175 Years of Linear Programming - Minimax and Cake Topography

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 7. 175 Years of Linear Programming - Minimax and Cake Topography. Vijay Chandru M R Rao. Series Article Volume 4 Issue 7 July 1999 pp 4-13. Fulltext. Click here to view fulltext PDF. Permanent link:

An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

Directory of Open Access Journals (Sweden)

Ľuboš Buzna

2014-01-01

Full Text Available We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve the p-median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.

Minimax robust power split in AF relays based on uncertain long-term CSI

KAUST Repository

Nisar, Muhammad Danish

2011-09-01

An optimal power control among source and relay nodes in presence of channel state information (CSI) is vital for an efficient amplify and forward (AF) based cooperative communication system. In this work, we study the optimal power split (power control) between the source and relay node in presence of an uncertainty in the CSI. The prime contribution is to solve the problem based on an uncertain long-term knowledge of both the first and second hop CSI (requiring less frequent updates), and under an aggregate network-level power constraint. We employ the minimax optimization methodology to arrive at the minimax robust optimal power split, that offers the best possible guarantee on the end-to-end signal to noise ratio (SNR). The derived closed form analytical expressions admit simple intuitive interpretations and are easy to implement in real-world AF relaying systems. Numerical results confirm the advantages of incorporating the presence of uncertainty into the optimization problem, and demonstrate the usefulness of the proposed minimax robust optimal power split. © 2011 IEEE.

Asymptotic expansion in the local limit theorem for the particle number in the grand canonical ensemble

International Nuclear Information System (INIS)

Pogosian, S.

1981-01-01

It is known that in the grand canonical ensemble (for the case of small density of particles) the fluctuations (approximately mod(Λ)sup(1/2)) in the particle number have an asymptotic normal distribution as Λ→infinity. A similar statement holds for the distribution of the particle number in a bounded domain evaluated with respect to the limiting Gibbs distribution. The author obtains an asymptotic expansion in the local limit theorem for the particle number in the grand canonical ensemble, by using the asymptotic expansion of the grand canonical partition function. The coefficients of this expansion are not constants but depend on the form of the domain Λ. More precisely, they are constant up to a correction which is small (for large Λ). The author obtains an explicit form for the second term of the asymptotic expansion in the local limit theorem for the particle number, and also gets the first correction terms for the coefficients of this expansion. (Auth.)

A minimax procedure in the context of sequential mastery testing

NARCIS (Netherlands)

Vos, Hendrik J.

1999-01-01

The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master or a nonmaster, or to continue sampling and administering another random test item. The framework of minimax sequential decision theory

Asymptotically exact solution of a local copper-oxide model

International Nuclear Information System (INIS)

Zhang Guangming; Yu Lu.

1994-03-01

We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities. (author). 15 refs, 1 fig

Minimax robust relay selection based on uncertain long-term CSI

KAUST Repository

Nisar, Muhammad Danish

2014-02-01

Cooperative communications via multiple relay nodes is known to provide the benefits of increase diversity and coverage. Simultaneous transmission via multiple relays, however, requires strong coordination between nodes either in terms of slot-based transmission or distributed space-time (ST) code implementation. Dynamically selecting a single best relay out of multiple relays and then using it alone for cooperative transmission alleviates the need for this strong coordination while still reaping the benefits of increased diversity and coverage. In this paper, we consider the design of relay selection (RS) under an imperfect knowledge of long-term channel state information (CSI) at the relay nodes, and we pursue minimax optimization to arrive at a robust RS approach that promises the best guarantee on the worst-case end-to-end signal-to-noise ratio (SNR). We provide some intuitive examples and extensive simulation results, not only in terms of worst-case SNR performance but also in terms of average bit-error-rate (BER) performance, to demonstrate the benefits of the proposed minimax robust RS scheme. © 2013 IEEE.

Redescription of Tarsonemus minimax and definition of its species-group in the genus Tarsonemus (Acari: Tarsonemidae) with descriptions of two new species

Science.gov (United States)

Wojciech L. Magowski; John C. Moser

2003-01-01

The Tarsonemus minimax species-group is established for bark beetle commensals of the genus Tarsonemus Canestrini and Fanzago, 1876. T. minimax Vitzthum 1926 is redescribed, and two new species, T. terebrans and T. typographi n. spp., are described and illustrated. A...

Asymptotically optimal data analysis for rejecting local realism

International Nuclear Information System (INIS)

Zhang, Yanbao; Glancy, Scott; Knill, Emanuel

2011-01-01

Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p value. We propose a prediction-based-ratio (PBR) analysis protocol whose p values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, e-print arXiv:quant-ph/0110137]. We find that the p values of the former can be too small and are therefore not statistically valid, while those derived from the latter are suboptimal. PBR p values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details.

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I. (The two antagonistic localizations and their asymptotic compatibility)

International Nuclear Information System (INIS)

Schroer, Bert; Freie Universitaet, Berlin

2010-02-01

It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distinction between Born localization in QM (which in the relativistic context changes its name to Newton- Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The Born-Newton-Wigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. The present division into two semi-autonomous essays is the result of a partition and extension of an originally one-part manuscript. (author)

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)

International Nuclear Information System (INIS)

Schroer, Bert

2010-01-01

It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distinction between Born-localization in QM (which in the relativistic context changes its name to Newton-Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The Born-Newton-Wigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. The present division into two semi-autonomous essays is the result of a partition and extension of an originally one-part manuscript. (author)

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I. (The two antagonistic localizations and their asymptotic compatibility)

Energy Technology Data Exchange (ETDEWEB)

Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Universitaet, Berlin (Germany). Inst. fuer Theoretische Physik

2010-02-15

It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distinction between Born localization in QM (which in the relativistic context changes its name to Newton- Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The Born-Newton-Wigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. The present division into two semi-autonomous essays is the result of a partition and extension of an originally one-part manuscript. (author)

Minimax rational approximation of the Fermi-Dirac distribution

Science.gov (United States)

Moussa, Jonathan E.

2016-10-01

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.

Primal Interior-Point Method for Large Sparse Minimax Optimization

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

2009-01-01

Roč. 45, č. 5 (2009), s. 841-864 ISSN 0023-5954 R&D Projects: GA AV ČR IAA1030405; GA ČR GP201/06/P397 Institutional research plan: CEZ:AV0Z10300504 Keywords : unconstrained optimization * large-scale optimization * minimax optimization * nonsmooth optimization * interior-point methods * modified Newton methods * variable metric methods * computational experiments Subject RIV: BA - General Mathematics Impact factor: 0.445, year: 2009 http://dml.cz/handle/10338.dmlcz/140034

Primal Interior Point Method for Minimization of Generalized Minimax Functions

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

2010-01-01

Roč. 46, č. 4 (2010), s. 697-721 ISSN 0023-5954 R&D Projects: GA ČR GA201/09/1957 Institutional research plan: CEZ:AV0Z10300504 Keywords : unconstrained optimization * large-scale optimization * nonsmooth optimization * generalized minimax optimization * interior-point methods * modified Newton methods * variable metric methods * global convergence * computational experiments Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://dml.cz/handle/10338.dmlcz/140779

Simultaneous feature selection and classification via Minimax Probability Machine

Directory of Open Access Journals (Sweden)

Liming Yang

2010-12-01

Full Text Available This paper presents a novel method for simultaneous feature selection and classification by incorporating a robust L1-norm into the objective function of Minimax Probability Machine (MPM. A fractional programming framework is derived by using a bound on the misclassification error involving the mean and covariance of the data. Furthermore, the problems are solved by the Quadratic Interpolation method. Experiments show that our methods can select fewer features to improve the generalization compared to MPM, which illustrates the effectiveness of the proposed algorithms.

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.

Global and local asymptotics for the busy period of an M/G/1 queue

NARCIS (Netherlands)

Denisov, D.E.; Shneer, V.

2010-01-01

We consider an M/G/1 queue with subexponential service times. We give a simple derivation of the global and local asymptotics for the busy period. Our analysis relies on the explicit formula for the joint distribution for the number of customers and the length of the busy period of an M/G/1 queue.

Local fields for asymptotic matching in multidimensional mode conversion

International Nuclear Information System (INIS)

Tracy, E. R.; Kaufman, A. N.; Jaun, A.

2007-01-01

The problem of resonant mode conversion in multiple spatial dimensions is considered. Using phase space methods, a complete theory is developed for constructing matched asymptotic expansions that fit incoming and outgoing WKB solutions. These results provide, for the first time, a complete and practical method for including multidimensional conversion in ray tracing algorithms. The paper provides a self-contained description of the following topics: (1) how to use eikonal (also known as ray tracing or WKB) methods to solve vector wave equations and how to detect conversion regions while following rays; (2) once conversion is detected, how to fit to a generic saddle structure in ray phase space associated with the most common type of conversion; (3) given the saddle structure, how to carry out a local projection of the full vector wave equation onto a local two-component normal form that governs the two resonantly interacting waves. This determines both the uncoupled dispersion functions and the coupling constant, which in turn determine the uncoupled WKB solutions; (4) given the normal form of the local two-component wave equation, how to find the particular solution that matches the amplitude, phase, and polarization of the incoming ray, to the amplitude, phase, and polarization of the two outgoing rays: the transmitted and converted rays

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

NARCIS (Netherlands)

Lambert, A.; Simatos, F.

2015-01-01

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive Lévy process with nonzero Lévy measure. In this paper, we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two

Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case

NARCIS (Netherlands)

Lambert, A.; Simatos, F.

2012-01-01

Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\\'evy process with non-zero L\\'evy measure. In this paper we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two

Efficient Minimax Design of Networks without Using Derivatives

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Niels Ole; Schjær-Jacobsen, Hans

1975-01-01

., which makes the gradient computation by the adjoint network method or related methods rather complicated, and often numerical errors are introduced in the gradients. Consequently, the algorithm is found to be of particular relevance in optimum design of practical microwave networks. The relative...... design results. Finally, optimum broad-band design of a practical coaxial transferred-electron reflection-type amplilier is carried out by means of the proposed method. The results are supported by experimental verification.......A new minimax network optimization algorithm not requiring derivatives has been developed. It is based on successive linear approximations to the nonlinear functions defining the problem. Adequate modeling of distributed parameter circuits for optimization purposes often involves parasitic, etc...

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.

APPLICATION OF A PRIMAL-DUAL INTERIOR POINT ALGORITHM USING EXACT SECOND ORDER INFORMATION WITH A NOVEL NON-MONOTONE LINE SEARCH METHOD TO GENERALLY CONSTRAINED MINIMAX OPTIMISATION PROBLEMS

Directory of Open Access Journals (Sweden)

INTAN S. AHMAD

2008-04-01

Full Text Available This work presents the application of a primal-dual interior point method to minimax optimisation problems. The algorithm differs significantly from previous approaches as it involves a novel non-monotone line search procedure, which is based on the use of standard penalty methods as the merit function used for line search. The crucial novel concept is the discretisation of the penalty parameter used over a finite range of orders of magnitude and the provision of a memory list for each such order. An implementation within a logarithmic barrier algorithm for bounds handling is presented with capabilities for large scale application. Case studies presented demonstrate the capabilities of the proposed methodology, which relies on the reformulation of minimax models into standard nonlinear optimisation models. Some previously reported case studies from the open literature have been solved, and with significantly better optimal solutions identified. We believe that the nature of the non-monotone line search scheme allows the search procedure to escape from local minima, hence the encouraging results obtained.

Perils of Asymptotics

International Nuclear Information System (INIS)

Dewar, R. L.

1995-01-01

A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs

A Minimax Regret Analysis of Flood Risk Management Strategies Under Climate Change Uncertainty and Emerging Information

NARCIS (Netherlands)

Pol, van der T.D.; Gabbert, S.; Weikard, H.P.; Ierland, van E.C.; Hendrix, E.M.T.

2017-01-01

This paper studies the dynamic application of the minimax regret (MR) decision criterion to identify robust flood risk management strategies under climate change uncertainty and emerging information. An MR method is developed that uses multiple learning scenarios, for example about sea level rise

On asymptotics and resurgent structures of enumerative Gromov-Witten invariants

International Nuclear Information System (INIS)

Couso-Santamaria, Ricardo; Schiappa, Ricardo; Geneve Univ.; Vaz, Ricardo; DESY Hamburg

2016-05-01

Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants - in their dependence upon genus and degree of the embedded curve - for several different threefold Calabi-Yau toric-varieties. In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial. This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy. This implies the existence of nonperturbative sectors controlling the asymptotics of the Gromov-Witten invariants, which could themselves have an enumerative-geometry interpretation. The examples addressed include: the resolved conifold; the local surfaces local P 2 and local P 1 x P 1 ; the local curves and Hurwitz theory; and the compact quintic. All examples suggest very rich interplays between resurgent asymptotics and enumerative problems in algebraic geometry.

On asymptotics and resurgent structures of enumerative Gromov-Witten invariants

Energy Technology Data Exchange (ETDEWEB)

Couso-Santamaria, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); Schiappa, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); Geneve Univ. (Switzerland). Dept. de Physique Theoretique et Section de Mathematiques; Vaz, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); DESY Hamburg (Germany). Theory Group

2016-05-15

Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants - in their dependence upon genus and degree of the embedded curve - for several different threefold Calabi-Yau toric-varieties. In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial. This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy. This implies the existence of nonperturbative sectors controlling the asymptotics of the Gromov-Witten invariants, which could themselves have an enumerative-geometry interpretation. The examples addressed include: the resolved conifold; the local surfaces local P{sup 2} and local P{sup 1} x P{sup 1}; the local curves and Hurwitz theory; and the compact quintic. All examples suggest very rich interplays between resurgent asymptotics and enumerative problems in algebraic geometry.

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....

On the calculation of the minimax-converse of the channel coding problem

OpenAIRE

Elkayam, Nir; Feder, Meir

2015-01-01

A minimax-converse has been suggested for the general channel coding problem by Polyanskiy etal. This converse comes in two flavors. The first flavor is generally used for the analysis of the coding problem with non-vanishing error probability and provides an upper bound on the rate given the error probability. The second flavor fixes the rate and provides a lower bound on the error probability. Both converses are given as a min-max optimization problem of an appropriate binary hypothesis tes...

A Projected Conjugate Gradient Method for Sparse Minimax Problems

DEFF Research Database (Denmark)

Madsen, Kaj; Jonasson, Kristjan

1993-01-01

A new method for nonlinear minimax problems is presented. The method is of the trust region type and based on sequential linear programming. It is a first order method that only uses first derivatives and does not approximate Hessians. The new method is well suited for large sparse problems...... as it only requires that software for sparse linear programming and a sparse symmetric positive definite equation solver are available. On each iteration a special linear/quadratic model of the function is minimized, but contrary to the usual practice in trust region methods the quadratic model is only...... with the method are presented. In fact, we find that the number of iterations required is comparable to that of state-of-the-art quasi-Newton codes....

A minimax stochastic optimal semi-active control strategy for uncertain quasi-integrable Hamiltonian systems using magneto-rheological dampers

DEFF Research Database (Denmark)

Feng, Ju; Ying, Zu-Guang; Zhu, Wei-Qiu

2012-01-01

A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncer...

Asymptotic numbers, asymptotic functions and distributions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-07-01

The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)

Asymptotic analysis of the local potential approximation to the Wetterich equation

Science.gov (United States)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D    2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

The intermediates take it all: asymptotics of higher criticism statistics and a powerful alternative based on equal local levels.

Science.gov (United States)

Gontscharuk, Veronika; Landwehr, Sandra; Finner, Helmut

2015-01-01

The higher criticism (HC) statistic, which can be seen as a normalized version of the famous Kolmogorov-Smirnov statistic, has a long history, dating back to the mid seventies. Originally, HC statistics were used in connection with goodness of fit (GOF) tests but they recently gained some attention in the context of testing the global null hypothesis in high dimensional data. The continuing interest for HC seems to be inspired by a series of nice asymptotic properties related to this statistic. For example, unlike Kolmogorov-Smirnov tests, GOF tests based on the HC statistic are known to be asymptotically sensitive in the moderate tails, hence it is favorably applied for detecting the presence of signals in sparse mixture models. However, some questions around the asymptotic behavior of the HC statistic are still open. We focus on two of them, namely, why a specific intermediate range is crucial for GOF tests based on the HC statistic and why the convergence of the HC distribution to the limiting one is extremely slow. Moreover, the inconsistency in the asymptotic and finite behavior of the HC statistic prompts us to provide a new HC test that has better finite properties than the original HC test while showing the same asymptotics. This test is motivated by the asymptotic behavior of the so-called local levels related to the original HC test. By means of numerical calculations and simulations we show that the new HC test is typically more powerful than the original HC test in normal mixture models. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A mini-max principle for drift waves and mesoscale fluctuations

International Nuclear Information System (INIS)

Itoh, S-I; Itoh, K

2011-01-01

A mini-max principle for the system of the drift waves and mesoscale fluctuations (e.g. zonal flows, etc) is studied. For the system of model equations a Lyapunov function is constructed, which takes the minimum when the stationary state is realized. The dynamical evolution describes the access to the state that is realized. The competition between different mesoscale fluctuations is explained. The origins of irreversibility that cause an approach to the stationary state are discussed. A selection rule among fluctuations is derived, and conditions, under which different kinds of mesocale fluctuations coexist, are investigated. An analogy of this minimum principle to the principle of 'minimum Helmholtz free energy' in thermal equilibrium is shown.

Methodology in robust and nonparametric statistics

CERN Document Server

Jurecková, Jana; Picek, Jan

2012-01-01

Introduction and SynopsisIntroductionSynopsisPreliminariesIntroductionInference in Linear ModelsRobustness ConceptsRobust and Minimax Estimation of LocationClippings from Probability and Asymptotic TheoryProblemsRobust Estimation of Location and RegressionIntroductionM-EstimatorsL-EstimatorsR-EstimatorsMinimum Distance and Pitman EstimatorsDifferentiable Statistical FunctionsProblemsAsymptotic Representations for L-Estimators

Large Deviations and Asymptotic Methods in Finance

CERN Document Server

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...

Systematic assignment of Feshbach resonances via an asymptotic bound state model

NARCIS (Netherlands)

Goosen, M.; Kokkelmans, SJ.J.M.F.

2008-01-01

We present an Asymptotic Bound state Model (ABM), which is useful to predict Feshbach resonances. The model utilizes asymptotic properties of the interaction potentials to represent coupled molecular wavefunctions. The bound states of this system give rise to Feshbach resonances, localized at the

Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators

Energy Technology Data Exchange (ETDEWEB)

Helmich-Paris, Benjamin, E-mail: b.helmichparis@vu.nl; Visscher, Lucas, E-mail: l.visscher@vu.nl

2016-09-15

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.

Comparison of application of various crossovers in solving inhomogeneous minimax problem modified by Goldberg model

Science.gov (United States)

Kobak, B. V.; Zhukovskiy, A. G.; Kuzin, A. P.

2018-05-01

This paper considers one of the classical NP complete problems - an inhomogeneous minimax problem. When solving such large-scale problem, there appear difficulties in obtaining an exact solution. Therefore, let us propose getting an optimum solution in an acceptable time. Among a wide range of genetic algorithm models, let us choose the modified Goldberg model, which earlier was successfully used by authors in solving NP complete problems. The classical Goldberg model uses a single-point crossover and a singlepoint mutation, which somewhat decreases the accuracy of the obtained results. In the article, let us propose using a full two-point crossover with various mutations previously researched. In addition, the work studied the necessary probability to apply it to the crossover in order to obtain results that are more accurate. Results of the computation experiment showed that the higher the probability of a crossover, the higher the quality of both the average results and the best solutions. In addition, it was found out that the higher the values of the number of individuals and the number of repetitions, the closer both the average results and the best solutions to the optimum. The paper shows how the use of a full two-point crossover increases the accuracy of solving an inhomogeneous minimax problem, while the time for getting the solution increases, but remains polynomial.

The positive action conjecture and asymptotically euclidean metrics in quantum gravity

International Nuclear Information System (INIS)

Gibbons, G.W.; Pope, C.N.

1979-01-01

The positive action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics on R 4 and a large class of more complicated topologies and for self-dual metrics. We show that if Rsupμsubμ >= 0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under an SU(2) or SO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric on K3 - the only simply connected compact manifold which admits a self-dual metric. (orig.) [de

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

Energy Technology Data Exchange (ETDEWEB)

An, Ok Song [SISSA and INFN, Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy); Department of Physics, Kim Il Sung University,Ryongnam Dong, TaeSong District, Pyongyang, D.P.R. (Korea, Republic of); ICTP,Strada Costiera 11, 34014 Trieste (Italy); Cvetič, Mirjam [Department of Physics and Astronomy, University of Pennsylvania,209 S 33rd St, Philadelphia, PA 19104 (United States); Center for Applied Mathematics and Theoretical Physics, University of Maribor,Mladinska 3, SI2000 Maribor (Slovenia); Papadimitriou, Ioannis [SISSA and INFN, Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy)

2016-03-14

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.

An improved partial bundle method for linearly constrained minimax problems

Directory of Open Access Journals (Sweden)

Chunming Tang

2016-02-01

Full Text Available In this paper, we propose an improved partial bundle method for solving linearly constrained minimax problems. In order to reduce the number of component function evaluations, we utilize a partial cutting-planes model to substitute for the traditional one. At each iteration, only one quadratic programming subproblem needs to be solved to obtain a new trial point. An improved descent test criterion is introduced to simplify the algorithm. The method produces a sequence of feasible trial points, and ensures that the objective function is monotonically decreasing on the sequence of stability centers. Global convergence of the algorithm is established. Moreover, we utilize the subgradient aggregation strategy to control the size of the bundle and therefore overcome the difficulty of computation and storage. Finally, some preliminary numerical results show that the proposed method is effective.

New rigorous asymptotic theorems for inverse scattering amplitudes

International Nuclear Information System (INIS)

Lomsadze, Sh.Yu.; Lomsadze, Yu.M.

1984-01-01

The rigorous asymptotic theorems both of integral and local types obtained earlier and establishing logarithmic and in some cases even power correlations aetdeen the real and imaginary parts of scattering amplitudes Fsub(+-) are extended to the inverse amplitudes 1/Fsub(+-). One also succeeds in establishing power correlations of a new type between the real and imaginary parts, both for the amplitudes themselves and for the inverse ones. All the obtained assertions are convenient to be tested in high energy experiments when the amplitudes show asymptotic behaviour

Quasi-extended asymptotic functions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-01-01

The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta 2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example

Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

International Nuclear Information System (INIS)

Zhang, Jia-Fang; Chen, Heshan

2014-01-01

This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution

Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system

Energy Technology Data Exchange (ETDEWEB)

Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

2015-11-30

We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.

