gravitational perturbations on asymptotically AdS black holes arising in Einstein and Lovelock theories. A decomposition in modes transforms the field equations into a set of wave equations with time independent potentials for auxiliary fields in the $x<0$ half of 1+1 Minkowski spacetime. We study systematically these equations for the case of potentials not diverging at the boundary and prove that there is always an instability if Robin boundary conditions with large $\\gamma$ (the quotient between the derivat...
Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas
Davies, Ian; Truman, Aubrey
1982-11-01
Imitating Schilder's results for Wiener integrals rigorous Laplace asymptotic expansions are proven for conditional Wiener integrals. Applications are given for deriving generalized Mehler kernel formulas, up to arbitrarily high orders in powers of ℏ, for exp{-TH(ℏ)/ℏ}(x, y), T>0 where H(ℏ)=[(-ℏ2/2)Δ1+V], Δ1 being the one-dimensional Laplacian, V being a real-valued potential V∈C∞(R), bounded below, together with its second derivative.
Institute of Scientific and Technical Information of China (English)
Wang Kaiyong; Wang Yuebao; Yin Chuancun
2011-01-01
This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptoties for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.
A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators
Hagstrom, T.; Hariharan, S. I.
1998-01-01
In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.
Directory of Open Access Journals (Sweden)
Sohel Rana
2014-01-01
Full Text Available Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE and finite element method (FEM. The non-Fourier heat conduction has been investigated where the maximum likelihood (ML and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML, another well-conditioned scheme, called mass effect (ME T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.
Institute of Scientific and Technical Information of China (English)
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
2013-01-01
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity, we call such Markov chains {\\it GI/GI/1-type Markov chains without disasters} because they are often used to analyze semi-Markovian queues without "disasters", which are negative customers who remove all the customers in the system (including themselves) o...
On the Conditions for the Orbitally Asymptotical Stability of the Almost
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system x′=f(x), x Rn , (1) where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability. For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e.
Directory of Open Access Journals (Sweden)
Vardanyan S. A.
2007-09-01
Full Text Available In the framework of the asymmetrical momental micropolar theory in the present work the boundary value problem of thermal stresses in a three-dimensional thin plate with independent fields of displacements and rotations is studied on the basis of asymptotic method. Depending on the values of physical dimensionless constants of the material three applied two-dimensional theories of thermoelasticity of micropolar thin plate are constructed (theories with independent rotations, with constrained rotations and with small shift rigidity.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Behzadan, A
2015-01-01
In this article we consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish existence of coupled non-CMC weak solutions for AF manifolds. As is the case for the analogous existence results for non-CMC solutions on closed manifolds and compact manifolds with boundary, our results here avoid the near-CMC assumption by assuming that the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small. The non-CMC rough solutions results here for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014 results on rough far-from-CMC positive Yamabe solutions for closed and compact manifolds with boundary. Similarly, our results may be viewed as extending the recent 2014 results for AF m...
Carro, Adrian; Miguel, Maxi San
2012-01-01
We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.
Verma, Ram U; Seol, Youngsoo
2016-01-01
First a new notion of the random exponential Hanson-Antczak type [Formula: see text]-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function [Formula: see text] of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. Furthermore, several sets of asymptotic sufficiency results in which various generalized exponential type [Formula: see text]-V-invexity assumptions are imposed on certain vector functions whose components are the individual as well as some combinations of the problem functions are examined and proved. To the best of our knowledge, all the established results on the semi-infinite aspects of the multi-objective fractional programming are new, which is a significantly new emerging field of the interdisciplinary research in nature. We also observed that the investigated results can be modified and applied to several special classes of nonlinear programming problems.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
Existence and Asymptotic Behavior of the Wave Equation with Dynamic Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Graber, Philip Jameson, E-mail: pjg9g@virginia.edu [University of Virginia, Department of Mathematics (United States); Said-Houari, Belkacem, E-mail: belkacem.saidhouari@kaust.edu.sa [King Abdullah University of Science and Technology (KAUST), Division of Mathematical and Computer Sciences and Engineering (Saudi Arabia)
2012-08-15
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time.
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Graber, Philip Jameson
2012-03-07
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.
Institute of Scientific and Technical Information of China (English)
CHEN Jun; CUI Bao-Tong; GAO Ming
2008-01-01
The global asymptotic stability of delayed Cohen-Grossberg neural networks with impulses is investigated. Based on the new suitable Lyapunov functions and the Jacobsthal inequality, a set of novel sufficient criteria are derived for the global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays and impulses.An illustrative example with its numerical simulations is given to demonstrate the effectiveness of the obtained results.
Institute of Scientific and Technical Information of China (English)
E. M. E. ZAYED
2003-01-01
The asymptotic expansions of the trace of the heat kernel Θ(t) = ∑∞ν=1 exp(-tλν) for smallpositive t, where {λν} are the eigenvalues of the negative Laplacian -△n = - ∑n i=1 ( / xi )2 in Rn(n= 2or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary (e)Ω1 and asmooth outer boundary (e)Ω2, where a finite number of piecewise smooth Robin boundary conditions((e)/(e)nj+rj)φ=0 on the components γj(j = 1, ..., k)of (e)Ω1 and on teh components γj(j = 1, ..., m) of (e)Ω2 are considered such that( (e)Ω1+ukj=1 Fj and (e)Ω2=Umj=k+1Fj )and where the coefficients (rj(j=1，…，m))are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gasenclosed in the general annular bounded domain Ω are given. Further results are also obtained.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Directory of Open Access Journals (Sweden)
Le Thi Phuong Ngoc
2016-01-01
Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Institute of Scientific and Technical Information of China (English)
E.M.E. ZAYED
2004-01-01
The asymptotic expansion of the heat kernel Θ(t)(∞∑=(i=0))exp (-λi) where({λi}∞i=1) Are the eigen-values of negative Laplacian( -△n=-n∑k=1(θ/θxk)2)in Rn(n=2 or 3) is studied for short-time t for a general bounded domainθΩwith a smooth boundary θΩ.In this paper, we consider the case of a finite number of the Dirichlet conditions φ=0 on Γi (i = J +1,….,J)and the Neumann conditions and (θφ/θ vi) = 0 on Γi (i = J+1,…,k) and the Robin condition (θφ/θ vi+γi) θ=(I=k+1,… m) where γi are piecewise smooth positive impedancem(θφ=mUi=1Γi. )We construct the required asymptotics in the form of a power series over t. The senior coe.cients inthis series are speci.ed as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a "special ideal gas", i.e., the set of non-interacting particles set up in abox with Dirichlet, Neumann and Robin boundary conditions for the appropriate wave function. Calculationof the thermodynamic quantities for the ideal gas such as the internal energy, pressure and speci.c heat revealsthat these quantities alone are incapable of distinguishing between two di.erent shapes of the domain. Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function; nevertheless, its formal theoretical motivation is of some interest.
Kiselev, O M
1999-01-01
The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficients, where the solution of the Painleve-1 equation has poles. The uniform smooth asymptotics are constructed in the interval, containing the critical point $t_*$.
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Strings from 3D gravity: asymptotic dynamics of AdS$_3$ gravity with free boundary conditions
Apolo, Luis
2015-01-01
Pure three-dimensional gravity in anti-de Sitter space can be formulated as an SL(2,R) $\\times$ SL(2,R) Chern-Simons theory, and the latter can be reduced to a WZW theory at the boundary. In this paper we show that AdS$_3$ gravity with free boundary conditions is described by a string theory at the boundary whose target spacetime is also AdS$_3$. While boundary conditions in the standard construction of Coussaert, Henneaux, and van Driel are enforced through constraints on the WZW currents, we find that free boundary conditions are partially enforced through the string Virasoro constraints.
Vogel, Edgar H
2012-01-01
The purpose of this study was to examine whether the progressive disappearance of short-latency conditioned responses, or inhibition of delay, observed in Pavlovian conditioning with long inter-stimulus intervals, could be reverted by the presentation of a novel stimulus. In one experiment, two groups of rabbits received extensive training with a short (250 ms) or a long (1500 ms) tone that overlapped and terminated with a periorbital shock unconditioned stimulus. After training, the presentation of an extraneous stimulus prior to tone onset produced a reinstatement of short latency CRs in the group trained with the long CS, but did not affect CR latency in the group trained with the short CS. This finding is consistent with Pavlov's (1927) view that conditioning with long conditioned stimuli involves the acquisition of response tendencies in the early portion of the stimulus that are subsequently suppressed by the development of an inhibitory process.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
王启华; 荆炳义
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Directory of Open Access Journals (Sweden)
Yijin Zhang
2013-01-01
Full Text Available This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system.
J.F. Kiviet; J. Niemczyk
2012-01-01
In designing Monte Carlo simulation studies for analyzing finite sample properties of econometric inference methods, one can use either IID drawings in each replication for any series of exogenous explanatory variables or condition on just one realization of these. The results will usually differ, a
Porta, G. M.; Ceriotti, G.; Thovert, J.-F.
2016-02-01
We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.
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 Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Mickley, G. Andrew; DiSorbo, Anthony; Wilson, Gina N.; Huffman, Jennifer; Bacik, Stephanie; Hoxha, Zana; Biada, Jaclyn M.; Kim, Ye-Hyun
2009-01-01
Conditioned taste aversions (CTAs) may be acquired when an animal consumes a novel taste (CS) and then experiences the symptoms of poisoning (US). This aversion may be extinguished by repeated exposure to the CS alone. However, following a latency period in which the CS is not presented, the CTA will spontaneously recover (SR). In the current…
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Asymptotic and Exact Expansions of Heat Traces
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Michał, E-mail: michal@eckstein.pl [Jagiellonian University, Faculty of Physics, Astronomy and Applied Computer Science (Poland); Zając, Artur, E-mail: artur.zajac@uj.edu.pl [Jagiellonian University, Faculty of Mathematics and Computer Science (Poland)
2015-12-15
We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
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...
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.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, M
2016-01-01
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 non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.
On the Asymptotic Distribution of Signal Fraction
Volobouev, Igor
2016-01-01
Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.
Liapunov structure and asymptotic expressions of linear differential systems
Institute of Scientific and Technical Information of China (English)
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
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.......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...
Litim, Daniel F
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.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes
M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractThe paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical
Asymptotic symmetries of de Sitter space-time
Energy Technology Data Exchange (ETDEWEB)
Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)
1981-01-01
The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
Directory of Open Access Journals (Sweden)
Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
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
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
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.
Confinement versus asymptotic freedom
Dubin, A Yu
2002-01-01
I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotically safe grand unification
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotic admissibility of priors and elliptic differential equations
Hartigan, J A
2010-01-01
We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.
On the asymptotics of the α-Farey transfer operator
Kautzsch, J.; Kesseböhmer, M.; Samuel, T.; Stratmann, B. O.
2015-01-01
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic α-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition α. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if the asymptotic behaviour of iterates of the transfer operator is known on the first element of the partition α, then the same asymptotic holds on any compact set bounded away from the indifferent fixed point.
Asymptotic stability properties of θ-methods for delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
Asymptotical Properties for Parabolic Systems of Neutral Type
Institute of Scientific and Technical Information of China (English)
CUI Bao-tong; HAN Mao-an
2005-01-01
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
Asymptotic Extension of Nonlinear Models with Bayesian Conditions%Bayes条件下非线性模型参数估计的渐近展开
Institute of Scientific and Technical Information of China (English)
吴一凡
2012-01-01
给出了在Bayes条件下非线性回归模型的参数估计，建立了非线性回归模型的几何结构，推广了Bates和Wates关于非线性回归模型的几何框架，用几何方法求出参数估计的随机展开，并讨论了若干与统计曲率相关的渐近性质，给出了该模型的极大似然估计的方差和偏差的近似表示．%In this paper, we propose a differential geometric framework for nonlinear model under Bayesian conditions. Our framework may be regarded as an extension of that presented by Bates & watts for nonlinear regression models. We use this geometric framework to discuss the parameter stochastic expansion by using the curvature in the nonlinear model. Some statistical properties of parameter are studied from the geometric point of view.
Directory of Open Access Journals (Sweden)
Xionghua Wu
2012-01-01
Full Text Available Let {}⊂(0,1 be such that →1 as →∞, let and be two positive numbers such that +=1, and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {}, we show the existence of a sequence {} satisfying the relation =(1−/(+(/ and prove that {} converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by 0∈,+1=(1−/(+(/+(/ converges strongly to the fixed point of .
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Asymptotic Existence of Nearly Kirkman Systems
Institute of Scientific and Technical Information of China (English)
沈灏; 储文松
1994-01-01
It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.
ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL
Institute of Scientific and Technical Information of China (English)
CUI Hengjian
2005-01-01
This paper addresses estimation and its asymptotics of mean transformation θ = E[h(X)] of a random variable X based on n iid. Observations from errors-in-variables model Y = X + v, where v is a measurement error with a known distribution and h(.) is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
Semilocal density functional theory with correct surface asymptotics
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds
An, Ok Song; Papadimitriou, Ioannis
2016-01-01
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associat...
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Asymptotic dynamics of three-dimensional gravity
Donnay, Laura
2016-01-01
These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\\mathbb R)\\times SL(2,\\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime.
On asymptotic flatness and Lorentz charges
Energy Technology Data Exchange (ETDEWEB)
Compere, Geoffrey [KdV Institute for Mathematics, Universiteit van Amsterdam (Netherlands); Dehouck, Francois; Virmani, Amitabh, E-mail: gcompere@uva.nl, E-mail: fdehouck@ulb.ac.be, E-mail: avirmani@ulb.ac.be [Physique Theorique et Mathematique, Universite Libre de Bruxelles, Bruxelles (Belgium)
2011-07-21
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Asymptotics of trimmed CUSUM statistics
Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318
2012-01-01
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Ruin problems and tail asymptotics
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...... by an underlying Harris recurrent Markov process some asymptotic results for the ruin probability are derived. Finally, a paper, which is separate in content from the rest of the thesis, treats a RESTART problem in the situation, where failures occur with decreasing intensity....
Asymptotic vacua with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
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 vacua with higher derivatives
Directory of Open Access Journals (Sweden)
Spiros Cotsakis
2016-04-01
Full Text Available 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.
BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
Liu Yue; Wang Zhengping
2007-01-01
This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N ＞ 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).
Asymptotic curved interface models in piezoelectric composites
Serpilli, Michele
2016-10-01
We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.
Asymptotics of the QMLE for General ARCH(q) Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders Christian
2009-01-01
Asymptotics of the QMLE for Non-Linear ARCH Models Dennis Kristensen, Columbia University Anders Rahbek, University of Copenhagen Abstract Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log......-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a finite log-moment, and finite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption...... that certain ratios involving the conditional variance function are suitably bounded, and that the rescaled errors have little more than fourth moment. We verify our general conditions, including identification, for a wide range of leading specific ARCH models....
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.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
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...
Singularities in asymptotically anti-de Sitter spacetimes
Ishibashi, Akihiro
2012-01-01
We consider singularity theorems in asymptotically anti-de Sitter (AdS) spacetimes. In the first part, we discuss the global methods used to show geodesic incompleteness and see that when the conditions imposed in Hawking and Penrose's singularity theorem are satisfied, a singularity must appear in asymptotically AdS spacetime. The recent observations of turbulent instability of asymptotically AdS spacetimes indicate that AdS spacetimes are generically singular even if a closed trapped surface, which is one of the main conditions of the Hawking and Penrose theorem, does not exist in the initial hypersurface. This may lead one to expect to obtain a singularity theorem without imposing the existence of a trapped set in asymptotically AdS spacetimes. This, however, does not appear to be the case. We consider, within the use of global methods, two such attempts and discuss difficulties in eliminating conditions concerning a trapped set from singularity theorems in asymptotically AdS spacetimes. Then in the second...
M-Estimation for Discrete Data. Asymptotic Distribution Theory and Implications.
1985-10-01
DATA: ASYMPTOTIC DISTRIBUTION THEORY AND IMPLICATIONS by 1 Douglas G. Simpson Departr.ient of Statistics University of Illinois Urbana, Illinois...asymptotic distribution theory of M-estimators especially relevant to discrete data, although Theorem 1 is somewhat broader in scope’. The main results are...The version (2.5) c (X9 / - ), where s(a)=9 / + (c) is defined by (2.3), is slightly more convenient. 3. Extended asymptotic distribution theory Conditions
Institute of Scientific and Technical Information of China (English)
LI Hong; L(U) Shu; ZHONG Shou-ming
2005-01-01
The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
Nonabelian Higgs models: paving the way for asymptotic freedom
Gies, Holger
2016-01-01
Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.
Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis
2016-03-01
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for {N}=2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification.
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Composite Operators in Asymptotic Safety
Pagani, Carlo
2016-01-01
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
Institute of Scientific and Technical Information of China (English)
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety 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 of an asymptotically free (perhaps magnetic dual) extension.
