Upper bounds on minimum cardinality of exact and approximate reducts
Chikalov, Igor
2010-01-01
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.
Exact BPS bound for noncommutative baby Skyrmions
International Nuclear Information System (INIS)
Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco
2013-01-01
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory
Fuzzy upper bounds and their applications
Energy Technology Data Exchange (ETDEWEB)
Soleimani-damaneh, M. [Department of Mathematics, Faculty of Mathematical Science and Computer Engineering, Teacher Training University, 599 Taleghani Avenue, Tehran 15618 (Iran, Islamic Republic of)], E-mail: soleimani_d@yahoo.com
2008-04-15
This paper considers the concept of fuzzy upper bounds and provides some relevant applications. Considering a fuzzy DEA model, the existence of a fuzzy upper bound for the objective function of the model is shown and an effective approach to solve that model is introduced. Some dual interpretations are provided, which are useful for practical purposes. Applications of the concept of fuzzy upper bounds in two physical problems are pointed out.
Upper bounds on superpartner masses from upper bounds on the Higgs boson mass.
Cabrera, M E; Casas, J A; Delgado, A
2012-01-13
The LHC is putting bounds on the Higgs boson mass. In this Letter we use those bounds to constrain the minimal supersymmetric standard model (MSSM) parameter space using the fact that, in supersymmetry, the Higgs mass is a function of the masses of sparticles, and therefore an upper bound on the Higgs mass translates into an upper bound for the masses for superpartners. We show that, although current bounds do not constrain the MSSM parameter space from above, once the Higgs mass bound improves big regions of this parameter space will be excluded, putting upper bounds on supersymmetry (SUSY) masses. On the other hand, for the case of split-SUSY we show that, for moderate or large tanβ, the present bounds on the Higgs mass imply that the common mass for scalars cannot be greater than 10(11) GeV. We show how these bounds will evolve as LHC continues to improve the limits on the Higgs mass.
Improved bounds on the epidemic threshold of exact SIS models on complex networks
Ruhi, Navid Azizan; Thrampoulidis, Christos; Hassibi, Babak
2017-01-01
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Improved bounds on the epidemic threshold of exact SIS models on complex networks
Ruhi, Navid Azizan
2017-01-05
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network\\'s adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Upper bounds for reversible circuits based on Young subgroups
DEFF Research Database (Denmark)
Abdessaied, Nabila; Soeken, Mathias; Thomsen, Michael Kirkedal
2014-01-01
We present tighter upper bounds on the number of Toffoli gates needed in reversible circuits. Both multiple controlled Toffoli gates and mixed polarity Toffoli gates have been considered for this purpose. The calculation of the bounds is based on a synthesis approach based on Young subgroups...... that results in circuits using a more generalized gate library. Starting from an upper bound for this library we derive new bounds which improve the existing bound by around 77%....
Upper and lower bounds in nonrelativistic scattering theory
International Nuclear Information System (INIS)
Darewych, J.W.; Pooran, R.
1980-01-01
We consider the problem of determining rigorous upper and lower bounds to the difference between the exact and approximate scattering phase shift, for the case of central potential scattering. The present work is based on the Kato identities and the phase-amplitude formalism of potential scattering developed by Calogero. For nonstationary approximations, a new first-order (in small quantities) bound is established which is particularly useful for partial waves other than s waves. Similar, but second-order, bounds are established for approximations which are stationary. Some previous results, based on the use of the Lippman--Schwinger equation are generalized, and some new bounds are established. These are illustrated, and compared to previous results, by a simple example. We discuss the advantages and disadvantages of the present results in comparison to those derived previously. Finally, we present the generalization of some of the present formalism to the case of many-channel scattering involving many-particle systems, and discuss some of the difficulties of their practical implementation
Thermodynamic Upper Bound on Broadband Light Coupling with Photonic Structures
Yu, Zongfu; Raman, Aaswath; Fan, Shanhui
2012-01-01
to an upper bound dictated by the second law of thermodynamics. Such bound limits how efficient light can be coupled to any photonic structure. As one example of application, we use this upper bound to derive the limit of light absorption in broadband solar
Precise Propagation of Upper and Lower Probability Bounds in System P
Gilio, Angelo
2000-01-01
In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, automatically obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of ...
Inequalities Involving Upper Bounds for Certain Matrix Operators
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 3. Inequalities Involving Upper Bounds for Certain Matrix Operators. R Lashkaripour D Foroutannia. Volume ... Keywords. Inequality; norm; summability matrix; Hausdorff matrix; Hilbert matrix; weighted sequence space; Lorentz sequence space.
An upper bound for the proton temperature anisotrophy
International Nuclear Information System (INIS)
Gary, S.P.
1994-01-01
This tutorial describes recent research concerning the upper bound on the hot proton temperature anisotropy imposed by wave-particle scattering due to enhanced fluctuations from the electromagnetic proton cyclotron anisotropy instability. This upper bound, which has been observed in both the magnetosheath and the outer magnetosphere, represents a limited closure relation for the equations of anisotropic magnetohydrodynamics. Such a closure relation has the potential to improve the predictive capability of large-scale anisotropic models of the magnetosphere
The question of an upper bound on entropy
International Nuclear Information System (INIS)
Qadir, A.
1982-08-01
We discuss the possibility, and significance, of an upper bound on entropy in the light of the arguments of Bekenstein and Unruh and Wald. We obtain a stricter bound than Bekenstein does, and point out some limitations with regard to its significance. (author)
Supergravity and upper bound on scale of supersymmetry breaking
International Nuclear Information System (INIS)
Kim, J.E.; Nishino, H.
1983-09-01
In locally supersymmetric grand unified models we show rather a model independent upper bound 3x10 11 GeV for the scale of supersymmetry breaking, which is derived by considering SU(2)xU(1) breaking at electro-weak mass scale. This bound necessarily implies the existence of new particles (superpartners) below 10 4 GeV. (author)
Thermodynamic Upper Bound on Broadband Light Coupling with Photonic Structures
Yu, Zongfu
2012-10-01
The coupling between free space radiation and optical media critically influences the performance of optical devices. We show that, for any given photonic structure, the sum of the external coupling rates for all its optical modes are subject to an upper bound dictated by the second law of thermodynamics. Such bound limits how efficient light can be coupled to any photonic structure. As one example of application, we use this upper bound to derive the limit of light absorption in broadband solar absorbers. © 2012 American Physical Society.
An upper bound on Q-star masses
International Nuclear Information System (INIS)
Hochron, D.R.; Selipsky, S.B.
1992-06-01
Q-stars (the gravitational generalization of Q-balls, strongly bound bulk matter that an appear in field theories of strongly interacting hadrons) are the only known impact objects consistent with the known bulk structure of nuclei and chiral symmetry that evade the Rhoades-Ruffini upper bound of 3.2M circle-dot . Generic bounds are quite weak: M Q-star circle-dot . If, however, we assume that the 1.558 ms pulsar is a Q-star, equilibrium. A stability criteria of rotating fluids place a much stronger upper bound of M c ≤ 5.3M circle-dot on such models under certain special assumptions. This has important implications for heavy compact objects such as Cygnus X-1
Upper bound of abutment scour in laboratory and field data
Benedict, Stephen
2016-01-01
The U.S. Geological Survey, in cooperation with the South Carolina Department of Transportation, conducted a field investigation of abutment scour in South Carolina and used those data to develop envelope curves that define the upper bound of abutment scour. To expand on this previous work, an additional cooperative investigation was initiated to combine the South Carolina data with abutment scour data from other sources and evaluate upper bound patterns with this larger data set. To facilitate this analysis, 446 laboratory and 331 field measurements of abutment scour were compiled into a digital database. This extensive database was used to evaluate the South Carolina abutment scour envelope curves and to develop additional envelope curves that reflected the upper bound of abutment scour depth for the laboratory and field data. The envelope curves provide simple but useful supplementary tools for assessing the potential maximum abutment scour depth in the field setting.
Upper Bounds for Ruin Probability with Stochastic Investment Return
Institute of Scientific and Technical Information of China (English)
ZHANG Lihong
2005-01-01
Risk models with stochastic investment return are widely held in practice, as well as in more challenging research fields. Risk theory is mainly concerned with ruin probability, and a tight bound for ruin probability is the best for practical use. This paper presents a discrete time risk model with stochastic investment return. Conditional expectation properties and martingale inequalities are used to obtain both exponential and non-exponential upper bounds for the ruin probability.
A Method for Upper Bounding on Network Access Speed
DEFF Research Database (Denmark)
Knudsen, Thomas Phillip; Patel, A.; Pedersen, Jens Myrup
2004-01-01
This paper presents a method for calculating an upper bound on network access speed growth and gives guidelines for further research experiments and simulations. The method is aimed at providing a basis for simulation of long term network development and resource management.......This paper presents a method for calculating an upper bound on network access speed growth and gives guidelines for further research experiments and simulations. The method is aimed at providing a basis for simulation of long term network development and resource management....
Upper bounds for Neyman-Pearson cooperative spectrum sensing
Zahabi, Sayed Jalal
2011-06-01
We consider a cooperative spectrum sensing scenario where the local sensors at the secondary users are viewed as one-level quantizers, and the quantized data are to be fused under Neyman-Pearson (N-P) criterion. We demonstrate how the N-P fusion results in a randomized test, which represents the total performance of our spectrum sensing scheme. We further introduce an upper performance bound for the overall primary user signal detection. An analytical procedure towards the upper bound and its relevant quantization setup at the local sensors are proposed and examined through simulations. © 2011 IEEE.
Upper bounds for Neyman-Pearson cooperative spectrum sensing
Zahabi, Sayed Jalal; Tadaion, Ali Akbar; Aissa, Sonia
2011-01-01
We consider a cooperative spectrum sensing scenario where the local sensors at the secondary users are viewed as one-level quantizers, and the quantized data are to be fused under Neyman-Pearson (N-P) criterion. We demonstrate how the N-P fusion results in a randomized test, which represents the total performance of our spectrum sensing scheme. We further introduce an upper performance bound for the overall primary user signal detection. An analytical procedure towards the upper bound and its relevant quantization setup at the local sensors are proposed and examined through simulations. © 2011 IEEE.
Higgs mass upper bound in the O(4) approximation
International Nuclear Information System (INIS)
Lin, L.
1991-01-01
In this paper the theoretical breakdown of the minimal standard model in four dimension is investigated when the mass of the Higgs particle is larger than the weak interaction scale. The triviality arguement for an upper bound on the Higgs mass is made quantitative on the lattice in large scale simulations of the spontaneously broken Higgs sector. The authors obtain an upper bound m H ≅640 GeV on the Higgs mass at a dimensionless correlation length ξ = 2 in lattice units.units
International Nuclear Information System (INIS)
Kim, Chang-Bae; Krommes, J.A.
1988-08-01
The work of Krommes and Smith on rigorous upper bounds for the turbulent transport of a passively advected scalar [/ital Ann. Phys./ 177:246 (1987)] is extended in two directions: (1) For their ''reference model,'' improved upper bounds are obtained by utilizing more sophisticated two-time constraints which include the effects of cross-correlations up to fourth order. Numerical solutions of the model stochastic differential equation are also obtained; they show that the new bounds compare quite favorably with the exact results, even at large Reynolds and Kubo numbers. (2) The theory is extended to take account of a finite spatial autocorrelation length L/sub c/. As a reasonably generic example, the problem of particle transport due to statistically specified stochastic magnetic fields in a collisionless turbulent plasma is revisited. A bound is obtained which reduces for small L/sub c/ to the quasilinear limit and for large L/sub c/ to the strong turbulence limit, and which provides a reasonable and rigorous interpolation for intermediate values of L/sub c/. 18 refs., 6 figs
Upper bound on the radii of black-hole photonspheres
International Nuclear Information System (INIS)
Hod, Shahar
2013-01-01
One of the most remarkable predictions of the general theory of relativity is the existence of black-hole “photonspheres”, compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by r γ ⩽3M, where M is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound
International Nuclear Information System (INIS)
Dodonov, V V
2012-01-01
Exact and approximate formulas for the upper bound of the relative energy difference of two Gaussian states with a fixed fidelity between them are derived. The reciprocal formulas for the upper bound of the fidelity for the fixed value of the relative energy difference are also obtained. The bounds appear higher for pure states than for mixed ones, and their maximal values correspond to squeezed vacuum states. In particular, to guarantee the relative energy difference less than 10%, for quite arbitrary Gaussian states, the fidelity between them must exceed the level 0.998866. (fast track communication)
Comparing two reliability upper bounds for multistate systems
International Nuclear Information System (INIS)
Meng, Fan C.
2005-01-01
The path-cut reliability bound due to Esary and Proschan [J. Am. Stat. Assoc. 65 (1970) 329] and the minimax reliability bound due to Barlow and Proschan [Statistical Theory of Reliability and Life Testing: Probability Models, 1981] for binary systems have been generalized to multistate systems by Block and Savits [J. Appl. Probab. 19 (1982) 391]. Some comparison results concerning the two multistate lower bounds for various types of multistate systems are given by Meng [Probab. Eng. Inform. Sci. 16 (2002) 485]. In this note we compare the two multistate upper bounds and present results which generalize some previous ones obtained by Maymin [J. Stat. Plan. Inference 16 (1987) 337] for binary systems. Examples are given to illustrate our results
Communication: An exact bound on the bridge function in integral equation theories.
Kast, Stefan M; Tomazic, Daniel
2012-11-07
We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.
Upper bound on compositeness scale from strong CP violation
International Nuclear Information System (INIS)
Nelson, A.; Stanford Univ., CA
1988-01-01
In this letter I estimate the size of corrections to the neutron electric dipole moment in composite-technicolor models. The natural size of the electric dipole moment is about 10 -25 e cm (f/3.5 TeV) 24 , where f is the compositeness scale. The current experimental bound of 1.2x10 -25 e cm on the electric dipole moment of the neutron provides an upper bound on the compositeness scale of 3.5 TeV. (orig.)
An upper and lower bound of the Medication Possession Ratio
Directory of Open Access Journals (Sweden)
Sperber CM
2017-08-01
Full Text Available Christian M Sperber, Suren R Samarasinghe, Grace P Lomax Patient Connect Limited, Guildford, UK Background: The Medication Possession Ratio (MPR is a ubiquitous and central measurement for adherence in the health care industry. However, attempts to standardize its calculation have failed, possibly due to the opacity of a single, static MPR, incapability of directly lending itself to a variety of studies, and challenges of comparing the value across studies. This work shows that the MPR strictly depends on the length of the time interval over which it is measured as well as on the dominant dispense quantity for short time intervals. Furthermore, removing a proportion of the patient cohort based on the number of acquisitions may also have a severe impact on the MPR. Therefore, it is suggested that the MPR is represented as a trend over a range of time intervals. To this end, an upper and lower bound of the MPR trend is developed with an upper bound acknowledging patients who change their treatment and the lower bound acknowledging patients who discontinue their treatment.Purpose: Introducing a representation of the MPR value as a trend rather than a static number by developing a quantitative description of an upper and lower bound of the MPR trend, while shedding light on the impacts on prefiltering the patient cohort.Patients and methods: Anonymized patient-level data was utilized as an example for a suggested calculation of an upper and lower bound of the MPR.Results: Representation of the MPR for a predefined time interval precludes a reliable MPR assessment. A quantitative approach is suggested to generate an upper and lower trend of the MPR while emphasizing the impact on removing patients with a limited number of acquisitions.Conclusion: An upper and lower trend makes the MPR more transparent and allows a better comparison across different studies. Removing patients with a limited number of acquisitions should be avoided. Keywords: MPR
Upper bounds on the entropy of radiation systems
Institute of Scientific and Technical Information of China (English)
汪定雄
1997-01-01
The upper bounds on the entropy of a radiation system confined to a spherical box are calculated in six cases by using the equation of state of radiation in flat spacetime and the equation of state of radiation near black-hole horizon,which was derived by Li and Liu (hereafter the Li-Liu equation).It turns out that the Li-Liu equation does have unique advantage in dealing with the entropy bound of critical self-gravitating radiation systems,while the usual equation of state will result in entropy divergence.In the case of non-self-gravitating radiation systems and non-critical self-gravitating radiation systems,there is no difference in the entropy bounds derived by these two equations of state.
Upper bounds on entangling rates of bipartite Hamiltonians
International Nuclear Information System (INIS)
Bravyi, Sergey
2007-01-01
We discuss upper bounds on the rate at which unitary evolution governed by a nonlocal Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c log(d) parallel H parallel, where d is the smallest dimension of the interacting particles parallel H parallel is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove an analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate - a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily
DEFF Research Database (Denmark)
Atamtürk, Alper; Muller, Laurent Flindt; Pisinger, David
2013-01-01
Motivated by addressing probabilistic 0-1 programs we study the conic quadratic knapsack polytope with generalized upper bound (GUB) constraints. In particular, we investigate separating and extending GUB cover inequalities. We show that, unlike in the linear case, determining whether a cover can...... be extended with a single variable is NP-hard. We describe and compare a number of exact and heuristic separation and extension algorithms which make use of the structure of the constraints. Computational experiments are performed for comparing the proposed separation and extension algorithms...
Upper bounds for the changes of natural frequencies due to dynamic partitioning techniques
International Nuclear Information System (INIS)
Peters, K.; Wagner, U.; Albus, E.
1981-01-01
Dynamic partitioning or substructuring is the reduction of degrees of freedom by neglecting the dynamical influence of higher modes of certain substructure. One of the major reasons for these techniques not being widely accepted is the lack of criteria to judge the accuracy of the computed data. So far as natural frequencies are concerned a theorem is formulated which gives upper bounds for the error due to dynamic substructuring. The theorem is tested by applying it to a special statically exact substructuring method which is gained from a fixed-mode approach. The error estimation turns out to be strict enough to decide on the validity of DOF-reduction. (orig.)
Upper Bound on the Hadronic Light-By-Light Contribution to the Muon g-2
International Nuclear Information System (INIS)
Erler, Jens; Sanchez, Genaro Toledo
2006-01-01
There are indications that hadronic loops in some electroweak observables are almost saturated by parton level effects. Taking this as the hypothesis for this work, we propose a genuine parton level estimate of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, a μ LBL (had). Our quark mass definitions and values are motivated in detail, and the simplicity of our approach allows for a transparent error estimate. For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses a μ LBL (had) is overestimated. Interpolating, this suggests quoting an upper bound. We obtain a μ LBL (had) -9 (95% C.L.)
On the upper bound in the Bohm sheath criterion
Energy Technology Data Exchange (ETDEWEB)
Kotelnikov, I. A., E-mail: I.A.Kotelnikov@inp.nsk.su; Skovorodin, D. I., E-mail: D.I.Skovorodin@inp.nsk.su [Russian Academy of Sciences, Budker Institute of Nuclear Physics, Siberian Branch (Russian Federation)
2016-02-15
The question is discussed about the existence of an upper bound in the Bohm sheath criterion, according to which the Debye sheath at the interface between plasma and a negatively charged electrode is stable only if the ion flow velocity in plasma exceeds the ion sound velocity. It is stated that, with an exception of some artificial ionization models, the Bohm sheath criterion is satisfied as an equality at the lower bound and the ion flow velocity is equal to the speed of sound. In the one-dimensional theory, a supersonic flow appears in an unrealistic model of a localized ion source the size of which is less than the Debye length; however, supersonic flows seem to be possible in the two- and three-dimensional cases. In the available numerical codes used to simulate charged particle sources with a plasma emitter, the presence of the upper bound in the Bohm sheath criterion is not supposed; however, the correspondence with experimental data is usually achieved if the ion flow velocity in plasma is close to the ion sound velocity.
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
International Nuclear Information System (INIS)
Destainville, N
2003-01-01
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium
Exact S-matrices for dn+1(2) affine Toda solitons and their bound states
International Nuclear Information System (INIS)
Gandenberger, G.M.; MacKay, N.J.
1995-01-01
We conjecture an exact S-matrix for the scattering of solitons in d n+1 (2) affine Toda field theory in terms of the R-matrix of the quantum group U q (c n (1) ). From this we construct the scattering amplitudes for all scalar bound states (breathers) of the theory. This S-matrix conjecture is justified by detailed examination of its pole structure. We show that a breather-particle identification holds by comparing the S-matrix elements for the lowest breathers with the S-matrix for the quantum particles in real affine Toda field theory, and discuss the implications for various forms of duality. (orig.)
Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique
Energy Technology Data Exchange (ETDEWEB)
Destainville, N [Laboratoire de Physique Theorique - IRSAMC, CNRS/Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04 (France)
2003-04-04
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.
An upper bound on right-chiral weak interactions
International Nuclear Information System (INIS)
Stephenson, G.J.; Goldman, T.; Maltman, K.
1990-01-01
Weak vertex corrections to the quark-gluon vertex functions produce differing form-factor corrections for quarks of differing chiralities. These differences grow with increasing four-momentum transfer in the gluon leg. Consequently, inclusive polarized proton--proton scattering to a final state jet should show a large parity-violating asymmetry at high energies. The absence of large signals at sufficiently high energies can be interpreted as being due to balancing vertex corrections from a right-handed weak vector boson of limited mass, and limits on the strength of such signals can, in principle, give upper bounds on that mass. 2 refs
An upper bound on right-Chiral weak interactions
International Nuclear Information System (INIS)
Stephenson, G.J.; Goldman, T.; Maltman, K.
1990-01-01
Weak vertex corrections to the quark-gluon vertex functions produce differing form-factor corrections for quarks of differing chiralities. These differences grow with increasing four-momentum transfer in the gluon leg. Consequently, inclusive polarized proton-proton scattering to a final state jet should show a large parity-violating asymmetry at high energies. The absence of large signals at sufficiently high energies can be interpreted as being due to balancing vertex corrections from a right-handed weak vector boson of limited mass, and limits on the strength of such signals can, in principle, give upper bounds on that mass
Finding upper bounds for software failure probabilities - experiments and results
International Nuclear Information System (INIS)
Kristiansen, Monica; Winther, Rune
2005-09-01
This report looks into some aspects of using Bayesian hypothesis testing to find upper bounds for software failure probabilities. In the first part, the report evaluates the Bayesian hypothesis testing approach for finding upper bounds for failure probabilities of single software components. The report shows how different choices of prior probability distributions for a software component's failure probability influence the number of tests required to obtain adequate confidence in a software component. In the evaluation, both the effect of the shape of the prior distribution as well as one's prior confidence in the software component were investigated. In addition, different choices of prior probability distributions are discussed based on their relevance in a software context. In the second part, ideas on how the Bayesian hypothesis testing approach can be extended to assess systems consisting of multiple software components are given. One of the main challenges when assessing systems consisting of multiple software components is to include dependency aspects in the software reliability models. However, different types of failure dependencies between software components must be modelled differently. Identifying different types of failure dependencies are therefore an important condition for choosing a prior probability distribution, which correctly reflects one's prior belief in the probability for software components failing dependently. In this report, software components include both general in-house software components, as well as pre-developed software components (e.g. COTS, SOUP, etc). (Author)
Marginal Consistency: Upper-Bounding Partition Functions over Commutative Semirings.
Werner, Tomás
2015-07-01
Many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring. By generalizing max-sum diffusion (one of convergent message passing algorithms for approximate MAP inference in graphical models), we propose an iterative algorithm to upper bound such partition functions over commutative semirings. The iteration of the algorithm is remarkably simple: change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal. In many commutative semirings, repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide. We call this state marginal consistency. During that, an upper bound on the partition function monotonically decreases. This abstract algorithm unifies several existing algorithms, including max-sum diffusion and basic constraint propagation (or local consistency) algorithms in constraint programming. We further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity (order). Finally, we discuss instances of the framework for several semirings, including the distributive lattice and the max-sum and sum-product semirings.
Rigorous upper bounds for transport due to passive advection by inhomogeneous turbulence
International Nuclear Information System (INIS)
Krommes, J.A.; Smith, R.A.
1987-05-01
A variational procedure, due originally to Howard and explored by Busse and others for self-consistent turbulence problems, is employed to determine rigorous upper bounds for the advection of a passive scalar through an inhomogeneous turbulent slab with arbitrary generalized Reynolds number R and Kubo number K. In the basic version of the method, the steady-state energy balance is used as a constraint; the resulting bound, though rigorous, is independent of K. A pedagogical reference model (one dimension, K = ∞) is described in detail; the bound compares favorably with the exact solution. The direct-interaction approximation is also worked out for this model; it is somewhat more accurate than the bound, but requires considerably more labor to solve. For the basic bound, a general formalism is presented for several dimensions, finite correlation length, and reasonably general boundary conditions. Part of the general method, in which a Green's function technique is employed, applies to self-consistent as well as to passive problems, and thereby generalizes previous results in the fluid literature. The formalism is extended for the first time to include time-dependent constraints, and a bound is deduced which explicitly depends on K and has the correct physical scalings in all regimes of R and K. Two applications from the theory of turbulent plasmas ae described: flux in velocity space, and test particle transport in stochastic magnetic fields. For the velocity space problem the simplest bound reproduces Dupree's original scaling for the strong turbulence diffusion coefficient. For the case of stochastic magnetic fields, the scaling of the bounds is described for the magnetic diffusion coefficient as well as for the particle diffusion coefficient in the so-called collisionless, fluid, and double-streaming regimes
International Nuclear Information System (INIS)
Logrado, P.G.; Vianna, J.D.M.
Upper and lower bounds for the energy eigenvalues is Schoenberg's perturbation-theory ground state are studied. After a review of the characteristic features of the partitioning techniques the perturbative expansion proposed by Schoenberg is generated from an exact operator equation. The upper and lower bounds for the ground state eigenvalue are derived by using reaction and wave operators concepts, the bracketing function and operator inequalities. (Author) [pt
Exact spinor-scalar bound states in a quantum field theory with scalar interactions
International Nuclear Information System (INIS)
Shpytko, Volodymyr; Darewych, Jurij
2001-01-01
We study two-particle systems in a model quantum field theory in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve for the mediating field in terms of the particle fields. This results in a Hamiltonian in which the mediating-field propagator appears directly in the interaction term. It is shown that exact two-particle eigenstates of the Hamiltonian can be determined. The resulting relativistic fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle limits. Analytical solutions for the bound state energy spectrum are obtained for the case of massless mediating fields
General upper bounds on the runtime of parallel evolutionary algorithms.
Lässig, Jörg; Sudholt, Dirk
2014-01-01
We present a general method for analyzing the runtime of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel runtime. This allows for a rigorous estimate of the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the performance guarantees improve with the density of the topology. Surprisingly, even sparse topologies such as ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors lead to the best guaranteed speedups, thus giving hints on how to parameterize parallel evolutionary algorithms.
Upper bound for the length of commutative algebras
International Nuclear Information System (INIS)
Markova, Ol'ga V
2009-01-01
By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field one means the least positive integer k such that the words of length not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, an upper bound for the length of a commutative algebra in terms of a function of two invariants of the algebra, the dimension and the maximal degree of the minimal polynomial for the elements of the algebra, is obtained. As a corollary, a formula for the length of the algebra of diagonal matrices over an arbitrary field is obtained. Bibliography: 8 titles.
Upper Bounds on Performance Measures of Heterogeneous // Queues
Directory of Open Access Journals (Sweden)
F. S. Q. Alves
2011-01-01
Full Text Available In many real-life queueing systems, the servers are often heterogeneous, namely they work at different rates. This paper provides a simple method to compute tight upper bounds on two important performance measures of single-class heterogeneous multi-server Markovian queueing systems, namely the average number in queue and the average waiting time in queue. This method is based on an expansion of the state space that is followed by an approximate reduction of the state space, only considering the most probable states. In most cases tested, we were able to approximate the actual behavior of the system with smaller errors than those obtained from traditional homogeneous multiserver Markovian queues, as shown by GPSS simulations. In addition, we have correlated the quality of the approximation with the degree of heterogeneity of the system, which was evaluated using its Gini index. Finally, we have shown that the bounds are robust and still useful, even considering quite different allocation strategies. A large number of simulation results show the accuracy of the proposed method that is better than that of classical homogeneous multiserver Markovian formulae in many situations.
An upper bound on the number of independent sets in a tree
DEFF Research Database (Denmark)
Pedersen, Anders Sune
2007-01-01
The main result of this paper is an upper bound on the number of independent sets in a tree in terms of the order and diameter of the tree. This new upper bound is a refinement of the bound given by Prodinger and Tichy [ Fibonacci Q., 20 (1982), no. 1, 16-21]. Finally, we give a sufficient...... condition for the new upper bound to be better thatn the upper bound given by Brigham, Chandrasekharan and Dutton [ Fibonacci Q., 31 (1993), no. 2, 98-104]....
An upper bound on the number of independent sets in a tree
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Pedersen, Anders Sune
The main result of this paper is an upper bound on the number of independent sets in a tree in terms of the order and diameter of the tree. This new upper bound is a refinement of the bound given by Prodinger and Tichy [Fibonacci Q., 20 (1982), no. 1, 16-21]. Finally, we give a sufficient condition...... for the new upper bound to be better than the upper bound given by Brigham, Chandrasekharan and Dutton [Fibonacci Q., 31 (1993), no. 2, 98-104]....
Upper bounds on the number of errors corrected by a convolutional code
DEFF Research Database (Denmark)
Justesen, Jørn
2004-01-01
We derive upper bounds on the weights of error patterns that can be corrected by a convolutional code with given parameters, or equivalently we give bounds on the code rate for a given set of error patterns. The bounds parallel the Hamming bound for block codes by relating the number of error...
Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC
Shakir, Muhammad; Durrani, Tariq S; Alouini, Mohamed-Slim
2011-01-01
demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity
Upper and lower Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model
International Nuclear Information System (INIS)
Gerhold, Philipp Frederik Clemens
2009-01-01
Motivated by the advent of the Large Hadron Collider (LHC) the aim of the present work is the non-perturbative determination of the cutoff-dependent upper and lower mass bounds of the Standard Model Higgs boson based on first principle calculations, in particular not relying on additional information such as the triviality property of the Higgs- Yukawa sector or indirect arguments like vacuum stability considerations. For that purpose the lattice approach is employed to allow for a non-perturbative investigation of a chirally invariant lattice Higgs-Yukawa model, serving here as a reasonable simplification of the full Standard Model, containing only those fields and interactions which are most essential for the intended Higgs boson mass determination. These are the complex Higgs doublet as well as the top and bottom quark fields and their mutual interactions. To maintain the chiral character of the Standard Model Higgs-fermion coupling also on the lattice, the latter model is constructed on the basis of the Neuberger overlap operator, obeying then an exact global lattice chiral symmetry. Respecting the fermionic degrees of freedom in a fully dynamical manner by virtue of a PHMC algorithm appropriately adapted to the here intended lattice calculations, such mass bounds can indeed be established with the aforementioned approach. Supported by analytical calculations performed in the framework of the constraint effective potential, the lower bound is found to be approximately m low H (Λ)=80 GeV at a cutoff of Λ=1000 GeV. The emergence of a lower Higgs boson mass bound is thus a manifest property of the pure Higgs-Yukawa sector that evolves directly from the Higgs-fermion interaction for a given set of Yukawa coupling constants. Its quantitative size, however, turns out to be non-universal in the sense, that it depends on the specific form, for instance, of the Higgs boson self-interaction. The upper Higgs boson mass bound is then established in the strong coupling
Upper Bounds on the BER Performance of MTCM-STBC Schemes over Shadowed Rician Fading Channels
Directory of Open Access Journals (Sweden)
M. Uysal
2004-08-01
Full Text Available Space-time block coding (STBC provides substantial diversity advantages with a low decoding complexity. However, these codes are not designed to achieve coding gains. Outer codes should be concatenated with STBC to provide additional coding gain. In this paper, we analyze the performance of concatenated trellis-coded STBC schemes over shadowed Rician frequency-flat fading channels. We derive an exact pairwise error probability (PEP expression that reveals the dominant factors affecting performance. Based on the derived PEP, in conjunction with the transfer function technique, we also present upper bounds on the bit error rate (BER, which are further shown to be tight through a Monte-Carlo simulation study.
Upper bound for the span of pencil graph
Parvathi, N.; Vimala Rani, A.
2018-04-01
An L(2,1)-Coloring or Radio Coloring or λ coloring of a graph is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x) ‑ f(y)| ≥ 2 if d(x,y) = 1 and |f(x) ‑ f(y)| ≥ 1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-coloring number or span number λ(G) of G is the smallest number k such that G has an L(2,1)-coloring with max{f(v) : v ∈ V(G)} = k. [2]The minimum number of colors used in L(2,1)-coloring is called the radio number rn(G) of G (Positive integer). Griggs and yeh conjectured that λ(G) ≤ Δ2 for any simple graph with maximum degree Δ>2. In this article, we consider some special graphs like, n-sunlet graph, pencil graph families and derive its upper bound of (G) and rn(G).