Scalar hairy black holes and solitons in asymptotically flat spacetimes

International Nuclear Information System (INIS)

Nucamendi, Ulises; Salgado, Marcelo

2003-01-01

A numerical analysis shows that the Einstein field equations allow static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. When regularity at the origin is imposed (i.e., in the absence of a horizon) globally regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential V(φ) of the theory is not positive semidefinite and 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

Dynamic model of minimax control over economic security state of the region in the presence of risks

Directory of Open Access Journals (Sweden)

Andrey Fedorovich Shorikov

2012-06-01

Full Text Available Investigation and solution of management of economic security state in the region (MESSR requires development of a dynamic economic-mathematical model that takes into account the presence of control actions, uncontrolled parameters (risk modeling errors, etc. and availability of information deficit. At the same time, the existing approaches to solving such problems are based primarily on static models and the use of stochastic modeling of the device, which is required for the application of knowledge of the probability characteristics of the main model parameters and special conditions for the realization of the process. We should note that to use the apparatus of stochastic modeling, very strict conditions are required, which in practice are usually not feasible in advance In this paper, we propose to use a deterministic approach for modeling and solving the original problem in the form of a dynamic programming problem of minimax control (optimization of a guaranteed result MESSR at the determined point of time, taking into account the availability of risks of deterministic and stochastic nature (combined risks model. At thesametime, under therisks in thesocial and economic system we understand thefactors that negatively catastrophically affect the results of the reviewed processes inside it. For an effective use, a technique of prediction and assessment of time rows and stochastic risks in MESSR optimization process is presented, which can serve as a basis for the development of appropriate computer software. To solve the problem of program minimax control MESSR in the presence of risks, we propose a method which is reduced to the realization of a finite number of solutions of linear and convex mathematical programming and discrete optimization problem. The proposed method makes it possible to develop efficient numerical procedures to implement computer simulation of the dynamics of the problem, build program minimax control and gain optimal

Renormalization and asymptotic freedom in quantum gravity

International Nuclear Information System (INIS)

Tomboulis, E.T.

1984-01-01

The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)

Asymptotics and Borel summability

CERN Document Server

Costin, Ovidiu

2008-01-01

Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us

Penrose inequality for asymptotically AdS spaces

International Nuclear Information System (INIS)

Itkin, Igor; Oz, Yaron

2012-01-01

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.

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.

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data.

Science.gov (United States)

Cai, T Tony; Zhang, Anru

2016-09-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data.

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data*

Science.gov (United States)

Cai, T. Tony; Zhang, Anru

2016-01-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data. PMID:27777471

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 boundary conditions for dissipative waves: General theory

Science.gov (United States)

Hagstrom, Thomas

1990-01-01

An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Asymptotic boundary conditions for dissipative waves - General theory

Science.gov (United States)

Hagstrom, Thomas

1991-01-01

An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Asymptotic Eigenstructures

Science.gov (United States)

Thompson, P. M.; Stein, G.

1980-01-01

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

Minimax approach problem with incomplete information for the two-level hierarchical discrete-time dynamical system

Energy Technology Data Exchange (ETDEWEB)

Shorikov, A. F. [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia and Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

2014-11-18

We consider a discrete-time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector linear or convex discrete-time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solution.

Extended asymptotic functions - some examples

International Nuclear Information System (INIS)

Todorov, T.D.

1981-01-01

Several examples of extended asymptotic functions of two variables are given. This type of asymptotic functions has been introduced as an extension of continuous ordinary functions. The presented examples are realizations of some Schwartz distributions delta(x), THETA(x), P(1/xsup(n)) and can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. The examples illustrate the method of construction of extended asymptotic functions similar to the distributions. The set formed by the extended asymptotic functions is also considered. It is shown, that this set is not closed with respect to addition and multiplication

Globally asymptotically stable analysis in a discrete time eco-epidemiological system

International Nuclear Information System (INIS)

Hu, Zengyun; Teng, Zhidong; Zhang, Tailei; Zhou, Qiming; Chen, Xi

2017-01-01

Highlights: • Dynamical behaviors of a discrete time eco-epidemiological system are discussed. • Global asymptotical stability of this system is obtained by an iteration scheme which can be expended to general dimensional discrete system. • More complex dynamical behaviors are obtained by numerical simulations. - Abstract: In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

Asymptotics of relativistic spin networks

International Nuclear Information System (INIS)

Barrett, John W; Steele, Christopher M

2003-01-01

The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol

Asymptotic inference for jump diffusions with state-dependent intensity

NARCIS (Netherlands)

Becheri, Gaia; Drost, Feico; Werker, Bas

2016-01-01

We establish the local asymptotic normality property for a class of ergodic parametric jump-diffusion processes with state-dependent intensity and known volatility function sampled at high frequency. We prove that the inference problem about the drift and jump parameters is adaptive with respect to

Asymptotic and geometrical quantization

International Nuclear Information System (INIS)

Karasev, M.V.; Maslov, V.P.

1984-01-01

The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered

Asymptotically Optimal Agents

OpenAIRE

Lattimore, Tor; Hutter, Marcus

2011-01-01

Artificial general intelligence aims to create agents capable of learning to solve arbitrary interesting problems. We define two versions of asymptotic optimality and prove that no agent can satisfy the strong version while in some cases, depending on discounting, there does exist a non-computable weak asymptotically optimal agent.

Asymptotic sequences over ideals and projectively equivalent ideals with respect to modules

International Nuclear Information System (INIS)

Naghipour, R.; Sedghi, M.

2007-09-01

Let R be a commutative Noetherian ring, and let N be a non-zero finitely generated R-module. The purpose of this paper is to show that if I and J are projectively equivalent ideals w.r.t. N, then a sequence x := x 1 , . . . , x n of elements of R is an asymptotic sequence over I w.r.t. N if and only if it is an asymptotic sequence over J w.r.t. N. Also, it is shown that if R is local, then the lengths of all maximal asymptotic sequences over an ideal I w.r.t. N are the same. As a consequence we derive a generalization of Rees' theorem. (author)

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

International Nuclear Information System (INIS)

Ammari, Zied

2000-01-01

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian

A minimax technique for time-domain design of preset digital equalizers using linear programming

Science.gov (United States)

Vaughn, G. L.; Houts, R. C.

1975-01-01

A linear programming technique is presented for the design of a preset finite-impulse response (FIR) digital filter to equalize the intersymbol interference (ISI) present in a baseband channel with known impulse response. A minimax technique is used which minimizes the maximum absolute error between the actual received waveform and a specified raised-cosine waveform. Transversal and frequency-sampling FIR digital filters are compared as to the accuracy of the approximation, the resultant ISI and the transmitted energy required. The transversal designs typically have slightly better waveform accuracy for a given distortion; however, the frequency-sampling equalizer uses fewer multipliers and requires less transmitted energy. A restricted transversal design is shown to use the least number of multipliers at the cost of a significant increase in energy and loss of waveform accuracy at the receiver.

Variationally Asymptotically Stable Difference Systems

Directory of Open Access Journals (Sweden)

Goo YoonHoe

2007-01-01

Full Text Available We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n∞-summable similarity and comparison principle. Furthermore we study the asymptotic equivalence between nonlinear difference systems and their variational difference systems by means of asymptotic equilibria of two systems.

Polynomial Asymptotes of the Second Kind

Science.gov (United States)

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…

PET image reconstruction: mean, variance, and optimal minimax criterion

International Nuclear Information System (INIS)

Liu, Huafeng; Guo, Min; Gao, Fei; Shi, Pengcheng; Xue, Liying; Nie, Jing

2015-01-01

Given the noise nature of positron emission tomography (PET) measurements, it is critical to know the image quality and reliability as well as expected radioactivity map (mean image) for both qualitative interpretation and quantitative analysis. While existing efforts have often been devoted to providing only the reconstructed mean image, we present a unified framework for joint estimation of the mean and corresponding variance of the radioactivity map based on an efficient optimal min–max criterion. The proposed framework formulates the PET image reconstruction problem to be a transformation from system uncertainties to estimation errors, where the minimax criterion is adopted to minimize the estimation errors with possibly maximized system uncertainties. The estimation errors, in the form of a covariance matrix, express the measurement uncertainties in a complete way. The framework is then optimized by ∞-norm optimization and solved with the corresponding H ∞ filter. Unlike conventional statistical reconstruction algorithms, that rely on the statistical modeling methods of the measurement data or noise, the proposed joint estimation stands from the point of view of signal energies and can handle from imperfect statistical assumptions to even no a priori statistical assumptions. The performance and accuracy of reconstructed mean and variance images are validated using Monte Carlo simulations. Experiments on phantom scans with a small animal PET scanner and real patient scans are also conducted for assessment of clinical potential. (paper)

Asymptotic numbers: Pt.1

International Nuclear Information System (INIS)

Todorov, T.D.

1980-01-01

The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed

Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence

International Nuclear Information System (INIS)

Zhang Tailei; Teng Zhidong

2008-01-01

In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Liapunov-LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence

Asymptotic Safety Guaranteed in Supersymmetry

Science.gov (United States)

Bond, Andrew D.; Litim, Daniel F.

2017-11-01

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.

Asymptotically anti-de Sitter spacetimes and scalar fields with a logarithmic branch

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge

2004-01-01

We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D≥3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the back-reaction of the scalar field, which has a logarithmic branch decreasing as r -(D-1)/2 ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative cosmological constant (conformal group in D-1 dimensions). The generators of the asymptotic symmetries are finite even when the logarithmic branch is considered but acquire, however, a contribution from the scalar field

A mutually profitable alliance - Asymptotic expansions and numerical computations

Science.gov (United States)

Euvrard, D.

Problems including the flow past a wing airfoil at Mach 1, and the two-dimensional flow past a partially immersed body are used to show the advantages of coupling a standard numerical method for the whole domain where everything is of the order of 1, with an appropriate asymptotic expansion in the vicinity of some singular point. Cases more closely linking the two approaches are then considered. In the localized finite element method, the asymptotic expansion at infinity becomes a convergent series and the problem reduces to a variational form. Combined analytical and numerical methods are used in the singularity distribution method and in the various couplings of finite elements and a Green integral representation to design a subroutine to compute the Green function and its derivatives.

Asymptotic structure of isolated systems

International Nuclear Information System (INIS)

Schmidt, B.G.

1979-01-01

The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)

Asymptotic state discrimination and a strict hierarchy in distinguishability norms

Energy Technology Data Exchange (ETDEWEB)

Chitambar, Eric [Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901 (United States); Hsieh, Min-Hsiu [Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology (FEIT), University of Technology Sydney - UTS, NSW 2007 (Australia)

2014-11-15

In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state discrimination, and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic LOCC. We use this new criterion to prove a gap in the LOCC and separable distinguishability norms. We then turn to the operational advantage of using two-way classical communication over one-way communication in LOCC processing. With a simple two-qubit product state ensemble, we demonstrate a strict majorization of the two-way LOCC norm over the one-way norm.

Asymptotic theory of two-dimensional trailing-edge flows

Science.gov (United States)

Melnik, R. E.; Chow, R.

1975-01-01

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

Generating asymptotically plane wave spacetimes

International Nuclear Information System (INIS)

Hubeny, Veronika E.; Rangamani, Mukund

2003-01-01

In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)

Asymptotic twistor theory and the Kerr theorem

International Nuclear Information System (INIS)

Newman, Ezra T

2006-01-01

We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds

Asymptotic integration of differential and difference equations

CERN Document Server

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...

The unitary conformal field theory behind 2D Asymptotic Safety

Energy Technology Data Exchange (ETDEWEB)

Nink, Andreas; Reuter, Martin [Institute of Physics, PRISMA & MITP, Johannes Gutenberg University Mainz,Staudingerweg 7, D-55099 Mainz (Germany)

2016-02-25

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 complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d>2 dimensions and Polyakov’s induced gravity action in two dimensions.

Asymptotic behaviour of Feynman integrals

International Nuclear Information System (INIS)

Bergere, M.C.

1980-01-01

In these lecture notes, we describe how to obtain the asymptotic behaviour of Feynman amplitudes; this technique has been already applied in several cases, but the general solution for any kind of asymptotic behaviour has not yet been found. From the mathematical point of view, the problem to solve is close to the following problem: find the asymptotic expansion at large lambda of the integral ∫...∫ [dx] esup(-LambdaP[x]) where P[x] is a polynomial of several variables. (orig.)

Nonminimal hints for asymptotic safety

Science.gov (United States)

Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran

2018-01-01

In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.

A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems

Directory of Open Access Journals (Sweden)

Ghasem Alizadeh Afrouzi

2006-10-01

Full Text Available In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem $$displaylines{ -u''(x+m(xu(x =lambda f(x,u(x,quad xin (a,b,cr u(a=u(b=0, }$$ where $lambda>0$, $f:[a,b]imes mathbb{R}o mathbb{R}$ is a continuous function which changes sign on $[a,b]imes mathbb{R}$ and $m(xin C([a,b]$ is a positive function.

Asymptotic functions and multiplication of distributions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-01-01

Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory

Asymptotic conformal invariance in a non-Abelian Chern-Simons-matter model

Energy Technology Data Exchange (ETDEWEB)

Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Campos e Particulas]. E-mail: acebal@cbpf.br

2002-08-01

One shows here the existence of solutions to the Callan-Symanzik equation for the non-Abelian SU(2) Chern-Simons-matter model which exhibits asymptotic conformal invariance to every order in perturbative theory. The conformal symmetry in the classical domain is shown to hold by means of a local criteria based on the trace of the energy-momentum tensor. By using recently exhibited regimes for the dependence between the several couplings in which the set of {beta}-functions vanish, the asymptotic conformal invariance of the model appears to be valid in the quantum domain. By considering the SU (n) case the possible non validity of the proof for a particular {eta} would be merely accidental. (author)

Exponential asymptotics of homoclinic snaking

International Nuclear Information System (INIS)

Dean, A D; Matthews, P C; Cox, S M; King, J R

2011-01-01

We study homoclinic snaking in the cubic-quintic Swift–Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319–54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement

Asymptotical representation of discrete groups

International Nuclear Information System (INIS)

Mishchenko, A.S.; Mohammad, N.

1995-08-01

If one has a unitary representation ρ: π → U(H) of the fundamental group π 1 (M) of the manifold M then one can do may useful things: 1. To construct a natural vector bundle over M; 2. To construct the cohomology groups with respect to the local system of coefficients; 3. To construct the signature of manifold M with respect to the local system of coefficients; and others. In particular, one can write the Hirzebruch formula which compares the signature with the characteristic classes of the manifold M, further based on this, find the homotopy invariant characteristic classes (i.e. the Novikov conjecture). Taking into account that the family of known representations is not sufficiently large, it would be interesting to extend this family to some larger one. Using the ideas of A.Connes, M.Gromov and H.Moscovici a proper notion of asymptotical representation is defined. (author). 7 refs

Fisher information and asymptotic normality in system identification for quantum Markov chains

International Nuclear Information System (INIS)

Guta, Madalin

2011-01-01

This paper deals with the problem of estimating the coupling constant θ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of θ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of θ=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.

Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories

International Nuclear Information System (INIS)

Gusynin, V.P.; Miranskij, V.A.

1986-01-01

An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed

Asymptotic inference in system identification for the atom maser.

Science.gov (United States)

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Journal Afrika Statistika ISSN 0852-0305 Asymptotic representation ...

African Journals Online (AJOL)

Asymptotic representation theorems for poverty indices ... Statistical asymptotic laws for these indices, particularly asymptotic normality, on which statistical inference on the ... population of individuals, each of which having a random income or ...

Asymptotic safety, emergence and minimal length

International Nuclear Information System (INIS)

Percacci, Roberto; Vacca, Gian Paolo

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 sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.

Asymptotic Poincare lemma and its applications

International Nuclear Information System (INIS)

Ziolkowski, R.W.; Deschamps, G.A.

1984-01-01

An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures

Renormalization group and asymptotic freedom

International Nuclear Information System (INIS)

Morris, J.R.

1978-01-01

Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions

Asymptotics of Laplace-Dirichlet integrals

International Nuclear Information System (INIS)

Kozlov, S.M.

1990-01-01

Here we consider the problem of the asymptotic expansion of the Laplace-Dirichlet integral. In homogenization theory such an integral represents the energy, and in general depends on the cohomology class. Here the asymptotic behaviour of this integral is found. The full text will appear in Functional Analysis and Applications, 1990, No.2. (author). 3 refs

A Minimax Network Flow Model for Characterizing the Impact of Slot Restrictions

Science.gov (United States)

Lee, Douglas W.; Patek, Stephen D.; Alexandrov, Natalia; Bass, Ellen J.; Kincaid, Rex K.

2010-01-01

This paper proposes a model for evaluating long-term measures to reduce congestion at airports in the National Airspace System (NAS). This model is constructed with the goal of assessing the global impacts of congestion management strategies, specifically slot restrictions. We develop the Minimax Node Throughput Problem (MINNTHRU), a multicommodity network flow model that provides insight into air traffic patterns when one minimizes the worst-case operation across all airports in a given network. MINNTHRU is thus formulated as a model where congestion arises from network topology. It reflects not market-driven airline objectives, but those of a regulatory authority seeking a distribution of air traffic beneficial to all airports, in response to congestion management measures. After discussing an algorithm for solving MINNTHRU for moderate-sized (30 nodes) and larger networks, we use this model to study the impacts of slot restrictions on the operation of an entire hub-spoke airport network. For both a small example network and a medium-sized network based on 30 airports in the NAS, we use MINNTHRU to demonstrate that increasing the severity of slot restrictions increases the traffic around unconstrained hub airports as well as the worst-case level of operation over all airports.

Asymptotic conditions and conserved quantities

International Nuclear Information System (INIS)

Koul, R.K.

1990-01-01

Two problems have been investigated in this dissertation. The first one deals with the relationship between stationary space-times which are flat at null infinity and stationary space-times which are asymptotic flat at space-like infinity. It is shown that the stationary space-times which are asymptotically flat, in the Penrose sense, at null infinity, are asymptotically flat at space-like infinity in the Geroch sense and metric at space like infinity is at least C 1 . In the converse it is shown that the stationary space-times which are asymptotically flat at space like infinity, in the Beig sense, are asymptotically flat at null infinity in the Penrose sense. The second problem addressed deals with the theories of arbitrary dimensions. The theories treated are the ones which have fiber bundle structure, outside some compact region. For these theories the criterion for the choice of the background metric is specified, and the boundary condition for the initial data set (q ab , P ab ) is given in terms of the background metric. Having these boundary conditions it is shown that the symplectic structure and the constraint functionals are well defined. The conserved quantities associated with internal Killing vector fields are specified. Lastly the energy relative to a fixed background and the total energy of the theory have been given. It is also shown that the total energy of the theory is independent of the choice of the background

Asymptotic Value Distribution for Solutions of the Schroedinger Equation

International Nuclear Information System (INIS)

Breimesser, S. V.; Pearson, D. B.

2000-01-01

We consider the Dirichlet Schroedinger operator T=-(d 2 /d x 2 )+V, acting in L 2 (0,∞), where Vis an arbitrary locally integrable potential which gives rise to absolutely continuous spectrum. Without any other restrictive assumptions on the potential V, the description of asymptotics for solutions of the Schroedinger equation is carried out within the context of the theory of value distribution for boundary values of analytic functions. The large x asymptotic behaviour of the solution v(x,λ) of the equation Tf(x,λ)=λf(x,λ), for λ in the support of the absolutely continuous part μ a.c. of the spectral measure μ, is linked to the spectral properties of this measure which are determined by the boundary value of the Weyl-Titchmarsh m-function. Our main result (Theorem 1) shows that the value distribution for v'(N,λ)/v(N,λ) approaches the associated value distribution of the Herglotz function m N (z) in the limit N → ∞, where m N (z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d 2 /d x 2 )+Vacting in L 2 (N,∞), with Dirichlet boundary condition at x=N. We will relate the analysis of spectral asymptotics for the absolutely continuous component of Schroedinger operators to geometrical properties of the upper half-plane, viewed as a hyperbolic space

Trinucleon asymptotic normalization constants including Coulomb effects

International Nuclear Information System (INIS)

Friar, J.L.; Gibson, B.F.; Lehman, D.R.; Payne, G.L.

1982-01-01

Exact theoretical expressions for calculating the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Coordinate-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the D-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the 3 He S-wave asymptotic norm by less than 1% relative to that of 3 H, that Coulomb effects decrease the 3 He D-wave asymptotic norm by approximately 8% relative to that of 3 H, and that the distorted-wave Born approximation D-state parameter, D 2 , is only 1% smaller in magnitude for 3 He than for 3 H due to compensating Coulomb effects

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Directory of Open Access Journals (Sweden)

G. M. N’Guérékata

2018-01-01

Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.

Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift

NARCIS (Netherlands)

Kamphorst, B.; Zwart, B.

2015-01-01

This paper addresses heavy-tailed asymptotics of functionals of a class of spectrally one-sided L\\'evy process that remain valid in a near-critical regime. This complements recent similar results that have been obtained for the all-time supremum of such processes. Specifically, we consider local

Robustness Recipes for Minimax Robust Optimization in Intensity Modulated Proton Therapy for Oropharyngeal Cancer Patients

Energy Technology Data Exchange (ETDEWEB)

Voort, Sebastian van der [Department of Radiation Oncology, Erasmus MC Cancer Institute, Rotterdam (Netherlands); Section of Nuclear Energy and Radiation Applications, Department of Radiation, Science and Technology, Delft University of Technology, Delft (Netherlands); Water, Steven van de [Department of Radiation Oncology, Erasmus MC Cancer Institute, Rotterdam (Netherlands); Perkó, Zoltán [Section of Nuclear Energy and Radiation Applications, Department of Radiation, Science and Technology, Delft University of Technology, Delft (Netherlands); Heijmen, Ben [Department of Radiation Oncology, Erasmus MC Cancer Institute, Rotterdam (Netherlands); Lathouwers, Danny [Section of Nuclear Energy and Radiation Applications, Department of Radiation, Science and Technology, Delft University of Technology, Delft (Netherlands); Hoogeman, Mischa, E-mail: m.hoogeman@erasmusmc.nl [Department of Radiation Oncology, Erasmus MC Cancer Institute, Rotterdam (Netherlands)

2016-05-01

Purpose: We aimed to derive a “robustness recipe” giving the range robustness (RR) and setup robustness (SR) settings (ie, the error values) that ensure adequate clinical target volume (CTV) coverage in oropharyngeal cancer patients for given gaussian distributions of systematic setup, random setup, and range errors (characterized by standard deviations of Σ, σ, and ρ, respectively) when used in minimax worst-case robust intensity modulated proton therapy (IMPT) optimization. Methods and Materials: For the analysis, contoured computed tomography (CT) scans of 9 unilateral and 9 bilateral patients were used. An IMPT plan was considered robust if, for at least 98% of the simulated fractionated treatments, 98% of the CTV received 95% or more of the prescribed dose. For fast assessment of the CTV coverage for given error distributions (ie, different values of Σ, σ, and ρ), polynomial chaos methods were used. Separate recipes were derived for the unilateral and bilateral cases using one patient from each group, and all 18 patients were included in the validation of the recipes. Results: Treatment plans for bilateral cases are intrinsically more robust than those for unilateral cases. The required RR only depends on the ρ, and SR can be fitted by second-order polynomials in Σ and σ. The formulas for the derived robustness recipes are as follows: Unilateral patients need SR = −0.15Σ{sup 2} + 0.27σ{sup 2} + 1.85Σ − 0.06σ + 1.22 and RR=3% for ρ = 1% and ρ = 2%; bilateral patients need SR = −0.07Σ{sup 2} + 0.19σ{sup 2} + 1.34Σ − 0.07σ + 1.17 and RR=3% and 4% for ρ = 1% and 2%, respectively. For the recipe validation, 2 plans were generated for each of the 18 patients corresponding to Σ = σ = 1.5 mm and ρ = 0% and 2%. Thirty-four plans had adequate CTV coverage in 98% or more of the simulated fractionated treatments; the remaining 2 had adequate coverage in 97.8% and 97.9%. Conclusions: Robustness recipes were derived that can

On maximal surfaces in asymptotically flat space-times

International Nuclear Information System (INIS)

Bartnik, R.; Chrusciel, P.T.; O Murchadha, N.