Asymptotically thermal responses for smoothly switched detectors
Fewster, Christopher J; Louko, Jorma
2015-01-01
Thermal phenomena in quantum field theory can be detected with the aid of particle detectors coupled to quantum fields along stationary worldlines, by testing whether the response of such a detector satisfies the detailed balance version of the KMS condition at a constant temperature. This relation holds when the interaction between the field and the detector has infinite time duration. Operationally, however, detectors interact with fields for a finite amount of time, controlled by a switching function of compact support, and the KMS detailed balance condition cannot hold exactly for finite time interactions at arbitrarily large detector energy gap. In this large energy gap regime, we show that, for an adiabatically switched Rindler detector, the Unruh temperature emerges asymptotically after the detector and the field have interacted for a time that is polynomially long in the large energy. We comment on the significance of the adiabaticity assumption in this result.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Asymptotic structure of the Einstein-Maxwell theory on AdS$_{3}$
Perez, Alfredo; Tempo, David; Troncoso, Ricardo
2015-01-01
The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to $\\mathbb{R}\\otimes U\\left(1\\right)\\otimes U\\left(1\\right)$. Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized b...
On an Asymptotic Behavior of Exponential Functional Equation
Institute of Scientific and Technical Information of China (English)
Soon Mo JUNG
2006-01-01
The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex)normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ‖x‖ + ‖y‖→∞ under some suitable conditions.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
Institute of Scientific and Technical Information of China (English)
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
The Asymptotic Limit for the 3D Boussinesq System
Institute of Scientific and Technical Information of China (English)
LI Lin-rui; WANG Ke; HONG Ming-li
2016-01-01
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coeﬃcient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosityν=0 or zero diffusivityη=0) in 2D case separately.
Asymptotic traveling wave solution for a credit rating migration problem
Liang, Jin; Wu, Yuan; Hu, Bei
2016-07-01
In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.
Conformal Phase Diagram of Complete Asymptotically Free Theories
Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.
Asymptotic distributions for a class of generalized $L$-statistics
Borovskikh, Yuri V; 10.3150/09-BEJ240
2010-01-01
We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$-statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$-statistics.
Asymptotic Distribution of the Jump Change-Point Estimator
Institute of Scientific and Technical Information of China (English)
Changchun TAN; Huifang NIU; Baiqi MIAO
2012-01-01
The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent identically distributed random variables with Eεi=0 and Var(εi) ＜ oo,with the help of the slip window method,the asymptotic distribution of the jump change-point estimator (T) is studied under the condition of the local alternative hypothesis.
On a new approach to asymptotic stabilization problems
Ivanchikov, A. A.; Kornev, A. A.; Ozeritskii, A. V.
2009-12-01
A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee-Infante equation in a circular domain by the boundary conditions is given.
New explicit global asymptotic stability criteria for higher order difference equations
El-Morshedy, Hassan A.
2007-12-01
New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-11-01
Asymptotic solutions of the multidimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.
ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS-IN-VARIABLES MODEL
Institute of Scientific and Technical Information of China (English)
ZHANG Sanguo; CHEN Xiru
2003-01-01
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
Uniformly Asymptotic Stability and Existence of Periodic Solutions and Almost Periodic Solutions
Institute of Scientific and Technical Information of China (English)
林发兴
1994-01-01
We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.
Institute of Scientific and Technical Information of China (English)
Jie Li DING; Xi Ru CHEN
2006-01-01
For generalized linear models (GLM), in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate (MLE)(β^)n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of(β^)n.
Institute of Scientific and Technical Information of China (English)
Wei-hua Mao; An-hua Wan
2006-01-01
The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established. Three illustrative examples are proposed to demonstrate the effectiveness of the conditions.
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.
On global asymptotic controllability of planar affine nonlinear systems
Institute of Scientific and Technical Information of China (English)
SUN Yimin; GUO Lei
2005-01-01
In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
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 co...
Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
de Lima, Levi Lopes
2012-01-01
We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\\geq 3$ an optimal Penrose inequality for certain graphs in hyperbolic space $\\mathbb H^{n+1}$ whose boundary has constant mean curvature $n-1$.
Asymptotic behaviour near extinction of continuous-state branching processes
Pardo, Juan Carlos; Berzunza, Gabriel
2016-01-01
In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a continuous state branching process whose branching mechanism satisfies a given condition and its reflected process at its infimum.
A new class of asymptotically non-chaotic vacuum singularities
Energy Technology Data Exchange (ETDEWEB)
Klinger, Paul, E-mail: paul.klinger@univie.ac.at
2015-12-15
The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.
Fast evaluation of asymptotic waveforms from gravitational perturbations
Benedict, Alex G; Lau, Stephen R
2012-01-01
In the context of blackhole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user's standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge-Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equa...
Equivariant spectral asymptotics for h-pseudodifferential operators
Weich, Tobias
2014-10-01
We prove equivariant spectral asymptotics for h-pseudodifferential operators for compact orthogonal group actions generalizing results of El Houakmi and Helffer ["Comportement semi-classique en présence de symétries: Action d'un groupe de Lie compact," Asymp. Anal. 5(2), 91-113 (1991)] and Cassanas ["Reduced Gutzwiller formula with symmetry: Case of a Lie group," J. Math. Pures Appl. 85(6), 719-742 (2006)]. Using recent results for certain oscillatory integrals with singular critical sets [P. Ramacher, "Singular equivariant asymptotics and Weyl's law: On the distribution of eigenvalues of an invariant elliptic operator," J. Reine Angew. Math. (Crelles J.) (to be published)], we can deduce a weak equivariant Weyl law. Furthermore, we can prove a complete asymptotic expansion for the Gutzwiller trace formula without any additional condition on the group action by a suitable generalization of the dynamical assumptions on the Hamilton flow.
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...
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotics of Lagged Fibonacci Sequences
Mertens, Stephan
2009-01-01
Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.
Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model
Directory of Open Access Journals (Sweden)
Shengmao Fu
2013-01-01
Full Text Available The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T, (u1T,u2T,u3T such that uiT≤uiT (i=1,2,3, and the sector {(u1,u2,u3:uiT≤ui≤uiT, i=1,2,3} is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
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 properties of the C-Metric
Sladek, Pavel
2010-01-01
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... 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 expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Under certain conditions, the dynamic equatioins of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.
Institute of Scientific and Technical Information of China (English)
肖黎明
2001-01-01
Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of themethod of asymptotic analysis.
The Asymptotic Standard Errors of Some Estimates of Uncertainty in the Two-Way Contingency Table
Brown, Morton B.
1975-01-01
Estimates of conditional uncertainty, contingent uncertainty, and normed modifications of contingent uncertainity have been proposed for the two-way contingency table. The asymptotic standard errors of the estimates are derived. (Author)
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice.
Harvey, Danielle J; Weng, Qian; Beckett, Laurel A
2010-06-15
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented.
An asymptotic model of the F layer
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
S-asymptotically -periodic Solutions of R-L Fractional Derivative-Integral Equation
Institute of Scientific and Technical Information of China (English)
WANG Bing
2015-01-01
The aim of this paper is to study the S-asymptotically ω-periodic solutions of R-L fractional derivative-integral equation:is a linear densely defined operator of sectorial type on a completed Banach space X, f is a continuous function satisfying a suitable Lipschitz type condition. We will use the contraction mapping theory to prove problem (1) and (2) has a unique S-asymptotically ω-periodic solution if the function f satisfies Lipshcitz condition.
Asymptotic properties of random matrices and pseudomatrices
Lenczewski, Romuald
2010-01-01
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
CHEN LiQun; C.W.LIM; HU QingQuan; DING Hu
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach.The asymptotic solution is sought for a beam equation with a nonlinear boundary condition.The steady-state responses are determined in primary resonance and subharmonic resonance.The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition.Multivaluedness occurs in the relations as a consequence of the nonlinearity.The stability of steady-state responses is analyzed by use of the Lyapunov linearized sta-bility theory.The stability analysis predicts the jumping phenomenon for certain parameters.The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales.The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
C.; W.; LIM
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic properties of the inhomogeneous Lotka-Von Foerster system.
Inaba, H
1988-01-01
"In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution." (SUMMARY IN FRE)
Asymptotics of nearly critical Galton-Watson processes with immigration
Kevei, Peter
2011-01-01
We investigate the inhomogeneous Galton--Watson processes with immigration, where $\\rho_n$ the offspring means in the $n^\\textrm{th}$ generation tends to 1. We show that if the second derivatives of the offspring generating functions go to 0 rapidly enough, then the asymptotics are the same as in the INAR(1) case, treated by Gy\\"orfi et al. We also determine the limit if this assumption does not hold showing the optimality of the conditions.
Complementarity between Gauge-Boson Compositeness and Asymptotic Freedom
Akama, K; Akama, Keiichi; Hattori, Takashi
1997-01-01
We derive and solve the compositeness condition for the SU(N_c) gauge boson at the next-to-leading order in 1/N_f (N_f is the number of flavors) to obtain the expression of the gauge coupling constant in terms of the compositeness scale. It turns out that the argument of gauge-boson compositeness is successful only for N_f/N_c>11/2, where the asymptotic freedom fails.
Asymptotic Expansions of Transition Densities for Hybrid Jump-Diffusions
Institute of Scientific and Technical Information of China (English)
Yuan-jin Liu; G.Yin
2004-01-01
A class of hybrid jump diffusions modulated by a Markov chain is considered in this work.The motivation stems from insurance risk models,and emerging applications in production planning and wireless communications.The models are hybrid in that they involve both continuous dynamics and discrete events.Under suitable conditions,asymptotic expansions of the transition densities for the underlying processes are developed.The formal expansions are validated and the error bounds obtained.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
Energy Technology Data Exchange (ETDEWEB)
Tracy, Craig A.; Widom, Harold, E-mail: widom@ucsc.edu [University of California, Department of Mathematics (United States)
2011-09-15
This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors' papers on the asymmetric simple exclusion process, from the derivation of exact formulas for configuration probabilities, through Fredholm determinant representation, to asymptotics with step initial condition establishing KPZ universality. Although complete proofs are in general not given, at least the main elements of them are.
Asymptotic analytical methods in fluid mechanics related to drag prediction
Inger, G. R.
1975-01-01
Some recent theoretical work of a purely analytical nature is described which promises to provide engineering predictions for the important drag-related phenomena of flow in the stall regime. This analytical work deals with rigorous asymptotic studies of the complete Navier-Stokes equations that govern the viscous flow around any aerodynamic body under conditions where boundary layer separation takes place from the body surface.
Asymptotics of thermal spectral functions
Caron-Huot, S
2009-01-01
We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...
Asymptotic Safety, Emergence and Minimal Length
Percacci, R
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.
Global asymptotic stability for Hopfield-type neural networks with diffusion effects
Institute of Scientific and Technical Information of China (English)
YAN Xiang-ping; LI Wan-tong
2007-01-01
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.
Institute of Scientific and Technical Information of China (English)
WANG XIONG-RUI; Ji You-qing
2011-01-01
In this paper,the iteration xn+1 =any + (1 - αn)Tk(n)i(n)xn for a family of asymptotically nonexpansive mappings T1,T2,...,TN is originally introduced in an uniformly convex Banach space.Motivated by recent papers,we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings.The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces,or from nonexpansive mappings to asymptotically nonexpansive mappings.
On the Asymptotic Limit of Flows Past a Ribbed Boundary
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka
2008-11-01
We consider a stationary Navier-Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional to a small parameter ɛ, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system of the Navier-Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is allowed without any constraint.
Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation
Institute of Scientific and Technical Information of China (English)
Mi-na Jiang; Yan-ling Xu
2005-01-01
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation ut + f(u)x = uxx +uxxt on the half line with the conditions u(0, t) =u-, u(∞, t) = u+ and u- ＜ u+, where the corresponding Cauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, because of the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signs of the characteristic speeds f′(u±) of boundary state u- = u(0) and the far fields states u+ = u(∞). In all cases both global existence of the solution and asymptotic behavior are shown under the smallness conditions.
Asymptotic Evolution of Random Unitary Operations
Novotny, J; Jex, I
2009-01-01
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
The Lorentzian proper vertex amplitude: Asymptotics
Engle, Jonathan; Zipfel, Antonia
2015-01-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
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...
Hermite polynomials and quasi-classical asymptotics
Energy Technology Data Exchange (ETDEWEB)
Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Engliš, Miroslav, E-mail: englis@math.cas.cz [Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1 (Czech Republic)
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
A Shortcut to LAD Estimator Asymptotics
1990-01-01
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with in...
The trouble with asymptotically safe inflation
Fang, Chao
2013-01-01
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
Asymptotic Analysis of Mixed Modes in Red Giant Stars
Jiang, C
2014-01-01
High precision space observations, such as made by the kepler and corot missions, allow us to detect mixed modes for $l = 1$ modes in their high signal-to-noise photometry data. By means of asteroseismology, the inner structure of red giant (RG) stars is revealed the first time with the help of mixed modes. We analyse these mixed modes of a 1.3 $M_{sun}$ RG model theoretically from the approximate asymptotic descriptions of oscillations. While fitting observed frequencies with the eigenvalue condition for mixed modes, a good estimate of period spacing and coupling strength is also acquired for more evolved models. We show that the behaviour of the mode inertia in a given mode varies dramatically when the coupling is strong. An approximation of period spacings is also obtained from the asymptotic dispersion relation, which provides a good estimate of the coupling strength as well as period spacing when g-mode-like mixed modes are sufficiently dense.
Asymptotically flat black holes with scalar hair: a review
Herdeiro, Carlos A R
2015-01-01
We consider the status of black hole solutions with non-trivial scalar fields but no gauge fields, in four dimensional asymptotically flat space-times, reviewing both classical results and recent developments. We start by providing a simple illustration on the physical difference between black holes in electro-vacuum and scalar-vacuum. Next, we review no-scalar-hair theorems. In particular, we detail an influential theorem by Bekenstein and stress three key assumptions: 1) the type of scalar field equation; 2) the spacetime symmetry inheritance by the scalar field; 3) an energy condition. Then, we list regular (on and outside the horizon), asymptotically flat BH solutions with scalar hair, organizing them by the assumption which is violated in each case and distinguishing primary from secondary hair. We provide a table summary of the state of the art.
Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems
Directory of Open Access Journals (Sweden)
Ewelina Seroka
2015-01-01
Full Text Available The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.
A Framework for Non-Asymptotic Quantum Information Theory
Tomamichel, Marco
2012-01-01
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\\'enyi entropies. We introduce the purified distance, a novel metric for unnormalized quantum states and use it to define smooth entropies as optimizations of the min- and max-entropies over a ball of close states. We explore various properties of these entropies, including data-processing inequalities, chain rules and their classical limits. The most important property is an entropic formulation of the asymptotic equipartition property, which implies that the smooth entropies converge to the von Neumann entropy in the limit of many independent copies. The smooth entropies also satisfy duality and entropic uncertainty relations that provide limits on the power of two different observers to predict the outcome of a measurement on a quantum system. Finally, we discuss three example...
Asymptotic behavior of singular solutions to semilinear fractional elliptic equations
Directory of Open Access Journals (Sweden)
Guowei Lin
2014-02-01
Full Text Available In this article we study the asymptotic behavior of positive singular solutions to the equation $$ (-\\Delta^{\\alpha} u+u^p=0\\quad\\text{in } \\Omega\\setminus\\{0\\}, $$ subject to the conditions $u=0$ in $\\Omega^c$ and $\\lim_{x\\to0}u(x=\\infty$, where $p\\geq1$, $\\Omega$ is an open bounded regular domain in $\\mathbb{R}^N$ ($N\\ge2$ containing the origin, and $(-\\Delta^\\alpha$ with $\\alpha\\in(0,1$ denotes the fractional Laplacian. We show that the asymptotic behavior of positive singular solutions is controlled by a radially symmetric solution with $\\Omega$ being a ball.
M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications.
1985-11-01
n 860 0029 M-ESTIMATION FOR DISCRETE DATA: ASYMPTOTIC DISTRIBUTION THEORY AND IMPLICATIONS by Douglas G. Simpson 1 Departraent of Statistics... distribution theory of M-estimators especially relevant to discrete data, although Theorem 1 is somewhat broader in scope’. The main results are given in...Extended asymptotic distribution theory Conditions for consistency of an M-estimator can be found in Huber (1964, 1967, 1981). Since the smoothness plays
Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory
Inahama, Yuzuru
2011-01-01
In this paper we study short time asymptotics of a density function of the solution of a stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H \\in (1/2, 1)$ when the coefficient vector fields satisfy an ellipticity condition at the starting point. We prove both on-diagonal and off-diagonal asymptotics under mild additional assumptions. Our main tool is Malliavin calculus, in particular, Watanabe's theory of generalized Wiener functionals.
