New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects
International Nuclear Information System (INIS)
Belkic, D.
1989-01-01
The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)
Hu, Qing-Qing; Freier, Christian; Leykauf, Bastian; Schkolnik, Vladimir; Yang, Jun; Krutzik, Markus; Peters, Achim
2017-09-01
Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the μ Gal regime (1 μ Gal =10-8m /s2 ≈10-9g ). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as 2.04 μ Gal . The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.
de Forges de Parny, L.; Rousseau, V. G.
2018-02-01
We study the quadratic Zeeman effect (QZE) in a system of antiferromagnetic spin-1 bosons on a square lattice and derive the ground-state phase diagrams by means of quantum Monte Carlo simulations and mean-field treatment. The QZE imbalances the populations of the magnetic sublevels σ =±1 and σ =0 , and therefore affects the magnetic and mobility properties of the phases. Both methods show that the tip of the even Mott lobes, stabilized by singlet state, is destroyed when turning on the QZE, thus leaving the space to the superfluid phase. Contrariwise, the tips of odd Mott lobes remain unaffected. Therefore, the Mott-superfluid transition with even filling strongly depends on the strength of the QZE, and we show that the QZE can act as a control parameter for this transition at fixed hopping. Using quantum Monte Carlo simulations, we elucidate the nature of the phase transitions and examine in detail the nematic order: the first-order Mott-superfluid transition with even filling observed in the absence of QZE becomes second order for weak QZE, in contradistinction to our mean-field results which predict a first-order transition in a larger range of QZE. Furthermore, a spin nematic order with director along the z axis is found in the odd Mott lobes and in the superfluid phase for energetically favored σ =±1 states. In the superfluid phase with even filling, the x y components of the nematic director remain finite only for moderate QZE.
International Nuclear Information System (INIS)
Bonilla, I.R.
1984-01-01
The gyromagnetic factors of the molecule NO 2 , in the Zeeman Effect, is measured under high resolution spectroscopy. The values 0.103 + - 0.007; 0.060 + - 0.005 and 0.045 + - 0.004 are found for the components α, β and γ respectively, by applying a magnetic field of 40 Gauss. For fields greater than 1 kilogauss decoupling of the electronic spin to the rotational angular momentum of the molecule is observed. Under this condition the value 1.86 + - 0.25 is obtained for the gyromagnetic factor. (Author) [pt
Quadratic Zeeman spectra for the hydrogen atom by means of semiclassical quantization
International Nuclear Information System (INIS)
Hasegawa, Hiroshi; Adachi, Satoshi
1988-01-01
The elliptic cylindrical coordinates of type I adapted to the Fock hypersphere in momentum space of the Kepler motion and their canonical momenta are used to construct an analytic form of the classical action integrals which yield an adequate parametrization of the KAM (Kolmogorov-Arnold-Moser) tori of the Kepler trajectories weakly perturbed by a uniform magnetic field. The semiclassical quantization formula so provided presents a prototype of the exact EBK (Einstein-Brillouin-Keller) quantization scheme, and the resulting quantized energies vs the magnetic field strength correspond to the quadratic Zeeman spectra of each Rydberg multiplet lifted by the perturbation. (author)
Exact solution of the classical mechanical quadratic Zeeman effect
Indian Academy of Sciences (India)
While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles ...
Detection of the OH Zeeman effect toward Orion A
International Nuclear Information System (INIS)
Troland, T.H.; Crutcher, R.M.; Kazes, I.; Paris Observatoire, Meudon, France; Kentucky Univ., Lexington)
1986-01-01
The Zeeman effect in the 18 cm OH absorption spectrum of Orion A is detected. From this effect, a line-of-sight magnetic field strength of - 125 + or - 20 is derived. At the same position, an H I Zeeman effect equivalent to a magnetic field of - 49 + or - 4 micro-G is found. Thus, the magnetic field in the molecular gas toward Orion A is significantly stronger than that in the atomic gas, contrary to the recent determination for the Cas A line of sight. Densities in the atomic and molecular regions toward Orion A are estimated and it is found that for this region the data are consistent with B proportional to n exp kappa, kappa = 0.3. 23 references
Zeeman effects in heavy electron superconductors
International Nuclear Information System (INIS)
Michal, Vincent
2012-01-01
Understanding the properties of newly discovered strongly correlated electron compounds is a considerable challenge for both fundamental matters and long-term industrial impact. Experimental activity on heavy electron metals and superconductors has lead to highlighting effects that depart from current knowledge. The thesis is aimed at modelling effects that have been observed in response to magnetic field in the heavy electron superconductor CeCoIn 5 . This consists of two parts. In the first time we deal with the vortex lattice state anomalous local magnetic field space variations as highlighted by small angle neutron scattering and muon spin rotation experiment. On the basis of the Ginzburg-Landau theory with account of spin effect, we analyse the local field inhomogeneity in the vortex lattice and derive expressions for the neutron scattering form factors and muon spin rotation static linewidth. The anomalous experimental data are shown to be result of spin driven supercurrents which circulate around the vortex cores and lead to an increase with external field in the internal field inhomogeneity on a distance of the order of the superconducting coherence length from the vortex axis. The importance of the effect is controlled by a single quantity (the Maki parameter). The second part is on nearly commensurate spin density wave transition in a quasi two-dimensional superconductor. It is motivated by observation of the confinement of spin density wave ordering inside the superconducting state of CeCoIn 5 in magnetic field. In the frame of the spin-fermion formulation we propose a mechanism for the ground state transition consisting in the field-induced slowing down of a collective spin density fluctuation mode (spin-exciton) to static ordering. This represents a scenario by which the transition to spin ordering is intrinsically related to superconductivity. (author) [fr
International Nuclear Information System (INIS)
Silverman, J.N.
1983-01-01
A generalized Euler transformation (GET) is introduced which provides a powerful alternative method of accurately summing strongly divergent Rayleigh-Schroedinger (RS) perturbation series when other summability methods fail or are difficult to apply. The GET is simple to implement and, unlike a number of other summation procedures, requires no a priori knowledge of the analytic properties of the function underlying the RS series. Application of the GET to the difficult problem of the RS weak-field ground-state eigenvalue series of the hydrogen atom in a magnetic field (quadratic Zeeman effect) yields sums of good accuracy over a very wide range of field strengths up to the most intense fields of 10 14 G. The GET results are compared with those obtained by other summing methods
Zeeman effect in sulfur monoxide: a tool to probe magnetic fields in star forming regions
DEFF Research Database (Denmark)
Cazzoli, Gabriele; Lattanzi, Valerio; Coriani, Sonia
2017-01-01
Context. Magnetic fields play a fundamental role in star formation processes and the best method to evaluate their intensity is to measure the Zeeman effect of atomic and molecular lines. However, a direct measurement of the Zeeman spectral pattern from interstellar molecular species is challengi...
Ground state magnetization of conduction electrons in graphene with Zeeman effect
Energy Technology Data Exchange (ETDEWEB)
Escudero, F., E-mail: federico.escudero@uns.edu.ar [Departamento de Física, Universidad Nacional del Sur, Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Instituto de Física del Sur (IFISUR, UNS-CONICET), Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Ardenghi, J.S., E-mail: jsardenhi@gmail.com [Departamento de Física, Universidad Nacional del Sur, Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Instituto de Física del Sur (IFISUR, UNS-CONICET), Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Sourrouille, L., E-mail: lsourrouille@yahoo.es [Departamento de Física, Universidad Nacional del Sur, Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Instituto de Física del Sur (IFISUR, UNS-CONICET), Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Jasen, P., E-mail: pvjasen@uns.edu.ar [Departamento de Física, Universidad Nacional del Sur, Av. Alem 1253, B8000CPB Bahía Blanca (Argentina); Instituto de Física del Sur (IFISUR, UNS-CONICET), Av. Alem 1253, B8000CPB Bahía Blanca (Argentina)
2017-05-01
In this work we address the ground state magnetization in graphene, considering the Zeeman effect and taking into account the conduction electrons in the long wavelength approximation. We obtain analytical expressions for the magnetization at T=0 K, where the oscillations given by the de Haas van Alphen (dHvA) effect are present. We find that the Zeeman effect modifies the magnetization by introducing new peaks associated with the spin splitting of the Landau levels. These peaks are very small for typical carrier densities in graphene, but become more important for higher densities. The obtained results provide insight of the way in which the Zeeman effect modifies the magnetization, which can be useful to control and manipulate the spin degrees of freedom. - Highlights: • The magnetization has peaks whenever the last energy level changes discontinuously. • The peaks amplitude depends on the electron density. • The Zeeman effect introduces new peaks in the magnetization.
Stark--Zeeman effect of metastable hydrogen molecules
International Nuclear Information System (INIS)
Kagann, R.H.
1975-01-01
The Stark effect of the N = 1 rotational level of orthohydrogen and the N = 2 rotational level of parahydrogen in the metastable c 3 PI/sub u/ electronic state has been measured using the molecular beam magnetic resonance method. The Stark effect of the metastable state is 10,000 times larger than that of the ground electronic state. The Stark effect of parahydrogen was found to be weakly dependent on static magnetic field strength, whereas the Stark effect of orthohydrogen was found to be more strongly dependent on the magnetic field strength. The Stark effect of orthohydrogen has been calculated using second-order perturbation theory with a pure Stark effect perturbation. The magnetic field dependence of the Stark effect was calculated using third-order perturbation theory with a mixed Stark--Zeeman effect double perturbation. A comparison of the experimental and theoretical values of α/sub perpendicular/ provides information on the electronic transition moment connecting the c 3 PI/sub u/ state to the a 3 Σ + /sub g/ state. The transition moment is needed to calculate the radiative lifetimes of the various vibrational levels of the c 3 PI/sub u/ state. The transition moment also enters the calculation of the quenching of this metastable state by an external electric field. There is a disagreement between theoretical predictions and the results of an experiment on the electric field quenching of the metastables. A test of the electronic transition moment may help shed light on this question. The experimental determination of the values of the transition moments allows one to test theory by comparing these values to those obtained by calculations employing ab initio wavefunctions
Zeeman effect in sulfur monoxide. A tool to probe magnetic fields in star forming regions
Cazzoli, Gabriele; Lattanzi, Valerio; Coriani, Sonia; Gauss, Jürgen; Codella, Claudio; Ramos, Andrés Asensio; Cernicharo, José; Puzzarini, Cristina
2017-09-01
Context. Magnetic fields play a fundamental role in star formation processes and the best method to evaluate their intensity is to measure the Zeeman effect of atomic and molecular lines. However, a direct measurement of the Zeeman spectral pattern from interstellar molecular species is challenging due to the high sensitivity and high spectral resolution required. So far, the Zeeman effect has been detected unambiguously in star forming regions for very few non-masing species, such as OH and CN. Aims: We decided to investigate the suitability of sulfur monoxide (SO), which is one of the most abundant species in star forming regions, for probing the intensity of magnetic fields via the Zeeman effect. Methods: We investigated the Zeeman effect for several rotational transitions of SO in the (sub-)mm spectral regions by using a frequency-modulated, computer-controlled spectrometer, and by applying a magnetic field parallel to the radiation propagation (I.e., perpendicular to the oscillating magnetic field of the radiation). To support the experimental determination of the g factors of SO, a systematic quantum-chemical investigation of these parameters for both SO and O2 has been carried out. Results: An effective experimental-computational strategy for providing accurate g factors as well as for identifying the rotational transitions showing the strongest Zeeman effect has been presented. Revised g factors have been obtained from a large number of SO rotational transitions between 86 and 389 GHz. In particular, the rotational transitions showing the largest Zeeman shifts are: N,J = 2, 2 ← 1, 1 (86.1 GHz), N,J = 4, 3 ← 3, 2 (159.0 GHz), N,J = 1, 1 ← 0, 1 (286.3 GHz), N,J = 2, 2 ← 1, 2 (309.5 GHz), and N,J = 2, 1 ← 1, 0 (329.4 GHz). Our investigation supports SO as a good candidate for probing magnetic fields in high-density star forming regions. The complete list of measured Zeeman components is only available at the CDS via anonymous ftp to http
On the Zeeman Effect in highly excited atoms: 2. Three-dimensional case
International Nuclear Information System (INIS)
Baseia, B.; Medeiros e Silva Filho, J.
1984-01-01
A previous result, found in two-dimensional hydrogen-atoms, is extended to the three-dimensional case. A mapping of a four-dimensional space R 4 onto R 3 , that establishes an equivalence between Coulomb and harmonic potentials, is used to show that the exact solution of the Zeeman effect in highly excited atoms, cannot be reached. (Author) [pt
Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots
Beugeling, Wouter; Uhrig, Götz S.; Anders, Frithjof B.
2017-09-01
The coherence of the electron spin in a semiconductor quantum dot is strongly enhanced by mode locking through nuclear focusing, where the synchronization of the electron spin to periodic pulsing is slowly transferred to the nuclear spins of the semiconductor material, mediated by the hyperfine interaction between these. The external magnetic field that drives the Larmor oscillations of the electron spin also subjects the nuclear spins to a Zeeman-like coupling, albeit a much weaker one. For typical magnetic fields used in experiments, the energy scale of the nuclear Zeeman effect is comparable to that of the hyperfine interaction, so that it is not negligible. In this work, we analyze the influence of the nuclear Zeeman effect on mode locking quantitatively. Within a perturbative framework, we calculate the Overhauser-field distribution after a prolonged period of pulsing. We find that the nuclear Zeeman effect can exchange resonant and nonresonant frequencies. We distinguish between models with a single type and with multiple types of nuclei. For the latter case, the positions of the resonances depend on the individual g factors, rather than on the average value.
International Nuclear Information System (INIS)
Larsson, Richard; Buehler, Stefan A.; Eriksson, Patrick; Mendrok, Jana
2014-01-01
This paper presents the practical theory that was used to implement the Zeeman effect using Stokes formalism in the Atmospheric Radiative Transfer Simulator (ARTS). ARTS now treats the Zeeman effect in a general manner for several gas species for all polarizations and takes into account variations in both magnetic and atmospheric fields along a full 3D geometry. We present how Zeeman splitting affects polarization in radiative transfer simulations and find that the effect may be large in Earth settings for polarized receivers in limb observing geometry. We find that not taking a spatially varying magnetic field into account can result in absolute errors in the measurement vector of at least 10 K in Earth magnetic field settings. The paper also presents qualitative tests for O 2 lines against previous models (61.15 GHz line) and satellite data from Odin-SMR (487.25 GHz line), and the overall consistency between previous models, satellite data, and the new ARTS Zeeman module seems encouraging. -- Highlights: • We implement the Zeeman effect with Stokes formalism in ARTS. • We give a practical theory for the implementation. • Examples of how the Zeeman effect change RT are presented. • Qualitative Odin-SMR O 2 limb sounding model indicates the Zeeman effect is necessary
International Nuclear Information System (INIS)
Lulu, B.A.
1980-09-01
The spectra of Sc I, Sc II, Sc III, and Sc IV are analyzed through the use of the Zeeman effect. A sliding spark of the author's design is used in conjunction with a 27 kilogauss electromagnet. The spectra have (reciprocal) dispersions of 0.2 to 0.5 A/mm. 10 Sc I levels, 16 Sc II levels and 5 Sc III levels show Zeeman splitting. No Sc IV Zeeman patterns were observed. 2 Sc I, 4 Sc II, and all of the Sc III level data are new
A New Analysis of Stark and Zeeman Effects on Hydrogen Lines in Magnetized DA White Dwarfs
Directory of Open Access Journals (Sweden)
Ny Kieu
2017-11-01
Full Text Available White dwarfs with magnetic field strengths larger than 10 T are understood to represent more than 10% of the total population of white dwarfs. The presence of such strong magnetic fields is clearly indicated by the Zeeman triplet structure visible on absorption lines. In this work, we discuss the line broadening mechanisms and focus on the sensitivity of hydrogen lines on the magnetic field. We perform new calculations in conditions relevant to magnetized DA stellar atmospheres using models inspired from magnetic fusion plasma spectroscopy. A white dwarf spectrum from the Sloan Digital Sky Survey (SDSS database is analyzed. An effective temperature is provided by an adjustment of the background radiation with a Planck function, and the magnetic field is inferred from absorption lines presenting a Zeeman triplet structure. An order-of-magnitude estimate for the electron density is also performed from Stark broadening analysis.
THE ZEEMAN EFFECT IN THE 44 GHZ CLASS I METHANOL MASER LINE TOWARD DR21(OH)
Energy Technology Data Exchange (ETDEWEB)
Momjian, E. [National Radio Astronomy Observatory, P.O. Box O, Socorro, NM 87801 (United States); Sarma, A. P., E-mail: emomjian@nrao.edu, E-mail: asarma@depaul.edu [Physics Department, DePaul University, 2219 N. Kenmore Avenue, Byrne Hall 211, Chicago, IL 60614 (United States)
2017-01-10
We report detection of the Zeeman effect in the 44 GHz Class I methanol maser line, toward the star-forming region DR21(OH). In a 219 Jy beam{sup −1} maser centered at an LSR velocity of 0.83 km s{sup −1}, we find a 20- σ detection of zB {sub los} = 53.5 ± 2.7 Hz. If 44 GHz methanol masers are excited at n ∼ 10{sup 7–8} cm{sup −3}, then the B versus n {sup 1/2} relation would imply, from comparison with Zeeman effect detections in the CN(1 − 0) line toward DR21(OH), that magnetic fields traced by 44 GHz methanol masers in DR21(OH) should be ∼10 mG. Combined with our detected zB {sub los} = 53.5 Hz, this would imply that the value of the 44 GHz methanol Zeeman splitting factor z is ∼5 Hz mG{sup −1}. Such small values of z would not be a surprise, as the methanol molecule is non-paramagnetic, like H{sub 2}O. Empirical attempts to determine z , as demonstrated, are important because there currently are no laboratory measurements or theoretically calculated values of z for the 44 GHz CH{sub 3}OH transition. Data from observations of a larger number of sources are needed to make such empirical determinations robust.
Hemmes, K.; WIND, M.M.; Lepoole, R.; Habing, P.E.
1994-01-01
Abstract of WO 9416310 (A1) Ellipsometer comprising at least a Zeeman laser (Z) to generate two beams (g1, g2) which are slightly shifted in frequency and (after transmission through a birefringent crystal (quarter-wave plate)) are both polarized linearly but perpendicular to one another, a
A classical treatment of the quadratic Zeeman effect in atomic hydrogen
Al-Laithy, M. A.; Farmer, C. M.; McDowell, M. R. C.
1985-03-01
A description of the non-relativistic classical motion of the electron of a hydrogen atom in the presence of a static magnetic field of arbitrary (non-relativistic) strength is given for arbitrary angular momentum. Applications are given to m = 0 and m = 3 at B = 26.877 kG.
Hemmes, K.; WIND, M.M.; Lepoole, R.; Habing, P.E.
1994-01-01
Abstract of WO 9416310 (A1) Ellipsometer comprising at least a Zeeman laser (Z) to generate two beams (g1, g2) which are slightly shifted in frequency and (after transmission through a birefringent crystal (quarter-wave plate)) are both polarized linearly but perpendicular to one another, a non-polarizing beam splitter (N) downstream of which a working beam (g'm2) mofidied by a sample (S) interferes with a reference beam (g1), a unit (W) for separating two orthogonal (p- and s-) components of...
Trends in measurement of solar vector magnetic fields using the Zeeman effect
International Nuclear Information System (INIS)
Harvey, J.W.
1985-01-01
Trends in spectropolarimetry as applied to the problem of Zeeman effect measurement are discussed. The use of detector arrays to improve observing efficiency is obtained. Which required new polarization modulation schemes that match the time required to read detector arrays. Another significant trend is narrowband filters, to improve angular and temporal coverage, and to Fourier transform spectrometers, to improve spectral coverage and precision. Low-polarization designs and improved methods for compensating instrumental polarization were developed. A requirement for high angular resolution suggests using adaptive optical devices to subdue the effects of bad seeing. The ultimate strategy to beat the seeing is to loft the telescope above the atmosphere such as is planned with a 30-cm telescope in 1985 and a 1250-cm telescope in 1990
Trends in measurement of solar vector magnetic fields using the Zeeman effect
Harvey, J. W.
1985-01-01
Trends in spectropolarimetry as applied to the problem of Zeeman effect measurement are discussed. The use of detector arrays to improve observing efficiency is obtained. Which required new polarization modulation schemes that match the time required to read detector arrays. Another significant trend is narrowband filters, to improve angular and temporal coverage, and to Fourier transform spectrometers, to improve spectral coverage and precision. Low-polarization designs and improved methods for compensating instrumental polarization were developed. A requirement for high angular resolution suggests using adaptive optical devices to subdue the effects of bad seeing. The ultimate strategy to beat the seeing is to loft the telescope above the atmosphere such as is planned with a 30-cm telescope in 1985 and a 1250-cm telescope in 1990.
International Nuclear Information System (INIS)
Zhang, Guangping; Lin, Bihong; Wu, Guocan
2017-01-01
Highlights: • A new model of the quantum dot refrigeration devices is established. • The effects of the Zeeman and Coulomb effects on performance are discussed. • Maximum cooling rate and coefficient of performance are calculated. • Upper boundary of the optimal region of the device is discussed. • Optimum choice criteria of some important parameters are provided. - Abstract: A general class of quantum dot refrigeration devices, which is consisting of a single orbital interacting quantum dot and two metal leads with different temperatures and chemical potentials, is established. In the model, not only the Zeeman splitting of energy levels resulting from an external magnetic field but also the effect of a linear fade of the Coulomb energy caused by the splitting are taken into account simultaneously. Based on the quantum master equation, the occupation probabilities of quantum states for the electron are determined under the steady state condition. The general expressions of the particle fluxes, heat flows, power input, cooling rate and the coefficient of performance (COP) are derived. The influences of the energy level and external magnetic field on the performance of the refrigerator are discussed in detail. By applying numerical simulations, three-dimensional diagrams of the cooling rate and COP varying with the magnetic field and energy level are given. The maximum COP and the optimal values of corresponding parameters as well as the maximum cooling rate are obtained. The optimal regions of the magnetic field and the energy level are determined. The optimized scopes of the COP and cooling rate are provided. Some important conclusions in the previous literatures can be directly deduced from the current model under the different extreme conditions.
Tahir, M.; Sabeeh, K.; Schwingenschlö gl, Udo; Shaukat, A.
2013-01-01
Since the discovery of graphene, a lot of interest has been attracted by the zeroth Landau level, which has no analog in the conventional two dimensional electron gas. Recently, lifting of the spin and valley degeneracies has been confirmed experimentally by capacitance measurements, while in transport experiments, this is difficult due to the scattering in the device. In this context, we model interaction effects on the quantum capacitance of graphene in the presence of a perpendicular magnetic field, finding good agreement with experiments. We demonstrate that the valley degeneracy is lifted by the substrate and by Kekule distortion, whereas the spin degeneracy is lifted by Zeeman interaction. The two cases can be distinguished by capacitance measurements.