1990-01-01

Existence of maximal and 'almost maximal' hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurface can be used to 'partially fix' an asymptotic Poincare group. (orig.)

On asymptotic continuity of functions of quantum states

International Nuclear Information System (INIS)

Synak-Radtke, Barbara; Horodecki, Michal

2006-01-01

A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this letter, we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called robustness under admixture. This allows us to show that relative entropy distance from a convex set including a maximally mixed state is asymptotically continuous. Subsequently, we consider arrowing-a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples. (letter to the editor)

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Science.gov (United States)

Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

2017-11-01

Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

Black holes and asymptotics of 2+1 gravity coupled to a scalar field

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge

2002-01-01

We consider 2+1 gravity minimally coupled to a self-interacting scalar field. The case in which the fall-off of the fields at infinity is slower than that of a localized distribution of matter is analyzed. It is found that the asymptotic symmetry group remains the same as in pure gravity (i.e., the conformal group). The generators of the asymptotic symmetries, however, acquire a contribution from the scalar field, but the algebra of the canonical generators possesses the standard central extension. In this context, new massive black hole solutions with a regular scalar field are found for a one-parameter family of potentials. These black holes are continuously connected to the standard zero mass black hole

Stationary solutions and asymptotic flatness I

International Nuclear Information System (INIS)

Reiris, Martin

2014-01-01

In general relativity, a stationary isolated system is defined as an asymptotically flat (AF) stationary spacetime with compact material sources. Other definitions that are less restrictive on the type of asymptotic could in principle be possible. Between this article and its sequel, we show that under basic assumptions, asymptotic flatness indeed follows as a consequence of Einstein's theory. In particular, it is proved that any vacuum stationary spacetime-end whose (quotient) manifold is diffeomorphic to R 3 minus a ball and whose Killing field has its norm bounded away from zero, is necessarily AF with Schwarzschildian fall off. The ‘excised’ ball would contain (if any) the actual material body, but this information is unnecessary to reach the conclusion. In this first article, we work with weakly asymptotically flat (WAF) stationary ends, a notion that generalizes as much as possible that of the AF end, and prove that WAF ends are AF with Schwarzschildian fall off. Physical and mathematical implications are also discussed. (paper)

Asymptotic Analysis of SPTA-Based Algorithms for No-Wait Flow Shop Scheduling Problem with Release Dates

Directory of Open Access Journals (Sweden)

Tao Ren

2014-01-01

Full Text Available We address the scheduling problem for a no-wait flow shop to optimize total completion time with release dates. With the tool of asymptotic analysis, we prove that the objective values of two SPTA-based algorithms converge to the optimal value for sufficiently large-sized problems. To further enhance the performance of the SPTA-based algorithms, an improvement scheme based on local search is provided for moderate scale problems. New lower bound is presented for evaluating the asymptotic optimality of the algorithms. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Asymptotic analysis of SPTA-based algorithms for no-wait flow shop scheduling problem with release dates.

Science.gov (United States)

Ren, Tao; Zhang, Chuan; Lin, Lin; Guo, Meiting; Xie, Xionghang

2014-01-01

We address the scheduling problem for a no-wait flow shop to optimize total completion time with release dates. With the tool of asymptotic analysis, we prove that the objective values of two SPTA-based algorithms converge to the optimal value for sufficiently large-sized problems. To further enhance the performance of the SPTA-based algorithms, an improvement scheme based on local search is provided for moderate scale problems. New lower bound is presented for evaluating the asymptotic optimality of the algorithms. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Symmetry breaking and asymptotic freedom in colour SU(3) gauge models

International Nuclear Information System (INIS)

Ma, E.

1976-01-01

A class of quark models based on the colour gauge group SU(3) is shown to be asymptotically free despite the complete breakdown of local symmetry to guarantee infrared stability. The symmetry breakdown is achieved by the presence of elementary scalar fields either through the Higgs mechanism or dynamically as first proposed by Coleman and Weinberg. Asymptotic freedom is preserved by imposing eigenvalue conditions on the coupling constants as first proposed by Chang. New quark species must be present, but below their production threshold, colour can still be a global symmetry which is approximate under SU(3), but exact under SU(2). Among the many implications of this class of models is the possibility of producing isolated quarks and gluons of non-zero mass without altering the short-distance behaviour of the superstrong interaction which binds them. (Auth.)

On the asymptotic evolution of finite energy Airy wave functions.

Science.gov (United States)

Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S

2015-06-15

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

Asymptotic theory of double layer and shielding of electric field at the edge of illuminated plasma

Energy Technology Data Exchange (ETDEWEB)

Benilov, M. S. [Departamento de Física, CCCEE, Universidade da Madeira, Largo do Município, 9000 Funchal (Portugal); Thomas, D. M. [Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)

2014-04-15

The method of matched asymptotic expansions is applied to the problem of a collisionless plasma generated by UV illumination localized in a central part of the plasma in the limiting case of small Debye length λ{sub D}. A second-approximation asymptotic solution is found for the double layer positioned at the boundary of the illuminated region and for the un-illuminated plasma for the plane geometry. Numerical calculations for different values of λ{sub D} are reported and found to confirm the asymptotic results. The net integral space charge of the double layer is asymptotically small, although in the plane geometry it is just sufficient to shield the ambipolar electric field existing in the illuminated region and thus to prevent it from penetrating into the un-illuminated region. The double layer has the same mathematical nature as the intermediate transition layer separating an active plasma and a collisionless sheath, and the underlying physics is also the same. In essence, the two layers represent the same physical object: a transonic layer.

Inference for Local Distributions at High Sampling Frequencies: A Bootstrap Approach

DEFF Research Database (Denmark)

Hounyo, Ulrich; Varneskov, Rasmus T.

of "large" jumps. Our locally dependent wild bootstrap (LDWB) accommodate issues related to the stochastic scale and jumps as well as account for a special block-wise dependence structure induced by sampling errors. We show that the LDWB replicates first and second-order limit theory from the usual...... empirical process and the stochastic scale estimate, respectively, as well as an asymptotic bias. Moreover, we design the LDWB sufficiently general to establish asymptotic equivalence between it and and a nonparametric local block bootstrap, also introduced here, up to second-order distribution theory....... Finally, we introduce LDWB-aided Kolmogorov-Smirnov tests for local Gaussianity as well as local von-Mises statistics, with and without bootstrap inference, and establish their asymptotic validity using the second-order distribution theory. The finite sample performance of CLT and LDWB-aided local...

Fixed point theorems in locally convex spaces—the Schauder mapping method

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S. Cobzaş

2006-03-01

Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.

Asymptotically warped anti-de Sitter spacetimes in topologically massive gravity

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo

2011-01-01

Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the ''massive graviton'') is switched on. An exact solution with this property is explicitly exhibited and possesses a slower falloff than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra. We show that the canonical generators are integrable and finite. When the graviton is not excited, our analysis is compared and contrasted with earlier results obtained through the covariant approach to conserved charges. In particular, we find agreement with the conserved charges of the warped AdS black holes as well as with the central charges in the algebra.

Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

International Nuclear Information System (INIS)

Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

2015-01-01

Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

FREQUENCY ANALYSIS OF RLE-BLOCKS REPETITIONS IN THE SERIES OF BINARY CODES WITH OPTIMAL MINIMAX CRITERION OF AUTOCORRELATION FUNCTION

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A. A. Kovylin

2013-01-01

Full Text Available The article describes the problem of searching for binary pseudo-random sequences with quasi-ideal autocorrelation function, which are to be used in contemporary communication systems, including mobile and wireless data transfer interfaces. In the synthesis of binary sequences sets, the target set is manning them based on the minimax criterion by which a sequence is considered to be optimal according to the intended application. In the course of the research the optimal sequences with order of up to 52 were obtained; the analysis of Run Length Encoding was carried out. The analysis showed regularities in the distribution of series number of different lengths in the codes that are optimal on the chosen criteria, which would make it possible to optimize the searching process for such codes in the future.

Asymptotic Conservation Laws in Classical Field Theory

International Nuclear Information System (INIS)

Anderson, I.M.; Torre, C.G.

1996-01-01

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society

Asymptotic symmetries, holography and topological hair

Science.gov (United States)

Mishra, Rashmish K.; Sundrum, Raman

2018-01-01

Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons

Subexponential loss rate asymptotics for Lévy processes

DEFF Research Database (Denmark)

Andersen, Lars Nørvang

2011-01-01

We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotic...... for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula....

ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM

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Kuzmina Ludmila Ivanovna

2017-11-01

Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.

Asymptotic work distributions in driven bistable systems

International Nuclear Information System (INIS)

Nickelsen, D; Engel, A

2012-01-01

The asymptotic tails of the probability distributions of thermodynamic quantities convey important information about the physics of nanoscopic systems driven out of equilibrium. We apply a recently proposed method to analytically determine the asymptotics of work distributions in Langevin systems to an one-dimensional model of single-molecule force spectroscopy. The results are in excellent agreement with numerical simulations, even in the centre of the distributions. We compare our findings with a recent proposal for an universal form of the asymptotics of work distributions in single-molecule experiments.

Large gauge symmetries and asymptotic states in QED

Energy Technology Data Exchange (ETDEWEB)

Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)

2016-12-19

Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.

Asymptotic analysis and boundary layers

CERN Document Server

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...

Asymptotic theory for regressions with smoothly changing parameters

DEFF Research Database (Denmark)

Hillebrand, Eric; Medeiros, Marcelo; Xu, Junyue

2013-01-01

We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual pT-rate and has...... an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....

A quantum kinematics for asymptotically flat gravity

Science.gov (United States)

Campiglia, Miguel; Varadarajan, Madhavan

2015-07-01

We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under 2π rotations.

Asymptotic evolution of quantum Markov chains

Energy Technology Data Exchange (ETDEWEB)

Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

2012-07-01

The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.

Criteria for exponential asymptotic stability in the large of ...

African Journals Online (AJOL)

The purpose of this study is to provide necessary and sufficient conditions for exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear systems with unbounded delays. A strong relationship is established between the two types of asymptotic stability. It is found that if the ...

Multiple-copy state discrimination: Thinking globally, acting locally

International Nuclear Information System (INIS)

Higgins, B. L.; Pryde, G. J.; Wiseman, H. M.; Doherty, A. C.; Bartlett, S. D.

2011-01-01

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies N, and in the asymptotic limit as N→∞. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here an adaptive measurement is one in which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite N) and the scaling of this error in the asymptotic limit. In the asymptotic limit, it is known analytically (and we verify numerically) that adaptive schemes have no advantage over the optimal fixed local scheme. Here we show moreover that, in this limit, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme except for states with less than 2% mixture. For finite N, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme for any degree of mixture.

Asymptotic Theory for Regressions with Smoothly Changing Parameters

DEFF Research Database (Denmark)

Hillebrand, Eric Tobias; Medeiros, Marcelo C.; Xu, Junyue

We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual square-root-of-T rate...... and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....

Asymptotic expansion of the Keesom integral

International Nuclear Information System (INIS)

Abbott, Paul C

2007-01-01

The asymptotic evaluation and expansion of the Keesom integral, K(a), is discussed at some length in Battezzati and Magnasco (2004 J. Phys. A: Math. Gen. 37 9677; 2005 J. Phys. A: Math. Gen. 38 6715). Here, using standard identities, it is shown that this triple integral can be reduced to a single integral from which the asymptotic behaviour is readily obtained using Laplace's method. (comment)

AGB [asymptotic giant branch]: Star evolution

International Nuclear Information System (INIS)

Becker, S.A.

1987-01-01

Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs

Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences

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Bipan Hazarika

2013-01-01

in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

Asymptotic geometric analysis, part I

CERN Document Server

Artstein-Avidan, Shiri

2015-01-01

The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen

Asymptotic safety guaranteed

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 ...

Cosmic censorship, persistent curvature and asymptotic causal pathology

International Nuclear Information System (INIS)

Newman, R.P.A.C.

1984-01-01

The paper examines cosmic censorship in general relativity theory. Conformally flat space-times; persistent curvature; weakly asymptotically simple and empty asymptotes; censorship conditions; and the censorship theorem; are all discussed. (U.K.)

Asymptotics of bivariate generating functions with algebraic singularities

Science.gov (United States)

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.

Asymptotic convergence for iterative optimization in electronic structure

International Nuclear Information System (INIS)

Lippert, Ross A.; Sears, Mark P.

2000-01-01

There have recently been a number of proposals for solving large electronic structure problems (local-density approximation, Hartree-Fock, and tight-binding methods) iteratively with a computational effort proportional to the size of the system. The effort needed to perform a single iteration in these schemes is well understood but the convergence rate has been an empirical matter. This paper will show that many of the proposed methods have a single underlying geometrical structure, which has a specific asymptotic convergence behavior, and that behavior can be understood in terms of some simple condition numbers based on the spectrum of the Hamiltonian. (c) 2000 The American Physical Society

Asymptotic expansions for high-contrast linear elasticity

KAUST Repository

Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan

2015-01-01

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 expansions for high-contrast linear elasticity

KAUST Repository

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.

On asymptotic analysis of spectral problems in elasticity

Directory of Open Access Journals (Sweden)

S.A. Nazarov

Full Text Available The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.

Lattice quantum gravity and asymptotic safety

Science.gov (United States)

Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.

2017-09-01

We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3 /2 , a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.

Asymptotically free SU(5) models

International Nuclear Information System (INIS)

Kogan, Ya.I.; Ter-Martirosyan, K.A.; Zhelonkin, A.V.

1981-01-01

The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles [ru

8. Asymptotically Flat and Regular Cauchy Data

Science.gov (United States)

Dain, Sergio

I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation

Science.gov (United States)

Luo, Xiao

2018-06-01

We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrödinger equation arising from the Chern-Simons theory Δ u + ω u +|x|^2u+ λ ( {{h^2}(| x | )}/{{{| x | ^2}}} + \\int \\limits _{| x | }^{ + ∞} {{h(s)}/s} {u^2}(s)ds) u = {| u | ^{p - 2}}u,\\quad x\\in R^2, where ω \\in R, λ >0, p>4 and h(s) = 1/2\\int \\limits _0^s {r{u^2}(r)dr} . Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

Delay-dependent asymptotic stability of a two-neuron system with different time delays

International Nuclear Information System (INIS)

Tu Fenghua; Liao Xiaofeng; Zhang Wei

2006-01-01

In this paper, we consider a two-neuron system with time-delayed connections between neurons. Based on the construction of Lyapunov functionals, we obtain sufficient criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. The obtained conditions are shown to be less conservative and restrictive than those reported in the literature. Some examples are included to illustrate our results

Asymptotics for the Kummer function of Bose plasmas

International Nuclear Information System (INIS)

Kowalenko, V.; Frankel, N.E.

1993-01-01

The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetised Bose plasmas at T = 0 K are presented for large and small values of its parameter, thereby displaying the function's asymptotic non-uniformity. The large parameter expansion plays a determining role in the behaviour of these Bose systems in the limit that the external magnetic field B →0. This particular expansion is generalised herein and its validity tested by determining the asymptotic expansion for the Hurwitz zeta function. 18 refs., 1 tab., 2 figs

Komar integrals in asymptotically anti-de Sitter space-times

International Nuclear Information System (INIS)

Magnon, A.

1985-01-01

Recently, boundary conditions governing the asymptotic behavior of the gravitational field in the presence of a negative cosmological constant have been introduced using Penrose's conformal techniques. The subsequent analysis has led to expressions of conserved quantities (associated with asymptotic symmetries) involving asymptotic Weyl curvature. On the other hand, if the underlying space-time is equipped with isometries, a generalization of the Komar integral which incorporates the cosmological constant is also available. Thus, in the presence of an isometry, one is faced with two apparently unrelated definitions. It is shown that these definitions agree. This coherence supports the choice of boundary conditions for asymptotically anti-de Sitter space-times and reinforces the definitions of conserved quantities

Preheating in an asymptotically safe quantum field theory

DEFF Research Database (Denmark)

Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert

2016-01-01

. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance...... fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F......We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J...

A method for summing nonalternating asymptotic series

International Nuclear Information System (INIS)

Kazakov, D.I.

1980-01-01

A method for reconstructing a function from its nonalternating asymptotic series is proposed. It can also be applied when only a limited number of coefficients and their high order asymptotic behaviour are known. The method is illustrated by examples of the ordinary simple integral simulating a functional integral in a theory with degenerate minimum and of the double-well unharmonic oscillator

Asymptotic Analysis in MIMO MRT/MRC Systems

Directory of Open Access Journals (Sweden)

Zhou Quan

2006-01-01

Full Text Available Through the analysis of the probability density function of the squared largest singular value of a complex Gaussian matrix at the origin and tail, we obtain two asymptotic results related to the multi-input multi-output (MIMO maximum-ratio-transmission/maximum-ratio-combining (MRT/MRC systems. One is the asymptotic error performance (in terms of SNR in a single-user system, and the other is the asymptotic system capacity (in terms of the number of users in the multiuser scenario when multiuser diversity is exploited. Similar results are also obtained for two other MIMO diversity schemes, space-time block coding and selection combining. Our results reveal a simple connection with system parameters, providing good insights for the design of MIMO diversity systems.

Inversion of quasi-periodic deviations between low-degree solar gravity mode eigenfrequencies and asymptotic theory eigenfrequencies

International Nuclear Information System (INIS)

Hill, H.A.; Gao, Qiang; Rosenwald, R.D.

1988-01-01

The fine structure found by Gu, Hill and Rosenwald between asymptotic theory eigenfrequencies and the observed eigenfrequencies reported by Hill and Gu is interpreted as the result of conditions not being met for the applicability of asymptotic theory at one or more radii in the solar interior. From an inversion of the observed fine structure, reasonably good agreement is obtained between observation and theory for either a localized perturbation in internal structure at r/R ∼ 0.06 or at r/R ∼ 0.23. The latter solution is, however, the better one. The amplitude of the perturbation in the mean molecular weight required to produce the fine structure is also inferred. 11 refs., 2 figs

Asymptotic expansions for high-contrast elliptic equations

KAUST Repository

Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan

2014-01-01

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.

Asymptotic expansions for high-contrast elliptic equations

KAUST Repository

Calo, Victor M.

2014-03-01

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.

Asymptotic failure rate of a continuously monitored system

International Nuclear Information System (INIS)

Grall, A.; Dieulle, L.; Berenguer, C.; Roussignol, M.

2006-01-01

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

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.

Asymptotic structure of space-time with a positive cosmological constant

Science.gov (United States)

Kesavan, Aruna

In general relativity a satisfactory framework for describing isolated systems exists when the cosmological constant Lambda is zero. The detailed analysis of the asymptotic structure of the gravitational field, which constitutes the framework of asymptotic flatness, lays the foundation for research in diverse areas in gravitational science. However, the framework is incomplete in two respects. First, asymptotic flatness provides well-defined expressions for physical observables such as energy and momentum as 'charges' of asymptotic symmetries at null infinity, [special character omitted] +. But the asymptotic symmetry group, called the Bondi-Metzner-Sachs group is infinite-dimensional and a tensorial expression for the 'charge' integral of an arbitrary BMS element is missing. We address this issue by providing a charge formula which is a 2-sphere integral over fields local to the 2-sphere and refers to no extraneous structure. The second, and more significant shortcoming is that observations have established that Lambda is not zero but positive in our universe. Can the framework describing isolated systems and their gravitational radiation be extended to incorporate this fact? In this dissertation we show that, unfortunately, the standard framework does not extend from the Lambda = 0 case to the Lambda > 0 case in a physically useful manner. In particular, we do not have an invariant notion of gravitational waves in the non-linear regime, nor an analog of the Bondi 'news tensor', nor positive energy theorems. In addition, we argue that the stronger boundary condition of conformal flatness of intrinsic metric on [special character omitted]+, which reduces the asymptotic symmetry group from Diff([special character omitted]) to the de Sitter group, is insufficient to characterize gravitational fluxes and is physically unreasonable. To obtain guidance for the full non-linear theory with Lambda > 0, linearized gravitational waves in de Sitter space-time are analyzed in

Comment on 'Asymptotic form of the Kohn-Sham correlation potential'

International Nuclear Information System (INIS)

Holas, A.

2008-01-01

For finite systems that have the energetically highest-occupied molecular orbital (HOMO) with an asymptotic nodal surface, Joubert demonstrated recently [Phys. Rev. A 76, 012501 (2007)] strongly anisotropic behavior (in the asymptotic large-r region) of the exact correlation potential of density-functional theory. As is shown by us, this result is a direct and simple consequence of the strong anisotropy of the exact exchange potential obtained by Della Sala and Goerling [Phys. Rev. Lett. 89, 033003 (2002); Della Sala and GoerlingJ. Chem. Phys. 116, 5374 (2002)] and the assumption about the asymptotic isotropy of the Kohn-Sham (KS) potential (based on the investigation of Almbladh and von Barth [Phys. Rev. B 31, 3231 (1985)] for atoms). Joubert's result remains a hypothesis only, because the last assumption is in contradiction with the asymptotic strong anisotropy of the KS potential for systems with asymptotic nodal surface of the HOMO, demonstrated by Wu, Ayers, and Yang [J. Chem. Phys. 119, 2978 (2003)]. The correlation potential in the asymptotic region, stemming from their results, is given

Asymptotic behaviour of two-point functions in multi-species models

Directory of Open Access Journals (Sweden)

Karol K. Kozlowski

2016-05-01

Full Text Available We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the SU(3-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.

Pseudo-random number generator based on asymptotic deterministic randomness

Science.gov (United States)

Wang, Kai; Pei, Wenjiang; Xia, Haishan; Cheung, Yiu-ming

2008-06-01

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.

Pseudo-random number generator based on asymptotic deterministic randomness

International Nuclear Information System (INIS)

Wang Kai; Pei Wenjiang; Xia Haishan; Cheung Yiuming

2008-01-01

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks

Asymptotic symmetries in de Sitter and inflationary spacetimes

Energy Technology Data Exchange (ETDEWEB)

Ferreira, Ricardo Z.; Sandora, McCullen; Sloth, Martin S., E-mail: ferreira@cp3.sdu.dk, E-mail: sandora@cp3.sdu.dk, E-mail: sloth@cp3.sdu.dk [CP3-Origins, Center for Cosmology and Particle Physics Phenomenology, University of Southern Denmark, Campusvej 55, 5230 Odense M (Denmark)

2017-04-01

Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, (0| 0'), between the unperturbed de Sitter vacuum |0), and the state | 0') obtained by acting N times with the charge. We show that when N→ M {sub p} {sup 2}/ H {sup 2} this overlap receives order one corrections and 0(0| 0')→ , which corresponds to an infrared perturbative breakdown after a time t {sub dS} ∼ M {sub p} {sup 2}/ H {sup 3} has elapsed, consistent with earlier arguments in the literature arguing for a perturbative breakdown on this timescale. We also discuss the generalization to inflation, and rederive the 3-point and one-loop consistency relations.