Upper Bound for Queue length in Regulated Burst Service Scheduling
Directory of Open Access Journals (Sweden)
Mahmood Daneshvar Farzanegan
2016-01-01
Full Text Available Quality of Service (QoS provisioning is very important in next computer/communication networks because of increasing multimedia services. Hence, very investigations are performed in this area. Scheduling algorithms effect QoS provisioning. Lately, a scheduling algorithm called Regulated Burst Service Scheduling (RBSS suggested by author in [1] to provide a better service to bursty and delay sensitive services such as video. One of the most significant feature in RBSS is considering burstiness of arrival traffic in scheduling algorithm. In this paper, an upper bound of queue length or buffer size and service curve are calculated by Network Calculus analysis for RBSS. Because in RBSS queue length is a parameter that is considered in scheduling arbitrator, analysis results a differential inequality to obtain service curve. To simplify, arrival traffic is assumed to be linear that is defined in the paper clearly. This paper help to analysis delay in RBSS for different traffic with different specifications. Therefore, QoS provisioning will be evaluated.
Power generation assets. Energy constraints, upper bounds and hedging strategies
Energy Technology Data Exchange (ETDEWEB)
Enge, Thomas
2010-09-20
The overall topic of this thesis is the valuation of power generation assets under energy and risk constraints. Our focus is on the modeling aspect i.e. to find the right balance between accuracy and computational feasibility. We define a new not yet investigated unit commitment problem that introduces an energy constraint to a thermal power plant. We define a continuous stochastic dynamic program with a nested mixed integer program (MIP). We introduce a fast implementation approach by replacing the MIP with an efficient matrix calculation and use principal component analysis to reduce the number of risk factors. We also provide a fast heuristic valuation approach for comparison. As both models can only provide lower bounds of the asset value, we investigate the theory of upper bounds for a proper validation of our power plant results. We review the primal dual algorithm for swing options by Meinshausen and Hambly and in particular clarify their notation and implementation. Then we provide an extension for swing options with multiple exercises at the same stage that we developed together with Prof. Bender, University of Braunschweig. We outline Prof. Bender's proof and describe the implementation in detail. Finally we provide a risk analysis for our thermal power plant. In particular we investigate strategies to reduce spot price risk to which power plants are significantly exposed. First, we focus on the measurement of spot price risk and propose three appropriate risk figures (Forward delta as opposed to Futures delta, synthetic spot delta and Earnings-at-Risk) and illustrate their application using a business case. Second we suggest risk mitigation strategies for both periods, before and in delivery. The latter tries to alter the dispatch policy i.e. pick less risky hours and accept a (desirably only slightly) smaller return. We introduce a benchmark that weighs risk versus return and that we will call EaR-efficient option value. We propose a mitigation
An upper bound on the number of errors corrected by a convolutional code
DEFF Research Database (Denmark)
Justesen, Jørn
2000-01-01
The number of errors that a convolutional codes can correct in a segment of the encoded sequence is upper bounded by the number of distinct syndrome sequences of the relevant length.......The number of errors that a convolutional codes can correct in a segment of the encoded sequence is upper bounded by the number of distinct syndrome sequences of the relevant length....
The upper bound of radiation energy in the Myers-Perry black hole collision
International Nuclear Information System (INIS)
Gwak, Bogeun; Lee, Bum-Hoon
2016-01-01
We have investigated the upper bound of the radiation energy in the head-on collision of two Myers-Perry black holes. Initially, the two black holes are far away from each other, and they become one black hole after the collision. We have obtained the upper bound of the radiation energy thermodynamically allowed in the process. The upper bound of the radiation energy is obtained in general dimensions. The radiation bound depends on the alignments of rotating axes for a given initial condition due to spin-spin interaction. We have found that the collision may not be occurred for a initially ultra-spinning black hole.
An Upper Bound on the Entropy of Constrained 2d Fields
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
1998-01-01
An upper bound on the entropy of constrained 2D fields is presented. The constraints have to be symmetric in (at least) one of the two directions. The bound generalizes (in a weaker form) the bound of Calkin and Wilf (see SIAM Journal of Discrete Mathematics, vol.11, p.54-60, 1998) which is valid...
Upper bound on the capacity of constrained three-dimensional codes
DEFF Research Database (Denmark)
Forchhammer, Søren
2000-01-01
An upper bound on the capacity of constrained three-dimensional codes is presented. The bound for two-dimensional codes of Calkin and Wilf (see SIAM Journal of Discrete Mathematics, vol.11, no.1, p.54-60, 1998) was extended to three dimensions by Nagy and Zeger. Both bounds apply to first order s...
Upper bounds on quantum uncertainty products and complexity measures
Energy Technology Data Exchange (ETDEWEB)
Guerrero, Angel; Sanchez-Moreno, Pablo; Dehesa, Jesus S. [Department of Atomic, Molecular and Nuclear Physics, University of Granada, Granada (Spain); Department of Applied Mathematics, University of Granada, Granada (Spain) and Institute Carlos I for Computational and Theoretical Physics, University of Granada, Granada (Spain); Department of Atomic, Molecular and Nuclear Physics, University of Granada, Granada (Spain); Institute Carlos I for Computational and Theoretical Physics, University of Granada, Granada (Spain)
2011-10-15
The position-momentum Shannon and Renyi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in terms of the Heisenberg-Kennard product . Moreover, the Cramer-Rao, Fisher-Shannon, and Lopez-Ruiz, Mancini, and Calbet shape measures of complexity (whose lower bounds have been recently found) are also bounded from above. The improvement of these bounds for systems subject to spherically symmetric potentials is also explicitly given. Finally, applications to hydrogenic and oscillator-like systems are done.
Upper Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa Model
Energy Technology Data Exchange (ETDEWEB)
Gerhold, P. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; John von Neumann-Institut fuer Computing NIC/DESY, Zeuthen (Germany); Jansen, K. [John von Neumann-Institut fuer Computing NIC/DESY, Zeuthen (Germany)
2010-02-15
We establish the cutoff-dependent upper Higgs boson mass bound by means of direct lattice computations in the framework of a chirally invariant lattice Higgs-Yukawa model emulating the same chiral Yukawa coupling structure as in the Higgs-fermion sector of the Standard Model. As expected from the triviality picture of the Higgs sector, we observe the upper mass bound to decrease with rising cutoff parameter {lambda}. Moreover, the strength of the fermionic contribution to the upper mass bound is explored by comparing to the corresponding analysis in the pure {phi}{sup 4}-theory. (orig.)
Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC
Shakir, Muhammad
2011-09-01
This article presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs). This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading matrix G and the channel path gain matrix Ω. This article demonstrates that the actual capacity converges to the theoretical upper bound under the constraints like low signal-to-noise ratios and limiting channel path gain among the MTs and the respective base station of interest. In order to determine the usefulness of the HUB, the behavior of the theoretical upper bound is critically observed specially when the inter-cell and the intra-cell time sharing schemes are employed. In this context, we derive an analytical form of HUB by employing an approximation approach based on the estimation of probability density function of trace of Hadamard product of two matrices, i.e., G and Ω. A closed form of expression has been derived to capture the effect of the MT distribution on the optimum joint decoding capacity of C-GCMAC. This article demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity of Wyner GCMAC.
Lower and Upper Bounds for Deniable Public-Key Encryption
DEFF Research Database (Denmark)
Bendlin, Rikke; Nielsen, Jesper Buus; Nordholt, Peter Sebastian
2011-01-01
the parties to change their internal state to make it look like a given ciphertext decrypts to a message different from what it really decrypts to. Deniable encryption was in this way introduced to allow to deny a message exchange and hence combat coercion. Depending on which parties can be coerced...... that it is impossible to construct a non-interactive bi-deniable public-key encryption scheme with better than polynomial security. Specifically, we give an explicit bound relating the security of the scheme to how efficient the scheme is in terms of key size. Our impossibility result establishes a lower bound...
Upper Bound for Neutron Emission from Sonoluminescing Bubbles in Deuterated Acetone
International Nuclear Information System (INIS)
Camara, C. G.; Putterman, S. J.; Hopkins, S. D.; Suslick, K. S.
2007-01-01
An experimental search for nuclear fusion inside imploding bubbles of degassed deuterated acetone at 0 degree sign C driven by a 15 atm sound field and seeded with a neutron generator reveals an upper bound that is a factor of 10 000 less than the signal reported by Taleyarkhan et al. The strength of our upper bound is limited by the weakness of sonoluminescence, which we ascribe to the relatively high vapor pressure of acetone
A New Upper Bound on the Infinity Norm of the Inverse of Nekrasov Matrices
Directory of Open Access Journals (Sweden)
Lei Gao
2014-01-01
Full Text Available A new upper bound which involves a parameter for the infinity norm of the inverse of Nekrasov matrices is given. And we determine the optimal value of the parameter such that the bound improves the results of Kolotilina, 2013. Numerical examples are given to illustrate the corresponding results.
Frisbee, Joseph H., Jr.
2015-01-01
Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do
The exact LPT-bound for maximizing the minimum completion time
Csirik, J.; Kellerer, H.; Woeginger, G.J.
1992-01-01
We consider the problem of assigning a set of jobs to a system of m identical processors in order to maximize the earliest processor completion time. It was known that the LPT-heuristic gives an approximation of worst case ratio at most 3/4. In this note we show that the exact worst case ratio of
Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza
2012-01-01
if the system is controllable or observable, but also it is required to know the degree of controllability or observability of the system. Gramian matrices were introduced to address this issue by providing a quantitative measure for controllability and observability. In many applications, the information...... of uncertain systems. In this paper, we derive upper and lower bounds of frequency interval gramians under perturbations of an A-matrix in the state-space form. These bounds are obtained by solving algebraic Riccati equations. The results are further used to obtain upper and lower bounds of the frequency...
Analytical upper bound on optimum joint decoding capacity of Wyner GCMAC using hadamard inequality
Shakir, Muhammad
2011-11-01
This paper presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs) across the cells. This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading and channel path gain matrices. In this context, we employ an approximation approach based on the estimation of probability density function (PDF) of Hadamard product of two matrices. A closed-form expression has been derived to capture the effect of variable user density in adjacent cells on optimal joint decoding capacity. The results of this paper demonstrate that the analytical HUB based on the proposed approximation approach converges to the theoretical results for medium range of signal to noise ratios and shows a comparable tighter bound on optimum joint decoding capacity. © 2011 IEEE.
Upper and Lower Bound Limit Loads for Thin-Walled Pressure Vessels Used for Aerosol Cans
Directory of Open Access Journals (Sweden)
Stephen John Hardy
2009-01-01
Full Text Available The elastic compensation method proposed by Mackenzie and Boyle is used to estimate the upper and lower bound limit (collapse loads for one-piece aluminium aerosol cans, which are thin-walled pressure vessels subjected to internal pressure loading. Elastic-plastic finite element predictions for yield and collapse pressures are found using axisymmetric models. However, it is shown that predictions for the elastic-plastic buckling of the vessel base require the use of a full three-dimensional model with a small unsymmetrical imperfection introduced. The finite element predictions for the internal pressure to cause complete failure via collapse fall within the upper and lower bounds. Hence the method, which involves only elastic analyses, can be used in place of complex elastic-plastic finite element analyses when upper and lower bound estimates are adequate for design purposes. Similarly, the lower bound value underpredicts the pressure at which first yield occurs.
Exact reliability formula and bounds for general k-out-of-n systems
International Nuclear Information System (INIS)
Koucky, Miroslav
2003-01-01
The paper deals with reliability of general k-out-of-n systems whose component failures need not be independent and identically distributed. The result is an exact closed form reliability formula which is based on Feller's result. The formula is efficient and easy to use for manual and computer computations. The approximations for the system reliability are given and are useful when dealing with large systems. Two examples illustrate the use of the results
The existence and the stability of solutions for equilibrium problems with lower and upper bounds
Directory of Open Access Journals (Sweden)
Congjun Zhang
2012-12-01
Full Text Available In this paper, we study a class of equilibrium problems with lower and upper bounds. We obtain some existence results of solutions for equilibrium problems with lower and upper bounds by employing some classical fixed-point theorems. We investigate the stability of the solution sets for the problems, and establish sufficient conditions for the upper semicontinuity, lower semicontinuity and continuity of the solution set mapping $S:Lambda_1imesLambda_2o2^{X}$ in a Hausdorff topological vector space, in the case where a set $K$ and a mapping $f$ are perturbed respectively by parameters $lambda$ and $mu.$
Greedy solution of ill-posed problems: error bounds and exact inversion
International Nuclear Information System (INIS)
Denis, L; Lorenz, D A; Trede, D
2009-01-01
The orthogonal matching pursuit (OMP) is a greedy algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general, and in particular for two deconvolution examples from mass spectrometry and digital holography, respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transferred to ill-posed inverse problems since here the atoms are typically far from orthogonal. The ill-posedness of the operator probably causes the correlation of two distinct atoms to become huge, i.e. that two atoms look much alike. Therefore, one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for the exact recovery of the support of noisy signals. In the two examples, mass spectrometry and digital holography, we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography, our analysis may be regarded as a first step to calculate the resolution power of droplet holography
An upper bound on the total inelastic cross section as a function of the total cross section
International Nuclear Information System (INIS)
Wu, Tai Tsun; Martin, Andre; Roy, Shasanka Mohan; Singh, Virendra
2011-01-01
Recently, Andre Martin has proved a rigorous upper bound on the inelastic cross sectionσ inel at high energy, which is one-fourth of the known Froissart-Martin-Lukaszuk upper bound on σ tot . Here, we obtain an upper bound on σ inel in terms of σ tot and show that the Martin bound on σ inel is improved significantly with this added information.
Membrane-based ethylene/ethane separation: The upper bound and beyond
Rungta, Meha
2013-08-02
Ethylene/ethane separation via cryogenic distillation is extremely energy-intensive, and membrane separation may provide an attractive alternative. In this paper, ethylene/ethane separation performance using polymeric membranes is summarized, and an experimental ethylene/ethane polymeric upper bound based on literature data is presented. A theoretical prediction of the ethylene/ethane upper bound is also presented, and shows good agreement with the experimental upper bound. Further, two ways to overcome the ethylene/ethane upper bound, based on increasing the sorption or diffusion selectivity, is also discussed, and a review on advanced membrane types such as facilitated transport membranes, zeolite and metal organic framework based membranes, and carbon molecular sieve membranes is presented. Of these, carbon membranes have shown the potential to surpass the polymeric ethylene/ethane upper bound performance. Furthermore, a convenient, potentially scalable method for tailoring the performance of carbon membranes for ethylene/ethane separation based on tuning the pyrolysis conditions has also been demonstrated. © 2013 American Institute of Chemical Engineers.
Upper bound on the non-colorability threshold of the 2+p-COL problem
International Nuclear Information System (INIS)
Cruz, R.
2004-10-01
The 2p-COL problem introduced by Walsh, smoothly interpolates between P and NP by mixing together the polynornial 2-coloring problem and the NP complete 3-coloring problem. A natural upper bound on the non colorability of the 2+p-COL problem in min {r-bar 2 /(1 - p)r-bar 3 }, where r-bar 2 and r-bar 3 are the upper bounds on 2-COL and 3-COL thresholds respectively. In this paper we improve this upper-bound for each 0.73 ≤ p 1. This means that for p ≥ 0.73 the 2+p-COL problem does not behave like the 2-COL problem. We use the method developed by Kaporis et al., which combines the concept of legal rigid colorings introduced by Achlioptas and Molloy with the occupancy problem for random allocations of balls into bins. (author)
An upper bound for codes for the noisy two-access binary adder channel
Tilborg, van H.C.A.
1986-01-01
Using earlier methods a combinatorial upper bound is derived for|C|. cdot |D|, where(C,D)is adelta-decodable code pair for the noisy two-access binary adder channel. Asymptotically, this bound reduces toR_{1}=R_{2} leq frac{3}{2} + elog_{2} e - (frac{1}{2} + e) log_{2} (1 + 2e)= frac{1}{2} - e +
A Method for Upper Bounding Long Term Growth of Network Access Speed
Directory of Open Access Journals (Sweden)
Thomas Phillip Knudsen
2006-06-01
Full Text Available The development in home Internet access speed has shown an exponential development with growth rates averaging 25% per year. For resource management in network provisioning it becomes an urgent question how long such growth can continue. This paper presents a method for calculating an upper bound to visual content driven growth, proceeding from datarate requirements for a full virtual environment. Scenarios and approaches for reducing datarate requirements are considered and discussed. The presented figures for an upper bound on network access speed are discussed and perspectives on further research presented.
The upper bound on the lightest Higgs mass in the NMSSM revisited
International Nuclear Information System (INIS)
Ellwanger, Ulrich; Hugonie, Cyril
2007-04-01
We update the upper bound on the lightest CP even Higgs mass in the NMSSM, which is given as a function of tanβ and λ. We include the available one and two loop corrections to the NMSSM Higgs masses, and constraints from the absence of Landau singularities below the GUT scale as well as from the stability of the NMSSM Higgs potential. For m top varying between 171.4 and 178 GeV, squark masses of 1 TeV and maximal mixing the upper bound is assumed near tanβ ∼ 2 and varies between 139.9 and 141.4 GeV
Upper bound on the efficiency of certain nonimaging concentrators in the physical-optics model
Welford, W. T.; Winston, R.
1982-09-01
Upper bounds on the performance of nonimaging concentrators are obtained within the framework of scalar-wave theory by using a simple approach to avoid complex calculations on multiple phase fronts. The approach consists in treating a theoretically perfect image-forming device and postulating that no non-image-forming concentrator can have a better performance than such an ideal image-forming system. The performance of such a system can be calculated according to wave theory, and this will provide, in accordance with the postulate, upper bounds on the performance of nonimaging systems. The method is demonstrated for a two-dimensional compound parabolic concentrator.
Entanglement-assisted zero-error capacity is upper-bounded by the Lovasz θ function
International Nuclear Information System (INIS)
Beigi, Salman
2010-01-01
The zero-error capacity of a classical channel is expressed in terms of the independence number of some graph and its tensor powers. This quantity is hard to compute even for small graphs such as the cycle of length seven, so upper bounds such as the Lovasz theta function play an important role in zero-error communication. In this paper, we show that the Lovasz theta function is an upper bound on the zero-error capacity even in the presence of entanglement between the sender and receiver.
A Method for Upper Bounding Long Term Growth of Network Access Speed
DEFF Research Database (Denmark)
Knudsen, Thomas Phillip; Pedersen, Jens Myrup; Madsen, Ole Brun
2004-01-01
The development in home Internet access speed has shown an exponential development with growth rates averaging 25% per year. For resource management in network provisioning it becomes an urgent question how long such growth can continue. This paper presents a method for calculating an upper bound...... to visual content driven growth, proceeding from datarate requirements for a full virtual environment. Scenarios and approaches for reducing datarate requirements are considered and discussed. The presented figures for an upper bound on network access speed are discussed and perspectives on further research...
Derivation of upper bound concentration of LLW for land disposal in Taiwan
International Nuclear Information System (INIS)
Chang, F.D.; Liou, C.T.; Su, M.F.; Tsai, S.C.
1989-01-01
The upper bound concentrations of radionuclides in the low level waste to be disposed in Taiwan are investigated based on a proposed reference site with all of the scenarios and exposure pathways reflecting the local conditions and environmental characteristics. The analysis reveals that most of the upper bound concentrations are determined from the scenario of intruder-agriculture. It can also be found that the Transuranic radionuclides and those with long half-lives are the dominant radionuclides which result in major radiological impact to the environment in this intruder-agriculture scenario
de Klerk, Etienne; Laurent, Monique; Sun, Zhao
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre (SIAM J Optim 21(3):864–885, 2011), obtained by searching for an optimal probability density function h on K which is a sum of squares of polynomials, so
de Klerk, E.; Laurent, M.; Sun, Z.
2014-01-01
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864--885], obtained by searching for an optimal probability density function h on K which is a sum of squares of
Upper bound for energy efficiency in multi-cell fibre-wireless access systems
Koonen, A.M.J.; Popov, M.; Wessing, H.
2013-01-01
Bringing radio access points closer to the end-users improves radio energy efficiency. However, taking into account both the radio and the optical parts of a fibre-wireless access system, the overall system energy efficiency has an upper bound determined by the relation between the energy
Lower and Upper Bounds in Zone Based Abstractions of Timed Automata
DEFF Research Database (Denmark)
Behrmann, Gerd; Bouyer, Patricia; Larsen, Kim Guldstrand
2004-01-01
Timed automata have an infinite semantics. For verification purposes, one usually uses zone based abstractions w.r.t. the maximal constants to which clocks of the timed automaton are compared. We show that by distinguishing maximal lower and upper bounds, significantly coarser abstractions can...... dramatically increases the scalability of the real-time model checker Uppaal....
Lower and Upper Bounds in Zone-Based Abstractions of Timed Automata
DEFF Research Database (Denmark)
Behrmann, Gerd; Bouyer, Patricia; Larsen, Kim Guldstrand
2005-01-01
The semantics of timed automata is defined using an infinite-state transition system. For verification purposes, one usually uses zone based abstractions w.r.t. the maximal constants to which clocks of the timed automaton are compared. We show that by distinguishing maximal lower and upper bounds...
Upper bound for energy efficiency in multi-cell fibre-wireless access systems
DEFF Research Database (Denmark)
Koonen, A.M.J.; Popov, M.; Wessing, Henrik
2013-01-01
Bringing radio access points closer to the end-users improves radio energy efficiency. However, taking into account both the radio and the optical parts of a fibre-wireless access system, the overall system energy efficiency has an upper bound determined by the relation between the energy...
DEFF Research Database (Denmark)
Lange-Hansen, Preben
1998-01-01
Purpose: None of the published formulae for obtaining upper bounds for residual deflections in elastoplastic structures with quasistatically varying loads (shakedown problems) has been able to result in theoretical maximum values of residual deflections. Therefore, the purpose of the report is to...
Local Model Checking of Weighted CTL with Upper-Bound Constraints
DEFF Research Database (Denmark)
Jensen, Jonas Finnemann; Larsen, Kim Guldstrand; Srba, Jiri
2013-01-01
We present a symbolic extension of dependency graphs by Liu and Smolka in order to model-check weighted Kripke structures against the logic CTL with upper-bound weight constraints. Our extension introduces a new type of edges into dependency graphs and lifts the computation of fixed-points from...
A New Methodology to Establish Upper Bounds on Open-Cell Foams Homogenized Properties
Directory of Open Access Journals (Sweden)
Z. Dimitrovová
2004-01-01
Full Text Available The methodology for determining the upper bounds on the homogenized linear elastic properties of cellular solids, described for the two-dimensional case in Dimitrovová and Faria (1999, is extended to three-dimensional open-cell foams. Besides the upper bounds, the methodology provides necessary and sufficient conditions on optimal media. These conditions are written in terms of generalized internal forces and geometrical parameters. In some cases dependence on internal forces can be replaced by geometrical expressions. In such cases, the optimality of some medium under consideration can be verified directly from the microstructure, without any additional calculation. Some of the bounds derived in this paper are published for the first time, along with a proof of their optimality.
Rate Reduction for State-labelled Markov Chains with Upper Time-bounded CSL Requirements
Directory of Open Access Journals (Sweden)
Bharath Siva Kumar Tati
2016-07-01
Full Text Available This paper presents algorithms for identifying and reducing a dedicated set of controllable transition rates of a state-labelled continuous-time Markov chain model. The purpose of the reduction is to make states to satisfy a given requirement, specified as a CSL upper time-bounded Until formula. We distinguish two different cases, depending on the type of probability bound. A natural partitioning of the state space allows us to develop possible solutions, leading to simple algorithms for both cases.
Upper Bounds for the Rate Distortion Function of Finite-Length Data Blocks of Gaussian WSS Sources
Directory of Open Access Journals (Sweden)
Jesús Gutiérrez-Gutiérrez
2017-10-01
Full Text Available In this paper, we present upper bounds for the rate distortion function (RDF of finite-length data blocks of Gaussian wide sense stationary (WSS sources and we propose coding strategies to achieve such bounds. In order to obtain those bounds, we previously derive new results on the discrete Fourier transform (DFT of WSS processes.
Effects of a potential fourth fermion generation on the upper and lower Higgs boson mass bounds
International Nuclear Information System (INIS)
Gerhold, Philipp; Kallarackal, Jim; Jansen, Karl
2010-12-01
We study the effect of a potential fourth fermion generation on the upper and lower Higgs boson mass bounds. This investigation is based on the numerical evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model. In particular, the considered model obeys a Ginsparg-Wilson version of the underlying SU(2) L x U(1) Y symmetry, being a global symmetry here due to the neglection of gauge fields in this model. We present our results on the modification of the upper and lower Higgs boson mass bounds induced by the presence of a hypothetical very heavy fourth quark doublet. Finally, we compare these findings to the standard scenario of three fermion generations. (orig.)
One-way quantum key distribution: Simple upper bound on the secret key rate
International Nuclear Information System (INIS)
Moroder, Tobias; Luetkenhaus, Norbert; Curty, Marcos
2006-01-01
We present a simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase. This method is based on a necessary precondition for one-way secret key distillation; the legitimate users need to prove that there exists no quantum state having a symmetric extension that is compatible with the available measurements results. The main advantage of the obtained upper bound is that it can be formulated as a semidefinite program, which can be efficiently solved. We illustrate our results by analyzing two well-known qubit-based QKD protocols: the four-state protocol and the six-state protocol
Upper Bounds Prediction of the Execution Time of Programs Running on ARM Cortex-A Systems
Fedotova , Irina; Krause , Bernd; Siemens , Eduard
2017-01-01
Part 6: Embedded and Real Time Systems; International audience; This paper describes the application of statistical analysis of the timing behavior for a generic real-time task model. Using specific processor of ARM Cortex-A series and an empirical approach of time values retrieval, the algorithm to predict the upper bounds for the task of the time acquisition operation has been formulated. For the experimental verification of the algorithm, we have used the robust Measurement-Based Probabili...
The upper bound of abutment scour defined by selected laboratory and field data
Benedict, Stephen; Caldwell, Andral W.
2015-01-01
The U.S. Geological Survey, in cooperation with the South Carolina Department of Transportation, conducted a field investigation of abutment scour in South Carolina and used that data to develop envelope curves defining the upper bound of abutment scour. To expand upon this previous work, an additional cooperative investigation was initiated to combine the South Carolina data with abutment-scour data from other sources and evaluate the upper bound of abutment scour with the larger data set. To facilitate this analysis, a literature review was made to identify potential sources of published abutment-scour data, and selected data, consisting of 446 laboratory and 331 field measurements, were compiled for the analysis. These data encompassed a wide range of laboratory and field conditions and represent field data from 6 states within the United States. The data set was used to evaluate the South Carolina abutment-scour envelope curves. Additionally, the data were used to evaluate a dimensionless abutment-scour envelope curve developed by Melville (1992), highlighting the distinct difference in the upper bound for laboratory and field data. The envelope curves evaluated in this investigation provide simple but useful tools for assessing the potential maximum abutment-scour depth in the field setting.
An upper bound solution for the spread extrusion of elliptical sections
International Nuclear Information System (INIS)
Abrinia, K.; Makaremi, M.
2007-01-01
The three dimensional problem of extrusion of elliptical sections with side material flow or spread has been formulated using the upper bound theory. The shape of the die for such a process is such that it could allow the material to flow sideways as well as in the forward direction. When flat faced dies are used a deforming region is developed with dead metal zones. Therefore this deforming region has been represented in the formulation based on the definitions of streamlines and stream surfaces. A generalized kinematically admissible velocity field was then derived for this formulation and strain rate components obtained for the upper bound solution. The general formulation for the deforming region and the velocity and strain rate fields allow for the optimization of the upper bound solution so that the nearest geometry of the deforming region and dead metal zone to the actual one was obtained.Using this geometry a die with similar surfaces to those of the dead metal zone is designed having converging and diverging surfaces to lead the material flow. The analysis was also carried out for this die and results were obtained showing a reduction in the extrusion pressure compared to the flat faced die. Effects of reduction of area, shape complexity, spread ratio and friction on the extrusion process were also investigated
Some novel inequalities for fuzzy variables on the variance and its rational upper bound
Directory of Open Access Journals (Sweden)
Xiajie Yi
2016-02-01
Full Text Available Abstract Variance is of great significance in measuring the degree of deviation, which has gained extensive usage in many fields in practical scenarios. The definition of the variance on the basis of the credibility measure was first put forward in 2002. Following this idea, the calculation of the accurate value of the variance for some special fuzzy variables, like the symmetric and asymmetric triangular fuzzy numbers and the Gaussian fuzzy numbers, is presented in this paper, which turns out to be far more complicated. Thus, in order to better implement variance in real-life projects like risk control and quality management, we suggest a rational upper bound of the variance based on an inequality, together with its calculation formula, which can largely simplify the calculation process within a reasonable range. Meanwhile, some discussions between the variance and its rational upper bound are presented to show the rationality of the latter. Furthermore, two inequalities regarding the rational upper bound of variance and standard deviation of the sum of two fuzzy variables and their individual variances and standard deviations are proved. Subsequently, some numerical examples are illustrated to show the effectiveness and the feasibility of the proposed inequalities.
Establishing the existence of a distance-based upper bound for a fuzzy DEA model using duality
International Nuclear Information System (INIS)
Soleimani-damaneh, M.
2009-01-01
In a recent paper [Soleimani-damaneh M. Fuzzy upper bounds and their applications. Chaos, Solitons and Fractals 2008;36:217-25.], I established the existence of a distance-based fuzzy upper bound for the objective function of a fuzzy DEA model, using the properties of a discussed signed distance, and provided an effective approach to solve that model. In this paper a new dual-based proof for the existence of the above-mentioned upper bound is provided which gives a useful insight into the theory of fuzzy DEA.
Lee, Harry; Wen, Baole; Doering, Charles
2017-11-01
The rate of viscous energy dissipation ɛ in incompressible Newtonian planar Couette flow (a horizontal shear layer) imposed with uniform boundary injection and suction is studied numerically. Specifically, fluid is steadily injected through the top plate with a constant rate at a constant angle of injection, and the same amount of fluid is sucked out vertically through the bottom plate at the same rate. This set-up leads to two control parameters, namely the angle of injection, θ, and the Reynolds number of the horizontal shear flow, Re . We numerically implement the `background field' variational problem formulated by Constantin and Doering with a one-dimensional unidirectional background field ϕ(z) , where z aligns with the distance between the plates. Computation is carried out at various levels of Re with θ = 0 , 0 .1° ,1° and 2°, respectively. The computed upper bounds on ɛ scale like Re0 as Re > 20 , 000 for each fixed θ, this agrees with Kolmogorov's hypothesis on isotropic turbulence. The outcome provides new upper bounds to ɛ among any solution to the underlying Navier-Stokes equations, and they are sharper than the analytical bounds presented in Doering et al. (2000). This research was partially supported by the NSF Award DMS-1515161, and the University of Michigan's Rackham Graduate Student Research Grant.
Tight upper bound for the maximal quantum value of the Svetlichny operators
Li, Ming; Shen, Shuqian; Jing, Naihuan; Fei, Shao-Ming; Li-Jost, Xianqing
2017-10-01
It is a challenging task to detect genuine multipartite nonlocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequality (SI) for several quantum states, including the white and color noised Greenberger-Horne-Zeilinger (GHZ) states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation of GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.
Wang, Dong; Tsui, Kwok-Leung
2018-01-01
Bearing-supported shafts are widely used in various machines. Due to harsh working environments, bearing performance degrades over time. To prevent unexpected bearing failures and accidents, bearing performance degradation assessment becomes an emerging topic in recent years. Bearing performance degradation assessment aims to evaluate the current health condition of a bearing through a bearing health indicator. In the past years, many signal processing and data mining based methods were proposed to construct bearing health indicators. However, the upper and lower bounds of these bearing health indicators were not theoretically calculated and they strongly depended on historical bearing data including normal and failure data. Besides, most health indicators are dimensional, which connotes that these health indicators are prone to be affected by varying operating conditions, such as varying speeds and loads. In this paper, based on the principle of squared envelope analysis, we focus on theoretical investigation of bearing performance degradation assessment in the case of additive Gaussian noises, including distribution establishment of squared envelope, construction of a generalized dimensionless bearing health indicator, and mathematical calculation of the upper and lower bounds of the generalized dimensionless bearing health indicator. Then, analyses of simulated and real bearing run to failure data are used as two case studies to illustrate how the generalized dimensionless health indicator works and demonstrate its effectiveness in bearing performance degradation assessment. Results show that squared envelope follows a noncentral chi-square distribution and the upper and lower bounds of the generalized dimensionless health indicator can be mathematically established. Moreover, the generalized dimensionless health indicator is sensitive to an incipient bearing defect in the process of bearing performance degradation.