Tahir, M.
2013-12-10
Since the discovery of graphene, a lot of interest has been attracted by the zeroth Landau level, which has no analog in the conventional two dimensional electron gas. Recently, lifting of the spin and valley degeneracies has been confirmed experimentally by capacitance measurements, while in transport experiments, this is difficult due to the scattering in the device. In this context, we model interaction effects on the quantum capacitance of graphene in the presence of a perpendicular magnetic field, finding good agreement with experiments. We demonstrate that the valley degeneracy is lifted by the substrate and by Kekule distortion, whereas the spin degeneracy is lifted by Zeeman interaction. The two cases can be distinguished by capacitance measurements.
International Nuclear Information System (INIS)
Tahir, M.; Sabeeh, K.; Shaukat, A.; Schwingenschlögl, U.
2013-01-01
Since the discovery of graphene, a lot of interest has been attracted by the zeroth Landau level, which has no analog in the conventional two dimensional electron gas. Recently, lifting of the spin and valley degeneracies has been confirmed experimentally by capacitance measurements, while in transport experiments, this is difficult due to the scattering in the device. In this context, we model interaction effects on the quantum capacitance of graphene in the presence of a perpendicular magnetic field, finding good agreement with experiments. We demonstrate that the valley degeneracy is lifted by the substrate and by Kekule distortion, whereas the spin degeneracy is lifted by Zeeman interaction. The two cases can be distinguished by capacitance measurements
Aperture synthesis observations of the 21 centimeter Zeeman effect toward Orion A
International Nuclear Information System (INIS)
Troland, T.H.; Heiles, C.; Goss, W.M.
1989-01-01
The VLA has been used to map the 21 cm Zeeman effect at 40 arcsec resolution in the absorbing H I gas in front of Orion A. Two such regions exist having typical velocities of 1 and 5 km/s; both almost certainly lie close to the H II region. Field strengths exceed 100 micro G in this H I gas. The field in the higher velocity component has been reliably detected across most of the continuum source. No field reversals exist. The distribution of line-of-sight field strengths derived for this component mimics that of tau(H I) for positions where the lines are not saturated, suggesting that the mass-to-flux ratio in this gas is approximately constant. The distribution of visual extinction across Orion A using existing radio and optical data is rederived. Maxima and minima of extinction are generally coincident with maxima and minima of magnetic field. This correspondence suggests that the observed association between field strength and tau(H I) is a real column density effect, that the effect encompasses all neutral gas in front of the source, and that the mass-to-flux ratio for this neutral gas is approximately constant. Results for Orion A lend weight to the conclusion that magnetic fields play a crucial role in the dynamics of interstellar material. 48 references
Measurement of quadratic electrogyration effect in castor oil
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Optogalvanic detection of the Zeeman effect in a hollow-cathode discharge
International Nuclear Information System (INIS)
Langlois, E.; Gagne, J.
1987-01-01
Optogalvanic detection of complex Zeeman patterns in a hollow-cathode lamp is investigated. Uranium lines with J 1 = 6 and J 2 = 7 are resolved, with our best results obtained using intermodulate optogalvanic spectroscopy (but this scheme is applicable only to lines giving strong signals). This detection method has a 40-MHz resolution, so a magnetic field of 0.1 T is sufficient to resolve most patterns. Weak lines can be studied with modulated optogalvanic spectroscopy. However, the stronger field required in this case perturbs the discharge. Although they are impractical for the measurement of component relative intensities, these detection methods may find applications in the determination of Lande g factors
Zeeman atomic absorption spectroscopy
International Nuclear Information System (INIS)
Loos-Vollebregt, M.T.C. de.
1980-01-01
A new method of background correction in atomic absorption spectroscopy has recently been introduced, based on the Zeeman splitting of spectral lines in a magnetic field. A theoretical analysis of the background correction capability observed in such instruments is presented. A Zeeman atomic absorption spectrometer utilizing a 50 Hz sine wave modulated magnetic field is described. (Auth.)
Bao, Guzhi; Wickenbrock, Arne; Rochester, Simon; Zhang, Weiping; Budker, Dmitry
2018-01-19
The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear Zeeman effect and heading error based on spin locking. In an all-optical synchronously pumped magnetometer with separate pump and probe beams, we apply a radio-frequency field which is in phase with the precessing magnetization. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with ∼100 Hz width in the Earth-field range into a single peak with a width of 22 Hz, whose position is largely independent of the orientation of the sensor within a range of orientation angles. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude, decreasing its width, and removing the important and limiting heading-error systematic.
Bao, Guzhi; Wickenbrock, Arne; Rochester, Simon; Zhang, Weiping; Budker, Dmitry
2018-01-01
The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear Zeeman effect and heading error based on spin locking. In an all-optical synchronously pumped magnetometer with separate pump and probe beams, we apply a radio-frequency field which is in phase with the precessing magnetization. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with ˜100 Hz width in the Earth-field range into a single peak with a width of 22 Hz, whose position is largely independent of the orientation of the sensor within a range of orientation angles. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude, decreasing its width, and removing the important and limiting heading-error systematic.
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
Zeeman atomic absorption spectrometry
International Nuclear Information System (INIS)
Hadeishi, T.; McLaughlin, R.
1978-08-01
The design and development of a Zeeman atomic absorption spectrometer for trace element analysis are described. An instruction manual is included which details the operation, adjustment, and maintenance. Specifications and circuit diagrams are given
DEFF Research Database (Denmark)
Larsen, Erik Huusfeldt; Ekelund, J.
1989-01-01
A method for the determination of total selenium in nutritional supplements and selenised yeast is described. The samples were ashed in nitric acid. Hydrochloric acid was used to prevent precipitation of, in particular, iron salts. After appropriate dilutions, the selenium was determined by Zeeman......-effect background corrected graphite furnace atomic absorption spectrometry. A furnace ashing step at 1100 °C was necessary in order to obtain a total recovery of selenium when present in the organic form. Palladium nitrate-magnesium nitrate was used as a matrix modifier. Independent methods were used to determine...... the content of selenium in a selenised yeast check sample. Accuracy was assured using this sample and by recovery experiments. Between-day random error showed a coefficient of variation of 4.2%. Results from the analysis of eight different commercial supplements were in good agreement with declared contents....
International Nuclear Information System (INIS)
Mao Wei; Zhang Shulian
2007-01-01
Optical feedback effects are studied in a birefringence-Zeeman dual frequency laser at high optical feedback levels. The intensity modulation features of the two orthogonally polarized lights are investigated in both isotropic optical feedback (IOF) and polarized optical feedback (POF). In IOF, the intensities of both beams are modulated simultaneously, and four zones, i.e., the e-light zone, the o-light and e-light zone, the o-light zone, and the no-light zone, are formed in a period corresponding to a half laser wavelength displacement of the feedback mirror. In POF, the two orthogonally polarized lights will oscillate alternately. Strong mode competition can be observed, and it affects the phase difference between the two beams greatly. The theoretical analysis is presented, which is in good agreement with the experimental results. The potential use of the experimental results is also discussed
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel
2016-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...
Steimle, Timothy C; Wang, Hailing; Gengler, Jamie J; Stoll, Michael; Meijer, Gerard
2008-10-28
The Zeeman tuning of the P(1)(0) line (nu=17 568.35 cm(-1)) of the A (7)Pi-X (7)Sigma(+) (0,0) band of manganese monohydride, MnH, has been investigated. The laser induced fluorescence spectrum of a supersonic molecular beam sample was recorded at a resolution of approximately 40 MHz and with field strengths of up to 362.0 mT. The observed spectrum was successfully fitted using a traditional effective Zeeman Hamiltonian to determine an effective magnetic g-factor for the J=2 level of the F(1)-spin component of the A (7)Pi(v=0) state. Spectral predictions of the P(1)(0) line at field strengths used in magnetic trapping experiments are presented.
The Zeeman effect in the (0,0) band of the A 7Π-X 7Σ+ transition of manganese monohydride, MnH
Steimle, Timothy C.; Wang, Hailing; Gengler, Jamie J.; Stoll, Michael; Meijer, Gerard
2008-10-01
The Zeeman tuning of the P1(0) line (ν =17 568.35 cm-1) of the A Π7-X Σ7+ (0,0) band of manganese monohydride, MnH, has been investigated. The laser induced fluorescence spectrum of a supersonic molecular beam sample was recorded at a resolution of approximately 40 MHz and with field strengths of up to 362.0 mT. The observed spectrum was successfully fitted using a traditional effective Zeeman Hamiltonian to determine an effective magnetic g-factor for the J =2 level of the F1-spin component of the A Π7(v =0) state. Spectral predictions of the P1(0) line at field strengths used in magnetic trapping experiments are presented.
International Nuclear Information System (INIS)
Nitta, Junsaku; Moulis, Sylvain; Kohda, Makoto
2011-01-01
Spin transport affected by competition between Zeeman effect and spin-orbit interaction (SOI) is investigated in order to check a proposed method to deduce the Rashba SOI α and Dresselhaus SOI β ratio. The experimentally obtained ratio α/β of the present sample is about 4 from angle dependence of magnetoconductance under in-plane magnetic field. The proposed method to detect the ratio by transport measurement is promising although further improvement of sample fabrication and measurement is required.
International Nuclear Information System (INIS)
Zhang Tongyi; Zhao Wei; Liu Xueming
2009-01-01
We have made a thorough theoretical investigation of the interplay of spin-orbit interactions (SOIs) resulting from Rashba, Dresselhaus and the lateral parabolic confining potential on the energy dispersion relation of the spin subbands in a parabolic quantum wire. The influence of an applied external magnetic field is also discussed. We show the interplay of different types of SOI, as well as the Zeeman effect, leads to rather complex and intriguing electrosubbands for different spin branches. The effect of different coupling strengths and different magnetic field strengths is also investigated.
Bieniek, Maciej; Korkusiński, Marek; Szulakowska, Ludmiła; Potasz, Paweł; Ozfidan, Isil; Hawrylak, Paweł
2018-02-01
We present here the minimal tight-binding model for a single layer of transition metal dichalcogenides (TMDCs) MX 2(M , metal; X , chalcogen) which illuminates the physics and captures band nesting, massive Dirac fermions, and valley Landé and Zeeman magnetic field effects. TMDCs share the hexagonal lattice with graphene but their electronic bands require much more complex atomic orbitals. Using symmetry arguments, a minimal basis consisting of three metal d orbitals and three chalcogen dimer p orbitals is constructed. The tunneling matrix elements between nearest-neighbor metal and chalcogen orbitals are explicitly derived at K ,-K , and Γ points of the Brillouin zone. The nearest-neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective 6 ×6 Hamiltonian giving correct composition of metal and chalcogen orbitals but not the direct gap at K points. The direct gap at K , correct masses, and conduction band minima at Q points responsible for band nesting are obtained by inclusion of next-neighbor Mo-Mo tunneling. The parameters of the next-nearest-neighbor model are successfully fitted to MX 2(M =Mo ; X =S ) density functional ab initio calculations of the highest valence and lowest conduction band dispersion along K -Γ line in the Brillouin zone. The effective two-band massive Dirac Hamiltonian for MoS2, Landé g factors, and valley Zeeman splitting are obtained.
Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yu.S.
1997-01-01
We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog of the g......We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog...
International Nuclear Information System (INIS)
Nikolić, S N; Radonjić, M; Krmpot, A J; Lučić, N M; Zlatković, B V; Jelenković, B M
2013-01-01
Electromagnetically induced transparency (EIT) due to Zeeman coherences in the Rb buffer gas cell is studied for different laser beam profiles, laser beam radii and intensities from 0.1 to 10 mW cm −2 . EIT line shapes can be approximated by the Lorentzian for wide Gaussian laser beam (6.5 mm in diameter) if laser intensity is weak and for a Π laser beam profile of the same diameter. Line shapes of EIT become non-Lorentzian for the Gaussian laser beam if it is narrow (1.3 mm in diameter) or if it has a higher intensity. EIT amplitudes and linewidths, for both laser beam profiles of the same diameter, have very similar behaviour regarding laser intensity and Rb cell temperature. EIT amplitudes are maximal at a certain laser beam intensity and this intensity is higher for narrower laser beams. The EIT linewidth estimated at zero laser intensity is about 50 nT or 0.7 kHz, which refers to 1.5 ms relaxation times of Zeeman coherences in 87 Rb atoms in our buffer gas cell. Blocking of the centre of the wide Gaussian laser beam in front of the photo detector yields Lorentzian profiles with a much better contrast to the linewidth ratio for EIT at higher intensities, above ∼2 mW cm −2 . (paper)
Sakaguchi, Hidetsugu; Sherman, E Ya; Malomed, Boris A
2016-09-01
We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudospinor system of Gross-Pitaevskii equations with self- and cross attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semivortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by ∼1.5×10^{4}. The results are obtained by means of combined analytical and numerical methods.
A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models
Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen
2012-01-01
Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…
Zamani, Ali; Azargoshasb, Tahereh; Niknam, Elahe
2017-10-01
In current article, the Zeeman effect is considered in the presence of simultaneous Rashba and Dresselhaus spin-orbit interactions (SOI) and under such circumstances the second and third harmonic generations (SHG and THG) of a GaAs quantum ring are investigated at finite temperature. The effective Hamiltonian is derived in cylindrical coordinate while the angular part is eliminated because of axial symmetry and the energy eigenvalues and eigenvectors of two lowest levels are obtained numerically. Eventually, the optical properties of such system are studied hiring compact density matrix approach. The results show that, an increase in the magnetic field, leads to blue shift in resonant peaks of both SHG and THG. Furthermore, by reducing the temperature, all the resonant peaks of both SHG and THG experience a red shift. Finally, the effect of the structure dimension is studied and results illustrate that variation of size leads to both red and blue shifts in resonant peaks.
Gravitation and quadratic forms
International Nuclear Information System (INIS)
Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha
2017-01-01
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Gravitation and quadratic forms
Energy Technology Data Exchange (ETDEWEB)
Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)
2017-03-31
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Fay, Temple H.
2012-01-01
Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…
Canavos, G. C.
1974-01-01
A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.
Quadratic interaction effect on the dark energy density in the universe
International Nuclear Information System (INIS)
Deveci, Derya G; Aydiner, Ekrem
2017-01-01
In this study, we deal with the holographic model of interacting dark components of dark energy and dark matter quadratic case of the equation of state parameter (EoS). The effective equations of states for the interacting holographic energy density are derived and the results are analyzed and compared with the solution of the linear form in the literature. The result of our work shows that the value of interaction term between dark components affects the fixed points at far future in the DE-dominated universe in the case of quadratic EoS parameter; it is a different result from the linear case in the theoretical results in the literature, and as the Quintom scenario the equations of state had coincidence at the cosmological constant boundary of –1 from above to below. (paper)
Zeeman en Einstein. Meeslepende metingen
Directory of Open Access Journals (Sweden)
Ad Maas
2016-10-01
Full Text Available Zeeman and EinsteinThis article discusses an early example of interferometric, experimental research related to Einstein’s Special Theory of Relativity. This research concerned two series of experiments on the velocity of light in moving media, conducted between 1914 and 1921 by the Amsterdam physicist Pieter Zeeman. With the first of these series, on the velocity of light in moving water, Zeeman obtained an important result that validated the so called ‘dispersion term’ of the formula for the velocity of light in moving media. Less clear is the scientific objective of the second series, in which Zeeman measured the velocity of light in moving solid media. It seems that Zeeman’s interest in this second series was triggered mainly by the technical challenges posed by these experiments. In this way, they reveal the increasing tendency of Zeeman’s later research to be led by technical and experimental challenges, rather than by the actual scientific developments.
Induced Kerr effects and self-guided beams in quasi-phase-matched quadratic media [CBC4
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yuri S.
1997-01-01
We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons......We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons...
Polishchuk, Alexander
2005-01-01
Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.
The Zeeman-split superconductivity with Rashba and Dresselhaus spin-orbit coupling
Zhao, Jingxiang; Yan, Xu; Gu, Qiang
2017-10-01
The superconductivity with Rashba and Dressehlaus spin-orbit coupling and Zeeman effect is investigated. The energy gaps of quasi-particles are carefully calculated. It is shown that the coexistence of two spin-orbit coupling might suppress superconductivity. Moreover, the Zeeman effect favors spin-triplet Cooper pairs.
International Nuclear Information System (INIS)
Sallah, M.; Margeanu, C. A.
2016-01-01
The space-fractional neutron transport equation is used to describe the neutrons transport in finite disturbed reactors. It is approximated using the Pomraning-Eddington technique to yield two space-fractional differential equations, in terms of neutron density and net neutron flux. These resultant equations are coupled into a fractional diffusion-like equation for the neutron density whose solution is obtained by using Laplace transformation method. The solution is represented in terms of the Mittag-Leffler function and its different orders. The scattering is considered as quadratic scattering to offer a more realistic, compact representation of the system, and to increase the accuracy of the estimated neutronic parameters. The results are presented graphically to illustrate the fractional parameter effect in addition to the effect of radiative-transfer properties on the physical parameters of interest (reflection coefficient, transmission coefficient, neutron energy, and net neutron flux). The neutron transport problem in finite disturbed reactor with quadratic scattering is considered in investigating the shielding effectiveness, by using MAVRIC shielding module from SCALE6 programs package. The fractional parameter can be used to adjust the analysed data on neutron energy and flux, both for the theoretical model and the neutron transport application. (authors)
Zeeman splitting of surface-scattered neutrons
International Nuclear Information System (INIS)
Felcher, G.P.; Adenwalla, S.; De Haan, V.O.; Van Well, A.A.
1995-01-01
If a beam of slow neutrons impinges on a solid at grazing incidence, the neutrons reflected can be used to probe the composition and magnetization of the solid near its surface. In this process, the incident and reflected neutrons generally have identical kinetic energies. Here we report the results of an experiment in which subtle inelastic scattering processes are revealed as relatively large deviations in scattering angle. The neutrons are scattered from a ferromagnetic surface in the presence of a strong ambient magnetic field, and exhibit a small but significant variation in kinetic energy as a function of the reflection angle. This effect is attributable to the Zeeman splitting of the energies of the neutron spin states due to the ambient magnetic field: some neutrons flip their spins upon reflection from the magnetized surface, thereby exchanging kinetic energy for magnetic potential energy. The subtle effects of Zeeman splitting are amplified by the extreme sensitivity of grazing-angle neutron scattering, and might also provide a useful spectroscopic tool if significant practical obstacles (such as low interaction cross-sections) can be overcome. (author)
International Nuclear Information System (INIS)
O'Donoghue, J.A.
1986-01-01
These letters discuss the problems associated with the fact that the normal tissue isoeffect formulae based on the Ellis equation (1969) do not correctly account for the late-occurring effects of fractionated radiotherapy, and with the extension of the linear quadratic model to include continuous low dose-rate radiotherapy with constant or decaying sources by R.G. Dale (1985). J.A. O'Donoghue points out that the 'late effects' and CRE curves correspond closely, whilst the 'acute effects; and CRE curves are in obvious disagreement. For continuous low-dose-rate radiotherapy, the CRE and late effects quadratic model are in agreement. Useful bibliography. (U.K.)
Parity nonconservation in Zeeman atomic transitions
International Nuclear Information System (INIS)
Kraftmakher, A.Ya.
1990-01-01
The abilities to observe the parity violation at the radiofrequency transitions between the hyperfine and Zeeman terms of the atomic levels are considered. The E-1 amplitudes fo the Zeeman transitions of heavy atoms in weak magnetic fields are larger, than for the light atoms hyperfine transitions at the same wavelength. 9 refs
International Nuclear Information System (INIS)
Lee, Steve P.; Leu, Min Y.; Smathers, James B.; McBride, William H.; Parker, Robert G.; Withers, H. Rodney
1995-01-01
Purpose: Radiotherapy plans based on physical dose distributions do not necessarily entirely reflect the biological effects under various fractionation schemes. Over the past decade, the linear-quadratic (LQ) model has emerged as a convenient tool to quantify biological effects for radiotherapy. In this work, we set out to construct a mechanism to display biologically oriented dose distribution based on the LQ model. Methods and Materials: A computer program that converts a physical dose distribution calculated by a commercially available treatment planning system to a biologically effective dose (BED) distribution has been developed and verified against theoretical calculations. This software accepts a user's input of biological parameters for each structure of interest (linear and quadratic dose-response and repopulation kinetic parameters), as well as treatment scheme factors (number of fractions, fractional dose, and treatment time). It then presents a two-dimensional BED display in conjunction with anatomical structures. Furthermore, to facilitate clinicians' intuitive comparison with conventional fractionation regimen, a conversion of BED to normalized isoeffective dose (NID) is also allowed. Results: Two sample cases serve to illustrate the application of our tool in clinical practice. (a) For an orthogonal wedged pair of x-ray beams treating a maxillary sinus tumor, the biological effect at the ipsilateral mandible can be quantified, thus illustrates the so-called 'double-trouble' effects very well. (b) For a typical four-field, evenly weighted prostate treatment using 10 MV x-rays, physical dosimetry predicts a comparable dose at the femoral necks between an alternate two-fields/day and four-fields/day schups. However, our BED display reveals an approximate 21% higher BED for the two-fields/day scheme. This excessive dose to the femoral necks can be eliminated if the treatment is delivered with a 3:2 (anterio-posterior/posterio-anterior (AP
Energy Technology Data Exchange (ETDEWEB)
Blinov, L. M., E-mail: lev39blinov@gmail.com; Lazarev, V V; Palto, S P; Yudin, S G [Russian Academy of Sciences, Shubnikov Institute of Crystallography (Russian Federation)
2012-04-15
The low-frequency quadratic electro-optical effect with a maximum electro-optical coefficient of g = 8 Multiplication-Sign 10{sup -19} m{sup 2}/V{sup 2} (i.e., four orders of magnitude greater than the standard high-frequency value) has been studied in thin films of ferroelectric polymer PVDF(70%)-TrFE(30%). The observed effect is related to the process of spontaneous polarization switching, during which the electron oscillators of C-F and C-H dipole groups rotate to become parallel to the applied field. As a result, the ellipsoid of the refractive index exhibits narrowing in the direction perpendicular to the field. The field dependence of the electro-optical coefficient g correlates with that of the apparent dielectric permittivity, which can be introduced under the condition of ferroelectric polarization switching. The observed electro-optical effect strongly decreases when the frequency increases up to several hundred hertz. The temperature dependence of the effect exhibits clearly pronounced hysteresis in the region of the ferroelectric phase transition.