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jiaqi MO; Wantao LIN
2008-01-01
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
PERMANENCE OF ASYMPTOTICALLY PERIODIC MULTISPECIES LOTKA-VOLTERRA COMPETITION PREDATOR-PREY SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.
Directory of Open Access Journals (Sweden)
Xueling Jiang
2014-01-01
Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Directory of Open Access Journals (Sweden)
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Institute of Scientific and Technical Information of China (English)
李大鸣; 张红萍; 高永祥
2002-01-01
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS
Institute of Scientific and Technical Information of China (English)
YUE LI; CHEN XIRU
2005-01-01
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka; Wolf, Joerg
We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.
Charnotskii, Mikhail; Baker, Gary J.
2011-06-01
Asymptotic theory of the finite beam scintillations (Charnotskii, WRM, 1994, JOSA A, 2010) provides an exhaustive description of the dependence of the beam scintillation index on the propagation conditions, beam size and focusing. However the complexity of the asymptotic configuration makes it difficult to apply these results for the practical calculations of the scintillation index (SI). We propose an estimation technique and demonstrate some examples of the calculations of the scintillation index dependence on the propagation path length, initial beam size, wavelength and turbulence strength for the beam geometries and propagation scenarios that are typical for applications. We suggest simple analytic bridging approximations that connect the specific asymptotes with the accuracy sufficient for the engineering estimates. Proposed technique covers propagation of the wide, narrow, collimated and focused beams under the weak and strong scintillation conditions. Direct numeric simulation of the beam waves propagation through turbulence expediently complements the asymptotic theory being most efficient when the governing scales difference is not very large. We performed numerical simulations of the beam wave propagation through turbulence for conditions that partially overlap with the major parameter space domains of the asymptotic theory. The results of the numeric simulation are used to confirm the asymptotic theory and estimate the accuracy of the bridging approximations.
Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and Regularity
Banados, M; Theisen, S
2016-01-01
In the context of (2+1)--dimensional SL(N,R)\\times SL(N,R) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metric-like higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turn on -- as demanded by regularity -- the asymptotics cannot be that of Brown-Henneaux.
Higher spin black holes in three dimensions: Remarks on asymptotics and regularity
Bañados, Máximo; Canto, Rodrigo; Theisen, Stefan
2016-07-01
In the context of (2 +1 )-dimensional S L (N ,R )×S L (N ,R ) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metriclike higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turned on—as demanded by regularity—the asymptotics cannot be that of Brown-Henneaux.
Canonical charges and asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Preis, Florian
2014-01-01
We study canonical conformal gravity in four dimensions and construct the gauge generators and the associated charges. Using slightly generalized boundary conditions compared to those in \\cite{Grumiller:2013mxa} we find that the charges associated with space-time diffeomorphisms are finite and conserved in time. They are also shown to agree with the Noether charges found in \\cite{Grumiller:2013mxa}. However, there exists no charge associated with Weyl transformations. Consequently the asymptotic symmetry algebra is isomorphic to the Lie algebra of the boundary condition preserving diffeomorphisms. For illustrative purposes we apply the results to the Mannheim--Kazanas--Riegert solution of conformal gravity.
Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space
Detournay, Stéphane
2016-01-01
In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{\\`e}re boundary conditions gr-qc/0610130. These new boundary conditions lead to an asymptotic symmetry algebra that is generated by a $\\mathfrak{bms}_3$ algebra and two affine $\\hat{\\mathfrak{u}}(1)$ current algebras. We then apply these boundary conditions to Topologically Massive Gravity (TMG) and determine how the presence of the gravitational Chern-Simons term affects the central extensions of the asymptotic symmetry algebra. We furthermore determine the thermal entropy of solutions obeying our new boundary conditions for both Einstein gravity and TMG.
A note on asymptotic expansions for Markov chains using operator theory
DEFF Research Database (Denmark)
Jensen, J.L.
1987-01-01
We consider asymptotic expansions for sums Sn on the form Sn = fhook0(X0) + fhook(X1, X0) + ... + fhook(Xn, Xn-1), where Xi is a Markov chain. Under different ergodicity conditions on the Markov chain and certain conditional moment conditions on fhook(Xi, Xi-1), a simple representation...
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...
Directory of Open Access Journals (Sweden)
Bashir Ali
2012-01-01
Full Text Available Let be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let ={(∶≥0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of , with functions ,∶[0,∞→[0,∞. Let ∶=(=∩≥0((≠∅ and ∶→ be a weakly contractive map. For some positive real numbers and satisfying +>1, let ∶→ be a -strongly accretive and -strictly pseudocontractive map. Let {} be an increasing sequence in [0,∞ with lim→∞=∞, and let {} and {} be sequences in (0,1] satisfying some conditions. Strong convergence of a viscosity iterative sequence to common fixed points of the family of uniformly asymptotically regular asymptotically nonexpansive semigroup, which also solves the variational inequality ⟨(−,(−⟩≤0, for all ∈, is proved in a framework of a real Banach space.
Asymptotically flat structure of hypergravity in three spacetime dimensions
Fuentealba, Oscar; Troncoso, Ricardo
2015-01-01
The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-$5/2$ field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS$_{3}$. It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W$_{\\left(2,4\\right)}$ algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined "Killing vector-spinors". The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or anti-periodic boundary conditio...
Asymptotic normality of recursive algorithms via martingale difference arrays
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Werner Schachinger
2001-12-01
Full Text Available We propose martingale central limit theorems as an tool to prove asymptotic normality of the costs of certain recursive algorithms which are subjected to random input data. The recursive algorithms that we have in mind are such that if input data of size N produce random costs L N, then L N = D L n + L N-n +R N for N ≥ n 0 ≥2, where n follows a certain distribution P N on the integers {0, … ,N} and L k = D L k for k≥0. L n, L N-n and R N are independent, conditional on n, and R N are random variables, which may also depend on n, corresponding to the cost of splitting the input data of size N (into subsets of size n and N-n and combining the results of the recursive calls to yield the overall result. We construct a martingale difference array with rows converging to Z N:= [L N- EL N ] / [√ Var L N ]. Under certain compatibility assumptions on the sequence (P N N≥0 we show that a pair of sufficient conditions (of Lyapunov type for Z N → D N(0,1 can be restated as a pair of conditions regarding asymptotic relations between three sequences. All these sequences satisfy the same type of linear equation, that is also the defining equation for the sequence (EL N N≥0 and thus very likely a well studied object. In the case that the P N are binomial distributions with the same parameter p, and for deterministic R N, we demonstrate the power of this approach. We derive very general sufficient conditions in terms of the sequence (R N N≥0 (and for the scale R N =N α a characterization of those α leading to asymptotic normality of Z N.
Parallelism, Uniqueness, and Large-Sample Asymptotics for the Dantzig Selector
Dicker, Lee
2012-01-01
The Dantzig selector (Candes 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 pred...
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
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...
Nanofluid surface wettability through asymptotic contact angle.
Vafaei, Saeid; Wen, Dongsheng; Borca-Tasciuc, Theodorian
2011-03-15
This investigation introduces the asymptotic contact angle as a criterion to quantify the surface wettability of nanofluids and determines the variation of solid surface tensions with nanofluid concentration and nanoparticle size. The asymptotic contact angle, which is only a function of gas-liquid-solid physical properties, is independent of droplet size for ideal surfaces and can be obtained by equating the normal component of interfacial force on an axisymmetric droplet to that of a spherical droplet. The technique is illustrated for a series of bismuth telluride nanofluids where the variation of surface wettability is measured and evaluated by asymptotic contact angles as a function of nanoparticle size, concentration, and substrate material. It is found that the variation of nanofluid concentration, nanoparticle size, and substrate modifies both the gas-liquid and solid surface tensions, which consequently affects the force balance at the triple line, the contact angle, and surface wettability.
Asymptotic analysis of outwardly propagating spherical flames
Institute of Scientific and Technical Information of China (English)
Yun-Chao Wu; Zheng Chen
2012-01-01
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.
On generalized Nariai solutions and their asymptotics
Beyer, Florian
2009-01-01
In this paper, we consider the class of generalized Nariai solutions of Einstein's field equations in vacuum with a positive cosmological constant. According to the cosmic no-hair conjecture, generic expanding solutions isotropize and approach the de-Sitter solution asymptotically, at least locally in space. The generalized Nariai solutions, however, show quite unusual asymptotics and hence should be non-generic in some sense. In the first part of the paper, we list the necessary facts and characterize the asymptotic behavior geometrically. In the second part, we study the question of non-genericity, which we are able to confirm within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. In subsequent papers, we will continue this research in more general classes of solutions.
Asymptotics of a horizontal liquid bridge
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
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.
Semiclassical Asymptotics on Manifolds with Boundary
Koldan, Nilufer; Shubin, Mikhail
2008-01-01
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.
de Reyna, Juan Arias
2012-01-01
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $\\li^{-1}(n)$, after having retained the first m terms, for $1\\le m\\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Asymptotic behavior of asynchronous stochasticapproximation
Institute of Scientific and Technical Information of China (English)
方海涛; 陈翰馥
2001-01-01
The pathwise convergence of a distributed, asynchronous stochastic approximation (SA) scheme is analyzed. The conditions imposed on the step size and noise are the weakest in comparison with the existing ones. The step sizes in different processors are allowed to be different, and the time_delays between processors are also allowed to be different and even time_varying.
Non-asymptotic Equipartition Properties for Independent and Identically Distributed Sources
Yang, En-Hui
2012-01-01
Given an independent and identically distributed source $X = \\{X_i \\}_{i=1}^{\\infty}$ with finite Shannon entropy or differential entropy (as the case may be) $H(X)$, the non-asymptotic equipartition property (NEP) with respect to $H(X)$ is established, which characterizes, for any finite block length $n$, how close $-{1\\over n} \\ln p(X_1 X_2...X_n)$ is to $H(X)$ by determining the information spectrum of $X_1 X_2...X_n $, i.e., the distribution of $-{1\\over n} \\ln p(X_1 X_2...X_n)$. Non-asymptotic equipartition properties (with respect to conditional entropy, mutual information, and relative entropy) in a similar nature are also established. These non-asymptotic equipartition properties are instrumental to the development of non-asymptotic coding (including both source and channel coding) results in information theory in the same way as the asymptotic equipartition property to all asymptotic coding theorems established so far in information theory. As an example, the NEP with respect to $H(X)$ is used to est...
Further evidence for asymptotic safety of quantum gravity
Falls, Kevin; Nikolakopoulos, Konstantinos; Rahmede, Christoph
2014-01-01
The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture.
Precise Asymptotics of Error Variance Estimator in Partially Linear Models
Institute of Scientific and Technical Information of China (English)
Shao-jun Guo; Min Chen; Feng Liu
2008-01-01
In this paper, we focus our attention on the precise asymptoties of error variance estimator in partially linear regression models, yi = xTi β + g(ti) +εi, 1 ≤i≤n, {εi,i = 1,... ,n } are i.i.d random errors with mean 0 and positive finite variance q2. Following the ideas of Allan Gut and Aurel Spataru[7,8] and Zhang[21],on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.
Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations
Institute of Scientific and Technical Information of China (English)
王其如; 李黎
1993-01-01
This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.
Multiple Solutions for a Fourth-order Asymptotically Linear Elliptic Problem
Institute of Scientific and Technical Information of China (English)
Ai Xia QIAN; Shu Jie LI
2006-01-01
Under simple conditions, we prove the existence of three solutions for a fourth-order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding functional.
Scattering by a topological defect connecting two asymptotically Minkowski spacetimes
Pitelli, J P M
2015-01-01
We study the stability and the scattering properties of a spacetime with a topological defect along a spherical bubble. This bubble connects two flat spacetimes which are asymptotically Minkowski, so that the resulting universe may be regarded as containing a wormhole. Its distinguished feature is the absence of exotic matter, i.e., its matter content respects all the energy conditions. Although this wormhole is nontraversable, waves and quantum particles can tunnel between both universes. Interestingly enough, the wave equation alone does not uniquely determine the evolution of scalar waves on this background, and the theory of self-adjoint extensions of symmetric operators is required to find the relevant boundary conditions in this context. Here we show that, for a particular boundary condition, this spacetime is stable and gives rise to a scattering pattern which is identical to the more usual thin-shell wormhole composed of exotic matter. Other boundary conditions of interest are also analyzed, including...
Asymptotic Distributions for Tests of Combined Significance.
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS
Institute of Scientific and Technical Information of China (English)
Chungou Zhang; Quane Wang
2007-01-01
In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.
Discrete Energy Asymptotics on a Riemannian circle
Brauchart, J S; Saff, E B
2009-01-01
We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\\Gamma$ in ${\\mathbb R}^p$, $p\\geq2$, as $N \\to \\infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\\sum_{j\
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, N.M.
1999-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Directory of Open Access Journals (Sweden)
Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
An asymptotically optimal nonparametric adaptive controller
Institute of Scientific and Technical Information of China (English)
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
The conformal approach to asymptotic analysis
Nicolas, Jean-Philippe
2015-01-01
This essay was written as an extended version of a talk given at a conference in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach to asymptotic analysis in general relativity, which is based on conformal geometric techniques, focusing on historical and recent aspects of two specialized topics~: conformal scattering and peeling.
Breaking a magnetic zero locus: asymptotic analysis
Raymond, Nicolas
2014-01-01
25 pages; This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
Asymptotically periodic solutions of Volterra integral equations
Directory of Open Access Journals (Sweden)
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.
Resonance asymptotics in the generalized Winter model
Exner, P; Exner, Pavel; Fraas, Martin
2006-01-01
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.
Asymptotic iteration approach to supersymmetric bistable potentials
Institute of Scientific and Technical Information of China (English)
H. Ciftci; O. ozer; P. Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.
Asymptotic property of solutions to the random cauchy problem for wave equations
Dôku, Isamu
1986-01-01
Based on the existence and uniqueness theorem for random wave equations, we consider asymptotic behaviors of solutions to the random initial value problem. We describe conditions for the equipartition of stochastic energy (or SE for short) by making use of the random spectral theory and, according to Goldstein's semigroup method, we prove the asymptotically equipartitioned SE theorem and the so-called virial theorem of classical mechanics, and also study the probabilistic characterization of the conditions for equipartition. In addition, we show at last the equipartition of SE from a finite time onwards.
Directory of Open Access Journals (Sweden)
Wong NC
2006-01-01
Full Text Available We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space . We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact. Our results improve and extend earlier and recent ones in the literature.
Asymptotic expansion of the wavelet transform with error term
Pathak, R.S.; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Matulich, Javier; Tempo, David; Troncoso, Ricardo
2014-01-01
A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components of the gauge fields that manifestly preserve the original asymptotic higher spin extension of the BMS$_{3}$ algebra, with the same central charge. By virtue of a suitable permissible gauge choice, it is shown that this set can be directly recovered as a limit of the boundary conditions that have been recently constructed in the case of negative cosmological constant, whose asymptotic symmetries are spanned by two copies of the centrally-extended W$_{3}$ algebra. Since the generalized asymptotic conditions allow to incorporate chemical potentials conjugated to the higher spin charges, a higher spin extension of locally flat cosmological spacetimes becomes naturally included within the set. It is shown that their thermodynamic properties can be successfully obtained exclusively in terms of gauge fields and the topology of...
Directory of Open Access Journals (Sweden)
M. Venkatesulu
1996-01-01
Full Text Available Solutions of initial value problems associated with a pair of ordinary differential systems (L1,L2 defined on two adjacent intervals I1 and I2 and satisfying certain interface-spatial conditions at the common end (interface point are studied.
Hyperbolic positive mass theorem under modified energy condition
Institute of Scientific and Technical Information of China (English)
XIE NaQing
2008-01-01
We provide two new positive mass theorems under respective modified energy conditions allowing Too negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang's previous result for modified asymptotically fiat initial data sets.
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 individual...... terms of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (2007b). We show that the MQMLE is asymptotically normal irrespectively of the existence of finite moments, as geometric ergodicity alone suffice. Moreover, our included simulations show that the MQMLE...... 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....
Locally Asymptotic-norming Property and Kadec Property
Institute of Scientific and Technical Information of China (English)
王建华
2002-01-01
In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
Li, Yongfeng; Cui, Jingan; Song, Xinyu
2009-01-01
In this paper, the nonautonomous competing two-species Lotka-Volterra models with impulsive effect are considered, where all the parameters are time-dependent and asymptotically approach the corresponding periodic functions. Under some conditions, it is shown that the semi-trivial positive solutions of the models asymptotically approach the semi-trivial positive periodic solutions of the corresponding periodic system. It is also shown that the positive solution of the models asymptotically approach the positive periodic solution of the corresponding periodic system.
Asymptotically anti-de Sitter Proca Stars
Duarte, Miguel
2016-01-01
We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully non-linear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in $5$ dimensions.