Improved upper bounds on Kaluza-Klein gravity with current Solar System experiments and observations
Energy Technology Data Exchange (ETDEWEB)
Deng, Xue-Mei [Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing (China); Xie, Yi [Nanjing University, School of Astronomy and Space Science, Nanjing (China); Shanghai Key Laboratory of Space Navigation and Position Techniques, Shanghai (China); Nanjing University, Ministry of Education, Key Laboratory of Modern Astronomy and Astrophysics, Nanjing (China)
2015-11-15
As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of Cassini to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very flat extra dimension in the Solar System, even in the vicinity of the Sun. (orig.)
International Nuclear Information System (INIS)
Miller, A.G.
1981-08-01
The limit analysis of a circumferential partial penetration defect around the intersection of a sphere and a cylinder has been investigated. An upper bound to the limit pressure has been determined by considering four independent mechanisms, and compared to an existing lower bound solution. (author)
Upper Bound Solution for the Face Stability of Shield Tunnel below the Water Table
Directory of Open Access Journals (Sweden)
Xilin Lu
2014-01-01
Full Text Available By FE simulation with Mohr-Coulomb perfect elastoplasticity model, the relationship between the support pressure and displacement of the shield tunnel face was obtained. According to the plastic strain distribution at collapse state, an appropriate failure mechanism was proposed for upper bound limit analysis, and the formula to calculate the limit support pressure was deduced. The limit support pressure was rearranged to be the summation of soil cohesion c, surcharge load q, and soil gravity γ multiplied by their corresponding coefficients Nc, Nq, and Nγ, and parametric studies were carried out on these coefficients. In order to consider the influence of seepage on the face stability, the pore water pressure distribution and the seepage force on the tunnel face were obtained by FE simulation. After adding the power of seepage force into the equation of the upper bound limit analysis, the total limit support pressure for stabilizing the tunnel face under seepage condition was obtained. The total limit support pressure was shown to increase almost linearly with the water table.
Directory of Open Access Journals (Sweden)
Ali Tavasoli
2012-01-01
Full Text Available Nonlinear vehicle control allocation is achieved through distributing the task of vehicle control among individual tire forces, which are constrained to nonlinear saturation conditions. A high-level sliding mode control with adaptive upper bounds is considered to assess the body yaw moment and lateral force for the vehicle motion. The proposed controller only requires the online adaptation of control gains without acquiring the knowledge of upper bounds on system uncertainties. Static and dynamic control allocation approaches have been formulated to distribute high-level control objectives among the system inputs. For static control allocation, the interior-point method is applied to solve the formulated nonlinear optimization problem. Based on the dynamic control allocation method, a dynamic update law is derived to allocate vehicle control to tire forces. The allocated tire forces are fed into a low-level control module, where the applied torque and active steering angle at each wheel are determined through a slip-ratio controller and an inverse tire model. Computer simulations are used to prove the significant effects of the proposed control allocation methods on improving the stability and handling performance. The advantages and limitations of each method have been discussed, and conclusions have been derived.
Effects of general relativity on glitch amplitudes and pulsar mass upper bounds
Antonelli, M.; Montoli, A.; Pizzochero, P. M.
2018-04-01
Pinning of vortex lines in the inner crust of a spinning neutron star may be the mechanism that enhances the differential rotation of the internal neutron superfluid, making it possible to freeze some amount of angular momentum which eventually can be released, thus causing a pulsar glitch. We investigate the general relativistic corrections to pulsar glitch amplitudes in the slow-rotation approximation, consistently with the stratified structure of the star. We thus provide a relativistic generalization of a previous Newtonian model that was recently used to estimate upper bounds on the masses of glitching pulsars. We find that the effect of general relativity on the glitch amplitudes obtained by emptying the whole angular momentum reservoir is less than 30 per cent. Moreover, we show that the Newtonian upper bounds on the masses of large glitchers obtained from observations of their maximum recorded event differ by less than a few percent from those calculated within the relativistic framework. This work can also serve as a basis to construct more sophisticated models of angular momentum reservoir in a relativistic context: in particular, we present two alternative scenarios for macroscopically rigid and slack pinned vortex lines, and we generalize the Feynman-Onsager relation to the case when both entrainment coupling between the fluids and a strong axisymmetric gravitational field are present.
Masson, Frederic; Knoepfler, Andreas; Mayer, Michael; Ulrich, Patrice; Heck, Bernhard
2010-05-01
In September 2008, the Institut de Physique du Globe de Strasbourg (Ecole et Observatoire des Sciences de la Terre, EOST) and the Geodetic Institute (GIK) of Karlsruhe University (TH) established a transnational cooperation called GURN (GNSS Upper Rhine Graben Network). Within the GURN initiative these institutions are cooperating in order to establish a highly precise and highly sensitive network of permanently operating GNSS sites for the detection of crustal movements in the Upper Rhine Graben region. At the beginning, the network consisted of the permanently operating GNSS sites of SAPOS®-Baden-Württemberg, different data providers in France (e.g. EOST, Teria, RGP) and some further sites (e.g. IGS). In July 2009, the network was extended to the South when swisstopo (Switzerland) and to the North when SAPOS®-Rheinland-Pfalz joined GURN. Therefore, actually the GNSS network consists of approx. 80 permanently operating reference sites. The presentation will discuss the actual status of GURN, main research goals, and will present first results concerning the data quality as well as time series of a first reprocessing of all available data since 2002 using GAMIT/GLOBK (EOST working group) and the Bernese GPS Software (GIK working group). Based on these time series, the velocity as well as strain fields will be calculated in the future. The GURN initiative is also aiming for the estimation of the upper bounds of deformation in the Upper Rhine Graben region.
Upper bounds of supersymmetric particle masses in a gaugino-originated radiative breaking scenario
International Nuclear Information System (INIS)
Goto, T.
1993-01-01
The mass spectrum of supersymmetric particles is studied in the radiative breaking scenario of the minimal supersymmetric standard model, with an assumption that all soft supersymmetry-breaking parameters other than the gaugino masses are vanishing at the Planck scale. The U(1) gaugino mass M 1X is taken to be an independent parameter, while the SU(2) and SU(3) gaugino masses are supposed to be unified. Within the ''natural'' range, the whole parameter space is scanned numerically and the consistent particle mass spectra with the experimental bounds are obtained. The supersymmetric particle masses are tightly bounded above as m eR approx-lt 100 GeV, etc., if the top quark is sufficiently heavy m top approx-gt 100 GeV and the minimal grand unified theory relation for three gaugino masses is satisfied. For a large |M 1X |, there is no restriction other than the naturalness for the upper bounds of supersymmetric particle masses
Using a Water Balance Model to Bound Potential Irrigation Development in the Upper Blue Nile Basin
Jain Figueroa, A.; McLaughlin, D.
2016-12-01
The Grand Ethiopian Renaissance Dam (GERD), on the Blue Nile is an example of water resource management underpinning food, water and energy security. Downstream countries have long expressed concern about water projects in Ethiopia because of possible diversions to agricultural uses that could reduce flow in the Nile. Such diversions are attractive to Ethiopia as a partial solution to its food security problems but they could also conflict with hydropower revenue from GERD. This research estimates an upper bound on diversions above the GERD project by considering the potential for irrigated agriculture expansion and, in particular, the availability of water and land resources for crop production. Although many studies have aimed to simulate downstream flows for various Nile basin management plans, few have taken the perspective of bounding the likely impacts of upstream agricultural development. The approach is to construct an optimization model to establish a bound on Upper Blue Nile (UBN) agricultural development, paying particular attention to soil suitability and seasonal variability in climate. The results show that land and climate constraints impose significant limitations on crop production. Only 25% of the land area is suitable for irrigation due to the soil, slope and temperature constraints. When precipitation is also considered only 11% of current land area could be used in a way that increases water consumption. The results suggest that Ethiopia could consume an additional 3.75 billion cubic meters (bcm) of water per year, through changes in land use and storage capacity. By exploiting this irrigation potential, Ethiopia could potentially decrease the annual flow downstream of the UBN by 8 percent from the current 46 bcm/y to the modeled 42 bcm/y.
NEW UPPER AND LOWER BOUNDS LINE OF SIGHT PATH LOSS MODELS FOR MOBILE PROPAGATION IN BUILDINGS
Directory of Open Access Journals (Sweden)
Supachai Phaiboon
2017-11-01
Full Text Available This paper proposes a method to predict line-of-sight (LOS path loss in buildings. We performed measurements in two different type of buildings at a frequency of 1.8 GHz and propose new upper and lower bounds path loss models which depend on max and min values of sample path loss data. This makes our models limit path loss within the boundary lines. The models include time-variant effects such as people moving and cars in parking areas with their influence on wave propagation that is very high. The results have shown that the proposed models will be useful for the system and cell design of indoor wireless communication systems.
Heterogeneous upper-bound finite element limit analysis of masonry walls out-of-plane loaded
Milani, G.; Zuccarello, F. A.; Olivito, R. S.; Tralli, A.
2007-11-01
A heterogeneous approach for FE upper bound limit analyses of out-of-plane loaded masonry panels is presented. Under the assumption of associated plasticity for the constituent materials, mortar joints are reduced to interfaces with a Mohr Coulomb failure criterion with tension cut-off and cap in compression, whereas for bricks both limited and unlimited strength are taken into account. At each interface, plastic dissipation can occur as a combination of out-of-plane shear, bending and torsion. In order to test the reliability of the model proposed, several examples of dry-joint panels out-of-plane loaded tested at the University of Calabria (Italy) are discussed. Numerical results are compared with experimental data for three different series of walls at different values of the in-plane compressive vertical loads applied. The comparisons show that reliable predictions of both collapse loads and failure mechanisms can be obtained by means of the numerical procedure employed.
International Nuclear Information System (INIS)
1989-01-01
The IAEA Safety Guide, Safety Series No. 77 (1986), Principles for Limiting Releases of Radioactive Effluents into the Environment, identifies the concept of upper bounds to individual dose. They are the fractions of the dose limit for members of the public allocated to the various different sources and practices which can give rise to individual exposure. This Guide is concerned with the contributions to individual dose which may arise from other sources in the same region and also from sources which are far away but which, because of the nature of the radionuclides involved, give rise to a global component of dose. Consideration is given to the need for control of such exposures and the means by which it could be achieved. The text may be seen as providing expansion of the guidance given in Safety Series No. 77. 24 refs
Upper bounds for the security of two distributed-phase reference protocols of quantum cryptography
International Nuclear Information System (INIS)
Branciard, Cyril; Gisin, Nicolas; Scarani, Valerio
2008-01-01
The differential-phase-shift (DPS) and the coherent-one-way (COW) are among the most practical protocols for quantum cryptography, and are therefore the object of fast-paced experimental developments. The assessment of their security is also a challenge for theorists: the existing tools, that allow to prove security against the most general attacks, do not apply to these two protocols in any straightforward way. We present new upper bounds for their security in the limit of large distances (d∼>50 km with typical values in optical fibers) by considering a large class of collective attacks, namely those in which the adversary attaches ancillary quantum systems to each pulse or to each pair of pulses. We introduce also two modified versions of the COW protocol, which may prove more robust than the original one
Upper-Lower Bounds Candidate Sets Searching Algorithm for Bayesian Network Structure Learning
Directory of Open Access Journals (Sweden)
Guangyi Liu
2014-01-01
Full Text Available Bayesian network is an important theoretical model in artificial intelligence field and also a powerful tool for processing uncertainty issues. Considering the slow convergence speed of current Bayesian network structure learning algorithms, a fast hybrid learning method is proposed in this paper. We start with further analysis of information provided by low-order conditional independence testing, and then two methods are given for constructing graph model of network, which is theoretically proved to be upper and lower bounds of the structure space of target network, so that candidate sets are given as a result; after that a search and scoring algorithm is operated based on the candidate sets to find the final structure of the network. Simulation results show that the algorithm proposed in this paper is more efficient than similar algorithms with the same learning precision.
Lower and Upper Bounds for the Node, Edge, and Arc Routing Problem
DEFF Research Database (Denmark)
Bach, Lukas; Wøhlk, Sanne; Hasle, Geir
The Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004. They also proposed a memetic algorithm procedure and defined a set of test instances: the so-called CBMix benchmark. The NEARP generalizes the classical CVRP, the CARP, and the General Routing Problem...... for the CARP. We also define two novel sets of test instances to complement the CBMix benchmark. The first is based on well-known CARP instances; the second consists of real life cases of newspaper delivery routing. We provide numerical results in the form 1 of lower and best known upper bounds for all...... instances of all three benchmarks. For two of the instances, the gap is closed....
An upper-bound assessment of the benefits of reducing perchlorate in drinking water.
Lutter, Randall
2014-10-01
The Environmental Protection Agency plans to issue new federal regulations to limit drinking water concentrations of perchlorate, which occurs naturally and results from the combustion of rocket fuel. This article presents an upper-bound estimate of the potential benefits of alternative maximum contaminant levels for perchlorate in drinking water. The results suggest that the economic benefits of reducing perchlorate concentrations in drinking water are likely to be low, i.e., under $2.9 million per year nationally, for several reasons. First, the prevalence of detectable perchlorate in public drinking water systems is low. Second, the population especially sensitive to effects of perchlorate, pregnant women who are moderately iodide deficient, represents a minority of all pregnant women. Third, and perhaps most importantly, reducing exposure to perchlorate in drinking water is a relatively ineffective way of increasing iodide uptake, a crucial step linking perchlorate to health effects of concern. © 2014 Society for Risk Analysis.
Energy Technology Data Exchange (ETDEWEB)
Datta, Nilanjana, E-mail: n.datta@statslab.cam.ac.uk [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Hsieh, Min-Hsiu, E-mail: Min-Hsiu.Hsieh@uts.edu.au [Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007 (Australia); Oppenheim, Jonathan, E-mail: j.oppenheim@ucl.ac.uk [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615 (Singapore)
2016-05-15
State redistribution is the protocol in which given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement. We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.
Frisbee, Joseph H., Jr.
2015-01-01
Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.
International Nuclear Information System (INIS)
Kapshay, V.N.; Skachkov, N.B.
1979-01-01
A composite system of two relativistic particles is studied on the basis of the Kadyshevsky quasipotential equation, in which the ''Coulomb'' potential is taken in the form of a propagator of the massless-scalar-particle exchange. The obtained exact solutions to this equation are shown to be a geometrical generalization of nonrelativistic Coulomb wave functions in the sense of change of the Euclidean geometry of momentum space to the Lobachevsky geometry
Capacity bounds for kth best path selection over generalized fading channels
Hanif, Muhammad Fainan; Yang, Hongchuan; Alouini, Mohamed-Slim
2014-01-01
Exact ergodic capacity calculation for fading wireless channels typically involves time-consuming numerical evaluation of infinite integrals. In this paper, lower and upper bounds on ergodic capacity for kth best path are presented. These bounds
Directory of Open Access Journals (Sweden)
Z. Li
2017-11-01
Full Text Available Export production reflects the amount of organic matter transferred from the ocean surface to depth through biological processes. This export is in large part controlled by nutrient and light availability, which are conditioned by mixed layer depth (MLD. In this study, building on Sverdrup's critical depth hypothesis, we derive a mechanistic model of an upper bound on carbon export based on the metabolic balance between photosynthesis and respiration as a function of MLD and temperature. We find that the upper bound is a positively skewed bell-shaped function of MLD. Specifically, the upper bound increases with deepening mixed layers down to a critical depth, beyond which a long tail of decreasing carbon export is associated with increasing heterotrophic activity and decreasing light availability. We also show that in cold regions the upper bound on carbon export decreases with increasing temperature when mixed layers are deep, but increases with temperature when mixed layers are shallow. A meta-analysis shows that our model envelopes field estimates of carbon export from the mixed layer. When compared to satellite export production estimates, our model indicates that export production in some regions of the Southern Ocean, particularly the subantarctic zone, is likely limited by light for a significant portion of the growing season.
Directory of Open Access Journals (Sweden)
Carolina Bermudo
2016-07-01
Full Text Available Focusing on incremental bulk metal forming processes, the indentation process is gaining interest as a fundamental part of these kinds of processes. This paper presents the analysis of the pressure obtained in indentation under the influence of different punch geometries. To this end, an innovative Upper Bound Theorem (UBT based solution is introduced. This new solution can be easily applied to estimate the necessary force that guarantees plastic deformation by an indentation process. In this work, we propose an accurate analytical approach to analyse indentation under different punches. The new Modular Upper Bound (MUB method presents a simpler and faster application. Additionally, its complexity is not considerably increased by the addition of more Triangular Rigid Zones. In addition, a two-dimensional indentation model is designed and implemented using the Finite Element Method (FEM. The comparison of the two methods applied to the indentation process analysed—the new Modular Upper Bound technique and the Finite Element Method—reveal close similarities, the new Modular Upper Bound being more computationally efficient.
Upper-bound fission product release assessment for large break LOCA in CANFLEX bundle reactor core
International Nuclear Information System (INIS)
Oh, Duk Ju; Lee, Kang Moon
1996-07-01
Quarter-core gap inventory assessment for CANDU-6 reactor core loaded with CANFLEX fuel bundles has been performed as one of the licensing safety analyses required for 24 natural uranium CANFLEX bundle irradiation in CANDU-6 reactor. The quarter-core gap inventory for the CANFLEX bundle core is 5 - 10 times lower than that for the standard bundle core, depending on the half-life of the isotope. The lower gap inventory of the CANFLEX bundle core is attributed to the lower linear power of the CANFLEX bundle compared with the standard bundle. However, the whole core total inventories for both the CANFLEX and standard bundle cores are nearly the same. The 6 - 8 times lower upper-bound fission product releases of the CANFLEX bundle core for large break LOCA than those of the standard bundle core imply that the loading of 24 natural uranium CANFLEX bundles would improve the predicted consequences of the postulated accident described in the Wolsung 2 safety report. 2 tabs., 6 figs., 3 refs. (Author)
Asymptotic upper bound of density for two-particle annihilating exclusion
International Nuclear Information System (INIS)
Belitsky, V.
1993-01-01
The authors consider a stochastic process which presents an evolution of particles of two types on Z d with annihilations between particles of opposite types. Initially, at each site of Z d , independently of other sites, the authors put a particle with probability 2p ≤ 1 and assign to it one of two types with equal chances. Each particle, independently from the others, waits an exponential time with mean 1, chooses one of its neighboring sites on the lattice Z d with equal probabilities, and jumps to the site chosen. If the site to which a particle attempts to move is occupied by another particle of the same type, the jump is suppressed; if it is occupied by a particle of the opposite type, then both are annihilated and disappear from the system. The considered process may serve as a model for the chemical reaction A + B → inert. The paper concerns an upper bound of p(t), the density of particles in the system at time t. The authors prove that p(t) -d/4 t ε when t > t(ε) for all ε > 0 in the dimensions d ≤ 4 and asymptotically p(t) -1 in the higher dimensions. In the proofs, the authors used the ideas and the technique developed by Bramson and Lebowitz and the tools which are customarily used to study a symmetric exclusion process. 8 refs
Chromatic polynomials of planar triangulations, the Tutte upper bound and chromatic zeros
International Nuclear Information System (INIS)
Shrock, Robert; Xu Yan
2012-01-01
Tutte proved that if G pt is a planar triangulation and P(G pt , q) is its chromatic polynomial, then |P(G pt , τ + 1)| ⩽ (τ − 1) n−5 , where τ=(1+√5 )/2 and n is the number of vertices in G pt . Here we study the ratio r(G pt ) = |P(G pt , τ + 1)|/(τ − 1) n−5 for a variety of planar triangulations. We construct infinite recursive families of planar triangulations G pt,m depending on a parameter m linearly related to n and show that if P(G pt,m , q) only involves a single power of a polynomial, then r(G pt,m ) approaches zero exponentially fast as n → ∞. We also construct infinite recursive families for which P(G pt,m , q) is a sum of powers of certain functions and show that for these, r(G pt,m ) may approach a finite nonzero constant as n → ∞. The connection between the Tutte upper bound and the observed chromatic zero(s) near to τ + 1 is investigated. We report the first known graph for which the zero(s) closest to τ + 1 is not real, but instead is a complex-conjugate pair. Finally, we discuss connections with the nonzero ground-state entropy of the Potts antiferromagnet on these families of graphs. (paper)
Sun, Wei; Chou, Chih-Ping; Stacy, Alan W; Ma, Huiyan; Unger, Jennifer; Gallaher, Peggy
2007-02-01
Cronbach's a is widely used in social science research to estimate the internal consistency of reliability of a measurement scale. However, when items are not strictly parallel, the Cronbach's a coefficient provides a lower-bound estimate of true reliability, and this estimate may be further biased downward when items are dichotomous. The estimation of standardized Cronbach's a for a scale with dichotomous items can be improved by using the upper bound of coefficient phi. SAS and SPSS macros have been developed in this article to obtain standardized Cronbach's a via this method. The simulation analysis showed that Cronbach's a from upper-bound phi might be appropriate for estimating the real reliability when standardized Cronbach's a is problematic.
International Nuclear Information System (INIS)
Chun, Moon Hyun; Park, Joo Wan; Nam, Ho Yun
1992-01-01
Improved analytical models have been proposed that can predict the lower and upper limits of the water hammer region for given flow conditions by incorporation of recent advances made in the understanding of phenomena associated with the condensation-induced water hammer into existing methods. Present models are applicable for steam-water counterflow in a long horizontal pipe geometry. Both lower and upper bounds of the water hammer region are expressed in terms of the 'critical inlet water flow rate' as a function of axial position. Water hammer region boundaries predicted by present and typical existing models are compared for particular flow conditions of the water hammer event occurred at San Onofre Unit 1 to assess the applicability of the models examined. The result shows that present models for lower and upper bounds of the water hammer region compare favorably with the best performing existing models
An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules
Directory of Open Access Journals (Sweden)
Angela Hsiang-Ling Chen
2014-09-01
Full Text Available Projects are an important part of our activities and regardless of their magnitude, scheduling is at the very core of every project. In an ideal world makespan minimization, which is the most commonly sought objective, would give us an advantage. However, every time we execute a project we have to deal with uncertainty; part of it coming from known sources and part remaining unknown until it affects us. For this reason, it is much more practical to focus on making our schedules robust, capable of handling uncertainty, and even to determine a range in which the project could be completed. In this paper we focus on an approach to determine such a range for the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP, a widely researched, NP-complete problem, but without adding any subjective considerations to its estimation. We do this by using a concept well known in the domain of thermodynamics, entropy and a three-stage approach. First we use Artificial Bee Colony (ABC—an effective and powerful meta-heuristic—to determine a schedule with minimized makespan which serves as a lower bound. The second stage defines buffer times and creates an upper bound makespan using an entropy function, with the advantage over other methods that it only considers elements which are inherent to the schedule itself and does not introduce any subjectivity to the buffer time generation. In the last stage, we use the ABC algorithm with an objective function that seeks to maximize robustness while staying within the makespan boundaries defined previously and in some cases even below the lower boundary. We evaluate our approach with two different benchmarks sets: when using the PSPLIB for the MRCPSP benchmark set, the computational results indicate that it is possible to generate robust schedules which generally result in an increase of less than 10% of the best known solutions while increasing the robustness in at least 20% for practically every
Establishing an upper bound on contact resistivity of ohmic contacts to n-GaN nanowires
International Nuclear Information System (INIS)
Blanchard, Paul; Bertness, Kris A; Harvey, Todd; Sanford, Norman
2014-01-01
Contact resistivity ρ c is an important figure of merit in evaluating and improving the performance of electronic and optoelectronic devices. Due to the small size, unique morphology, and uncertain transport properties of semiconductor nanowires (NWs), measuring ρ c of contacts to NWs can be particularly challenging. In this work, Si-doped n-GaN NWs were grown by molecular beam epitaxy. Four-contact structures with 20 nm Ti/200 nm Al contacts were fabricated on individual NWs by photolithography, and the contacts were annealed to achieve ohmic behavior. Two-point resistances R 23 and four-point collinear resistances R 23collinear were measured between the middle two contacts on each NW. These resistances were then modeled by taking into account the non-uniform distribution of current flow along the length of each contact. Contrary to the assumption that the resistance difference R 23 −R 23collinear is equal to the total contact resistance R c , the distributed-current-flow contact model shows that R 23 −R 23collinear ≪ R c when ρ c is sufficiently small. Indeed, the measured R 23 −R 23collinear was so small in these devices that it was within the measurement uncertainty, meaning that it was not possible to directly calculate ρ c from these data. However, it was possible to calculate an upper bound on ρ c for each device based on the largest possible value of R 23 −R 23collinear . In addition, we took into account the large uncertainties in the NW transport properties by numerically maximizing ρ c with respect to the uncertainty range of each measured and assumed parameter in the contact model. The resulting upper limits on ρ c ranged from 4.2 × 10 −6 to 7.6 × 10 −6 Ω cm 2 , indicating that 20 nm Ti/200 nm Al is a good choice of ohmic contact for moderately-doped n-GaN NWs. The measurement and numerical analysis demonstrated here offer a general approach to modeling ohmic contact resistivity via NW four
Paul L. Patterson; Mark Finco
2009-01-01
This paper explores the information FIA data can produce regarding forest types that were not sampled and develops the equations necessary to define the upper confidence bounds on not-sampled forest types. The problem is reduced to a Bernoulli variable. This simplification allows the upper confidence bounds to be calculated based on Cochran (1977). Examples are...
International Nuclear Information System (INIS)
Zhang Min-Min; Mei Dong-Cheng; Wang Can-Jun
2011-01-01
The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U B (t) of the time derivative of the information entropy. The results show that there is a critical value of τ (delay time), and U B (t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, τ can induce a reentrance transition. Delay time τ also causes a reversal behaviour in U B (t)-λ plot, where λ denotes the degree of the correlation between the two noises. (general)
Upper bounds on Higgs and top quark masses in the flipped SU(5)xU(1) superstring model
Energy Technology Data Exchange (ETDEWEB)
Durand, L.; Lopez, J.L.
1989-02-02
In this letter, we use a simplified method to calculate high-energy unitarity constraints on grand unified broken supersymmetric models. We apply the method to the ''flipped'' SU(5)xU(1) superstring model, obtain the constraints at a grand unified mass scale M/sub G/=4x10/sup 16/ GeV, and then use the renormalization group equations to evolve the constraints to the low-energy mass scale M/sub W/. We find upper bounds on the low-energy superpotential parameters which in turn imply absolute upper bounds on the top quark mass, m/sub t/< or approx.200 GeV, and on the lightest neutral Higgs boson mass, Msub(H/sub 1//sup 0/)< or approx.155 GeV. We also obtain an upper bound on Msub(H/sub 1//sup 0/) as a function of m/sub t/ which shows that for favored values of the ratio of Higgs vacuum expectation values Msub(H/sub 1//sup 0/)< or approx.125 GeV.
Anisotropic inflation reexamined: upper bound on broken rotational invariance during inflation
International Nuclear Information System (INIS)
Naruko, Atsushi; Yamaguchi, Masahide; Komatsu, Eiichiro
2015-01-01
The presence of a light vector field coupled to a scalar field during inflation makes a distinct prediction: the observed correlation functions of the cosmic microwave background (CMB) become statistically anisotropic. We study the implications of the current bound on statistical anisotropy derived from the Planck 2013 CMB temperature data for such a model. The previous calculations based on the attractor solution indicate that the magnitude of anisotropy in the power spectrum is proportional to N 2 , where N is the number of e-folds of inflation counted from the end of inflation. In this paper, we show that the attractor solution is not necessarily compatible with the current bound, and derive new predictions using another branch of anisotropic inflation. In addition, we improve upon the calculation of the mode function of perturbations by including the leading-order slow-roll corrections. We find that the anisotropy is roughly proportional to [2(ε H +4η H )/3−4(c−1)] −2 , where ε H and η H are the usual slow-roll parameters and c is the parameter in the model, regardless of the form of potential of an inflaton field. The bound from Planck implies that breaking of rotational invariance during inflation (characterized by the background homogeneous shear divided by the Hubble rate) is limited to be less than O(10 −9 ). This bound is many orders of magnitude smaller than the amplitude of breaking of time translation invariance, which is observed to be O(10 −2 )
International Nuclear Information System (INIS)
Gerhold, Philipp; Jansen, Karl
2009-12-01
We study a lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model, in particular, obeying a Ginsparg- Wilson version of the underlying SU(2) L x U(1) Y symmetry, being a global symmetry here due to the neglection of gauge fields in this model. In this paper we present our results on the cutoffdependent upper Higgs boson mass bound at several selected values of the cutoff parameter Λ. (orig.)
Directory of Open Access Journals (Sweden)
Carolina Bermudo
2017-05-01
Full Text Available The application of incremental processes in the manufacturing industry is having a great development in recent years. The first stage of an Incremental Forming Process can be defined as an indentation. Because of this, the indentation process is starting to be widely studied, not only as a hardening test but also as a forming process. Thus, in this work, an analysis of the indentation process under the new Modular Upper Bound perspective has been performed. The modular implementation has several advantages, including the possibility of the introduction of different parameters to extend the study, such as the friction effect, the temperature or the hardening effect studied in this paper. The main objective of the present work is to analyze the three hardening models developed depending on the material characteristics. In order to support the validation of the hardening models, finite element analyses of diverse materials under an indentation are carried out. Results obtained from the Modular Upper Bound are in concordance with the results obtained from the numerical analyses. In addition, the numerical and analytical methods are in concordance with the results previously obtained in the experimental indentation of annealed aluminum A92030. Due to the introduction of the hardening factor, the new modular distribution is a suitable option for the analysis of indentation process.
Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels
Xia, Minghua; Aissa, Sonia; Wu, Yik-Chung
2012-01-01
to evaluate the outage performance of the system under study. The analytical results of outage probability coincide exactly with Monte-Carlo simulation results and outperform the previously reported upper bounds in the low and medium SNR regions.
Bounds for Asian basket options
Deelstra, Griselda; Diallo, Ibrahima; Vanmaele, Michèle
2008-09-01
In this paper we propose pricing bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework. We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151-168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3-33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55-57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51-90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1-52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity.
Energy Technology Data Exchange (ETDEWEB)
Luque, A., E-mail: a.luque@upm.es [Instituto de Energía Solar, Universidad Politécnica de Madrid (Spain); Mellor, A.; Tobías, I.; Antolín, E.; Linares, P.G.; Ramiro, I.; Martí, A. [Instituto de Energía Solar, Universidad Politécnica de Madrid (Spain)
2013-03-15
The effective mass Schrödinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band—which are similar to those originated in quantum wires and quantum wells—coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.
International Nuclear Information System (INIS)
Xue, T; Roundy, S; Ma, X; Rahn, C
2014-01-01
Energy harvesting from human motion addresses the growing need for battery-free health and wellness sensors in wearable applications. The major obstacles to harvesting energy in such applications are low and random frequencies due to the nature of human motion. This paper presents a generalized rotational harvester model in 3 dimensions to determine the upper bound of power output from real world measured data. Simulation results indicate much space for improvement on power generation comparing to existing devices. We have developed a rotational energy harvester for human motion that attempts to close the gap between theoretical possibility and demonstrated devices. Like previous work, it makes use of magnetically plucked piezoelectric beams. However, it more fully utilizes the space available and has many degrees of freedom available for optimization. Finally we present a prototype harvester based on the coupled harvester model with preliminary experimental validation
Energy Technology Data Exchange (ETDEWEB)
Mishima, J.; Sutter, S.L.; Hawley, K.A.; Jenkins, C.E.; Napier, B.A.
1986-02-01
The Geologic Disposal Alternative, the In-Place Stabilization and Disposal Alternative, and the Reference Disposal Alternative are being evaluated for disposal of Hanford defense high-level, transuranic, and tank wastes. Environmental impacts associated with disposal of these wastes according to the alternatives listed above include potential doses to the downwind population from operation during the application of the handling and processing techniques comprising each disposal alternative. Scenarios for operational accident and abnormal operational events are postulated, on the basis of the currently available information, for the application of the techniques employed for each waste class for each disposal alternative. From these scenarios, an upper-bound airborne release of radioactive material was postulated for each waste class and disposal alternative. Potential downwind radiologic impacts were calculated from these upper-bound events. In all three alternatives, the single postulated event with the largest calculated radiologic impact for any waste class is an explosion of a mixture of ferri/ferro cyanide precipitates during the mechanical retrieval or microwave drying of the salt cake in single shell waste tanks. The anticipated downwind dose (70-year dose commitment) to the maximally exposed individual is 3 rem with a total population dose of 7000 man-rem. The same individual would receive 7 rem from natural background radiation during the same time period, and the same population would receive 3,000,000 man-rem. Radiological impacts to the public from all other postulated accidents would be less than that from this accident; furthermore, the radiological impacts resulting from this accident would be less than one-half that from the natural background radiation dose.