Energy Technology Data Exchange (ETDEWEB)
Borges, Aline R. [Instituto de Química, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS (Brazil); Instituto Nacional de Ciência e Tecnologia do CNPq–INCT de Energia e Ambiente, Universidade Federal da Bahia, Salvador, BA (Brazil); Becker, Emilene M.; Dessuy, Morgana B. [Instituto de Química, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS (Brazil); Vale, Maria Goreti R., E-mail: mgrvale@ufrgs.br [Instituto de Química, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS (Brazil); Instituto Nacional de Ciência e Tecnologia do CNPq–INCT de Energia e Ambiente, Universidade Federal da Bahia, Salvador, BA (Brazil); Welz, Bernhard [Instituto Nacional de Ciência e Tecnologia do CNPq–INCT de Energia e Ambiente, Universidade Federal da Bahia, Salvador, BA (Brazil); Departamento de Química, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil)
2014-02-01
In this work, chemical modifiers in solution (Pd/Mg, NH{sub 4}H{sub 2}PO{sub 4} and NH{sub 4}NO{sub 3}/Pd) were compared with permanent modifiers (Ir and Ru) for the determination of lead in fertilizer and limestone samples using slurry sampling and graphite furnace atomic absorption spectrometry with Zeeman-effect background correction. The analytical line at 283.3 nm was used due to some spectral interference observed at 217.0 nm. The NH{sub 4}H{sub 2}PO{sub 4} was abandoned due to severe spectral interference even at the 283.3-nm line. For Pd/Mg and NH{sub 4}NO{sub 3}/Pd the optimum pyrolysis and atomization temperatures were 900 °C and 1900 °C, respectively. For Ru and Ir, the integrated absorbance signal was stable up to pyrolysis temperatures of 700 °C and 900 °C, respectively, and up to atomization temperature of 1700 °C. The limit of detection (LOD) was 17 ng g{sup −1} using Pd/Mg and 29 ng g{sup −1} using NH{sub 4}NO{sub 3}/Pd. Among the permanent modifiers investigated, the LOD was 22 ng g{sup −1} Pb for Ir and 10 ng g{sup −1} Pb for Ru. The accuracy of the method was evaluated using the certified reference material NIST SRM 695. Although Ru provided lower LOD, which can be attributed to a lower blank signal, only the modifiers in solution showed concordant values of Pb concentration for the NIST SRM 695 and the most of analyzed samples. Moreover, the Pd/Mg modifier provided the highest sensitivity and for this reason it is more suitable for the determination of Pb in fertilizers samples in slurry; besides this it presented a better signal-to-noise ratio than NH{sub 4}NO{sub 3}/Pd. - Highlights: • Lead has been determined in fertilizers using slurry sampling GF AAS. • The mixture of palladium and magnesium nitrates was found to be the ideal chemical modifier. • Calibration could be carried out against aqueous standard solutions. • The proposed method is much faster than the EPA method, which includes sample digestion.
International Nuclear Information System (INIS)
Gunning, Mark J.; Raab, Roger E.; Kucharczyk, Wlodimierz
2001-01-01
Measurements of the magnitude and the sign of certain quadratic electro-optic coefficients of potassium dihydrogen phosphate (KDP) and ammonium dihydrogen phosphate (ADP) were made with an actively stabilized Michelson interferometer. The results obtained for these coefficients are, in units of 10 -20 m 2 V -2 (as opposed to literature values of order 10 -18 m 2 V -2 ), as follows: (KDP)g xxxx =-3.4±0.5, g yyxx =-0.2±0.4, and g zzxx =-0.7±0.4; (ADP)g xxxx =-7.4±1.0, g yyxx =-1.7±0.9, and g zzxx =-1.4±0.9. The quadratic Faust--Henry coefficient describing the lattice and the electronic contributions to the quadratic electro-optic effect in KDP and ADP is estimated from our results. These show that the nonlinear susceptibility responsible for the quadratic electro-optic effect in these crystals is due mainly to nonlinear interactions of the low-frequency electric field with the crystal lattice. Copyright 2001 Optical Society of America
Lu, Peng
2015-10-01
Cooperation is vital in human societies and therefore is widely investigated in the evolutionary game theory. Varieties of mechanisms have been proposed to overcome temptation and promote cooperation. Existing studies usually believe that agents are rational, but irrationalism such as emotions and feelings matters as well. Winner and loser are defined by their payoffs. In addition to admiring and imitating winners, the mechanism of sympathizing and imitating losers is introduced into the model as an alternative action rule, and each one plays the prisoners' dilemma game with eight neighbors under the influence of both irrationalism and rationalism. Rationalism refers to imitating winner to get highest payoff, and irrationalism means that people sympathize and adopt the actions of losers. As it is widely recognized that temptation reduces cooperation, this study focuses on the effect of sympathy on cooperation within a certain group or society. If it overcomes temptation that leads to defection, sympathy will be a powerful mechanism to promote cooperative behavior. Simulation results indicate that sympathy and temptation shares similar quadratic relationships with cooperation. Both sympathy and temptation undermine cooperation below their thresholds, and they both promote cooperation above their thresholds. Temptation not only reduces cooperation but also promote it as temptation goes beyond the threshold. Although sympathy is a good merit or human nature that is beneficial to society, a crisis or collapse of cooperation is inevitable when the sympathy propensity is relatively smaller. After cooperation reaches a minimal bottom, it then rises increasingly and dramatically, which brings a much brighter future of the society.
Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord
International Nuclear Information System (INIS)
Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University
1993-01-01
The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab
International Nuclear Information System (INIS)
Deguchi, K; Imagawa, T; Shikama, T; Hasuo, M
2009-01-01
We have measured the relaxation rate of alignment of neon atoms in a 2p 2 (in Paschen notation) level, which were excited by a linearly polarized laser pulse in a glow discharge plasma at 77 K, in a magnetic field of up to 3 T in the Voigt configuration. The relaxation rate decreased with an increase in the magnetic field strength of up to 0.5 T and showed no magnetic field dependence above 0.5 T. We developed a Monte Carlo simulation method to calculate alignment relaxation, or disalignment, by radiation re-absorption of atomic resonance lines in a magnetic field. The simulated result was found to be consistent with the observed magnetic field dependence. We analysed the results of the simulation from a point of competition between the Zeeman splitting and the Doppler broadening of the transition lines from the 2p 2 level.
Magnetic Field Measurements In Magnetized Plasmas Using Zeeman Broadening Diagnostics
Haque, Showera; Wallace, Matthew; Presura, Radu; Neill, Paul
2017-10-01
The Zeeman effect has been used to measure the magnetic field in high energy density plasmas. This method is limited when plasma conditions are such that the line broadening due to the high plasma density and temperature surpasses the Zeeman splitting. We have measured magnetic fields in magnetized laser plasmas under conditions where the Zeeman splitting was not spectrally resolved. The magnetic field strength was determined from the difference in widths of two doublet components, using an idea proposed by Tessarin et al. (2011). Time-gated spectra with one-dimensional space-resolution were obtained at the Nevada Terawatt Facility for laser plasmas created by 20 J, 1 ns Leopard laser pulses, and expanding in the azimuthal magnetic field produced by the 0.6 MA Zebra pulsed power generator. We explore the response of the Al III 4s 2S1/2 - 4p 2P1 / 2 , 3 / 2 doublet components to the external magnetic field spatially along the plasma. Radial magnetic field and electron density profiles were measured within the plasma plume. This work was supported by the DOE/OFES Grant DE-SC0008829 and DOE/NNSA contract DE-FC52-06NA27616.
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
International Nuclear Information System (INIS)
Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-01-01
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported
Energy Technology Data Exchange (ETDEWEB)
Lepri, Fabio G. [Departamento de Quimica, Universidade Federal de Santa Catarina, 88040-900 Florianopolis, SC (Brazil); Welz, Bernhard, E-mail: w.bernardo@terra.com.b [Departamento de Quimica, Universidade Federal de Santa Catarina, 88040-900 Florianopolis, SC (Brazil); Dessuy, Morgana B.; Vale, Maria Goreti R. [Instituto de Quimica, Universidade Federal do Rio Grande do Sul, Av. Bento Goncalves, 9500, 91501-970 Porto Alegre-RS (Brazil); Bohrer, Denise [Departamento de Quimica, Universidade Federal de Santa Maria, 97110-905 Santa Maria, RS (Brazil); Loos-Vollebregt, Margaretha T.C. de [Delft University of Technology, Faculty of Applied Sciences, Analytical Biotechnology, Julianalaan 137, 2628 BL Delft (Netherlands); Department of Analytical Chemistry, Ghent University, Krijgslaan 281 - S12, B-9000 Ghent (Belgium); Mao Donghuang; Becker-Ross, Helmut [ISAS, Institute for Analytical Sciences, Department of Interface Spectroscopy, Albert-Einstein Str. 9, 12489 Berlin (Germany)
2010-01-15
The determination of phosphorus by graphite furnace atomic absorption spectrometry at the non-resonance line at 213.6 nm, and the capability of Zeeman-effect background correction (Z-BC) to deal with the fine-structured background absorption due to the PO molecule have been investigated in the presence of selected chemical modifiers. Two line source atomic absorption spectrometers, one with a longitudinally heated and the other with a transversely heated graphite tube atomizer have been used in this study, as well as two prototype high-resolution continuum source atomic absorption spectrometers, one of which had a longitudinally arranged magnet at the furnace. It has been found that Z-BC is capable correcting very well the background caused by the PO molecule, and also that of the NO molecule, which has been encountered when the Pd + Ca mixed modifier was used. Both spectra exhibited some Zeeman splitting, which, however, did not cause any artifacts or correction errors. The practical significance of this study is to confirm that accurate results can be obtained for the determination of phosphorus using Z-BC. The best sensitivity with a characteristic mass of m{sub 0} = 11 ng P has been obtained with the pure Pd modifier, which also caused the lowest background level. The characteristic mass obtained with the mixed Pd+Ca modifier depended on the equipment used and was between m{sub 0} = 9 ng P and m{sub 0} = 15 ng P, and the background signal was higher. The major problem of Z-BC remains the relatively restricted linear working range.
Optimal Quadratic Programming Algorithms
Dostal, Zdenek
2009-01-01
Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…
Quadratic spatial soliton interactions
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
Janssen, D.M.; Paas, L.J.
2014-01-01
The authors hypothesize and find that an advertising model's body size has an inverted U-shaped relationship with ad attitude in the apparel product category, in which moderately thin advertising models are optimal. They assess the moderating effect of consumers' fashion leadership on this quadratic
Dickmann, M
2015-01-01
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in
Ellis, John; Sueiro, Maria
2014-01-01
Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
A Zeeman slower for diatomic molecules
Petzold, M.; Kaebert, P.; Gersema, P.; Siercke, M.; Ospelkaus, S.
2018-04-01
We present a novel slowing scheme for beams of laser-coolable diatomic molecules reminiscent of Zeeman slowing of atomic beams. The scheme results in efficient compression of the one-dimensional velocity distribution to velocities trappable by magnetic or magneto-optical traps. We experimentally demonstrate our method in an atomic testbed and show an enhancement of flux below v = 35 m s‑1 by a factor of ≈20 compared to white light slowing. 3D Monte Carlo simulations performed to model the experiment show excellent agreement. We apply the same simulations to the prototype molecule 88Sr19F and expect 15% of the initial flux to be continuously compressed in a narrow velocity window at around 10 m s‑1. This is the first experimentally shown continuous and dissipative slowing technique in molecule-like level structures, promising to provide the missing link for the preparation of large ultracold molecular ensembles.
Duarte, Jonathan T.
2010-01-01
Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…
Soudackov, Alexander V; Hammes-Schiffer, Sharon
2015-11-21
Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton
International Nuclear Information System (INIS)
Soudackov, Alexander V.; Hammes-Schiffer, Sharon
2015-01-01
Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton
Zamani, A.; Azargoshasb, T.; Niknam, E.
2017-10-01
Effects of applied magnetic field, temperature and dimensions on the optical absorption coefficients (AC) and refractive index (RI) changes of a GaAs quantum ring are investigated in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI). To this end, the finite difference method (FDM) is used in order to numerically calculate the energy eigenvalues and eigenstates of the system while the compact density matrix approach is hired to calculate the optical properties. It is shown that application of magnetic field, temperature as well as the geometrical size in the presence of spin-orbit interactions, alter the electronic structure and consequently influence the linear and third-order nonlinear optical absorption coefficients as well as the refractive index changes of the system. Results show an obvious blue shift in optical curves with enhancing external magnetic field and temperature while the increment of dimensions result in red shift.
Zamani, A.; Setareh, F.; Azargoshasb, T.; Niknam, E.
2017-10-01
A wide variety of semiconductor nanostructures have been fabricated experimentally and both theoretical and experimental investigations of their features imply the great role they have in new generation technological devices. However, mathematical modeling provide a powerful means due to definitive goal of predicting the features and understanding of such structures behavior under different circumstances. Therefore, effective Hamiltonian for an electron in a quantum ring with axial symmetry in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI) is derived. Here we report our study of the electronic structure and electron g-factor in the presence of spin-orbit (SO) couplings under the influence of external magnetic field at finite temperature. This investigation shows that, when Rashba and Dresselhaus couplings are simultaneously present, the degeneracy is removed and energy levels split into two branches. Furthermore, with enhancing the applied magnetic field, separation of former degenerate levels increases and also avoided crossings (anti-crossing) in the energy spectra is detected. It is also discussed how the energy levels of the system can be adjusted with variation of temperature as well as the magnetic field and geometrical sizes.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
DEFF Research Database (Denmark)
Esbensen, B.K.; Bache, Morten; Krolikowski, W.
2012-01-01
We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....
ZEST: A Fast Code for Simulating Zeeman-Stark Line-Shape Functions
Directory of Open Access Journals (Sweden)
Franck Gilleron
2018-03-01
Full Text Available We present the ZEST code, dedicated to the calculation of line shapes broadened by Zeeman and Stark effects. As concerns the Stark effect, the model is based on the Standard Lineshape Theory in which ions are treated in the quasi-static approximation, whereas the effects of electrons are represented by weak collisions in the framework of a binary collision relaxation theory. A static magnetic field may be taken into account in the radiator Hamiltonian in the dipole approximation, which leads to additional Zeeman splitting patterns. Ion dynamics effects are implemented using the fast Frequency-Fluctuation Model. For fast calculations, the static ion microfield distribution in the plasma is evaluated using analytic fits of Monte-Carlo simulations, which depend only on the ion-ion coupling parameter and the electron-ion screening factor.
Zeeman catastrophe machines as a toolkit for teaching chaos
International Nuclear Information System (INIS)
Nagy, Péter; Tasnádi, Péter
2014-01-01
The investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics in the basic course of mechanics taught to engineering students. In this paper, it will be demonstrated that the Zeeman machine can be a versatile and motivating tool for students to acquire introductory knowledge about chaotic motion via interactive simulations. The Zeeman catastrophe machine is a typical example of a quasi-static system with hysteresis. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple, the experimental investigation and the theoretical description can be connected intuitively. Although the Zeeman machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman machine, a wide range of chaotic properties of the simple systems can be demonstrated, such as bifurcation diagrams, chaotic attractors, transient chaos, Lyapunov exponents and so on. This paper is organically linked to our website (http://csodafizika.hu/zeeman) where the discussed simulation programs can be downloaded. In a second paper, the novel construction of a network of Zeeman machines will be presented to study the properties of cooperative systems. (paper)
THE HANLE AND ZEEMAN POLARIZATION SIGNALS OF THE SOLAR Ca II 8542 Å LINE
Energy Technology Data Exchange (ETDEWEB)
Štěpán, Jiri [Astronomical Institute ASCR, Fričova 298, 251 65 Ondřejov (Czech Republic); Bueno, Javier Trujillo [Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife (Spain)
2016-07-20
We highlight the main results of a three-dimensional (3D) multilevel radiative transfer investigation about the solar disk-center polarization of the Ca ii 8542 Å line. First, through the use of a 3D model of the solar atmosphere, we investigate the linear polarization that occurs due to the atomic level polarization produced by the absorption and scattering of anisotropic radiation, taking into account the symmetry-breaking effects caused by its thermal, dynamic, and magnetic structure. Second, we study the contribution of the Zeeman effect to the linear and circular polarization. Finally, we show examples of the Stokes profiles produced by the joint action of the atomic level polarization and the Hanle and Zeeman effects. We find that the Zeeman effect tends to dominate the linear polarization signals only in the localized patches of opposite magnetic polarity, where the magnetic field is relatively strong and slightly inclined; outside such very localized patches, the linear polarization is often dominated by the contribution of atomic level polarization. We demonstrate that a correct modeling of this last contribution requires taking into account the symmetry-breaking effects caused by the thermal, dynamic, and magnetic structure of the solar atmosphere, and that in the 3D model used the Hanle effect in forward-scattering geometry (disk-center observation) mainly reduces the polarization corresponding to the zero-field case. We emphasize that, in general, a reliable modeling of the linear polarization in the Ca ii 8542 Å line requires taking into account the joint action of atomic level polarization and the Hanle and Zeeman effects.
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
ZEEMAN DOPPLER MAPS: ALWAYS UNIQUE, NEVER SPURIOUS?
Energy Technology Data Exchange (ETDEWEB)
Stift, Martin J.; Leone, Francesco [Armagh Observatory, College Hill, Armagh BT61 9DG (United Kingdom)
2017-01-01
Numerical models of atomic diffusion in magnetic atmospheres of ApBp stars predict abundance structures that differ from the empirical maps derived with (Zeeman) Doppler mapping (ZDM). An in-depth analysis of this apparent disagreement investigates the detectability by means of ZDM of a variety of abundance structures, including (warped) rings predicted by theory, but also complex spot-like structures. Even when spectra of high signal-to-noise ratio are available, it can prove difficult or altogether impossible to correctly recover shapes, positions, and abundances of a mere handful of spots, notwithstanding the use of all four Stokes parameters and an exactly known field geometry; the recovery of (warped) rings can be equally challenging. Inversions of complex abundance maps that are based on just one or two spectral lines usually permit multiple solutions. It turns out that it can by no means be guaranteed that any of the regularization functions in general use for ZDM (maximum entropy or Tikhonov) will lead to a true abundance map instead of some spurious one. Attention is drawn to the need for a study that would elucidate the relation between the stratified, field-dependent abundance structures predicted by diffusion theory on the one hand, and empirical maps obtained by means of “canonical” ZDM, i.e., with mean atmospheres and unstratified abundances, on the other hand. Finally, we point out difficulties arising from the three-dimensional nature of the atomic diffusion process in magnetic ApBp star atmospheres.
Threshold nonlinear absorption in Zeeman transitions
International Nuclear Information System (INIS)
Narayanan, Andal; Hazra, Abheera; Sandhya, S N
2010-01-01
We experimentally study the absorption spectroscopy from a collection of gaseous 87 Rb atoms at room temperature irradiated with three fields. Two of these fields are in a pump-probe saturation absorption configuration. The third field co-propagates with the pump field. The three fields address Zeeman degenerate transitions between hyperfine levels 5S 1/2 , F = 1 and 5P 3/2 , F = 0, F = 1 around the D2 line. We find a sub-natural absorption resonance in the counter-propagating probe field for equal detunings of all three fields. This absorption arises in conjunction with the appearance of increased transmission due to electro-magnetically induced transparency in the co-propagating fields. The novel feature of this absorption is its onset only for the blue of 5P 3/2 , F = 0, as the laser frequency is scanned through the excited states 5P 3/2 , F = 0, F = 1 and F = 2. The absorption rapidly rises to near maximum values within a narrow band of frequency near 5P 3/2 , F = 0. Our experimental results are compared with a dressed atom model. We find the threshold absorption to be a result of coherent interaction between the dressed states of our system.
Isotope separation utilizing Zeeman compensated magnetic extraction
International Nuclear Information System (INIS)
Forsen, H.K.
1978-01-01
A vapor flow of elemental uranium is directed into a region where narrow band, tuned laser radiation is repeatedly applied to provide at least two energy step selective ionization of the U 235 isotope in the vapor flow. A magnetic field is applied in the region of the ionized U 235 which creates a Lorentz force on the moving ions directing them toward one of a plurality of collection plates placed generally parallel to the vapor flow to permit collection of the U 235 particles in substantially enriched proportions as compared to the concentration in the vapor flow generally. To prevent a broadening of the absorption lines for both the U 235 and U 238 isotopes in the vapor flow from the applied magnetic field and thus prevent substantial reduction in the selectivity of the excitation and ionization, the magnetic field is preferably applied in a time varying magnitude which is phased with respect to the repetitive application of laser radiation to provide a relatively low field strength and corresponding small Zeeman splitting during selective excitation and ionization of the U 235 particles
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Spin-flip transitions between Zeeman sublevels in semiconductor quantum dots
International Nuclear Information System (INIS)
Khaetskii, Alexander V.; Nazarov, Yuli V.
2001-01-01
We have studied spin-flip transitions between Zeeman sublevels in GaAs electron quantum dots. Several different mechanisms which originate from spin-orbit coupling are shown to be responsible for such processes. It is shown that spin-lattice relaxation for the electron localized in a quantum dot is much less effective than for the free electron. The spin-flip rates due to several other mechanisms not related to the spin-orbit interaction are also estimated
Indian Academy of Sciences (India)
V. Suresh University Of Hyderabad Hyderabad
2008-10-31
Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Anisotropic semivortices in dipolar spinor condensates controlled by Zeeman splitting
Liao, Bingjin; Li, Shoubo; Huang, Chunqing; Luo, Zhihuan; Pang, Wei; Tan, Haishu; Malomed, Boris A.; Li, Yongyao
2017-10-01
Spatially anisotropic solitary vortices, i.e., bright anisotropic vortex solitons (AVSs), supported by anisotropic dipole-dipole interactions, were recently predicted in spin-orbit-coupled binary Bose-Einstein condensates (BECs), in the form of two-dimensional semivortices (complexes built of zero-vorticity and vortical components). We demonstrate that the shape of the AVSs—horizontal or vertical, with respect to the in-plane polarization of the atomic dipole moments in the underlying BEC—may be effectively controlled by the strength Ω of the Zeeman splitting (ZS). A transition from the horizontal to vertical shape with the increase of Ω is found numerically and explained analytically. At the transition point, the AVS assumes the shape of an elliptical ring. The mobility of horizontal AVSs is studied, too, with the conclusion that, with the increase of Ω , their negative effective mass changes the sign to positive via a point at which the effective mass diverges. Lastly, we report a new species of inverted AVSs, with the zero-vorticity and vortex component placed in lower- and higher-energy components, as defined by the ZS. They are excited states, with respect to the ground states provided by the usual AVSs. Quite surprisingly, inverted AVSs are stable in a large parameter region.
Very Large Array H I Zeeman Observations of the Cygnus X Region: DR 22 and ON 2
Mayo, E. A.; Troland, T. H.