Asymptotic Behaviour Near a Nonlinear Sink
Calder, Matt S
2010-01-01
In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.
Asymptotics of high order noise corrections
Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre
1999-01-01
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.
Asymptotic analysis of the Forward Search
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made....... The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure....
Asymptotic Enumeration of RNA Structures with Pseudoknots
Jin, Emma Y
2007-01-01
In this paper we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the sub exponential factors for $k$-noncrossing RNA structures. Our results are based on the generating function for the number of $k$-noncrossing RNA pseudoknot structures, ${\\sf S}_k(n)$, derived in \\cite{Reidys:07pseu}, where $k-1$ denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function $\\sum_{n\\ge 0}{\\sf S}_k(n)z^n$ and obtain for $k=2$ and $k=3$ the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary $k$ singular expansions exist and via transfer theorems of analytic combinatorics we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula ${\\sf S}_3(n) \\sim \\frac{10.4724\\cdot 4!}{n(n...
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
Adaptive Molecular Resolution Approach in Hamiltonian Form: An Asymptotic Analysis
Zhu, Jinglong; Site, Luigi Delle
2016-01-01
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer/transition region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. \\blue{Such conditions show that molecular simulations in the current computational implementation require systems of large size and thus a Hamiltonian approach as the one proposed, at this stage, would not be practica...
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-03-24
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.
Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
Directory of Open Access Journals (Sweden)
Xinhong Zhang
2013-07-01
Full Text Available This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic permanence are established for the n-dimensional model. Asymptotic pathwise behavior of n-dimensional Gilpin-Ayala mutualism model with jumps is also discussed. Finally numerical examples are introduced to illustrate the results developed.
Directory of Open Access Journals (Sweden)
Hai Zhang
2014-01-01
Full Text Available We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.
Institute of Scientific and Technical Information of China (English)
Xia ZHOU; Shou Ming ZHONG
2011-01-01
In this paper the asymptotical stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan's results.
Langer, S F J; Habazettl, H; Kuebler, W M; Pries, A R
2005-01-01
The left ventricular isovolumic pressure decay, obtained by cardiac catheterization, is widely characterized by the time constant tau of the exponential regression p(t)=Pomega+(P0-Pomega)exp(-t/tau). However, several authors prefer to prefix Pomega=0 instead of coestimating the pressure asymptote empirically; others present tau values estimated by both methods that often lead to discordant results and interpretation of lusitropic changes. The present study aims to clarify the relations between the tau estimates from both methods and to decide for the more reliable estimate. The effect of presetting a zero asymptote on the tau estimate was investigated mathematically and empirically, based on left ventricular pressure decay data from isolated ejecting rat and guinea pig hearts at different preload and during spontaneous decrease of cardiac function. Estimating tau with preset Pomega=0 always yields smaller values than the regression with empirically estimated asymptote if the latter is negative and vice versa. The sequences of tau estimates from both methods can therefore proceed in reverse direction if tau and Pomega change in opposite directions between the measurements. This is exemplified by data obtained during an increasing preload in spontaneously depressed isolated hearts. The estimation of the time constant of isovolumic pressure fall with a preset zero asymptote is heavily biased and cannot be used for comparing the lusitropic state of the heart in hemodynamic conditions with considerably altered pressure asymptotes.
S-asymptotically periodic solutions for partial differential equations with finite delay
Directory of Open Access Journals (Sweden)
William Dimbour
2011-09-01
Full Text Available In this article, we give some sufficient conditions for the existence and uniqueness of S-asymptotically periodic (mild solutions for some partial functional differential equations. To illustrate our main result, we study a diffusion equation with delay.
Sinharay, Sandip
2015-01-01
The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…
ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR NEUTRAL-TYPE SYSTEMS
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
By Lyapunov functional method, sufficient conditions for the asymptotic stability of a class of neutral-type systems are discussed in this paper. This work extends some results on the stability of neutral-type systems in the previous papers. Several numerical examples are listed in the end of this paper to confirm our results.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation
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Gong Fei
2009-01-01
Full Text Available We study the asymptotic behavior of the solutions for the following nonlinear difference equation where the initial conditions are arbitrary nonnegative real numbers, are nonnegative integers, , and are positive constants. Moreover, some numerical simulations to the equation are given to illustrate our results.
Asymptotic solutions for laminar flow in a channel with uniformly accelerating rigid porous walls
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.
Institute of Scientific and Technical Information of China (English)
王金良; 周笠
2003-01-01
In this paper,our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior.In case the coefficients are periodic,we give some sufficient conditions for the existence and uniqueness of periodic solution.Furthermore,we also study the effect of time-delay on the solution.
A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems
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Stojanović Sreten B.
2007-01-01
Full Text Available This paper presents a Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems. Based on the methods, delay-independent stability condition is derived. A numerical example has been working out to show the applicability of results derived.
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION ON TIME SCALES
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.
Uniform Asymptotic Normality of the Matrix-variate Beta-distribution
Institute of Scientific and Technical Information of China (English)
Kai Can LI; He TANG
2012-01-01
With the upper bound of Kullback-Leibler distance between a matrix variate Beta-distribution and a normal distribution,this paper gives the conditions under which a matrix-variate Betadistribution will approach uniformly and asymptotically a normal distribution.
Asymptotic theory for weakly non-linear wave equations in semi-infinite domains
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Chirakkal V. Easwaran
2004-01-01
Full Text Available We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.
ASYMPTOTICS OF INITIAL BOUNDARY VALUE PROBLEMS OF BIPOLAR HYDRODYNAMIC MODEL FOR SEMICONDUCTORS
Institute of Scientific and Technical Information of China (English)
Ju Qiangchang
2004-01-01
In this paper, we study the asymptotic behavior of the solutions to the bipolar hydrodynamic model with Dirichlet boundary conditions. It is shown that the initial boundary problem of the model admits a global smooth solution which decays to the steady state exponentially fast.
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice✩
Harvey, Danielle J.; Weng, Qian; Beckett, Laurel A.
2010-01-01
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented. PMID:20436940
Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis
Vetyukov, Yury
2014-01-01
This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exa...
Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions
Barnich, Glenn; Tempo, David; Troncoso, Ricardo
2015-01-01
The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS$_{3}$, but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.
Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity
Florchinger, Patrick
2016-07-01
The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Taming perturbative divergences in asymptotically safe gravity
Energy Technology Data Exchange (ETDEWEB)
Benedetti, Dario, E-mail: dbenedetti@perimeterinstitute.c [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada); Machado, Pedro F., E-mail: p.f.machado@uu.n [Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank, E-mail: Frank.Saueressig@cea.f [Institut de Physique Theorique, CEA Saclay, F-91191 Gif-Sur-Yvette Cedex (France); CNRS URA 2306, F-91191 Gif-Sur-Yvette Cedex (France)
2010-01-01
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.
Homogenization and asymptotics for small transaction costs
Soner, H Mete
2012-01-01
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.
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
The ADM mass of asymptotically flat hypersurfaces
de Lima, Levi Lopes
2011-01-01
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.
Asymptotics for a generalization of Hermite polynomials
Alfaro, M; Peña, A; Rezola, M L
2009-01-01
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler--Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.
Vacuum Potential and its Asymptotic Variation
Dahal, Pravin
2016-09-01
The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.
Singular asymptotic expansions in nonlinear rotordynamics
Day, W. B.
1985-01-01
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
Directory of Open Access Journals (Sweden)
Zhihe Jin
2011-12-01
Full Text Available This work investigates transient heat conduction in a functionally graded plate (FGM plate subjected to gradual cooling/heating at its boundaries. The thermal properties of the FGM are assumed to be continuous and piecewise differentiable functions of the coordinate in the plate thickness direction. A linear ramp function describes the cooling/heating rates at the plate boundaries. A multi-layered material model and Laplace transform are employed to obtain the transformed temperatures at the interfaces between the layers. An asymptotic analysis and an integration technique are then used to obtain a closed form asymptotic solution of the temperature field in the FGM plate for short times. The thermal stress intensity factor (TSIF for an edge crack in the FGM plate calculated based on the asymptotic temperature solution shows that the asymptotic solution can capture the peak TSIFs under the finite cooling rate conditions.
ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS
Institute of Scientific and Technical Information of China (English)
Zeng Luchuan
2006-01-01
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Ban ach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.
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.
Asymptotically AdS spacetimes with a timelike Kasner singularity
Ren, Jie
2016-07-01
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.
Asymptotic Stability of Neutral Differential Equations with Unbounded Delay
Institute of Scientific and Technical Information of China (English)
YE Hai-ping; GAO Guo-zhu
2002-01-01
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt [x(t)- P(t)x(h(t))] + Q(t)x(q(t)) -R(t)x(r(t))= 0, t ≥ t0,where P(t)∈ C([t0, ∞), R), Q(t), R(t) ∈ C([t0,∞ ), R+ ), and h, q, r: [ t0, ∞ ) → R are continuously differentiable and strictly increasing, h( t) ＜ t, q( t) ＜t, r(t) ＜ t for all t ≥ t0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Asymptotic behaviour of the Weyl tensor in higher dimensions
Ortaggio, Marcello
2014-01-01
We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence is assumed to "expand" in all directions near infinity (but it is otherwise generic), which includes in particular asymptotically flat spacetimes. In contrast to the well-known four-dimensional peeling property, the fall-off rate of various Weyl components depends substantially on the chosen boundary conditions, and is also influenced by the presence of a cosmological constant. The leading component is always algebraically special, but in various cases it can be of type N, III or II.
Asymptotic behaviour of Maxwell fields in higher dimensions
Ortaggio, Marcello
2014-01-01
We study the fall-off behaviour of test electromagnetic fields in higher dimensions as one approaches infinity along a congruence of "expanding" null geodesics. The considered backgrounds are Einstein spacetimes including, in particular, (asymptotically) flat and (anti-)de Sitter spacetimes. Various possible boundary conditions result in different characteristic fall-offs, in which the leading component can be of any algebraic type (N, II or G). In particular, the peeling-off of radiative fields F=Nr^{1-n/2}+Gr^{-n/2}+... differs from the standard four-dimensional one (instead it qualitatively resembles the recently determined behaviour of the Weyl tensor in higher dimensions). General p-form fields are also briefly discussed. In even n dimensions, the special case p=n/2 displays unique properties and peels off in the "standard way" as F=Nr^{1-n/2}+IIr^{-n/2}+.... A few explicit examples are mentioned.
Asymptotic Behavior of an Elastic Satellite with Internal Friction
Haus, E.; Bambusi, D.
2015-12-01
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a suitable nondegeneracy condition there are only three possible outcomes for the dynamics: (i) the orbit of the satellite is unbounded, (ii) the satellite falls on the planet, (iii) the satellite is captured in synchronous resonance i.e. its orbit is asymptotic to a motion in which the barycenter moves on a circular orbit, and the satellite moves rigidly, always showing the same face to the planet. The result is obtained by making use of LaSalle's invariance principle and by a careful kinematic analysis showing that energy stops dissipating only on synchronous orbits. We also use in quite an extensive way the fact that conservative elastodynamics is a Hamiltonian system invariant under the action of the rotation group.
Asymptotic Behavior of an Elastic Satellite with Internal Friction
Energy Technology Data Exchange (ETDEWEB)
Haus, E., E-mail: emanuele.haus@unina.it [Università di Napoli Federico II Via Cintia, Dipartimento di Matematica e Applicazioni R. Caccioppoli (Italy); Bambusi, D., E-mail: dario.bambusi@unimi.it [Università degli Studi di Milano, DIpartimento di Matematica F. Enriques (Italy)
2015-12-15
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a suitable nondegeneracy condition there are only three possible outcomes for the dynamics: (i) the orbit of the satellite is unbounded, (ii) the satellite falls on the planet, (iii) the satellite is captured in synchronous resonance i.e. its orbit is asymptotic to a motion in which the barycenter moves on a circular orbit, and the satellite moves rigidly, always showing the same face to the planet. The result is obtained by making use of LaSalle’s invariance principle and by a careful kinematic analysis showing that energy stops dissipating only on synchronous orbits. We also use in quite an extensive way the fact that conservative elastodynamics is a Hamiltonian system invariant under the action of the rotation group.
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.
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M; Lemos, José P S
2016-01-01
There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to...
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M.; Flachi, Antonino; Lemos, José P. S.
2016-06-01
There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti-de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti-de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.
Asymptotic behaviour of electro-$\\Lambda$ spacetimes
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\\Lambda=0$. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with the Bondi mass-loss formula in any un...
Lattice Quantum Gravity and Asymptotic Safety
Laiho, J; Coumbe, D; Du, D; Neelakanta, J T
2016-01-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we identify the target symmetry as the Hamiltonian canonical symmetry, which is closely related to, but not identical to, four-dimensional diffeomorphism invariance. After introducing and fine-tuning a non-trivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3/2, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue tha...
Asymptotic analysis of the Nörlund and Stirling polynomials
Directory of Open Access Journals (Sweden)
Mark Daniel Ward
2012-04-01
Full Text Available We provide a full asymptotic analysis of the N{\\"o}rlund polynomials and Stirling polynomials. We give a general asymptotic expansion---to any desired degree of accuracy---when the parameter is not an integer. We use singularity analysis, Hankel contours, and transfer theory. This investigation was motivated by a need for such a complete asymptotic description, with parameter 1/2, during this author's recent solution of Wilf's 3rd (previously Unsolved Problem.
ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT
Institute of Scientific and Technical Information of China (English)
A.Eisinberg; G.Franzè; N.Salerno
2001-01-01
Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2015-02-01
We compute, via numerical simulations, the nonperturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
Asymptotics of orthogonal polynomials and point perturbation on the unit circle
Wong, Manwah Lilian
2010-01-01
In the first five sections, we deal with the class of probability measures with asymptotically periodic Verblunsky coefficients of p-type bounded variation. The goal is to investigate the perturbation of the Verblunsky coefficients when we add a pure point to a gap of the essential spectrum. For the asymptotically constant case, we give an asymptotic formula for the orthonormal polynomials in the gap, prove that the perturbation term converges and show the limit explicitly. Furthermore, we prove that the perturbation is of bounded variation. Then we generalize the method to the asymptotically periodic case and prove similar results. In the last two sections, we show that the bounded variation condition can be removed if a certain symmetry condition is satisfied. Finally, we consider the special case when the Verblunsky coefficients are real with the rate of convergence being c_n . We prove that the rate of convergence of the perturbation is in fact O(c_n). In particular, the special case c_n = 1/n will serve ...
Asymptotic behavior of marginally trapped tubes in spherically symmetric black hole spacetimes
Williams, Catherine M.
We begin by reviewing some fundamental features of general relativity, then outline the mathematical definitions of black holes, trapped surfaces, and marginally trapped tubes, first in general terms, then rigorously in the context of spherical symmetry. We describe explicitly the reduction of Einstein's equation on a spherically symmetric 4-dimensional Lorentzian manifold to a system of partial differential equations on a subset of 2-dimensional Minkowski space. We discuss the asymptotic behavior of marginally trapped tubes in the Schwarzschild, Vaidya, and Reisner-Nordstrom solutions to Einstein's equations in spherical symmetry, as well as in Einstein-Maxwell-scalar field black hole spacetimes generated by evolving certain classes of asymptotically flat initial data. Our first main result gives conditions on a general stress-energy tensor Talphabeta in a spherically symmetric black hole spacetime that are sufficient to guarantee that the black hole will contain a marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Here "general" means that the matter model is arbitrary, subject only to a certain positive energy condition. A certain matter field decay rate, known as Price law decay in the literature, is not required per se for this asymptotic result, but such decay does imply that the marginally trapped tube has finite length with respect to the induced metric. In our second main result, we give two separate applications of the first theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.
Asymptotic behavior of a stochastic non-autonomous predator-prey model with impulsive perturbations
Wu, Ruihua; Zou, Xiaoling; Wang, Ke
2015-03-01
This paper is concerned with a stochastic non-autonomous Lotka-Volterra predator-prey model with impulsive effects. The asymptotic properties are examined. Sufficient conditions for persistence and extinction are obtained, our results demonstrate that the impulse has important effects on the persistence and extinction of the species. We also show that the solution is stochastically ultimate bounded under some conditions. Finally, several simulation figures are introduced to confirm our main results.
Institute of Scientific and Technical Information of China (English)
YIN; Changming; ZHAO; Lincheng; WEI; Chengdong
2006-01-01
In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
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....
ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS
Institute of Scientific and Technical Information of China (English)
ZHU Xiao-feng; LI Xiu-chun
2006-01-01
Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds are discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
Introduction to Asymptotic Giant Branch Stars
El Eid, Mounib F.