International Nuclear Information System (INIS)
Mishima, J.; Sutter, S.L.; Hawley, K.A.; Jenkins, C.E.; Napier, B.A.
1986-02-01
The Geologic Disposal Alternative, the In-Place Stabilization and Disposal Alternative, and the Reference Disposal Alternative are being evaluated for disposal of Hanford defense high-level, transuranic, and tank wastes. Environmental impacts associated with disposal of these wastes according to the alternatives listed above include potential doses to the downwind population from operation during the application of the handling and processing techniques comprising each disposal alternative. Scenarios for operational accident and abnormal operational events are postulated, on the basis of the currently available information, for the application of the techniques employed for each waste class for each disposal alternative. From these scenarios, an upper-bound airborne release of radioactive material was postulated for each waste class and disposal alternative. Potential downwind radiologic impacts were calculated from these upper-bound events. In all three alternatives, the single postulated event with the largest calculated radiologic impact for any waste class is an explosion of a mixture of ferri/ferro cyanide precipitates during the mechanical retrieval or microwave drying of the salt cake in single shell waste tanks. The anticipated downwind dose (70-year dose commitment) to the maximally exposed individual is 3 rem with a total population dose of 7000 man-rem. The same individual would receive 7 rem from natural background radiation during the same time period, and the same population would receive 3,000,000 man-rem. Radiological impacts to the public from all other postulated accidents would be less than that from this accident; furthermore, the radiological impacts resulting from this accident would be less than one-half that from the natural background radiation dose
Upper and lower bounds for disadvantage factors as a test of algorithm used in a synthesis method
International Nuclear Information System (INIS)
Nanneh, M.M.; Ackroyd, R.T.
1991-01-01
A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for uranium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa. (author). 15 refs., 8 tabs., 9 figs
Upper and lower bounds for disadvantage factors as a test of an algorithm used in a synthesis method
International Nuclear Information System (INIS)
Ackroyd, R.T.; Nanneh, M.M.
1988-01-01
A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for urnaium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa. (author)
Wen, Baole; Chini, Gregory P.; Kerswell, Rich R.; Doering, Charles R.
2015-10-01
An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu˜PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L =2 √{2 },Nu≤0.106 Pr0Ra5/12 , which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.
Liu, X.; Bassis, J. N.
2015-12-01
With observations showing accelerated mass loss from the Greenland Ice Sheet due to surface melt, the Greenland Ice Sheet is becoming one of the most significant contributors to sea level rise. The contribution of the Greenland Ice Sheet o sea level rise is likely to accelerate in the coming decade and centuries as atmospheric temperatures continue to rise, potentially triggering ever larger surface melt rates. However, at present considerable uncertainty remains in projecting the contribution to sea level of the Greenland Ice Sheet both due to uncertainty in atmospheric forcing and the ice sheet response to climate forcing. Here we seek an upper bound on the contribution of surface melt from the Greenland to sea level rise in the coming century using a surface energy balance model coupled to an englacial model. We use IPCC Representative Concentration Pathways (RCP8.5, RCP6, RCP4.5, RCP2.6) climate scenarios from an ensemble of global climate models in our simulations to project the maximum rate of ice volume loss and related sea-level rise associated with surface melting. To estimate the upper bound, we assume the Greenland Ice Sheet is perpetually covered in thick clouds, which maximize longwave radiation to the ice sheet. We further assume that deposition of black carbon darkens the ice substantially turning it nearly black, substantially reducing its albedo. Although assuming that all melt water not stored in the snow/firn is instantaneously transported off the ice sheet increases mass loss in the short term, refreezing of retained water warms the ice and may lead to more melt in the long term. Hence we examine both assumptions and use the scenario that leads to the most surface melt by 2100. Preliminary models results suggest that under the most aggressive climate forcing, surface melt from the Greenland Ice Sheet contributes ~1 m to sea level by the year 2100. This is a significant contribution and ignores dynamic effects. We also examined a lower bound
Directory of Open Access Journals (Sweden)
Schlömerkemper Anja
2015-01-01
Full Text Available A major open problem in the mathematical analysis of martensitic phase transformations is the derivation of explicit formulae for the set of recoverable strains and for the relaxed energy of the system. These are governed by the mathematical notion of quasiconvexity. Here we focus on bounds on these quasiconvex hulls and envelopes in the setting of geometrically-linear elasticity. Firstly, we will present mathematical results on triples of transformation strains. This yields further insight into the quasiconvex hull of the twelve transformation strains in cubic-to-monoclinic phase transformations. Secondly, we consider bounds on the energy of such materials based on the so-called energy of mixing thus obtaining a lamination upper bound on the quasiconvex envelope of the energy. Here we present a new algorithm that yields improved upper bounds and allows us to relate numerical results for the lamination upper bound on the energy with theoretical inner bounds on the quasiconvex hull of triples of transformation strains.
Capacity bounds for kth best path selection over generalized fading channels
Hanif, Muhammad Fainan
2014-02-01
Exact ergodic capacity calculation for fading wireless channels typically involves time-consuming numerical evaluation of infinite integrals. In this paper, lower and upper bounds on ergodic capacity for kth best path are presented. These bounds have simple analytic expressions which allow their fast evaluation. Numerical results show that the newly proposed bounds closely approximate the exact ergodic capacity for a large variety of system configurations. © 1997-2012 IEEE.
Qiu, Shanwen; Abdelaziz, Mohamed Ewis; Abdel Latif, Fadl Hicham Fadl; Claudel, Christian G.
2013-01-01
In this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental
Energy Technology Data Exchange (ETDEWEB)
Goswami, Gurupada; Majee, Pradip; Bag, Bidhan Chandra [Department of Chemistry, Visva-Bharati, Santiniketan 731 235 (India); Barik, Debashis [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India)
2006-09-15
In this paper we have studied upper bound of time derivative of information entropy for colored cross-correlated noise driven open systems. The upper bound is calculated based on the Fokker-Planck equation and the Schwartz inequality principle. Our results consider the effect of the noise correlation strength and correlation time due to the correlation between additive and multiplicative white noises on the upper bound as well as relaxation time. The interplay of deterministic and random forces reveals extremal nature of the upper bound and its deviation from the time derivative of information entropy. (author)
Directory of Open Access Journals (Sweden)
Daniel Khoshnoudirad
2015-09-01
Full Text Available The aim of the paper is to bring new combinatorial analytical properties of the Farey diagrams of order $(m,n$, which are associated to the $(m,n$-cubes. The latter are the pieces of discrete planes occurring in discrete geometry, theoretical computer sciences, and combinatorial number theory. We give a new upper bound for the number of Farey vertices $FV(m,n$ obtained as intersections points of Farey lines ([14]: $$\\exists C>0, \\forall (m,n\\in\\mathbb{N}^{*2},\\quad \\Big|FV(m,n\\Big| \\leq C m^2 n^2 (m+n \\ln^2 (mn$$ Using it, in particular, we show that the number of $(m,n$-cubes $\\mathcal{U}_{m,n}$ verifies: $$\\exists C>0, \\forall (m,n\\in\\mathbb{N}^{*2},\\quad \\Big|\\mathcal{U}_{m,n}\\Big| \\leq C m^3 n^3 (m+n \\ln^2 (mn$$ which is an important improvement of the result previously obtained in [6], which was a polynomial of degree 8. This work uses combinatorics, graph theory, and elementary and analytical number theory.
Amos-type bounds for modified Bessel function ratios☆
Hornik, Kurt; Grün, Bettina
2013-01-01
We systematically investigate lower and upper bounds for the modified Bessel function ratio Rν=Iν+1/Iν by functions of the form Gα,β(t)=t/(α+t2+β2) in case Rν is positive for all t>0, or equivalently, where ν≥−1 or ν is a negative integer. For ν≥−1, we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If ν≥−1/2, the minimal elements are tangent to Rν in exactly one point 0≤t≤∞, and have Rν as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if ν is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively. PMID:24926105
Amos-type bounds for modified Bessel function ratios.
Hornik, Kurt; Grün, Bettina
2013-12-01
We systematically investigate lower and upper bounds for the modified Bessel function ratio [Formula: see text] by functions of the form [Formula: see text] in case [Formula: see text] is positive for all [Formula: see text], or equivalently, where [Formula: see text] or [Formula: see text] is a negative integer. For [Formula: see text], we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If [Formula: see text], the minimal elements are tangent to [Formula: see text] in exactly one point [Formula: see text], and have [Formula: see text] as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if [Formula: see text] is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.
Qiu, Shanwen
2013-09-01
In this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.
Qiu, Shanwen
2012-07-01
In this article, we propose a new grid-free and exact solution method for computing solutions associated with an hybrid traffic flow model based on the Lighthill- Whitham-Richards (LWR) partial differential equation. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a fixed acceleration otherwise. We first present a grid-free solution method for the LWR equation based on the minimization of component functions. We then show that this solution method can be extended to compute the solutions to the hybrid model by proper modification of the component functions, for any concave fundamental diagram. We derive these functions analytically for the specific case of a triangular fundamental diagram. We also show that the proposed computational method can handle fixed or moving bottlenecks.
Exactly soluble models for surface partition of large clusters
International Nuclear Information System (INIS)
Bugaev, K.A.; Bugaev, K.A.; Elliott, J.B.
2007-01-01
The surface partition of large clusters is studied analytically within a framework of the 'Hills and Dales Model'. Three formulations are solved exactly by using the Laplace-Fourier transformation method. In the limit of small amplitude deformations, the 'Hills and Dales Model' gives the upper and lower bounds for the surface entropy coefficient of large clusters. The found surface entropy coefficients are compared with those of large clusters within the 2- and 3-dimensional Ising models
Rutkevich, Sergei B; Diehl, H W
2015-06-01
The O(n) ϕ(4) model on a strip bounded by a pair of planar free surfaces at separation L can be solved exactly in the large-n limit in terms of the eigenvalues and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. The scaling limit of a continuum version of this model is considered. It is shown that the self-consistent potential can be eliminated in favor of scattering data by means of appropriately extended methods of inverse scattering theory. The scattering data (Jost function) associated with the self-consistent potential are determined for the L=∞ semi-infinite case in the scaling regime for all values of the temperature scaling field t=(T-T(c))/T(c) above and below the bulk critical temperature T(c). These results are used in conjunction with semiclassical and boundary-operator expansions and a trace formula to derive exact analytical results for a number of quantities such as two-point functions, universal amplitudes of two excess surface quantities, the universal amplitude difference associated with the thermal singularity of the surface free energy, and potential coefficients. The asymptotic behaviors of the scaled eigenenergies and eigenfunctions of the self-consistent Schrödinger equation as function of x=t(L/ξ(+))(1/ν) are determined for x→-∞. In addition, the asymptotic x→-∞ forms of the universal finite-size scaling functions Θ(x) and ϑ(x) of the residual free energy and the Casimir force are computed exactly to order 1/x, including their x(-1)ln|x| anomalies.
Page, Don N.
2018-01-01
In an asymptotically flat spacetime of dimension d >3 and with the Newtonian gravitational constant G , a spherical black hole of initial horizon radius rh and mass M ˜rhd -3/G has a total decay time to Hawking emission of td˜rhd -1/G ˜G2 /(d -3 )M(d -1 )/(d -3 ) which grows without bound as the radius rh and mass M are taken to infinity. However, in asymptotically anti-de Sitter spacetime with a length scale ℓ and with absorbing boundary conditions at infinity, the total Hawking decay time does not diverge as the mass and radius go to infinity but instead remains bounded by a time of the order of ℓd-1/G .
DEFF Research Database (Denmark)
Krabbenhøft, Sven; Damkilde, Lars; Krabbenhøft, Kristian
2013-01-01
. These factors only take into account the inclination of the slope, whereas other parameters, which may play a role, such as the distance from the footing to the slope, the width of the footing and the strength of the soil are ignored. The present work comprises finite element based upper- and lower...
International Nuclear Information System (INIS)
Bello-Rivas, Juan M.; Elber, Ron
2015-01-01
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied
Abdullah, Dahlan; Suwilo, Saib; Tulus; Mawengkang, Herman; Efendi, Syahril
2017-09-01
The higher education system in Indonesia can be considered not only as an important source of developing knowledge in the country, but also could create positive living conditions for the country. Therefore it is not surprising that enrollments in higher education continue to expand. However, the implication of this situation, the Indonesian government is necessarily to support more funds. In the interest of accountability, it is essential to measure the efficiency for this higher institution. Data envelopment analysis (DEA) is a method to evaluate the technical efficiency of production units which have multiple input and output. The higher learning institution considered in this paper is Malikussaleh University located in Lhokseumawe, a city in Aceh province of Indonesia. This paper develops a method to evaluate efficiency for all departments in Malikussaleh University using DEA with bounded output. Accordingly, we present some important differences in efficiency of those departments. Finally we discuss the effort should be done by these departments in order to become efficient.
International Nuclear Information System (INIS)
Zeger, J.
1993-01-01
Organized criminals also tried to illegally transfer nuclear material through Austria. Two important questions have to be answered after the material is sized by police authorities: What is the composition of the material and where does it come from? By application of a broad range of analytical techniques, which were developed or refined by our experts, it is possible to measure the exact amount and isotopic composition of uranium and plutonium in any kind of samples. The criminalistic application is only a byproduct of the large scale work on controlling the peaceful application of nuclear energy, which is done in contract with the IAEA in the context of the 'Network of Analytical Laboratories'
Energy Technology Data Exchange (ETDEWEB)
Takahashi, Ryuichi; Asada, Hideki [Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561 (Japan)
2013-05-01
The latest result in the Sloan Digital Sky Survey Quasar Lens Search (SQLS) has set the first cosmological constraints on negative-mass compact objects and Ellis wormholes. There are no multiple images lensed by the above two exotic objects for {approx}50, 000 distant quasars in the SQLS data. Therefore, an upper bound is put on the cosmic abundances of these lenses. The number density of negative-mass compact objects is n < 10{sup -8}(10{sup -4}) h {sup 3} Mpc{sup -3} at the mass scale |M| > 10{sup 15}(10{sup 12}) M{sub Sun }, which corresponds to the cosmological density parameter |{Omega}| < 10{sup -4} at the galaxy and cluster mass range |M| = 10{sup 12-15} M{sub Sun }. The number density of the Ellis wormhole is n < 10{sup -4} h {sup 3} Mpc{sup -3} for a range of the throat radius a = 10-10{sup 4} pc, which is much smaller than the Einstein ring radius.
International Nuclear Information System (INIS)
Spiegler, P.
1981-09-01
As part of the assessment of the potential radiological consequences of the proposed Waste Isolation Pilot Plant (WIPP), this report evaluates the post-closure radiation dose commitments associated with a possible breach event which involves dissolution of the repository by groundwaters and subsequent transport of the nuclear waste through an aquifer to a well assumed to exist at a point 3 miles downstream from the repository. The concentrations of uranium and plutonium isotopes at the well are based on the nuclear waste inventory presently proposed for WIPP and basic assumptions concerning the transport of waste as well as treatment to reduce the salinity of the water. The concentrations of U-233, Pu-239, and Pu-240, all radionuclides originally emplaced as waste in the repository, would exceed current EPA drinking water limits. The concentrations of U-234, U-235, and U-236, all decay products of plutonium isotopes originally emplaced as waste, would be well below current EPA drinking water limits. The 50-year dose commitments from one year of drinking treated water contaminated with U-233 or Pu-239 and Pu-240 were found to be comparable to a one-year dose from natural background. The 50-year dose commitments from one year of drinking milk would be no more than about 1/5 the dose obtained from ingestion of treated water. These doses are considered upper bounds because of several very conservative assumptions which are discussed in the report
Physical Uncertainty Bounds (PUB)
Energy Technology Data Exchange (ETDEWEB)
Vaughan, Diane Elizabeth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Preston, Dean L. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-19
This paper introduces and motivates the need for a new methodology for determining upper bounds on the uncertainties in simulations of engineered systems due to limited fidelity in the composite continuum-level physics models needed to simulate the systems. We show that traditional uncertainty quantification methods provide, at best, a lower bound on this uncertainty. We propose to obtain bounds on the simulation uncertainties by first determining bounds on the physical quantities or processes relevant to system performance. By bounding these physics processes, as opposed to carrying out statistical analyses of the parameter sets of specific physics models or simply switching out the available physics models, one can obtain upper bounds on the uncertainties in simulated quantities of interest.
Exact current to a spherical electrode in a collisionless, large-Debye-length magnetoplasma
International Nuclear Information System (INIS)
Sonmor, L.J.; Laframboise, J.G.
1991-01-01
Exact calculations of the steady-state current drawn from a collisionless, Maxwellian plasma in a uniform magnetic field by a spherical, perfectly absorbing electrode are presented for a range of dimensionless electrode potentials and magnetic-field strengths. These calculations are valid in the limit of large Debye length. The results are compared with the theory of Rubinstein and Laframboise, which gives upper and lower bounds for both the attracted-species and the repelled-species current. It is found that as the electrode potential increases from space potential with magnetic-field strength fixed, the electron (i.e., attracted-species) current decreases, but not as quickly as the adiabatic-limit (effectively lower-bound) current. The ion current also diverges immediately from the adiabatic-limit current. As the electrode potential increases further, the electron current rises and moves monotonically toward the canonical upper bound, which is the warm-plasma generalization of the well-known Parker and Murphy upper bound. It is unclear whether the current approaches the upper bound asymptotically as the electrode potential becomes large, or instead a constant proportion of the upper bound which varies with magnetic-field strength. The dependence on magnetic-field strength is more complicated. As expected for small fixed electrode potentials, the attracted-species current approaches the adiabatic-limit current monotonically as the magnetic-field strength increases. However, for large electrode potentials this pattern reverses: the current approaches the canonical upper bound monotonically as the magnetic-field strength increases. These patterns are expected to persist when the Debye length is finite. Interpretation of these results leads to an inference that for large electrode potentials, the effect of decreasing the Debye length may be to reduce the current, as in the nonmagnetic case
International Nuclear Information System (INIS)
Golden, L.B.
1968-01-01
In atomic structure calculations, one has to evaluate the Slater integrals. In the present program, the authors evaluate exactly the Slater integral when hydrogenic wave functions are used for the bound-state orbitals. When hydrogenic wave functions are used, the Slater integrals involve integrands which can be written in the form of a product of an exponential, exp(ax) and a known analytic polynomial function, f(x). By repeated partial integration such an integral can be expressed in terms of a finite series involving the exponential, the polynomial function and its derivatives. PL/1-FORMAC has a built-in subroutine that will analytically find the derivatives of any multinomial. Thus, the finite series and hence the Slater integral can be evaluated analytically. (Auth.)
Universal bounds in even-spin CFTs
Energy Technology Data Exchange (ETDEWEB)
Qualls, Joshua D. [Department of Physics, National Taiwan University,Taipei, Taiwan (China)
2015-12-01
We prove using invariance under the modular S− and ST−transformations that every unitary two-dimensional conformal field theory (CFT) having only even-spin primary operators (with no extended chiral algebra and with right- and left-central charges c,c̃>1) contains a primary operator with dimension Δ{sub 1} satisfying 0<Δ{sub 1}<((c+c̃)/24)+0.09280…. After deriving both analytical and numerical bounds, we discuss how to extend our methods to bound higher conformal dimensions before deriving lower and upper bounds on the number of primary operators in a given energy range. Using the AdS{sub 3}/CFT{sub 2} dictionary, the bound on Δ{sub 1} proves the lightest massive excitation in appropriate theories of 3D matter and gravity with cosmological constant Λ<0 can be no heavier than 1/8G{sub N}+O(√(−Λ)); the bounds on the number of operators are related via AdS/CFT to the entropy of states in the dual gravitational theory. In the flat-space approximation, the limiting mass is exactly that of the lightest BTZ black hole.
Exact evaluation of entropic quantities in a solvable two-particle model
International Nuclear Information System (INIS)
Glasser, M.L.; Nagy, I.
2013-01-01
It has long been known that the von Neumann entropy S N and the Jozsa–Robb–Wootters subentropy Q JRW [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin's natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.
Exact evaluation of entropic quantities in a solvable two-particle model
Energy Technology Data Exchange (ETDEWEB)
Glasser, M.L., E-mail: laryg@clarkson.edu [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States); Donostia International Physics Center, P. Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Nagy, I. [Donostia International Physics Center, P. Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest (Hungary)
2013-11-08
It has long been known that the von Neumann entropy S{sub N} and the Jozsa–Robb–Wootters subentropy Q{sub JRW} [R. Jozsa, et al., Phys. Rev. A 49 (1994) 668] are, respectively, upper and lower bounds on the accessible information one can obtain about the identity of a pure state by performing a quantum measurement on a system whose pure state is initially unknown. We determine these bounds exactly in terms of the occupation numbers of normalized natural orbitals of an externally confined interacting two-particle model system. The occupation numbers are obtained via a sign-correct direct decomposition of the underlying exact Schrödinger wave function in terms of an infinite sum of products of Löwdin's natural orbitals, avoiding thus the solution of the eigenvalue problem with the corresponding reduced one-particle matrix.
Bounds on poloidal kinetic energy in plane layer convection
Tilgner, A.
2017-12-01
A numerical method is presented that conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with earlier results. These bounds imply upper bounds for the poloidal energy, which follow directly from the definitions of dissipation and energy. The same constraints used for computing upper bounds on the heat transport lead to improved bounds for the poloidal energy.
Energy Technology Data Exchange (ETDEWEB)
Rubio, E. M.; Domingo, R.; Gonzalez, C.; Sanz, A.
2004-07-01
To study the optimised geometrical configuration to carry out mechanical drawing of plates is the main objective of this paper. To accomplish this objective, a comparative analysis of some suitable geometrical and kinematic configurations of the material located in the deformation zone has been made. Concretely, several triangular rigid zone models have been chosen, for each one, the overall energy involved in the process have been calculated and an estimation of its different components has been made. The calculation of the energy has been achieved applying the Upper Bound Theorem under plane strain and partial friction conditions. In addition, the range of use for the selected configurations has been established. (Author) 19 refs.
Directory of Open Access Journals (Sweden)
Julien Martin
Full Text Available The explosion of the Deepwater Horizon drilling platform created the largest marine oil spill in U.S. history. As part of the Natural Resource Damage Assessment process, we applied an innovative modeling approach to obtain upper estimates for occupancy and for number of manatees in areas potentially affected by the oil spill. Our data consisted of aerial survey counts in waters of the Florida Panhandle, Alabama and Mississippi. Our method, which uses a Bayesian approach, allows for the propagation of uncertainty associated with estimates from empirical data and from the published literature. We illustrate that it is possible to derive estimates of occupancy rate and upper estimates of the number of manatees present at the time of sampling, even when no manatees were observed in our sampled plots during surveys. We estimated that fewer than 2.4% of potentially affected manatee habitat in our Florida study area may have been occupied by manatees. The upper estimate for the number of manatees present in potentially impacted areas (within our study area was estimated with our model to be 74 (95%CI 46 to 107. This upper estimate for the number of manatees was conditioned on the upper 95%CI value of the occupancy rate. In other words, based on our estimates, it is highly probable that there were 107 or fewer manatees in our study area during the time of our surveys. Because our analyses apply to habitats considered likely manatee habitats, our inference is restricted to these sites and to the time frame of our surveys. Given that manatees may be hard to see during aerial surveys, it was important to account for imperfect detection. The approach that we described can be useful for determining the best allocation of resources for monitoring and conservation.
International Nuclear Information System (INIS)
Ushveridze, A.G.
1992-01-01
This paper reports that quasi-exactly solvable (QES) models realize principally new type of exact solvability in quantum physics. These models are distinguished by the fact that the Schrodinger equations for them can be solved exactly only for certain limited parts of the spectrum, but not for the whole spectrum. They occupy an intermediate position between the exactly the authors solvable (ES) models and all the others. The number of energy levels for which the spectral problems can be solved exactly refer below to as the order of QES model. From the mathematical point of view the existence of QES models is not surprising. Indeed, if the term exact solvability expresses the possibility of total explicit diagonalization of infinite Hamiltonian matrix, then the term quasi-exact solvability implies the situation when the Hamiltonian matrix can be reduced explicitly to the block-diagonal form with one of the appearing blocks being finite
International Nuclear Information System (INIS)
Orzalesi, C.A.
1979-01-01
In relativistic quantum theory, bound states generate forces in the crossed channel; such forces can affect the binding and self-consistent solutions should be sought for the bound-state problem. The author investigates how self-consistency can be achieved by successive approximations, in a simple scalar model and with successive relativistic eikonal approximations (EAs). Within the generalized ladder approximation, some exact properties of the resulting ''first generation'' bound states are discussed. The binding energies in this approximation are rather small even for rather large values of the primary coupling constant. The coupling of the constituent particles to the first-generation reggeon is determined by a suitable EA and a new generalized ladder amplitude is constructed with rungs given either by the primary gluons or by the first-generation reggeons. The resulting new (second-generation) bound states are found in a reggeized EA. The size of the corrections to the binding energies due to the rebinding effects is surprisingly large. The procedure is then iterated, so as to find - again in an EA - the third-generation bound states. The procedure is found to be self-consistent already at this stage: the third-generation bound states coincide with those of second generation, and no further rebinding takes place in the higher iterations of the approximation method. Features - good and bad - of the model are discussed, as well as the possible relevance of rebinding mechanisms in hadron dynamics. (author)
International Nuclear Information System (INIS)
Tuchman, Y.; Sack, N.; Barkat, Z.
1978-01-01
Envelope ejection leading to a planetary nebula has been recently shown to occur as the terminal point of the Mira stage. The ejection is due to a diverging pulsational instability, not to a dynamical one. It is found that in this case (and for Population I, mixing length=1 pressure scale height) the upper mass limit for formation of planetary nebulae is at least 6 M/sub sun/. It thus follows that the lower mass limit for realization of carbon detonation model configurations is also at last 6 M/sub sun/
International Nuclear Information System (INIS)
Bianco, F. B.; Zhang, Z.-W.; King, S.-K.; Wang, J.-H.; Lee, T.; Lin, H.-C.; Lehner, M. J.; Mondal, S.; Giammarco, J.; Holman, M. J.; Alcock, C.; Coehlo, N. K.; Axelrod, T.; Byun, Y.-I.; Kim, D.-W.; Chen, W. P.; Cook, K. H.; Dave, R.; De Pater, I.; Lissauer, J. J.
2010-01-01
We have analyzed the first 3.75 years of data from the Taiwanese American Occultation Survey (TAOS). TAOS monitors bright stars to search for occultations by Kuiper Belt objects (KBOs). This data set comprises 5 x 10 5 star hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this data set. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan and Sari, Kenyon and Bromley, Benavidez and Campo Bagatin, and Fraser. A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is composed of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.
Improved Lower Bounds on the Price of Stability of Undirected Network Design Games
Bilò, Vittorio; Caragiannis, Ioannis; Fanelli, Angelo; Monaco, Gianpiero
Bounding the price of stability of undirected network design games with fair cost allocation is a challenging open problem in the Algorithmic Game Theory research agenda. Even though the generalization of such games in directed networks is well understood in terms of the price of stability (it is exactly H n , the n-th harmonic number, for games with n players), far less is known for network design games in undirected networks. The upper bound carries over to this case as well while the best known lower bound is 42/23 ≈ 1.826. For more restricted but interesting variants of such games such as broadcast and multicast games, sublogarithmic upper bounds are known while the best known lower bound is 12/7 ≈ 1.714. In the current paper, we improve the lower bounds as follows. We break the psychological barrier of 2 by showing that the price of stability of undirected network design games is at least 348/155 ≈ 2.245. Our proof uses a recursive construction of a network design game with a simple gadget as the main building block. For broadcast and multicast games, we present new lower bounds of 20/11 ≈ 1.818 and 1.862, respectively.
Exact nonparametric confidence bands for the survivor function.
Matthews, David
2013-10-12
A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan-Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden-Decker-Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin's lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. It was begun while the author was visiting the Department of Statistics, University of Auckland, and completed during a subsequent sojourn at the Medical Research Council Biostatistics Unit in Cambridge. The support of both institutions, in addition to that of NSERC and the University of Waterloo, is greatly appreciated.
Energy Technology Data Exchange (ETDEWEB)
Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Swaidan, Raja
2015-08-20
Intrinsically ultramicroporous (<7 Å) polymers represent a new paradigm in materials development for membrane-based gas separation. In particular, they demonstrate that uniting intrachain “rigidity”, the traditional design metric of highly permeable polymers of intrinsic microporosity (PIMs), with gas-sieving ultramicroporosity yields high-performance gas separation membranes. Highly ultramicroporous PIMs have redefined the state-of-the-art in large-scale air (e.g., O2/N2) and hydrogen recovery (e.g., H2/N2, H2/CH4) applications with unprecedented molecular sieving gas transport properties. Accordingly, presented herein are new 2015 permeability/selectivity “upper bounds” for large-scale commercial membrane-based air and hydrogen applications that accommodate the substantial performance enhancements of recent PIMs over preceding polymers. A subtle balance between intrachain rigidity and interchain spacing has been achieved in the amorphous microstructures of PIMs, fine-tuned using unique bridged-bicyclic building blocks (i.e., triptycene, ethanoanthracene and Tröger’s base) in both ladder and semiladder (e.g., polyimide) structures.
Information theoretic bounds for compressed sensing in SAR imaging
International Nuclear Information System (INIS)
Jingxiong, Zhang; Ke, Yang; Jianzhong, Guo
2014-01-01
Compressed sensing (CS) is a new framework for sampling and reconstructing sparse signals from measurements significantly fewer than those prescribed by Nyquist rate in the Shannon sampling theorem. This new strategy, applied in various application areas including synthetic aperture radar (SAR), relies on two principles: sparsity, which is related to the signals of interest, and incoherence, which refers to the sensing modality. An important question in CS-based SAR system design concerns sampling rate necessary and sufficient for exact or approximate recovery of sparse signals. In the literature, bounds of measurements (or sampling rate) in CS have been proposed from the perspective of information theory. However, these information-theoretic bounds need to be reviewed and, if necessary, validated for CS-based SAR imaging, as there are various assumptions made in the derivations of lower and upper bounds on sub-Nyquist sampling rates, which may not hold true in CS-based SAR imaging. In this paper, information-theoretic bounds of sampling rate will be analyzed. For this, the SAR measurement system is modeled as an information channel, with channel capacity and rate-distortion characteristics evaluated to enable the determination of sampling rates required for recovery of sparse scenes. Experiments based on simulated data will be undertaken to test the theoretic bounds against empirical results about sampling rates required to achieve certain detection error probabilities
Exact Boundary Controllability of Electromagnetic Fields in a General Region
International Nuclear Information System (INIS)
Eller, M. M.; Masters, J. E.
2002-01-01
We prove exact controllability for Maxwell's system with variable coefficients in a bounded domain by a current flux in the boundary. The proof relies on a duality argument which reduces the proof of exact controllability to the proof of continuous observability for the homogeneous adjoint system. There is no geometric restriction imposed on the domain
Determining Normal-Distribution Tolerance Bounds Graphically
Mezzacappa, M. A.
1983-01-01
Graphical method requires calculations and table lookup. Distribution established from only three points: mean upper and lower confidence bounds and lower confidence bound of standard deviation. Method requires only few calculations with simple equations. Graphical procedure establishes best-fit line for measured data and bounds for selected confidence level and any distribution percentile.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts
Exact quasinormal modes for a special class of black holes
International Nuclear Information System (INIS)
Oliva, Julio; Troncoso, Ricardo
2010-01-01
Analytic exact expressions for the quasinormal modes of scalar and electromagnetic perturbations around a special class of black holes are found in d≥3 dimensions. It is shown that the size of the black hole provides a lower bound for the angular momentum of the perturbation. Quasinormal modes appear when this bound is fulfilled; otherwise the excitations become purely damped.
Heskes, Tom; Eisinga, Rob; Breitling, Rainer
2014-11-21
The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution. We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood. We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .
Spectral bisection algorithm for solving Schrodinger equation using upper and lower solutions
Directory of Open Access Journals (Sweden)
Qutaibeh Deeb Katatbeh
2007-10-01
Full Text Available This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schr"odinger equation $ -Deltapsi(r+V(rpsi(r=Epsi(r$ in $N$ spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for the ground state eigenfunctions of Schrodinger equation. We determine also lower and upper solutions for the exact wave function of the ground state eigenfunctions using the computed upper and lower bounds for the eigenvalues obtained by variational methods. In other words, by using this criteria, we prove that the substitution of the lower(upper bound of the eigenvalue in Schrodinger equation leads to an upper(lower solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses Raielgh-Ritz theorem. Meanwhile, the second approach uses a new numerical spectral bisection technique. We apply our results for a wide class of potentials in quantum mechanics such as sum of power-law potentials in quantum mechanics.
Capacity Bounds for Parallel Optical Wireless Channels
Chaaban, Anas; Rezki, Zouheir; Alouini, Mohamed-Slim
2016-01-01
A system consisting of parallel optical wireless channels with a total average intensity constraint is studied. Capacity upper and lower bounds for this system are derived. Under perfect channel-state information at the transmitter (CSIT), the bounds have to be optimized with respect to the power allocation over the parallel channels. The optimization of the lower bound is non-convex, however, the KKT conditions can be used to find a list of possible solutions one of which is optimal. The optimal solution can then be found by an exhaustive search algorithm, which is computationally expensive. To overcome this, we propose low-complexity power allocation algorithms which are nearly optimal. The optimized capacity lower bound nearly coincides with the capacity at high SNR. Without CSIT, our capacity bounds lead to upper and lower bounds on the outage probability. The outage probability bounds meet at high SNR. The system with average and peak intensity constraints is also discussed.
International Nuclear Information System (INIS)
Raju Viswanathan, R.
1991-09-01
We study examples of one dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behaviour and the Morse potential (which corresponds to a γ = -1 model) has the interesting feature that there are no quantum corrections to the scaling behaviour in the continuum limit. (author). 5 refs
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact approaches for scaffolding
Weller, Mathias; Chateau, Annie; Giroudeau, Rodolphe
2015-01-01
This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We ex...
Prepotential approach to exact and quasi-exact solvabilities
International Nuclear Information System (INIS)
Ho, C.-L.
2008-01-01
Exact and quasi-exact solvabilities of the one-dimensional Schroedinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the potential as well as the eigenfunctions and eigenvalues simultaneously. The novel feature of the present work is the realization that both exact and quasi-exact solvabilities can be solely classified by two integers, the degrees of two polynomials which determine the change of variable and the zeroth order prepotential. Most of the well-known exactly and quasi-exactly solvable models, and many new quasi-exactly solvable ones, can be generated by appropriately choosing the two polynomials. This approach can be easily extended to the constructions of exactly and quasi-exactly solvable Dirac, Pauli, and Fokker-Planck equations
Sharp Bounds for Symmetric and Asymmetric Diophantine Approximation
Institute of Scientific and Technical Information of China (English)
Cornelis KRAAIKAMP; Ionica SMEETS
2011-01-01
In 2004,Tong found bounds for the approximation quality of a regular continued fraction convergent to a rational number,expressed in bounds for both the previous and next approximation.The authors sharpen his results with a geometric method and give both sharp upper and lower bounds.The asymptotic frequencies that these bounds occur are also calculated.
Energy Technology Data Exchange (ETDEWEB)
Buras, Andrzej J. [TUM Institute for Advanced Study,Lichtenbergstr. 2a, D-85748 Garching (Germany); Physik Department, TU München,James-Franck-Straße, D-85748 Garching (Germany); Gérard, Jean-Marc [Centre for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)
2015-12-01
We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B{sub 6}{sup (1/2)} and B{sub 8}{sup (3/2)} parametrizing the K→ππ matrix elements 〈Q{sub 6}〉{sub 0} and 〈Q{sub 8}〉{sub 2} of the dominant QCD and electroweak operators receive both negativeO(1/N) corrections such that B{sub 6}{sup (1/2)}≤B{sub 8}{sup (3/2)}<1 in agreement with the recent lattice results of the RBC-UKQCD collaboration. We also point out that the pattern of the size of the hadronic matrix elements of all QCD and electroweak penguin operators Q{sub i} contributing to the K→ππ amplitudes A{sub 0} and A{sub 2}, obtained by this lattice collaboration, provides further support to our large N approach. In particular, the lattice result for the matrix element 〈Q{sub 8}〉{sub 0} implies for the corresponding parameter B{sub 8}{sup (1/2)}=1.0±0.2 to be compared with large N value B{sub 8}{sup (1/2)}=1.1±0.1. We discuss briefly the implications of these findings for the ratio ε{sup ′}/ε. In fact, with the precise value for B{sub 8}{sup (3/2)} from RBC-UKQCD collaboration, our upper bound on B{sub 6}{sup (1/2)} implies ε{sup ′}/ε in the SM roughly by a factor of two below its experimental value (16.6±2.3)×10{sup −4}. We also briefly comment on the parameter B̂{sub K} and the ΔI=1/2 rule.
OPRA capacity bounds for selection diversity over generalized fading channels
Hanif, Muhammad Fainan; Yang, Hongchuan; Alouini, Mohamed-Slim
2014-01-01
, lower and upper bounds on OPRA capacity for selection diversity scheme are presented. These bounds hold for variety of fading channels including log-normal and generalized Gamma distributed models and have very simple analytic expressions for easy
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels
Xia, Minghua
2012-10-01
In this correspondence, considering dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying over Nakagami- m fading channels, the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) is derived. In particular, when the fading shape factors m1 and m2 at consecutive hops take non-integer values, the bivariate H-function and G -function are exploited to obtain an exact analytical expression for the CDF. The obtained CDF is then applied to evaluate the outage performance of the system under study. The analytical results of outage probability coincide exactly with Monte-Carlo simulation results and outperform the previously reported upper bounds in the low and medium SNR regions.
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
An exact approach for aggregated formulations
DEFF Research Database (Denmark)
Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan
Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...... optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem....
New bounds on isotropic Lorentz violation
International Nuclear Information System (INIS)
Carone, Christopher D.; Sher, Marc; Vanderhaeghen, Marc
2006-01-01
Violations of Lorentz invariance that appear via operators of dimension four or less are completely parametrized in the Standard Model Extension (SME). In the pure photonic sector of the SME, there are 19 dimensionless, Lorentz-violating parameters. Eighteen of these have experimental upper bounds ranging between 10 -11 and 10 -32 ; the remaining parameter, k-tilde tr , is isotropic and has a much weaker bound of order 10 -4 . In this Brief Report, we point out that k-tilde tr gives a significant contribution to the anomalous magnetic moment of the electron and find a new upper bound of order 10 -8 . With reasonable assumptions, we further show that this bound may be improved to 10 -14 by considering the renormalization of other Lorentz-violating parameters that are more tightly constrained. Using similar renormalization arguments, we also estimate bounds on Lorentz-violating parameters in the pure gluonic sector of QCD
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Exact Controllability and Perturbation Analysis for Elastic Beams
International Nuclear Information System (INIS)
Moreles, Miguel Angel
2004-01-01
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials
Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System
Goluskin, David
2018-04-01
We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be proved using Lyapunov functions. Nonnegativity is enforced by requiring the polynomials to be sums of squares, a condition which is then formulated as a semidefinite program (SDP) that can be solved computationally. Although such computations are subject to numerical error, we demonstrate two ways to obtain rigorous results: using interval arithmetic to control the error of an approximate SDP solution, and finding exact analytical solutions to relatively small SDPs. Previous formulations are extended to allow for bounds depending analytically on parametric variables. These methods are illustrated using the Lorenz equations, a system with three state variables ( x, y, z) and three parameters (β ,σ ,r). Bounds are reported for infinite-time averages of all eighteen moments x^ly^mz^n up to quartic degree that are symmetric under (x,y)\\mapsto (-x,-y). These bounds apply to all solutions regardless of stability, including chaotic trajectories, periodic orbits, and equilibrium points. The analytical approach yields two novel bounds that are sharp: the mean of z^3 can be no larger than its value of (r-1)^3 at the nonzero equilibria, and the mean of xy^3 must be nonnegative. The interval arithmetic approach is applied at the standard chaotic parameters to bound eleven average moments that all appear to be maximized on the shortest periodic orbit. Our best upper bound on each such average exceeds its value on the maximizing orbit by less than 1%. Many bounds reported here are much tighter than would be possible without computer assistance.
Entropy Bounds for Constrained Two-Dimensional Fields
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Justesen, Jørn
1999-01-01
The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived.......The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived....
Solving the minimum flow problem with interval bounds and flows
Indian Academy of Sciences (India)
... with crisp data. In this paper, the idea of Ghiyasvand was extended for solving the minimum ﬂow problem with interval-valued lower, upper bounds and ﬂows. This problem can be solved using two minimum ﬂow problems with crisp data. Then, this result is extended to networks with fuzzy lower, upper bounds and ﬂows.
Variational lower bound on the scattering length
International Nuclear Information System (INIS)
Rosenberg, L.; Spruch, L.
1975-01-01
The scattering length A characterizes the zero-energy scattering of one system by another. It was shown some time ago that a variational upper bound on A could be obtained using methods, of the Rayleigh-Ritz type, which are commonly employed to obtain upper bounds on energy eigenvalues. Here we formulate a method for obtaining a variational lower bound on A. Once again the essential idea is to express the scattering length as a variational estimate plus an error term and then to reduce the problem of bounding the error term to one involving bounds on energy eigenvalues. In particular, the variational lower bound on A is rigorously established provided a certin modified Hamiltonian can be shown to have no discrete states lying below the level of the continuum threshold. It is unfortunately true that necessary conditions for the existence of bound states are not available for multiparticle systems in general. However, in the case of positron-atom scattering the adiabatic approximation can be introduced as an (essentially) solvable comparison problem to rigorously establish the nonexistence of bound states of the modified Hamiltonian. It has recently been shown how the validity of the variational upper bound on A can be maintained when the target ground-state wave function is imprecisely known. Similar methods can be used to maintain the variational lower bound on A. Since the bound is variational, the error in the calculated scattering length will be of second order in the error in the wave function. The use of the adiabatic approximation in the present context places no limitation in principle on the accuracy achievable
de Klerk, Etienne; Laurent, Monique
We consider the problem of minimizing a continuous function f over a compact set K. We compare the hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864-885] to bounds that may be obtained from simulated annealing. We show that, when f is a polynomial and K a convex
Bogomol'nyi bounds for cosmic strings
International Nuclear Information System (INIS)
Comtet, A.; Gibbons, G.W.; Cambridge Univ.
1987-09-01
We establish Bogomol'nyi inequalities for the deficit angle of some cylindrically symmetric asymptotically local flat (CALF) spacetimes containing cosmic strings. These results prove the stability against arbitrary cylindrical deformations of those configurations which saturate the bound. Such configurations satisfy first order equations which can, in some cases, be solved exactly
Exact piecewise flat gravitational waves
van de Meent, M.
2011-01-01
We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to
CONDITIONS FOR EXACT CAVALIERI ESTIMATION
Directory of Open Access Journals (Sweden)
Mónica Tinajero-Bravo
2014-03-01
Full Text Available Exact Cavalieri estimation amounts to zero variance estimation of an integral with systematic observations along a sampling axis. A sufficient condition is given, both in the continuous and the discrete cases, for exact Cavalieri sampling. The conclusions suggest improvements on the current stereological application of fractionator-type sampling.
Covariant two-particle wave functions for model quasipotentials admitting exact solutions
International Nuclear Information System (INIS)
Kapshaj, V.N.; Skachkov, N.B.
1983-01-01
Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials
Covariant two-particle wave functions for model quasipotential allowing exact solutions
International Nuclear Information System (INIS)
Kapshaj, V.N.; Skachkov, N.B.
1982-01-01
Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials
Exact solution of the N-dimensional generalized Dirac-Coulomb equation
International Nuclear Information System (INIS)
Tutik, R.S.
1992-01-01
An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)
Mohri, Mehryar; Rostamizadeh, Afshin
2013-01-01
We present a brief survey of existing mistake bounds and introduce novel bounds for the Perceptron or the kernel Perceptron algorithm. Our novel bounds generalize beyond standard margin-loss type bounds, allow for any convex and Lipschitz loss function, and admit a very simple proof.
On the dimension of subspaces with bounded Schmidt rank
International Nuclear Information System (INIS)
Cubitt, Toby; Montanaro, Ashley; Winter, Andreas
2008-01-01
We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al. [e-print arXiv:quant-ph/0407049; Commun. Math. Phys., 265, 95 (2006)], which show that in large dxd-dimensional systems there exist random subspaces of dimension almost d 2 , all of whose states have entropy of entanglement at least log d-O(1). It is also a generalization of results on the dimension of completely entangled subspaces, which have connections with the construction of unextendible product bases. Here we take as entanglement measure the Schmidt rank, and determine, for every pair of local dimensions d A and d B , and every r, the largest dimension of a subspace consisting only of entangled states of Schmidt rank r or larger. This exact answer is a significant improvement on the best bounds that can be obtained using the random subspace techniques in Hayden et al. We also determine the converse: the largest dimension of a subspace with an upper bound on the Schmidt rank. Finally, we discuss the question of subspaces containing only states with Schmidt equal to r
Dielectric structures with bound modes for microcavity lasers
Visser, P.M.; Allaart, K.; Lenstra, D.
2002-01-01
Cavity modes of dielectric microsphcres and vertical cavity surface emitting lasers, in spite of their high Q, are never exactly bound, but have a finite width due to leakage at the borders. We propose types of microstructures that sustain three-dimensionally bound modes of the radiation field when
Circuit lower bounds in bounded arithmetics
Czech Academy of Sciences Publication Activity Database
Pich, Ján
2015-01-01
Roč. 166, č. 1 (2015), s. 29-45 ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Keywords : bounded arithmetic * circuit lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.582, year: 2015 http://www.sciencedirect.com/science/article/pii/S0168007214000888
Exact cosmological solutions for MOG
International Nuclear Information System (INIS)
Roshan, Mahmood
2015-01-01
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Finding Maximal Pairs with Bounded Gap
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Lyngsø, Rune B.; Pedersen, Christian N. S.
1999-01-01
. In this paper we present methods for finding all maximal pairs under various constraints on the gap. In a string of length n we can find all maximal pairs with gap in an upper and lower bounded interval in time O(n log n+z) where z is the number of reported pairs. If the upper bound is removed the time reduces...... to O(n+z). Since a tandem repeat is a pair where the gap is zero, our methods can be seen as a generalization of finding tandem repeats. The running time of our methods equals the running time of well known methods for finding tandem repeats....
Energy Technology Data Exchange (ETDEWEB)
Fox, Zachary [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Neuert, Gregor [Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, Tennessee 37232 (United States); Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, Tennessee 37232 (United States); Department of Biomedical Engineering, Vanderbilt University School of Engineering, Nashville, Tennessee 37232 (United States); Munsky, Brian [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States)
2016-08-21
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.
Semiclassical and quantum field theoretic bounds for traversable Lorentzian stringy wormholes
International Nuclear Information System (INIS)
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-01-01
A lower bound on the size of a Lorentzian wormhole can be obtained by semiclassically introducing the Planck cutoff on the magnitude of tidal forces (Horowitz-Ross constraint). Also, an upper bound is provided by the quantum field theoretic constraint in the form of the Ford-Roman Quantum Inequality for massless minimally coupled scalar fields. To date, however, exact static solutions belonging to this scalar field theory have not been worked out to verify these bounds. To fill this gap, we examine the wormhole features of two examples from the Einstein frame description of the vacuum low energy string theory in four dimensions which is the same as the minimally coupled scalar field theory. Analyses in this paper support the conclusion of Ford and Roman that wormholes in this theory can have sizes that are indeed only a few order of magnitudes larger than the Planck scale. It is shown that the two types of bounds are also compatible. In the process, we point out a 'wormhole' analog of naked black holes
Positivity bounds on double parton distributions
International Nuclear Information System (INIS)
Diehl, Markus; Kasemets, Tomas
2013-03-01
Double hard scattering in proton-proton collisions is described in terms of double parton distributions. We derive bounds on these distributions that follow from their interpretation as probability densities, taking into account all possible spin correlations between two partons in an unpolarized proton. These bounds constrain the size of the polarized distributions and can for instance be used to set upper limits on the effects of spin correlations in double hard scattering. We show that the bounds are stable under leading-order DGLAP evolution to higher scales.
Quasi-bound states in continuum
International Nuclear Information System (INIS)
Nakamura, Hiroaki; Hatano, Naomichi; Garmon, Sterling; Petrosky, Tomio
2007-08-01
We report the prediction of quasi-bound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for a wide region of parameter space. These quasi-bound states are generated in a quantum wire with two channels and an adatom, when the energy bands of the two channels overlap. A would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second QBIC lays above the lower energy band). (author)
An exactly soluble Hartree problem in an external potential
International Nuclear Information System (INIS)
Gunn, J.C.; Gunn, J.M.F.
1987-09-01
The problem of N bosons interacting with each other via repulsive delta function interactions and with an external, attractive, delta function potential is solved within the Hartree approximation, exactly. It is found that if the interparticle interactions are above a certain value, there is no bound state. Thus the bound state does not just expand to compensate for the increase in the repulsive Hartree potential. Moreover as the interaction strength is increased to that value, the ground state wave function develops a pole at the position of the attractive potential. (author)
The laser second threshold: Its exact analytical dependence on detuning and relaxation rates
International Nuclear Information System (INIS)
Bakasov, A.A.; Abraham, N.B.
1992-11-01
An exact analysis has been carried out for general analytical expressions for the second threshold of a single-mode homogeneously broadened laser and for the initial pulsation frequency at the second threshold for arbitrary physical values of the relaxation rates, and at arbitrary detuning between the cavity frequency and the atomic resonance frequency. These expressions also give correspondingly exact forms for asymptotic cases that have previously studied with some approximations. Earlier approximate results are partly confirmed and partly improved by these more general expressions. The physical status of various expressions and approximations is re-considered and specified more clearly, including an analysis of which reasonably can be attained in lasers or masers. A general analytical proof is given that for larger detuning of the laser cavity from resonance a higher value of the laser excitation is required to destabilize the steady state solution (the second threshold). We also present results for the minimum value of the second threshold at fixed detuning as a function of the other parameters of the system and on the dependence of the ratio of the second threshold to the first threshold as a function of detuning. Minima of the second threshold and of the threshold ratio occur only if the population relaxation rate is equal to zero. The minima of the threshold ratio are shown to be bounded from above as well as from below (as functions of the relaxation rates, so long as the second threshold exists). The upper bound on the threshold ratio is equal to 17. The variation of the second threshold in the semi-infinite parameter space of the decay rates is shown at various detunings in plots with a finite domain by normalizing the material relaxation rates to the cavity decay rate. (author). 53 refs, 22 figs, 3 tabs
Bounds for the probability distribution function of the linear ACD process
Fernandes, Marcelo
2003-01-01
Rio de Janeiro This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.
MAXIMUM r-REGULAR INDUCED SUBGRAPH PROBLEM: FAST EXPONENTIAL ALGORITHMS AND COMBINATORIAL BOUNDS
DEFF Research Database (Denmark)
Gupta, S.; Raman, V.; Saurabh, S.
2012-01-01
We show that for a fixed r, the number of maximal r-regular induced subgraphs in any graph with n vertices is upper bounded by O(c(n)), where c is a positive constant strictly less than 2. This bound generalizes the well-known result of Moon and Moser, who showed an upper bound of 3(n/3) on the n...
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Breinbjerg, Olav
2011-01-01
A new lower bound for the radiation $Q$ of electrically small spherical magnetic dipole antennas with solid magnetodielectric core is derived in closed form using the exact theory. The new bound approaches the Chu lower bound from above as the antenna electrical size decreases. For $ka, the new...... bound is lower than the bounds for spherical magnetic as well as electric dipole antennas composed of impressed electric currents in free space....
International Nuclear Information System (INIS)
Tezuka, Hirokazu.
1984-10-01
Scattering of a particle by bound nucleons is discussed. Effects of nucleons that are bound in a nucleus are taken as a structure function. The way how to calculate the structure function is given. (author)
The covariant entropy bound in gravitational collapse
International Nuclear Information System (INIS)
Gao, Sijie; Lemos, Jose P. S.
2004-01-01
We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, L, of the old black hole then terminates at the singularity. We show that the entropy crossing L does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process. (author)
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Bounding the bias of contrastive divergence learning
DEFF Research Database (Denmark)
Fischer, Anja; Igel, Christian
2011-01-01
Optimization based on k-step contrastive divergence (CD) has become a common way to train restricted Boltzmann machines (RBMs). The k-step CD is a biased estimator of the log-likelihood gradient relying on Gibbs sampling. We derive a new upper bound for this bias. Its magnitude depends on k...
Exact solitary waves of the Fisher equation
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2005-01-01
New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given
Combinatorial bounds on the α-divergence of univariate mixture models
Nielsen, Frank; Sun, Ke
2017-01-01
We derive lower- and upper-bounds of α-divergence between univariate mixture models with components in the exponential family. Three pairs of bounds are presented in order with increasing quality and increasing computational cost. They are verified
On the Applicability of Lower Bounds for Solving Rectilinear
DEFF Research Database (Denmark)
Clausen, Jens; Karisch, Stefan E.; Perregaard, M.
1998-01-01
. Recently, lower bounds based on decomposition were proposed for the so called rectilinear QAP that proved to be the strongest for a large class of problem instances. We investigate the strength of these bounds when applied not only at the root node of a search tree but as the bound function used......The quadratic assignment problem (QAP) belongs to the hard core of NP-hard optimization problems. After almost forty years of research only relatively small instances can be solved to optimality. The reason is that the quality of the lower bounds available for exact methods is not sufficient...
Quantum bounds on Bell inequalities
Pál, Károly F.; Vértesi, Tamás
2009-02-01
We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real-component Hilbert spaces using numerical optimization. Out of these inequalities 129 have been introduced here. In 43 cases higher-dimensional component spaces gave larger violation than qubits, and in three occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.
Spectral computations for bounded operators
Ahues, Mario; Limaye, Balmohan
2001-01-01
Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for research scientists, Spectral Computations for Bounded Operators addresses the issue of solving eigenvalue problems for operators on infinite dimensional spaces. From a review of classical spectral theory through concrete approximation techniques to finite dimensional situations that can be implemented on a computer, this volume illustrates the marriage of pure and applied mathematics. It contains a variety of recent developments, including a new type of approximation that encompasses a variety of approximation methods but is simple to verify in practice. It also suggests a new stopping criterion for the QR Method and outlines advances in both the iterative refineme...
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
Bounds on the order of vanishing of eigenfunctions of Schroedinger operators
International Nuclear Information System (INIS)
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.
1990-01-01
We study L 2 -solutions of (-Δ+V-E)ψ = 0 in R n , n ≥ 2 and derive a sharp upper bound to l x 0 (ψ) in terms of x 0 , E and V under rather restrictive assumptions on V. We show for V smooth that an upper bound to l x 0 (ψ) implies an upper bound to the dimension of the eigenspace associated to E. 16 refs. (Authors)
International Nuclear Information System (INIS)
Inoue, J.; Ohtaka, K.
2004-01-01
We study virtual bound states in photonics, which are a vectorial extension of electron virtual bound states. The condition for these states is derived. It is found that the Mie resonant state which satisfies the condition that the size parameter is less than the angular momentum should be interpreted as a photon virtual bound state. In order to confirm the validity of the concept, we compare the photonic density of states, the width of which represents the lifetime of the photon virtual bound states, with numerical results
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias
2010-01-01
) resultant by means of mixed volume, as well as recent advances on aggregate root bounds for univariate polynomials, and are applicable to arbitrary positive dimensional systems. We improve upon Canny's gap theorem [7] by a factor of O(dn-1), where d bounds the degree of the polynomials, and n is the number...... bound on the number of steps that subdivision-based algorithms perform in order to isolate all real roots of a polynomial system. This leads to the first complexity bound of Milne's algorithm [22] in 2D....
Exact models for isotropic matter
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Yang, Jihua; Zhao, Liqin
2018-05-01
In this paper, by using Picard-Fuchs equations and Chebyshev criterion, we study the upper bounds of the number of limit cycles given by the first order Melnikov function for discontinuous differential systems, which can bifurcate from the periodic orbits of quadratic reversible centers of genus one (r19): x ˙ = y - 12x2 + 16y2, y ˙ = - x - 16 xy, and (r20): x ˙ = y + 4x2, y ˙ = - x + 16 xy, and the periodic orbits of the quadratic isochronous centers (S1) : x ˙ = - y +x2 -y2, y ˙ = x + 2 xy, and (S2) : x ˙ = - y +x2, y ˙ = x + xy. The systems (r19) and (r20) are perturbed inside the class of polynomial differential systems of degree n and the system (S1) and (S2) are perturbed inside the class of quadratic polynomial differential systems. The discontinuity is the line y = 0. It is proved that the upper bounds of the number of limit cycles for systems (r19) and (r20) are respectively 4 n - 3 (n ≥ 4) and 4 n + 3 (n ≥ 3) counting the multiplicity, and the maximum numbers of limit cycles bifurcating from the period annuluses of the isochronous centers (S1) and (S2) are exactly 5 and 6 (counting the multiplicity) on each period annulus respectively.
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Bounds on the Effect of Progressive Structural Degradation
DEFF Research Database (Denmark)
Achtziger, Wolfgang; Bendsøe, Martin P; Taylor, John E.
1997-01-01
Problem formulations are presented for the evaluation of upper and lower bounds on the effect of progressive structural degradation. For the purposes of this study, degradation effect is measured by an increase in global structural compliance (flexibility). Thus the stated bounds are given simply...
Bounds on the Effect of Progressive Structural Degradation
DEFF Research Database (Denmark)
Achtziger, W.; Bendsøe, Martin P; Taylor, John E.
1998-01-01
Problem formulations are presented for the evaluation of upper and lower bounds on the effect of progressive structural degradation. For the purposes of this study, degradation effect is measured by an increase in global structural compliance (flexibility). Thus the slated bounds are given simply...
The linear programming bound for binary linear codes
Brouwer, A.E.
1993-01-01
Combining Delsarte's (1973) linear programming bound with the information that certain weights cannot occur, new upper bounds for dmin (n,k), the maximum possible minimum distance of a binary linear code with given word length n and dimension k, are derived.
Criteria for exact qudit universality
International Nuclear Information System (INIS)
Brennen, Gavin K.; O'Leary, Dianne P.; Bullock, Stephen S.
2005-01-01
We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H jk x =(ℎ/2π)Ω(vertical bar k> jk y =(ℎ/2π)Ω(i vertical bar k> jk x,y are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=(ℎ/2π)Ω vertical bar d-1,d-1> 87 Rb and construct an optimal gate sequence using Raman laser pulses
Uniform Bounds for Black--Scholes Implied Volatility
Tehranchi, Michael Rummine
2016-01-01
In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulas for implied volatility at extreme strikes and/or maturities. the Society for Industrial and Applied Mathematics 10.1137/14095248X
Uniform bounds for Black--Scholes implied volatility
Tehranchi, Michael R.
2015-01-01
In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulae for implied volatility at extreme strikes and/or maturities.
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...... with the proposed explicit noise-model extension....
Bounded Intention Planning Revisited
Sievers Silvan; Wehrle Martin; Helmert Malte
2014-01-01
Bounded intention planning provides a pruning technique for optimal planning that has been proposed several years ago. In addition partial order reduction techniques based on stubborn sets have recently been investigated for this purpose. In this paper we revisit bounded intention planning in the view of stubborn sets.
Bounding species distribution models
Directory of Open Access Journals (Sweden)
Thomas J. STOHLGREN, Catherine S. JARNEVICH, Wayne E. ESAIAS,Jeffrey T. MORISETTE
2011-10-01
Full Text Available Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for “clamping” model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART and maximum entropy (Maxent models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5: 642–647, 2011].
Bounding Species Distribution Models
Stohlgren, Thomas J.; Jarnevich, Cahterine S.; Morisette, Jeffrey T.; Esaias, Wayne E.
2011-01-01
Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647, 2011].
Bounds on the pomeron intercept from accelerator data
International Nuclear Information System (INIS)
Luna, E.G.S.; Menon, M.J.
2002-01-01
Taking into account the discrepancies in the pp and p-bar p total cross section data at √8 = 1.8 TeV, we estimate upper and lower bounds for the soft pomeron intercept. We make use of the Donnachie-Landshoff parameterization for the total cross section and derivative analyticity relations in order to calculate the ρ parameter. Individual and global fits to these quantities and tests with the subtraction constant allow to infer α IP (0) = 1.092 as upper bound and α IP (0) = 1.077 as lower bound. (author)
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Nuclear Information System (INIS)
Diabate, S.; Strack, S.
1993-01-01
Tritium released into the environment may be incorporated into organic matter. Organically bound tritium in that case will show retention times in organisms that are considerably longer than those of tritiated water which has significant consequences on dose estimates. This article reviews the most important processes of organically bound tritium production and transport through food networks. Metabolic reactions in plant and animal organisms with tritiated water as a reaction partner are of great importance in this respect. The most important production process, in quantitative terms, is photosynthesis in green plants. The translocation of organically bound tritium from the leaves to edible parts of crop plants should be considered in models of organically bound tritium behavior. Organically bound tritium enters the human body on several pathways, either from the primary producers (vegetable food) or at a higher tropic level (animal food). Animal experiments have shown that the dose due to ingestion of organically bound tritium can be up to twice as high as a comparable intake of tritiated water in gaseous or liquid form. In the environment, organically bound tritium in plants and animals is often found to have higher specific tritium concentrations than tissue water. This is not due to some tritium enrichment effects but to the fact that no equilibrium conditions are reached under natural conditions. 66 refs
International Nuclear Information System (INIS)
Toki, Hiroshi; Yamazaki, Toshimitsu
1989-01-01
The standard method of pionic atom formation does not produce deeply bound pionic atoms. A study is made on the properties of deeply bound pionic atom states by using the standard pion-nucleus optical potential. Another study is made to estimate the cross sections of the formation of ls pionic atom states by various methods. The pion-nucleus optical potential is determined by weakly bound pionic atom states and pion nucleus scattering. Although this potential may not be valid for deeply bound pionic atoms, it should provide some hint on binding energies and level widths of deeply bound states. The width of the ls state comes out to be 0.3 MeV and is well separated from the rest. The charge dependence of the ls state is investigated. The binding energies and the widths increase linearly with Z azbove a Z of 30. The report then discusses various methods to populate deeply bound pionic atoms. In particular, 'pion exchange' reactions are proposed. (n, pπ) reaction is discussed first. The cross section is calculated by assuming the in- and out-going nucleons on-shell and the produced pion in (n1) pionic atom states. Then, (n, dπ - ) cross sections are estimated. (p, 2 Heπ - ) reaction would have cross sections similar to the cross section of (n, dπ - ) reaction. In conclusion, it seems best to do (n, p) experiment on heavy nuclei for deeply bound pionic atom. (Nogami, K.)
Exact axially symmetric galactic dynamos
Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.
2018-05-01
We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.
Generalized surface tension bounds in vacuum decay
Masoumi, Ali; Paban, Sonia; Weinberg, Erick J.
2018-02-01
Coleman and De Luccia (CDL) showed that gravitational effects can prevent the decay by bubble nucleation of a Minkowski or AdS false vacuum. In their thin-wall approximation this happens whenever the surface tension in the bubble wall exceeds an upper bound proportional to the difference of the square roots of the true and false vacuum energy densities. Recently it was shown that there is another type of thin-wall regime that differs from that of CDL in that the radius of curvature grows substantially as one moves through the wall. Not only does the CDL derivation of the bound fail in this case, but also its very formulation becomes ambiguous because the surface tension is not well defined. We propose a definition of the surface tension and show that it obeys a bound similar in form to that of the CDL case. We then show that both thin-wall bounds are special cases of a more general bound that is satisfied for all bounce solutions with Minkowski or AdS false vacua. We discuss the limit where the parameters of the theory attain critical values and the bound is saturated. The bounce solution then disappears and a static planar domain wall solution appears in its stead. The scalar field potential then is of the form expected in supergravity, but this is only guaranteed along the trajectory in field space traced out by the bounce.
Bounds and estimates for the linearly perturbed eigenvalue problem
International Nuclear Information System (INIS)
Raddatz, W.D.
1983-01-01
This thesis considers the problem of bounding and estimating the discrete portion of the spectrum of a linearly perturbed self-adjoint operator, M(x). It is supposed that one knows an incomplete set of data consisting in the first few coefficients of the Taylor series expansions of one or more of the eigenvalues of M(x) about x = 0. The foundations of the variational study of eigen-values are first presented. These are then used to construct the best possible upper bounds and estimates using various sets of given information. Lower bounds are obtained by estimating the error in the upper bounds. The extension of these bounds and estimates to the eigenvalues of the doubly-perturbed operator M(x,y) is discussed. The results presented have numerous practical application in the physical sciences, including problems in atomic physics and the theory of vibrations of acoustical and mechanical systems
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Quantum decay model with exact explicit analytical solution
Marchewka, Avi; Granot, Er'El
2009-01-01
A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.