Numerical algorithms for uniform Airy-type asymptotic expansions

NARCIS (Netherlands)

N.M. Temme (Nico)

1997-01-01

textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing

H. David Politzer, Asymptotic Freedom, and Strong Interaction

Science.gov (United States)

dropdown arrow Site Map A-Z Index Menu Synopsis H. David Politzer, Asymptotic Freedom, and Strong Interaction Resources with Additional Information H. David Politzer Photo Credit: California Institute of Technology H. David Politzer has won the 2004 Nobel Prize in Physics 'for the discovery of asymptotic freedom

Robust methods and asymptotic theory in nonlinear econometrics

CERN Document Server

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 ...

Stark resonances: asymptotics and distributional Borel sum

International Nuclear Information System (INIS)

Caliceti, E.; Grecchi, V.; Maioli, M.

1993-01-01

We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by Distributional Borel Sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the ''resonances'' of the anharmonic and double well oscillators. (orig.)

Asymptotic freedom without guilt

International Nuclear Information System (INIS)

Ma, E.

1979-01-01

The notion of asymptotic freedom in quantum chromodynamics is explained on general physical grounds, without invoking the formal arguments of renormalizable quantum field theory. The related concept of quark confinement is also discussed along the same line. 5 references

Conformal Phase Diagram of Complete Asymptotically Free Theories

DEFF Research Database (Denmark)

Pica, Claudio; Ryttov, Thomas A.; Sannino, Francesco

2017-01-01

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 representation theorems for poverty indices | Lo | Afrika ...

African Journals Online (AJOL)

Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...

Behavior of asymptotically electro-Λ spacetimes

Science.gov (United States)

Saw, Vee-Liem

2017-04-01

We present the asymptotic solutions for spacetimes with nonzero cosmological constant Λ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with Λ ≠0 . The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass loss of an isolated electrogravitating system with cosmological constant. In a universe with Λ >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 I and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with Λ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces nonconformal flatness of I . These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where Λ =0 , to now incorporate the cosmological constant Λ .

Numerical integration of asymptotic solutions of ordinary differential equations

Science.gov (United States)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Exact asymptotic expansions for solutions of multi-dimensional renewal equations

International Nuclear Information System (INIS)

Sgibnev, M S

2006-01-01

We derive expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations. The effect of the roots of the characteristic equation on the asymptotic representation of solutions is taken into account. The resulting formulae are used to investigate the asymptotic behaviour of the average number of particles in age-dependent branching processes having several types of particles

Asymptotic stability of a catalyst particle

DEFF Research Database (Denmark)

Wedel, Stig; Michelsen, Michael L.; Villadsen, John

1977-01-01

The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...

Non-Asymptotic Confidence Sets for Circular Means

Directory of Open Access Journals (Sweden)

Thomas Hotz

2016-10-01

Full Text Available The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set.

Asymptotic freedom

International Nuclear Information System (INIS)

Meyer, P.

1978-01-01

After having established the renormalization group equations and the possibilities of fixed points for the effective coupling constants the non abelian gauge theories are shown to have the property of asymptotic freedom. These results are applied to the colour gauge group of the strong interactions of quarks and gluons. The behavior of the moments of the structure functions of the deep inelastic scattering of leptons on nucleons (scaling and its logarithmic violations) is then deduced with using the Wilson's operator product expansion [fr

Cookbook asymptotics for spiral and scroll waves in excitable media.

Science.gov (United States)

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.

Asymptotic propagators and trajectories in plasma turbulence theory. The importance of irreversibility, asymptoticity and non-Markovian terms

International Nuclear Information System (INIS)

Misguich, J.H.

1978-09-01

The physical meaning of perturbed trajectories in turbulent fields is analysed. Special care is devoted to the asymptotic description of average trajectories for long time intervals, as occuring in many recent plasma turbulence theories. Equivalence is proved between asymptotic average trajectories described as well (i) by the propagators V(t,t-tau) for retrodiction and Wsub(J)(t,t+tau) for prediction, and (ii) by the long time secular behavior of the solution of the equations of motion. This confirms the equivalence between perturbed orbit theories and renormalized theories, including non-Markovian contributions

An asymptotical machine

Science.gov (United States)

Cristallini, Achille

2016-07-01

A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.

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.

Asymptotic safety of gravity with matter

Science.gov (United States)

Christiansen, Nicolai; Litim, Daniel F.; Pawlowski, Jan M.; Reichert, Manuel

2018-05-01

We study the asymptotic safety conjecture for quantum gravity in the presence of matter fields. A general line of reasoning is put forward explaining why gravitons dominate the high-energy behavior, largely independently of the matter fields as long as these remain sufficiently weakly coupled. Our considerations are put to work for gravity coupled to Yang-Mills theories with the help of the functional renormalization group. In an expansion about flat backgrounds, explicit results for beta functions, fixed points, universal exponents, and scaling solutions are given in systematic approximations exploiting running propagators, vertices, and background couplings. Invariably, we find that the gauge coupling becomes asymptotically free while the gravitational sector becomes asymptotically safe. The dependence on matter field multiplicities is weak. We also explain how the scheme dependence, which is more pronounced, can be handled without changing the physics. Our findings offer a new interpretation of many earlier results, which is explained in detail. The results generalize to theories with minimally coupled scalar and fermionic matter. Some implications for the ultraviolet closure of the Standard Model or its extensions are given.

Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

OpenAIRE

Cortazar, C.; Elgueta, M.; Quiros, F.; Wolanski, N.

2011-01-01

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\\mathbb{R}^N\\setminus\\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves...

Asymptotically anti-de Sitter spacetimes in topologically massive gravity

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo

2009-01-01

We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter μ (μ≠0). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point |μl|=1 (where l is the anti-de Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.

Asymptotic series and functional integrals in quantum field theory

International Nuclear Information System (INIS)

Shirkov, D.V.

1979-01-01

Investigations of the methods for analyzing ultra-violet and infrared asymptotics in the quantum field theory (QFT) have been reviewed. A powerful method of the QFT analysis connected with the group property of renormalized transformations has been created at the first stage. The result of the studies of the second period is the constructive solution of the problem of outgoing the framework of weak coupling. At the third stage of studies essential are the asymptotic series and functional integrals in the QFT, which are used for obtaining the asymptotic type of the power expansion coefficients in the coupling constant at high values of the exponents for a number of simple models. Further advance to higher values of the coupling constant requires surmounting the difficulties resulting from the asymptotic character of expansions and a constructive application in the region of strong coupling (g >> 1)

Asymptotically shear-free and twist-free null geodesic congruences

International Nuclear Information System (INIS)

Kozameh, Carlos; Newman, Ezra T

2007-01-01

The Robinson-Trautman spacetime is a special case of asymptotically flat spacetimes that possess asymptotically shear-free and twist-free (surface forming) null geodesic congruences. In this paper we show that, although they are rare, a larger class of asymptotically flat spacetimes with this property does exist. In particular, we display the class of spacetimes that possess this dual property and demonstrate how these congruences can be found. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighbouring congruences with this dual property

Heat Kernel Asymptotics of Zaremba Boundary Value Problem

Energy Technology Data Exchange (ETDEWEB)

Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu

2004-03-15

The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

Directory of Open Access Journals (Sweden)

Timothy M. Adamo

2009-09-01

Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

Directory of Open Access Journals (Sweden)

Timothy M. Adamo

2012-01-01

Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, H-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi's integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation.

Science.gov (United States)

Adamo, Timothy M; Newman, Ezra T; Kozameh, Carlos

2012-01-01

A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, [Formula: see text]-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum-conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Szegö Kernels and Asymptotic Expansions for Legendre Polynomials

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Roberto Paoletti

2017-01-01

Full Text Available We present a geometric approach to the asymptotics of the Legendre polynomials Pk,n+1, based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of [-1,1].

Asymptotic theory of time varying networks with burstiness and heterogeneous activation patterns

Science.gov (United States)

Burioni, Raffaella; Ubaldi, Enrico; Vezzani, Alessandro

2017-05-01

The recent availability of large-scale, time-resolved and high quality digital datasets has allowed for a deeper understanding of the structure and properties of many real-world networks. The empirical evidence of a temporal dimension prompted the switch of paradigm from a static representation of networks to a time varying one. In this work we briefly review the framework of time-varying-networks in real world social systems, especially focusing on the activity-driven paradigm. We develop a framework that allows for the encoding of three generative mechanisms that seem to play a central role in the social networks’ evolution: the individual’s propensity to engage in social interactions, its strategy in allocate these interactions among its alters and the burstiness of interactions amongst social actors. The functional forms and probability distributions encoding these mechanisms are typically data driven. A natural question arises if different classes of strategies and burstiness distributions, with different local scale behavior and analogous asymptotics can lead to the same long time and large scale structure of the evolving networks. We consider the problem in its full generality, by investigating and solving the system dynamics in the asymptotic limit, for general classes of ties allocation mechanisms and waiting time probability distributions. We show that the asymptotic network evolution is driven by a few characteristics of these functional forms, that can be extracted from direct measurements on large datasets.

Time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles

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Ha, Seung-Yeal; Ko, Dongnam; Zhang, Xiongtao; Zhang, Yinglong

2017-07-01

We study the time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles. For this, we use a coupled hydrodynamic Cucker-Smale system and discuss two frameworks, leading to mono-cluster and bi-cluster flockings asymptotically depending on initial configurations, coupling strengths, and the far-field decay property of communication weights. Under the proposed two frameworks, we show that mono-cluster and bi-cluster flockings emerge asymptotically exponentially fast and algebraically slow, respectively. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system.

Asymptotically Safe Standard Model Extensions arXiv

CERN Document Server

Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

We consider theories with a large number NF of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in NF. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.

Composite asymptotic expansions and scaling wall turbulence.

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Panton, Ronald L

2007-03-15

In this article, the assumptions and reasoning that yield composite asymptotic expansions for wall turbulence are discussed. Particular attention is paid to the scaling quantities that are used to render the variables non-dimensional and of order one. An asymptotic expansion is proposed for the streamwise Reynolds stress that accounts for the active and inactive turbulence by using different scalings. The idea is tested with the data from the channel flows and appears to have merit.

arXiv Asymptotically Safe Standard Model Extensions?

CERN Document Server

Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

2018-05-15

We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1/NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.

Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point

International Nuclear Information System (INIS)

Giribet, Gaston; Goya, Andres; Leston, Mauricio

2011-01-01

Chiral gravity admits asymptotically AdS 3 solutions that are not locally equivalent to AdS 3 ; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS 3 solutions to chiral gravity is relevant to understanding the quantum theory. Here, we discuss a special family of nonlocally AdS 3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS 3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS 3 space without being locally equivalent to it appear. Defining the boundary stress tensor for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.

On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians

International Nuclear Information System (INIS)

O'Reilly, E.P.; Weaire, D.

1984-01-01

The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)

Asymptotic time dependent neutron transport in multidimensional systems

International Nuclear Information System (INIS)

Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.

1983-01-01

A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated

Some asymptotic properties of functions holomorphic in tubular domains

International Nuclear Information System (INIS)

Zavialov, B.I.

1988-10-01

For the function holomorphic in curved tubular domain the connection between asymptotic behaviour of real part of its boundary value at a given point of base manifold and asymptotic behaviour of the whole function from the inside of this domain is studied. (author). 3 refs

Asymptotically double lacunry equivalent sequences defined by Orlicz functions

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Ayhan Esi

2014-04-01

Full Text Available This paper presents the following definition which is natural combition of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences x=(x_{k,l} and y=(y_{k,l} are said to be M-asymptotically double equivalent to multiple L provided that for every ε>0, P-lim_{k,l}M(((|((x_{k,l}/(y_{k,l}-L|/ρ=0, for some ρ>0, (denoted by x∽y and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems.

The scaling of population persistence with carrying capacity does not asymptote in populations of a fish experiencing extreme climate variability.

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White, Richard S A; Wintle, Brendan A; McHugh, Peter A; Booker, Douglas J; McIntosh, Angus R

2017-06-14

Despite growing concerns regarding increasing frequency of extreme climate events and declining population sizes, the influence of environmental stochasticity on the relationship between population carrying capacity and time-to-extinction has received little empirical attention. While time-to-extinction increases exponentially with carrying capacity in constant environments, theoretical models suggest increasing environmental stochasticity causes asymptotic scaling, thus making minimum viable carrying capacity vastly uncertain in variable environments. Using empirical estimates of environmental stochasticity in fish metapopulations, we showed that increasing environmental stochasticity resulting from extreme droughts was insufficient to create asymptotic scaling of time-to-extinction with carrying capacity in local populations as predicted by theory. Local time-to-extinction increased with carrying capacity due to declining sensitivity to demographic stochasticity, and the slope of this relationship declined significantly as environmental stochasticity increased. However, recent 1 in 25 yr extreme droughts were insufficient to extirpate populations with large carrying capacity. Consequently, large populations may be more resilient to environmental stochasticity than previously thought. The lack of carrying capacity-related asymptotes in persistence under extreme climate variability reveals how small populations affected by habitat loss or overharvesting, may be disproportionately threatened by increases in extreme climate events with global warming. © 2017 The Author(s).

Multipartite entanglement gambling: The power of asymptotic state transformations assisted by a sublinear amount of quantum communication

International Nuclear Information System (INIS)

Thapliyal, Ashish V.; Smolin, John A.

2003-01-01

Reversible state transformations under entanglement nonincreasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end more powerful versions of state transformations (or reducibilities), namely, LOCCq (asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC (asymptotic LOCC with catalysis) have been considered in the literature. In this paper we show that LOCCq state transformations are only as powerful as asymptotic LOCC state transformations for multipartite pure states. The basic tool we use is multipartite entanglement gambling: Any pure multipartite entangled state can be transformed to an Einstein-Podolsky-Rosen pair shared by some pair of parties and any irreducible m-party pure state (m≥2) can be used to create any other state (pure or mixed) using LOCC. We consider applications of multipartite entanglement gambling to multipartite distillability and to characterizations of multipartite minimal entanglement generating sets. We briefly consider generalizations of this result to mixed states by defining the class of cat-distillable states, i.e., states from which cat states (vertical bar 0 xm >+vertical bar 1 xm >) may be distilled

Coulomb string tension, asymptotic string tension, and the gluon chain

OpenAIRE

Greensite, Jeff; Szczepaniak, Adam P.

2014-01-01

We compute, via numerical simulations, the non-perturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that 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.

Directions for model building from asymptotic safety

Science.gov (United States)

Bond, Andrew D.; Hiller, Gudrun; Kowalska, Kamila; Litim, Daniel F.

2017-08-01

Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of SU(3) C × SU(2) L . Possible signatures at colliders are worked out and include R-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants.

Global asymptotic stability of density dependent integral population projection models.

Science.gov (United States)

Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart

2012-02-01

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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Pituk Mihály

2007-01-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Asymptotic structure of isolated systems

International Nuclear Information System (INIS)

Beig, R.

1988-01-01

I discuss the general ideas underlying the subject of ''asymptotics'' in general relativity and describe the current status of the concepts resulting from these ideas. My main concern will be the problem of consistency. By this I mean the question as to whether the geometric assumptions inherent in these concepts are compatible with the dynamics of the theory, as determined by Einstein's equations. This rather strong bias forces me to leave untouched several issues related to asymptotics, discussed in the recent literature, some of which are perhaps thought equally, or more important, by other workers in the field. In addition I shall, for coherence of presentation, mainly consider Einstein's equations in vacuo. When attention is confined to small neighbourhoods of null and spacelike infinity, this restriction is not important, but is surely relevant for more global issues. (author)

Asymptotic analysis to the effect of temperature gradient on the propagation of triple flames

Science.gov (United States)

Al-Malki, Faisal

2018-05-01

We study asymptotically in this paper the influence of the temperature gradient across the mixing layer on the propagation triple flames formed inside a porous wall channel. The study begins by formulating the problem mathematically using the thermo-diffusive model and then presents a thorough asymptotic analysis of the problem in the limit of large activation energy and thin flames. Analytical formulae for the local burning speed, the flame shape and the propagation speed in terms of the temperature gradient parameter have been derived. It was shown that varying the feed temperatures can significantly enhance the burning of the reactants up to a critical threshold, beyond which no solutions can be obtained. In addition, the study showed that increasing the temperature at the boundaries will modify the usual triple structure of the flame by inverting the upper premixed branch and extending it to the boundary, which may have great implications on the safety of the adopted combustion chambers.

Regge asymptotics of scattering with flavour exchange in QCD

International Nuclear Information System (INIS)

Kirschner, R.

1994-06-01

The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated. (orig.)

On the asymptotics of dimers on tori

OpenAIRE

Kenyon, Richard W.; Sun, Nike; Wilson, David B.

2013-01-01

We study asymptotics of the dimer model on large toric graphs. Let $\\mathbb L$ be a weighted $\\mathbb{Z}^2$-periodic planar graph, and let $\\mathbb{Z}^2 E$ be a large-index sublattice of $\\mathbb{Z}^2$. For $\\mathbb L$ bipartite we show that the dimer partition function on the quotient $\\mathbb{L}/(\\mathbb{Z}^2 E)$ has the asymptotic expansion $\\exp[A f_0 + \\text{fsc} + o(1)]$, where $A$ is the area of $\\mathbb{L}/(\\mathbb{Z}^2 E)$, $f_0$ is the free energy density in the bulk, and $\\text{fsc...

Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size

Science.gov (United States)

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

Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.

Directory of Open Access Journals (Sweden)

Richard B King

Full Text Available 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

An asymptotic formula of the divergent bilateral basic hypergeometric series

OpenAIRE

Morita, Takeshi

2012-01-01

We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\\psi_0 (a;-;q,\\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\\to 1-0$ of our asymptotic formula.

Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces

Science.gov (United States)

Ruess, W. M.; Phong, V. Q.

Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.

Caustics, counting maps and semi-classical asymptotics

Science.gov (United States)

Ercolani, N. M.

2011-02-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain

Caustics, counting maps and semi-classical asymptotics

International Nuclear Information System (INIS)

Ercolani, N M

2011-01-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z 0 (t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain

Asymptotics for a special solution to the second member of the Painleve I hierarchy

International Nuclear Information System (INIS)

Claeys, T

2010-01-01

We study the asymptotic behavior of a special smooth solution y(x, t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of the Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x, t) if x → ±∞ (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.

Watermelon configurations with wall interaction: exact and asymptotic results

Energy Technology Data Exchange (ETDEWEB)

Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)

2006-06-15

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

Watermelon configurations with wall interaction: exact and asymptotic results

International Nuclear Information System (INIS)

Krattenthaler, C

2006-01-01

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature

Watermelon configurations with wall interaction: exact and asymptotic results

Science.gov (United States)

Krattenthaler, C.

2006-06-01

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Directory of Open Access Journals (Sweden)

Ravi P. Agarwal

2007-04-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Numerical Asymptotic Solutions Of Differential Equations

Science.gov (United States)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Problem of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks

International Nuclear Information System (INIS)

Shorikov, A. F.

2015-01-01

This article discusses a discrete-time dynamical system consisting of a set a controllable objects (region and forming it municipalities). The dynamics each of these is described by the corresponding vector nonlinear discrete-time recurrent vector equations and its control system consist from two levels: basic (control level I) that is dominating and subordinate level (control level II). Both levels have different criterions of functioning and united a priori by determined informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we proposed in this work an economical and mathematical model of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks and the general scheme for its solving

Problem of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks

Energy Technology Data Exchange (ETDEWEB)

Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

2015-11-30

This article discusses a discrete-time dynamical system consisting of a set a controllable objects (region and forming it municipalities). The dynamics each of these is described by the corresponding vector nonlinear discrete-time recurrent vector equations and its control system consist from two levels: basic (control level I) that is dominating and subordinate level (control level II). Both levels have different criterions of functioning and united a priori by determined informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we proposed in this work an economical and mathematical model of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks and the general scheme for its solving.

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

International Nuclear Information System (INIS)

Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun

2016-01-01

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

Spectral asymptotics of a strong δ′ interaction supported by a surface

International Nuclear Information System (INIS)

Exner, Pavel; Jex, Michal

2014-01-01

Highlights: • Attractive δ ′ interactions supported by a smooth surface are considered. • Surfaces can be either infinite and asymptotically planar, or compact and closed. • Spectral asymptotics is determined by the geometry of the interaction support. - Abstract: We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive δ ′ interaction supported by a smooth surface in R 3 , either infinite and asymptotically planar, or compact and closed. Its second term is found to be determined by a Schrödinger type operator with an effective potential expressed in terms of the interaction support curvatures

Error estimates in horocycle averages asymptotics: challenges from string theory

NARCIS (Netherlands)

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 chaos expansions in finance theory and practice

CERN Document Server

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...

Contact mechanics of articular cartilage layers asymptotic models

CERN Document Server

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...

The unusual asymptotics of three-sided prudent polygons

International Nuclear Information System (INIS)

Beaton, Nicholas R; Guttmann, Anthony J; Flajolet, Philippe

2010-01-01

We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10 -8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models. (fast track communication)

Asymptotic Solution of the Theory of Shells Boundary Value Problem

Directory of Open Access Journals (Sweden)

I. V. Andrianov

2007-01-01

Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.

Asymptotics for the ratio and the zeros of multiple Charlier polynomials

OpenAIRE

Ndayiragije, François; Van Assche, Walter

2011-01-01

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depend on the degree of the polynomial, in which case we obtain another asymptotic distributio...

Asymptotic strength of thermal pulses in the helium shell burning

Energy Technology Data Exchange (ETDEWEB)

Fujimoto, M Y [Niigata Univ. (Japan); Sugimoto, D

1979-03-01

Secular growth in the strength of the recurrent thermal pulses of helium shell burning is discussed for the purpose of determining its asymptotic strength. It is shown that the pulse grows stronger if the helium zone has been cooled more before the initiation of the pulse. The secular growth of the pulse is related with the increasing degree of cooling. Thermal pulses are computed for an initial model corresponding to the maximum possible cooling, i.e., for a model in which the steady-state entropy distribution was realized in the helium zone. Such thermal pulses are shown to give an upper bound to the asymptotic strength, which is close enough to the asymptotic strength itself for relatively large core masses. Numerical results are given for the core mass of 1.07 M sub(sun), for which the asymptotic strength is found to be 9 x 10/sup 6/ L sub(sun). Thermal pulses are also computed for an initial model which has been cooled artificially more than the steady-state model. The first pulse results in a much greater strength than in the normal model, but a later pulse approaches the normal asymptotic value. Such models are also discussed in relation to the shell flashes on accreting white dwarfs.

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...

Global asymptotic stability of delayed Cohen-Grossberg neural networks

International Nuclear Information System (INIS)

Wu Wei; Cui Baotong; Huang Min

2007-01-01

In this letter, the global asymptotic stability of a class of Cohen-Grossberg neural networks with time-varying delays is discussed. A new set of sufficient conditions for the neural networks are proposed to guarantee the global asymptotic convergence. Our criteria represent an extension of the existing results in literatures. An example is also presented to compare our results with the previous results

The asymptotic variance of departures in critically loaded queues

NARCIS (Netherlands)

Al Hanbali, Ahmad; Mandjes, M.R.H.; Nazarathy, Y.; Whitt, W.

2011-01-01

We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case where the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies limt→∞varD(t) / t = λ(1 - 2 / π)(ca2 +

Asymptotic symmetries of Rindler space at the horizon and null infinity

International Nuclear Information System (INIS)

Chung, Hyeyoun

2010-01-01

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.

Large time asymptotics of solutions of the equations of principal chiral field

International Nuclear Information System (INIS)

Sukhanov, V.V.