2016-04-01
A brief introduction on the main characteristics of the asymptotic giant branch stars (briefly: AGB) is presented. We describe a link to observations and outline basic features of theoretical modeling of these important evolutionary phases of stars. The most important aspects of the AGB stars is not only because they are the progenitors of white dwarfs, but also they represent the site of almost half of the heavy element formation beyond iron in the galaxy. These elements and their isotopes are produced by the s-process nucleosynthesis, which is a neutron capture process competing with the β- radioactive decay. The neutron source is mainly due to the reaction 13C(α,n)16O reaction. It is still a challenging problem to obtain the right amount of 13 C that can lead to s-process abundances compatible with observation. Some ideas are presented in this context.
Dimensionally reduced gravity theories are asymptotically safe
Energy Technology Data Exchange (ETDEWEB)
Niedermaier, Max E-mail: max@phys.univ-tours.fr
2003-11-24
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the 'area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow possesses a non-trivial UV stable fixed point at which the trace anomaly vanishes. The main exception is a minimal coupling of 4D Einstein gravity to massless free scalars, in which case the scalars decouple from gravity at the fixed point.
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...
Entropy Production during Asymptotically Safe Inflation
Directory of Open Access Journals (Sweden)
Martin Reuter
2011-01-01
Full Text Available The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.
Asymptotic Linear Stability of Solitary Water Waves
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Holographic Renormalization of Asymptotically Flat Gravity
Park, Miok
2012-01-01
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \\rightarrow \\infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.
Asymptotic sampling formulae for Lambda-coalescents
Berestycki, Julien; Limic, Vlada
2012-01-01
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.
Asymptotic analysis of ultra-relativistic charge
Burton, D A; Tucker, R W; Burton, David A.; Gratus, Jonathan; Tucker, Robin W.
2006-01-01
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneo...
Universality and asymptotic scaling in drilling percolation
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
Asymptotic Behavior of Excitable Cellular Automata
Durrett, R; Durrett, Richard; Griffeath, David
1993-01-01
Abstract: We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, the "shape" of its neighbor set, threshold value for contact updating, and number of possible states per site. GHM and CCA are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Earlier work by Fisch, Gravner, and Griffeath studied the ergodic behavior of these excitable cellular automata on Z^2, and identified two distinct (but closely-related) elaborate phase portraits as the parameters vary. In particular, they noted the emergence of asymptotic phase diagrams (and Euclidean dynamics) in a well-defined threshold-range scaling limit. In this study we present several rigorous results and som...
The asymptotic safety scenario in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Saueressig, Frank [Institute of Physics, University of Mainz, D-55099 Mainz (Germany)
2011-07-01
Asymptotic safety offers the possibility that gravity constitutes a consistent and predictive quantum field theory within Wilsons generalized framework of renormalization. The key ingredient of this scenario is a non-trivial fixed point of the gravitational renormalization group flow which governs the UV behavior of the theory. The fixed point itself thereby guarantees the absence of unphysical UV divergences while its associated finite-dimensional UV-critical surface ensures the predictivity of the resulting quantum theory. This talk summarizes the evidence for the existence of such a fixed point, which emerged from the flow equation for the effective average action, the gravitational beta-functions in 2+{epsilon} dimensions, the 2-Killing vector reduction of the gravitational path-integral and lattice simulations. Possible phenomenological consequences are discussed in detail.
Hydrodynamics, resurgence and trans-asymptotics
Basar, Gokce
2015-01-01
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...
Asymptotic 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...
Grassmann scalar fields and asymptotic freedom
Energy Technology Data Exchange (ETDEWEB)
Palumbo, F. [INFN, Laboratori Nazionali di Frascati, Rome (Italy)
1996-03-01
The authors extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in particle physics is related to the possibility that they describe fermionic composites analogous to the Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive self interaction.
Modeling of nanoplastic by asymptotic homogenization method
Institute of Scientific and Technical Information of China (English)
张为民; 何伟; 李亚; 张平; 张淳源
2008-01-01
The so-called nanoplastic is a new simple name for the polymer/layered silicate nanocomposite,which possesses excellent properties.The asymptotic homogenization method(AHM) was applied to determine numerically the effective elastic modulus of a two-phase nanoplastic with different particle aspect ratios,different ratios of elastic modulus of the effective particle to that of the matrix and different volume fractions.A simple representative volume element was proposed,which is assumed that the effective particles are uniform well-aligned and perfectly bonded in an isotropic matrix and have periodic structure.Some different theoretical models and the experimental results were compared.The numerical results are good in agreement with the experimental results.
Chiral fermions in asymptotically safe quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2016-05-15
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)
Asymptotic 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.
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.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval
Institute of Scientific and Technical Information of China (English)
Quansen Jiu; Tao Pan
2003-01-01
This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) =u_,u(1,t) = u+ and the initial data u(x, 0) = u0(x), where u_ ≠ u+ and f is a given function satisfying f″ (u) ＞ 0 for u under consideration. By means of energy estimates method and under some more regular conditions on the initial data, both the global existence and the asymptotic behavior are obtained. When u_ ＜ u+, which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for u_ ＞ u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, which means that |u_ - u+| is small. Moreover, exponential decay rates are both given.
离散时延双神经元网络的渐近稳定性%Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays
Institute of Scientific and Technical Information of China (English)
李绍文; 李绍荣; 廖晓峰
2003-01-01
New sufficient conditions for the asymptotic stability of a two-neuron network with different time delays are derived. These conditions lead to delay-dependent and delay-independent asymptotic stability. Our results are shown to be less conservative and restrictive than those reported in the literature. Some examples are given to illustrate the correctness of our results.
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.
Numerical and asymptotic aspects of parabolic cylinder functions
Temme, N.M.
2000-01-01
Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are
Asymptotic 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.
Asymptotic Hyperstability of Dynamic Systems with Point Delays
Directory of Open Access Journals (Sweden)
M. De la Sen
2005-01-01
Full Text Available It is proved that a linear time-invariant system with internal point delays is asymptotically hyperstable independent of the delays if an associate delay-free system is asymptotically hyperstable and the delayed dynamics are sufficiently small.
Small-x asymptotics of structure function $g_2$
Ermolaev, B I
1997-01-01
Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.
Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
Wei Shi-long; Guo Wei-ping
2015-01-01
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
Global asymptotic stability of cellular neural networks with multiple delays
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.
Diversity-Multiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems
Loyka, Sergey
2007-01-01
Diversity-multiplexing tradeoff (DMT) presents a compact framework to compare various MIMO systems and channels in terms of the two main advantages they provide (i.e. high data rate and/or low error rate). This tradeoff was characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The asymptotic DMT overestimates the finite-SNR one [2]. In this paper, using the recent results on the asymptotic (in the number of antennas) outage capacity distribution, we derive and analyze the finite-SNR DMT for a broad class of channels (not necessarily Rayleigh fading). Based on this, we give the convergence conditions for the asymptotic DMT to be approached by the finite-SNR one. The multiplexing gain definition is shown to affect critically the convergence point: when the multiplexing gain is defined via the mean (ergodic) capacity, the convergence takes place at realistic SNR values. Furthermore, in this case the diversity gain can also be used to estimate the outage probabilit...
A generalisation of the Gilbert-Varshamov bound and its asymptotic evaluation
Tolhuizen, Ludo
2011-01-01
The Gilbert-Varshamov (GV) lower bound on the maximum cardinality of a q-ary code of length n with minimum Hamming distance at least d can be obtained by application of Turan's theorem to the graph with vertex set {0,1,..,q-1}^n in which two vertices are joined if and only if their Hamming distance is at least d. We generalize the GV bound by applying Turan's theorem to the graph with vertex set C^n, where C is a q-ary code of length m and two vertices are joined if and only if their Hamming distance at least d. We asymptotically evaluate the resulting bound for n-> \\infty and d \\delta mn for fixed \\delta > 0, and derive conditions on the distance distribution of C that are necessary and sufficient for the asymptotic generalized bound to beat the asymptotic GV bound. By invoking the Delsarte inequalities, we conclude that no improvement on the asymptotic GV bound is obtained. By using a sharpening of Turan's theorem due to Caro and Wei, we improve on our bound. It is undecided if there exists a code C for whi...
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
Hod, Shahar
2015-01-01
The spheroidal harmonics $S_{lm}(\\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues $\\{A_{lm}(c)\\}$ of these functions have been determined by many authors. However, it should be emphasized that all previous asymptotic analyzes were restricted either to the regime $m\\to\\infty$ with a fixed value of $c$, or to the complementary regime $|c|\\to\\infty$ with a fixed value of $m$. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both $m$ and $c$. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit $m\\to\\infty$ and $|c|\\to\\infty$ with a fixed $m/c$ ratio.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
Hod, Shahar
2015-06-01
The spheroidal harmonics Slm (θ ; c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm (c) } of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m → ∞ with a fixed value of c, or to the complementary regime | c | → ∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m → ∞ and | c | → ∞ with a fixed m / c ratio.
Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals
Pan, Chi-Ruei; Chai, Jeng-Da
2013-01-01
Aiming to remedy the incorrect asymptotic behavior of conventional semilocal exchange-correlation (XC) density functionals for finite systems, we propose an asymptotic correction scheme, wherein an exchange density functional whose functional derivative has the correct (-1/r) asymptote can be directly added to any semilocal density functional. In contrast to semilocal approximations, our resulting exchange kernel in reciprocal space exhibits the desirable singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for describing the excitonic effects in non-metallic solids. By applying this scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the properties that are sensitive to the asymptote are significantly improved, while the predictions of the properties that are insensitive to the asymptote remain essentially the same as PBE. Relative to the popular model XC potential scheme, our scheme is sig...
INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION
Directory of Open Access Journals (Sweden)
A. I. Popov
2015-09-01
Full Text Available Subject of Research. Creation of asymptotic expansions for solutions of partial differential equations with small parameter reduces, usually, to consequent solving of the Sturm-Liouville problems chain. To find some term of the series, the non-homogeneous Sturm-Liouville problem with the inhomogeneity depending on the previous term needs to be solved. At the same time, the corresponding homogeneous problem has a non-trivial solution. Hence, the solvability problem occures for the non-homogeneous Sturm-Liouville problem for functions or formal power series. The paper deals with creation of such asymptotic expansions. Method. To prove the necessary condition, we use conventional integration technique of the whole equation and boundary conditions. To prove the sufficient condition, we create an appropriate Cauchy problem (which is always solvable and analyze its solution. We deal with the general case of power series and make no hypotheses about the series convergence. Main Result. Necessary and sufficient conditions of solvability for the non-homogeneous Sturm-Liouville problem in general case for formal power series are proved in the paper. As a particular case, the result is valid for functions instead of formal power series. Practical Relevance. The result is usable at creation of the solutions for partial differential equation in the form of power series. The result is general and is applicable to particular cases of such solutions, e.g., to asymptotic series or to functions (convergent power series.
Zollanvari, Amin; Genton, Marc G
2013-08-01
We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
Zollanvari, Amin
2013-05-24
We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion
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Dan Li
2014-01-01
Full Text Available This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of our model; (c the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival may lead to extinction of the population.
Directory of Open Access Journals (Sweden)
Wuneng Zhou
2014-01-01
Full Text Available The problem of almost sure (a.s. asymptotic adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching is researched. Firstly, we proposed a new criterion of a.s. asymptotic stability for a general neutral-type stochastic differential equation which extends the existing results. Secondly, based upon this stability criterion, by making use of Lyapunov functional method and designing an adaptive controller, we obtained a condition of a.s. asymptotic adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching. The synchronization condition is expressed as linear matrix inequality which can be easily solved by Matlab. Finally, we introduced a numerical example to illustrate the effectiveness of the method and result obtained in this paper.
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Liang-cai Zhao
2012-01-01
Full Text Available The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.
Asymptotic behavior of the likelihood function of covariance matrices of spatial Gaussian processes
DEFF Research Database (Denmark)
Zimmermann, Ralf
2010-01-01
The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood......: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood-based Kriging model training...
A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0 Spaces
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Ali Abkar
2017-02-01
Full Text Available In this paper we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings on CAT(0 spaces. We prove a strong convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm.
Asymptotically anti-de Sitter space-times: symmetries and conservation laws revisited
Barnich, G.; Brandt, F.; Claes, K.
2004-02-01
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat metric induced on the boundary. The fall-off conditions for the metric perturbations that guarantee finiteness of the associated conserved charges are derived.
Institute of Scientific and Technical Information of China (English)
Xu Rui(徐瑞); Chen Lansun(陈兰荪); M.A.J. Chaplain
2003-01-01
A delayed n-species nonautonomous Lotka-Volterra type competitive systemwithout dominating instantaneous negative feedback is investigated. By means of a suitableLyapunov functional, sufficient conditions are derived for the global asymptotic stability ofthe positive solutions of the system. As a corollary, it is shown that the global asymptoticstability of the positive solution is maintained provided that the delayed negative feedbacksdominate other interspecific interaction effects with delays and the delays are sufficientlysmall.
A family of asymptotically stable control laws for flexible robots based on a passivity approach
Lanari, Leonardo; Wen, John T.
1991-01-01
A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.
On the Asymptotic of an Eigenvalue Problem with 2 Interior Singularities
Indian Academy of Sciences (India)
A Neamaty; S Haghaieghy
2009-11-01
In this paper we consider the linear differential equation of the form $$-y''(x)+q(x)y(x)= y(x),\\quad -∞ < a < x < b < ∞$$ where satisfies Dirichlet boundary conditions and is a real-valued function which has even number of singularities at $c_1,\\ldots,c_{2n}\\in(a, b)$. We will study the asymptotic eigenvalue near the singularity points.
Delay-Dependent Asymptotic Stability of Cohen-Grossberg Models with Multiple Time-Varying Delays
Directory of Open Access Journals (Sweden)
Xiaofeng Liao
2007-01-01
Full Text Available Dynamical behavior of a class of Cohen-Grossberg models with multiple time-varying delays is studied in detail. Sufficient delay-dependent criteria to ensure local and global asymptotic stabilities of the equilibrium of this network are derived by constructing suitable Lyapunov functionals. 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.
Guesmia, Senoussi
2008-05-01
We study here the asymptotic behavior of the solution of a hyperbolic problem defined on a cylindrical domain when l-->[infinity]. We show that, under very general assumptions, the solution of this problem converges faster than any power of towards the solution of another hyperbolic problem, defined on [0,T]×[omega], in any bounded subdomain. We give both necessary and sufficient conditions for this convergence to occur.
Directory of Open Access Journals (Sweden)
Bin-Chao Deng
2014-01-01
Full Text Available This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.
Global asymptotic stability of a class of nonlinear systems with parametric uncertainty
Institute of Scientific and Technical Information of China (English)
Cai Xiushan; Lǜ Ganyun; Zhang Changfiang; He Xiuhui
2009-01-01
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems axe deduced. The simulation shows the effectiveness of the method.
Asymptotic Weighted-Periodicity of the Impulsive Parabolic Equation with Time Delay
Institute of Scientific and Technical Information of China (English)
Jin-liang Wang; Hui-feng Li
2007-01-01
The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted.The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".
Jacobi-Sobolev Orthogonal Polynomials: Asymptotics for N-Coherence of Measures
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Marcellán Francisco
2011-01-01
Full Text Available Let us introduce the Sobolev-type inner product , where and , , with and for all A Mehler-Heine-type formula and the inner strong asymptotics on as well as some estimates for the polynomials orthogonal with respect to the above Sobolev inner product are obtained. Necessary conditions for the norm convergence of Fourier expansions in terms of such Sobolev orthogonal polynomials are given.
Asymptotic state behaviour and its modeling for saturated sand
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A new double hardening elasto-plastic model is proposed in this paper based on the existing unified hardening model (UH model). By assuming that there is part coupling effect between the plastic volumetric strain and plastic shear strain, hardening parameters consisting of a coupled and an uncoupled components are adopted in this model. A unique feature of this model is that it can describe not only the conventional drained and undrained behaviors of soil, but also the stress-strain relationships of soil under partially drained conditions which can be volumetric compression or dilation. Adopting the asymptotic state concept, simple equations for estimating the limiting stress ratio under undrained or earth pressure at rest (i.e. K0) conditions are derived. The new model is relatively simple to be adopted in practice for two reasons. First, the same soil parameters as in Cam-clay model are used except the addition of one extra parameter, the stress ratio at the characteristic state. Second, all the parameters can be determined using conventional triaxial compression tests.
Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons
Côte, Raphaël; Muñoz, Claudio; Pilod, Didier; Simpson, Gideon
2016-05-01
We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation appearing in Plasma Physics, and having mixed KdV and nonlinear Schrödinger (NLS) dynamics, are strongly asymptotically stable in the energy space. We also prove that the sum of well-arranged solitons is stable in the same space. Orbital stability of ZK solitons is well-known since the work of de Bouard [Proc R Soc Edinburgh 126:89-112, 1996]. Our proofs follow the ideas of Martel [SIAM J Math Anal 157:759-781, 2006] and Martel and Merle [Math Ann 341:391-427, 2008], applied for generalized KdV equations in one dimension. In particular, we extend to the high dimensional case several monotonicity properties for suitable half-portions of mass and energy; we also prove a new Liouville type property that characterizes ZK solitons, and a key Virial identity for the linear and nonlinear part of the ZK dynamics, obtained independently of the mixed KdV-NLS dynamics. This last Virial identity relies on a simple sign condition which is numerically tested for the two and three dimensional cases with no additional spectral assumptions required. Possible extensions to higher dimensions and different nonlinearities could be obtained after a suitable local well-posedness theory in the energy space, and the verification of a corresponding sign condition.
Eventually and asymptotically positive semigroups on Banach lattices
Daners, Daniel; Glück, Jochen; Kennedy, James B.
2016-09-01
We develop a theory of eventually positive C0-semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the corresponding Cauchy problem becomes positive for large times. We give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators, complementing existing results on spaces of continuous functions. This enables us to treat a range of new examples including the square of the Laplacian with Dirichlet boundary conditions, the bi-Laplacian on Lp-spaces, the Dirichlet-to-Neumann operator on L2 and the Laplacian with non-local boundary conditions on L2 within the one unified theory. We also introduce and analyse a weaker notion of eventual positivity which we call "asymptotic positivity", where trajectories associated with positive initial data converge to the positive cone in the Banach lattice as t → ∞. This allows us to discuss further examples which do not fall within the above-mentioned framework, among them a network flow with non-positive mass transition and a certain delay differential equation.
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.
Adaptive molecular resolution approach in Hamiltonian form: An asymptotic analysis
Zhu, Jinglong; Klein, Rupert; Delle Site, Luigi
2016-10-01
Adaptive molecular resolution approaches in molecular dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer (transition) region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined, and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size, and thus a Hamiltonian approach such as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes.
Asymptotics of Heavy-Meson Form Factors
Grozin, A.G.; Grozin, Andrey G.; Neubert, Matthias
1997-01-01
Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\\ll |v\\cdot v'|\\ll m_Q/\\Lambda$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\\cdot v'|\\gg m_Q/\\Lambda$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\\cdot v'|\\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\\cdot v'\\sim m_b/\\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\\cdot v'\\sim -m_b/\\Lambda$). We obtain the evolution equations and sum rules ...
Truly Minimal Unification Asymptotically Strong Panacea ?
Aulakh, Charanjit S
2002-01-01
We propose Susy GUTs have a UV {\\it{attractor}} at $E\\sim \\Lambda_{cU} \\sim 10^{17} GeV $ where gauge symmetries ``confine'' forming singlet condensates at scales $E\\sim\\Lambda_{cU}$. The length $l_U\\sim \\Lambda_{cU}^{-1}$ characterizies the {\\it{size}} of gauge non- singlet particles yielding a picture dual to the Dual Standard model of Vachaspati. This Asymptotic Slavery (AS) fixed point is driven by realistic Fermion Mass(FM) Higgs content which implies AS. This defines a dynamical morphogenetic scenario dependent on the dynamics of UV strong N=1 Susy Gauge-Chiral(SGC) theories. Such systems are already understood in the AF case but ignored in the AS case. Analogy to the AFSGC suggests the perturbative SM gauge group of the Grand Desert confines at GUT scales i.e GUT symmetry is ``non-restored''. Restoration before confinement and self-inconsistency are the two other (less likely) logical possibilities. Truly Minimal (TM) SU(5) and SO(10) models with matter and FM Higgs only are defined; AM (adjoint multip...
Asymptotic dynamics of inertial particles with memory
Langlois, Gabriel Provencher; Haller, George
2014-01-01
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $\\mathcal O(\\epsilon)$-close to the fluid velocity, where $0<\\epsilon\\ll 1$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of existence and uniqueness of global solutions to the Maxey--Riley equation, a nonlinear system of fractional-order differential equ...
Asymptotic Solutions of Serial Radial Fuel Shuffling
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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.
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 Solution of the Theory of Shells Boundary Value Problem
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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.
Uniform Asymptotic Expansion for the Incomplete Beta Function
Nemes, Gergő; Olde Daalhuis, Adri B.
2016-10-01
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
Asymptotic failure rate of a continuously monitored system
Energy Technology Data Exchange (ETDEWEB)
Grall, A. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: antoine.grall@utt.fr; Dieulle, L. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: laurence.dieulle@utt.fr; Berenguer, C. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: christophe.berenguer@utt.fr; Roussignol, M. [Laboratoire d' Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, 5 bd Descartes, Champs sur Marne, 77454 Marne la Vallee, Cedex 2 (France)]. E-mail: michel.roussignol@univ-mlv.fr
2006-02-01
This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.
Kolmogorov turbulence by matched asymptotic expansions
Lundgren, Thomas S.
2003-04-01
The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.
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 ...
Asymptotics of 6j and 10j symbols
Freidel, L; Freidel, Laurent; Louapre, David
2003-01-01
It is well known that the building blocks for state sum models of quantum gravity is given by 6j and 10j symbols. In this work we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics we recover the Ponzano-Regge formula for the SU(2) 6j-symbol. We show how the asymptotics of the various Lorentzian $6j$-symbols can be obtained by the same methods. Finally we compute the asymptotic expansion of the 10j symbol which is shown to be non-oscillating in agreement with a recent result of Baez et al. We discuss the physical origin of these behavior and a way to modify the Barrett-Crane model to cure this disease.
Research on temperature profiles of honeycomb regenerator with asymptotic analysis
Institute of Scientific and Technical Information of China (English)
AI Yuan-fang; MEI Chi; HUANG Guo-dong; JIANG Shao-jian; CHEN Hong-rong
2006-01-01
An asymptotic semi-analytical method for heat transfer in counter-flow honeycomb regenerator is proposed. By introducing a combined heat-transfer coefficient between the gas and solid phase, a heat transfer model is built based on the thin-walled assumption. The dimensionless thermal equation is deduced by considering solid heat conduction along the passage length. The asymptotic analysis is used for the small parameter of heat conduction term in equation. The first order asymptotic solution to temperature distribution under weak solid heat conduction is achieved after Laplace transformation through the multiple scales method and the symbolic manipulation function in MATLAB. Semi-analytical solutions agree with tests and finite-difference numerical results. It is proved possible for the asymptotic analysis to improve the effectiveness, economics and precision of thermal research on regenerator.
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
Asymptotic distributions in the projection pursuit based canonical correlation analysis
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.
High frequency asymptotics of antenna/structure interactions
Coats, J.
2002-01-01
This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors. We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point. In chapter 5 we review and extend the asymptotic results concerning illuminat...
Quick asymptotic expansion aided by a variational principle
Energy Technology Data Exchange (ETDEWEB)
Hameiri, Eliezer [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2013-02-15
It is shown how expanding asymptotically a variational functional can yield the asymptotic expansion of its Euler equation. The procedure is simple but novel and requires taking the variation of the expanded functional with respect to the leading order of the originally unknown function, even though the leading order of this function has already been determined in a previous order. An example is worked out that of a large aspect ratio tokamak plasma equilibrium state with relatively strong flows and high plasma beta.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah; Pawlowski, Jan M
2011-01-01
We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Asymptotic freedom of Yang-Mills theory with gravity
Energy Technology Data Exchange (ETDEWEB)
Folkerts, Sarah, E-mail: Sarah.Folkerts@physik.uni-muenchen.de [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom); Pawlowski, Jan M. [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); ExtreMe Matter Inst. EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany)
2012-03-19
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
An asymptotically exact theory of smart sandwich shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.
Asymptotic behaviour for a diffusion equation governed by nonlocal interactions
Ovono, Armel Andami
2010-01-01
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.
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.
ASYMPTOTIC BEHAVIOR OF ECKHOFF'S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined.Asymptotic behavior of approximate calculation of the so-called "jumps" is studied and asymptotic L2 constants of the rate of convergence of the method are computed.
High-order topological asymptotic expansion for Stokes equations
Directory of Open Access Journals (Sweden)
Mohamed Abdelwahed
2016-06-01
Full Text Available We use the topological sensitivity analysis method to solve various optimization problems. It consists of studying the asymptotic expansion of the objective function relative to a perturbation of the domain topology. This expansion becomes insufficient in some applications when it is limited to the first order topological derivative. We present a new topological sensitivity analysis for the Stokes equations based on a high order asymptotic expansion. The derived result is valid for different class of shape functions.
Asymptotical stability analysis of linear fractional differential systems
Institute of Scientific and Technical Information of China (English)
LI Chang-pin; ZHAO Zhen-gang
2009-01-01
It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts,electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.
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.
Asymptotic symmetries and charges in de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Anninos, Dionysios; Ng, Gim Seng; Strominger, Andrew, E-mail: gng@fas.harvard.edu [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA 02138 (United States)
2011-09-07
The asymptotic symmetry group (ASG) at future null infinity (I{sup +}) of asymptotically four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I{sup +}. Finite charges are constructed for each choice of ASG generator together with a two-surface on I{sup +}. A conservation equation is derived relating the evolution of the charges with the radiation flux through I{sup +}.
Asymptotic behaviour of extinction probability of interacting branching collision processes
Chen, Anyue; Li, Junping; Chen, Yiqing; Zhou, Dingxuan
2014-01-01
Although the exact expressions for the extinction probabilities of the Interacting Branching Collision Processes (IBCP) were very recently given by Chen et al. [4], some of these expressions are very complicated; hence, useful information regarding asymptotic behaviour, for example, is harder to obtain. Also, these exact expressions take very different forms for different cases and thus seem lacking in homogeneity. In this paper, we show that the asymptotic behaviour of these extr...
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Directory of Open Access Journals (Sweden)
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
Random attractors for asymptotically upper semicompact multivalue random semiflows
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
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 behavior of large polygonal Wilson loops in confining gauge theories
Pobylitsa, P V
2016-01-01
In the framework of effective string theory (EST), the asymptotic behavior of a large Wilson loop in confining gauge theories can be expressed via Laplace determinant with Dirichlet boundary condition on the Wilson contour. For a general polygonal region, Laplace determinant can be computed using the conformal anomaly and Schwarz-Christoffel transformation. One can construct ratios of polygonal Wilson loops whose large-size limit can be expressed via computable Laplace determinants and is independent of the (confining) gauge group. These ratios are computed for hexagon polygons both in EST and by Monte Carlo (MC) lattice simulations for the tree-dimensional lattice Z2 gauge theory (dual to Ising model) near its critical point. For large hexagon Wilson loops a perfect agreement is observed between the asymptotic EST expressions and the lattice MC results.
Asymptotic analysis for Nakagami-m fading channels with relay selection
Zhong, Caijun
2011-06-01
In this paper, we analyze the asymptotic outage probability performance of both decode-and-forward (DF) and amplify-and-forward (AF) relaying systems using partial relay selection and the "best" relay selection schemes for Nakagami-m fading channels. We derive their respective outage probability expressions in the asymptotic high signal-to-noise ratio (SNR) regime, from which the diversity order and coding gain are analyzed. In addition, we investigate the impact of power allocation between the source and relay terminals and derive the diversity-multiplexing tradeoff (DMT) for these relay selection systems. The theoretical findings suggest that partial relay selection can improve the diversity of the system and can achieve the same DMT as the "best" relay selection scheme under certain conditions. © 2011 IEEE.
Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time
Institute of Scientific and Technical Information of China (English)
G Yin; Dung Tien Nguyen
2009-01-01
This work develops asymptotic expansions for solutions of systems of backward equations of timeinhomogeneons Markov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Markov chains often have large state spaces, which make the computational tasks infeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε＞ 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Markov chains including also transient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions are constructed. Then error bounds are obtained.
Vagov, A; Zalipaev, V V
2009-01-01
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wavefunctions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.
Asymptotical stability of stochastic neural networks with multiple time-varying delays
Zhou, Xianghui; Zhou, Wuneng; Dai, Anding; Yang, Jun; Xie, Lili
2015-03-01
The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations
Directory of Open Access Journals (Sweden)
Bonforte Matteo
2007-01-01
Full Text Available We investigate local and global properties of positive solutions to the fast diffusion equation in the good exponent range , corresponding to general nonnegative initial data. For the Cauchy problem posed in the whole Euclidean space , we prove sharp local positivity estimates (weak Harnack inequalities and elliptic Harnack inequalities; also a slight improvement of the intrinsic Harnack inequality is given. We use them to derive sharp global positivity estimates and a global Harnack principle. Consequences of these latter estimates in terms of fine asymptotics are shown. For the mixed initial and boundary value problem posed in a bounded domain of with homogeneous Dirichlet condition, we prove weak, intrinsic, and elliptic Harnack inequalities for intermediate times. We also prove elliptic Harnack inequalities near the extinction time, as a consequence of the study of the fine asymptotic behavior near the finite extinction time.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Global robust asymptotic stability of variable-time impulsive BAM neural networks.
Saylı, Mustafa; Yılmaz, Enes
2014-12-01
In this paper, the global robust asymptotic stability of the equilibrium point for a more general class of bidirectional associative memory (BAM) neural networks with variable time of impulses is addressed. Unlike most existing studies, the case of non-fix time impulses is focused on in the present study. By means of B-equivalence method, which was introduced in Akhmet (2003, 2005, 2009, 2010), Akhmet and Perestyuk (1990) and Akhmet and Turan (2009), we reduce these networks to a fix time impulsive neural networks system. Sufficient conditions ensuring the existence, uniqueness and global robust asymptotic stability of the equilibrium point are obtained by employing an appropriate Lyapunov function and linear matrix inequality (LMI). Finally, we give one illustrative example to show the effectiveness of the theoretical results.
Institute of Scientific and Technical Information of China (English)
Shisheng ZHANG; Lin WANG; Yunhe ZHAO
2013-01-01
The purpose of this article is first to introduce the concept of multi-valued totally Quasi-φ-asymptotically nonexpansive semi-groups,which contains many kinds of semigroups as its special cases,and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-φ-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces.The results presented in this article improve and extend the corresponding results announced by many authors recently.
Wu, Ailong; Zeng, Zhigang
2016-02-01
We show that the ω-periodic fractional-order fuzzy neural networks cannot generate non-constant ω-periodic signals. In addition, several sufficient conditions are obtained to ascertain the boundedness and global Mittag-Leffler stability of fractional-order fuzzy neural networks. Furthermore, S-asymptotical ω-periodicity and global asymptotical ω-periodicity of fractional-order fuzzy neural networks is also characterized. The obtained criteria improve and extend the existing related results. To illustrate and compare the theoretical criteria, some numerical examples with simulation results are discussed in detail.
Directory of Open Access Journals (Sweden)
Wei-Qi Deng
2013-01-01
Full Text Available Let be a nonempty, closed, and convex subset of a real uniformly convex Banach space . Let and be two infinite families of asymptotically nonexpansive mappings from to itself with . For an arbitrary initial point , is defined as follows: , , , where and with and satisfying the positive integer equation: , ; and are two countable subsets of and respectively; , , , , , and are sequences in for some , satisfying and . Under some suitable conditions, a strong convergence theorem for common fixed points of the mappings and is obtained. The results extend those of the authors whose related researches are restricted to the situation of finite families of asymptotically nonexpansive mappings.
Nal, P L
2002-01-01
We consider the asymptotic stability and the boundedness with probability one of solutions of linear lto stochastic differential equations not reduced to the Cauchy form and give some numerical examples to show that our sufficient conditions for the asymptotic stability with probability one of solutions are more general and more effective than those of Korenevskij and Mitropoloshij. Moreover, our results can also be applied to the case when the unperturbed linear deterministic system is not assumed to be stable.
Testing monotonicity of a hazard: asymptotic distribution theory
Groeneboom, Piet
2011-01-01
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates, which use the monotonicity constraint, and either the empirical distribution function or the empirical cumulative hazard. They measure the excursions of the empirical estimates with respect to the isotonic estimates, due to local non-monotonicity. Asymptotic normality of the test statistics, if the hazard is strictly increasing on [0,a], is established under mild conditions. This is done by first approximating the global empirical distance by an distance with respect to the underlying distribution function. The resulting integral is treated as sum of increasingly many local integrals to which a CLT can be applied. The behavior of the local integrals is determined by a canonical process: the difference between the stochastic process x -> W(x)+x^2 where W is standard two-sid...
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.
Asymptotic theory of nonparametric regression estimates with censored data
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right_censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, Cp and FPE criteria in the process of selecting the parameters.