Bounded Rationality and Budgeting
Ibrahim, Mukdad
2016-01-01
This article discusses the theory of bounded rationality which had been introduced by Herbert Simon in the 1950s. Simon introduced the notion of bounded rationality stating that while decision-makers strive for rationality, they are limited by the effect of the environment, their information process capacity and by the constraints on their information storage and retrieval capabilities. Moreover, this article tries to specifically blend this notion into budgeting, using the foundations of inc...
Tate, Stephen James
2013-10-01
In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
Exact Bremsstrahlung and effective couplings
Energy Technology Data Exchange (ETDEWEB)
Mitev, Vladimir [Institut für Physik, WA THEP, Johannes Gutenberg-Universität Mainz,Staudingerweg 7, 55128 Mainz (Germany); Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Pomoni, Elli [DESY Hamburg, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany); Physics Division, National Technical University of Athens,15780 Zografou Campus, Athens (Greece)
2016-06-13
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N=2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the N=4 SYM ones, we obtain interpolating functions f(g{sup 2}) such that a given N=2 SCFT observable is obtained by replacing in the corresponding N=4 SYM result the coupling constant by f(g{sup 2}). These “exact effective couplings” encode the finite, relative renormalization between the N=2 and the N=4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
High Resolution Thermometry for EXACT
Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.
2000-01-01
High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.
Mass Deformed Exact S-parameter in Conformal Theories
DEFF Research Database (Denmark)
Sannino, Francesco
2010-01-01
the existence of a universal lower bound on the opportunely normalized S parameter and explore its theoretical and phenomenological implications. Our exact results constitute an ideal framework to correctly interpret the lattice studies of the conformal window of strongly interacting theories....... leads to drastically different limiting values of S. Our results apply to any fermion matter representation and can be used as benchmark for the determination of certain relevant properties of the conformal window of any generic vector like gauge theory with fermionic matter. We finally suggest...
Fitness levels with tail bounds for the analysis of randomized search heuristics
DEFF Research Database (Denmark)
Witt, Carsten
2014-01-01
The fitness-level method, also called the method of f-based partitions, is an intuitive and widely used technique for the running time analysis of randomized search heuristics. It was originally defined to prove upper and lower bounds on the expected running time. Recently, upper tail bounds were...
Random trees between two walls: exact partition function
International Nuclear Information System (INIS)
Bouttier, J; Di Francesco, P; Guitter, E
2003-01-01
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labelled by integers representing their position in the target space, with the solid-on-solid constraint that adjacent vertices have labels differing by ±1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p function with constrained periods. These results are used to analyse the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs
Exact analytic solutions generated from stipulated Morse and trigonometric Scarf potentials
International Nuclear Information System (INIS)
Saikia, N; Ahmed, S A S
2011-01-01
The extended transformation method has been applied to the exactly solvable stipulated Morse potential and trigonometric Scarf potential, to generate a set of exactly solvable quantum systems (QSs) in any chosen dimension. Bound state solutions of the exactly solvable potentials are given. The generated QSs are generally of Sturmian form. We also report a system case-specific regrouping technique to convert a Sturmian QS to a normal QS. A second-order application of the transformation method is given. The normalizability of the generated QSs is generally given in Sturmian form.
New bound on MIS and MIN-CDS for a unit ball graph
Directory of Open Access Journals (Sweden)
D.A. Mojdeh
2017-09-01
Full Text Available The size of the maximum independent set (MIS in a graph G is called the independence number. The size of the minimum connected dominating set (MIN-CDS in G is called the connected domination number. The aim of this paper is to determine two better upper bounds of the independence number; dependent on the connected domination number for a unit ball graph. Further, we improve the upper bound to obtain the best bound with respect to the upper bounds obtained thus far.
Bagherinejad, Jafar; Niknam, Azar
2018-03-01
In this paper, a leader-follower competitive facility location problem considering the reactions of the competitors is studied. A model for locating new facilities and determining levels of quality for the facilities of the leader firm is proposed. Moreover, changes in the location and quality of existing facilities in a competitive market where a competitor offers the same goods or services are taken into account. The competitor could react by opening new facilities, closing existing ones, and adjusting the quality levels of its existing facilities. The market share, captured by each facility, depends on its distance to customer and its quality that is calculated based on the probabilistic Huff's model. Each firm aims to maximize its profit subject to constraints on quality levels and budget of setting up new facilities. This problem is formulated as a bi-level mixed integer non-linear model. The model is solved using a combination of Tabu Search with an exact method. The performance of the proposed algorithm is compared with an upper bound that is achieved by applying Karush-Kuhn-Tucker conditions. Computational results show that our algorithm finds near the upper bound solutions in a reasonable time.
Bounds for phase-shifts and deductions in potential scattering
International Nuclear Information System (INIS)
Sidharth, B.G.
1979-01-01
Starting from the radial Schroedinger equation and using the Cauchy-Schwarz inequality, expressions have been derived for bounds for phase-shifts in potential scattering and the deductions are verified in special cases such as the spherically symmetric square-well potential, where exact solutions are already known. (K.B.)
Simple bounds and monotonicity results for finite multi-server exponential tandem queues
Dijk, van N.M.; Wal, van der J.
1989-01-01
Simple and computationally attractive lower and upper bounds are presented for the call congestion such as those representing multi-server loss or delay stations. Numerical computations indicate a potential usefulness of the bounds for quick engineering purposes. The bounds correspond to
Rigorous bounds on the free energy of electron-phonon models
Raedt, Hans De; Michielsen, Kristel
1997-01-01
We present a collection of rigorous upper and lower bounds to the free energy of electron-phonon models with linear electron-phonon interaction. These bounds are used to compare different variational approaches. It is shown rigorously that the ground states corresponding to the sharpest bounds do
Andreev bound states. Some quasiclassical reflections
International Nuclear Information System (INIS)
Lin, Y.; Leggett, A. J.
2014-01-01
We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for “normal” reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it
Andreev bound states. Some quasiclassical reflections
Energy Technology Data Exchange (ETDEWEB)
Lin, Y., E-mail: yiriolin@illinois.edu; Leggett, A. J. [University of Illinois at Urhana-Champaign, Dept. of Physics (United States)
2014-12-15
We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for “normal” reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.
Architecture-independent power bound for vibration energy harvesters
International Nuclear Information System (INIS)
Halvorsen, E; Le, C P; Mitcheson, P D; Yeatman, E M
2013-01-01
The maximum output power of energy harvesters driven by harmonic vibrations is well known for a range of specific harvester architectures. An architecture-independent bound based on the mechanical input-power also exists and gives a strict limit on achievable power with one mechanical degree of freedom, but is a least upper bound only for lossless devices. We report a new theoretical bound on the output power of vibration energy harvesters that includes parasitic, linear mechanical damping while still being architecture independent. This bound greatly improves the previous bound at moderate force amplitudes and is compared to the performance of established harvester architectures which are shown to agree with it in limiting cases. The bound is a hard limit on achievable power with one mechanical degree of freedom and can not be circumvented by transducer or power-electronic-interface design
Sharp bounds for periodic solutions of Lipschitzian differential equations
International Nuclear Information System (INIS)
Zevin, A A
2009-01-01
A general system of Lipschitzian differential equations, containing simultaneously terms without delay and with arbitrary constant and time-varying delays, is considered. For the autonomous case, a lower bound for the period of nonconstant periodic solutions, expressed in the respective supremum Lipschitz constants, is found. For nonautonomous periodic equations, explicit upper bounds for the amplitudes and maximum derivatives of periodic solutions are obtained. For all n ≥ 2, the bounds do not depend on n and, in general, are different from that for n = 1. All the bounds are sharp; they are attained in linear differential equations with piece-wise constant deviating arguments. A relation between the obtained bounds and the sharp bounds in other metrics is established
``Carbon Credits'' for Resource-Bounded Computations Using Amortised Analysis
Jost, Steffen; Loidl, Hans-Wolfgang; Hammond, Kevin; Scaife, Norman; Hofmann, Martin
Bounding resource usage is important for a number of areas, notably real-time embedded systems and safety-critical systems. In this paper, we present a fully automatic static type-based analysis for inferring upper bounds on resource usage for programs involving general algebraic datatypes and full recursion. Our method can easily be used to bound any countable resource, without needing to revisit proofs. We apply the analysis to the important metrics of worst-case execution time, stack- and heap-space usage. Our results from several realistic embedded control applications demonstrate good matches between our inferred bounds and measured worst-case costs for heap and stack usage. For time usage we infer good bounds for one application. Where we obtain less tight bounds, this is due to the use of software floating-point libraries.
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Faust, Sebastian; Mukherjee, Pratyay
2013-01-01
Related key attacks (RKAs) are powerful cryptanalytic attacks where an adversary can change the secret key and observe the effect of such changes at the output. The state of the art in RKA security protects against an a-priori unbounded number of certain algebraic induced key relations, e.......g., affine functions or polynomials of bounded degree. In this work, we show that it is possible to go beyond the algebraic barrier and achieve security against arbitrary key relations, by restricting the number of tampering queries the adversary is allowed to ask for. The latter restriction is necessary......-protocols (including the Okamoto scheme, for instance) are secure even if the adversary can arbitrarily tamper with the prover’s state a bounded number of times and obtain some bounded amount of leakage. Interestingly, for the Okamoto scheme we can allow also independent tampering with the public parameters. We show...
Massive Galileon positivity bounds
de Rham, Claudia; Melville, Scott; Tolley, Andrew J.; Zhou, Shuang-Yong
2017-09-01
The EFT coefficients in any gapped, scalar, Lorentz invariant field theory must satisfy positivity requirements if there is to exist a local, analytic Wilsonian UV completion. We apply these bounds to the tree level scattering amplitudes for a massive Galileon. The addition of a mass term, which does not spoil the non-renormalization theorem of the Galileon and preserves the Galileon symmetry at loop level, is necessary to satisfy the lowest order positivity bound. We further show that a careful choice of successively higher derivative corrections are necessary to satisfy the higher order positivity bounds. There is then no obstruction to a local UV completion from considerations of tree level 2-to-2 scattering alone. To demonstrate this we give an explicit example of such a UV completion.
Higgs mass bounds from a chirally invariant lattice Higgs-Yukawa model with overlap fermions
International Nuclear Information System (INIS)
Gerhold, Philipp; Kallarackal, Jim
2008-10-01
We study the parameter dependence of the Higgs mass in a chirally invariant lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model. Eventually, the aim is to establish upper and lower Higgs mass bounds. Here we present our preliminary results on the lower Higgs mass bound at several selected values for the cutoff and give a brief outlook towards the upper Higgs mass bound. (orig.)
A tighter bound for the self-stabilization time in Hermanʼs algorithm
DEFF Research Database (Denmark)
Feng, Yuan; Zhang, Lijun
2013-01-01
We study the expected self-stabilization time of Hermanʼs algorithm. For N processors the lower bound is 427N2 (0.148N2), and an upper bound of 0.64N2 is presented in Kiefer et al. (2011) [4]. In this paper we give a tighter upper bound 0.521N2. © 2013 Published by Elsevier B.V....
Thermalization Time Bounds for Pauli Stabilizer Hamiltonians
Temme, Kristan
2017-03-01
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of N-qubits, serve as one of the most frequently considered candidates for a self-correcting quantum memory. A spectral gap bound on the Davies generator establishes an upper limit on the life time of such a quantum memory and can be used to estimate the time until the system relaxes to thermal equilibrium when brought into contact with a thermal heat bath. The bound can be shown to behave as {λ ≥ O(N^{-1} exp(-2β overline{ɛ}))}, where {overline{ɛ}} is a generalization of the well known energy barrier for logical operators. Particularly in the low temperature regime we expect this bound to provide the correct asymptotic scaling of the gap with the system size up to a factor of N -1. Furthermore, we discuss conditions and provide scenarios where this factor can be removed and a constant lower bound can be proven.
The Balloon Popping Problem Revisited: Lower and Upper Bounds
Jung, Hyunwoo; Chwa, Kyung-Yong
We consider the balloon popping problem introduced by Immorlica et al. in 2007 [13]. This problem is directly related to the problem of profit maximization in online auctions, where an auctioneer is selling a collection of identical items to anonymous unit-demand bidders. The auctioneer has the full knowledge of bidders’ private valuations for the items and tries to maximize his profit. Compared with the profit of fixed price schemes, the competitive ratio of Immorlica et al.’s algorithm was in the range [1.64, 4.33]. In this paper, we narrow the gap to [1.659, 2].
Upper Bound Performance Estimation for Copper Based Broadband Access
DEFF Research Database (Denmark)
Jensen, Michael; Gutierrez Lopez, Jose Manuel
2012-01-01
of copper based access connections at a household level by using Geographical Information System data. This can be combined with different configurations of DSLAMs distributions, in order to calculate the required number of active equipment points to guarantee certain QoS levels. This method can be used...
Pareto upper confidence bounds algorithms : an empirical study
Drugan, M.M.; Nowé, A.; Manderick, B.
2014-01-01
Many real-world stochastic environments are inherently multi-objective environments with conflicting objectives. The multi-objective multi-armed bandits (MOMAB) are extensions of the classical, i.e. single objective, multi-armed bandits to reward vectors and multi-objective optimisation techniques
Upper bound on the cutoff in lattice electroweak theory
International Nuclear Information System (INIS)
Veselov, A.I.; Zubkov, M.A.
2008-01-01
We investigate numerically lattice Weinberg-Salam model without fermions for realistic values of the fine structure constant and the Weinberg angle. We also analyze the data of the previous numerical investigations of lattice Electroweak theory. We have found that moving along the line of constant physics when the lattice spacing a is decreased, one should leave the physical Higgs phase of the theory at a certain value of a. Our estimate of the minimal value of the lattice spacing is a c = [430 ± 40 GeV] -1 .
The exact solutions of the Schroedinger equation with the Morse potential via Laplace transforms
International Nuclear Information System (INIS)
Chen Gang
2004-01-01
In this Letter, we reduce the second-order differential equation about the one-dimensional Schroedinger equation with the Morse potential reduced to the first-order differential equation in terms of Laplace transforms and then obtain the exact bound state solutions
Exact explicit travelling wave solutions for (n + 1)-dimensional Klein-Gordon-Zakharov equations
International Nuclear Information System (INIS)
Li Jibin
2007-01-01
Using the methods of dynamical systems for the (n + 1)-dimensional KGS nonlinear wave equations, five classes of exact explicit parametric representations of the bounded travelling solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are given
Appell, Jürgen; Merentes Díaz, Nelson José
2013-01-01
This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analytical properties of nonlinear composition operators in spaces of such functions; applications to Fourier analysis, nonlinear integral equations, and boundary value problems. The book is written for non-specialists. Every chapter closes with a list of exercises and open problems.
Exactly soluble dynamics of (p,q) string near macroscopic fundamental strings
International Nuclear Information System (INIS)
Bak, Dongsu; Rey, Soojong; Yee, Houng
2004-01-01
We study dynamics of type-IIB bound-state of a Dirichlet string and n fundamental strings in the background of N fundamental strings. Because of supergravity potential, the bound-state string is pulled to the background fundamental strings, whose motion is described by open string rolling radion field. The string coupling can be made controllably weak and, in the limit 1 2 st n 2 st N, the bound-state energy involved is small compared to the string scale. We thus propose rolling dynamics of open string radion in this system as an exactly solvable analog for rolling dynamics of open string tachyon in decaying D-brane. The dynamics bears a novel feature that the worldsheet electric field increases monotonically to the critical value as the bound-state string falls into the background string. Close to the background string, D string constituent inside the bound-state string decouples from fundamental string constituents. (author)
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
International Nuclear Information System (INIS)
Singh, Parampreet; Wilson-Ewing, Edward
2014-01-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann–Lemaître–Robertson–Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar–Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann–Lemaître–Robertson–Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role. (paper)
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
Singh, Parampreet; Wilson-Ewing, Edward
2014-02-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaître-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaître-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
International Nuclear Information System (INIS)
Helene, O.A.M.
1982-08-01
The determination of the upper limit of peak area in a multi-channel spectra, with a known significance level is discussed. This problem is specially important when the peak area is masked by the background statistical fluctuations. The problem is exactly solved and, thus, the results are valid in experiments with small number of events. The results are submitted to a Monte Carlo test and applied to the 92 Nb beta decay. (Author) [pt
Exact solutions for rotating charged dust
International Nuclear Information System (INIS)
Islam, J.N.
1984-01-01
Earlier work by the author on rotating charged dust is summarized. An incomplete class of exact solutions for differentially rotating charged dust in Newton-Maxwell theory for the equal mass and charge case that was found earlier is completed. A new global exact solution for cylindrically symmetric differentially rotating charged dust in Newton-Maxwell theory is presented. Lastly, a new exact solution for cylindrically symmetric rigidly rotating charged dust in general relativity is given. (author)
Exact, E = 0, classical and quantum solutions for general power-law oscillators
International Nuclear Information System (INIS)
Nieto, M.M.; Daboul, J.
1994-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -γ/r ν , γ > 0 and -∞ 0 (t))] 1/μ , with μ = ν/2 - 1 ≠ 0. For ν > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when ν > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed
Bounds on quantum confinement effects in metal nanoparticles
Blackman, G. Neal; Genov, Dentcho A.
2018-03-01
Quantum size effects on the permittivity of metal nanoparticles are investigated using the quantum box model. Explicit upper and lower bounds are derived for the permittivity and relaxation rates due to quantum confinement effects. These bounds are verified numerically, and the size dependence and frequency dependence of the empirical Drude size parameter is extracted from the model. Results suggest that the common practice of empirically modifying the dielectric function can lead to inaccurate predictions for highly uniform distributions of finite-sized particles.
Sharp Bounds by Probability-Generating Functions and Variable Drift
DEFF Research Database (Denmark)
Doerr, Benjamin; Fouz, Mahmoud; Witt, Carsten
2011-01-01
We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al....... (GECCO 2010) in several respects. First, the upper bound on the expected running time of the most successful quasirandom evolutionary algorithm for the OneMax function is improved from 1.28nln n to 0.982nlnn, which breaks the barrier of nln n posed by coupon-collector processes. Compared to the classical...
Kahneman, Daniel
2002-01-01
The work cited by the Nobel committee was done jointly with the late Amos Tversky (1937-1996) during a long and unusually close collaboration. Together, we explored the psychology of intuitive beliefs and choices and examined their bounded rationality. This essay presents a current perspective on the three major topics of our joint work: heuristics of judgment, risky choice, and framing effects. In all three domains we studied intuitions - thoughts and preferences that come to mind quickly an...
Bounded Satisfiability for PCTL
Bertrand, Nathalie; Fearnley, John; Schewe, Sven
2012-01-01
While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability, as well as its finite model property, are long standing open problems. While general satisfiability is an intriguing challenge from a purely theoretical point of view, we argue that general solutions would not be of interest to practitioners: such solutions could be too big to be implementable or even infinite. Inspired by bounded synthesis techniques, we turn to the more appl...
Extremal black holes as exact string solutions
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution
Exact Solutions for Einstein's Hyperbolic Geometric Flow
International Nuclear Information System (INIS)
He Chunlei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow
On exact solutions of scattering problems
International Nuclear Information System (INIS)
Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.
1982-01-01
Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Exact, almost and delayed fault detection
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....
OPRA capacity bounds for selection diversity over generalized fading channels
Hanif, Muhammad Fainan
2014-05-01
Channel side information at the transmitter can increase the average capacity by enabling optimal power and rate adaptation. The resulting optimal power and rate adaptation (OPRA) capacity rarely has a closed-form analytic expression. In this paper, lower and upper bounds on OPRA capacity for selection diversity scheme are presented. These bounds hold for variety of fading channels including log-normal and generalized Gamma distributed models and have very simple analytic expressions for easy evaluation even for kth best path selection. Some selected numerical results show that the newly proposed bounds closely approximate the actual OPRA capacity. © 2014 IEEE.
Finite energy bounds for $\\piN$ scattering
Grassberger, P; Schwela, D
1974-01-01
Upper bounds on energy averaged pi N cross sections are given. Using low energy data and data from pi N backward scattering and NN to pi pi annihilation, it is found that sigma /sub tot/
Extrinsic Isoperimetric Analysis on Submanifolds with Curvatures bounded from below
DEFF Research Database (Denmark)
Markvorsen, Steen; Palmer, Vicente
2010-01-01
and on the radial part of the intrinsic unit normals at the boundaries of the extrinsic spheres, respectively. In the same vein we also establish lower bounds on the mean exit time for Brownian motions in the extrinsic balls, i.e. lower bounds for the time it takes (on average) for Brownian particles to diffuse......We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial part of the mean curvature vector field...... within the extrinsic ball from a given starting point before they hit the boundary of the extrinsic ball. In those cases, where we may extend our analysis to hold all the way to infinity, we apply a capacity comparison technique to obtain a sufficient condition for the submanifolds to be parabolic, i...
Generalized Hofmann quantum process fidelity bounds for quantum filters
Sedlák, Michal; Fiurášek, Jaromír
2016-04-01
We propose and investigate bounds on the quantum process fidelity of quantum filters, i.e., probabilistic quantum operations represented by a single Kraus operator K . These bounds generalize the Hofmann bounds on the quantum process fidelity of unitary operations [H. F. Hofmann, Phys. Rev. Lett. 94, 160504 (2005), 10.1103/PhysRevLett.94.160504] and are based on probing the quantum filter with pure states forming two mutually unbiased bases. Determination of these bounds therefore requires far fewer measurements than full quantum process tomography. We find that it is particularly suitable to construct one of the probe bases from the right eigenstates of K , because in this case the bounds are tight in the sense that if the actual filter coincides with the ideal one, then both the lower and the upper bounds are equal to 1. We theoretically investigate the application of these bounds to a two-qubit optical quantum filter formed by the interference of two photons on a partially polarizing beam splitter. For an experimentally convenient choice of factorized input states and measurements we study the tightness of the bounds. We show that more stringent bounds can be obtained by more sophisticated processing of the data using convex optimization and we compare our methods for different choices of the input probe states.
Asymptotic Sharpness of Bounds on Hypertrees
Directory of Open Access Journals (Sweden)
Lin Yi
2017-08-01
Full Text Available The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most (nk−1$\\left( {\\matrix{n \\cr {k - 1} } } \\right$ edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.
Universal bounds on current fluctuations.
Pietzonka, Patrick; Barato, Andre C; Seifert, Udo
2016-05-01
For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.
Energy Technology Data Exchange (ETDEWEB)
Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States); Shenker, Stephen H. [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA (United States); Stanford, Douglas [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States)
2016-08-17
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ{sub L}≤2πk{sub B}T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Exact optics - III. Schwarzschild's spectrograph camera revised
Willstrop, R. V.
2004-03-01
Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.
Quaternionic formulation of the exact parity model
Energy Technology Data Exchange (ETDEWEB)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-02-28
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.
Quaternionic formulation of the exact parity model
International Nuclear Information System (INIS)
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-01-01
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs
An exactly solvable three-dimensional nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Morris, J. R.
2013-01-01
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states
An exactly solvable three-dimensional nonlinear quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Partial transpose of random quantum states: Exact formulas and meanders
Energy Technology Data Exchange (ETDEWEB)
Fukuda, Motohisa [Zentrum Mathematik, M5, Technische Universitaet Muenchen, Boltzmannstrasse 3, 85748 Garching (Germany); Sniady, Piotr [Zentrum Mathematik, M5, Technische Universitaet Muenchen, Boltzmannstrasse 3, 85748 Garching (Germany); Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-956 Warszawa (Poland); Institute of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw (Poland)
2013-04-15
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by approximating the matrix of trace 1 by the Wishart matrix of random trace) and shown to be the semicircular distribution or the free difference of two free Poisson distributions, depending on how dimensions of the concerned spaces grow. Our use of Wishart matrices gives exact combinatorial formulas for the moments of the partial transpose of the random state. We find three natural asymptotic regimes in terms of geodesics on the permutation groups. Two of them correspond to the above two cases; the third one turns out to be a new matrix model for the meander polynomials. Moreover, we prove the convergence to the semicircular distribution together with its extreme eigenvalues under weaker assumptions, and show large deviation bound for the latter.
Partial transpose of random quantum states: Exact formulas and meanders
Fukuda, Motohisa; Śniady, Piotr
2013-04-01
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by approximating the matrix of trace 1 by the Wishart matrix of random trace) and shown to be the semicircular distribution or the free difference of two free Poisson distributions, depending on how dimensions of the concerned spaces grow. Our use of Wishart matrices gives exact combinatorial formulas for the moments of the partial transpose of the random state. We find three natural asymptotic regimes in terms of geodesics on the permutation groups. Two of them correspond to the above two cases; the third one turns out to be a new matrix model for the meander polynomials. Moreover, we prove the convergence to the semicircular distribution together with its extreme eigenvalues under weaker assumptions, and show large deviation bound for the latter.
An Exact Confidence Region in Multivariate Calibration
Mathew, Thomas; Kasala, Subramanyam
1994-01-01
In the multivariate calibration problem using a multivariate linear model, an exact confidence region is constructed. It is shown that the region is always nonempty and is invariant under nonsingular transformations.
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
Exact solutions, numerical relativity and gravitational radiation
International Nuclear Information System (INIS)
Winicour, J.
1986-01-01
In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
On exactly soluble model in quantum electrodynamics
International Nuclear Information System (INIS)
Bogolubov, N.N.; Shumovsky, A.S.; Fam Le Kien
1984-01-01
Equations of motion describing the dynamics of three-level atom of ladder type interacting with two modes of quantized radiation field are solved exactly. Evolution of level population and photon rumbers under different unitial conditions is irvestigated
Determination of bounds on failure probability in the presence of ...
Indian Academy of Sciences (India)
In particular, fuzzy set theory provides a more rational framework for ..... indicating that the random variations inT andO2 do not affect failure probability significantly. ... The upper-bound for PF shown in figure 6 can be used in decision-making.
Lower bounds for protrusion replacement by counting equivalence classes
Jansen, B.M.P.; Wulms, J.J.H.M.; Guo, J.; Hermelin, D.
2017-01-01
Garnero et al. [SIAM J. Discrete Math. 2015, 29(4):1864-1894] recently introduced a framework based on dynamic programming to make applications of the protrusion replacement technique constructive and to obtain explicit upper bounds on the involved constants. They show that for several graph
Lower bounds for protrusion replacement by counting equivalence classes
Jansen, B.M.P.; Wulms, J.J.H.M.
2016-01-01
Garnero et al. [SIAM J. Discrete Math. 2015, 29(4):1864--1894] recently introduced a framework based on dynamic programming to make applications of the protrusion replacement technique constructive and to obtain explicit upper bounds on the involved constants. They show that for several graph
Optimal portfolio selection for cashflows with bounded capital at risk
Vyncke, D.; Goovaerts, M.J.; Dhaene, J.L.M.; Vanduffel, S.
2005-01-01
We consider a continuous-time Markowitz type portfolio problem that consists of minimizing the discounted cost of a given cash-fl ow under the constraint of a restricted Capital at Risk. In a Black-Scholes setting, upper and lower bounds are obtained by means of simple analytical expressions that
International Nuclear Information System (INIS)
Ikhdair, S.M.; Sever, R.
2007-01-01
The exact solution of the one-dimensional Klein-Gordon equation of the PT-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Analytic progress on exact lattice chiral symmetry
International Nuclear Information System (INIS)
Kikukawa, Y.
2002-01-01
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)
Exact and approximate multiple diffraction calculations
International Nuclear Information System (INIS)
Alexander, Y.; Wallace, S.J.; Sparrow, D.A.
1976-08-01
A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation
International Nuclear Information System (INIS)
Ritchie, Burke
2006-01-01
The Hamiltonian for Dirac's second-order equation depends nonlinearly on the potential V and the energy E. For this reason the magnetic contribution to the Hamiltonian for s-waves, which has a short range, is attractive for a repulsive Coulomb potential (V>0) and repulsive for an attractive Coulomb potential (V 2 . Usually solutions are found in the regime E=mc 2 +ε , where except for high Z, ε 2 . Here it is shown that for V>0 the attractive magnetic term and the linear repulsive term combine to support a bound state near E=0.5mc 2 corresponding to a binding energy E b =-ε =0.5mc 2
Dynamic Garment Simulation based on Hybrid Bounding Volume Hierarchy
Directory of Open Access Journals (Sweden)
Zhu Dongyong
2016-12-01
Full Text Available In order to solve the computing speed and efficiency problem of existing dynamic clothing simulation, this paper presents a dynamic garment simulation based on a hybrid bounding volume hierarchy. It firstly uses MCASG graph theory to do the primary segmentation for a given three-dimensional human body model. And then it applies K-means cluster to do the secondary segmentation to collect the human body’s upper arms, lower arms, upper legs, lower legs, trunk, hip and woman’s chest as the elementary units of dynamic clothing simulation. According to different shapes of these elementary units, it chooses the closest and most efficient hybrid bounding box to specify these units, such as cylinder bounding box and elliptic cylinder bounding box. During the process of constructing these bounding boxes, it uses the least squares method and slices of the human body to get the related parameters. This approach makes it possible to use the least amount of bounding boxes to create close collision detection regions for the appearance of the human body. A spring-mass model based on a triangular mesh of the clothing model is finally constructed for dynamic simulation. The simulation result shows the feasibility and superiority of the method described.
Quasi-exactly solvable relativistic soft-core Coulomb models
Energy Technology Data Exchange (ETDEWEB)
Agboola, Davids, E-mail: davagboola@gmail.com; Zhang, Yao-Zhong, E-mail: yzz@maths.uq.edu.au
2012-09-15
By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.
Exact method for numerically analyzing a model of local denaturation in superhelically stressed DNA
International Nuclear Information System (INIS)
Fye, R.M.; Benham, C.J.
1999-01-01
Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method. The algorithm implementing our technique requires O(N 2 ) operations and O(N) memory to analyze a DNA domain containing N base pairs. However, to analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm is constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations, and has an analytically bounded error. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (M<0.05N) for kilobase length molecules under physiologically relevant conditions. Calculations are performed on the superhelical pBR322 DNA sequence to test the accuracy of the method. With no free parameters in the model, the locations and extents of local denaturation predicted by this analysis are in quantitatively precise agreement with in vitro experimental measurements
Quantum quenches to the attractive one-dimensional Bose gas: exact results
Directory of Open Access Journals (Sweden)
Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler
2016-09-01
Full Text Available We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.
Diffraction scattering of strongly bound system
International Nuclear Information System (INIS)
Kuzmichev, V.E.
1982-04-01
The scattering of a hadron on a strongly bound system of two hadrons (dihadron) is considered in the high-energy limit for the relative hadron-dihadron motion. The dihadron scatterer motion and the internal interaction are included in our consideration. It is shown that only small values of the internal transfer momentum of dihadron particles bring the principal contribution to the three-particle propagator in eikonal approximation. On the basis of the exact analytical solution of the integral equation for the total Green function the scattering amplitude is derived. It is shown that the scattering amplitude contains only single, double, and triple scattering terms. The three new terms to the Glauber formula for the total cross section are obtained. These terms decrease both the true total hadron-hadron cross section and the screening correction. (orig.)
Estimation variance bounds of importance sampling simulations in digital communication systems
Lu, D.; Yao, K.
1991-01-01
In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.
Exact parallel maximum clique algorithm for general and protein graphs.
Depolli, Matjaž; Konc, Janez; Rozman, Kati; Trobec, Roman; Janežič, Dušanka
2013-09-23
A new exact parallel maximum clique algorithm MaxCliquePara, which finds the maximum clique (the fully connected subgraph) in undirected general and protein graphs, is presented. First, a new branch and bound algorithm for finding a maximum clique on a single computer core, which builds on ideas presented in two published state of the art sequential algorithms is implemented. The new sequential MaxCliqueSeq algorithm is faster than the reference algorithms on both DIMACS benchmark graphs as well as on protein-derived product graphs used for protein structural comparisons. Next, the MaxCliqueSeq algorithm is parallelized by splitting the branch-and-bound search tree to multiple cores, resulting in MaxCliquePara algorithm. The ability to exploit all cores efficiently makes the new parallel MaxCliquePara algorithm markedly superior to other tested algorithms. On a 12-core computer, the parallelization provides up to 2 orders of magnitude faster execution on the large DIMACS benchmark graphs and up to an order of magnitude faster execution on protein product graphs. The algorithms are freely accessible on http://commsys.ijs.si/~matjaz/maxclique.