1990-01-01

Asymptotic behaviour of solutions of the equations of principal chiral field when one of the arguments tends to infinity is investigated. Asymptotics of solutions of the corresponding spectral problem is investigated as well. explicit formulas are constructed which connect the coefficients of the asymptotic decomposition of the potential with the data of the corresponding inverse problem by means of a birational transformation

The PN theory as an asymptotic limit of transport theory in planar geometry. 1

International Nuclear Information System (INIS)

Larsen, E.W.; Pomraning, G.C.

1991-01-01

In this paper the P N theory is shown to be an asymptotic limit of transport theory for an optically thick planar-geometry system with small absorption and highly anisotropic scattering. The asymptotic analysis shows that the solution in the interior of the system is described by the standard P N equations for which initial, boundary, and interface conditions are determined by asymptotic initial, boundary layer, and interface layer calculations. The asymptotic initial, (reflecting) boundary, and interface conditions for the P N equations agree with conventional formulations. However, at a boundary having a prescribed incident flux, the asymptotic boundary layer analysis yields P N boundary conditions that differ from previous formulations. Numerical transport and P N results are presented to substantiate this asymptotic theory

Design of Biomass Combined Heat and Power (CHP Systems based on Economic Risk using Minimax Regret Criterion

Directory of Open Access Journals (Sweden)

Ling Wen Choong

2018-01-01

Full Text Available It is a great challenge to identify optimum technologies for CHP systems that utilise biomass and convert it into heat and power. In this respect, industry decision makers are lacking in confidence to invest in biomass CHP due to economic risk from varying energy demand. This research work presents a linear programming systematic framework to design biomass CHP system based on potential loss of profit due to varying energy demand. Minimax Regret Criterion (MRC approach was used to assess maximum regret between selections of the given biomass CHP design based on energy demand. Based on this, the model determined an optimal biomass CHP design with minimum regret in economic opportunity. As Feed-in Tariff (FiT rates affects the revenue of the CHP plant, sensitivity analysis was then performed on FiT rates on the selection of biomass CHP design. Besides, design analysis on the trend of the optimum design selected by model was conducted. To demonstrate the proposed framework in this research, a case study was solved using the proposed approach. The case study focused on designing a biomass CHP system for a palm oil mill (POM due to large energy potential of oil palm biomass in Malaysia.

ADM Mass for Asymptotically de Sitter Space-Time

International Nuclear Information System (INIS)

Huang Shiming; Yue Ruihong; Jia Dongyan

2010-01-01

In this paper, an ADM mass formula for asymptotically de Sitter(dS) space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the (d + 3)-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well. (general)

Gravitational charges of transverse asymptotically AdS spacetimes

International Nuclear Information System (INIS)

Cebeci, Hakan; Sarioglu, Oezguer; Tekin, Bayram

2006-01-01

Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to

Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

International Nuclear Information System (INIS)

Harada, Tomohiro; Maeda, Hideki; Carr, B. J.

2008-01-01

Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0 1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically 'quasi-Friedmann', in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions

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...

Numerical relativity and asymptotic flatness

International Nuclear Information System (INIS)

Deadman, E; Stewart, J M

2009-01-01

It is highly plausible that the region of spacetime far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al (1962 Proc. R. Soc. A 269 21-51), Sachs (1962 Proc. R. Soc. A 270 103-26) and Newman and Unti (1962 J. Math. Phys. 3 891-901), rely on careful, clever, a priori choices of a chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap. Starting from data available in a typical numerical evolution, we construct a chart and tetrad which are, asymptotically, sufficiently close to the theoretical ones, so that the key concepts of the Bondi news function, Bondi mass and its rate of decrease can be estimated. In particular, these estimates can be expressed in the numerical relativist's chart as numerical relativity recipes.

Ratio asymptotics of Hermite-Pade polynomials for Nikishin systems

International Nuclear Information System (INIS)

Aptekarev, A I; Lopez, Guillermo L; Rocha, I A

2005-01-01

The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.

Asymptotic density and effective negligibility

Science.gov (United States)

Astor, Eric P.

In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both

On calculating double logarithmical asymptotics of vertex functions defined on the mass shell

International Nuclear Information System (INIS)

Belokurov, V.V.; Usyukina, N.I.

1981-01-01

The essence of the calculation method of double logarithmical asymptotics of vertex functions defined on the mass shell is presented. Using the method the asymptotics of the form-factor of electron is calculated. The ladder and cross-ladder diagrams are asymptotically considerable in every order of the perturbation theory. The way in which the asymptotics of the 4-order diagrams is calculated has been shown. The diagrams of this order and reduction procedures for them are given in a graphic form. The photon mass μ 2 not equal to 0 plays the role of a regulator, removing infrared divergencies. The double logarithmical asymptotics of the form-factor of electron on the mass shell is calculated rigorously in an arbitrary order of the perturbation theory [ru

Non-Weyl asymptotics for quantum graphs with general coupling conditions

International Nuclear Information System (INIS)

Davies, E Brian; Exner, Pavel; Lipovsky, JirI

2010-01-01

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.

Inverted hierarchy and asymptotic freedom in grand unified supersymmetric theories

International Nuclear Information System (INIS)

Aratyn, H.

1983-01-01

The interrelation between an inverted hierarchy mechanism and asymptotic freedom in supersymmetric theories is analyzed in two models for which we performed a detailed analysis of the effective potentials and effective couplings. We find it difficult to accommodate an inverted hierarchy together with asymptotic freedom for the matter-Yukawa couplings. (orig.)

Effective action for composite operators and chiral symmetry breakdown in asymptotically free and non-asymptotically free gauge theories

International Nuclear Information System (INIS)

Gusynin, V.P.; Miranskij, V.A.

1987-01-01

An essential distinction in the relaization of the PCAC dynamics in asymptotically free and non-asymptotically free (with a non-trivial ultraviolet-stable fixed point) gauge theories is revealed. For the latter theories an analytical expressions for the condensate is obtained in the two-loop approximation and arguments of support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed. Besides, the mass relations for pseudoscalar mesons in arbitrary Θ-sector are obtained in the first order in fermion bare masses and the impossibility for spontaneous P and CP-symmetries breaking in vector-like gauge theories at Θ=0 is shown

Non-pionic effects in deuteron asymptotic observables

International Nuclear Information System (INIS)

Ballot, J.L.; Robilotta, M.R.

1991-01-01

It is well known that pion dynamics dominates deuteron asymptotic observables, especially η, the D/S ratio and Q, the quadrupole moment. A procedure has been discussed earlier that allows the unambiguous determination of the pion contribution to these observables as function of the pion-nucleon coupling constant. This problem is discussed in the framework of a specific model for the nucleon-nucleon interaction, namely the potential developed by the Tourreil, Rouben and Sprung. The contribution of non-pionic dynamics to deuteron asymptotic observables is investigated. It is shown that effects due to ρ and ω exchanges are negligible. (K.A.) 8 refs., 1 fig., 1 tab

Vacuum energy in asymptotically flat 2 + 1 gravity

Energy Technology Data Exchange (ETDEWEB)

Miskovic, Olivera, E-mail: olivera.miskovic@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago (Chile); Roy, Debraj, E-mail: roy.debraj@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)

2017-04-10

We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.

Vacuum energy in asymptotically flat 2 + 1 gravity

International Nuclear Information System (INIS)

Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj

2017-01-01

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.

High-energy localized eigenstates in a Fabry-Perot graphene resonator in a magnetic field

Science.gov (United States)

Zalipaev, V. V.

2012-06-01

A semiclassical analysis of the high-energy eigenstates of Dirac fermions inside a graphene monolayer nanoribbon resonator of Fabry-Perot type in a magnetic field with zigzag boundary conditions is discussed. A semiclassical asymptotic method of construction of Maslov spectral series of energy spectrum and eigenfunctions, localized in an asymptotically small neighborhood of a periodic orbit, is developed for the graphene Dirac system. The isolated periodic orbit is confined between two flat boundaries. The analysis involves constructing a localized asymptotic solution to the Dirac system (electron-hole Gaussian beam). Then, the stability of a continuous family of periodic orbits (POs) confined between reflecting boundaries of the resonator is studied. The asymptotics of the eigenfunctions are constructed as a superposition of two Gaussian beams propagating in opposite directions between two reflecting points of the periodic orbit. The asymptotics of the energy spectrum are obtained by means of the generalized Bohr-Sommerfeld quantization condition only for stable POs. It provides two parts of semiclassical Maslov spectral series with positive and negative energies, for electrons and holes, correspondingly, with two different Hamiltonian dynamics and families of classical trajectories. The presence of electrostatic potential is vital as it makes a family of periodic orbit stable. For one subclass of lens-shaped periodic orbits, for a piecewise linear potential, localized eigenstates were computed numerically by the finite element method using COMSOL, and proved to be in very good agreement with the ones computed semiclassically.

More on asymptotically anti-de Sitter spaces in topologically massive gravity

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo

2010-01-01

Recently, the asymptotic behavior of three-dimensional anti-de Sitter (AdS) gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two dimensional conformal group and that included a falloff of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely, the chirality that has the milder behavior at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast, both chiralities are subdominant with respect to the asymptotic behavior of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).

Game theory to characterize solutions of a discrete-time Hamilton-Jacobi equation

International Nuclear Information System (INIS)

Toledo, Porfirio

2013-01-01

We study the behavior of solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework of game theory. The solutions of this problem represent the optimal payoff of a zero-sum game of two players, where the number of moves between the players converges to infinity. A real number, called the critical value, plays a central role in this work; this number is the asymptotic average action of optimal trajectories. The aim of this paper is to show the existence and characterization of solutions of a Hamilton-Jacobi equation for this kind of games

Asymptotic stability of a genetic network under impulsive control

International Nuclear Information System (INIS)

Li Fangfei; Sun Jitao

2010-01-01

The study of the stability of genetic network is an important motif for the understanding of the living organism at both molecular and cellular levels. In this Letter, we provide a theoretical method for analyzing the asymptotic stability of a genetic network under impulsive control. And the sufficient conditions of its asymptotic stability under impulsive control are obtained. Finally, an example is given to illustrate the effectiveness of the obtained method.

Asymptotic freedom and the symplectic and G2 groups

International Nuclear Information System (INIS)

Chaichian, M; Kolmakov, Yu. N.; Nelipa, N. F.

1978-01-01

It is shown that the symplectic Sp(4), Sp(6) and the exceptional G 2 gauge field theories with complete Spontaneous symmetry breaking through the Higgs mechanism are not asymptotically free. This, together with earlier results for other groups, hints at the existence of a general theorem according to which it would no longer be possible for asymptotic freedom to coexist with the absence of infrared divergences. (author)

On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability

Directory of Open Access Journals (Sweden)

Işık Mahmut

2017-01-01

Full Text Available In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.

Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions

International Nuclear Information System (INIS)

Dolan, Brian P

2014-01-01

Conditions for thermodynamic stability of asymptotically anti-de Sitter (AdS) rotating black holes in D-dimensions are determined. Local thermodynamic stability requires not only positivity conditions on the specific heat and the moment of inertia tensor but it is also necessary that the adiabatic compressibility be positive. It is shown that, in the absence of a cosmological constant, neither rotation nor charge is sufficient to ensure full local thermodynamic stability of a black hole. Thermodynamic stability properties of AdS Myers–Perry black holes are investigated for both singly spinning and multi-spinning black holes. Simple expressions are obtained for the specific heat and moment of inertia tensor in any dimension. An analytic expression is obtained for the boundary of the region of parameter space in which such space-times are thermodynamically stable. (paper)

On the asymptotic stability of nonlinear mechanical switched systems

Science.gov (United States)

Platonov, A. V.

2018-05-01

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

Polymers and Random graphs: Asymptotic equivalence to branching processes

International Nuclear Information System (INIS)

Spouge, J.L.

1985-01-01

In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RA/sub f/ Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RA/sub f/ distribution (in which the sol distribution ''sticks'' after gelation), while the Rings Allowed model tended to the Flory version of the RA/sub f/ distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation ''sticking.'' Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics

Asymptotic solving method for sea-air coupled oscillator ENSO model

International Nuclear Information System (INIS)

Zhou Xian-Chun; Yao Jing-Sun; Mo Jia-Qi

2012-01-01

The ENSO is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interaction. In this article, we create an asymptotic solving method for the nonlinear system of the ENSO model. The asymptotic solution is obtained. And then we can furnish weather forecasts theoretically and other behaviors and rules for the atmosphere-ocean oscillator of the ENSO. (general)

A multigroup flux-limited asymptotic diffusion Fokker-Planck equation

International Nuclear Information System (INIS)

Liu Chengan

1987-01-01

A more perfrect flux-limited method is applied to combine with asymptotic diffusion theory of the radiation transpore, and the high peaked component in the scattering angle is treated with Fokker-Planck methods, thus the flux-limited asymptotic diffusion Fokker-Planck equation has been founded. Since the equation is of diffusion form, it retains the simplity and the convenience of the classical diffusion theory, and improves precision in describing radiation transport problems

Asymptotic normalization coefficients and astrophysical factors

International Nuclear Information System (INIS)

Mukhamedzhanov, A.M.; Azhari, A.; Clark, H.L.; Gagliardi, C.A.; Lui, Y.-W.; Sattarov, A.; Trache, L.; Tribble, R.E.; Burjan, V.; Kroha, V.; Carstoiu, F.

2000-01-01

The S factor for the direct capture reaction 7 Be(p,γ) 8 B can be found at astrophysical energies from the asymptotic normalization coefficients (ANC's) which provide the normalization of the tails of the overlap functions for 8 B → 7 Be + p. Peripheral transfer reactions offer a technique to determine these ANC's. Using this technique, the 10 B( 7 Be, 8 B) 9 Be and 14 N( 7 Be, 8 B) 13 C reactions have been used to measure the asymptotic normalization coefficient for 7 Be(p, γ) 8 B. These results provide an indirect determination of S 17 (0). Analysis of the existing 9 Be(p, γ) 10 B experimental data within the framework of the R-matrix method demonstrates that experimentally measured ANC's can provide a reasonable determination of direct radiative capture rates. (author)

Asymptotic properties of a simple random motion

International Nuclear Information System (INIS)

Ravishankar, K.

1988-01-01

A random walker in R/sup N/ is considered. At each step the walker picks a point in R/sup N/ from a fixed finite set of destination points. Having chosen the point, the walker moves a fraction r (r < 1) of the distance toward the point along a straight line. Assuming that the successive destination points are chosen independently, it is shown that the asymptotic distribution of the walker's position has the same mean as the destination point distribution. An estimate is obtained for the fraction of time the walker stays within a ball centered at the mean value for almost every destination sequence. Examples show that the asymptotic distribution could have intricate structure

Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model

International Nuclear Information System (INIS)

Scarfone, Leonard M.

2010-01-01

The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D 3 occurring in periodic intervals over the range of 0< D<27 of particular interest. This differs from the original Lee model which has been shown by several authors, using these same concepts, to be asymptotically free only for D<4.

The importance and use of asymptotic freedom beyond the leading order

International Nuclear Information System (INIS)

Duke, D.W.

1979-05-01

The theoretical and phenomenological importance of asymptotic freedom beyond the leading order is discussed. The two main topics are (1) the determination of the fundamental scale Λ, and (2) ambiguities in parton model definitions when using the higher order effects of asymptotic freedom. (author)

Modeling broadband poroelastic propagation using an asymptotic approach

Energy Technology Data Exchange (ETDEWEB)

Vasco, Donald W.

2009-05-01

An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.

Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

International Nuclear Information System (INIS)

Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

2009-01-01

The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

Naturalness of asymptotically safe Higgs

DEFF Research Database (Denmark)

Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro

2017-01-01

that the scalars can be lighter than Λ. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around Λ ~ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful...

3D face recognition with asymptotic cones based principal curvatures

KAUST Repository

Tang, Yinhang

2015-05-01

The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.

3D face recognition with asymptotic cones based principal curvatures

KAUST Repository

Tang, Yinhang; Sun, Xiang; Huang, Di; Morvan, Jean-Marie; Wang, Yunhong; Chen, Liming

2015-01-01

The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.

Derivative analyticity relations and asymptotic energies

International Nuclear Information System (INIS)

Fischer, J.

1976-01-01

On the basis of general principles of the S-matrix theory theorems are derived showing that derivative analyticity relations analogous to those of Bronzen, Kane and Sukhatme hold at asymptotic energies if the high-energy limits of certain physical quantities exist

Asymptotical behaviour of pion electromagnetic form factor in QCD

International Nuclear Information System (INIS)

Efremov, A.V.; Radyushkin, A.V.

1978-01-01

In the framework of the renormalizable quantum field theory a new approach is developed to the investigation of asymptotical behaviour of two-particle bound state electromagnetic form factor. It is shown that the behaviour of the pion EM form factor in quantum chromodynamics at sufficiently large momentum transfers is controlled by the short-distance dynamics only. The formula is obtained which expresses the asymptotical behaviour of the pion form factor in terms of the fundamental constants of the theory

Asymptotic convertibility of entanglement: An information-spectrum approach to entanglement concentration and dilution

Science.gov (United States)

Jiao, Yong; Wakakuwa, Eyuri; Ogawa, Tomohiro

2018-02-01

We consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication (LOCC). We adopt an information-spectrum approach to address cases where each element of the sequences is not necessarily a tensor power of a bipartite pure state. We derive necessary and sufficient conditions for the LOCC convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences. Based on these results, we also provide simple proofs for previously known results on the optimal rates of entanglement concentration and dilution of general sequences of bipartite pure states.

Asymptotic Expansions - Methods and Applications

International Nuclear Information System (INIS)

Harlander, R.

1999-01-01

Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed. (author)

Centrally extended symmetry algebra of asymptotically Goedel spacetimes

International Nuclear Information System (INIS)

Compere, Geoffrey; Detournay, Stephane

2007-01-01

We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative

Deep inelastic scattering in an asymptotically free gauge theory

International Nuclear Information System (INIS)

Fujiwara, Tsutomu

1977-01-01

This paper reviews the success of the asymptotically free gauge theory which describes the deep inelastic lepton-hadron scattering. The asymptotically free gauge theory was discussed as well as the reason why the parton has the nature like free particles by the aid of the field theory. The asymptotically free gauge theory (AFGT) gives the prediction that the Bjorken scaling gives rise to logarithmic violation. The theory was applied to the exchange processes of single photon and two photons. First, this paper describes the approaches to the Bjorken scaling. The approaches are the discussion of the scaling law dependent on the model and the discussion of the scaling law independent of the model. The field theoretical treatment in described. This is called the method of the renormalization group introduced by Wilson. The asymptotically free gauge theory was formed on the basis of the Callan-Symanzik equation (CSE) and of the Weinberg's power counting theorem. The exact Bjorken scaling does not hold in the quantum field theory, at least there must be logarithmic violation. The pattern of the scaling violation cannot be clarified by the present data. Discussions concerning two gamma process are presented. The measurement of the photon-photon scattering process will give the judgement whether the prediction of the AFGT is correct or not. (Kato, T.)

On iterative procedures of asymptotic inference

NARCIS (Netherlands)

K.O. Dzhaparidze (Kacha)

1983-01-01

textabstractAbstract  An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then

First-passage time asymptotics over moving boundaries for random walk bridges

NARCIS (Netherlands)

Sloothaak, F.; Zwart, B.; Wachtel, V.

2017-01-01

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with

Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction

International Nuclear Information System (INIS)

Ha, Seung-Yeal; Ha, Taeyoung; Kim, Jong-Ho

2010-01-01

We study the asymptotic flocking dynamics for the Cucker-Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.

Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction

Energy Technology Data Exchange (ETDEWEB)

Ha, Seung-Yeal [Department of Mathematical Sciences, Seoul National University, Seoul 151-747 (Korea, Republic of); Ha, Taeyoung; Kim, Jong-Ho, E-mail: syha@snu.ac.k, E-mail: tha@nims.re.k, E-mail: jhkim@nims.re.k [National Institute for Mathematical Sciences, 385-16, 3F Tower Koreana, Doryong-dong, Yuseong-gu, Daejeon, 305-340 (Korea, Republic of)

2010-08-06

We study the asymptotic flocking dynamics for the Cucker-Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.

Asymptotic formulae for solutions of the two-group integral neutron-transport equation

International Nuclear Information System (INIS)

Duracz, T.

1976-01-01

The steady-state, two-group integral neutron-transport equation is considered for two cases. First, for plane geometry, formulae for the asymptotic flux are obtained, under assumptions of homogeneous medium with isotropic scattering, extended to infinity (whole space and half-space), with sources vanishing at infinity as 0(esup(-IXI)). Next, for spherical geometry, the Milne problem is considered and formulae for the asymptotic flux are obtained. These formulae have the form of asymptotic expansions for small and large radii of the black sphere. (orig.) [de

The Asymptotic Safety Scenario in Quantum Gravity.

Science.gov (United States)

Niedermaier, Max; Reuter, Martin

2006-01-01

The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.

Self similar asymptotics of the drift ion acoustic waves

International Nuclear Information System (INIS)

Taranov, V.B.

2004-01-01

A 3D model for the coupled drift and ion acoustic waves is considered. It is shown that self-similar solutions can exist due to the symmetry extension in asymptotic regimes. The form of these solutions is determined in the presence of the magnetic shear as well as in the shear less case. Some of the most symmetric exact solutions are obtained explicitly. In particular, solutions describing asymptotics of zonal flow interaction with monochromatic waves are presented and corresponding frequency shifts are determined

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.

Perturbed asymptotically linear problems

OpenAIRE

Bartolo, R.; Candela, A. M.; Salvatore, A.

2012-01-01

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...

Holography in asymptotically flat spacetimes and the BMS group

International Nuclear Information System (INIS)

Arcioni, Giovanni; Dappiaggi, Claudio

2004-01-01

In a previous paper (Arcioni G and Dappiaggi C 2003 Preprint hep-th/0306142) we have started to explore the holographic principle in the case of asymptotically flat spacetimes and analysed, in particular, different aspects of the Bondi-Metzner-Sachs (BMS) group, namely the asymptotic symmetry group of any asymptotically flat spacetime. We continue this investigation in this paper. Having in mind an S-matrix approach with future and past null infinity playing the role of holographic screens on which the BMS group acts, we connect the IR sectors of the gravitational field with the representation theory of the BMS group. We analyse the (complicated) mapping between bulk and boundary symmetries pointing out differences with respect to the anti-de Sitter (AdS)/CFT set up. Finally, we construct a BMS phase space and a free Hamiltonian for fields transforming with respect to BMS representations. The last step is supposed to be an explorative investigation of the boundary data living on the degenerate null manifold at infinity

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...

An asymptotic problem in renewal theory

NARCIS (Netherlands)

Klamkin, M.S.; van Lint, J.H.

1972-01-01

A special problem in renewal theory is considered. The asymptotic behavior of the renewal function was studied by W. L. Smith. Here we show that his result with an exponentially small remainder term follows from a theorem of De Bruijn on Volterra integral equations.

Asymptotic structure of the Einstein-Maxwell theory on AdS{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Pérez, Alfredo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Riquelme, Miguel [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Tempo, David [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)

2016-02-02

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 ℝ⊗U(1)⊗U(1). Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and U(1). This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

Science.gov (United States)

Chen, Boshan; Chen, Jiejie

2015-08-01

We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Asymptotic symmetries on the Kerr-Newman horizon without the anomaly of diffeomorphism invariance

International Nuclear Information System (INIS)

Koga, Jun-ichirou

2008-01-01

We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr-Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the classical central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are sufficiently many classical configurations that constitute a single macroscopic state, while these configurations are distinguished physically

Selected asymptotic methods with applications to electromagnetics and antennas

CERN Document Server

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 inverse periods of reflected reactors above prompt critical

International Nuclear Information System (INIS)

Spriggs, G.D.; Busch, R.D.