2012-02-01
We have used the Very Large Array to study the Zeeman effect in 21 cm H I absorption lines from two star-forming regions in the Cygnus X complex, DR 22 and ON 2. We measure the line-of-sight magnetic field toward these regions, finding B los = -84 ± 11 μG toward the DR 22 H II region and B los < 50 μG toward each of the two H II regions in ON 2. We interpret these results in terms of two different models. In one model, we assume that the H I Zeeman effect is a measure of magnetic fields in the associated molecular clouds. If so, then the DR 22 molecular cloud is magnetically subcritical, that is, magnetically dominated. The ON 2 molecular clouds are magnetically supercritical. In a second model, we assume that the H I Zeeman effect is a measure of magnetic fields in photon-dominated regions where the gas has been compressed (and the field amplified) by absorption of stellar radiation. We find that this second model, where the measured field strength has been affected by star formation, accounts well for the DR 22 H I Zeeman effect. This same model, however, overpredicts the magnetic field in ON 2. ON 2 may be a region where the magnetic field is energetically insignificant or where the field happens to lie nearly in the plane of the sky.
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Cascaded Quadratic Soliton Compression in Waveguide Structures
DEFF Research Database (Denmark)
Guo, Hairun
between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...
Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao
2018-04-01
We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.
Quadratic soliton self-reflection at a quadratically nonlinear interface
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
Chaotic behaviour of Zeeman machines at introductory course of mechanics
Nagy, Péter; Tasnádi, Péter
2016-05-01
Investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics into the basic course of mechanics taught to engineering students. In the present paper it will be demonstrated that Zeeman Machine can be a versatile and motivating tool for students to get introductory knowledge about chaotic motion via interactive simulations. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple the experimental investigation and the theoretical description can be connected intuitively. Although Zeeman Machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman Machine a wide range of chaotic properties of the simple systems can be demonstrated such as bifurcation diagrams, chaotic attractors, transient chaos and so on. The main goal of this paper is the presentation of an interactive learning material for teaching the basic features of the chaotic systems through the investigation of the Zeeman Machine.
Chaotic behaviour of Zeeman machines at introductory course of mechanics
International Nuclear Information System (INIS)
Nagy, P.; Tasnádi, P.
2015-01-01
Investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics into the basic course of mechanics taught to engineering students. In the present paper it will be demonstrated that Zeeman Machine can be a versatile and motivating tool for students to get introductory knowledge about chaotic motion via interactive simulations. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple the experimental investigation and the theoretical description can be connected intuitively. Although Zeeman Machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman Machine a wide range of chaotic properties of the simple systems can be demonstrated such as bifurcation diagrams, chaotic attractors, transient chaos and so on. The main goal of this paper is the presentation of an interactive learning material for teaching the basic features of the chaotic systems through the investigation of the Zeeman Machine. 1. –
Characterization of a magnetic trap by polarization dependent Zeeman spectroscopy
DEFF Research Database (Denmark)
Nielsen, Carsten Vandel; Lyngsøe, Jens Kristian; Thorseth, Anders
2008-01-01
This paper demonstrates a detailed experimental study of our cloverleaf magnetic trap for sodium atoms. By using polarization dependent Zeeman spectroscopy of our atomic beam, passing the magnetic trap region, we have determined important trap parameters such as gradients, their curvatures...
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Quadratic brackets from symplectic forms
International Nuclear Information System (INIS)
Alekseev, Anton Yu.; Todorov, Ivan T.
1994-01-01
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....
Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz
2015-04-01
Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Zhang, Chenxiao; Lian, Jing; Jiang, Zongshan; Guo, Jianbo; Guo, Yankai; Gou, Chenye
2016-01-01
In this study the effect of trace elements on methanogenesis was investigated during mixed anaerobic fermentation using a single-factor experiment in the present study. The most effective concentrations of Fe"0, Fe"2"+, Co"2"+ and Ni"2"+ that were added were 1500, 250, 0.3 and 0.6 mg/L, respectively. The optimal trace element combination was 0.58 mg/L Ni"2"+, 1200 mg/L Fe"0 and 0.34 mg/L Co"2"+ by the ternary quadratic general rotary unitised design method. The degree of influence exerted by trace elements on the cumulative methane yields decreased in the order of Ni"2"+, Fe"0 and Co"2"+, and the maximum CH_4 yield was 241.6 mL/g volatile solids (VS), according to a regression equation. The non-dissolved organic carbon hydrolytic process showed a good fit with the first-order kinetic model. The maximum value of CH_4 was 312.87 mL/g VS. Compared to the control, the bioconversion efficiencies of CH_4 and CO_2 production increased by 36.76% and 74.50%, respectively, at the optimal trace element combination. The obtained results provide new knowledge for improvements in the efficiency of anaerobic fermentation biogas production
Phase control of a Zeeman-split He-Ne gas laser by variation of the gaseous discharge voltage.
Shelton, W N; Hunt, R H
1992-07-20
Zeeman-split lasers are useful for precise positioning or motion control. In applications that employ such a laser to control closely the position of a moving system, phase noise in the Zeeman frequency is a serious problem. Control of low-frequency phase noise can be obtained through variation of the external magnetic field by way of a solenoid wound around the laser tube. It is the finding in this work that control of the residual higher-frequency noise of a He-Ne laser can be obtained through small variations of the high voltage that is used to effect the gaseous discharge in the laser tube. The application of the present system is to the control of the path difference in a Fourier-transform interferometric spectrometer.
International Nuclear Information System (INIS)
Shibamoto, Yuta; Otsuka, Shinya; Iwata, Hiromitsu; Sugie, Chikao; Ogino, Hiroyuki; Tomita, Natsuo
2012-01-01
Since the dose delivery pattern in high-precision radiotherapy is different from that in conventional radiation, radiobiological assessment of the physical dose used in stereotactic irradiation and intensity-modulated radiotherapy has become necessary. In these treatments, the daily dose is usually given intermittently over a time longer than that used in conventional radiotherapy. During prolonged radiation delivery, sublethal damage repair takes place, leading to the decreased effect of radiation. This phenomenon is almost universarily observed in vitro. In in vivo tumors, however, this decrease in effect can be counterbalanced by rapid reoxygenation, which has been demonstrated in a laboratory study. Studies on reoxygenation in human tumors are warranted to better evaluate the influence of prolonged radiation delivery. Another issue related to radiosurgery and hypofractionated stereotactic radiotherapy is the mathematical model for dose evaluation and conversion. Many clinicians use the linear-quadratic (LQ) model and biologically effective dose (BED) to estimate the effects of various radiation schedules, but it has been suggested that the LQ model is not applicable to high doses per fraction. Recent experimental studies verified the inadequacy of the LQ model in converting hypofractionated doses into single doses. The LQ model overestimates the effect of high fractional doses of radiation. BED is particularly incorrect when it is used for tumor responses in vivo, since it does not take reoxygenation into account. For normal tissue responses, improved models have been proposed, but, for in vivo tumor responses, the currently available models are not satisfactory, and better ones should be proposed in future studies. (author)
Stability in quadratic torsion theories
Energy Technology Data Exchange (ETDEWEB)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-11-15
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Stability in quadratic torsion theories
International Nuclear Information System (INIS)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado
2017-01-01
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Collision assisted Zeeman cooling with multiple types of atoms
Hamilton, Mathew S.; Wilson, Rebekah F.; Roberts, Jacob L.
2014-01-01
Through a combination of spin-exchange collisions in a magnetic field and optical pumping, it is possible to cool a gas of atoms without requiring the loss of atoms from the gas. This technique, collision assisted Zeeman cooling (CAZ), was developed theoretically assuming a single atomic species [G. Ferrari, Eur. Phys. J. D 13, 67 (2001)]. We have extended this cooling technique to a system of two atomic species rather than just one and have developed a simple analytic model describing the cooling rate. We find that the two-isotope CAZ cooling scheme has a clear theoretical advantage in systems that are reabsorption limited.
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
On quadratic variation of martingales
Indian Academy of Sciences (India)
On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...
Quadratic divergences and dimensional regularisation
International Nuclear Information System (INIS)
Jack, I.; Jones, D.R.T.
1990-01-01
We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)
Application of Zeeman spatial beam-splitting in polarized neutron reflectometry
Kozhevnikov, S. V.; Ignatovich, V. K.; Radu, F.
2017-01-01
Neutron Zeeman spatial beam-splitting is considered at reflection from magnetically noncollinear films. Two applications of Zeeman beam-splitting phenomenon in polarized neutron reflectometry are discussed. One is the construction of polarizing devices with high polarizing efficiency. Another one is the investigations of magnetically noncollinear films with low spin-flip probability. Experimental results are presented for illustration.
Networks of Zeeman catastrophe machines for the investigation of complex systems
International Nuclear Information System (INIS)
Nagy, Péter; Tasnádi, Péter
2014-01-01
The investigation of chaotic motion and cooperative systems presents a great opportunity to involve modern physics into the basic course of mechanics taught to BSc-level students. In our previous paper (2014 Eur. J. Phys. 35 015018), it was demonstrated that a Zeeman machine can be a versatile and motivating tool for students to gain introductory knowledge about chaotic motion via interactive simulations. Although the Zeeman machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also very interesting and show typical chaotic features. In this paper, we present a novel construction consisting of Zeeman machines linked into a network. Although Zeeman networks can be built with almost arbitrary topology, our discussion is restricted to a system where Zeeman machines are arranged in a two-dimensional periodical lattice and the angular variables of the machines are limited to discrete values only. It will be shown that the Zeeman-crystal is appropriate for studying the properties of a broad range of complex systems. Using NetLogo simulations (second- and first-order) phase transitions, its ferromagnetic- and anti-ferromagnetic-type behaviour is demonstrated. A limiting case of the theoretical model of Zeeman-crystal leads to a model that is analogous to the Potts clock model used frequently in statistical physics. The present paper is organically linked to our website (http://csodafizika.hu/zeeman) where downloadable simulations, which are discussed in the paper, can be found. (paper)
AN ARECIBO SURVEY FOR ZEEMAN SPLITTING IN OH MEGAMASER GALAXIES
International Nuclear Information System (INIS)
McBride, James; Heiles, Carl
2013-01-01
We present the results of a comprehensive survey using the Arecibo Observatory for Zeeman splitting of OH lines in OH megamasers (OHMs). A total of 77 sources were observed with the Arecibo telescope. Of these, maser emission could not be detected for eight sources, and two sources were only ambiguously detected. Another 27 sources were detected at low signal-to-noise ratios or with interference that prevented placing any useful limits on the presence of magnetic fields. In 26 sources, it was possible to place upper limits on the magnitude of magnetic fields, typically between 10 and 30 mG. For 14 sources, the Stokes V spectra exhibit features consistent with Zeeman splitting. Eleven of these 14 are new detections, and the remaining three are re-detections of Stokes V detections in Robishaw et al. Among confident new detections, we derive magnetic fields associated with maser regions with magnitudes ranging from 6.1 to 27.6 mG. The distribution of magnetic field strengths suggests the magnetic fields in OH masing clouds in OHMs are larger than those in Galactic OH masers. The results are consistent with magnetic fields playing a dynamically important role in OH masing clouds in OHMs.
Directory of Open Access Journals (Sweden)
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Quadratic third-order tensor optimization problem with quadratic constraints
Directory of Open Access Journals (Sweden)
Lixing Yang
2014-05-01
Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.
International Nuclear Information System (INIS)
Lopez de la Cruz, J.; Gutierrez, M.A.
2008-01-01
This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed
Determination of ion temperatures from Zeeman broadened spectral lines in the edge of Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Klepper, C.C.; Isler, R.C.; Tobin, S.J.; Hogan, J.T. [Oak Ridge National Lab., TN (United States). Fusion Energy Div.; Hess, W.R. [Association EURATOM-CEA sur la Fusion Controlee, St-Paul-lez-Durance (France). Centre d`Etudes de Cadarache
1994-09-01
The authors have examined a {sup 3}P {yields} {sup 3}S multiplet of C III in Tore Supra in order to assess the possibility of determining the ion temperatures from transitions where the Zeeman effect cannot be neglected compared to the Doppler broadening. The preliminary studies lead them to believe that with good quality data the temperatures can be determined within about 20% in the 20--30 eV range and within about 50% in the neighborhood of 5 eV by fitting the entire multiplet rather than a semi-isolated feature, even though certain parameters important for the analysis, such as polarization effects of the optics, are not well characterized. In order to quantify these conclusions more precisely, future work will concentrate on developing numerical fitting routines and on examining the validity of the assumption that the distribution function for low ionization stages is Maxwellian.
Determination of ion temperatures from Zeeman broadened spectral lines in the edge of Tore Supra
International Nuclear Information System (INIS)
Klepper, C.C.; Isler, R.C.; Tobin, S.J.; Hogan, J.T.; Hess, W.R.
1994-01-01
The authors have examined a 3 P → 3 S multiplet of C III in Tore Supra in order to assess the possibility of determining the ion temperatures from transitions where the Zeeman effect cannot be neglected compared to the Doppler broadening. The preliminary studies lead them to believe that with good quality data the temperatures can be determined within about 20% in the 20--30 eV range and within about 50% in the neighborhood of 5 eV by fitting the entire multiplet rather than a semi-isolated feature, even though certain parameters important for the analysis, such as polarization effects of the optics, are not well characterized. In order to quantify these conclusions more precisely, future work will concentrate on developing numerical fitting routines and on examining the validity of the assumption that the distribution function for low ionization stages is Maxwellian
Wu, Y. J.; Shen, C.; Tan, Q. H.; Shi, J.; Liu, X. F.; Wu, Z. H.; Zhang, J.; Tan, P. H.; Zheng, H. Z.
2018-04-01
The valley Zeeman splitting of monolayer two-dimensional (2D) materials in the magnetic field plays an important role in the valley and spin manipulations. In general, a high magnetic field (6-65 T) and low temperature (2-30 K) were two key measurement conditions to observe the resolvable valley Zeeman splitting of monolayer 2D materials in current reported experiments. In this study, we experimentally demonstrate an effective measurement scheme by employing magnetic circular dichroism (MCD) spectroscopy, which enables us to distinguish the valley Zeeman splitting under a relatively low magnetic field of 1 T at room temperature. MCD peaks related to both A and B excitonic transitions in monolayer MoS2 can be clearly observed. Based on the MCD spectra under different magnetic fields (-3 to 3 T), we obtained the valley Zeeman splitting energy and the g-factors of A and B excitons, respectively. Our results show that MCD spectroscopy is a high-sensitive magneto-optical technique to explore the valley and spin manipulation in 2D materials.
Li, Yang; Xia, Houlin; Wu, Mingquan; Wang, Jiabo; Lu, Xiaohua; Wei, Shizhang; Li, Kun; Wang, Lifu; Wang, Ruilin; Zhao, Pan; Zhao, Yanling; Xiao, Xiaohe
2017-01-01
Skin infectious disease is a common public health problem due to the emergence of drug-resistant bacteria caused by the antibiotic misuse. Dracontomelon dao (Blanco) Merr. et Rolfe, a traditional Chinese medicine, has been used for the treatment of various skin infectious diseases over 1000 of years. Previous reports have demonstrated that the leaves of D. dao present favorable antibacterial activity against Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus, and Bacillus subtitles. The flavonoids are the main components of the ethyl acetate extract of D. dao leaf. However, the correlation between flavonoids and antibacterial activities is yet to be determined. In this study, the combined antibacterial activities of these flavonoids were investigated. Three samples with the different concentrations of flavonoids (S1–S3) were obtained. By microcalorimetric measurements, the results showed that the IC50 value of S2 was lower than those of S1 and S3. The contents of main flavonoids (including Luteolin, L-Epicatechin, Cianidanol, and Quercetin) in S1–S3 were various, confirmed by the method of the Ultra High Performance Liquid Chromatography (UPLC). Based on the method of quadratic general rotary unitized design, the antibacterial effect of single flavonoid, and the potential synergistic effects between Luteolin and Quercetin, Luteolin and Cianidanol were calculated, which were also proved by microcalorimetric analysis. The antibacterial activities of main flavonoids were Luteolin > Cianidanol > Quercetin > L-Epicatechin. Meanwhile, the synergistic effects of Luteolin and Cianidanol (PL+C = 1.425), Quercetin and Luteolin (PL+Q = 1.129) on anti-microbial activity were validated. Finally, we found that the contents of Luteolin, L-Epicatechin, Cianidanol, Quercetin were 1061.00–1061.00, 189.14–262.86, 15,990.33–16,973.62, 6799.67–7662.64 ng·ml−1 respectively, with the antibacterial rate over 60.00%. In conclusion, this study could provide
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
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...
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
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in
Studies on atom deceleration process by using the Zeeman-tuned technique
International Nuclear Information System (INIS)
Bagnato, V.S.
1990-01-01
The Zeeman-tuned technique to slow an atomic beam of sodium atoms was detailed studied. A new technique to study the deceleration which consists in monitoring the fluorescence along the deceleration path is used. This allows a direct observation of the process and open possibilities to investigate the adiabatic following of atoms in the magnetic field, and others very important aspects of the process. With a single laser and some modification of the magnetic field profile it is possible stop atoms outside the slower solenoid, which make a lot of experiments much simpler. A systematic study of the optical pumping effects and adiabatic following conditions allow to produce a very strong slow motion atomic beam. (author)
Yee, J. H.; Gjerloev, J.; Wu, D.; Schwartz, M. J.
2017-01-01
Using the O2 118 GHz spectral radiance measurements obtained by the Microwave Limb Sounder instrument on board the Aura spacecraft, we demonstrate that the Zeeman effect can be used to remotely measure the magnetic field perturbations produced by the auroral electrojet near the Hall current closure altitudes. Our derived current-induced magnetic field perturbations are found to be highly correlated with those coincidently obtained by ground magnetometers. These perturbations are also found to be linearly correlated with auroral electrojet strength. The statistically derived polar maps of our measured magnetic field perturbation reveal a spatial-temporal morphology consistent with that produced by the Hall current during substorms and storms. With today's technology, a constellation of compact, low-power, high spectral-resolution cubesats would have the capability to provide high precision and spatiotemporal magnetic field samplings needed for auroral electrojet measurements to gain insights into the spatiotemporal behavior of the auroral electrojet system.
Mercury pollution surveys in Riga by Zeeman atomic absorption spectroscopy
International Nuclear Information System (INIS)
Gavare, Z.; Bogans, E.; Svagere, A.
2008-01-01
Practical sessions of mercury pollution measurements in Riga (Latvia) have been performed in several districts using an RA-915+ Zeeman atomic absorption spectrometer coupled with a global positioning system (GPS). The measurements were taken from a driving car and in different days at one particular location (the Institute of Atomic Physics and Spectroscopy) for monitoring the changes in atmospheric mercury concentration. GPS was used to relate the measurement results to particular places, which made it possible to create a digitalized database of pollution for different geographic coordinates in different time spans. The measurements have shown that the background level of mercury concentration in Riga does not exceed 5 ng/m 3 , although there are several areas of elevated mercury pollution that need particular attention. (Authors)
Spatiotemporal Evolution of Hanle and Zeeman Synthetic Polarization in a Chromospheric Spectral Line
Energy Technology Data Exchange (ETDEWEB)
Carlin, E. S.; Bianda, M., E-mail: escarlin@irsol.es [Istituto Ricerche Solari Locarno, 6600, Locarno, Switzerland, associated to USI, Università della Svizzera Italiana (Switzerland)
2017-07-01
Due to the quick evolution of the solar chromosphere, its magnetic field cannot be inferred reliably without accounting for the temporal variations of its polarized light. This has been broadly overlooked in the modeling and interpretation of the polarization, due to technical problems (e.g., lack of temporal resolution or of time-dependent MHD solar models) and/or because many polarization measurements can apparently be explained without dynamics. Here, we show that the temporal evolution is critical for explaining the spectral-line scattering polarization because of its sensitivity to rapidly varying physical quantities and the possibility of signal cancellations and attenuation during extended time integration. For studying the combined effect of time-varying magnetic fields and kinematics, we solved the 1.5D non-LTE problem of the second kind in time-dependent 3D R-MHD solar models and synthesized the Hanle and Zeeman polarization in forward scattering for the chromospheric λ 4227 line. We find that the quiet-Sun polarization amplitudes depend on the periodicity and spectral coherence of the signal enhancements produced by kinematics, but that substantially larger linear polarization signals should exist all over the solar disk for short integration times. The spectral morphology of the polarization is discussed as a combination of Hanle, Zeeman, partial redistribution and dynamic effects. We give physical references for observations by degrading and characterizing our slit time series in different spatiotemporal resolutions. The implications of our results for the interpretation of the second solar spectrum and for the investigation of the solar atmospheric heatings are discussed.
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Interface-Induced Zeeman-Protected Superconductivity in Ultrathin Crystalline Lead Films
Directory of Open Access Journals (Sweden)
Yi Liu
2018-04-01
Full Text Available Two-dimensional (2D superconducting systems are of great importance for exploring exotic quantum physics. The recent development of fabrication techniques has stimulated studies of high-quality single-crystalline 2D superconductors, where intrinsic properties give rise to unprecedented physical phenomena. Here, we report the observation of Zeeman-type spin-orbit interaction protected superconductivity (Zeeman-protected superconductivity in 4-monolayer (ML to 6-ML crystalline Pb films grown on striped incommensurate Pb layers on Si(111 substrates by molecular beam epitaxy. An anomalously large in-plane critical field far beyond the Pauli limit is detected, which can be attributed to the Zeeman-protected superconductivity due to the in-plane inversion symmetry breaking at the interface. Our work demonstrates that, in superconducting heterostructures, the interface can induce Zeeman-type spin-orbit interactions and modulate the superconductivity.
Interface-Induced Zeeman-Protected Superconductivity in Ultrathin Crystalline Lead Films
Liu, Yi; Wang, Ziqiao; Zhang, Xuefeng; Liu, Chaofei; Liu, Yongjie; Zhou, Zhimou; Wang, Junfeng; Wang, Qingyan; Liu, Yanzhao; Xi, Chuanying; Tian, Mingliang; Liu, Haiwen; Feng, Ji; Xie, X. C.; Wang, Jian
2018-04-01
Two-dimensional (2D) superconducting systems are of great importance for exploring exotic quantum physics. The recent development of fabrication techniques has stimulated studies of high-quality single-crystalline 2D superconductors, where intrinsic properties give rise to unprecedented physical phenomena. Here, we report the observation of Zeeman-type spin-orbit interaction protected superconductivity (Zeeman-protected superconductivity) in 4-monolayer (ML) to 6-ML crystalline Pb films grown on striped incommensurate Pb layers on Si(111) substrates by molecular beam epitaxy. An anomalously large in-plane critical field far beyond the Pauli limit is detected, which can be attributed to the Zeeman-protected superconductivity due to the in-plane inversion symmetry breaking at the interface. Our work demonstrates that, in superconducting heterostructures, the interface can induce Zeeman-type spin-orbit interactions and modulate the superconductivity.
Green, J. A.; Gray, M. D.; Robishaw, T.; Caswell, J. L.; McClure-Griffiths, N. M.