Hung, Tran Loc; Giang, Le Truong
2016-01-01
Using the Stein-Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.
Models for light QCD bound states
International Nuclear Information System (INIS)
LaCourse, D.P.
1992-01-01
After a brief overview of Regge, tower, and heavy-quark experimental data, this thesis examines two massless wave equations relevant to quark bound states. We establish general conditions on the Lorentz scalar and Lorentz vector potentials which yield arbitrary leading Regge trajectories for the case of circular classical motion. A semi-classical approximation which includes radial motion reproduces remarkably well the exact solutions. Conditions for tower structure are examined, and found to be incompatible with conditions which give a Nambu stringlike Regge slope. The author then proposes a generalization of the usual potential model of quark bound states in which the confining flux tube is a dynamical object carrying both angular momentum and energy. The Q bar Q-string system with spinless quarks is quantized using an implicit operator technique and the resulting relativistic wave equation is solved. For heavy quarks the usual Schroedinger valence-quark model is recovered. The Regge slope with light quarks agree with the classical rotating-string result and is significantly larger and the effects of short-range forces are also considered. A relativistic generalization of the quantized flux tube model predicts the glueball ground state mass to be √3/α' ≅ 1.9 GeV where α' is the normal Regge slope. The groundstate as well as excited levels like considerably above the expectations of previous models and also above various proposed experimental candidates. The glueball Regge slope is only about three-eighths that for valence quark hadrons. A semi-classical calculation of the Regge slope is in good agreement with a numerically exact value
Homoclinic orbits around spinning black holes. I. Exact solution for the Kerr separatrix
International Nuclear Information System (INIS)
Levin, Janna; Perez-Giz, Gabe
2009-01-01
For equatorial Kerr orbits, we show that each separatrix between bound and plunging geodesics is a homoclinic orbit--an orbit that asymptotes to an energetically-bound, unstable circular orbit. We derive exact expressions for these trajectories in terms of elementary functions. We also clarify the formal connection between the separatrix and zoom-whirl orbits and show that, contrary to popular belief, zoom-whirl behavior is not intrinsically a near-separatrix phenomenon. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. Although they refer to geodesic motion, the exact solutions for the Kerr separatrix could be useful for analytic or numerical studies of eccentric transitions from orbital to plunging motion under the dissipative effects of gravitational radiation.
Capacity bounds for parallel IM-DD optical wireless channels
Chaaban, Anas; Rezki, Zouheir; Alouini, Mohamed-Slim
2016-01-01
A system consisting of parallel intensity-modulation direct-detection optical wireless channels with a total average intensity constraint is studied. Capacity upper and lower bounds for this system are derived. If channel-state information is available at the transmitter, the bounds have to be optimized with respect to intensity allocation over the parallel channels. The optimization of the lower bound is non-convex, however, the Karush-Kuhn-Tucker conditions can be used to find a list of possible solutions one of which is optimal. The optimal solution can then be found by an exhaustive search algorithm, which is computationally expensive. To overcome this, we propose a low-complexity intensity allocation algorithm which is nearly optimal. The optimized capacity lower bound coincides with the capacity at high signal-to-noise ratio. © 2016 IEEE.
Bounds on the moment of inertia of nonrotating neutron stars
International Nuclear Information System (INIS)
Sabbadini, A.G.; Hartle, J.B.
1977-01-01
Upper and lower bounds are placed on the moments of inertia of relativistic, spherical, perfect fluid neutron stars assuming that the pressure p and density p are positive and that (dp/drho) is positive. Bounds are obtained (a) for the moment of inertia of a star with given mass and radius, (b) for the moment of inertia of neutron stars for which the equation of state is known below a given density rho/sub omicron/and (c) for the mass-moment of inertia relation for stars whose equation of state is known below a given density rho/sub omicron/The bounds are optimum ones in the sense that there always exists a configuration consistent with the assumptions having a moment of inertia equal to that of the bound. The implications of the results for the maximum mass of slowly rotating neutron stars are discussed
Capacity bounds for parallel IM-DD optical wireless channels
Chaaban, Anas
2016-07-26
A system consisting of parallel intensity-modulation direct-detection optical wireless channels with a total average intensity constraint is studied. Capacity upper and lower bounds for this system are derived. If channel-state information is available at the transmitter, the bounds have to be optimized with respect to intensity allocation over the parallel channels. The optimization of the lower bound is non-convex, however, the Karush-Kuhn-Tucker conditions can be used to find a list of possible solutions one of which is optimal. The optimal solution can then be found by an exhaustive search algorithm, which is computationally expensive. To overcome this, we propose a low-complexity intensity allocation algorithm which is nearly optimal. The optimized capacity lower bound coincides with the capacity at high signal-to-noise ratio. © 2016 IEEE.
Bounds on the Capacity of Weakly constrained two-dimensional Codes
DEFF Research Database (Denmark)
Forchhammer, Søren
2002-01-01
Upper and lower bounds are presented for the capacity of weakly constrained two-dimensional codes. The maximum entropy is calculated for two simple models of 2-D codes constraining the probability of neighboring 1s as an example. For given models of the coded data, upper and lower bounds...... on the capacity for 2-D channel models based on occurrences of neighboring 1s are considered....
Bounding approaches to system identification
Norton, John; Piet-Lahanier, Hélène; Walter, Éric
1996-01-01
In response to the growing interest in bounding error approaches, the editors of this volume offer the first collection of papers to describe advances in techniques and applications of bounding of the parameters, or state variables, of uncertain dynamical systems. Contributors explore the application of the bounding approach as an alternative to the probabilistic analysis of such systems, relating its importance to robust control-system design.
Bound state and localization of excitation in many-body open systems
Cui, H. T.; Shen, H. Z.; Hou, S. C.; Yi, X. X.
2018-04-01
We study the exact bound state and time evolution for single excitations in one-dimensional X X Z spin chains within a non-Markovian reservoir. For the bound state, a common feature is the localization of single excitations, which means the spontaneous emission of excitations into the reservoir is prohibited. Exceptionally, the pseudo-bound state can be found, for which the single excitation has a finite probability of emission into the reservoir. In addition, a critical energy scale for bound states is also identified, below which only one bound state exists, and it is also the pseudo-bound state. The effect of quasirandom disorder in the spin chain is also discussed; such disorder induces the single excitation to locate at some spin sites. Furthermore, to display the effect of bound state and disorder on the preservation of quantum information, the time evolution of single excitations in spin chains is studied exactly. An interesting observation is that the excitation can stay at its initial location with high probability only when the bound state and disorder coexist. In contrast, when either one of them is absent, the information of the initial state can be erased completely or becomes mixed. This finding shows that the combination of bound state and disorder can provide an ideal mechanism for quantum memory.
Integrals of the motion and exact solutions of the problem of two dispersing delta-wells
International Nuclear Information System (INIS)
Man'ko, V.I.; Chikhachev, A.S.
1998-01-01
An exact solution is analyzed for the analogs of bound and scattering states in a nonstationary quantum mechanical system whose potential has the form of two dispersing delta-wells. For the delta-potentials explicit (in the form of operator kernels) expressions are found for the integrals of the motion that depend on time and transform to the known integrals of the motion for a free quantum particle as the interaction force with the potential approaches zero
Market access through bound tariffs
DEFF Research Database (Denmark)
Sala, Davide; Yalcin, Erdal; Schröder, Philipp
2010-01-01
on the risk that exporters face in destination markets. The present paper formalizes the underlying interaction of risk, fixed export costs and firms' market entry decisions based on techniques known from the real options literature; doing so we highlight the important role of bound tariffs at the extensive...... margin of trade. We find that bound tariffs are more effective with higher risk destination markets, that a large binding overhang may still command substantial market access, and that reductions in bound tariffs generate effective market access even when bound rates are above current and longterm...
Market Access through Bound Tariffs
DEFF Research Database (Denmark)
Sala, Davide; Schröder, Philipp J.H.; Yalcin, Erdal
on the risk that exporters face in destination markets. The present paper formalizes the underlying interaction of risk, fixed export costs and firms' market entry decisions based on techniques known from the real options literature; doing so we highlight the important role of bound tariffs at the extensive...... margin of trade. We find that bound tariffs are more effective with higher risk destination markets, that a large binding overhang may still command substantial market access, and that reductions in bound tariffs generate effective market access even when bound rates are above current and long...
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Classes of exact Einstein Maxwell solutions
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Quivers of Bound Path Algebras and Bound Path Coalgebras
Directory of Open Access Journals (Sweden)
Dr. Intan Muchtadi
2010-09-01
Full Text Available bras and coalgebras can be represented as quiver (directed graph, and from quiver we can construct algebras and coalgebras called path algebras and path coalgebras. In this paper we show that the quiver of a bound path coalgebra (resp. algebra is the dual quiver of its bound path algebra (resp. coalgebra.
A tight excess risk bound via a unified PAC-Bayesian-Rademacher-Shtarkov-MDL complexity
P.D. Grünwald (Peter); N.A. Mehta (Nishant)
2017-01-01
htmlabstractWe present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper bounded in terms of data-independent Rademacher
Combinatorial bounds on the α-divergence of univariate mixture models
Nielsen, Frank
2017-06-20
We derive lower- and upper-bounds of α-divergence between univariate mixture models with components in the exponential family. Three pairs of bounds are presented in order with increasing quality and increasing computational cost. They are verified empirically through simulated Gaussian mixture models. The presented methodology generalizes to other divergence families relying on Hellinger-type integrals.
Efficiency bounds for nonequilibrium heat engines
International Nuclear Information System (INIS)
Mehta, Pankaj; Polkovnikov, Anatoli
2013-01-01
We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. -- Highlights: ► Derived efficiency bounds for heat engines working with a single reservoir. ► Analyzed both ergodic and non-ergodic engines. ► Showed that non-ergodic engines can be more efficient. ► Extended fundamental thermodynamic relation to arbitrary nonequilibrium processes
Exactly solvable birth and death processes
International Nuclear Information System (INIS)
Sasaki, Ryu
2009-01-01
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q x (with x being the population) corresponding to the q-Racah polynomial.
Product differentiation under bounded rationality
Vermeulen, B.; Poutré, La J.A.; Kok, de A.G.; Pyka, A.; Handa, H.; Ishibuchi, H.; Ong, Y.-S.; Tan, K.-C.
2015-01-01
We study product differentiation equilibria and dynamics on the Salop circle under bounded rationality. Due to bounded rationality, firms tend to agglomerate in pairs. Upon adding a second tier of component suppliers, downstream assemblers may escape pairwise horizontal agglomeration. Moreover, we
Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.
1993-01-01
The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).
Exactly solvable energy-dependent potentials
International Nuclear Information System (INIS)
Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.
2009-01-01
We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.
Exact relativistic cylindrical solution of disordered radiation
International Nuclear Information System (INIS)
Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.
1976-05-01
A source free disordered distribution of electromagnetic radiation is considered in Einstein' theory, and a time independent exact solution with cylindrical symmetry is obtained. The gravitation and pressure effects of the radiation alone are sufficient to give the distribution an equilibrium. A finite maximum concentration is found on the axis of symmetry, and decreases monotonically to zero outwards. Timelike and null geodesics are discussed
New exact solutions for two nonlinear equations
International Nuclear Information System (INIS)
Wang Quandi; Tang Minying
2008-01-01
In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended
Exact Optimum Design of Segmented Thermoelectric Generators
Directory of Open Access Journals (Sweden)
M. Zare
2016-01-01
Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.
Exactly marginal deformations from exceptional generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-01-27
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Exactly solvable position dependent mass schroedinger equation
International Nuclear Information System (INIS)
Koc, R.; Tuetuencueler, H.; Koercuek, E.
2002-01-01
Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...
Metabolism of organically bound tritium
International Nuclear Information System (INIS)
Travis, C.C.
1984-01-01
The classic methodology for estimating dose to man from environmental tritium ignores the fact that organically bound tritium in foodstuffs may be directly assimilated in the bound compartment of tissues without previous oxidation. We propose a four-compartment model consisting of a free body water compartment, two organic compartments, and a small, rapidly metabolizing compartment. The utility of this model lies in the ability to input organically bound tritium in foodstuffs directly into the organic compartments of the model. We found that organically bound tritium in foodstuffs can increase cumulative total body dose by a factor of 1.7 to 4.5 times the free body water dose alone, depending on the bound-to-loose ratio of tritium in the diet. Model predictions are compared with empirical measurements of tritium in human urine and tissue samples, and appear to be in close agreement. 10 references, 4 figures, 3 tables
Dissipative motion perturbation theory and exact solutions
International Nuclear Information System (INIS)
Lodder, J.J.
1976-06-01
Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion
Unitarity bounds on angular distribution in multiparticle production - II
International Nuclear Information System (INIS)
Divakaran, P.P.; Kugler, M.; Soffer, J.
1976-01-01
Upper bounds which follow from unitarity are derived for the angular distribution of the detected particle C in the inclusive process AB→C+anything at a finite energy, in terms of the corresponding elastic amplitudes for a fixed value of the forward inelastic cross-section and for a fixed value of the total inelastic cross-section for the production of C. In comparison with the pp→p+anything data at 24GeV/c, some improvement on previous bounds is observed [fr
Phase-space dynamics of opposition control in wall-bounded turbulent flows
Hwang, Yongyun; Ibrahim, Joseph; Yang, Qiang; Doohan, Patrick
2017-11-01
The phase-space dynamics of wall-bounded shear flow in the presence of opposition control is explored by examining the behaviours of a pair of nonlinear equilibrium solutions (exact coherent structures), edge state and life time of turbulence at low Reynolds numbers. While the control modifies statistics and phase-space location of the edge state and the lower-branch equilibrium solution very little, it is also found to regularise the periodic orbit on the edge state by reverting a period-doubling bifurcation. Only the upper-branch equilibrium solution and mean turbulent state are significantly modified by the control, and, in phase space, they gradually approach the edge state on increasing the control gain. It is found that this behaviour results in a significant reduction of the life time of turbulence, indicating that the opposition control significantly increases the probability that the turbulent solution trajectory passes through the edge state. Finally, it is shown that the opposition control increases the critical Reynolds number of the onset of the equilibrium solutions, indicating its capability of transition delay. This work is sponsored by the Engineering and Physical Sciences Research Council (EPSRC) in the UK (EP/N019342/1).
Curvature bound from gravitational catalysis
Gies, Holger; Martini, Riccardo
2018-04-01
We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.
The Exact Limit of Some Cubic Towers
DEFF Research Database (Denmark)
Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut
2017-01-01
Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as go...
Efficiently computing exact geodesic loops within finite steps.
Xin, Shi-Qing; He, Ying; Fu, Chi-Wing
2012-06-01
Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.
A gauged baby Skyrme model and a novel BPS bound
International Nuclear Information System (INIS)
Adam, C; Naya, C; Sanchez-Guillen, J; Wereszczynski, A
2013-01-01
The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. Its action functional consist of a potential term, a kinetic term quadratic in derivatives (the 'nonlinear sigma model term') and the Skyrme term quartic in first derivatives. The limiting case of vanishing sigma model term (the so-called BPS baby Skyrme model) is known to support exact soliton solutions saturating a BPS bound which exists for this model. Further, the BPS model has infinitely many symmetries and conservation laws. Recently it was found that the gauged version of the BPS baby Skyrme model with gauge group U(1) and the usual Maxwell term, too, has a BPS bound and BPS solutions saturating this bound. This BPS bound is determined by a superpotential which has to obey a superpotential equation, in close analogy to the situation in supergravity. Further, the BPS bound and the corresponding BPS solitons only may exist for potentials such that the superpotential equation has a global solution. We also briefly describe some properties of soliton solutions.
Combining Alphas via Bounded Regression
Directory of Open Access Journals (Sweden)
Zura Kakushadze
2015-11-01
Full Text Available We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications, typically, there is insufficient history to compute a sample covariance matrix (SCM for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples.
Improved Range Searching Lower Bounds
DEFF Research Database (Denmark)
Larsen, Kasper Green; Nguyen, Huy L.
2012-01-01
by constructing a hard input set and query set, and then invoking Chazelle and Rosenberg's [CGTA'96] general theorem on the complexity of navigation in the pointer machine. For the group model, we show that input sets and query sets that are hard for range reporting in the pointer machine (i.e. by Chazelle...... and Rosenberg's theorem), are also hard for dynamic range searching in the group model. This theorem allows us to reuse decades of research on range reporting lower bounds to immediately obtain a range of new group model lower bounds. Amongst others, this includes an improved lower bound for the fundamental...
Entanglement negativity bounds for fermionic Gaussian states
Eisert, Jens; Eisler, Viktor; Zimborás, Zoltán
2018-04-01
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.
A conditionally exactly solvable generalization of the inverse square root potential
Energy Technology Data Exchange (ETDEWEB)
Ishkhanyan, A.M., E-mail: aishkhanyan@gmail.com [Institute for Physical Research, NAS of Armenia, Ashtarak 0203 (Armenia); Armenian State Pedagogical University, Yerevan 0010 (Armenia); Institute of Physics and Technology, National Research Tomsk Polytechnic University, Tomsk 634050 (Russian Federation)
2016-11-25
We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum. - Highlights: • We present a conditionally exactly solvable singular potential for 1D Schrödinger equation. • Each of the two fundamental solutions is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. • The exact equation for the energy spectrum is written using two Hermite functions that do not reduce to polynomials.
Exact WKB analysis and cluster algebras
International Nuclear Information System (INIS)
Iwaki, Kohei; Nakanishi, Tomoki
2014-01-01
We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras. Under a continuous deformation of the potential of the Schrödinger equation on a compact Riemann surface, the Stokes graph may change the topology. We call this phenomenon the mutation of Stokes graphs. Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon. We show that the Voros symbols mutate as variables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes automorphisms associated with periods of cluster algebras. The paper also includes an extensive introduction of the exact WKB analysis and the surface realization of cluster algebras for nonexperts. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
Exact computation of the 9-j symbols
International Nuclear Information System (INIS)
Lai Shantao; Chiu Jingnan
1992-01-01
A useful algebraic formula for the 9-j symbol has been rewritten for convenient use on a computer. A simple FORTRAN program for the exact computation of 9-j symbols has been written for the VAX with VMS version V5,4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9-j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9-j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3-j, 6-j and 9-j symbols are available through electronic mail upon request. (orig.)
Lattice sigma models with exact supersymmetry
International Nuclear Information System (INIS)
Simon Catterall; Sofiane Ghadab
2004-01-01
We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and twisted versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and exhibit no fermion doubling. In the two and four dimensional theories we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions. (author)
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
New exact solutions of the Dirac equation
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.
1980-01-01
Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Exact diagonalization library for quantum electron models
Iskakov, Sergei; Danilov, Michael
2018-04-01
We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.
Exact coherent structures in an asymptotically reduced description of parallel shear flows
Beaume, Cédric; Knobloch, Edgar; Chini, Gregory P.; Julien, Keith
2015-02-01
A reduced description of shear flows motivated by the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow (Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501) is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for a sinusoidal, body-forced shear flow. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced equations provide a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows.
Exact coherent structures in an asymptotically reduced description of parallel shear flows
International Nuclear Information System (INIS)
Beaume, Cédric; Knobloch, Edgar; Chini, Gregory P; Julien, Keith
2015-01-01
A reduced description of shear flows motivated by the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow (Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501) is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for a sinusoidal, body-forced shear flow. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced equations provide a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows. (paper)
ON COMPUTING UPPER LIMITS TO SOURCE INTENSITIES
International Nuclear Information System (INIS)
Kashyap, Vinay L.; Siemiginowska, Aneta; Van Dyk, David A.; Xu Jin; Connors, Alanna; Freeman, Peter E.; Zezas, Andreas
2010-01-01
A common problem in astrophysics is determining how bright a source could be and still not be detected in an observation. Despite the simplicity with which the problem can be stated, the solution involves complicated statistical issues that require careful analysis. In contrast to the more familiar confidence bound, this concept has never been formally analyzed, leading to a great variety of often ad hoc solutions. Here we formulate and describe the problem in a self-consistent manner. Detection significance is usually defined by the acceptable proportion of false positives (background fluctuations that are claimed as detections, or Type I error), and we invoke the complementary concept of false negatives (real sources that go undetected, or Type II error), based on the statistical power of a test, to compute an upper limit to the detectable source intensity. To determine the minimum intensity that a source must have for it to be detected, we first define a detection threshold and then compute the probabilities of detecting sources of various intensities at the given threshold. The intensity that corresponds to the specified Type II error probability defines that minimum intensity and is identified as the upper limit. Thus, an upper limit is a characteristic of the detection procedure rather than the strength of any particular source. It should not be confused with confidence intervals or other estimates of source intensity. This is particularly important given the large number of catalogs that are being generated from increasingly sensitive surveys. We discuss, with examples, the differences between these upper limits and confidence bounds. Both measures are useful quantities that should be reported in order to extract the most science from catalogs, though they answer different statistical questions: an upper bound describes an inference range on the source intensity, while an upper limit calibrates the detection process. We provide a recipe for computing upper
Exactly and completely integrable nonlinear dynamical systems
International Nuclear Information System (INIS)
Leznov, A.N.; Savel'ev, M.V.
1987-01-01
The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions
International Nuclear Information System (INIS)
Cannoni, Mirco
2015-01-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x * = m χ /T * . The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y 0 , is where the maximum departure of the WIMPs abundance Y from the thermal value Y 0 is reached. For each mass m χ and total annihilation cross section left angle σ ann υ r right angle, the temperature x * and the actual WIMPs abundance Y(x * ) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x * . The matching of the two abundances at x * is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)
Cannoni, Mirco
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.
Exact Theory of Compressible Fluid Turbulence
Drivas, Theodore; Eyink, Gregory
2017-11-01
We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.
Evidence for a bound on the lifetime of de Sitter space
International Nuclear Information System (INIS)
Freivogel, Ben; Lippert, Matthew
2008-01-01
Recent work has suggested a surprising new upper bound on the lifetime of de Sitter vacua in string theory. The bound is parametrically longer than the Hubble time but parametrically shorter than the recurrence time. We investigate whether the bound is satisfied in a particular class of de Sitter solutions, the KKLT vacua. Despite the freedom to make the supersymmetry breaking scale exponentially small, which naively would lead to extremely stable vacua, we find that the lifetime is always less than about exp(10 22 ) Hubble times, in agreement with the proposed bound. This result, however, is contingent on several estimates and assumptions; in particular, we rely on a conjectural upper bound on the Euler number of the Calabi-Yau fourfolds used in KKLT compactifications.
Capacity Bounds on the Downlink of Symmetric, Multi-Relay, Single-Receiver C-RAN Networks
Directory of Open Access Journals (Sweden)
Shirin Saeedi Bidokhti
2017-11-01
Full Text Available The downlink of symmetric Cloud Radio Access Networks (C-RANs with multiple relays and a single receiver is studied. Lower and upper bounds are derived on the capacity. The lower bound is achieved by Marton’s coding, which facilitates dependence among the multiple-access channel inputs. The upper bound uses Ozarow’s technique to augment the system with an auxiliary random variable. The bounds are studied over scalar Gaussian C-RANs and are shown to meet and characterize the capacity for interesting regimes of operation.
Schulz, Marc Daniel; Dusuel, Sébastien; Vidal, Julien
2016-11-01
We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.
On functions of bounded semivariation
Czech Academy of Sciences Publication Activity Database
Monteiro, Giselle Antunes
2015-01-01
Roč. 40, č. 2 (2015), s. 233-276 ISSN 0147-1937 Institutional support: RVO:67985840 Keywords : semivariation * functions of bounded variation * regulated functions Subject RIV: BA - General Mathematics http://projecteuclid.org/euclid.rae/1491271216
Computational Lower Bounds Using Diagonalization
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 14; Issue 7. Computational Lower Bounds Using Diagonalization - Languages, Turing Machines and Complexity Classes. M V Panduranga Rao. General Article Volume 14 Issue 7 July 2009 pp 682-690 ...
Analytic quantum bounds on Bell inequalities
International Nuclear Information System (INIS)
Filipp, S.; Svozil, K.
2005-01-01
Full text: Can realism be combined with the quantum world? An important tool to investigate in this question are Bell's inequalities and violations thereof - they represent a cornerstone of our present understanding of quantum mechanics and therefore the description of nature. Here we present a simple algebraic method to calculate violations for any measurement arrangements that are maximal in the sense that quantum mechanics does not allow a stronger violation. Having two or more polarization analyzers available and a source producing photon-pairs in arbitrary polarization states Bell-type inequalities tell us which probabilities for measuring the polarization in particular directions are viable in a deterministic theory. Quantum mechanics does not obey these rules, but yields a violation of these inequalities. The questions is to what extent the inequalities are violated. Making use of a min-max principle analytical expressions can be found for the 'fine structure' of the maximal violations of arbitrary Bell-like inequalities, i. e. the upper bound reachable by any state when the analyzers measure in given directions. Knowing these bounds is useful for experimental tests of the validity of quantum mechanics and can serve as a prerequisite to answer the even more pressing question, why no stronger violation has been observed until now. (author)
Dynamic bounds coupled with Monte Carlo simulations
Energy Technology Data Exchange (ETDEWEB)
Rajabalinejad, M., E-mail: M.Rajabalinejad@tudelft.n [Faculty of Civil Engineering, Delft University of Technology, Delft (Netherlands); Meester, L.E. [Delft Institute of Applied Mathematics, Delft University of Technology, Delft (Netherlands); Gelder, P.H.A.J.M. van; Vrijling, J.K. [Faculty of Civil Engineering, Delft University of Technology, Delft (Netherlands)
2011-02-15
For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.
International Nuclear Information System (INIS)
Yahiaoui, S.-A.; Bentaiba, M.
2011-01-01
We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)
Quasi-exact solutions of nonlinear differential equations
Kudryashov, Nikolay A.; Kochanov, Mark B.
2014-01-01
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.
Angular-momentum nonclassicality by breaking classical bounds on statistics
Energy Technology Data Exchange (ETDEWEB)
Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, E-28040 Madrid (Spain); Rivas, Angel [Departamento de Fisica Teorica I, Facultad de Ciencias Fisicas, Universidad Complutense, E-28040 Madrid (Spain)
2011-10-15
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are very general and independent of other typical quantum signatures of nonclassical behavior such as sub-Poissonian statistics, squeezing, or oscillatory statistics, being insensitive to the nonclassical behavior displayed by other variables.
Robust bounds on risk-sensitive functionals via Renyi divergence
Atar, Rami; Chowdhary, Kamaljit; Dupuis, Paul
2013-01-01
We extend the duality between exponential integrals and relative entropy to a variational formula for exponential integrals involving the Renyi divergence. This formula characterizes the dependence of risk-sensitive functionals and related quantities determined by tail behavior to perturbations in the underlying distributions, in terms of the Renyi divergence. The characterization gives rise to upper and lower bounds that are meaningful for all values of a large deviation scaling parameter, a...
Learning with Generalization Capability by Kernel Methods of Bounded Complexity
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Sanguineti, M.
2005-01-01
Roč. 21, č. 3 (2005), s. 350-367 ISSN 0885-064X R&D Projects: GA AV ČR 1ET100300419 Institutional research plan: CEZ:AV0Z10300504 Keywords : supervised learning * generalization * model complexity * kernel methods * minimization of regularized empirical errors * upper bounds on rates of approximate optimization Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2005
Bounds for the propagation speed of combustion flames
International Nuclear Information System (INIS)
Fort, Joaquim; Campos, Daniel; Gonzalez, Josep R; Velayos, Joaquim
2004-01-01
We focus on a combustion model for premixed flames based on two coupled equations determining the spatial dynamics of temperature and fuel density. We rewrite these equations as a classical reaction-diffusion model, so that we can apply some known methods for the prediction of lower and upper bounds to the front speed. The predictions are compared to simulations, which show that our new bounds substantially improve those following from the linearization method, used in the previous work of Fort et al (2000 J. Phys. A: Math. Gen. 33 6953). Radiative losses lead to pulses rather than fronts. We find a bound for their speed which (in contrast to the linearization one) correctly predicts the order of magnitude of the flame speed
Reduced conservatism in stability robustness bounds by state transformation
Yedavalli, R. K.; Liang, Z.
1986-01-01
This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.
Bounds for the propagation speed of combustion flames
Energy Technology Data Exchange (ETDEWEB)
Fort, Joaquim [Departament de FIsica, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain); Campos, Daniel [Grup de FIsica EstadIstica, Departament de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Spain); Gonzalez, Josep R [Grup de Mecanica de Fluids, Departament d' Enginyeria Mecanica, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain); Velayos, Joaquim [Grup de Mecanica de Fluids, Departament d' Enginyeria Mecanica, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-23
We focus on a combustion model for premixed flames based on two coupled equations determining the spatial dynamics of temperature and fuel density. We rewrite these equations as a classical reaction-diffusion model, so that we can apply some known methods for the prediction of lower and upper bounds to the front speed. The predictions are compared to simulations, which show that our new bounds substantially improve those following from the linearization method, used in the previous work of Fort et al (2000 J. Phys. A: Math. Gen. 33 6953). Radiative losses lead to pulses rather than fronts. We find a bound for their speed which (in contrast to the linearization one) correctly predicts the order of magnitude of the flame speed.
Model independent bounds on magnetic moments of Majorana neutrinos
International Nuclear Information System (INIS)
Bell, Nicole F.; Gorchtein, Mikhail; Ramsey-Musolf, Michael J.; Vogel, Petr; Wang, Peng
2006-01-01
We analyze the implications of neutrino masses for the magnitude of neutrino magnetic moments. By considering electroweak radiative corrections to the neutrino mass, we derive model-independent naturalness upper bounds on neutrino magnetic moments, μ ν , generated by physics above the electroweak scale. For Dirac neutrinos, the bound is several orders of magnitude more stringent than present experimental limits. However, for Majorana neutrinos the magnetic moment contribution to the mass is Yukawa suppressed. The bounds we derive for magnetic moments of Majorana neutrinos are weaker than present experimental limits if μ ν is generated by new physics at ∼1 TeV, and surpass current experimental sensitivity only for new physics scales >10-100 TeV. The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles
Bootstrap bound for conformal multi-flavor QCD on lattice
Energy Technology Data Exchange (ETDEWEB)
Nakayama, Yu [Department of Physics, Rikkyo University,Toshima, Tokyo 171-8501 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo,5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583 (Japan)
2016-07-08
The recent work by Iha et al. shows an upper bound on mass anomalous dimension γ{sub m} of multi-flavor massless QCD at the renormalization group fixed point from the conformal bootstrap in SU(N{sub F}){sub V} symmetric conformal field theories under the assumption that the fixed point is realizable with the lattice regularization based on staggered fermions. We show that the almost identical but slightly stronger bound applies to the regularization based on Wilson fermions (or domain wall fermions) by studying the conformal bootstrap in SU(N{sub f}){sub L}×SU(N{sub f}){sub R} symmetric conformal field theories. For N{sub f}=8, our bound implies γ{sub m}<1.31 to avoid dangerously irrelevant operators that are not compatible with the lattice symmetry.
Quantum Bocce: Magnon–magnon collisions between propagating and bound states in 1D spin chains
International Nuclear Information System (INIS)
Longo, Paolo; Greentree, Andrew D.; Busch, Kurt; Cole, Jared H.
2013-01-01
The dynamics of two magnons in a Heisenberg spin chain under the influence of a non-uniform magnetic field is investigated by means of a numerical wave-function-based approach using a Holstein–Primakoff transformation. The magnetic field is localized in space such that it supports exactly one single-particle bound state. We study the interaction of this bound mode with an incoming spin wave and the interplay between transmittance, energy and momentum matching. We find analytic criteria for maximizing the interconversion between propagating single-magnon modes and true propagating two-magnon states. The manipulation of bound and propagating magnons is an essential step towards quantum magnonics.
Computing a Non-trivial Lower Bound on the Joint Entropy between Two Images
Energy Technology Data Exchange (ETDEWEB)
Perumalla, Kalyan S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-03-01
In this report, a non-trivial lower bound on the joint entropy of two non-identical images is developed, which is greater than the individual entropies of the images. The lower bound is the least joint entropy possible among all pairs of images that have the same histograms as those of the given images. New algorithms are presented to compute the joint entropy lower bound with a computation time proportional to S log S where S is the number of histogram bins of the images. This is faster than the traditional methods of computing the exact joint entropy with a computation time that is quadratic in S .
Computing variational bounds for flow through random aggregates of Spheres
International Nuclear Information System (INIS)
Berryman, J.G.