1995-01-01

It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector

Asymptotic solution of the non-isothermal Cahn-Hilliard system

International Nuclear Information System (INIS)

Omel'yanov, G.A.

1995-05-01

The non-isothermal Cahn-Hillard questions with a small parameter in the n-dimensional case (n = 2.3) are considered. The small parameter is proportional both to the relaxation time and to the linear scale of transition zone, so the large time process is examined. The asymptotic solution describing the free interface dynamics is constructed. As the small parameter tends to zero, the limiting solution satisfies the modified Stefan problem with corrected Gibbs-Thomson law. The justification of the asymptotic solution is proved. (author). 26 refs

Asymptotic solutions of diffusion models for risk reserves

Directory of Open Access Journals (Sweden)

S. Shao

2003-01-01

Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.

Asymptotic expansion of unsteady gravity flow of a power-law fluid ...

African Journals Online (AJOL)

We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...

Asymptotic adaptive bipartite entanglement-distillation protocol

International Nuclear Information System (INIS)

Hostens, Erik; Dehaene, Jeroen; De Moor, Bart

2006-01-01

We present an asymptotic bipartite entanglement-distillation protocol that outperforms all existing asymptotic schemes. This protocol is based on the breeding protocol with the incorporation of two-way classical communication. Like breeding, the protocol starts with an infinite number of copies of a Bell-diagonal mixed state. Breeding can be carried out as successive stages of partial information extraction, yielding the same result: one bit of information is gained at the cost (measurement) of one pure Bell state pair (ebit). The basic principle of our protocol is at every stage to replace measurements on ebits by measurements on a finite number of copies, whenever there are two equiprobable outcomes. In that case, the entropy of the global state is reduced by more than one bit. Therefore, every such replacement results in an improvement of the protocol. We explain how our protocol is organized as to have as many replacements as possible. The yield is then calculated for Werner states

Integrable theories that are asymptotically CFT

CERN Document Server

Evans, J M; Jonathan M Evans; Timothy J Hollowood

1995-01-01

A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...

Model Hadron asymptotic behaviour

International Nuclear Information System (INIS)

Kralchevsky, P.; Nikolov, A.

1983-01-01

The work is devoted to the problem of solving a set of asymptotic equations describing the model hardon interaction. More specifically an interactive procedure consisting of two stages is proposed and the first stage is exhaustively studied here. The principle of contracting transformations has been applied for this purpose. Under rather general and natural assumptions, solutions in a series of metric spaces suitable for physical applications have been found. For each of these spaces a solution with unique definiteness is found. (authors)

Power correction to the asymptotics of the pion electromagnetic form factor

International Nuclear Information System (INIS)

Geshkenbein, B.V.; Terentyev, M.V.

1982-01-01

The contribution of the power correction approximately (μ 2 /Q 2 ) 2 enhanced by the factor approximately μ 2 /anti m 2 , to the pion form factor (FF) is calculated (here μ is the pion mass, anti m=1/2(msub(u)+msub(α)) is the mean value of the u- and d-quark masses, Q 2 =-(p-p') 2 > 0, where p, p' are meson momenta at initial and final state. It is shown that the only source of large corrections is due to the contribution of the local pseudoscalar current. The main (approximately 1/Q 2 ) asymptotics of FF associated with the axial current contribution, is derived. The contribution (approximately 1/Q 4 ) of the pseudoscalar current is calculated

The BFKL high energy asymptotic in the next-to-leading approximation

International Nuclear Information System (INIS)

Levin, Eugene

1999-01-01

We discuss the high energy asymptotic in the next-to-leading (NLO) BFKL equation. We find a general solution for the Green functions and consider two properties of the NLO BFKL kernel: running QCD coupling and large NLO corrections to the conformal part of the kernel. Both these effects lead to Regge-BFKL asymptotic only in the limited range of energy (y = ln(s/qq 0 ) ≤ (α S ) ((-5)/(3)) ) and change the energy behaviour of the amplitude for higher values of energy. We confirm the oscillation in the total cross section found by D.A. Ross [SHEP-98-06, hep-ph/9804332] in the NLO BFKL asymptotic, which shows that the NLO BFKL has a serious pathology

Asymptotic mass degeneracies in conformal field theories

International Nuclear Information System (INIS)

Kani, I.; Vafa, C.

1990-01-01

By applying a method of Hardy and Ramanujan to characters of rational conformal field theories, we find an asymptotic expansion for degeneracy of states in the limit of large mass which is exact for strings propagating in more than two uncompactified space-time dimensions. Moreover we explore how the rationality of the conformal theory is reflected in the degeneracy of states. We also consider the one loop partition function for strings, restricted to physical states, for arbitrary (irrational) conformal theories, and obtain an asymptotic expansion for it in the limit that the torus degenerates. This expansion depends only on the spectrum of (physical and unphysical) relevant operators in the theory. We see how rationality is consistent with the smoothness of mass degeneracies as a function of moduli. (orig.)

The Asymptotic Safety Scenario in Quantum Gravity

Directory of Open Access Journals (Sweden)

Niedermaier Max

2006-12-01

Full Text Available The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.

Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian

2011-01-01

The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...

Asymptotic near freedom

International Nuclear Information System (INIS)

Bailin, D.

1974-01-01

It is proved that the characteristic power deviations from scaling of the theories which are not asymptotically free should be detectable in the N.A.L. muon experiments. The Yukawa theories here considered have SU(3) non-singlet structure function moments varying as a power of -q 2 , namely (-q 2 ) at power -p. The maximum value of p is determined to be 2/3:SU3 and 1:SU2. The outstanding question is whether the Yukawa theories considered do in fact have fixed points satisfying the inequalities, and thus simultaneous (non-trivial) zeroes of β(g) and β(lambda) have to be found

Supersymmetric asymptotic safety is not guaranteed

DEFF Research Database (Denmark)

Intriligator, Kenneth; Sannino, Francesco

2015-01-01

in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...

Generalized heat kernel coefficients for a new asymptotic expansion

International Nuclear Information System (INIS)

Osipov, Alexander A.; Hiller, Brigitte

2003-01-01

The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified

Global Asymptotic Stability of Switched Neural Networks with Delays

Directory of Open Access Journals (Sweden)

Zhenyu Lu

2015-01-01

Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.

Asymptotic analysis of spatial discretizations in implicit Monte Carlo

International Nuclear Information System (INIS)

Densmore, Jeffery D.

2009-01-01

We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.

Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations

International Nuclear Information System (INIS)

Cronstrom, C.

1987-01-01

In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaël

2017-06-23

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaë l; Opitz, Thomas; Thibaud, Emeric

2017-01-01

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

EMC effect: asymptotic freedom with nuclear targets

International Nuclear Information System (INIS)

West, G.B.

1984-01-01

General features of the EMC effect are discussed within the framework of quantum chromodynamics as expressed via the operator product expansion and asymptotic freedom. These techniques are reviewed with emphasis on the target dependence. 22 references

Asymptotic Likelihood Distribution for Correlated & Constrained Systems

CERN Document Server

Agarwal, Ujjwal

2016-01-01

It describes my work as summer student at CERN. The report discusses the asymptotic distribution of the likelihood ratio for total no. of parameters being h and 2 out of these being are constrained and correlated.

Structure of the gravitational field at spatial infinity. II. Asymptotically Minkowskian space--times

International Nuclear Information System (INIS)

Persides, S.

1980-01-01

A new formulation is established for the study of the asymptotic structure at spatial infinity of asymptotically Minkowskian space--times. First, the concept of an asymptotically simple space--time at spatial infinity is defined. This is a (physical) space--time (M,g) which can be imbedded in an unphysical space--time (M,g) with a boundary S, a C/sup infinity/ metric g and a C/sup infinity/ scalar field Ω such that Ω=0 on S, Ω>0 on M-S, and g/sup munu/ + g/sup mulambda/ g/sup nurho/ Ω/sub vertical-barlambda/ Ω/sub vertical-barrho/=Ω -2 g/sup murho/ +Ω -4 g/sup mulambda/ g/sup nurho/ Ω/sub ;/lambda Ω/sub ;/rho on M. Then an almost asymptotically flat space--time (AAFS) is defined as an asymptotically simple space--time for which S is isometric to the unit timelike hyperboloid and g/sup munu/ Ω/sub vertical-barmu/ Ω/sub vertical-barnu/ =Ω -4 g/sup munu/ Ω/sub ;/μΩ/sub ;/ν=-1 on S. Equivalent definitions are given in terms of the existence of coordinate systems in which g/sub munu/ or g/sub munu/ have simple explicitly given forms. The group of asymptotic symmetries of (M,g) is studied and is found to be isomorphic to the Lorentz group. The asymptotic behavior of an AAFS is studied. It is proven that the conformal metric g/sub munu/=Ω 2 g/sub munu/ gives C/sup lambdamurhonu/=0, Ω -1 C/sup lambdamurhonu/ Ω/sub ;/μ =0, Ω -2 C/sup lambdamurhonu/ Ω/sub ;/μ Ω/sub ;/ν=0 on S

Value function in economic growth model

Science.gov (United States)

Bagno, Alexander; Tarasyev, Alexandr A.; Tarasyev, Alexander M.

2017-11-01

Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton-Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals and an example is given to illustrate construction of the value function in economic growth models.

Assessing model fit in latent class analysis when asymptotics do not hold

NARCIS (Netherlands)

van Kollenburg, Geert H.; Mulder, Joris; Vermunt, Jeroen K.

2015-01-01

The application of latent class (LC) analysis involves evaluating the LC model using goodness-of-fit statistics. To assess the misfit of a specified model, say with the Pearson chi-squared statistic, a p-value can be obtained using an asymptotic reference distribution. However, asymptotic p-values

Spectral asymptotic in the large coupling limit

CERN Document Server

Bruneau, V

2002-01-01

In this paper, we study a singular perturbation of an eigenvalues problem related to supra-conductor wave guides. Using boundary layer tools we perform a complete asymptotic expansion of the eigenvalues as the conductivity tends to $+\\infty$.

Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations

Directory of Open Access Journals (Sweden)

Bahman Ghazanfari

2013-08-01

Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.

Asymptotic kinetic theory of magnetized plasmas: quasi-particle concept

International Nuclear Information System (INIS)

Sosenko, P.P.; Zagorodny, A.H.

2004-01-01

The asymptotic kinetic theory of magnetized plasmas is elaborated within the context of general statistical approach and asymptotic methods, developed by M. Krylov and M. Bohol'ubov, for linear and non-linear dynamic systems with a rapidly rotating phase. The quasi-particles are introduced already on the microscopic level. Asymptotic expansions enable to close the description for slow processes, and to relate consistently particles and guiding centres to quasi-particles. The kinetic equation for quasi-particles is derived. It makes a basis for the reduced description of slow collective phenomena in the medium. The kinetic equation for quasi-particles takes into account self-consistent interaction fields, quasi-particle collisions and collective-fluctuation-induced relaxation of quasi-particle distribution function. The relationships between the distribution functions for particles, guiding centres and quasi-particles are derived taking into account fluctuations, which can be especially important in turbulent states. In this way macroscopic (statistical) particle properties can be obtained from those of quasi-particles in the general case of non-equilibrium. (authors)

Inverse curvature flows in asymptotically Robertson Walker spaces

Science.gov (United States)

Kröner, Heiko

2018-04-01

In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by 1 / F where F is a homogeneous degree one curvature function of class (K*) of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric.

Universal dual amplitudes and asymptotic expansions for gg→ H and H→ γ γ in four dimensions

Science.gov (United States)

Driencourt-Mangin, Félix; Rodrigo, Germán; Sborlini, Germán F. R.

2018-03-01

Though the one-loop amplitudes of the Higgs boson to massless gauge bosons are finite because there is no direct interaction at tree level in the Standard Model, a well-defined regularization scheme is still required for their correct evaluation. We reanalyze these amplitudes in the framework of the four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show how a local renormalization solves potential regularization ambiguities. The Higgs boson interactions are also used to illustrate new additional advantages of this formalism. We show that LTD naturally leads to very compact integrand expressions in four space-time dimensions of the one-loop amplitude with virtual electroweak gauge bosons. They exhibit the same functional form as the amplitudes with top quarks and charged scalars, thus opening further possibilities for simplifications in higher-order computations. Another outstanding application is the straightforward implementation of asymptotic expansions by using dual amplitudes. One of the main benefits of the LTD representation is that it is supported in a Euclidean space. This characteristic feature naturally leads to simpler asymptotic expansions.

Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix

International Nuclear Information System (INIS)

Griffin, J.J.; Dworzecka, M.

1982-01-01

The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases

Asymptotically flat structure of hypergravity in three spacetime dimensions

Energy Technology Data Exchange (ETDEWEB)

Fuentealba, Oscar [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Matulich, Javier; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)

2015-10-02

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{sub 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{sub (2,4)} 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 antiperiodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree s+(1/2) in the energy, where s is the spin of the fermionic generators.

Translation-invariant global charges in a local scattering theory of massless particles

International Nuclear Information System (INIS)

Strube, D.

1989-01-01

The present thesis is dedicated to the study for specifically translation-invariant charges in the framework of a Wightman field theory without mass gap. The aim consists thereby in the determination of the effect of the charge operator on asymptotic scattering states of massless particles. In the first section the most important results in the massive case and of the present thesis in the massless case are presented. The object of the second section is the construction of asymptotic scattering states. In the third section the charge operator, which is first only defined on strictly local vectors, is extended to these scattering states, on which it acts additively. Finally an infinitesimal transformation of scalar asymptotic fields is determined. By this for the special case of translation-invariant generators and scalar massless asymptotic fields the same results is present as in the massive case. (orig./HSI) [de

Ultraviolet asymptotic behavior of the photon propagator in dimensionally regularized quantum electrodynamics

International Nuclear Information System (INIS)

Krasnikov, N.V.

1991-01-01

Study of the ultraviolet behavior of asymptotically nonfree theories is one of the most important problems of quantum field theory. Unfortunately, not too much is known about the ultraviolet properties in asymptotically nonfree theories; the main obstacle is the growth of the effective coupling constant in the ultraviolet region, which renders perturbation theory inapplicable. It is shown that in quantum electrodynamics in n = 4 + 2 var-epsilon space-time (var-epsilon > 0) the photon propagator has the ultraviolet asymptotic behavior D(k 2 ) ∼ (k 2 ) -1-var-epsilon . In the case var-epsilon R ≤ -3π var-epsilon + O(var-epsilon 2 )

High frequency asymptotic methods

International Nuclear Information System (INIS)

Bouche, D.; Dessarce, R.; Gay, J.; Vermersch, S.

1991-01-01

The asymptotic methods allow us to compute the interaction of high frequency electromagnetic waves with structures. After an outline of their foundations with emphasis on the geometrical theory of diffraction, it is shown how to use these methods to evaluate the radar cross section (RCS) of complex tri-dimensional objects of great size compared to the wave-length. The different stages in simulating phenomena which contribute to the RCS are reviewed: physical theory of diffraction, multiple interactions computed by shooting rays, research for creeping rays. (author). 7 refs., 6 figs., 3 insets

Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well.

Science.gov (United States)

Du, Miao; Tian, Lixin; Wang, Jun; Zhang, Fubao

2016-03-01

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V , K , a , and f , we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.

Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation

Directory of Open Access Journals (Sweden)

Yuncheng You

2008-12-01

Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.

Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes

Directory of Open Access Journals (Sweden)

Maria Crespo

2017-08-01

Full Text Available In this work, we present an asymptotic analysis of a coupled system of two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacteria, called biomass, and a diluted organic contaminant (e.g., nitrates, called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the linearization method to give sufficient conditions for the linear asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

Asymptotic Poisson distribution for the number of system failures of a monotone system

International Nuclear Information System (INIS)

Aven, Terje; Haukis, Harald

1997-01-01

It is well known that for highly available monotone systems, the time to the first system failure is approximately exponentially distributed. Various normalising factors can be used as the parameter of the exponential distribution to ensure the asymptotic exponentiality. More generally, it can be shown that the number of system failures is asymptotic Poisson distributed. In this paper we study the performance of some of the normalising factors by using Monte Carlo simulation. The results show that the exponential/Poisson distribution gives in general very good approximations for highly available components. The asymptotic failure rate of the system gives best results when the process is in steady state, whereas other normalising factors seem preferable when the process is not in steady state. From a computational point of view the asymptotic system failure rate is most attractive

On the asymptotics of the Gell-Mann-Low function in quantum field theory

International Nuclear Information System (INIS)

Kazakov, D.I.; Popov, V.S.

2003-01-01

The problem of reconstructing the Gell-Mann-Low function in quantum field theory starting with its asymptotic series with the first terms calculated by perturbation theory is discussed. And though in a strict mathematical sense this is not unambiguously realizable, under reasonable assumptions about the function it appears to be possible to reconstruct it in some finite interval of g. However, any attempts to find its asymptotics as g→∞ from our point of view are not justified. We also present the conditions under which the sum of the asymptotic series may decrease at infinity

Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes

International Nuclear Information System (INIS)

Bachoc, Francois

2014-01-01

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar regularity parameter. Consistency and asymptotic normality are proved for the Maximum Likelihood and Cross Validation estimators of the covariance parameters. The asymptotic covariance matrices of the covariance parameter estimators are deterministic functions of the regularity parameter. By means of an exhaustive study of the asymptotic covariance matrices, it is shown that the estimation is improved when the regular grid is strongly perturbed. Hence, an asymptotic confirmation is given to the commonly admitted fact that using groups of observation points with small spacing is beneficial to covariance function estimation. Finally, the prediction error, using a consistent estimator of the covariance parameters, is analyzed in detail. (authors)

Asymptotic behavior of the warm inflation scenario with viscous pressure

International Nuclear Information System (INIS)

Mimoso, Jose P.; Nunes, Ana; Pavon, Diego

2006-01-01

We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic behavior of these models and show that the existence of a late-time scaling regime depends not only on an asymptotic behavior of the scalar field potential, but also on an appropriate asymptotic behavior of the inflaton decay rate. There are scaling solutions whenever the latter evolves to become proportional to the Hubble rate of expansion regardless of the steepness of the scalar field exponential potential. We show from thermodynamic arguments that the scaling regime is associated with a power-law dependence of the matter-radiation temperature on the scale factor, which allows a mild variation of the temperature of the matter/radiation fluid. We also show that the late-time contribution of the dissipative terms alleviates the depletion of matter, and increases the duration of inflation

Asymptotic absolute continuity for perturbed time-dependent ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

We study the notion of asymptotic velocity for a class of perturbed time- ... for Mathematical Physics and Stochastics, funded by a grant from the Danish National Research Foun- .... Using (2.4) we can readily continue α(t) to the whole half-axis.

Asymptotically Safe Standard Model via Vectorlike Fermions

Science.gov (United States)

Mann, R. B.; Meffe, J. R.; Sannino, F.; Steele, T. G.; Wang, Z. W.; Zhang, C.

2017-12-01

We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet fixed point.

Fast-slow asymptotics for a Markov chain model of fast sodium current

Science.gov (United States)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

Asymptotics of pion electromagnetics form factor in scale invariant quark model

International Nuclear Information System (INIS)

Efremov, A.V.; Radyushkin, A.V.

1976-01-01

A consistent relativistic approach is proposed to the investigation of asymptotic behaviour of form factor of a system, composed of two spinor particles, interacting with the vector of (pseudo) scalar neutral field. It is shown that the assumption of finite and small asymptotical value of quark-gluon interaction invariant charge at small distances (g 9 2 9 2 ln(-Q 2 ) 2 values (Q 2 is squared momentum)

Mass loss by stars at the stage of the asymptotic giant branch

International Nuclear Information System (INIS)

Frantsman, Y.L.

1986-01-01

For a given initial stellar mass function, star formation function, and initial chemical composition, distributions have been constructed for stars of the asymptotic giant branch by luminosity, and for white dwarfs by mass, by calculating the approximate evolution of a large number of stars. Variants are calculated with different assumptions about the mass loss in the asymptotic branch. Theory can be reconciled with observation only if it is assumed that at this stage there is also a still large mass loss in addition to the stellar wind and the ejection of a planetary nebula shell. This provides the explanation for the absence in the Magellanic clouds of carbon stars with M /sub bol/ 1.0M /sub ./. The degenerate carbon-oxygen nuclei of stars evolving along the asymptotic giant branch cannot attain the Chandrasekhar limit on account of the great mass loss by the stars. The luminosity of stars of the asymptotic giant branch in the globular clusters of the Magellanic Clouds is a good indicator of the age of the clusters

Asymptotic behavior of quark masses induced by instantons

International Nuclear Information System (INIS)

Carneiro, C.E.I.; Frenkel, J.

1984-02-01

A simple argument which shows that the dynamical mass induced by interactions of massless quarks with pseudo-particle configurations, behaves like p -6 for asymptotically large quark momenta is presented. (Author) [pt

Non-linear and signal energy optimal asymptotic filter design

Directory of Open Access Journals (Sweden)

Josef Hrusak

2003-10-01

Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.

Asymptotics for the minimum covariance determinant estimator

NARCIS (Netherlands)

Butler, R.W.; Davies, P.L.; Jhun, M.

1993-01-01

Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown

Asymptotic expansion and statistical description of turbulent systems

International Nuclear Information System (INIS)

Hagan, W.K. III.

1986-01-01

A new approach to studying turbulent systems is presented in which an asymptotic expansion of the general dynamical equations is performed prior to the application of statistical methods for describing the evolution of the system. This approach has been applied to two specific systems: anomalous drift wave turbulence in plasmas and homogeneous, isotropic turbulence in fluids. For the plasma case, the time and length scales of the turbulent state result in the asymptotic expansion of the Vlasov/Poisson equations taking the form of nonlinear gyrokinetic theory. Questions regarding this theory and modern Hamiltonian perturbation methods are discussed and resolved. A new alternative Hamiltonian method is described. The Eulerian Direct Interaction Approximation (EDIA) is slightly reformulated and applied to the equations of nonlinear gyrokinetic theory. Using a similarity transformation technique, expressions for the thermal diffusivity are derived from the EDIA equations for various geometries, including a tokamak. In particular, the unique result for generalized geometry may be of use in evaluating fusion reactor designs and theories of anomalous thermal transport in tokamaks. Finally, a new and useful property of the EDIA is pointed out. For the fluid case, an asymptotic expansion is applied to the Navier-Stokes equation and the results lead to the speculation that such an approach may resolve the problem of predicting the Kolmogorov inertial range energy spectrum for homogeneous, isotropic turbulence. 45 refs., 3 figs

Induction motor IFOC based speed-controlled drive with asymptotic disturbance compensation

Directory of Open Access Journals (Sweden)

Stojić Đorđe M.