2014-06-01
Recent comparisons of magnetic field directions derived from maser Zeeman splitting with those derived from continuum source rotation measures have prompted new analysis of the propagation of the Zeeman split components, and the inferred field orientation. In order to do this, we first review differing electric field polarization conventions used in past studies. With these clearly and consistently defined, we then show that for a given Zeeman splitting spectrum, the magnetic field direction is fully determined and predictable on theoretical grounds: when a magnetic field is oriented away from the observer, the left-hand circular polarization is observed at higher frequency and the right-hand polarization at lower frequency. This is consistent with classical Lorentzian derivations. The consequent interpretation of recent measurements then raises the possibility of a reversal between the large-scale field (traced by rotation measures) and the small-scale field (traced by maser Zeeman splitting).
Quadratic reactivity fuel cycle model
International Nuclear Information System (INIS)
Lewins, J.D.
1985-01-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper
Comparison between linear quadratic and early time dose models
International Nuclear Information System (INIS)
Chougule, A.A.; Supe, S.J.
1993-01-01
During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs
Energy Technology Data Exchange (ETDEWEB)
Ballester, E. Alsina; Bueno, J. Trujillo [Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife (Spain); Belluzzi, L., E-mail: ealsina@iac.es [Istituto Ricerche Solari Locarno, CH-6605 Locarno Monti (Switzerland)
2017-02-10
The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from a theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle–Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code that solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that magneto-optical effects have a strong impact on the linear polarization signals that PRD effects produce in the wings of strong resonance lines. We also show that the weak-field approximation has to be used with caution when PRD effects are considered.
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
Quadratically convergent MCSCF scheme using Fock operators
International Nuclear Information System (INIS)
Das, G.
1981-01-01
A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Entanglement and Zeeman interaction in diluted magnetic semiconductor quantum dot
International Nuclear Information System (INIS)
Hichri, A.; Jaziri, S.
2004-01-01
We present theoretically the Zeeman coupling and exchange-induced swap action in spin-based quantum dot quantum computer models in the presence of magnetic field. We study the valence and conduction band states in a double quantum dots made in diluted magnetic semiconductor. The latter have been proven to be very useful in building an all-semiconductor platform for spintronics. Due to a strong p-d exchange interaction in diluted magnetic semiconductor (Cd 0.57 Mn 0.43 Te), the relative contribution of this component is strongly affected by an external magnetic field, a feature that is absent in nonmagnetic double quantum dots. We determine the energy spectrum as a function of magnetic field within the Hund-Mulliken molecular-orbit approach and by including the Coulomb interaction. Since we show that the ground state of the two carriers confined in a vertically coupled quantum dots provide a possible realization for a gate of a quantum computer, the crossing between the lowest states, caused by the giant spin splitting, can be observed as a pronounced jump in the magnetization of small magnetic field amplitude. Finally, we determine the swap time as a function of magnetic field and the inter dot distance. We estimate quantitatively swap errors caused by the field, establishing that error correction would, in principle, be possible in the presence of nonuniform magnetic field in realistic structures
Zeeman spectroscopy of Zn-H complex in germanium
International Nuclear Information System (INIS)
Prabakar, J.P.C.; Vickers, R.E.M.; Fisher, P.
1998-01-01
Full text: A divalent substitutional zinc atom in germanium complexed with an interstitial hydrogen atom gives rise to a monovalent acceptor of trigonal symmetry. The axial nature of this complex splits the four-fold degenerate states associated with substitutional point defects into two two-fold degenerate states. Zeeman spectra of the Zn-H complex have been observed for B along and crystallographic directions in the Voigt configuration using linearly polarised radiation. Spectra of the C and D lines for B ≤ 2 Tesla are essentially identical to those of these lines of group III impurities; here B is the field strength. At all fields, splitting of the excited state of the D lines is identical to that for group III acceptors in germanium. The magnetic field dependence of the D components for both E parallel B and E perpendicular B and the selection rules demand that only one of the two two-fold 1s-like energy levels is occupied at the temperatures used instead of both. The results confirm piezospectroscopic studies which demonstrated that the axes of the complexes are along the four covalent bond directions of the host
Multiobjective Optimization Involving Quadratic Functions
Directory of Open Access Journals (Sweden)
Oscar Brito Augusto
2014-01-01
Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
Energy Technology Data Exchange (ETDEWEB)
Casabianca, T.; Bitonte, R.; Epifani, M.; Ubaldi, C. [ENEA, Divisione Tecnologie Ingegneria e Servizi Ambientali, Centro Ricerche Trisaia, MT (Italy)
2001-07-01
In the framework of SIMOA project have been investigated methods to evaluate the level of soil contamination due to heavy metals. In this wok, it is discussed a procedure to measure topsoil bioavailable fraction of seven heavy metals (Cd, Cu, Pb, Ni, Cr, Hg). The adopted procedure is based on acid digestion followed by instrumental detection by means of graphite furnace atomic-absorption spectrophotometry (GFAAS) using Zeeman effect to reduce background contribution. Details of samples preparation and analysis, experimental setup optimization and statistical data analysis are presented, together with a discussion on method accuracy and data interpretation. [Italian] Nell'ambito del progetto SIMOA (Sistema Integrato di Monitoraggio Ambientale) per il monitoraggio ambientale nel bacino del Basento (Regione Basilicata, Italia), vengono investigati i metodi per il controllo dei livelli di inquinamento del suolo da parte di metalli pesanti. Nel presente lavoro viene proposta una procedura per determinare il livello di concentrazione della frazione biodisponibile di sette metalli pesanti (Cadmio, Rame, Piombo, Nickel, Cromo, Mercurio) in campion di suolo superficiale. Il metodo e' basato su di un trattamento di digestione acida in forno a microonde cui segue la rivelazione strumentale mediante spettrofotometria di assorbimento atomico in fornetto di grafite (GFAAS) con effetto Zeeman per la correzione del fondo. Si descrivono in dettaglio le fasi di preparazione dei campioni, la metodologia di misura e l'analisi statistica dei dati, oltre ad una discussione sull'attendibilita' del metodo e sui futuri sviluppi.
Quadratic independence of coordinate functions of certain ...
Indian Academy of Sciences (India)
... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.
Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...
African Journals Online (AJOL)
Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...
International Nuclear Information System (INIS)
Chen, J C H; Klochan, O; Micolich, A P; Hamilton, A R; Martin, T P; Ho, L H; Zuelicke, U; Reuter, D; Wieck, A D
2010-01-01
In this paper, We study the Zeeman spin-splitting in hole quantum wires oriented along the [011] and [01 1-bar] crystallographic axes of a high mobility undoped (100)-oriented AlGaAs/GaAs heterostructure. Our data show that the spin-splitting can be switched 'on' (finite g*) or 'off' (zero g*) by rotating the field from a parallel to a perpendicular orientation with respect to the wire, and the properties of the wire are identical for the two orientations with respect to the crystallographic axes. We also find that the g-factor in the parallel orientation decreases as the wire is narrowed. This is in contrast to electron quantum wires, where the g-factor is enhanced by exchange effects as the wire is narrowed. This is evidence for a k-dependent Zeeman splitting that arises from the spin-3/2 nature of holes.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Gain scheduled linear quadratic control for quadcopter
Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.
2017-12-01
This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng
2013-01-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Numerical simulation of a high-brightness lithium ion gun for a Zeeman polarimetry on JT-60U
International Nuclear Information System (INIS)
Kojima, Atsushi; Kamiya, Kensaku; Fujita, Takaaki; Kamada, Yutaka; Iguchi, Harukazu
2007-01-01
A lithium ion gun is under construction for a lithium beam Zeeman polarimetry on JT-60U. The performance of the prototype ion gun has been estimated by the numerical simulation taking the space charge effects into account. The target values of the ion gun are the beam energy of 30 keV, the beam current of 10 mA and the beam divergence angle within 0.13 degrees. The low divergence of 0.13 degrees is required for the geometry of the Zeeman polarimetry on JT-60U where the observation area is 6.5 m away from the neutralizer. The numerical simulation needs to be carried out for the design study because the requirement of the divergence angle is severe for the development of the high-brightness ion gun. The simulation results show the beam loss of 50% caused by the clash to the electrode such as the cathode and the neutralizer. Moreover, the beam transport efficiency from the neutralizer to the observation area is low due to the broadening of the divergence angle. The total beam efficiency is about 5%. Extracted beam profile affects the beam focusing and the efficiency. The peaked profile achieves better efficiency than the hollow one. As a result, beam current of 1 mA is obtained at the observation area by the simulation for the prototype ion gun. (author)
Zeeman effect: new outlook on old perturbation theory
International Nuclear Information System (INIS)
Turbiner, A.V.
1980-01-01
The problem of hydrogen atom placed in constant external magnetic field is studied. The properties of ordinary perturbation theory (in powers of the field) in the framework of a new approach proposed earlier are investigated. The ground state are considered in detailed while the excited states are discussed only in brief. It is shown that the ''wave function corrections'' with in this approach are simpler than within ordinary one and contain a finite number of harmonics with polynomial coefficients. Some coefficients of these polynomials are found explicitly
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
Quadratic Poisson brackets compatible with an algebra structure
Balinsky, A. A.; Burman, Yu.
1994-01-01
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
A study of nuclear relaxation to the electron non-Zeeman system
International Nuclear Information System (INIS)
Honten, J. van.
1979-01-01
An examination of the nuclear spin-lattice relaxation mechanism in a series of diluted copper-caesium Tutton salt crystals, containing different percentages of D 2 O in the waters of hydration, is described. Results of relaxation measurements are presented and a strong angular dependence is observed. It is proved, however, that under most experimental conditions applied, the bottleneck in the relaxation path is not the cross-relaxation but the thermal contact between the proton Zeeman system and the electron dipole-dipole interaction system. Hence the proton spin-lattice relaxation measurements have enabled determination of the time constant of this thermal contact. The microscopic coupling process which provides thermal contact, is a simultaneous transition of two electron spins and one proton spin. This so-called three-spin transition is described and calculations presented. Double resonance experiments are performed, where the resonance signal of deuterium or caesium spins is saturated and the effect on the proton resonance signal observed. (C.F.)
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao
2015-01-01
be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution
Schur Stability Regions for Complex Quadratic Polynomials
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Quadratic Functionals with General Boundary Conditions
International Nuclear Information System (INIS)
Dosla, Z.; Dosly, O.
1997-01-01
The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions
Linear quadratic optimization for positive LTI system
Muhafzan, Yenti, Syafrida Wirma; Zulakmal
2017-05-01
Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.
International Nuclear Information System (INIS)
Carlson, David J.; Stewart, Robert D.; Semenenko, Vladimir A.
2006-01-01
The poor treatment prognosis for tumors with high levels of hypoxia is usually attributed to the decreased sensitivity of hypoxic cells to ionizing radiation. Mechanistic considerations suggest that linear quadratic (LQ) survival model radiosensitivity parameters for hypoxic (H) and aerobic (A) cells are related by α H =α A /oxygen enhancement ratio (OER) and (α/β) H =OER(α/β) A . The OER parameter may be interpreted as the ratio of the dose to the hypoxic cells to the dose to the aerobic cells required to produce the same number of DSBs per cell. The validity of these expressions is tested against survival data for mammalian cells irradiated in vitro with low- and high-LET radiation. Estimates of hypoxic and aerobic radiosensitivity parameters are derived from independent and simultaneous least-squares fits to the survival data. An external bootstrap procedure is used to test whether independent fits to the survival data give significantly better predictions than simultaneous fits to the aerobic and hypoxic data. For low-LET radiation, estimates of the OER derived from the in vitro data are between 2.3 and 3.3 for extreme levels of hypoxia. The estimated range for the OER is similar to the oxygen enhancement ratios reported in the literature for the initial yield of DSBs. The half-time for sublethal damage repair was found to be independent of oxygen concentration. Analysis of patient survival data for cervix cancer suggests an average OER less than or equal to 1.5, which corresponds to a pO 2 of 5 mm Hg (0.66%) in the in vitro experiments. Because the OER derived from the cervix cancer data is averaged over cells at all oxygen levels, cells irradiated in vivo under extreme levels of hypoxia (<0.5 mm Hg) may have an OER substantially higher than 1.5. The reported analyses of in vitro data, as well as mechanistic considerations, provide strong support for the expressions relating hypoxic and aerobic radiosensitivity parameters. The formulas are also useful
New diagnostic technique for Zeeman-compensated atomic beam slowing: technique and results
Molenaar, P.A.; Straten, P. van der; Heideman, H.G.M.; Metcalf, H.
1997-01-01
We have developed a new diagnostic tool for the study of Zeeman-compensated slowing of an alkali atomic beam. Our time-of-flight technique measures the longitudinal veloc- ity distribution of the slowed atoms with a resolution below the Doppler limit of 30 cm/s. Furthermore, it can map
Tahir, Muhammad
2013-05-01
We show that the surface states of magnetic topological insulators realize an activated behavior and Shubnikov de Haas oscillations. Applying an external magnetic field perpendicular to the surface of the topological insulator in the presence of Zeeman interaction, we investigate the opening of a gap at the Dirac point, making the surface Dirac fermions massive, and the effects on the transport properties. Analytical expressions are derived for the collisional conductivity for elastic impurity scattering in the first Born approximation. We also calculate the Hall conductivity using the Kubo formalism. Evidence for a transition from gapless to gapped surface states at n = 0 and activated transport is found from the temperature and magnetic-field dependence of the collisional and Hall conductivities. © Copyright EPLA, 2013.
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Bound constrained quadratic programming via piecewise
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.
1999-01-01
of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...
On orthogonality preserving quadratic stochastic operators
International Nuclear Information System (INIS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-01-01
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
VERY LARGE ARRAY OH ZEEMAN OBSERVATIONS OF THE STAR-FORMING REGION S88B
Energy Technology Data Exchange (ETDEWEB)
Sarma, A. P.; Eftimova, M. [Physics Department, DePaul University, 2219 N. Kenmore Ave., Byrne Hall 211, Chicago, IL 60614 (United States); Brogan, C. L. [National Radio Astronomy Observatory, Charlottesville, VA 22903 (United States); Bourke, T. L. [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 (United States); Troland, T. H., E-mail: asarma@depaul.edu [Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506 (United States)
2013-04-10
We present observations of the Zeeman effect in OH thermal absorption main lines at 1665 and 1667 MHz taken with the Very Large Array toward the star-forming region S88B. The OH absorption profiles toward this source are complicated, and contain several blended components toward a number of positions. Almost all of the OH absorbing gas is located in the eastern parts of S88B, toward the compact continuum source S88B-2 and the eastern parts of the extended continuum source S88B-1. The ratio of 1665/1667 MHz OH line intensities indicates the gas is likely highly clumped, in agreement with other molecular emission line observations in the literature. S88-B appears to present a similar geometry to the well-known star-forming region M17, in that there is an edge-on eastward progression from ionized to molecular gas. The detected magnetic fields appear to mirror this eastward transition; we detected line-of-sight magnetic fields ranging from 90 to 400 {mu}G, with the lowest values of the field to the southwest of the S88B-1 continuum peak, and the highest values to its northeast. We used the detected fields to assess the importance of the magnetic field in S88B by a number of methods; we calculated the ratio of thermal to magnetic pressures, we calculated the critical field necessary to completely support the cloud against self-gravity and compared it to the observed field, and we calculated the ratio of mass to magnetic flux in terms of the critical value of this parameter. All these methods indicated that the magnetic field in S88B is dynamically significant, and should provide an important source of support against gravity. Moreover, the magnetic energy density is in approximate equipartition with the turbulent energy density, again pointing to the importance of the magnetic field in this region.
VERY LARGE ARRAY OH ZEEMAN OBSERVATIONS OF THE STAR-FORMING REGION S88B
International Nuclear Information System (INIS)
Sarma, A. P.; Eftimova, M.; Brogan, C. L.; Bourke, T. L.; Troland, T. H.
2013-01-01
We present observations of the Zeeman effect in OH thermal absorption main lines at 1665 and 1667 MHz taken with the Very Large Array toward the star-forming region S88B. The OH absorption profiles toward this source are complicated, and contain several blended components toward a number of positions. Almost all of the OH absorbing gas is located in the eastern parts of S88B, toward the compact continuum source S88B-2 and the eastern parts of the extended continuum source S88B-1. The ratio of 1665/1667 MHz OH line intensities indicates the gas is likely highly clumped, in agreement with other molecular emission line observations in the literature. S88-B appears to present a similar geometry to the well-known star-forming region M17, in that there is an edge-on eastward progression from ionized to molecular gas. The detected magnetic fields appear to mirror this eastward transition; we detected line-of-sight magnetic fields ranging from 90 to 400 μG, with the lowest values of the field to the southwest of the S88B-1 continuum peak, and the highest values to its northeast. We used the detected fields to assess the importance of the magnetic field in S88B by a number of methods; we calculated the ratio of thermal to magnetic pressures, we calculated the critical field necessary to completely support the cloud against self-gravity and compared it to the observed field, and we calculated the ratio of mass to magnetic flux in terms of the critical value of this parameter. All these methods indicated that the magnetic field in S88B is dynamically significant, and should provide an important source of support against gravity. Moreover, the magnetic energy density is in approximate equipartition with the turbulent energy density, again pointing to the importance of the magnetic field in this region.
Quadratic mass relations in topological bootstrap theory
International Nuclear Information System (INIS)
Jones, C.E.; Uschersohn, J.
1980-01-01
From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY
Directory of Open Access Journals (Sweden)
Damián Fernández
2014-12-01
Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
orthogonal and scaling transformations of quadratic functions
African Journals Online (AJOL)
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functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.
Fundamental quadratic variational principle underlying general relativity
International Nuclear Information System (INIS)
Atkins, W.K.
1983-01-01
The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed
Investigating Students' Mathematical Difficulties with Quadratic Equations
O'Connor, Bronwyn Reid; Norton, Stephen
2016-01-01
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
Commuting quantum traces for quadratic algebras
International Nuclear Information System (INIS)
Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve
2005-01-01
Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians
Design of reinforced areas of concrete column using quadratic polynomials
Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.
2017-11-01
Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Directory of Open Access Journals (Sweden)
Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
Suppression of Zeeman relaxation in cold collisions of 2P1/2 atoms
International Nuclear Information System (INIS)
Tscherbul, T. V.; Dalgarno, A.; Buchachenko, A. A.; Lu, M.-J.; Weinstein, J. D.
2009-01-01
We present a combined experimental and theoretical study of angular momentum depolarization in cold collisions of 2 P atoms in the presence of an external magnetic field. We show that collision-induced Zeeman relaxation of Ga( 2 P 1/2 ) and In( 2 P 1/2 ) atoms in cold 4 He gas is dramatically suppressed compared to atoms in 2 P 3/2 states. Using rigorous quantum-scattering calculations based on ab initio interaction potentials, we demonstrate that Zeeman transitions in collisions of atoms in 2 P 1/2 electronic states occur via couplings to the 2 P 3/2 state induced by the anisotropy of the interaction potential. Our results suggest the feasibility of sympathetic cooling and magnetic trapping of 2 P 1/2 -state atoms, such as halogens, thereby opening up exciting areas of research in precision spectroscopy and cold-controlled chemistry.
International Nuclear Information System (INIS)
Malykin, G B; Pozdnyakova, V I
2015-01-01
It is shown that when an equal-arm Michelson interferometer is involved in rotation (for example, Earth's rotation around its axis or around the Sun) and its arms are oriented differently with respect to the plane of rotation, a phase difference arises between the light rays that pass through different arms. This phase difference is due to the fact that the arms experience variously the Newtonian (nonrelativistic) scalar gravitational potential of the Coriolis forces. It is shown that the phase difference is proportional to the length of the interferometer arm, the square of the angular velocity of the rotation, and the square of the distance from the center of rotation — hence, the proposal to call this phenomenon the quadratic Sagnac effect. In the present paper, we consider, as an illustrative example, the results of the once well-known experiments of D C Miller, who claimed to observe the translational motion of Earth relative to the hypothetical ‘luminiferous ether’. It is shown that this claim can actually be explained by the fact that, because of the orbital revolution of Earth, the time dilations in the orthogonal arms of the Michelson interferometer are influenced differently by the scalar gravitational potential of the Coriolis forces. (methodological notes)
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Doppler-Zeeman Mapping of the Rapidly Rotating Magnetic CP Star HD37776
Khokhlova, V. L.; Vasilchenko, D. V.; Stepanov, V. V.; Romanyuk, I. I.
2000-03-01
We present the results of our analysis of magnetic-field configuration and abundance anomalies on the surface of the rapidly rotating, chemically peculiar helium-strong variable B2 V star HD37776 with unresolved Zeeman components of spectral lines. Simultaneous inversion of the observed Stokes I and V profiles, which realizes the method of Doppler-Zeeman mapping (Vasilchenko et al. 1996), has been applied for the first time. Spectroscopic observations were carried out with the Main stellar spectrograph of the 6-m Special Astrophysical Observatory telescope equipped with a Zeeman analyzer and a CCD array, which allowed spectra in right- and left-hand circularly polarized light to be taken simultaneously at a signal-to-noise ratio S/N > 200 (Romanyuk et al. 1999). The profile width of winged spectral lines (reaching 5 A) is determined by Zeeman line splitting; however, the observed Zeeman components are blurred and unresolved because of the rapid stellar rotation. When solving the inverse problem, we sought for the magnetic-field configuration in the form of a combination of arbitrarily oriented dipole, quadrupole, and octupole placed at the stellar center. The observed Stokes I and V profiles for eight spectral lines of He, OII, AlIII, SiIII, and FeIII averaged over the visible stellar surface were used as input data. We constructed a model of the magnetic field from the condition of coincidence of magnetic maps obtained from different lines of different chemical elements and from the condition of a minimum profile residual. This model is a combination of centered coaxial dipole and quadrupole with the dominant quadrupole component at 30 deg < i < 50 deg, beta = 40 deg, and a maximum surface field strength H_s = 60 kG. A comparison of our abundance maps with the field configuration shows that the He concentration is at a maximum in the regions of maximum radial field, while the maximum concentrations of O, Al, Si, and Fe coincide with the regions of maximum
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...
Quadratic Interpolation and Linear Lifting Design
Directory of Open Access Journals (Sweden)
Joel Solé
2007-03-01
Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Temporal quadratic expansion nodal Green's function method
International Nuclear Information System (INIS)
Liu Cong; Jing Xingqing; Xu Xiaolin
2000-01-01
A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method
SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.
Walking solitons in quadratic nonlinear media
Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru
1996-01-01
We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
Least Squares Problems with Absolute Quadratic Constraints
Directory of Open Access Journals (Sweden)
R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
Quadratic tracer dynamical models tobacco growth
International Nuclear Information System (INIS)
Qiang Jiyi; Hua Cuncai; Wang Shaohua
2011-01-01
In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
Roesler, Elizabeth L.; Grabowski, Timothy B.
2018-01-01
Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.