Precise Asymptotics of Complete Moment Convergence on Moving Average
Institute of Scientific and Technical Information of China (English)
Zheng Yan LIN; Hui ZHOU
2012-01-01
Let {(ξ)i,-∞ ＜ i ＜ ∞} be a doubly infinite sequence of identically distributed (φ)-mixing random variables with zero means and finite variances,{ai,-∞ ＜ i ＜ ∞} be an absolutely summable sequence of real numbers and Xk =∑+∞ i=-∞ aiξi+k be a moving average process.Under some proper moment conditions,the precise asymptotics are established for limε↘0 1/-logε∞Σn=1 1/n2 ES2nI{｜Sn｜≥nε} =2EZ2.where Z ～ N(0,γ2),γ2 =σ2(∑∞ i=-∞ ai)2,and lim ε↘0 ε2δ Σ∞ n=2 (log n)δ-1/n2 ES2nI{｜Sn｜≥√n log nε}=γ2δ+2/δE｜N｜2δ+2.
Institute of Scientific and Technical Information of China (English)
Cuimei ZHANG; Wencheng CHEN; Yu YANG
2006-01-01
In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Holling Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.
Directory of Open Access Journals (Sweden)
Gurucharan Singh Saluja
2010-01-01
Full Text Available In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.
Directory of Open Access Journals (Sweden)
Yazheng Dang
2013-01-01
Full Text Available Inspired by the Moudafi (2010, we propose an algorithm for solving the split common fixed-point problem for a wide class of asymptotically quasi-nonexpansive operators and the weak and strong convergence of the algorithm are shown under some suitable conditions in Hilbert spaces. The algorithm and its convergence results improve and develop previous results for split feasibility problems.
LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks
Institute of Scientific and Technical Information of China (English)
ZHANG Sen-lin; LIU Mei-qin
2005-01-01
Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is advanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs' stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).
Asymptotic normality of the QMLE in the level-effect ARCH model
DEFF Research Database (Denmark)
Dahl, Christian Møller; Iglesias, Emma M.
In this paper consistency and asymptotic normality of the quasi maximum like-lihood estimator in the level-effect ARCH model of Chan, Karolyi, Longstaff and Sanders (1992) is established. We consider explicitly the case where the parameters of the conditional heteroskedastic process...... are in the stationary region and discuss carefully how the results can be extended to the region where the conditional heteroskedastic process is nonstationary. The results illustrate that Jensen and Rahbek's (2004a,2004b) approach can be extended further than to traditional ARCH and GARCH models....
Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid
Liu, Guowei
2016-10-01
This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and ɛ -regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the "Condition (C)", the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.
Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlo cal Source
Institute of Scientific and Technical Information of China (English)
JIANG Liang-jun
2015-01-01
In this paper, we deal with the blow-up property of the solution to the diffusion equation ut=∆u+a(x)f(u) RΩh(u)dx, x∈Ω, t>0 subject to the null Dirichlet boundary condition. We will show that under certain conditions, the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Especially, in case of f(s)=sp, h(s)=sq, 0≤p≤1, p+q>1, we obtain the asymptotic behavior of the blow up solution.
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
Asymptotics of bivariate generating functions with algebraic singularities
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations
Directory of Open Access Journals (Sweden)
Aimin Liu
2014-01-01
Full Text Available This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations dxt=Atxt+Ft,xt,xtdt+H(t,xt,xt∘dW(t. A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup {Tt}t≥0 is essentially removed, which is generated by the linear densely defined operator A∶D(A⊂L2(ℙ,ℍ→L2(ℙ,ℍ, only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.
Institute of Scientific and Technical Information of China (English)
薛强; 梁冰; 刘晓丽; 李宏艳
2003-01-01
The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport , a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid-solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure,pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure-saturation-permeability in laboratory.
The asymptotic field of a dynamically growing crack in a viscoelastic materia
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A mechanical model of a fracturing viscoelastic material was developed to investigate viscous effects in a dynamically growing crack-tip field.It was shown that in the stable creep-growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, and stress and strain have the same singularity, namely, (σ,ε)αγ-1/(n-1).The asymptotic solution of separating variables of stress, stain and displacement in the crack-tip field was obtained by asymptotic analysis, and the resulting numerical value of stress and strain in the crack-tip field was obtained by the shooting method and the boundary condition of a mode I crack.Through numerical calculation, it was shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M.When n→∞, the asymptotic solution of a viscoelastic material can be degenerated into that of Freund's elastic-ideally plastic material by analyzing basic equations.
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
asymptotics for open-loop window flow control
Directory of Open Access Journals (Sweden)
Arthur W. Berger
1994-01-01
Full Text Available An open-loop window flow-control scheme regulates the flow into a system by allowing at most a specified window size W of flow in any interval of length L. The sliding window considers all subintervals of length L, while the jumping window considers consecutive disjoint intervals of length L. To better understand how these window control schemes perform for stationary sources, we describe for a large class of stochastic input processes the asymptotic behavior of the maximum flow in such window intervals over a time interval [0,T] as T and Lget large, with T substantially bigger than L. We use strong approximations to show that when T≫L≫logT an invariance principle holds, so that the asymptotic behavior depends on the stochastic input process only via its rate and asymptotic variability parameters. In considerable generality, the sliding and jumping windows are asymptotically equivalent. We also develop an approximate relation between the two maximum window sizes. We apply the asymptotic results to develop approximations for the means and standard deviations of the two maximum window contents. We apply computer simulation to evaluate and refine these approximations.
Directory of Open Access Journals (Sweden)
M. A. Davydova
2016-01-01
Full Text Available In the present work the model boundary value problem for a stationary singularly perturbed reaction-diﬀusion-advection equation arising at the description of gas impurity transfer processes in an ecosystem ”forest – swamp” is considered. Application of a boundary functions method and an asymptotic method of diﬀerential inequalities allow to construct an asymptotics of the boundary layer type solution, to prove the existence of the solution with such an asymptotics and its asymptotic stability by Lyapunov as the stationary solution of the corresponding parabolic problem with the deﬁnition of local area of boundary layer type solution formation. The latter has a certain importance for applications, since it allows to reveal the solution describing one of the most probable conditions of the ecosystem. In the ﬁnal part of the work suﬃcient conditions for existence of solutions with interior transitional layers (contrast structures are discussed.
Hahn, Y. K.
2014-12-01
The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree-Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.
Detailed ultraviolet asymptotics for AdS scalar field perturbations
Evnin, Oleg
2016-01-01
We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.
The unitary conformal field theory behind 2D Asymptotic Safety
Nink, Andreas
2015-01-01
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge $c=25$. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a...
Asymptotics of a singularly perturbed GUE partition function
Mezzadri, F
2010-01-01
We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.
Scalar hairy black holes and solitons in asymptotically flat spacetimes
Nucamendi, U; Nucamendi, Ulises; Salgado, Marcelo
2003-01-01
A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\\phi)$ of the theory is ``finetuned'' such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture.
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 symmetries of QED and Weinberg's soft photon theorem
Campiglia, Miguel
2015-01-01
Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.
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...
Holography of 3D Asymptotically Flat Black Holes
Fareghbal, Reza
2014-01-01
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking flat-space limit (zero cosmological constant limit) of New Massive Gravity (NMG). We propose that the dual field theory of the flat-space limit of NMG can be described by a Contracted Conformal Field Theory (CCFT). Using Flat/CCFT correspondence we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. Furthermore, by taking appropriate limit of the Cardy formula in the parent CFT, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.
Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials
Gómez-Ullate, David; Milson, Robert
2012-01-01
The location and asymptotic behaviour for large n of the zeros of exceptional Jacobi and Laguerre polynomials are discussed. The zeros of exceptional polynomials fall into two classes: the regular zeros, which lie in the interval of orthogonality and the exceptional zeros, which lie outside that interval. We show that the regular zeros have two interlacing properties: one is the natural interlacing between consecutive polynomials as a consequence of their Sturm-Liouville character, while the other one shows interlacing between the zeros of exceptional and classical polynomials. A generalization of the classical Heine-Mehler formula is provided for the exceptional polynomials, which allows to derive the asymptotic behaviour of their regular zeros. We also describe the location and the asymptotic behaviour of the exceptional zeros, which converge for large n to fixed values.
Holography of 3D asymptotically flat black holes
Fareghbal, Reza; Hosseini, Seyed Morteza
2015-04-01
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS3 group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.
Exact and Asymptotic Measures of Multipartite Pure State Entanglement
Bennett, C H; Rohrlich, D E; Smolin, J A; Thapliyal, A V; Bennett, Charles H.; Popescu, Sandu; Rohrlich, Daniel; Smolin, John A.; Thapliyal, Ashish V.
1999-01-01
In an effort to simplify the classification of pure entangled states of multi (m) -partite quantum systems, we study exactly and asymptotically (in n) reversible transformations among n'th tensor powers of such states (ie n copies of the state shared among the same m parties) under local quantum operations and classical communication (LOCC). With regard to exact transformations, we show that two states whose 1-party entropies agree are either locally-unitarily (LU) equivalent or else LOCC-incomparable. Asymptotic transformations result in a simpler classification than exact transformations. We show that m-partite pure states having an m-way Schmidt decomposition are simply parameterizable, with the partial entropy across any nontrivial partition representing the number of standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the state in question. For general m-partite states, partial entropies across different partitions need not be equal, and since partial entropies are conserved by asymp...
Generalized multiplicative error models: Asymptotic inference and empirical analysis
Li, Qian
This dissertation consists of two parts. The first part focuses on extended Multiplicative Error Models (MEM) that include two extreme cases for nonnegative series. These extreme cases are common phenomena in high-frequency financial time series. The Location MEM(p,q) model incorporates a location parameter so that the series are required to have positive lower bounds. The estimator for the location parameter turns out to be the minimum of all the observations and is shown to be consistent. The second case captures the nontrivial fraction of zero outcomes feature in a series and combines a so-called Zero-Augmented general F distribution with linear MEM(p,q). Under certain strict stationary and moment conditions, we establish a consistency and asymptotic normality of the semiparametric estimation for these two new models. The second part of this dissertation examines the differences and similarities between trades in the home market and trades in the foreign market of cross-listed stocks. We exploit the multiplicative framework to model trading duration, volume per trade and price volatility for Canadian shares that are cross-listed in the New York Stock Exchange (NYSE) and the Toronto Stock Exchange (TSX). We explore the clustering effect, interaction between trading variables, and the time needed for price equilibrium after a perturbation for each market. The clustering effect is studied through the use of univariate MEM(1,1) on each variable, while the interactions among duration, volume and price volatility are captured by a multivariate system of MEM(p,q). After estimating these models by a standard QMLE procedure, we exploit the Impulse Response function to compute the calendar time for a perturbation in these variables to be absorbed into price variance, and use common statistical tests to identify the difference between the two markets in each aspect. These differences are of considerable interest to traders, stock exchanges and policy makers.
Asymptotic Performance of Sparse Signal Detection Using Convex Programming Method
Institute of Scientific and Technical Information of China (English)
LEI Chuan; ZHANG Jun
2012-01-01
The detection of sparse signals against background noise is considered.Detecting signals of such kind is difficult since only a small portion of the signal carries information.Prior knowledge is usually assumed to ease detection.In this paper,we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available.Under a Neyman-Pearson hypothesis-testing framework,a new detection scheme is proposed by combining a generalized likelihood ratio test (GLRT)-like test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations.We characterize large sample behavior of the proposed method by analyzing its asymptotic performance.Specifically,we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the (e)2 norm energy of the sparse signals.Both the false alarm rate and the miss rate tend to zero at vanishing signal-to-noise ratio (SNR),as long as the signal energy grows at least logarithmically with the problem dimension.Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection.We derive the oracle error exponent assuming signal knowledge.Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent.We complement our study with numerical experiments,showing that the proposed method performs in the vicinity of the likelihood ratio test (LRT) method in the finite sample scenario and the error probability degrades exponentially with the number of observations.
Asymptotic Properties of Parabolic Systems for Null-Recurrent Switching Diffusions
Institute of Scientific and Technical Information of China (English)
R.Z.Khasminskii; C.Zhu; G.Yin
2007-01-01
This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions,which are diffusion processes modulated by continuous-time Markov chains.A sufficient condition for null recurrence is presented.Moreover,convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established.Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain.To verify the condition,boundary value problems(BVPs)for parabolic systems are treated,which are not the usual two-point BVP type.An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.
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.
Asymptotic heat transfer model in thin liquid films
Chhay, Marx; Gisclon, Marguerite; Ruyer-Quil, Christian
2015-01-01
In this article, we present a modelling of heat transfer occuring through a liquid film flowing down a vertical wall. This model is formally derived thanks to asymptotic developpment, by considering the physical ratio of typical length scales of the study. A new Nusselt thermal solution is proposed, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms in the asymptotic model are numerically pointed out. The comparisons are provided against the resolution of the full Fourier equations in a steady state frame.
Asymptotic zero distribution of a class of hypergeometric polynomials
Driver, K.A.; Johnston, S. J.
2011-01-01
We prove that the zeros of ${}_2F_1(-n,\\frac{n+1}{2};\\frac{n+3}{2};z)$ asymptotically approach the section of the lemniscate $\\{z: |z(1-z)^2|=4/27; \\textrm{Re}(z)>1/3\\}$ as $n\\rightarrow \\infty$. In recent papers (cf. \\cite{KMF}, \\cite{orive}), Mart\\'inez-Finkelshtein and Kuijlaars and their co-authors have used Riemann-Hilbert methods to derive the asymptotic zero distribution of Jacobi polynomials $P_n^{(\\alpha_n,\\beta_n)}$ when the limits $\\ds A=\\lim_{n\\rightarrow \\infty}\\frac{\\alpha_n}{n}...
Asymptotic Marginal Tax Rate of Individual Income Tax in China
Institute of Scientific and Technical Information of China (English)
ZHENYA; LIU; WU; YANG; DAVID; DICKINSON
2014-01-01
This paper examines the asymptotic marginal rate of individual income tax which maximizes China’s social welfare through numerical simulation based on the elasticity of China’s labor supply, income distribution and the social objectives of redistribution in accordance with the optimal direct taxation theory. Taking advantage of the optimal direct taxation model with consideration of the income effect, it comes to the conclusion that combined with China’s reality, the asymptotic marginal rate of individual labor income tax in China should be between 35% and 40%.
Counting spanning trees on fractal graphs and their asymptotic complexity
Anema, Jason A.; Tsougkas, Konstantinos
2016-09-01
Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.
Scalar and Asymptotic Scalar Derivatives Theory and Applications
Isac, George
2008-01-01
This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. Scalar and Asymptotic Derivatives: Theory and Applications also presents the material in relation to Euclidean spaces, Hilbert spaces, Banach spaces, Riemannian manifolds, and Hadamard manifolds. This book is
The Asymptotic Limits of Zero Modes of Massless Dirac Operators
Saitō, Yoshimi; Umeda, Tomio
2008-01-01
Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q( x) are discussed, where α = (α1, α2, α3) is the triple of 4 × 4 Dirac matrices, D = 1/i nabla_x, and Q( x) = ( q jk ( x)) is a 4 × 4 Hermitian matrix-valued function with | q jk ( x) | ≤ C -ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of | x|2 f ( x) as | x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q( x) f ( x).
Selected asymptotic methods with applications to electromagnetics and antennas
Fikioris, George; Bakas, Odysseas N
2013-01-01
This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som
Asymptotic control theory for a system of linear oscillators
Fedorov, Aleksey; Ovseevich, Alexander
2013-01-01
We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the...
Asymptotic teleportation scheme as a universal programmable quantum processor.
Ishizaka, Satoshi; Hiroshima, Tohya
2008-12-12
We consider a scheme of quantum teleportation where a receiver has multiple (N) output ports and obtains the teleported state by merely selecting one of the N ports according to the outcome of the sender's measurement. We demonstrate that such teleportation is possible by showing an explicit protocol where N pairs of maximally entangled qubits are employed. The optimal measurement performed by a sender is the square-root measurement, and a perfect teleportation fidelity is asymptotically achieved for a large N limit. Such asymptotic teleportation can be utilized as a universal programmable processor.
Vacuum energy in asymptotically flat 2+1 gravity
Miskovic, Olivera; Roy, Debraj
2016-01-01
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincare group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian
Pushnitski, Alexander; Villegas-Blas, Carlos
2011-01-01
We consider the Landau Hamiltonian (i.e. the 2D Schroedinger operator with constant magnetic field) perturbed by an electric potential V which decays sufficiently fast at infinity. The spectrum of the perturbed Hamiltonian consists of clusters of eigenvalues which accumulate to the Landau levels. Applying a suitable version of the anti-Wick quantization, we investigate the asymptotic distribution of the eigenvalues within a given cluster as the number of the cluster tends to infinity. We obtain an explicit description of the asymptotic density of the eigenvalues in terms of the Radon transform of the perturbation potential V.