2012-01-01

Full Text Available This paper presents the design of digitally controlled speed electrical drive, with the asymptotic compensation of external disturbances, implemented by using the IFOC (Indirect Field Oriented Control torque controlled induction motor. The asymptotic disturbance compensation is achieved by using the DOB (Disturbance Observer with the IMP (Internal Model Principle. When compared to the existing IMP-based DOB solutions, in this paper the robust stability and disturbance compensation are improved by implementing the minimal order DOB filter. Also, the IMP-based DOB design is improved by employing the asymptotic compensation of all elemental or more complex external disturbances. The dynamic model of the IFOC torque electrical drive is, also, included in the speed-controller and DOB section design. The simulation and experimental measurements presented in the paper illustrate the effectiveness and robustness of the proposed control scheme.

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

Science.gov (United States)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

Methods and Algorithms for Approximating the Gamma Function and Related Functions. A survey. Part I: Asymptotic Series

Directory of Open Access Journals (Sweden)

Cristinel Mortici

2015-01-01

Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.

Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups

International Nuclear Information System (INIS)

Drozhzhinov, Yurii N; Zav'yalov, Boris I

2012-01-01

We give a complete description of distributions that are asymptotically homogeneous (including the case of critical index of the asymptotic scale) along the trajectories determined by continuous multiplicative one-parameter transformation groups such that the real parts of all eigenvalues of the infinitesimal matrix are positive. To do this, we introduce and study special spaces of distributions. As an application of our results, we describe distributions that are homogeneous along such groups.

Ghost anomalous dimension in asymptotically safe quantum gravity

International Nuclear Information System (INIS)

Eichhorn, Astrid; Gies, Holger

2010-01-01

We compute the ghost anomalous dimension within the asymptotic-safety scenario for quantum gravity. For a class of covariant gauge fixings and using a functional renormalization group scheme, the anomalous dimension η c is negative, implying an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed point, we observe a maximum value of η c ≅-0.78 for the Landau-deWitt gauge within the given scheme and truncation. Most importantly, the backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the non-Gaussian fixed point with only mild modifications of the fixed-point values for the gravitational coupling and cosmological constant and the associated critical exponents; also their gauge dependence is slightly reduced. Our results provide further evidence for the asymptotic-safety scenario of quantum gravity.

Hadronic Form Factors in Asymptotically Free Field Theories

Science.gov (United States)

Gross, D. J.; Treiman, S. B.

1974-01-01

The breakdown of Bjorken scaling in asymptotically free gauge theories of the strong interactions is explored for its implications on the large q{sup 2} behavior of nucleon form factors. Duality arguments of Bloom and Gilman suggest a connection between the form factors and the threshold properties of the deep inelastic structure functions. The latter are addressed directly in an analysis of asymptotically free theories; and through the duality connection we are then led to statements about the form factors. For very large q{sup 2} the form factors are predicted to fall faster than any inverse power of q{sup 2}. For the more modest range of q{sup 2} reached in existing experiments the agreement with data is fairly good, though this may well be fortuitous. Extrapolations beyond this range are presented.

Molten salt reactor as asymptotic safety nuclear system

International Nuclear Information System (INIS)

Novikov, V.M.; Ignatyev, V.V.

1989-01-01

Safety is becoming the main and priority problem of the nuclear power development. An increase of the active safety measures could hardly be considered as the proper way to achieve the asymptotically high level of nuclear safety. It seem that the more realistic way to achieve such a goal is to minimize risk factors and to maximize the use of inherent and passive safety properties. The passive inherent safety features of the liquid fuel molten salt reactor (MSR) technology are making it attractive for future energy generation. The achievement of the asymptotic safety in MSR is being connected with the minimization of such risk factors as a reactivity excess, radioactivity stored, decay heat, non nuclear energy stored in core. In this paper safety peculiarities of the different MSR concepts are discussed

Asymptotic matching of the solar-system gravitational yields

International Nuclear Information System (INIS)

Kopejkin, S.M.

1989-01-01

In the framework of the general relativity, the structure of the Solar-system gravitational fields is investigated and the relativistic formulae of transformation between nonrotating in the dynamical sense harmonic reference systems - barycentric, planetocentric and topocentric (satelite) ones - are derived by the method of the asymptotic mathing of components of the metric tensor. The derived formulae generalize the linear Poincare transformation in the case of curved space-time. With the help of the asymptotic matching formulae, the relationships between relativistic time scales inside the Solar system have been established, the equations of relativistic precession of the space axis of one reference system with respect to another one have been derived, the equations of translational motion of the center-of-mass of planets (the Sun) and their satellites have been obtained

The Barrett–Crane model: asymptotic measure factor

International Nuclear Information System (INIS)

Kamiński, Wojciech; Steinhaus, Sebastian

2014-01-01

The original spin foam model construction for 4D gravity by Barrett and Crane suffers from a few troubling issues. In the simple examples of the vertex amplitude they can be summarized as the existence of contributions to the asymptotics from non-geometric configurations. Even restricted to geometric contributions the amplitude is not completely worked out. While the phase is known to be the Regge action, the so-called measure factor has remained mysterious for a decade. In the toy model case of the 6j symbol this measure factor has a nice geometric interpretation of V −1/2 leading to speculations that a similar interpretation should be possible also in the 4D case. In this paper we provide the first geometric interpretation of the geometric part of the asymptotic for the spin foam consisting of two glued 4-simplices (decomposition of the 4-sphere) in the Barrett–Crane model in the large internal spin regime. (paper)

The Barrett-Crane model: asymptotic measure factor

Science.gov (United States)

Kamiński, Wojciech; Steinhaus, Sebastian

2014-04-01

The original spin foam model construction for 4D gravity by Barrett and Crane suffers from a few troubling issues. In the simple examples of the vertex amplitude they can be summarized as the existence of contributions to the asymptotics from non-geometric configurations. Even restricted to geometric contributions the amplitude is not completely worked out. While the phase is known to be the Regge action, the so-called measure factor has remained mysterious for a decade. In the toy model case of the 6j symbol this measure factor has a nice geometric interpretation of V-1/2 leading to speculations that a similar interpretation should be possible also in the 4D case. In this paper we provide the first geometric interpretation of the geometric part of the asymptotic for the spin foam consisting of two glued 4-simplices (decomposition of the 4-sphere) in the Barrett-Crane model in the large internal spin regime.

A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis

Directory of Open Access Journals (Sweden)

R. Fares

2012-01-01

Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.

Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models

OpenAIRE

Zhang, Xin

2016-01-01

Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or smal...

Large degree asymptotics of generalized Bessel polynomials

NARCIS (Netherlands)

J.L. López; N.M. Temme (Nico)

2011-01-01

textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the

Infrared studies of asymptotic giant branch stars

International Nuclear Information System (INIS)

Willems, F.J.

1987-01-01

In this thesis studies are presented of asymptotic giant branch stars, which are thought to be an important link in the evolution of the galaxy. The studies were performed on the basis of data collected by the IRAS, the infrared astronomical satelite. 233 refs.; 33 figs.; 16 tabs

Infrared divergences in the asymptotically not free Yang-Mills theory

International Nuclear Information System (INIS)

Fajzullaev, B.A.

1979-01-01

Shown is analogy of infrared asymptotics (with the accuracy up to the multiplier in the degree index) of Green fermion functions in quantum electrodynamics as well as in nonabelian asymptotics free and not free models. Infrared asymptotics of Green functions of calibrating boson in accordance with Appelquist and Carazzone theorem does not depend on the present massive fermions. The calculations showed that in the fermion models interacting with nonabelian calibrating fields, infrared divergences in the physical processes are not reduced no matter whether they are free or not free. So, in these models the point αsub(c)=0 will always be infrared-instable no matter whether αsub(c)=0 is ultraviolet-stable or not. This result is in agreement with one of the Appelquist-Carazzone theorem consequences stating that if the calibrating group is divided into direct product of several subgroups and they are connected only by exchange of a heavy particle, then the charge of each subgroup is subjected (within the infrared limit) to its renormgroup equation

Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

Energy Technology Data Exchange (ETDEWEB)

Lakhin, V.P. [NRC “Kurchatov Institute”, Moscow (Russian Federation); Sorokina, E.A., E-mail: sorokina.ekaterina@gmail.com [NRC “Kurchatov Institute”, Moscow (Russian Federation); Peoples' Friendship University of Russia, Moscow (Russian Federation)

2014-01-24

The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique.

Asymptotic freedom and Zweig's rule

International Nuclear Information System (INIS)

Appelquist, Th.

1977-01-01

Some theoretical aspects of applying short distance physics (asymptotic freedom) are discussed to prove the correctness of the quantum chromodynamics. Properties of new particles that depend only on short distance physics can be dealt with perturbatively. The new mesons are assumed to be CantiC bound states, where C is a new heavy quark. With this in mind some comments are made on the calculation of total widths for the direct decay of different CantiC states into ordinary hadrons

Analyticity of event horizons of five-dimensional multi-black holes with nontrivial asymptotic structure

International Nuclear Information System (INIS)

Kimura, Masashi

2008-01-01

We show that there exist five-dimensional multi-black hole solutions which have analytic event horizons when the space-time has nontrivial asymptotic structure, unlike the case of five-dimensional multi-black hole solutions in asymptotically flat space-time.

Mass loss by stars on the asymptotic giant branch

International Nuclear Information System (INIS)

Frantsman, Yu.L.

1986-01-01

The theoretical populations of white dwarfs and carbon stars were generated for Salpeter initial mass function and constant stellar birth rate history. The effect of very strong mass loss on the mass distribution of white dwarfs and luminosity distribution of carbon stars is discussed and the results are compared with observations. This comparison suggested that a signioficant mass loss by stars on the asymptotic giant branch occurs besides stellar wind and planetary nebulae ejection. Thus it is possible to explain the absence of carbon stars with Msub(bol) 1.0 Msub(sun). The luminosity of asymptotic giant branch stars in the globular clusters of the Magellanic Clouds appears to be a very good indicator of the age

Asymptotics of the filtration problem for suspension in porous media

Directory of Open Access Journals (Sweden)

Kuzmina Ludmila Ivanovna

2015-01-01

Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.

Asymptotic description of plasma turbulence: Krylov-Bogoliubov methods and quasi-particles

International Nuclear Information System (INIS)

Sosenko, P.P.; Bertrand, P.; Decyk, V.K.

2001-01-01

The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov-Bogoliubov averaging method. The correspondence between the general asymptotic methods, elaborated by M. Krylov and M.Bogoliubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. It is shown that the modification of the Poisson equation in the asymptotic theory is due to the non-conservation of the magnetic moment and gyrophase trembling. it is shown that the second-order modification of the adiabatic invariant can determine the conditions of global plasma stability and introduces new nonlinear terms into the reduced Poisson equation. Such a modification is important for several plasma orderings, e.g. NHD type ordering. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed. A consistent asymptotic model is proposed in which the polarization drift is included into the quasi-particle equations of motion and the particle and quasi-particle velocities are equal. It is shown that in such models there are additional modifications of the reduced Poisson equation. The latter becomes even more complicated in contrast to earlier suggestions

Asymptotics with a positive cosmological constant: I. Basic framework

Science.gov (United States)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2015-01-01

The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant Λ is zero. The resulting framework lies at the foundation of research in diverse areas in gravitational science. Examples include: (i) positive energy theorems in geometric analysis; (ii) the coordinate invariant characterization of gravitational waves in full, nonlinear general relativity; (iii) computations of the energy-momentum emission in gravitational collapse and binary mergers in numerical relativity and relativistic astrophysics; and (iv) constructions of asymptotic Hilbert spaces to calculate S-matrices and analyze the issue of information loss in the quantum evaporation of black holes. However, by now observations have led to a strong consensus that Λ is positive in our universe. In this paper we show that, unfortunately, the standard framework does not extend from the Λ =0 case to the Λ \\gt 0 case in a physically useful manner. In particular, we do not have positive energy theorems, nor an invariant notion of gravitational waves in the nonlinear regime, nor asymptotic Hilbert spaces in dynamical situations of semi-classical gravity. A suitable framework to address these conceptual issues of direct physical importance is developed in subsequent papers.

The asymptotic expansion method via symbolic computation

OpenAIRE

Navarro, Juan F.

2012-01-01

This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

Asymptotic inversion of the Erlang B formula

NARCIS (Netherlands)

Leeuwaarden, van J.S.H.; Temme, N.M.

2008-01-01

The Erlang B formula represents the steady-state blocking probability in the Erlang loss model or M=M=s=s queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we make use of

Asymptotic behaviour of firmly non expansive sequences

International Nuclear Information System (INIS)

Rouhani, B.D.

1993-04-01

We introduce the notion of firmly non expansive sequences in a Banach space and present several results concerning their asymptotic behaviour extending previous results and giving an affirmative answer to an open question raised by S. Reich and I. Shafir. Applications to averaged mappings are also given. (author). 16 refs

Consolidation of a WSN and Minimax Method to Rapidly Neutralise Intruders in Strategic Installations

Directory of Open Access Journals (Sweden)

Angela Ribeiro

2012-03-01

Full Text Available Due to the sensitive international situation caused by still-recent terrorist attacks, there is a common need to protect the safety of large spaces such as government buildings, airports and power stations. To address this problem, developments in several research fields, such as video and cognitive audio, decision support systems, human interface, computer architecture, communications networks and communications security, should be integrated with the goal of achieving advanced security systems capable of checking all of the specified requirements and spanning the gap that presently exists in the current market. This paper describes the implementation of a decision system for crisis management in infrastructural building security. Specifically, it describes the implementation of a decision system in the management of building intrusions. The positions of the unidentified persons are reported with the help of a Wireless Sensor Network (WSN. The goal is to achieve an intelligent system capable of making the best decision in real time in order to quickly neutralise one or more intruders who threaten strategic installations. It is assumed that the intruders’ behaviour is inferred through sequences of sensors’ activations and their fusion. This article presents a general approach to selecting the optimum operation from the available neutralisation strategies based on a Minimax algorithm. The distances among different scenario elements will be used to measure the risk of the scene, so a path planning technique will be integrated in order to attain a good performance. Different actions to be executed over the elements of the scene such as moving a guard, blocking a door or turning on an alarm will be used to neutralise the crisis. This set of actions executed to stop the crisis is known as the neutralisation strategy. Finally, the system has been tested in simulations of real situations, and the results have been evaluated according to the final

Consolidation of a WSN and Minimax method to rapidly neutralise intruders in strategic installations.

Science.gov (United States)

Conesa-Muñoz, Jesus; Ribeiro, Angela

2012-01-01

Due to the sensitive international situation caused by still-recent terrorist attacks, there is a common need to protect the safety of large spaces such as government buildings, airports and power stations. To address this problem, developments in several research fields, such as video and cognitive audio, decision support systems, human interface, computer architecture, communications networks and communications security, should be integrated with the goal of achieving advanced security systems capable of checking all of the specified requirements and spanning the gap that presently exists in the current market. This paper describes the implementation of a decision system for crisis management in infrastructural building security. Specifically, it describes the implementation of a decision system in the management of building intrusions. The positions of the unidentified persons are reported with the help of a Wireless Sensor Network (WSN). The goal is to achieve an intelligent system capable of making the best decision in real time in order to quickly neutralise one or more intruders who threaten strategic installations. It is assumed that the intruders' behaviour is inferred through sequences of sensors' activations and their fusion. This article presents a general approach to selecting the optimum operation from the available neutralisation strategies based on a Minimax algorithm. The distances among different scenario elements will be used to measure the risk of the scene, so a path planning technique will be integrated in order to attain a good performance. Different actions to be executed over the elements of the scene such as moving a guard, blocking a door or turning on an alarm will be used to neutralise the crisis. This set of actions executed to stop the crisis is known as the neutralisation strategy. Finally, the system has been tested in simulations of real situations, and the results have been evaluated according to the final state of the intruders

Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media

Science.gov (United States)

Gallican, Valentin; Brenner, Renald; Suquet, Pierre

2017-11-01

This article addresses the asymptotic response of viscoelastic heterogeneous media in the frequency domain, at high and low frequencies, for different types of elementary linear viscoelastic constituents. By resorting to stationary principles for complex viscoelasticity and adopting a classification of the viscoelastic behaviours based on the nature of their asymptotic regimes, either elastic or viscous, four exact relations are obtained on the overall viscoelastic complex moduli in each case. Two relations are related to the asymptotic uncoupled heterogeneous problems, while the two remaining ones result from the viscoelastic coupling that manifests itself in the transient regime. These results also provide exact conditions on certain integrals in time of the effective relaxation spectrum. This general setting encompasses the results obtained in preceding studies on mixtures of Maxwell constituents [1,2]. xml:lang="fr"

A min-max variational principle

International Nuclear Information System (INIS)

Georgiev, P.G.

1995-11-01

In this paper a variational principle for min-max problems is proved that is of the same spirit as Deville-Godefroy-Zizler's variational principle for minimization problems. A localization theorem in which the mini-max points for the perturbed function with respect top a given ε-min-max point are localized is presented. 3 refs

Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers

Science.gov (United States)

Hou, Yumei; Sethi, Suresh P.; Zhang, Hanqin; Zhang, Qing

2006-05-01

We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.

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.

The Asymptotic Expansion Method via Symbolic Computation

Directory of Open Access Journals (Sweden)

Juan F. Navarro

2012-01-01

Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

Some asymptotic theory for variance function smoothing | Kibua ...

African Journals Online (AJOL)

Simple selection of the smoothing parameter is suggested. Both homoscedastic and heteroscedastic regression models are considered. Keywords: Asymptotic, Smoothing, Kernel, Bandwidth, Bias, Variance, Mean squared error, Homoscedastic, Heteroscedastic. > East African Journal of Statistics Vol. 1 (1) 2005: pp. 9-22 ...

First-passage time asymptotics over moving boundaries for random walk bridges

OpenAIRE

Sloothaak, F.; Zwart, B.; Wachtel, V.

2017-01-01

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the re...

Asymptotic elastic energy in simple metals

International Nuclear Information System (INIS)

Khalifeh, J.M.

1983-07-01

The asymptotic form of the elastic binding energy ΔEsup(as)(R) between two Mg atoms in Al is expressed as a product of a lattice Green function and the dipole force tensor P. The quantity P is obtained by a nearly free electron model in which the impurity effect is introduced by a screened Ashcroft pseudopotential characterized by an excess charge ΔZ and a core radius rsub(j). (author)

Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations

Science.gov (United States)

Choi, Sangmin; Kol, Uri; Akhoury, Ratindranath

2018-01-01

Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary transition induced by the scattering process.

Asymptotic problems for stochastic partial differential equations

Science.gov (United States)

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.

Asymptotic freedom in the theory of the strong interaction. Comment on the nobel prize in physics 2004

International Nuclear Information System (INIS)

Zhang Zhaoxi

2005-01-01

The 2004 Nobel Prize in Physics was awarded to David J. Gross, Frank Wilczek and H. David Politzer for their decisive contributions to the theory of the asymptotic freedom of the strong interaction (a fundamental interaction). The fundamental elements of quantum chromodynamics (QCD) and the theory of the strong interaction are briefly reviewed in their historical context. How to achieve asymptotic freedom is introduced and its physical meaning explained. The latest experimental tests of asymptotic freedom are presented, and it is shown that the theoretical prediction agrees excellently with the experimental measurements. Perturbative QCD which is based on the asymptotic freedom is outlined. It is pointed out that the theoretical discovery and experimental proof of the asymptotic freedom are crucial for QCD to be the correct theory of strong interaction. Certain frontier research areas of QCD, such as 'color confinement', are mentioned. The discovery and confirmation of asymptotic freedom has indeed deeply affected particle physics, and has led to QCD becoming a main content of the standard model, and to further development of the so-called grand unification theories of interactions. (author)

Asymptotic analysis of methane-hydrogen-air mixtures

NARCIS (Netherlands)

Hermanns, R.T.E.; Bastiaans, R.J.M.; Goey, de L.P.H.

2005-01-01

In this paper an asymptotic analysis of de Goey et al.concerning premixed stoichiometric methane-hydrogen-air flames is analyzed in depth. The analysis is performed with up to 50 mole percent of hydrogen in the fuel, at gas inlet temperatures ranging from 300 K to 650 K and pressures from 1 to 15

On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces

Directory of Open Access Journals (Sweden)

A. Lastra

2014-01-01

Full Text Available We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichlet-like series whose exponents are positive real numbers which accumulate to the origin.

Asymptotic behavior of second-order impulsive differential equations

Directory of Open Access Journals (Sweden)

Haifeng Liu

2011-02-01

Full Text Available In this article, we study the asymptotic behavior of all solutions of 2-th order nonlinear delay differential equation with impulses. Our main tools are impulsive differential inequalities and the Riccati transformation. We illustrate the results by an example.

Asymptotics for Estimating Equations in Hidden Markov Models

DEFF Research Database (Denmark)

Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

AdS-like spectrum of the asymptotically Goedel space-times

International Nuclear Information System (INIS)

Konoplya, R. A.; Zhidenko, A.

2011-01-01

A black hole immersed in a rotating universe, described by the Gimon-Hashimoto solution, is tested on stability against scalar field perturbations. Unlike the previous studies on perturbations of this solution, which dealt only with the limit of slow universe rotation j, we managed to separate variables in the perturbation equation for the general case of arbitrary rotation. This leads to qualitatively different dynamics of perturbations, because the exact effective potential does not allow for Schwarzschild-like asymptotic of the wave function in the form of purely outgoing waves. The Dirichlet boundary conditions are allowed instead, which result in a totally different spectrum of asymptotically Goedel black holes: the spectrum of quasinormal frequencies is similar to the one of asymptotically anti-de Sitter black holes. At large and intermediate overtones N, the spectrum is equidistant in N. In the limit of small black holes, quasinormal modes (QNMs) approach the normal modes of the empty Goedel space-time. There is no evidence of instability in the found frequencies, which supports the idea that the existence of closed timelike curves (CTCs) and the onset of instability correlate (if at all) not in a straightforward way.

Higher order corrections to asymptotic-de Sitter inflation

Science.gov (United States)

Mohsenzadeh, M.; Yusofi, E.

2017-08-01

Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.

Asymptotic SER performance comparison of MPSK and MDPSK in wireless fading channels

KAUST Repository

Song, Xuegui; Yang, Fan; Cheng, Julian; Alouini, Mohamed-Slim

2015-01-01

We propose a general framework to investigate asymptotic relative performance between M-ary phase-shift keying (MPSK) and M-ary differential phase-shift keying (MDPSK) in wireless fading channels. Using this framework, we provide an alternative derivation for the closed-form expression of the asymptotic performance loss of MDPSK w.r.t. MPSK in an additive white Gaussian noise channel. The same performance loss is also shown to be true for the lognormal fading channels.

Asymptotic SER performance comparison of MPSK and MDPSK in wireless fading channels

KAUST Repository

Song, Xuegui

2015-02-01

We propose a general framework to investigate asymptotic relative performance between M-ary phase-shift keying (MPSK) and M-ary differential phase-shift keying (MDPSK) in wireless fading channels. Using this framework, we provide an alternative derivation for the closed-form expression of the asymptotic performance loss of MDPSK w.r.t. MPSK in an additive white Gaussian noise channel. The same performance loss is also shown to be true for the lognormal fading channels.

Asymptotics for Associated Random Variables

CERN Document Server

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

Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

E.U. Ofoedu

2015-11-01

Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$.  Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid

2012-01-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan

2012-08-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Asymptotic behavior of Bayes estimators for hidden Markov models with application to ion channels

NARCIS (Netherlands)

de Gunst, M.C.M.; Shcherbakova, O.V.