International Nuclear Information System (INIS)
Malykin, G B; Pozdnyakova, V I
2015-01-01
The paper 'Quadratic Sagnac effect — the influence of the gravitational potential of the Coriolis force on the phase difference between the arms of a rotating Michelson interferometer (an explanation of D C Miller's experimental results, 1921 – 1926)' (Usp. Fiz. Nauk 185 431 (2015) [Phys. Usp. 58 398 (2015)]) is amended and supplemented with information concerning earlier work on the influence of rotation on Michelson – Morley's nonzero results. (letters to the editors)
International Nuclear Information System (INIS)
Trimeche, Azer
2013-01-01
This work focuses on the study and implementation of a new technique of deceleration of a supersonic beam of paramagnetic particles using a co-moving progressive wave of magnetic field. This technique relies on a method of slowing based on Stern-Gerlach forces acting on a paramagnetic system in motion in the presence of a co-propagating magnetic field. This highly innovative approach has the advantage of being applicable to a wide range of species and opens up new opportunities. A suitable theoretical approach is followed, that allows for a direct link between theory, programming of experimental parameters, and experimental results in a systematic, rational and predictive manner. The understanding and control of the dynamics of trapping at a given speed, acceleration and deceleration require decoupling between the transverse and longitudinal effects of the wave. These effects are clearly visible when the added uniform magnetic field limits the transverse effects of the progressive wave of magnetic field. The outlooks for the new Zeeman Stern Gerlach decelerator are numerous. Deceleration paramagnetic molecules, free radicals and neutrons are possible. (author) [fr
Quadratic stochastic operators: Results and open problems
International Nuclear Information System (INIS)
Ganikhodzhaev, R.N.; Rozikov, U.A.
2009-03-01
The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)
Sequential Quadratic Programming Algorithms for Optimization
1989-08-01
quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the
Investigation of different magnetic field configurations using an electrical, modular Zeeman slower
Energy Technology Data Exchange (ETDEWEB)
Ohayon, Ben; Ron, Guy, E-mail: gron@racah.phys.huji.ac.il [Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2015-10-15
We present a method of constructing an automatically reconfigurable, modular, electronic Zeeman slower, which is remotely controlled. This setup is used to investigate the ability of different magnetic field profiles to slow thermal atoms to the capture velocity of a magneto-optical-trap. We show that a simple numerical optimization process yields better results than the commonly used approach for deciding on the appropriate field and comes close to the optimum field, found by utilizing a fast feedback loop which uses a genetic algorithm. Our new numerical method is easily adaptable to a variety of existing slower designs and may be beneficial where feedback is unavailable.
New diagnostic technique for Zeeman-compensated atomic beam slowing: technique and results
Molenaar, P.A.; Straten, P. van der; Heideman, H.G.M.; Metcalf, H.
1997-01-01
We have developed a new diagnostic tool for the study of Zeeman-compensated slowing of an alkali atomic beam. Our time-of-flight technique measures the longitudinal veloc- ity distribution of the slowed atoms with a resolution below the Doppler limit of 30 cm/s. Furthermore, it can map the position and velocity distribution of atoms in either ground hyperfine level inside the solenoid without any devices inside the solenoid. The technique reveals the optical pumping ef- fects, and shows in de...
Xu, Zhongxiao; Wu, Yuelong; Tian, Long; Chen, Lirong; Zhang, Zhiying; Yan, Zhihui; Li, Shujing; Wang, Hai; Xie, Changde; Peng, Kunchi
2013-12-13
Long-lived and high-fidelity memory for a photonic polarization qubit (PPQ) is crucial for constructing quantum networks. We present a millisecond storage system based on electromagnetically induced transparency, in which a moderate magnetic field is applied on a cold-atom cloud to lift Zeeman degeneracy and, thus, the PPQ states are stored as two magnetic-field-insensitive spin waves. Especially, the influence of magnetic-field-sensitive spin waves on the storage performances is almost totally avoided. The measured average fidelities of the polarization states are 98.6% at 200 μs and 78.4% at 4.5 ms, respectively.
Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator
International Nuclear Information System (INIS)
Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping
2017-01-01
A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)
Hanle-Zeeman Scattering Matrix for Magnetic Dipole Transitions
Energy Technology Data Exchange (ETDEWEB)
Megha, A.; Sampoorna, M.; Nagendra, K. N.; Sankarasubramanian, K., E-mail: megha@iiap.res.in, E-mail: sampoorna@iiap.res.in, E-mail: knn@iiap.res.in, E-mail: sankar@iiap.res.in [Indian Institute of Astrophysics, Koramangala, Bengaluru 560 034 (India)
2017-06-01
The polarization of the light that is scattered by the coronal ions is influenced by the anisotropic illumination from the photosphere and the magnetic field structuring in the solar corona. The properties of the coronal magnetic fields can be well studied by understanding the polarization properties of coronal forbidden emission lines that arise from magnetic dipole ( M 1) transitions in the highly ionized atoms that are present in the corona. We present the classical scattering theory of the forbidden lines for a more general case of arbitrary-strength magnetic fields. We derive the scattering matrix for M 1 transitions using the classical magnetic dipole model of Casini and Lin and applying the scattering matrix approach of Stenflo. We consider a two-level atom model and neglect collisional effects. The scattering matrix so derived is used to study the Stokes profiles formed in coronal conditions in those regions where the radiative excitations dominate collisional excitations. To this end, we take into account the integration over a cone of an unpolarized radiation from the solar disk incident on the scattering atoms. Furthermore, we also integrate along the line of sight to calculate the emerging polarized line profiles. We consider radial and dipole magnetic field configurations and spherically symmetric density distributions. For our studies we adopt the atomic parameters corresponding to the [Fe xiii] 10747 Å coronal forbidden line. We also discuss the nature of the scattering matrix for M 1 transitions and compare it with that for the electric dipole ( E 1) transitions.
Zeeman relaxation of MnH (X7Σ+) in collisions with 3He: Mechanism and comparison with experiment
International Nuclear Information System (INIS)
Turpin, F.; Stoecklin, T.; Halvick, Ph.
2011-01-01
We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH ( 7 Σ) in collisions with 3 He. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with ΔM j >2 give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.
Zeeman relaxation of MnH (X7Σ+) in collisions with He3: Mechanism and comparison with experiment
Turpin, F.; Stoecklin, T.; Halvick, Ph.
2011-03-01
We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of MnH (7Σ) in collisions with He3. We analyze the collisional Zeeman transition mechanism as a function of the final diatomic state and its variation as a function of an applied magnetic field. We show that as a result of this mechanism the levels with ΔMj>2 give negligible contributions to the Zeemam relaxation cross section. We also compare our results to the experimental cross sections obtained from the buffer-gas cooling and magnetic trapping of this molecule and investigate the dependence of the Zeeman relaxation cross section on the accuracy of the three-body interaction at ultralow energies.
On a quadratic inverse eigenvalue problem
International Nuclear Information System (INIS)
Cai, Yunfeng; Xu, Shufang
2009-01-01
This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Quadratic forms for Feynman-Kac semigroups
International Nuclear Information System (INIS)
Hibey, Joseph L.; Charalambous, Charalambos D.
2006-01-01
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
Hugdal, Henning G.; Sudbø, Asle
2018-01-01
We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the noninteracting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger-type interaction, while the pairing symmetry of the bands is indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction n of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning n . Moreover, n also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral px±i py type state for out-of-plane fields, to a nodal p -wave-type state for purely in-plane fields.
Zihlmann, Simon; Cummings, Aron W.; Garcia, Jose H.; Kedves, Máté; Watanabe, Kenji; Taniguchi, Takashi; Schönenberger, Christian; Makk, Péter
2018-02-01
Large spin-orbital proximity effects have been predicted in graphene interfaced with a transition-metal dichalcogenide layer. Whereas clear evidence for an enhanced spin-orbit coupling has been found at large carrier densities, the type of spin-orbit coupling and its relaxation mechanism remained unknown. We show an increased spin-orbit coupling close to the charge neutrality point in graphene, where topological states are expected to appear. Single-layer graphene encapsulated between the transition-metal dichalcogenide WSe2 and h -BN is found to exhibit exceptional quality with mobilities as high as 1 ×105 cm2 V-1 s-1. At the same time clear weak antilocalization indicates strong spin-orbit coupling, and a large spin relaxation anisotropy due to the presence of a dominating symmetric spin-orbit coupling is found. Doping-dependent measurements show that the spin relaxation of the in-plane spins is largely dominated by a valley-Zeeman spin-orbit coupling and that the intrinsic spin-orbit coupling plays a minor role in spin relaxation. The strong spin-valley coupling opens new possibilities in exploring spin and valley degree of freedom in graphene with the realization of new concepts in spin manipulation.
Ordinary matter, dark matter, and dark energy on normal Zeeman space-times
Imre Szabó, Zoltán
2017-01-01
Zeeman space-times are new, relativistic, and operator based Hamiltonian models representing multi-particle systems. They are established on Lorentzian pseudo Riemannian manifolds whose Laplacian immediately appears in the form of original quantum physical wave operators. In classical quantum theory they emerge, differently, from the Hamilton formalism and the correspondence principle. Nonetheless, this new model does not just reiterate the well known conceptions but holds the key to solving open problems of quantum theory. Most remarkably, it represents the dark matter, dark energy, and ordinary matter by the same ratios how they show up in experiments. Another remarkable agreement with reality is that the ordinary matter appears to be non-expanding and is described in consent with observations. The theory also explains gravitation, moreover, the Hamilton operators of all energy and matter formations, together with their physical properties, are solely derived from the Laplacian of the Zeeman space-time. By this reason, it is called Monistic Wave Laplacian which symbolizes an all-comprehensive unification of all matter and energy formations. This paper only outlines the normal case where the particles do not have proper spin but just angular momentum. The complete anomalous theory is detailed in [Sz2, Sz3, Sz4, Sz5, Sz6, Sz7].
Doppler-Zeeman mapping of the magnetic CP star HD 215441
Khokhlova, V. L.; Vasilchenko, D. V.; Stepanov, V. V.; Tsymbal, V. V.
1997-07-01
The method of Vasilchenko et al. (1996) is used to obtain a Doppler-Zeeman map of the magnetic CP star HD 215441. The magnetic field is approximated by a magnetic dipole that is arbitrarily shifted from the star center. The solution of the inverse problem yields the dipole parameters and the maps of Si, Ti, Cr, and Fe abundance anomalies; the coordinates of local magnetic vectors on the star surface are computed. A comparison of the distribution of abundance anomalies and the magnetic-field configuration reveals that in the region where the magnetic-field lines are vertical (near the magnetic pole), Si, Ti and Cr are highly deficient, while the Fe enhancement is strongest. In the regions where the magnetic-field lines are horizontal (near the magnetic equator), Si, Ti and Cr show the greatest overabundance. In these regions, the Fe abundance is also slightly enhanced and exhibits, as it were, a secondary maximum. The factors that limit the accuracy of Doppler-Zeeman mapping are reviewed.
Directory of Open Access Journals (Sweden)
Yong Li
2014-01-01
Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
Universality of quadratic to linear magnetoresistance crossover in disordered conductors
Lara, Silvia; Ramakrishnan, Navneeth; Lai, Ying Tong; Adam, Shaffique
Many experiments measuring Magnetoresistance (MR) showed unsaturating linear behavior at high magnetic fields and quadratic behavior at low fields. In the literature, two very different theoretical models have been used to explain this classical MR as a consequence of sample disorder. The phenomenological Random Resistor Network (RRN) model constructs a grid of four-terminal resistors each with a varying random resistance. The Effective Medium Theory (EMT) model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. In this theoretical work, we demonstrate numerically that both the RRN and EMT models belong to the same universality class, and that a single parameter (the ratio of the fluctuations in the carrier density to the average carrier density) completely determines both the magnitude of the MR and the B-field scale for the crossover from quadratic to linear MR. By considering several experimental data sets in the literature, ranging from thin films of InSb to graphene to Weyl semimetals like Na3Bi, we show that this disorder-induced mechanism for MR is in good agreement with the experiments, and that this comparison of MR with theory reveals information about the spatial carrier density inhomogeneity. This work was supported by the National Research Foundation of Singapore (NRF-NRFF2012-01).
STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION
Directory of Open Access Journals (Sweden)
KOSOLAP A. I.
2015-11-01
Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.
DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers
Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro
2016-10-01
This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.
Electroweak vacuum stability and finite quadratic radiative corrections
Energy Technology Data Exchange (ETDEWEB)
Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)
2015-07-15
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.
Exact cancellation of quadratic divergences in top condensation models
International Nuclear Information System (INIS)
Blumhofer, A.
1995-01-01
We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))
Distance matrices and quadratic embedding of graphs
Directory of Open Access Journals (Sweden)
Nobuaki Obata
2018-04-01
Full Text Available A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
International Nuclear Information System (INIS)
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-01-01
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules
Charged black holes in quadratic gravity
International Nuclear Information System (INIS)
Matyjasek, Jerzy; Tryniecki, Dariusz
2004-01-01
Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by r + =|e|. Similarly to the classical Reissner-Nordstroem solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
A ''quadratized'' augmented plane wave method
International Nuclear Information System (INIS)
Smrcka, L.
1982-02-01
The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)
Quadratic gravity in first order formalism
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)
2017-10-01
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium
Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong
2018-05-01
In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.
Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space
International Nuclear Information System (INIS)
Daszkiewicz, Marcin; Walczyk, Cezary J.
2008-01-01
The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces
International Nuclear Information System (INIS)
Hong-Bin, Zhang; Jian-Wei, Xia; Yong-Bin, Yu; Chuang-Yin, Dang
2010-01-01
This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results
Energy Technology Data Exchange (ETDEWEB)
Perkins, Jr, R C; Dalton, L R [Vanderbilt Univ., Nashville, Tenn. (USA). Dept. of Chemistry; Kispert, L D
1977-04-01
Frequency-swept absorption ELDOR signals for the CH/sub 2/COO/sup -/radical in zinc acetate depend upon Zeeman modulation frequency, the signals going from a positive to a negative sense as the Zeeman modulation frequency is varied from 100 to 1 kHz. A mathematical formulation derived explicitly considering applied electromagnetic radiation and Zeeman modulation fields is employed to computer-simulate the experimentally observed effects.
Orthogonal and Scaling Transformations of Quadratic Functions with ...
African Journals Online (AJOL)
In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
A Linear Programming Reformulation of the Standard Quadratic Optimization Problem
de Klerk, E.; Pasechnik, D.V.
2005-01-01
The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially
Analysis of Students' Error in Learning of Quadratic Equations
Zakaria, Effandi; Ibrahim; Maat, Siti Mistima
2010-01-01
The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…
Sketching the General Quadratic Equation Using Dynamic Geometry Software
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
Tangent Lines without Derivatives for Quadratic and Cubic Equations
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Visualising the Roots of Quadratic Equations with Complex Coefficients
Bardell, Nicholas S.
2014-01-01
This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…
Zeeman structure of red lines of lanthanum observed by laser spectroscopy methods
Sobolewski, Ł. M.; Windholz, L.; Kwela, J.
2017-11-01
Laser Induced Fluorescence (LIF) Spectroscopy and Optogalvanic (OG) Spectroscopy were used for the investigation of the Zeeman hyperfine (hf) structures of 27 spectral lines of La I in the wavelength range between 633.86 and 667.54 nm. As a source of free La atoms a hollow cathode discharge lamp was used. Spectra were recorded in the presence of a relatively weak magnetic field (about 800G) produced by a permanent magnet, for two linear polarization directions of the exciting laser beam. As a result of the measurements, we determined for the first time the Landé gJ- factors of 18 levels of La I. The Landé gJ- factors of 12 other levels were re-investigated and determined with higher accuracy.
Experimental studies of a zeeman-tuned xenon laser differential absorption apparatus.
Linford, G J
1973-06-01
A Zeeman-tuned cw xenon laser differential absorption device is described. The xenon laser was tuned by axial magnetic fields up to 5500 G generated by an unusually large water-cooled dc solenoid. Xenon laser lines at 3.37 micro, 3.51 micro, and 3.99 micro were tuned over ranges of 6 A, 6 A, and 11 A, respectively. To date, this apparatus has been used principally to study the details of formaldehyde absorption lines lying near the 3 .508-micro xenon laser transition. These experiments revealed that the observed absorption spectrum of formaldehyde exhibits a sufficiently unique spectral structure that the present technique may readily be used to measure relative concentrations of formaldehyde in samples of polluted air.
High-fidelity state detection and tomography of a single-ion Zeeman qubit
International Nuclear Information System (INIS)
Keselman, A; Glickman, Y; Akerman, N; Kotler, S; Ozeri, R
2011-01-01
We demonstrate high-fidelity Zeeman qubit state detection in a single trapped 88 Sr + ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm, followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent estimates of the detection error threshold required for fault-tolerant computation, whereas high-fidelity state tomography opens the way for high-precision quantum process tomography.
High-fidelity state detection and tomography of a single-ion Zeeman qubit
Energy Technology Data Exchange (ETDEWEB)
Keselman, A; Glickman, Y; Akerman, N; Kotler, S; Ozeri, R, E-mail: ozeri@weizmann.ac.il [Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel)
2011-07-15
We demonstrate high-fidelity Zeeman qubit state detection in a single trapped {sup 88}Sr{sup +} ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm, followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent estimates of the detection error threshold required for fault-tolerant computation, whereas high-fidelity state tomography opens the way for high-precision quantum process tomography.
Ultra-narrow EIA spectra of 85Rb atom in a degenerate Zeeman multiplet system
Rehman, Hafeez Ur; Qureshi, Muhammad Mohsin; Noh, Heung-Ryoul; Kim, Jin-Tae
2015-05-01
Ultra-narrow EIA spectral features of thermal 85Rb atom with respect to coupling Rabi frequencies in a degenerate Zeeman multiplet system have been unraveled in the cases of same (σ+ -σ+ , π ∥ π) and orthogonal (σ+ -σ- , π ⊥ π)polarization configurations. The EIA signals with subnatural linewidth of ~ 100 kHz even in the cases of same circular and linear polarizations of coupling and probe laser have been obtained for the first time theoretically and experimentally. In weak coupling power limit of orthogonal polarization configurations, time-dependent transfer of coherence plays major role in the splitting of the EIA spectra while in strong coupling power, Mollow triplet-like mechanism due to strong power bring into broad split feature. The experimental ultra-narrow EIA features using one laser combined with an AOM match well with simulated spectra obtained by using generalized time-dependent optical Bloch equations.
International Nuclear Information System (INIS)
Mukherjee, Nandini
2010-01-01
A comprehensive theoretical analysis is developed for the vectorial phase conjugation using resonant four-wave mixing (FWM) in a highly degenerate rotational vibrational molecular system. The dynamic Stark shifts, saturation, and Doppler broadening are included for a realistic analysis. It is shown that the electromagnetically induced multilevel coherence controls the nonlinear wave mixing yielding interesting results for the phase conjugate (PC) reflectivity. It turns out that the efficiency of the PC reflectivity is decided by the relative phase of the Zeeman coherence and the population grating. When these two contributions are aligned in phase by a small detuning of the pump frequency, a large PC reflectivity (∼20%) is obtained with moderate pump intensity (∼500 mW/cm 2 ).
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.
Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers
Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan
2018-03-01
Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.
International Nuclear Information System (INIS)
2005-01-01
Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces
Are ghost surfaces quadratic-flux-minimizing?
International Nuclear Information System (INIS)
Hudson, S.R.; Dewar, R.L.
2009-01-01
Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
Securing Digital Audio using Complex Quadratic Map
Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi
2018-03-01
In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.
Results of radiotherapy in craniopharyngiomas analysed by the linear quadratic model
Energy Technology Data Exchange (ETDEWEB)
Guerkaynak, M. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Oezyar, E. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Zorlu, F. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Akyol, F.H. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Lale Atahan, I. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey)
1994-12-31
In 23 craniopharyngioma patients treated by limited surgery and external radiotherapy, the results concerning local control were analysed by linear quadratic formula. A biologically effective dose (BED) of 55 Gy, calculated with time factor and an {alpha}/{beta} value of 10 Gy, seemed to be adequate for local control. (orig.).
An Analysis and Design for Nonlinear Quadratic Systems Subject to Nested Saturation
Directory of Open Access Journals (Sweden)
Minsong Zhang
2013-01-01
Full Text Available This paper considers the stability problem for nonlinear quadratic systems with nested saturation input. The interesting treatment method proposed to nested saturation here is put into use a well-established linear differential control tool. And the new conclusions include the existing conclusion on this issue and have less conservatism than before. Simulation example illustrates the effectiveness of the established methodologies.
Directory of Open Access Journals (Sweden)
H. Jafari
2010-07-01
Full Text Available In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM.Comparisons are made between the Adomian decomposition method (ADM, the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.; Mitake, Hiroyoshi
2015-01-01
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular
Berridge, S.J.; Schumacher, J.M.
2004-01-01
We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator.Once such an approximation is known, one can solve the pricing problem by time stepping in an explicit
A contiguous-quadrat sampling exercise in a shrub-invaded ...
African Journals Online (AJOL)
In each quadrat, we recorded the species present and counted the number of woody alien plants. Chromolaena diminished under annual burning. Species richness and turnover increased in all transects over time. The 25m transect was as efficient as the 30m transect; however, the latter was influenced by an edge effect, ...
Analysis of a monetary union enlargement in the framework of linear-quadratic differential games
Plasmans, J.E.J.; Engwerda, J.C.; van Aarle, B.; Michalak, T.
2009-01-01
"This paper studies the effects of a monetary union enlargement using the techniques and outcomes from an extensive research project on macroeconomic policy coordination in the EMU. Our approach is characterized by two main pillars: (i) linear-quadratic differential games to capture externalities,
International Nuclear Information System (INIS)
McGavin, Dennis G; Tennant, W Craighead
2009-01-01
In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS 3 and BS 5 . Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, 1-bar Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
A revisit to quadratic programming with fuzzy parameters
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.
Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems
International Nuclear Information System (INIS)
Scott, D.S.; Ward, R.C.
1981-01-01
Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices
Directory of Open Access Journals (Sweden)
Linlin Gao
2015-11-01
Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
A perturbative solution for gravitational waves in quadratic gravity
International Nuclear Information System (INIS)
Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de
2003-01-01
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin
Accurate nonlocal theory for cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: +174Yb and +171Yb
Brown, Natalie C.; Brown, Kenneth R.
2018-05-01
Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit (+174Yb) to a hyperfine qubit (+171Yb) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using +174Yb if the magnetic field can be stabilized with fluctuations smaller than 10 μ G .
Performance of the Zeeman analyzer system of the McDonald Observatory 2.7 meter telescope
Vogt, S. S.; Tull, R. G.; Kelton, P. W.
1980-01-01
The paper describes a multichannel photoelectric Zeeman analyzer at the coude spectrograph of the McDonald 2.7 m reflector. A comparison of Lick and McDonald observations of HD 153882 reveals no significant difference in slopes or zero points of the two magnetic fields indicating that the systematic scale difference of 30-40% is probably instrumental in origin. Observations of the magnetic variable beta Cor Bor revealed a more nearly sinusoidal magnetic curve with less internal scatter than the photographically determined field measures of the Lick and Mauna Kea Zeeman systems. Investigation of periodicity in the secularly varying magnetic minima of beta Cor Bor did not yield evidence of previously noted periodicities other than that expected from the time structure of the data sampling.