1983-01-01
Known formulas for variational bounds on Darcy's constant for slow flow through porous media depend on two-point and three-poiint spatial correlation functions. Certain bounds due to Prager and Doi depending only a two-point correlation functions have been calculated for the first time for random aggregates of spheres with packing fractions (eta) up to eta = 0.64. Three radial distribution functions for hard spheres were tested for eta up to 0.49: (1) the uniform distribution or ''well-stirred approximation,'' (2) the Percus Yevick approximation, and (3) the semi-empirical distribution of Verlet and Weis. The empirical radial distribution functions of Benett andd Finney were used for packing fractions near the random-close-packing limit (eta/sub RCP/dapprox.0.64). An accurate multidimensional Monte Carlo integration method (VEGAS) developed by Lepage was used to compute the required two-point correlation functions. The results show that Doi's bounds are preferred for eta>0.10 while Prager's bounds are preferred for eta>0.10. The ''upper bounds'' computed using the well-stirred approximation actually become negative (which is physically impossible) as eta increases, indicating the very limited value of this approximation. The other two choices of radial distribution function give reasonable results for eta up to 0.49. However, these bounds do not decrease with eta as fast as expected for large eta. It is concluded that variational bounds dependent on three-point correlation functions are required to obtain more accurate bounds on Darcy's constant for large eta
Exact string theory model of closed timelike curves and cosmological singularities
International Nuclear Information System (INIS)
Johnson, Clifford V.; Svendsen, Harald G.
2004-01-01
We study an exact model of string theory propagating in a space-time containing regions with closed timelike curves (CTCs) separated from a finite cosmological region bounded by a big bang and a big crunch. The model is an nontrivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of α ' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by timelike curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in general relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-big bang cosmological scenarios
Energy Technology Data Exchange (ETDEWEB)
Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature x{sub *} = m{sub χ}/T{sub *}. The point x., which coincides with the stationary point of the equation for the quantity Δ = Y-Y{sub 0}, is where the maximum departure of the WIMPs abundance Y from the thermal value Y{sub 0} is reached. For each mass m{sub χ} and total annihilation cross section left angle σ{sub ann}υ{sub r} right angle, the temperature x{sub *} and the actual WIMPs abundance Y(x{sub *}) are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval x ≥ x{sub *}. The matching of the two abundances at x{sub *} is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1.2 % in the case of S-wave and P-wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics. (orig.)
Bound states of the Dirac equation with some physical potentials by the Nikiforov-Uvarov method
Energy Technology Data Exchange (ETDEWEB)
Setare, Mohammad R; Haidari, S [Department of Physics, University of Kurdistan, Pasdaran Avenue, Sanandaj (Iran, Islamic Republic of)], E-mail: rezakord@ipm.ir, E-mail: heidary.somayeh@gmail.com
2010-01-15
Exact analytical solutions for the s-wave Dirac equation with the reflectionless-type, Rosen-Morse and Manning-Rosen potentials are obtained, under the condition of spin symmetry. We obtained bound state energy eigenvalues and corresponding spinor wave function in the framework of the Nikiforov-Uvarov (NU) method.
An exact solution in Einstein-Cartan
International Nuclear Information System (INIS)
Roque, W.L.
1982-01-01
The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Exactly soluble problems in statistical mechanics
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem
A cluster expansion for bound three-alpha particles as a three-body problem
International Nuclear Information System (INIS)
Osman, A.
1981-08-01
A three-body model is proposed to study the nuclear bound states. The nucleus is described as a bound state of three clusters. A cluster expansion is introduced for the three cluster bound state problem. The present integral equations are treated by simple approximate solutions, which lead to effective potentials by using the present cluster expansion. The 12 C nucleus is described as a three-alpha particle bound state. The binding energy of 12 C is calculated numerically using the present cluster expansion as bound three-alpha clusters. The present three-body cluster expansion calculations are very near to the exact three-body calculations using separable potentials. The present theoretical calculations are in good agreement with the experimental measurements. (author)
Exact and Heuristic Algorithms for Runway Scheduling
Malik, Waqar A.; Jung, Yoon C.
2016-01-01
This paper explores the Single Runway Scheduling (SRS) problem with arrivals, departures, and crossing aircraft on the airport surface. Constraints for wake vortex separations, departure area navigation separations and departure time window restrictions are explicitly considered. The main objective of this research is to develop exact and heuristic based algorithms that can be used in real-time decision support tools for Air Traffic Control Tower (ATCT) controllers. The paper provides a multi-objective dynamic programming (DP) based algorithm that finds the exact solution to the SRS problem, but may prove unusable for application in real-time environment due to large computation times for moderate sized problems. We next propose a second algorithm that uses heuristics to restrict the search space for the DP based algorithm. A third algorithm based on a combination of insertion and local search (ILS) heuristics is then presented. Simulation conducted for the east side of Dallas/Fort Worth International Airport allows comparison of the three proposed algorithms and indicates that the ILS algorithm performs favorably in its ability to find efficient solutions and its computation times.
Exact model reduction of combinatorial reaction networks
Directory of Open Access Journals (Sweden)
Fey Dirk
2008-08-01
Full Text Available Abstract Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.
Exact combinatorial approach to finite coagulating systems
Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr
2018-02-01
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
Exact simulation of max-stable processes.
Dombry, Clément; Engelke, Sebastian; Oesting, Marco
2016-06-01
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown-Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed.
Exact collisional moments for plasma fluid theories
Pfefferle, David; Hirvijoki, Eero; Lingam, Manasvi
2017-10-01
The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities, and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas, that relies on the Chapman-Enskog method, as well as to deriving collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rate.
Explicitly broken supersymmetry with exactly massless moduli
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Freedman, Daniel Z. [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); Center for Theoretical Physics and Department of Mathematics,Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Zhao, Yue [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-16
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a supergravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Simulation bounds for system availability
International Nuclear Information System (INIS)
Tietjen, G.L.; Waller, R.A.
1976-01-01
System availability is a dominant factor in the practicality of nuclear power electrical generating plants. A proposed model for obtaining either lower bounds or interval estimates on availability uses observed data on ''n'' failure-to-repair cycles of the system to estimate the parameters in the time-to-failure and time-to-repair models. These estimates are then used in simulating failure/repair cycles of the system. The availability estimate is obtained for each of 5000 samples of ''n'' failure/repair cycles to form a distribution of estimates. Specific percentile points of those simulated distributions are selected as lower simulation bounds or simulation interval bounds for the system availability. The method is illustrated with operational data from two nuclear plants for which an exponential time-to-failure and a lognormal time-to-repair are assumed
An exact approach for aggregated formulations
DEFF Research Database (Denmark)
Gamst, Mette; Spoorendonk, Simon
Aggregating formulations is a powerful approach for transforming problems into taking more tractable forms. Aggregated formulations can, though, have drawbacks: some information may get lost in the aggregation and { put in a branch-and-bound context { branching may become very di_cult and even....... The paper includes general considerations on types of problems for which the method is of particular interest. Furthermore, we prove the correctness of the procedure and consider how to include extensions such as cutting planes and advanced branching strategies....
Scaling Limits and Generic Bounds for Exploration Processes
Bermolen, Paola; Jonckheere, Matthieu; Sanders, Jaron
2017-12-01
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.
Volume dependence of N-body bound states
König, Sebastian; Lee, Dean
2018-04-01
We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.
Relativistic bound state wave functions
International Nuclear Information System (INIS)
Micu, L.
2005-01-01
A particular method of writing the bound state wave functions in relativistic form is applied to the solutions of the Dirac equation with confining potentials in order to obtain a relativistic description of a quark antiquark bound system representing a given meson. Concerning the role of the effective constituent in the present approach we first observe that without this additional constituent we couldn't expand the bound state wave function in terms of products of free states. Indeed, we notice that if the wave function depends on the relative coordinates only, all the expansion coefficients would be infinite. Secondly we remark that the effective constituent enabled us to give a Lorentz covariant meaning to the potential energy of the bound system which is now seen as the 4th component of a 4-momentum. On the other side, by relating the effective constituent to the quantum fluctuations of the background field which generate the binding, we provided a justification for the existence of some spatial degrees of freedom accompanying the interaction potential. These ones, which are quite unusual in quantum mechanics, in our model are the natural consequence of the the independence of the quarks and can be seen as the effect of the imperfect cancellation of the vector momenta during the quantum fluctuations. Related with all these we remark that the adequate representation for the relativistic description of a bound system is the momentum representation, because of the transparent and easy way of writing the conservation laws and the transformation properties of the wave functions. The only condition to be fulfilled is to find a suitable way to take into account the potential energy of the bound system. A particular feature of the present approach is that the confining forces are due to a kind of glue where both quarks are embedded. This recalls other bound state models where the wave function is factorized in terms of constituent wave functions and the confinement is
International Nuclear Information System (INIS)
Zouzou, S.
1986-01-01
In the framework of simple non-relativistic potential models, we examine the system consisting of two quarks and two antiquarks with equal or unequal masses. We search for possible bound states below the threshold for the spontaneous dissociation into two mesons. We solve the four body problem by empirical or systematic variational methods and we include the virtual meson-meson components of the wave function. With standard two-body potentials, there is no proliferation of multiquarks. With unequal quark masses, we obtain however exotic (anti Qanti Qqq) bound states with a baryonic antidiquark-quark-quark structure very analogous to the heavy flavoured (Q'qq) baryons. (orig.)
Bound entanglement and local realism
International Nuclear Information System (INIS)
Kaszlikowski, Dagomir; Zukowski, Marek; Gnacinski, Piotr
2002-01-01
We show using a numerical approach, which gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et al. [Phys. Rev. Lett. 82, 5385 (1999)] admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation
Analysis of a convenient information bound for general quantum channels
International Nuclear Information System (INIS)
O'Loan, C J
2007-01-01
Open questions from Sarovar and Milburn (2006 J. Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for quasi-classical models their bound is achievable and they gave a necessary and sufficient condition for positive operator-valued measures (POVMs) attaining this bound. They asked (i) whether their bound is attainable more generally (ii) whether explicit expressions for optimal POVMs can be derived from the attainability condition. We show that the symmetric logarithmic derivative (SLD) quantum information is less than or equal to the SM bound, i.e., H(θ) ≤ C Y (θ) and we find conditions for equality. As the Fisher information is less than or equal to the SLD quantum information, i.e., F M (θ) ≤ H(θ), we can deduce when equality holds in F M (θ) ≤ C Y (θ). Equality does not hold for all channels. As a consequence, the attainability condition cannot be used to test for optimal POVMs for all channels. These results are extended to multi-parameter channels
International Nuclear Information System (INIS)
Potter, W.E.
2005-01-01
The exact probability density function for paired counting can be expressed in terms of modified Bessel functions of integral order when the expected blank count is known. Exact decision levels and detection limits can be computed in a straightforward manner. For many applications perturbing half-integer corrections to Gaussian distributions yields satisfactory results for decision levels. When there is concern about the uncertainty for the expected value of the blank count, a way to bound the errors of both types using confidence intervals for the expected blank count is discussed. (author)
Some exact solutions to the translation-invariant N-body problem
International Nuclear Information System (INIS)
Hall, R.L.
1978-01-01
It is shown that Schroedinger's equation for a translation-invariant system consisting of N particles with arbitrary masses interacting via Hooke's law pair potentials with the same coupling constant can be solved exactly; explicit solutions are found for the case N = 3. Exact solutions are also found explicitly for the translation-invariant problem in which a particle with mass m 0 interacts with N identical particles of mass m 1 via Hooke's law pair potential with coupling constant k 0 2 , and the identical particles interact with each other via Hooke's law pair potentials with coupling constant k 1 2 . The latter solution provides a basis problem for an energy lower-bound method for translation-invariant atom-like systems. (author)
International Nuclear Information System (INIS)
Tyson, Jon
2009-01-01
Matrix monotonicity is used to obtain upper bounds on minimum-error distinguishability of arbitrary ensembles of mixed quantum states. This generalizes one direction of a two-sided bound recently obtained by the author [J. Tyson, J. Math. Phys. 50, 032106 (2009)]. It is shown that the previously obtained special case has unique properties.
Exact solutions for some discrete models of the Boltzmann equation
International Nuclear Information System (INIS)
Cabannes, H.; Hong Tiem, D.
1987-01-01
For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr
Semiclassical bounds in magnetic bottles
Czech Academy of Sciences Publication Activity Database
Barseghyan, Diana; Exner, Pavel; Kovařík, H.; Weidl, T.
2016-01-01
Roč. 28, č. 1 (2016), s. 1650002 ISSN 0129-055X R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : magnetic Laplacian * discrete spectrum * eigenvalue bounds Subject RIV: BE - Theoretical Physics Impact factor: 1.426, year: 2016
Positivity bounds for Sivers functions
International Nuclear Information System (INIS)
Kang Zhongbo; Soffer, Jacques
2011-01-01
We generalize a positivity constraint derived initially for parity-conserving processes to the parity-violating ones, and use it to derive non-trivial bounds on several Sivers functions, entering in the theoretical description of single spin asymmetry for various processes.
Bound states of 'dressed' particles
International Nuclear Information System (INIS)
Shirokov, M.I.
1994-01-01
A new approach to the problem of bound states in relativistic quantum field theories is suggested. It uses the creation - destruction operators of 'dresses' particles which have been granted by Faddeev's (1963) 'dressing' formalism. Peculiarities of the proposed approach as compared to the known ones are discussed. 8 refs. (author)
Quantum lower bound for sorting
Shi, Yaoyun
2000-01-01
We prove that \\Omega(n log(n)) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1) comparisons must be made. The previous known lower bound is \\Omega(n).
Unconditional lower bounds against advice
Buhrman, H.; Fortnow, L.; Santhanam, R.
2009-01-01
We show several unconditional lower bounds for exponential time classes against polynomial time classes with advice, including: (1) For any constant c, NEXP not in P^{NP[n^c]} (2) For any constant c, MAEXP not in MA/n^c (3) BPEXP not in BPP/n^{o(1)}. It was previously unknown even whether NEXP in
Exact Solution and Exotic Fluid in Cosmology
Directory of Open Access Journals (Sweden)
Phillial Oh
2012-09-01
Full Text Available We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed.
A search for exact superstring vacua
Peterman, Andreas; Zichichi, Antonino
1994-01-01
We investigate $2d$ sigma-models with a $2+N$ dimensional Minkowski signature target space metric and Killing symmetry, specifically supersymmetrized, and see under which conditions they might lead to corresponding exact string vacua. It appears that the issue relies heavily on the properties of the vector $M_{\\mu}$, a reparametrization term, which needs to possess a definite form for the Weyl invariance to be satisfied. We give, in the $n = 1$ supersymmetric case, two non-renormalization theorems from which we can relate the $u$ component of $M_{\\mu}$ to the $\\beta^G_{uu}$ function. We work out this $(u,u)$ component of the $\\beta^G$ function and find a non-vanishing contribution at four loops. Therefore, it turns out that at order $\\alpha^{\\prime 4}$, there are in general non-vanishing contributions to $M_u$ that prevent us from deducing superstring vacua in closed form.
Interference-exact radiative transfer equation
DEFF Research Database (Denmark)
Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani
2017-01-01
Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....
Exact iterative reconstruction for the interior problem
International Nuclear Information System (INIS)
Zeng, Gengsheng L; Gullberg, Grant T
2009-01-01
There is a trend in single photon emission computed tomography (SPECT) that small and dedicated imaging systems are becoming popular. For example, many companies are developing small dedicated cardiac SPECT systems with different designs. These dedicated systems have a smaller field of view (FOV) than a full-size clinical system. Thus data truncation has become the norm rather than the exception in these systems. Therefore, it is important to develop region of interest (ROI) reconstruction algorithms using truncated data. This paper is a stepping stone toward this direction. This paper shows that the common generic iterative image reconstruction algorithms are able to exactly reconstruct the ROI under the conditions that the convex ROI is fully sampled and the image value in a sub-region within the ROI is known. If the ROI includes a sub-region that is outside the patient body, then the conditions can be easily satisfied.
On truncations of the exact renormalization group
Morris, T R
1994-01-01
We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
Exact solutions to operator differential equations
International Nuclear Information System (INIS)
Bender, C.M.
1992-01-01
In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Exactly soluble QCD and confinement of quarks
International Nuclear Information System (INIS)
Rusakov, B.
1997-01-01
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation [B. Rusakov, Phys. Lett. B 398 (1997) 331]. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no area law in the non-compact theory. (orig.)
Binding energies of two deltas bound states
International Nuclear Information System (INIS)
Sato, Hiroshi; Saito, Koichi.
1982-06-01
Bound states of the two-deltas system are investigated by employing the realistic one boson exchange potential. It is found that there exist many bound states in each isospin channel and also found that the tensor interaction plays important role in producing these bound states. Relationship between these bound states and dibaryon resonances is discussed. (J.P.N.)
Exact classical scaling formalism for nonreactive processes
International Nuclear Information System (INIS)
DePristo, A.E.
1981-01-01
A general nonreactive collision system is considered with internal molecular variables (p, r) and/or (I, theta) of arbitrary dimensions and relative translational variables (P, R) of three or less dimensions. We derive an exact classical scaling formalism which relates the collisional change in any function of molecular variables directly to the initial values of these variables. The collision dynamics is then described by an explicit function of the initial point in the internal molecular phase space, for a fixed point in the relative translational phase space. In other words, the systematic variation of the internal molecular properties (e.g., actions and average internal kinetic energies) is given as a function of the initial internal action-angle variables. A simple three term approximation to the exact formalism is derived, the natural variables of which are the internal action I and internal linear momenta p. For the final average internal kinetic energies T, the result is T-T/sup( 0 ) = α+βp/sup( 0 )+γI/sup( 0 ), where the superscripted ''0'' indicates the initial value. The parameters α, β, and γ in this scaling theory are directly related to the moments of the change in average internal kinetic energy. Utilizing a very limited number of input moments generated from classical trajectory calculations, the scaling can be used to predict the entire distribution of final internal variables as a function of initial internal actions and linear momenta. Initial examples for atom--collinear harmonic oscillator collision systems are presented in detail, with the scaling predictions (e.g., moments and quasiclassical histogram transition probabilities) being generally very good to excellent quantitatively
New exact solutions of the mBBM equation
International Nuclear Information System (INIS)
Zhang Zhe; Li Desheng
2013-01-01
The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)
A. Vandevelde; J.A. Hoogeveen; C.A.J. Hurkens (Cor); J.K. Lenstra (Jan Karel)
2005-01-01
htmlabstractThe multiprocessor flow-shop is the generalization of the flow-shop in which each machine is replaced by a set of identical machines. As finding a minimum-length schedule is NP-hard, we set out to find good lower and upper bounds. The lower bounds are based on relaxation of the
Vandevelde, A.; Hoogeveen, J.A.; Hurkens, C.A.J.; Lenstra, J.K.
2005-01-01
The multiprocessor flow-shop is the generalization of the flow-shop in which each machine is replaced by a set of identical machines. As finding a minimum-length schedule is NP-hard, we set out to find good lower and upper bounds. The lower bounds are based on relaxation of the capacities of all
Jargalsaikhan, Bolor
Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out
Exact solitary waves of the Korteveg - de Vries - Burgers equation
Kudryashov, N. A.
2004-01-01
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.
Congenital eversion of upper eyelids: Case report and management
Directory of Open Access Journals (Sweden)
Maheshwari Rajat
2006-01-01
Full Text Available Congenital eversion of the upper eyelids is a rare condition, the exact cause of which remains unknown. It is more frequently associated with Down′s syndrome and black babies. If diagnosed early and treated properly, the condition can be managed without surgery. We report a case of congenital bilateral severe upper eyelid eversion in a normal infant, born by vaginal delivery. The case was conservatively managed by lubricants, antibiotics and eyelid patching.
Exploring L1 model space in search of conductivity bounds for the MT problem
Wheelock, B. D.; Parker, R. L.
2013-12-01
Geophysical inverse problems of the type encountered in electromagnetic techniques are highly non-unique. As a result, any single inverted model, though feasible, is at best inconclusive and at worst misleading. In this paper, we use modified inversion methods to establish bounds on electrical conductivity within a model of the earth. Our method consists of two steps, each making use of the 1-norm in model regularization. Both 1-norm minimization problems are framed without approximation as non-negative least-squares (NNLS) problems. First, we must identify a parsimonious set of regions within the model for which upper and lower bounds on average conductivity will be sought. This is accomplished by minimizing the 1-norm of spatial variation, which produces a model with a limited number of homogeneous regions; in fact, the number of homogeneous regions will never be greater than the number of data, regardless of the number of free parameters supplied. The second step establishes bounds for each of these regions with pairs of inversions. The new suite of inversions also uses a 1-norm penalty, but applied to the conductivity values themselves, rather than the spatial variation thereof. In the bounding step we use the 1-norm of our model parameters because it is proportional to average conductivity. For a lower bound on average conductivity, the 1-norm within a bounding region is minimized. For an upper bound on average conductivity, the 1-norm everywhere outside a bounding region is minimized. The latter minimization has the effect of concentrating conductance into the bounding region. Taken together, these bounds are a measure of the uncertainty in the associated region of our model. Starting with a blocky inverse solution is key in the selection of the bounding regions. Of course, there is a tradeoff between resolution and uncertainty: an increase in resolution (smaller bounding regions), results in greater uncertainty (wider bounds). Minimization of the 1-norm of
A symmetric Roos bound for linear codes
Duursma, I.M.; Pellikaan, G.R.
2006-01-01
The van Lint–Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound
Exact generating function for 2-convex polygons
International Nuclear Information System (INIS)
James, W R G; Jensen, I; Guttmann, A J
2008-01-01
Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their 'concavity index', m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure based on series expansions. We then proceed to prove this result for the more general case of the full anisotropic generating function, in which steps in the x and y directions are distinguished. In doing so, we develop tools that would allow for the case m > 2 to be studied
Bounds for percolation thresholds on directed and undirected graphs
Hamilton, Kathleen; Pryadko, Leonid
2015-03-01
Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.
Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume
1998-01-01
We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.
Bounds and maximum principles for the solution of the linear transport equation
International Nuclear Information System (INIS)
Larsen, E.W.
1981-01-01
Pointwise bounds are derived for the solution of time-independent linear transport problems with surface sources in convex spatial domains. Under specified conditions, upper bounds are derived which, as a function of position, decrease with distance from the boundary. Also, sufficient conditions are obtained for the existence of maximum and minimum principles, and a counterexample is given which shows that such principles do not always exist
Large Deviation Bounds for a Polling System with Two Queues and Multiple Servers
Wei, Fen
2004-01-01
In this paper, we present large deviation bounds for a discrete-time polling system consisting of two-par-allel queues and m servers. The arrival process in each queue is an arbitrary, and possibly correlated, stochastic process. Each server (serves) independently serves the two queues according to a Bernoulli service schedule. Using large deviation techniques, we analyze the tail behavior of the stationary distribution of the queue length processes, and derive upper and lower bounds of the b...
The ultimate security bounds of quantum key distribution protocols
International Nuclear Information System (INIS)
Nikolopoulos, G.M.; Alber, G.
2005-01-01
Full text: Quantum key distribution (QKD) protocols exploit quantum correlations in order to establish a secure key between two legitimate users. Recent work on QKD has revealed a remarkable link between quantum and secret correlations. In this talk we report on recent results concerning the ultimate upper security bounds of various QKD schemes (i.e., the maximal disturbance up to which the two legitimate users share quantum correlations) under the assumption of general coherent attacks. In particular, we derive an analytic expression for the ultimate upper security bound of QKD schemes that use two mutually unbiased bases. As long as the two legitimate users focus on the sifted key and treat each pair of data independently during the post processing, our results are valid for arbitrary dimensions of the information carriers. The bound we have derived is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is also discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions, however, such equivalence is generally no longer valid. (author)
Distortion-Rate Bounds for Distributed Estimation Using Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Nihar Jindal
2008-03-01
Full Text Available We deal with centralized and distributed rate-constrained estimation of random signal vectors performed using a network of wireless sensors (encoders communicating with a fusion center (decoder. For this context, we determine lower and upper bounds on the corresponding distortion-rate (D-R function. The nonachievable lower bound is obtained by considering centralized estimation with a single-sensor which has all observation data available, and by determining the associated D-R function in closed-form. Interestingly, this D-R function can be achieved using an estimate first compress afterwards (EC approach, where the sensor (i forms the minimum mean-square error (MMSE estimate for the signal of interest; and (ii optimally (in the MSE sense compresses and transmits it to the FC that reconstructs it. We further derive a novel alternating scheme to numerically determine an achievable upper bound of the D-R function for general distributed estimation using multiple sensors. The proposed algorithm tackles an analytically intractable minimization problem, while it accounts for sensor data correlations. The obtained upper bound is tighter than the one determined by having each sensor performing MSE optimal encoding independently of the others. Numerical examples indicate that the algorithm performs well and yields D-R upper bounds which are relatively tight with respect to analytical alternatives obtained without taking into account the cross-correlations among sensor data.
International Nuclear Information System (INIS)
Mikkelsen, H.H.; Flyvbjerg, H.
1991-05-01
The time-dependent Schroedinger equation for a Coulomb collision between a heavy point charge and a harmonically bound electron is solved exactly numerically. The energy transferred to the electron is studied as a function of impact parameter and projectile charge. Special attention is given to the Barkas effect, and the transition from light ion to heavy ion stopping. All results are compared with classical and recent approximate results, whose precision and ranges of validity are discussed. (orig.)
Asymptotically exact expression for the energies of the 3Se Rydberg series in a two-electron system
International Nuclear Information System (INIS)
Ivanov, I.A.; Bromley, M.W.J.; Mitroy, J.
2002-01-01
The 1sns 3 S e Rydberg series in a two-electron system with the charge of the nucleus, Z≅1, is treated by means of the quantum-defect theory. Comparison with configuration interaction calculations suggests that the quantum-defect expression for the energy levels becomes asymptotically exact as Z→1. This provides an analytic description of the disappearance of the 1sns 3 S e bound states when Z approaches the critical value of 1
Computer simulation of bounded plasmas
International Nuclear Information System (INIS)
Lawson, W.S.
1987-01-01
The problems of simulating a one-dimensional bounded plasma system using particles in a gridded space are systematically explored and solutions to them are given. Such problems include the injection of particles at the boundaries, the solution of Poisson's equation, and the inclusion of an external circuit between the confining boundaries. A recently discovered artificial cooling effect is explained as being a side-effect of quiet injection, and its potential for causing serious but subtle errors in bounded simulation is noted. The methods described in the first part of the thesis are then applied to the simulation of an extension of the Pierce diode problem, specifically a Pierce diode modified by an external circuit between the electrodes. The results of these simulations agree to high accuracy with theory when a theory exists, and also show some interesting chaotic behavior in certain parameter regimes. The chaotic behavior is described in detail
Bounded Rationality in Transposition Processes
DEFF Research Database (Denmark)
Vollaard, Hans; Martinsen, Dorte Sindbjerg
2014-01-01
Studies explaining the timeliness and correctness of the transposition of EU directives into national legislation have provided rather inconclusive findings. They do not offer a clear-cut prediction concerning the transposition of the patients’ rights directive, which is one of the first that con......Studies explaining the timeliness and correctness of the transposition of EU directives into national legislation have provided rather inconclusive findings. They do not offer a clear-cut prediction concerning the transposition of the patients’ rights directive, which is one of the first...... that concerns the organisation and financing of national healthcare systems. This article applies the perspective of bounded rationality to explain (irregularities in) the timely and correct transposition of EU directives. The cognitive and organisational constraints long posited by the bounded rationality...
2013-03-26
...; Comment Request; Upward Bound and Upward Bound Math Science Annual Performance Report AGENCY: The Office... considered public records. Title of Collection: Upward Bound and Upward Bound Math Science Annual Performance...) and Upward Bound Math and Science (UBMS) Programs. The Department is requesting a new APR because of...
Bounds on the mass and the moment of inertia of nonrotating neutron stars
International Nuclear Information System (INIS)
Sabbadini, A.G.
1976-01-01
Bounds are placed on the mass and the moment of inertia of relativistic, spherical, perfect fluid neutron stars, under minimal assumptions on the equation of state of neutron star matter above nuclear densities. The assumptions are: the pressure p, the density rho, and the derivative dp/d rho are positive. The equation of state is assumed to be known below the density rho 0 = 5 x 10 14 g/cm 3 . The upper bound on the mass of a nonrotating neutron star, under these assumptions, is found to be 5 M/sub solar mass/. Upper and lower bounds on the moment of inertia are derived: for a spherical star of given mass and radius (without assuming a specific equation of state in any density region); for a spherical neutron star of arbitrary mass and radius; for a spherical neutron star of given mass. These bounds are optimum ones, in the sense that there always exists a configuration consistent with the assumptions, having a moment of inertia equal to the bound. Using these results for the moment of inertia, the correction to the upper bound on the mass due to slow rotation is discussed
Spectrum of gluino bound states
International Nuclear Information System (INIS)
Chanowitz, M.; Sharpe, S.; California Univ., Berkeley
1983-01-01
Using the bag model to first order in αsub(s) we find that if light gluinos exist they will appear as constituents of electrically charged bound states which are stable against strong interaction decay. We review the present experimental constraints and conclude that light, long-lived charged hadrons containing gluinos might exist with lifetimes between 2x10 - 8 and 10 - 14 s. (orig.)
Computational experience with a parallel algorithm for tetrangle inequality bound smoothing.
Rajan, K; Deo, N
1999-09-01
Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the 2(n(n-1)) atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the 2(n(n-1)) pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and infinity. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality--the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley-Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the (4n) quadruples requires O(n4) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n3 log n) time on a REW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with O(log(n)n) processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.
Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy
Energy Technology Data Exchange (ETDEWEB)
Tews, Ingo [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550 (United States); Lattimer, James M. [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States); Ohnishi, Akira [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Kolomeitsev, Evgeni E., E-mail: itews@uw.edu, E-mail: james.lattimer@stonybrook.edu, E-mail: ohnishi@yukawa.kyoto-u.ac.jp, E-mail: e.kolomeitsev@gsi.de [Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, SK-97401 Banska Bystrica (Slovakia)
2017-10-20
We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter S {sub 0}. In addition, for assumed values of S {sub 0} above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter L , which describes the lowest-order density dependence of the symmetry energy. A lower bound on neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust–core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.
Upper Gastrointestinal (GI) Series
... standard barium upper GI series, which uses only barium a double-contrast upper GI series, which uses both air and ... evenly coat your upper GI tract with the barium. If you are having a double-contrast study, you will swallow gas-forming crystals that ...
Cyclotron transitions of bound ions
Bezchastnov, Victor G.; Pavlov, George G.
2017-06-01
A charged particle in a magnetic field possesses discrete energy levels associated with particle rotation around the field lines. The radiative transitions between these levels are the well-known cyclotron transitions. We show that a bound complex of particles with a nonzero net charge displays analogous transitions between the states of confined motion of the entire complex in the field. The latter bound-ion cyclotron transitions are affected by a coupling between the collective and internal motions of the complex and, as a result, differ from the transitions of a "reference" bare ion with the same mass and charge. We analyze the cyclotron transitions for complex ions by including the coupling within a rigorous quantum approach. Particular attention is paid to comparison of the transition energies and oscillator strengths to those of the bare ion. Selection rules based on integrals of collective motion are derived for the bound-ion cyclotron transitions analytically, and the perturbation and coupled-channel approaches are developed to study the transitions quantitatively. Representative examples are considered and discussed for positive and negative atomic and cluster ions.
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
Exact-exchange-based quasiparticle calculations
International Nuclear Information System (INIS)
Aulbur, Wilfried G.; Staedele, Martin; Goerling, Andreas
2000-01-01
One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society
Generalized exact holographic mapping with wavelets
Lee, Ching Hua
2017-12-01
The idea of renormalization and scale invariance is pervasive across disciplines. It has not only drawn numerous surprising connections between physical systems under the guise of holographic duality, but has also inspired the development of wavelet theory now widely used in signal processing. Synergizing on these two developments, we describe in this paper a generalized exact holographic mapping that maps a generic N -dimensional lattice system to a (N +1 )-dimensional holographic dual, with the emergent dimension representing scale. In previous works, this was achieved via the iterations of the simplest of all unitary mappings, the Haar mapping, which fails to preserve the form of most Hamiltonians. By taking advantage of the full generality of biorthogonal wavelets, our new generalized holographic mapping framework is able to preserve the form of a large class of lattice Hamiltonians. By explicitly separating features that are fundamentally associated with the physical system from those that are basis specific, we also obtain a clearer understanding of how the resultant bulk geometry arises. For instance, the number of nonvanishing moments of the high-pass wavelet filter is revealed to be proportional to the radius of the dual anti-de Sitter space geometry. We conclude by proposing modifications to the mapping for systems with generic Fermi pockets.
STELLAR: fast and exact local alignments
Directory of Open Access Journals (Sweden)
Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study