Asymptotic dynamics, large gauge transformations and infrared symmetries
Gomez, Cesar
2016-01-01
Infrared finite S matrices enjoy an infinite family of symmetries, namely decoupling of asymptotic soft modes with arbitrary direction. The infrared structure of the theory manifests itself in the form of vacuum degeneracy and in nontrivial asymptotic dynamics. These two ingredients are unified in the infrared finite S matrix symmetries and can be disentangled as soft and hard components of corresponding charges. When these two components are disentangled, the nontrivial role of large gauge transformations becomes manifest. The soft decoupling symmetry of the physical S matrix leads to relations between the corresponding soft/hard decompositions for the in and out states that can encode crucial nontrivial information about the scattering process.
Phases of (Asymptotically) Safe Chiral Theories with(out) Scalars
Molgaard, Esben
2016-01-01
We unveil the dynamics of four dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case of chiral gauge theories with scalars.
Precise Asymptotics for Random Matrices and Random Growth Models
Institute of Scientific and Technical Information of China (English)
Zhong Gen SU
2008-01-01
The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models.We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.
Modeling quasi-static poroelastic propagation using an asymptotic approach
Energy Technology Data Exchange (ETDEWEB)
Vasco, D.W.
2007-11-01
solution. Unfortunately, analytic solutions are only available for highly idealized conditions, such as a uniform (Rudnicki(1986)) or one-dimensional (Simon et al.(1984)Simon, Zienkiewicz, & Paul; Gajo & Mongiovi(1995); Wang & Kumpel(2003)) medium. In this paper I derive an asymptotic, semi-analytic solution for coupled deformation and flow. The approach is similar to trajectory- or ray-based methods used to model elastic and electromagnetic wave propagation (Aki & Richards(1980); Kline & Kay(1979); Kravtsov & Orlov(1990); Keller & Lewis(1995)) and, more recently, diffusive propagation (Virieux et al.(1994)Virieux, Flores-Luna, & Gibert; Vasco et al.(2000)Vasco, Karasaki, & Keers; Shapiro et al.(2002)Shapiro, Rothert, Rath, & Rindschwentner; Vasco(2007)). The asymptotic solution is valid in the presence of smoothly-varying, heterogeneous flow properties. The situation I am modeling is that of a formation with heterogeneous flow properties and uniform mechanical properties. The boundaries of the layer may vary arbitrary and can define discontinuities in both flow and mechanical properties. Thus, using the techniques presented here, it is possible to model a stack of irregular layers with differing mechanical properties. Within each layer the hydraulic conductivity and porosity can vary smoothly but with an arbitrarily large magnitude. The advantages of this approach are that it produces explicit, semi-analytic expressions for the arrival time and amplitude of the Biot slow and fast waves, expressions which are valid in a medium with heterogeneous properties. As shown here, the semi-analytic expressions provide insight into the nature of pressure and deformation signals recorded at an observation point. Finally, the technique requires considerably fewer computer resources than does a fully numerical treatment.
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
Directory of Open Access Journals (Sweden)
Jacqueline Fleckinger
2001-12-01
Full Text Available We study the asymptotic behavior of positive solutions $u$ of $$ -Delta_p u(x = V(x u(x^{p-1}, quad p>1; x in Omega,$$ and related partial differential inequalities, as well as conditions for existence of such solutions. Here, $Omega$ contains the exterior of a ball in $mathbb{R}^N$ $1
LONG-TIME ASYMPTOTIC FOR THE DAMPED BOUSSINESQ EQUATION IN A CIRCLE
Institute of Scientific and Technical Information of China (English)
Zhang Yi; Lin Qun; Lai Shaoyong
2005-01-01
The first initial-boundary value problem for the following equation utt - a△utt - 2b△ut = α△3u - β△2u + △u + γ△(u2) in a unit circle is considered. The existence of strong solution is established in the space Co([0, ∞), HST(0, 1)), s ＜ 7/2, and the solutions are constructed in the form of series in the small parameter present in the initial conditions. For 5/2 ＜ s ＜ 7/2, the uniqueness is proved. The long-time asymptotics is obtained in the explicit form.
Levchenko, E. A.; Shapovalov, A. V.; Trifonov, A. Yu
2016-07-01
In this paper we construct asymptotic solutions for the nonlocal multidimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation in the class of functions concentrated on a one-dimensional manifold (curve) using a semiclassical approximation technique. We show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov in the class of functions concentrated at a point (zero-dimensional manifold) together with an additional operator condition. The general approach is exemplified by constructing a two-dimensional two-parametric solution, which describes quasi-steady-state patterns on a circumference.
Asymptotic cosmological regimes in scalar-torsion gravity with a perfect fluid
Energy Technology Data Exchange (ETDEWEB)
Skugoreva, Maria A. [Kazan Federal University, Kazan (Russian Federation); Toporensky, Alexey V. [Kazan Federal University, Kazan (Russian Federation); Lomonosov Moscow State University, Sternberg Astronomical Institute, Moscow (Russian Federation)
2016-06-15
We consider the cosmological dynamics of a nonminimally coupled scalar field in scalar-torsion gravity in the presence of hydrodynamical matter. The potential of the scalar field have been chosen as power law with negative index, this type of potentials is usually used in quintessence scenarios. We identify several asymptotic regimes, including de Sitter, kinetic dominance, kinetic tracker, and tracker solutions and study the conditions for their existence and stability. We show that for each combination of coupling constant and potential power index one of the regimes studied in the present paper is stable to the future. (orig.)
Asymptotic Behavior of a Structure Made by a Plate and a Straight Rod
Institute of Scientific and Technical Information of China (English)
Dominique BLANCHARD; Georges GRISO
2013-01-01
This paper is devoted to describing the asymptotic behavior of a structure made by a thin plate and a thin perpendicular rod in the framework of nonlinear elasticity.The authors scale the applied forces in such a way that the level of the total elastic energy leads to the Von-Kármán's equations (or the linear model for smaller forces) in the plate and to a one-dimensional rod-model at the limit.The junction conditions include in particular the continuity of the bending in the plate and the stretching in the rod at the junction.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Asymptotic behavior of stochastic multi-group epidemic models with distributed delays
Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed
2017-02-01
In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0 > 1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.
Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains
Pereira, Marcone Corrêa
2016-10-01
In this work we are interested in the asymptotic behavior of a family of solutions of a semilinear elliptic problem with homogeneous Neumann boundary condition defined in a two-dimensional bounded set which degenerates to the unit interval as a positive parameter {ɛ} goes to zero. Here we also allow that upper and lower boundaries from this singular region present highly oscillatory behavior with different orders and variable profile. Combining results from linear homogenization theory and nonlinear analyzes we get the limit problem showing upper and lower semicontinuity of the solutions at {ɛ=0}.
Institute of Scientific and Technical Information of China (English)
Wang Shaoli; Feng Xinlong; He Yinnian
2011-01-01
This article proposes a diffused hepatitis B virus (HBV) model with CTLimmune response and nonlinear incidence for the control of viral infections.By means of different Lyapunov functions,the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained.Global stability of the positive equilibrium of the model is also considered.The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
Asymptotic Normality of LS Estimate in Simple Linear EV Regression Model
Institute of Scientific and Technical Information of China (English)
Jixue LIU
2006-01-01
Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model.In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.
Ritchie, R.H.; Sakakura, A.Y.
1956-01-01
The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.
Asymptotic solution for high vorticity regions in incompressible 3D Euler equations
Agafontsev, D S; Mailybaev, A A
2016-01-01
Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution. This solution combines a shear flow aligned with an asymmetric straining flow, and is characterized by a single asymmetry parameter and an arbitrary transversal vorticity profile. The analysis is based on detailed comparison with numerical simulations performed using a pseudo-spectral method in anisotropic grids of up to 972 x 2048 x 4096.
Institute of Scientific and Technical Information of China (English)
Qibing GAO; Yaohua WU; Chunhua ZHU; Zhanfeng WANG
2008-01-01
In generalized linear models with fixed design, under the assumption ~ →∞ and otherregularity conditions, the asymptotic normality of maximum quasi-likelihood estimator (β)n, which is the root of the quasi-likelihood equation with natural link function ∑n/i=1Xi(yi-μ(X1/iβ))=0, is obtained,where λ/-n denotes the minimum eigenvalue of ∑n/i=1XiX/1/i, Xi are bounded p x q regressors, and yi are q × 1 responses.
Modified Hybrid Block Iterative Algorithm for Uniformly Quasi--Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
Qiansheng Feng
2012-01-01
Full Text Available Saewan and Kumam (2010 have proved the convergence theorems for finding the set of solutions of a general equilibrium problems and the common fixed point set of a family of closed and uniformly quasi--asymptotically nonexpansive mappings in a uniformly smooth and strictly convex Banach space E with Kadec-Klee property. In this paper, authors prove the convergence theorems and do not need the Kadec-Klee property of Banach space and some other conditions used in the paper of S. Saewan and P. Kumam. Therefore, the results presented in this paper improve and extend some recent results.
Asymptotic analysis of singular solutions of the scalar and mean curvature equations
Directory of Open Access Journals (Sweden)
Gonzalo García
2005-01-01
Full Text Available We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics in ℝ+n, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in ℝ+n that if a solution satisfies a Kazdan-Warner-type identity, then the conformal metric can be realized as a smooth metric on S+n.
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.
Institute of Scientific and Technical Information of China (English)
阮炯; 王军平; 郭德典
2004-01-01
In this paper, we first introduce the model of discrete-time neural networks with generalized input-output function and present a proof of the existence of a fixed point by Schauder fixed-point principle. Secondly, we study the uniformly asymptotical stability of equilibrium in non-autonomous discrete-time neural networks and give some sufficient conditions that guarantee the stability of it by using the converse theorem of Lyapunov function. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories.
Asymptotic cosmological regimes in scalar-torsion gravity with a perfect fluid
Skugoreva, Maria
2016-01-01
We consider cosmological dynamics of nonminimally coupled scalar field in the scalar-torsion gravity in the presence of a hydrodynamical matter. Potential of the scalar field have been chosen as power-law with negative index, this type of potentials is usually used in quintessence scenarios. We identify several asymptotic regimes, including de Sitter, kinetic dominance, kinetic tracker and tracker solution and study conditions for their existence and stability. We show that for each combination of coupling constant and potential power index one of regimes studied in the present paper is stable to the future.
Asymptotic Distribution of Coefficients of Skewness and Kurtosis
Directory of Open Access Journals (Sweden)
Narges Abbasi
2009-01-01
Full Text Available Problem statement: In literature, a classic method which has been used to recognize the distribution so far is the measurement of its skewedness and kurtosis. However, there remains a question: how would these measurements work for skewed normal distribution when the size of the sample is large? Approach: This research aimed to determine the asymptotic distribution of skewedness and kurtosis measures in skewed normal distribution. In conducting this research, two groups of inferential findings will help. First, skewed normal distribution which has already been studied by a lot of researchers and we apply its characteristics. Second, there is the U-statistics theory which guides us to the determining of asymptotic distribution measures for skewedness and kurtosis. The combination of these two will solve the problem of this study. Results: Asymptotic distribution of measures for skewdness and kurtosis falls in the normal families. With the size of large samples, the values of expectation of these measures are also determined. By letting zero for skewedness parameter, asymptotic distribution for normal distribution can also be obtained. Conclusion: The findings of this study show new characteristics for skew normal distribution and this results in a new way for skew normal distribution recognition.
DISSIPATION AND DISPERSION APPROXIMATION TO HYDRODYNAMICAL EQUATIONS AND ASYMPTOTIC LIMIT
Institute of Scientific and Technical Information of China (English)
Hsiao Ling; Li Hailiang
2008-01-01
The compressible Euler equations with dissipation and/or dispersion correction are widely used in the area of applied sciences, for instance, plasma physics,charge transport in semiconductor devices, astrophysics, geophysics, etc. We consider the compressible Euler equation with density-dependent (degenerate) viscosities and capillarity, and investigate the global existence of weak solutions and asymptotic limit.
Asymptotic analysis of the Carrier-Pearson problem
Directory of Open Access Journals (Sweden)
Chunqing Lu
2003-02-01
Full Text Available This paper provides a rigorous analysis of the asymptotic behavior of the solution for the boundary-value problem begin{gather*} epsilon ^2u''+u^2-1 =0,quad -1
Asymptotic behaviour of the stochastic Gilpin-Ayala competition models
Lian, Baosheng; Hu, Shigeng
2008-03-01
In this paper, we investigate a stochastic Gilpin-Ayala competition system, which is more general and more realistic than the classical Lotka-Volterra competition system.We discuss the asymptotic behaviour in detail of the stochastic Gilpin-Ayala competition system, and comparing the classical Lotka-Volterra with Gilpin-Ayala competition system, we find that the latter has better properties.
Penrose inequality for asymptotically AdS spaces
Energy Technology Data Exchange (ETDEWEB)
Itkin, Igor [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel); Oz, Yaron, E-mail: yaronoz@post.tau.ac.il [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel)
2012-02-28
In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.
A convergence theorem for asymptotic expansions of Feynman amplitudes
Energy Technology Data Exchange (ETDEWEB)
Mabouisson, A.P.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1999-06-01
The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to {infinity}, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)
Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence
Directory of Open Access Journals (Sweden)
Xueping Hu
2012-01-01
Full Text Available By applying the moment inequality for asymptotically almost negatively associated (in short AANA random sequence and truncated method, we get the three series theorems for AANA random variables. Moreover, a strong convergence property for the partial sums of AANA random sequence is obtained. In addition, we also study strong convergence property for weighted sums of AANA random sequence.
ASYMPTOTIC STABILITY OF A SINGULAR SYSTEM WITH DISTRIBUTED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the stability theory of functional differential equations, this paper studies the asymptotic stability of a singular system with distributed delays by constructing suitable Lyapunov functionals and applying the linear matrix inequalities. A numerical example is given to show the effectiveness of the main results.
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
Asymptotic stability of solutions to elastic systems with structural damping
Directory of Open Access Journals (Sweden)
Hongxia Fan
2014-11-01
Full Text Available In this article, we study the asymptotic stability of solutions for the initial value problems of second order evolution equations in Banach spaces, which can model elastic systems with structural damping. The discussion is based on exponentially stable semigroups theory. Applications to the vibration equation of elastic beams with structural damping are also considered.
Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)
Institute of Scientific and Technical Information of China (English)
WEIBOCHENG
1996-01-01
A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.
Asymptotic freedom of gluons in the Fock space
Głazek, Stanisław D
2015-01-01
Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective particles to quantum Yang-Mills theory.
Hilbert manifold structure for asymptotically hyperbolic relativistic initial data
Fougeirol, Jérémie
2016-01-01
We provide a Hilbert manifold structure {\\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
The asymptotic limits of zero modes of massless Dirac operators
Saito, Yoshimi
2007-01-01
Asymptotic behaviors of zero modes of the massless Dirac operator $H=\\alpha\\cdot D + Q(x)$ are discussed, where $\\alpha= (\\alpha_1, \\alpha_2, \\alpha_3)$ is the triple of $4 \\times 4$ Dirac matrices, $ D=\\frac{1}{i} \
A Variational Model for an Asymptotic Magnetogydrodynamic System
Institute of Scientific and Technical Information of China (English)
JihuanHE
1998-01-01
In the present paper an asymptotic gas magnetohydrodynamic system is formulated in variational principles for the first time via the semi-inverse method proposed by He.Thus,a new theoretical basis for the finite element method is founded and a new versatile way to deal with discontinuity(shock)is suggested.
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.
Causality violation in asymptotically flat space-times
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1976-10-04
It is shown that a region containing closed timelike lines cannot evolve from regular initial data in a singularity-free asymptotically flat space-time. Furthermore, the causality assumption made in the black-hole uniqueness proofs is justified: It is demonstrated that no physically realistc nonsingular black hole can have a causality-violating exterior. (AIP)
Asymptotic Formulae for Multivariate Kantorovich Type Generalized Sampling Series
Institute of Scientific and Technical Information of China (English)
Carlo BARDARO; Ilaria MANTELLINI
2011-01-01
In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given.Moreover a quantitative version in terms of some moduli of smoothness is established.Finally some particular examples of kernels are discussed,as the Bochner-Riesz kernel and the multivariate splines.
Strong asymptotics for Lp extremal polynomials off a complex curve
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Rabah Khaldi
2004-01-01
Full Text Available We study the asymptotic behavior of Lp(σ extremal polynomials with respect to a measure of the form σ=α+γ, where α is a measure concentrated on a rectifiable Jordan curve in the complex plane and γ is a discrete measure concentrated on an infinite number of mass points.
Geometry of exponential family nonlinear models and some asymptotic inference
Institute of Scientific and Technical Information of China (English)
韦博成
1995-01-01
A differential geometric framework in Euclidean space for exponential family nonlinear models is presented. Based on this framework, some asymptotic inference related to statistical curvatures and Fisher information are studied. This geometric framework can also be extended to more genera) dass of models and used to study some other problems.