International Nuclear Information System (INIS)
Jiang Xiaojun; Zhang Haichao; Wang Yuzhu
2016-01-01
We report the experimental investigation of electromagnetically induced transparency (EIT) in a Zeeman-sublevels Λ-type system of cold 87 Rb atoms in free space. We use the Zeeman substates of the hyperfine energy states 5 2 S 1/2 , F = 2 and 5 2 P 3/2 , F′ = 2 of 87 Rb D 2 line to form a Λ-type EIT scheme. The EIT signal is obtained by scanning the probe light over 1 MHz in 4 ms with an 80 MHz arbitrary waveform generator. More than 97% transparency and 100 kHz EIT window are observed. This EIT scheme is suited for an application of pulsed coherent storage atom clock (Yan B, et al. 2009 Phys. Rev. A 79 063820). (paper)
Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control
Härkegård, Ola
2004-01-01
When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...
Quadratic measurement and conditional state preparation in an optomechanical system
DEFF Research Database (Denmark)
A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.
2014-01-01
We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Staff turnover in hotels : exploring the quadratic and linear relationships.
Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.
2015-01-01
The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....
On wave-packet dynamics in a decaying quadratic potential
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Henriksen, Niels Engholm
1997-01-01
We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....
The stability of quadratic-reciprocal functional equation
Song, Aimin; Song, Minwei
2018-04-01
A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
Quadratic programming with fuzzy parameters: A membership function approach
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.
Ramachandran, R.; Narasimhan, P. T.
The results of theoretical and experimental studies of Zeeman-perturbed nuclear quadrupole spin echo envelope modulations (ZSEEM) for spin 3/2 nuclei in polycrystalline specimens are presented. The response of the Zeeman-perturbed spin ensemble to resonant two pulse excitations has been calculated using the density matrix formalism. The theoretical calculation assumes a parallel orientation of the external r.f. and static Zeeman fields and an arbitrary orientation of these fields to the principal axes system of the electric field gradient. A numerical powder averaging procedure has been adopted to simulate the response of the polycrystalline specimens. Using a coherent pulsed nuclear quadrupole resonance spectrometer the ZSEEM patterns of the 35Cl nuclei have been recorded in polycrystalline specimens of potassium chlorate, barium chlorate, mercuric chloride (two sites) and antimony trichloride (two sites) using the π/2-τ-π/2 sequence. The theoretical and experimental ZSEEM patterns have been compared. In the case of mercuric chloride, the experimental 35Cl ZSEEM patterns are found to be nearly identical for the two sites and correspond to a near-zero value of the asymmetry parameter, η, of the electric field gradient tensor. The difference in the η values for the two 35Cl sites (η ˜0·06 and η˜0·16) in antimony trichloride is clearly reflected in the experimental and theoretical ZSEEM patterns. The present study indicates the feasibility of evaluating η for spin 3/2 nuclei in polycrystalline specimens from ZSEEM investigations.
FIRST ZEEMAN DOPPLER IMAGING OF A COOL STAR USING ALL FOUR STOKES PARAMETERS
International Nuclear Information System (INIS)
Rosén, L.; Kochukhov, O.; Wade, G. A.
2015-01-01
Magnetic fields are ubiquitous in active cool stars, but they are in general complex and weak. Current Zeeman Doppler imaging (ZDI) studies of cool star magnetic fields chiefly employ circular polarization observations because linear polarization is difficult to detect and requires a more sophisticated radiative transfer modeling to interpret. But it has been shown in previous theoretical studies, and in the observational analyses of magnetic Ap stars, that including linear polarization in the magnetic inversion process makes it possible to correctly recover many otherwise lost or misinterpreted magnetic features. We have obtained phase-resolved observations in all four Stokes parameters of the RS CVn star II Peg at two separate epochs. Here we present temperature and magnetic field maps reconstructed for this star using all four Stokes parameters. This is the very first such ZDI study of a cool active star. Our magnetic inversions reveal a highly structured magnetic field topology for both epochs. The strength of some surface features is doubled or even quadrupled when linear polarization is taken into account. The total magnetic energy of the reconstructed field map also becomes about 2.1–3.5 times higher. The overall complexity is also increased as the field energy is shifted toward higher harmonic modes when four Stokes parameters are used. As a consequence, the potential field extrapolation of the four Stokes parameter ZDI results indicates that magnetic field becomes weaker at a distance of several stellar radii due to a decrease of the large-scale field component
Quadratic stabilisability of multi-agent systems under switching topologies
Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long
2014-12-01
This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.
Linear versus quadratic portfolio optimization model with transaction cost
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
The quadratic reciprocity law a collection of classical proofs
Baumgart, Oswald
2015-01-01
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
International Nuclear Information System (INIS)
Marquette, Ian
2011-01-01
There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.
The bounds of feasible space on constrained nonconvex quadratic programming
Zhu, Jinghao
2008-03-01
This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.
DEFF Research Database (Denmark)
Zeng, Xianglong; Guo, Hairun; Zhou, Binbin
2012-01-01
We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression...... with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest...... soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency...
Large N saddle formulation of quadratic building block theories
International Nuclear Information System (INIS)
Halpern, M.B.
1980-01-01
I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)
Remarks on second-order quadratic systems in algebras
Directory of Open Access Journals (Sweden)
Art Sagle
2017-10-01
Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Quantum tomography and classical propagator for quadratic quantum systems
International Nuclear Information System (INIS)
Man'ko, O.V.
1999-03-01
The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
Subgroups of class groups of algebraic quadratic function fields
International Nuclear Information System (INIS)
Wang Kunpeng; Zhang Xianke
2001-09-01
Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)
Smoothing optimization of supporting quadratic surfaces with Zernike polynomials
Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu
2018-03-01
A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.
The quantum cosmological wavefunction at very early times for a quadratic gravity theory
International Nuclear Information System (INIS)
Davis, Simon
2003-01-01
The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times
An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2003-01-01
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....
An Extended Quadratic Frobenius Primality Test with Average- and Worst-Case Error Estimate
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2006-01-01
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....
An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2001-01-01
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....
Optical-response properties in hybrid optomechanical systems with quadratic coupling
Sun, Xue-Jian; Wang, Xin; Liu, Li-Na; Liu, Wen-Xiao; Fang, Ai-Ping; Li, Hong-Rong
2018-02-01
We theoretically investigate the optical-response properties of the four-mode quadratically coupled optomechanical system (OMS), in which two standard OMSs with quadratic coupling are coupled to each other via a common waveguide. In the presence of a strong control field applied to one cavity and a weak probe field applied to the other, we show that by suitably tuning the system parameters, there appears the normal mode splitting, optomechanically induced absorption, and double or triple electromagnetically induced transparency phenomena in the probe absorption spectrum. In particular, the explicit physical explanations for those fantastic phenomena are detailed discussed. Moreover, we also show that our proposal can be exploited to implement the optical switch as well as the slow and fast light effects.
Quadratic and coulomb terms for the spectrum of a three-electron quantum dot
International Nuclear Information System (INIS)
Hassanabadi, H.; Hamzavi, M.; Zarrinkamar, S.; Rajabi, A.A.
2010-01-01
We consider the Hamiltonian of a three-electron quantum dot composed of quadratic plus Coulomb terms and calculate the system's spectra. We next apply the hyperradius to reduce the three-body Schroedinger equation into a one-variable differential equation that is solvable. To avoid the complexity, the Taylor expansion of the effective potential is enters the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schroedinger equation in terms of the Wigner parameter. Using a quasi-analytical approach, we have calculated the energy eigenvalues of the Schroedinger equation corresponding to a three-electron quantum dot. In addition to the hyperspherical coordinates, much of mathematical complexity has been avoided using the idea of Taylor expansion for the potential. For the potential, we have considered quadratic plus Coulomb terms. The obtained energy eigenvalues in terms of the Wigner parameter are given in tabular form. (author)
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
International Nuclear Information System (INIS)
Crommelin, D.T.; Vanden-Eijnden, E.
2006-01-01
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows
International Nuclear Information System (INIS)
Romalis, M.V.; Cates, G.D.
1998-01-01
We describe a method of 3 He polarimetry relying on the polarization-dependent frequency shift of the Rb Zeeman resonance. Our method is ideally suited for on-line measurements of the 3 He polarization produced by spin-exchange optical pumping. To calibrate the frequency shift we performed an accurate measurement of the imaginary part of the Rb- 3 He spin-exchange cross section in the temperature range typical for spin-exchange optical pumping of 3 He. We also present a detailed study of possible systematic errors in the frequency shift polarimetry. copyright 1998 The American Physical Society
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
Directory of Open Access Journals (Sweden)
E. L. Shishkina
2016-12-01
Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.
Feedback nash equilibria for linear quadratic descriptor differential games
Engwerda, J.C.; Salmah, S.
2012-01-01
In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
Initial post dynamic buckling of a quadratic-cubic column ...
African Journals Online (AJOL)
In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...
Quadratic algebras in the noncommutative integration method of wave equation
International Nuclear Information System (INIS)
Varaksin, O.L.
1995-01-01
The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
On Fredholm-Stieltjes quadratic integral equation with supremum
International Nuclear Information System (INIS)
Darwish, M.A.
2007-08-01
We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)
Quadratic theory and feedback controllers for linear time delay systems
International Nuclear Information System (INIS)
Lee, E.B.
1976-01-01
Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)
Pareto optimality in infinite horizon linear quadratic differential games
Reddy, P.V.; Engwerda, J.C.
2013-01-01
In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal
Special cases of the quadratic shortest path problem
Sotirov, Renata; Hu, Hao
2017-01-01
The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP
On misclassication probabilities of linear and quadratic classiers ...
African Journals Online (AJOL)
We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...
Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games
Engwerda, J.C.; Salmah, Y.
2010-01-01
In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.
Visualising the Complex Roots of Quadratic Equations with Real Coefficients
Bardell, Nicholas S.
2012-01-01
The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Linear and quadratic in temperature resistivity from holography
Energy Technology Data Exchange (ETDEWEB)
Ge, Xian-Hui [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing, 100049 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Wu, Shang-Yu [Department of Electrophysics, National Chiao Tung University,Hsinchu 300 (China); Wu, Shao-Feng [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China)
2016-11-22
We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.
Underprediction of human skin erythema at low doses per fraction by the linear quadratic model
International Nuclear Information System (INIS)
Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang
1996-01-01
Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model
Constraints on both the quadratic and quartic symmetry energy coefficients by 2β --decay energies
Wan, Niu; Xu, Chang; Ren, Zhongzhou; Liu, Jie
2018-05-01
In this Rapid Communication, the 2 β- -decay energies Q (2 β-) given in the atomic mass evaluation are used to extract not only the quadratic volume symmetry energy coefficient csymv, but also the quartic one csym,4 v. Based on the modified Bethe-Weizsäcker nuclear mass formula of the liquid-drop model, the decay energy Q (2 β-) is found to be closely related to both the quadratic and quartic symmetry energy coefficients csymv and csym,4 v. There are totally 449 data of decay energies Q (2 β-) used in the present analysis where the candidate nuclei are carefully chosen by fulfilling the following criteria: (1) large neutron-proton number difference N -Z , (2) large isospin asymmetry I , and (3) limited shell effect. The values of csymv and csym,4 v are extracted to be 29.345 and 3.634 MeV, respectively. Moreover, the quadratic surface-volume symmetry energy coefficient ratio is determined to be κ =csyms/csymv=1.356 .
Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program
International Nuclear Information System (INIS)
Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.
1990-01-01
Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)
International Nuclear Information System (INIS)
2002-01-01
Calculations with the quadratic lineal model for medium rate using the equation dose-effect. Several calculations for system of low dose rate brachytherapy plus teletherapy, calculations for brachytherapy with medium dose rate together with teletherapy, dose for fraction and the one numbers of fractions in medium rate
Rashba-Zeeman-effect-induced spin filtering energy windows in a quantum wire
International Nuclear Information System (INIS)
Xiao, Xianbo; Nie, Wenjie; Chen, Zhaoxia; Zhou, Guanghui; Li, Fei
2014-01-01
We perform a numerical study on the spin-resolved transport in a quantum wire (QW) under the modulation of both Rashba spin-orbit coupling (SOC) and a perpendicular magnetic field by using the developed Usuki transfer-matrix method in combination with the Landauer-Büttiker formalism. Wide spin filtering energy windows can be achieved in this system for unpolarized spin injection. In addition, both the width of energy window and the magnitude of spin conductance within these energy windows can be tuned by varying Rashba SOC strength, which can be apprehended by analyzing the energy dispersions and spin-polarized density distributions inside the QW, respectively. Further study also demonstrates that these Rashba-SOC-controlled spin filtering energy windows show a strong robustness against disorders. These findings may not only benefit to further understand the spin-dependent transport properties of a QW in the presence of external fields but also provide a theoretical instruction to design a spin filter device.
Rashba-Zeeman-effect-induced spin filtering energy windows in a quantum wire
Energy Technology Data Exchange (ETDEWEB)
Xiao, Xianbo, E-mail: xxb-11@hotmail.com; Nie, Wenjie [School of Computer, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004 (China); Chen, Zhaoxia [School of Mechatronics Engineering, East China Jiaotong University, Nanchang 330013 (China); Zhou, Guanghui [Department of Physics and Key Laboratory for Low-Dimensional Quantum Structures and Manipulation (Ministry of Education), Hunan Normal University, Changsha 410081 (China); Li, Fei, E-mail: wltlifei@sina.com [Office of Scientific Research, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004 (China)
2014-06-14
We perform a numerical study on the spin-resolved transport in a quantum wire (QW) under the modulation of both Rashba spin-orbit coupling (SOC) and a perpendicular magnetic field by using the developed Usuki transfer-matrix method in combination with the Landauer-Büttiker formalism. Wide spin filtering energy windows can be achieved in this system for unpolarized spin injection. In addition, both the width of energy window and the magnitude of spin conductance within these energy windows can be tuned by varying Rashba SOC strength, which can be apprehended by analyzing the energy dispersions and spin-polarized density distributions inside the QW, respectively. Further study also demonstrates that these Rashba-SOC-controlled spin filtering energy windows show a strong robustness against disorders. These findings may not only benefit to further understand the spin-dependent transport properties of a QW in the presence of external fields but also provide a theoretical instruction to design a spin filter device.
Algebra with polynomial commutation relations for Zeeman effect in Coulomb-Dirac field
International Nuclear Information System (INIS)
Karasev, M.V.; Novikova, E.M.
2005-01-01
One studies a model of a particle motion in the field of electromagnetic monopole (the Coulomb-Dirac field) disturbed by homogeneous magnetic and inhomogeneous electric fields. The quantum averaging is followed by occurrence of the integrated system the Hamiltonian of which is represented by the algebra elements with polynomial commutation relations. One forms irreducible representations of the mentioned algebra and its hypergeometric coherent states. One obtains the representation of the eigenfunction of the assumption problem and specifies the asymptotics of eigenvalues in the first order of perturbation theory [ru
Algebraic theory of Stark-Zeeman dynamic effect in hydrogen-like atom
International Nuclear Information System (INIS)
Fursa, D.V.; Yudin, G.L.
1990-01-01
The problems of calculating time evolution operator within the given n-shell (here n is main quantum number) for the hydrogen atom located in non-stationary electric and magnetic fields is under investigation. Making use of the Fock SO(4) group reduces this problem to the set of problems with linear realization of the dynamic symmetry group for which the evolution operator is the operator of corresponding groups representation. The types of evolution operator parametrization in the form of exponents product (the Wei-Norman method) any by means of D-functions connected with Euler angles and Cayley-Klein parameters are discussed. It is shown that the problem of evolution operator calculation can be reduced to investigation of a pair of two-level systems. 35 refs
The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system
International Nuclear Information System (INIS)
Li, Chengzhi; Llibre, Jaume
2009-01-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles
Induced motion of domain walls in multiferroics with quadratic interaction
Energy Technology Data Exchange (ETDEWEB)
Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)
2013-10-15
We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.
Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials
International Nuclear Information System (INIS)
Aquilanti, V; Marinelli, D; Marzuoli, A
2014-01-01
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed
Quadratic grating apodized photon sieves for simultaneous multiplane microscopy
Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin
2017-10-01
We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Linear Quadratic Controller with Fault Detection in Compact Disk Players
DEFF Research Database (Denmark)
Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.
2001-01-01
The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Information sets as permutation cycles for quadratic residue codes
Directory of Open Access Journals (Sweden)
Richard A. Jenson
1982-01-01
Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.
On a linear-quadratic problem with Caputo derivative
Directory of Open Access Journals (Sweden)
Dariusz Idczak
2016-01-01
Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
Stationary walking solitons in bulk quadratic nonlinear media
Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís
1997-01-01
We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Design of Linear-Quadratic-Regulator for a CSTR process
Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.
2017-11-01
This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.
A Note on 5-bit Quadratic Permutations’ Classification
Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali
2017-01-01
Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...
Integrable systems with quadratic nonlinearity in Fourier space
International Nuclear Information System (INIS)
Marikhin, V.G.
2003-01-01
The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed
Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering
International Nuclear Information System (INIS)
Sjoestrand, N.G.
1981-01-01
Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)
General quadratic gauge theory: constraint structure, symmetries and physical functions
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)
2005-06-17
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.
Quadratic time dependent Hamiltonians and separation of variables
International Nuclear Information System (INIS)
Anzaldo-Meneses, A.
2017-01-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.
Fast, multiple optimizations of quadratic dose objective functions in IMRT
International Nuclear Information System (INIS)
Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M
2006-01-01
Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved
Energy Technology Data Exchange (ETDEWEB)
Kruger, Pamela C. [Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, P.O. Box 509, Albany, NY 12201-0509 (United States); Parsons, Patrick J. [Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, P.O. Box 509, Albany, NY 12201-0509 (United States); Lead Poisoning/Trace Elements Laboratory, Wadsworth Center, New York State Department of Health, P.O. Box 509, Albany, NY 12201-0509 (United States)], E-mail: patrick.parsons@wadsworth.org
2007-03-15
Excessive exposure to aluminum (Al) can produce serious health consequences in people with impaired renal function, especially those undergoing hemodialysis. Al can accumulate in the brain and in bone, causing dialysis-related encephalopathy and renal osteodystrophy. Thus, dialysis patients are routinely monitored for Al overload, through measurement of their serum Al. Electrothermal atomic absorption spectrometry (ETAAS) is widely used for serum Al determination. Here, we assess the analytical performances of three ETAAS instruments, equipped with different background correction systems and heating arrangements, for the determination of serum Al. Specifically, we compare (1) a Perkin Elmer (PE) Model 3110 AAS, equipped with a longitudinally (end) heated graphite atomizer (HGA) and continuum-source (deuterium) background correction, with (2) a PE Model 4100ZL AAS equipped with a transversely heated graphite atomizer (THGA) and longitudinal Zeeman background correction, and (3) a PE Model Z5100 AAS equipped with a HGA and transverse Zeeman background correction. We were able to transfer the method for serum Al previously established for the Z5100 and 4100ZL instruments to the 3110, with only minor modifications. As with the Zeeman instruments, matrix-matched calibration was not required for the 3110 and, thus, aqueous calibration standards were used. However, the 309.3-nm line was chosen for analysis on the 3110 due to failure of the continuum background correction system at the 396.2-nm line. A small, seemingly insignificant overcorrection error was observed in the background channel on the 3110 instrument at the 309.3-nm line. On the 4100ZL, signal oscillation was observed in the atomization profile. The sensitivity, or characteristic mass (m{sub 0}), for Al at the 309.3-nm line on the 3110 AAS was found to be 12.1 {+-} 0.6 pg, compared to 16.1 {+-} 0.7 pg for the Z5100, and 23.3 {+-} 1.3 pg for the 4100ZL at the 396.2-nm line. However, the instrumental detection
DEFF Research Database (Denmark)
Larsen, Erik Huusfeldt; Rasmussen, L.
1991-01-01
-degrees-C and then further ashed at 1 100-degrees-C with argon as the purge gas. Zeeman background correction was used in the atomisation step at 2 300-degrees-C. The detection limit was 0.7 ng/g. Direct detection of chromium in milk, using only argon as purge gas, was inferior. Non-homogeneous and solid...
Lesmana, E.; Chaerani, D.; Khansa, H. N.
2018-03-01
Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method
Kobayashi, Shinji; Nishimiya, Nobuo; Suzuki, Masao
2017-10-01
The saturated absorption lines of neutral titanium were measured in the region of 9950-14380 cm-1 using a Ti:sapphire ring laser. A facing target sputtering system was used to obtain the gaseous state of a Ti I atom. The Zeeman splitting of 38 transitions was observed under the condition that the electric field component of a linearly polarized laser beam was parallel to the magnetic field. The gJ factors of the odd parity states were determined for 28 states belonging to 3d24s4p and 3d34p using those of the even parity states reported by Stachowska in 1997. The gJ factors of z5P1,2,3 levels were newly determined. gJ of y3F2, y3D2, z3P2, and z5S2 levels were refined.
International Nuclear Information System (INIS)
Blecker, Carlo R.; Hermann, Gerd M.
2009-01-01
Atomic absorption and coherent forward scattering spectrometry by using a near-infrared diode laser with and without Zeeman and wavelength modulation were carried out with graphite furnace electrothermal atomization. Analytical curves and limits of detection were compared. The magnetic field was modulated with 50 Hz, and the wavelength of the diode laser with 10 kHz. Coherent forward scattering was measured with crossed and slightly uncrossed polarizers. The results show that the detection limits of atomic absorption spectrometry are roughly the same as those of coherent forward scattering spectrometry with crossed polarizers. According to the theory with bright flicker noise limited laser sources the detection limits and linear ranges obtained with coherent forward scattering spectrometry with slightly uncrossed polarizers are significantly better than those obtained with crossed polarizers and with atomic absorption spectrometry. This is due to the fact that employing approaches of polarization spectroscopy reduce laser intensity fluctuations to their signal carried fractions
Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm
Directory of Open Access Journals (Sweden)
Wei Xie
2007-01-01
Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.
Wang, Xunyi; Parameswaran, Srikanth; Bagul, Darshan Mahendra; Kishore, Rajiv
2018-04-18
We studied the impact of online social support on patient self-care behavior in an online health community for human immunodeficiency virus (HIV) patients. We conceptualized emotional and informational support provided by community members into nuanced sub-dimensions. We explored how the direct and interaction effects of these sub-dimensions impact the self-care behavior of a support seeker. We used data from 330 255 posts in 30 050 threads from POZ, an online health community for HIV patients. Our key variables-self-care behaviori, objective informationj, experiential supportj, and emotional tonej-were operationalized using linguistic analysis with self-generated dictionaries and Python libraries. We tested our hypotheses using Tobit regression. Out of 6 null hypotheses, 5 were rejected. Objective information and emotional tone had an inverted-U relationship with self-care behavior. Experiential information and community involvement were positively related to self-care behavior. Community involvement amplified the inverted-U relationship between emotional tone and self-care behavior. No significant interaction effect was found between experiential support and objective information. Beyond a threshold, both informational and emotional online social support had a deleterious impact on self-care behavior of HIV patients. Our results suggested that caution should be exercised in the use of online health community interventions for HIV patients, and perhaps patients with other stigmatized chronic diseases.