2008-01-01

In this paper we study the asymptotic behavior of Bayes estimators for hidden Markov models as the number of observations goes to infinity. The theorem that we prove is similar to the Bernstein-von Mises theorem on the asymptotic behavior of the posterior distribution for the case of independent

Laminar flow and convective transport processes scaling principles and asymptotic analysis

CERN Document Server

Brenner, Howard

1992-01-01

Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered.A unique feat

Asymptotic expansions for the Gaussian unitary ensemble

DEFF Research Database (Denmark)

Haagerup, Uffe; Thorbjørnsen, Steen

2012-01-01

Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...

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...

The asymptotic behavior of Frobenius-Perron operator with local lower-bound function

International Nuclear Information System (INIS)

Ding Yiming

2003-01-01

Let (X,Σ,μ) be a σ-finite measure space, S:X→X be a nonsingular transformation and P S :L 1 →L 1 be the Frobenius-Perron operator associated with S. It is proved that if P S satisfies the local lower-bound function condition then for every f is a subset of D the sequence {P S n f} converges strongly to a stationary density of P S as n→∞. The statistical stability of S is also concerned via the local lower-bound function method

Coordinate asymptotics of the (3→3) wave functions for a three charged particle system

International Nuclear Information System (INIS)

Merkur'ev, S.P.

1977-01-01

Coordinate asymptotics of the (3 → 3) wave functions for three particles system with Coulomb interaction in the scattering problem is plotted. (3 → 3) and (3 → 2) process cases are considered, when the particles are not connected at the initial state. For coordinate asymptotics plotting the basis functions are used which meet Schroedinger equation in the eikonal approximation. The wave functions coordinate asymptotics plotting method is described far from special directions. Wave function asymptotical form is studied in the range of special directions and (3 → 3) scattering amplitude singularities are described. All data are given in accordance with the system with 2 charged particles only. The model in question is of special interest because of the described ppn system the studying of which is of great importance in nuclear physics. Final formulae are discussed for the most general case of three charged particles. Boundary problems for Schroedinger equation are shown to give the only way of definition for the (3 → 3) wave functions. It is pointed out that in special directions wave function coordinate asymptotics is presented with accuracy that gives the possibility to set such a boundary problem

Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

DEFF Research Database (Denmark)

Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors...

Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

Saeidi Shahram

2010-01-01

Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.

Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models

International Nuclear Information System (INIS)

Gulisashvili, Archil; Stein, Elias M.

2010-01-01

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.

Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

International Nuclear Information System (INIS)

Chen, S.-F.

2009-01-01

The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.

On Small Deviation Asymptotics In L2 of Some Mixed Gaussian Processes

Directory of Open Access Journals (Sweden)

Alexander I. Nazarov

2018-04-01

Full Text Available We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of the Wiener process and the Brownian bridge. We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen–Loève expansion together with spectral asymptotics of differential operators and complex analysis methods.

Quantum gravity and the functional renormalization group the road towards asymptotic safety

CERN Document Server

Reuter, Martin

2018-01-01

During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering thi...

Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis

CERN Document Server

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...

Using Minimax Regret Optimization to Search for Multi-Stakeholder Solutions to Deeply Uncertain Flood Hazards under Climate Change

Science.gov (United States)

Kirshen, P. H.; Hecht, J. S.; Vogel, R. M.

2015-12-01

Prescribing long-term urban floodplain management plans under the deep uncertainty of climate change is a challenging endeavor. To address this, we have implemented and tested with stakeholders a parsimonious multi-stage mixed integer programming (MIP) model that identifies the optimal time period(s) for implementing publicly and privately financed adaptation measures. Publicly funded measures include reach-scale flood barriers, flood insurance, and buyout programs to encourage property owners in flood-prone areas to retreat from the floodplain. Measures privately funded by property owners consist of property-scale floodproofing options, such as raising building foundations, as well as investments in flood insurance or retreat from flood-prone areas. The objective function to minimize the sum of flood control and damage costs in all planning stages for different property types during floods of different severities. There are constraints over time for flow mass balances, construction of flood management alternatives and their cumulative implementation, budget allocations, and binary decisions. Damages are adjusted for flood control investments. In recognition of the deep uncertainty of GCM-derived climate change scenarios, we employ the minimax regret criterion to identify adaptation portfolios robust to different climate change trajectories. As an example, we identify publicly and privately funded adaptation measures for a stylized community based on the estuarine community of Exeter, New Hampshire, USA. We explore the sensitivity of recommended portfolios to different ranges of climate changes, and costs associated with economies of scale and flexible infrastructure design as well as different municipal budget constraints.

Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere

Science.gov (United States)

Tang, He; Sun, Wenke

2018-05-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Existence and Asymptotic Stability of Periodic Solutions of the Reaction-Diffusion Equations in the Case of a Rapid Reaction

Science.gov (United States)

Nefedov, N. N.; Nikulin, E. I.

2018-01-01

A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.

Asymptotic behavior of tidal damping in alluvial estuaries

NARCIS (Netherlands)

Cai, H.; Savenije, H.H.G.

2013-01-01

Tidal wave propagation can be described analytically by a set of four implicit equations, i.e., the phase lag equation, the scaling equation, the damping equation, and the celerity equation. It is demonstrated that this system of equations has an asymptotic solution for an infinite channel,

Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

OpenAIRE

Agafonov, S. I.

2005-01-01

It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

Asymptotic behavior for a quadratic nonlinear Schrodinger equation

Directory of Open Access Journals (Sweden)

Pavel I. Naumkin

2008-02-01

Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

Asymptotic stabilization of nonlinear systems using state feedback

International Nuclear Information System (INIS)

D'Attellis, Carlos

1990-01-01

This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

Asymptotic Translation Length in the Curve Complex

OpenAIRE

Valdivia, Aaron D.

2013-01-01

We show that when the genus and punctures of a surface are directly proportional by some rational number the minimal asymptotic translation length in the curve complex has behavior inverse to the square of the Euler characteristic. We also show that when the genus is fixed and the number of punctures varies the behavior is inverse to the Euler characteristic.

To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2007-01-01

We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'

Asymptotic behaviour of the scattering phase for non-trapping metrics

International Nuclear Information System (INIS)

Popov, G.S.

1982-01-01

The asymptotic behaviour of the scattering phase is considered at infinity for an elliptic, self-adjoint, second order differential operator H, defined either in Rsup(n) or in an unbounded domain Ω contains Rsup(n) with Dirichlet or Neumann boundary conditions. The operator H has the form H=- δsub(g)+hD+V where δsub(g) is the Laplace-Beltrami operator related to a Riemann metric g in anti Ω. Provided a non-trapping hypothesis is fulfilled and H coincides with the Laplace operator δ in a neighbourhood of infinity, an asymptotic development of the scattering phase s(lambda) is obtained for lambda → infinity. The first coefficients in this development are found

Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims

Institute of Scientific and Technical Information of China (English)

Li WEI

2012-01-01

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large.Under the assumption that the claim-size distribution is exponential,we establish an explicit asymptotic formula.Some straightforward consequences of this formula match existing results in the field.

Asymptotic behaviour of unbounded trajectories for some non-autonomous systems in a Hilbert space

International Nuclear Information System (INIS)

Djafari Rouhani, B.

1990-07-01

The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banach spaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

Science.gov (United States)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

Science.gov (United States)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Asymptotic distribution of products of sums of independent random ...

Indian Academy of Sciences (India)

integrable random variables (r.v.) are asymptotically log-normal. This fact ... the product of the partial sums of i.i.d. positive random variables as follows. .... Now define ..... by Henan Province Foundation and Frontier Technology Research Plan.

Confinement and asymptotic freedom seen with a golden eye

International Nuclear Information System (INIS)

Elokaby, A.

2009-01-01

The present short note is an attempt to reconcile the current conventional understanding of quarks confinement and asymptotic freedom with the results found by El Naschie using the exact renormalization equation of his quantum golden field theory.

An asymptotic safety scenario for gauged chiral Higgs-Yukawa models

International Nuclear Information System (INIS)

Gies, Holger; Rechenberger, Stefan; Scherer, Michael M.; Zambelli, Luca

2013-01-01

We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative - though weak-coupling - threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaussian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a ''walking'' mid-momentum regime. (orig.)

An asymptotic safety scenario for gauged chiral Higgs-Yukawa models

Science.gov (United States)

Gies, Holger; Rechenberger, Stefan; Scherer, Michael M.; Zambelli, Luca

2013-12-01

We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative—though weak-coupling—threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaußian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a "walking" mid-momentum regime.

Asymptotics for the greatest zeros of solutions of a particular O.D.E.

Directory of Open Access Journals (Sweden)

Silvia Noschese

1994-05-01

Full Text Available This paper deals with the Liouville-Stekeloff method for approximating solutions of homogeneous linear ODE and a general result due to Tricomi which provides estimates for the zeros of functions by means of the knowledge of an asymptotic representation. From the classical tools we deduce information about the asymptotics of the greatest zeros of a class of solutions of a particular ODE, including the classical Hermite polynomials.

Two-parameter asymptotics in magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Max

2010-01-01

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.

Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

Science.gov (United States)

Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemí

2012-08-01

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u t = J* u- u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on {R^NsetminusΩ} . When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.

TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS

DEFF Research Database (Denmark)

Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.

2017-01-01

We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle...

Asymptotic integration of a linear fourth order differential equation of Poincaré type

Directory of Open Access Journals (Sweden)

Anibal Coronel

2015-11-01

Full Text Available This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of constants. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of the perturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solution. The next result concerns with the asymptotic behavior of the solutions of the nonlinear third order equation. The fourth main theorem is introduced to establish the existence of a fundamental system of solutions and to precise the formulas for the asymptotic behavior of the linear fourth order differential equation. In addition, we present an example to show that the results introduced in this paper can be applied in situations where the assumptions of some classical theorems are not satisfied.

On approach to double asymptotic scaling at low x

International Nuclear Information System (INIS)

Choudhury, D.K.

1994-10-01

We obtain the finite x correlations to the gluon structure function which exhibits double asymptotic scaling at low x. The technique used is the GLAP equation for gluon approximated at low x by a Taylor expansion. (author). 27 refs

On some asymptotic relations in the Boltzmann-Enskog model

International Nuclear Information System (INIS)

Sadovnikov, B.I.; Inozemtseva, N.G.

1977-04-01

The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator

High energy asymptotics of the scattering amplitude for the ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Keywords. Scattering matrix; asymptotic expansion; high energy; diagonal singula- ..... (see subsection 2 of § 3) with functions of the generator of dilations. A = 1. 2 d ..... ness in quantum scattering theory, Ann. Inst. Henri Poincaré, Phys. Théor.

The P(phi)2 Green's functions; asymptotic perturbation expansion

International Nuclear Information System (INIS)

Dimock, J.

1976-01-01

The real time Green's functions in the P(phi) 2 quantum field theory are infinitely differentiable functions of the coupling constant lambda up to and including lamba=0. It follows that the perturbation series are asymptotic as lambda→0 + . (Auth.)

Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

Directory of Open Access Journals (Sweden)

Pengcheng HAN

2017-12-01

Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.

Asymptotic solution for the El Niño time delay sea—air oscillator model

International Nuclear Information System (INIS)

Mo Jia-Qi; Lin Wan-Tao; Lin Yi-Hua

2011-01-01

A sea—air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Niño-southern oscillation (ENSO) model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature (SST) anomaly and the related physical quantities. (general)

Asymptotic analysis for Nakagami-m fading channels with relay selection

KAUST Repository

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.

Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

2010-05-15

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries

International Nuclear Information System (INIS)

Han, Muxin; Krajewski, Thomas

2014-01-01

A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of SL(2,C). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation. (paper)

Large-degree asymptotics of rational Painlevé-II functions: noncritical behaviour

International Nuclear Information System (INIS)

Buckingham, Robert J; Miller, Peter D

2014-01-01

Rational solutions of the inhomogeneous Painlevé-II equation and of a related coupled Painlevé-II system have recently arisen in studies of fluid vortices and of the sine-Gordon equation. For the sine-Gordon application in particular it is of interest to understand the large-degree asymptotic behaviour of the rational Painlevé-II functions. We explicitly compute the leading-order large-degree asymptotics of these two families of rational functions valid in the whole complex plane with the exception of a neighbourhood of a certain piecewise-smooth closed curve. We obtain rigorous error bounds by using the Deift–Zhou nonlinear steepest-descent method for Riemann–Hilbert problems. (paper)

Oracle posterior rates in the White Noise Model

NARCIS (Netherlands)

Babenko, A.

2010-01-01

All the results about posterior rates obtained until now are related to the optimal (minimax) rates for the estimation problem over the corresponding nonparametric smoothness classes, i.e. of a global nature. In the meantime, a new local approach to optimality has been developed within the

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

Science.gov (United States)

Banks, H T; Holm, Kathleen; Robbins, Danielle

2010-11-01

We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.

Adaptive Asymptotical Synchronization for Stochastic Complex Networks with Time-Delay and Markovian Switching

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 freedom in extended conformal supergravities

International Nuclear Information System (INIS)

Fradkin, E.S.; Tseytlin, A.A.

1982-01-01

We present the calculation of the one-loop β-function in extended conformal supergravities. N = 1, 2, 3 theories (free or coupled to the Einstein supergravities) are found to the asymptotically free (like the N = 0 Weyl theory) while the N = 4 theory becomes finite under some plausible hypothesis. The results support the possibility to solve the problem of ghosts in these theories. The obtained sequence of SU(N) β-functions appears to be in remarkable correspondence with that for gauged O(N) supergravity theories. (orig.)

Asymptotic Delay Analysis for Cross-Layer Delay-Based Routing in Ad Hoc Networks

Directory of Open Access Journals (Sweden)

Philippe Jacquet

2007-01-01

Full Text Available This paper addresses the problem of the evaluation of the delay distribution via analytical means in IEEE 802.11 wireless ad hoc networks. We show that the asymptotic delay distribution can be expressed as a power law. Based on the latter result, we present a cross-layer delay estimation protocol and we derive new delay-distribution-based routing algorithms, which are well adapted to the QoS requirements of real-time multimedia applications. In fact, multimedia services are not sensitive to average delays, but rather to the asymptotic delay distributions. Indeed, video streaming applications drop frames when they are received beyond a delay threshold, determined by the buffer size. Although delay-distribution-based routing is an NP-hard problem, we show that it can be solved in polynomial time when the delay threshold is large, because of the asymptotic power law distribution of the link delays.

Asymptotic safety of quantum gravity beyond Ricci scalars

Science.gov (United States)

Falls, Kevin; King, Callum R.; Litim, Daniel F.; Nikolakopoulos, Kostas; Rahmede, Christoph

2018-04-01

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f (R ) -type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

Science.gov (United States)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

On extracting physical content from asymptotically flat spacetime metrics

International Nuclear Information System (INIS)

Kozameh, C; Newman, E T; Silva-Ortigoza, G

2008-01-01

A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi-Metzner-Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

Energy Technology Data Exchange (ETDEWEB)

Hahn, Y.K., E-mail: ykhahn22@verizon.net

2014-12-15

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. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the

Asymptotics of the QMLE for General ARCH(q) Models

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbek, Anders Christian

2009-01-01

-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...

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

NARCIS (Netherlands)

Caldeira Costa, R.N.

2012-01-01

In this work we elaborate on an extension of the AdS/CFT framework to a sub-class of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family

Asymptotic behavior of Maxwell fields in higher dimensions

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello

2014-01-01

Roč. 90, č. 12 (2014), s. 124020 ISSN 1550-7998 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * asymptotic structure * classical general relativity Subject RIV: BA - General Mathematics Impact factor: 4.643, year: 2014 http://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.124020

Formal matched asymptotics for degenerate Ricci flow neckpinches

International Nuclear Information System (INIS)

Angenent, Sigurd B; Isenberg, James; Knopf, Dan

2011-01-01

Gu and Zhu (2008 Commun. Anal. Geom. 16 467–94) have shown that type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on S n+1 (n≥2). In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Asymptotic behavior of Maxwell fields in higher dimensions

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello

2014-01-01

Roč. 90, č. 12 (2014), s. 124020 ISSN 1550-7998 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * asymptotic structure * classical general relativity Subject RIV: BA - General Mathematics Impact factor: 4.643, year: 2014 http://journals. aps .org/prd/abstract/10.1103/PhysRevD.90.124020

Optimization of Parameters of Asymptotically Stable Systems

Directory of Open Access Journals (Sweden)

Anna Guerman

2011-01-01

Full Text Available This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.

From A to Z : Asymptotic expansions by van Zwet

NARCIS (Netherlands)

Albers, Willem/Wim; de Gunst, Mathisca; Klaasen, Chris; van der Vaart, Aad

2001-01-01

Refinements of first order asymptotic results axe reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and [/-statistics. After these special classes, the question about a general second

Asymptotic Stabilization of Non-holonomic Port-controlled Hamiltonian Systems

DEFF Research Database (Denmark)

Sørensen, Mathias Jesper; Bendtsen, Jan Dimon; Andersen, Palle

2004-01-01

A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class of mob...

Asymptotical construction of a fully coupled, Reissner–Mindlin model for piezoelectric composite plates

International Nuclear Information System (INIS)

Liao Lin; Yu Wenbin

2008-01-01

The variational asymptotic method is used to construct a fully coupled Reissner–Mindlin model for piezoelectric composite plates with some surfaces parallel to the reference surface coated with electrodes. Taking advantage of the smallness of the plate thickness, we asymptotically split the original three-dimensional electromechanical problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The through-the-thickness analysis serves as a link between the original three-dimensional analysis and the plate analysis by providing a constitutive model for the plate analysis and recovering the three-dimensional field variables in terms of two-dimensional plate global responses. The present theory is implemented into the computer program VAPAS (variational asymptotic plate and shell analysis). The resulting model is as simple as an equivalent single-layer, first-order shear deformation theory with accuracy comparable to higher-order layerwise theories. Various numerical examples have been used to validate the present model

Asymptotics of the quantum invariants for surgeries on the figure 8 knot

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Hansen, Søren Kold

2006-01-01

a formula for the leading asymptotics of the invariants in the limit of large quantum level. We analyze this expression using the saddle point method. We construct a certain surjection from the set of stationary points for the relevant phase functions onto the space of conjugacy classes of nonabelian SL(2......, ℂ)-representations of the fundamental group of M and prove that the values of these phase functions at the relevant stationary points equals the classical Chern–Simons invariants of the corresponding flat SU(2)-connections. Our findings are in agreement with the asymptotic expansion conjecture...

State Estimation for a Biological Phosphorus Removal Process using an Asymptotic Observer

DEFF Research Database (Denmark)

Larose, Claude Alain; Jørgensen, Sten Bay

2001-01-01

This study investigated the use of an asymptotic observer for state estimation in a continuous biological phosphorus removal process. The estimated states are the concentration of heterotrophic, autotrophic, and phosphorus accumulating organisms, polyphosphate, glycogen and PHA. The reaction scheme...... if the convergence, driven by the dilution rate, was slow (from 15 to 60 days). The propagation of the measurement noise and a bias in the estimation of glycogen and PHA could be the result of the high condition number of one of the matrices used in the algorithm of the asymptotic observer for the aerated tanks....

Asymptotics of empirical eigenstructure for high dimensional spiked covariance.

Science.gov (United States)

Wang, Weichen; Fan, Jianqing

2017-06-01

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies.

Lower bound for the oracle projection posterior convergence rate

NARCIS (Netherlands)

Babenko, A.; Belitser, E.N.

2011-01-01

In Babenko and Belitser (2010), a new notion for the posterior concentration rate is proposed, the so-called oracle risk rate, the best possible rate over an appropriately chosen estimators family, which is a local quantity (as compared, e.g., with global minimax rates). The program of oracle

Asymptotically exact localized expansions for signals in the time–frequency domain

International Nuclear Information System (INIS)

Muzhikyan, Aramazd H; Avanesyan, Gagik T

2012-01-01

Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in the time–frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative geometry of the time–frequency plane. Signals are visualized using the constructed graphical representation. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Thermodynamics and phase transition of black hole in an asymptotically safe gravity

International Nuclear Information System (INIS)

Ma, Meng-Sen

2014-01-01

We study the effects of quantum gravitational correction on the thermodynamics of black holes in the asymptotic safety scenario. Owing to the quantum-corrected Schwarzschild metric, the thermodynamic quantities are also corrected and a Hawking–Page-type phase transition may exist. We also employ the concept of thermodynamic geometry to the black hole to characterize the phase transition. By introducing a cavity enclosing the black hole, we apply the spatially finite boundary conditions to further investigate the thermodynamic phase transition of the black hole. It is shown that the larger and small black holes are both locally stable according to heat capacity. According to free energy, we find that the quantum-corrected black hole has similar thermodynamic phase structure to that of RN–AdS black hole. In addition, we also discuss the possibility of the phase transition between the black hole and the hot curved space. Above a certain temperature T 0 , the black hole is more probable than the hot space

Global asymptotic stability of Cohen-Grossberg neural networks with constant and variable delays

International Nuclear Information System (INIS)

Wu Wei; Cui Baotong; Huang Min

2007-01-01

Global asymptotic stability of Cohen-Grossberg neural networks with constant and variable delays is studied. Some sufficient conditions for the neural networks are proposed to guarantee the global asymptotic convergence by using different Lyapunov functionals. Our criteria represent an extension of the existing results in literatures. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed Cohen-Grossberg neural networks. Those conditions are less restrictive than those given in the earlier reference

Asymptotic properties of axisymmetric Stokes flow of a viscous liquid with intersecting boundaries

International Nuclear Information System (INIS)

Voinov, O.V.

2004-01-01

The general axisymmetric problem on the liquid flow by the low Reynolds number when the boundary surfaces (both of the solid body and free one) are intersecting at the certain angle on the moving line, is considered. The work is aimed at establishing the asymptotic regularities of the behavior of the current function and voltages in the small vicinity of the intersection (contact) line of the boundary surfaces. The asymptotic analysis makes it possible to consider the arbitrary axisymmetric Stokes flow with the intersecting boundaries [ru

Large order asymptotics and convergent perturbation theory for critical indices of the φ4 model in 4 - ε expansion

International Nuclear Information System (INIS)

Honkonen, J.; Komarova, M.; Nalimov, M.

2002-01-01

Large order asymptotic behaviour of renormalization constants in the minimal subtraction scheme for the φ 4 (4 - ε) theory is discussed. Well-known results of the asymptotic 4 - ε expansion of critical indices are shown to be far from the large order asymptotic value. A convergent series for the model φ 4 (4 - ε) is then considered. Radius of convergence of the series for Green functions and for renormalisation group functions is studied. The results of the convergent expansion of critical indices in the 4 - ε scheme are revalued using the knowledge of large order asymptotics. Specific features of this procedure are discussed (Authors)

An asymptotic analysis for an integrable variant of the Lotka–Volterra prey–predator model via a determinant expansion technique

Directory of Open Access Journals (Sweden)

Masato Shinjo

2015-12-01

Full Text Available The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.

Ground state solutions for asymptotically periodic Schrodinger equations with critical growth

Directory of Open Access Journals (Sweden)

Hui Zhang

2013-10-01

Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.

The Asymptotic Solution for the Steady Variable-Viscosity Free ...

African Journals Online (AJOL)

Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...

Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas

NARCIS (Netherlands)

Can, S.U.; Einmahl, John; Laeven, R.J.A.

2017-01-01

Consider a random sample from a continuous multivariate distribution function F with copula C. In order to test the null hypothesis that C belongs to a certain parametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a