On using the linear-quadratic model in daily clinical practice
International Nuclear Information System (INIS)
Yaes, R.J.; Patel, P.; Maruyama, Y.
1991-01-01
To facilitate its use in the clinic, Barendsen's formulation of the Linear-Quadratic (LQ) model is modified by expressing isoeffect doses in terms of the Standard Effective Dose, Ds, the isoeffective dose for the standard fractionation schedule of 2 Gy fractions given once per day, 5 days per week. For any arbitrary fractionation schedule, where total dose D is given in N fractions of size d in a total time T, the corresponding Standard Effective Dose, Ds, will be proportional to the total dose D and the proportionality constant will be called the Standard Relative Effectiveness, SRE, to distinguish it from Barendsen's Relative Effectiveness, RE. Thus, Ds = SRE.D. The constant SRE depends on the parameters of the fractionation schedule, and on the tumor or normal tissue being irradiated. For the simple LQ model with no time dependence, which is applicable to late reacting tissue, SRE = [(d + delta)/(2 + delta)], where d is the fraction size and delta = alpha/beta is the alpha/beta ratio for the tissue of interest, with both d and delta expressed in units of Gy. Application of this method to the Linear Quadratic model with a time dependence, the LQ + time model, and to low dose rate brachytherapy will be discussed. To clarify the method of calculation, and to demonstrate its simplicity, examples from the clinical literature will be used
Vacuum solutions of Bianchi cosmologies in quadratic gravity
International Nuclear Information System (INIS)
Deus, Juliano Alves de; Muller, Daniel
2011-01-01
Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)
Lipschitz stability of the K-quadratic functional equation | Chahbi ...
African Journals Online (AJOL)
Let N be the set of all positive integers, G an Abelian group with a metric d and E a normed space. For any f : G → E we define the k-quadratic difference of the function f by the formula Qk ƒ(x; y) := 2ƒ(x) + 2k2ƒ(y) - f(x + ky) - f(x - ky) for x; y ∈ G and k ∈ N. Under some assumptions about f and Qkƒ we prove that if Qkƒ is ...
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Kesler, Robert; Arias, Darío Mena
2017-09-01
For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
BRST operator for superconformal algebras with quadratic nonlinearity
International Nuclear Information System (INIS)
Khviengia, Z.; Sezgin, E.
1993-07-01
We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs
Quadratic integrand double-hybrid made spin-component-scaled
Energy Technology Data Exchange (ETDEWEB)
Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Sancho-García, Juan C.; Pérez-Jiménez, Ángel J. [Departamento de Química Física, Universidad de Alicante, E-03080 Alicante (Spain); Adamo, Carlo [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris IRCP, F-75005 Paris (France); Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris (France)
2016-03-28
We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
International Nuclear Information System (INIS)
Sekine, Jun
2006-01-01
The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula
Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori
T. Sardari, Naser
2018-03-01
Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.
Abelian groups and quadratic residues in weak arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2010-01-01
Roč. 56, č. 3 (2010), s. 262-278 ISSN 0942-5616 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * abelian group * Fermat's little theorem * quadratic reciprocity Subject RIV: BA - General Mathematics Impact factor: 0.361, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/malq.200910009/abstract;jsessionid=9F636FFACB84C025FD90C7E6880350DD.f03t03
Analysis of electroperforated materials using the quadrat counts method
Energy Technology Data Exchange (ETDEWEB)
Miranda, E; Garzon, C; Garcia-Garcia, J [Departament d' Enginyeria Electronica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); MartInez-Cisneros, C; Alonso, J, E-mail: enrique.miranda@uab.cat [Departament de Quimica AnalItica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain)
2011-06-23
The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.
C1 Rational Quadratic Trigonometric Interpolation Spline for Data Visualization
Directory of Open Access Journals (Sweden)
Shengjun Liu
2015-01-01
Full Text Available A new C1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h3. Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...
Linear-quadratic model predictions for tumor control probability
International Nuclear Information System (INIS)
Yaes, R.J.
1987-01-01
Sigmoid dose-response curves for tumor control are calculated from the linear-quadratic model parameters α and Β, obtained from human epidermoid carcinoma cell lines, and are much steeper than the clinical dose-response curves for head and neck cancers. One possible explanation is the presence of small radiation-resistant clones arising from mutations in an initially homogeneous tumor. Using the mutation theory of Delbruck and Luria and of Goldie and Coldman, the authors discuss the implications of such radiation-resistant clones for clinical radiation therapy
Sub-quadratic decoding of one-point hermitian codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter
2015-01-01
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....
Field equations for gravity quadratic in the curvature
International Nuclear Information System (INIS)
Rose, B.
1992-01-01
Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs
Quadratic Hamiltonians on non-symmetric Poisson structures
International Nuclear Information System (INIS)
Arribas, M.; Blesa, F.; Elipe, A.
2007-01-01
Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases
Cyclic subgroups in class groups of real quadratic fields
International Nuclear Information System (INIS)
Washington, L.C.; Zhang Xianke.
1994-01-01
While examining the class numbers of the real quadratic field Q(√n 2 + 3n + 9), we observed that the class number is often a multiple of 3. There is a simple explanation for this, namely -27 = (2n + 3) 2 - 4(n 2 + 3n + 9), so the cubes of the prime ideals above 3 are principal. If the prime ideals themselves are non-principal then 3 must divide the class number. In the present paper, we study this idea from a couple different directions. In the first section we present a criterion that allows us to show that the ideal class group of a real quadratic field has a cyclic subgroup of a given order n. We then give several families of fields to which this criterion applies, hence in which the ideal class groups contain elements of order n. In the second section, we discuss the situation where there is only a potential element of order p (=an odd prime) in the class group, such as the situation described above. We present a modification of the Cohen-Lenstra heuristics for the probability that in this situation the class number is actually a multiple of p. We also extend this idea to predict how often the potential element of order p is actually non-trivial. Both of these predictions agree fairly well with the numerical data. (author). 14 refs, 2 tabs
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
Learning quadratic receptive fields from neural responses to natural stimuli.
Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper
2013-07-01
Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.
On bent and semi-bent quadratic Boolean functions
DEFF Research Database (Denmark)
Charpin, P.; Pasalic, Enes; Tavernier, C.
2005-01-01
correlation and high nonlinearity. We say that such a sequence is generated by a semi-bent function. Some new families of such function, represented by f(x) = Sigma(i=1)(n-1/2) c(i)Tr(x(2t+1)), n odd and c(i) is an element of F-2, have recently (2002) been introduced by Khoo et al. We first generalize......The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross...... their results to even n. We further investigate the conditions on the choice of ci for explicit definitions of new infinite families having three and four trace terms. Also, a class of nonpermutation polynomials whose composition with a quadratic function yields again a quadratic semi-bent function is specified...
Quadratic dependence of the spin-induced Hall voltage on longitudinal electric field
International Nuclear Information System (INIS)
Miah, M. Idrish
2008-01-01
The effect of optically induced spins in semiconductors in the low electric field is investigated. Here we report an experiment which investigates the effect of a longitudinal electric field (E) on the spin-polarized carriers generated by a circularly polarized light in semiconductors. Our experiment observes the effect as a spin-induced anomalous Hall voltage (V AH ) resulting from spin-carrier electrons accumulating at the transverse edges of the sample. Unlike the ordinary Hall effect, a quadratic dependence of V AH on E is observed, which agrees with the results of the recent theoretical investigations. It is also found that V AH depends on the doping density. The results are discussed
Quadratic dependence of the spin-induced Hall voltage on longitudinal electric field
Energy Technology Data Exchange (ETDEWEB)
Miah, M. Idrish [Nanoscale Science and Technology Centre, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); Department of Physics, University of Chittagong, Chittagong 4331 (Bangladesh)], E-mail: m.miah@griffith.edu.au
2008-10-15
The effect of optically induced spins in semiconductors in the low electric field is investigated. Here we report an experiment which investigates the effect of a longitudinal electric field (E) on the spin-polarized carriers generated by a circularly polarized light in semiconductors. Our experiment observes the effect as a spin-induced anomalous Hall voltage (V{sub AH}) resulting from spin-carrier electrons accumulating at the transverse edges of the sample. Unlike the ordinary Hall effect, a quadratic dependence of V{sub AH} on E is observed, which agrees with the results of the recent theoretical investigations. It is also found that V{sub AH} depends on the doping density. The results are discussed.
Energy Technology Data Exchange (ETDEWEB)
Chao, R.M.; Ko, S.H.; Lin, I.H. [Department of Systems and Naval Mechatronics Engineering, National Cheng Kung University, Tainan, Taiwan 701 (China); Pai, F.S. [Department of Electronic Engineering, National University of Tainan (China); Chang, C.C. [Department of Environment and Energy, National University of Tainan (China)
2009-12-15
The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)
Obstacle Avoidance for Redundant Manipulators Utilizing a Backward Quadratic Search Algorithm
Directory of Open Access Journals (Sweden)
Tianjian Hu
2016-06-01
Full Text Available Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the clamping velocity, are discussed, along with a comparison of computational load between previous methods and BQSA. Simulations of a planar seven-link manipulator and a PUMA 560 robot verify the effectiveness of BQSA.
Identify Beta-Hairpin Motifs with Quadratic Discriminant Algorithm Based on the Chemical Shifts.
Directory of Open Access Journals (Sweden)
Feng YongE
Full Text Available Successful prediction of the beta-hairpin motif will be helpful for understanding the of the fold recognition. Some algorithms have been proposed for the prediction of beta-hairpin motifs. However, the parameters used by these methods were primarily based on the amino acid sequences. Here, we proposed a novel model for predicting beta-hairpin structure based on the chemical shift. Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in not beta-hairpin and beta-hairpin motifs. Secondly, we used these chemical shifts as features combined with three algorithms to predict beta-hairpin structure. Finally, we achieved the best prediction, namely sensitivity of 92%, the specificity of 94% with 0.85 of Mathew's correlation coefficient using quadratic discriminant analysis algorithm, which is clearly superior to the same method for the prediction of beta-hairpin structure from 20 amino acid compositions in the three-fold cross-validation. Our finding showed that the chemical shift is an effective parameter for beta-hairpin prediction, suggesting the quadratic discriminant analysis is a powerful algorithm for the prediction of beta-hairpin.
Directory of Open Access Journals (Sweden)
N. Bhardwaj
2008-01-01
Full Text Available In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b Lateral vibration characteristics of F-Fplates is more sensitive towards parametric changes in material orthotropy and foundation stiffness than C-C and S-Splates; (c Effect of quadratical thickness variation on fundamental frequency is more significant in cases of C-C and S-S plates than that of F-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d Fundamental mode of vibration of C-C and S-Splates is axisymmetrical while that of F-Fplates is asymmetrical.
Zhang, Zhongheng; Ji, Xuqing
2016-10-13
Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO 2 ) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO 2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO 2 and its interaction with other covariates were explored. A total of 199,125 PaO 2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO 2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO 2 on mortality risk was in quadratic form. There was significant interaction between PaO 2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO 2 on SOFA score was nonlinear. The study shows that the effect of PaO 2 on mortality risk is in quadratic function form, and there is significant interaction between PaO 2 and severity of illness.
The Model and Quadratic Stability Problem of Buck Converter in DCM
Directory of Open Access Journals (Sweden)
Li Xiaojing
2016-01-01
Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.
A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming
National Research Council Canada - National Science Library
Ye, Y; Gueler, O; Tapia, Richard A; Zhang, Y
1991-01-01
...)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap...
Sun, Fadi; Ye, Jinwu; Liu, Wu-Ming
2017-08-01
In this work, we study strongly interacting spinor atoms in a lattice subject to a two dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the four commensurate phases. New excitation spectra above all the five phases, especially on the IC-SKX phase are computed. Three different classes of quantum commensurate to in-commensurate transitions from the IC-SKX to its four neighboring commensurate phases are identified. Finite temperature behaviors and transitions are discussed. The critical temperatures of all the phases can be raised above that reachable by current cold atom cooling techniques simply by tuning the number of atoms N per site. In view of recent impressive experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the current and near future cold atom experiments. Applications to various materials such as MnSi, {Fe}}0.5 {Co}}0.5Si, especially the complex incommensurate magnetic ordering in Li2IrO3 are given.
Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations
DEFF Research Database (Denmark)
Sørensen, Dan Erik Krarup
1996-01-01
We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...
Diagonalizing quadratic bosonic operators by non-autonomous flow equations
Bach, Volker
2016-01-01
The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
Directory of Open Access Journals (Sweden)
J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
Absence of the Gribov ambiguity in a quadratic gauge
International Nuclear Information System (INIS)
Raval, Haresh
2016-01-01
The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S 3 , when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge. (orig.)
Absence of the Gribov ambiguity in a quadratic gauge
Energy Technology Data Exchange (ETDEWEB)
Raval, Haresh [Indian Institute of Technology, Bombay, Department of Physics, Mumbai (India)
2016-05-15
The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold S{sup 3}, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge. (orig.)
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Trajectory generation for manipulators using linear quadratic optimal tracking
Directory of Open Access Journals (Sweden)
Olav Egeland
1989-04-01
Full Text Available The reference trajectory is normally known in advance in manipulator control which makes it possible to apply linear quadratic optimal tracking. This gives a control system which rounds corners and generates optimal feedforward. The method may be used for references consisting of straight-line segments as an alternative to the two-step method of using splines to smooth the reference and then applying feedforward. In addition, the method can be used for more complex trajectories. The actual dynamics of the manipulator are taken into account, and this results in smooth and accurate tracking. The method has been applied in combination with the computed torque technique and excellent performance was demonstrated in a simulation study. The method has also been applied experimentally to an industrial spray-painting robot where a saw-tooth reference was tracked. The corner was rounded extremely well, and the steady-state tracking error was eliminated by the optimal feedforward.
Quadratic rational rotations of the torus and dual lattice maps
Kouptsov, K L; Vivaldi, F
2002-01-01
We develop a general formalism for computed-assisted proofs concerning the orbit structure of certain non ergodic piecewise affine maps of the torus, whose eigenvalues are roots of unity. For a specific class of maps, we prove that if the trace is a quadratic irrational (the simplest nontrivial case, comprising 8 maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of exceptional families. The proof is based on exact computations with algebraic numbers, where units play the role of scaling parameters. Exploiting a duality existing between these maps and lattice maps representing rounded-off planar rotations, we establish the global periodicity of the latter systems, for a set of orbits of full density.
Low photon count based digital holography for quadratic phase cryptography.
Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T
2017-07-15
Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.
Limits to compression with cascaded quadratic soliton compressors
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2008-01-01
We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong....... This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find......, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account....
Wind turbine power tracking using an improved multimodel quadratic approach.
Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier
2010-07-01
In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.
Quadratic Finite Element Method for 1D Deterministic Transport
International Nuclear Information System (INIS)
Tolar, D R Jr.; Ferguson, J M
2004-01-01
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms
Schwarz and multilevel methods for quadratic spline collocation
Energy Technology Data Exchange (ETDEWEB)
Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Estimation of stature from sternum - Exploring the quadratic models.
Saraf, Ashish; Kanchan, Tanuj; Krishan, Kewal; Ateriya, Navneet; Setia, Puneet
2018-04-14
Identification of the dead is significant in examination of unknown, decomposed and mutilated human remains. Establishing the biological profile is the central issue in such a scenario, and stature estimation remains one of the important criteria in this regard. The present study was undertaken to estimate stature from different parts of the sternum. A sample of 100 sterna was obtained from individuals during the medicolegal autopsies. Length of the deceased and various measurements of the sternum were measured. Student's t-test was performed to find the sex differences in stature and sternal measurements included in the study. Correlation between stature and sternal measurements were analysed using Karl Pearson's correlation, and linear and quadratic regression models were derived. All the measurements were found to be significantly larger in males than females. Stature correlated best with the combined length of sternum, among males (R = 0.894), females (R = 0.859), and for the total sample (R = 0.891). The study showed that the models derived for stature estimation from combined length of sternum are likely to give the most accurate estimates of stature in forensic case work when compared to manubrium and mesosternum. Accuracy of stature estimation further increased with quadratic models derived for the mesosternum among males and combined length of sternum among males and females when compared to linear regression models. Future studies in different geographical locations and a larger sample size are proposed to confirm the study observations. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.
Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen
2014-02-01
This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.
Energy Technology Data Exchange (ETDEWEB)
Cvetkovic, J. [Inst. of Agriculture, Skopje (Yugoslavia); Stafilov, T. [Inst. of Chemistry, Faculty of Science Sts. Cyril and Methodius Univ., Skopje (Yugoslavia); Mihajlovic, D. [RZ Tehnicka Kontrola, Skopje (Yugoslavia)
2001-08-01
A mixed matrix modifier of nickel and strontium nitrates was used as a chemical modifier for the determination of selenium in wines by Zeeman electrothermal atomic absorption spectrometry. Wine samples were heated on a boiling water bath with small amounts of nitric acid and hydrogen peroxide. For complete elimination of interference, especially from sulfates and phosphates, selenium is complexed with ammonium pyrolidinedithiocarbamate (APDTC), extracted into methyl isobutyl ketone (MIBK), and measured by ETAAS. The graphite furnace temperature program was optimized for both aqueous and organic solutions. Pyrolysis temperatures of 1300 C and 800 C were chosen for aqueous and organic solutions, respectively; 2700 C and 2100 C were used as optimum atomization temperatures for aqueous and organic solutions, respectively. The optimum modifier mass established is markedly lower than those presented in the literature. The platform atomization ensures pretreatment stabilization up to 1100 C and 1600 C, respectively, for organic and aqueous selenium solutions. The procedure was verified by the method of standard addition. The investigated wine samples originated from the different regions of the Republic of Macedonia. The selenium concentration varied from not detectable to 0.93 {mu}g L{sup -1}. (orig.)
International Nuclear Information System (INIS)
Kolesov, Roman; Scully, Marlan O.; Kocharovskaya, Olga
2006-01-01
Coherent population trapping (CPT) in a three-level atomic medium pumped by two subsequent short optical pulses is considered under the condition of negligible population decay from the excited optical state. It is shown that the amount of atomic population transferred to the excited state by the combined action of the pulses strongly depends on the phase of the ground-state coherence excited by the first pulse at the arrival time of the second pulse. Oscillatory behavior of optical excitation efficiency on the time delay between the pulses is predicted. It is also shown that saturating optical pulses can produce population inversion in a resonantly pumped quasi-two-level system. A class of solid materials in which the predicted phenomena can be observed at room temperature is found. It includes some rare-earth and transition-metal doped dielectric crystals where Orbach relaxation between ground-state Zeeman states is suppressed: ruby, alexandrite, and several others. On the basis of the theoretical predictions, experimental observation of Ramsey fringes in CPT spectrum of ruby is reported
Zhou, Minchuan; Zhou, Zifan; Shahriar, Selim M.
2017-11-01
Previously, we had proposed an optically-pumped five-level Gain EIT (GEIT) system, which has a transparency dip superimposed on a gain profile and exhibits a negative dispersion suitable for the white-light-cavity signal-recycling (WLC-SR) scheme of the interferometric gravitational wave detector (Zhou et al., 2015). Using this system as the negative dispersion medium (NDM) in the WLC-SR, we get an enhancement in the quantum noise (QN) limited sensitivity-bandwidth product by a factor of ∼ 18. Here, we show how to realize this GEIT system in a realistic platform, using non-degenerate Zeeman sublevels in cold Rb atoms, employing anomalous dispersion at 795 nm. Using the Caves model for a phase insensitive linear amplifier, we show that an enhancement of the sensitivity-bandwidth product by a factor of ∼ 17 is possible for potentially realizable experimental parameters. While the current LIGO apparatus uses light at 1064 nm, a future embodiment thereof may operate at a wavelength that is consistent with the wavelength considered here.
International Nuclear Information System (INIS)
Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-01-01
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained
International Nuclear Information System (INIS)
Ayvaz, Muzaffer; Demiralp, Metin
2011-01-01
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
de Klerk, E.; Sotirov, R.
2007-01-01
We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,
DEFF Research Database (Denmark)
Bache, Morten; Moses, J.; Wise, F.W.
2010-01-01
Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)].......Erratum for [M. Bache, J. Moses, and F. W. Wise, "Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities," J. Opt. Soc. Am. B 24, 2752-2762 (2007)]....
Directory of Open Access Journals (Sweden)
Xuewen Mu
2015-01-01
quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.
The regular indefinite linear-quadratic problem with linear endpoint constraints
Soethoudt, J.M.; Trentelman, H.L.
1989-01-01
This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that
A Novel Single Switch Transformerless Quadratic DC/DC Buck-Boost Converter
DEFF Research Database (Denmark)
Mostaan, Ali; A. Gorji, Saman; N. Soltani, Mohsen
2017-01-01
A novel quadratic buck-boost DC/DC converter is presented in this study. The proposed converter utilizes only one active switch and can step-up/down the input voltage, while the existing single switch quadratic buck/boost converters can only work in step-up or step-down mode. First, the proposed ...
Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
Pathak, H. K.; Grewal, A. S.
2002-01-01
This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…
Estimating sample size for a small-quadrat method of botanical ...
African Journals Online (AJOL)
Reports the results of a study conducted to determine an appropriate sample size for a small-quadrat method of botanical survey for application in the Mixed Bushveld of South Africa. Species density and grass density were measured using a small-quadrat method in eight plant communities in the Nylsvley Nature Reserve.
Heinkenschloss, Matthias
2005-01-01
We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.
Directory of Open Access Journals (Sweden)
M. R. Monazzam ، P. Nassiri
2009-10-01
Full Text Available This paper presents the results of an investigation on the acoustic performance of tilted profile parallel barriers with quadratic residue diffuser (QRD tops and faces. A 2D boundary element method (BEM is used to predict the barrier insertion loss. The results of rigid and with absorptive coverage are also calculated for comparisons. Using QRD on the top surface and faces of all tilted profile parallel barrier models introduced here is found to improve the efficiency of barriers compared with rigid equivalent parallel barrier at the examined receiver positions. Applying a QRD with frequency design of 400 Hz on 5 degrees tilted parallel barrier improves the overall performance of its equivalent rigid barrier by 1.8 dB(A. Increase in the treated surfaces with reactive elements shifts the effective performance toward lower frequencies. It is found that by tilting the barriers from 0 to 10 degrees in parallel set up, the degradation effects in parallel barriers is reduced but the absorption effect of fibrous materials and also diffusivity of the quadratic residue diffuser is reduced significantly. In this case all the designed barriers have better performance with 10 degrees tilting in parallel set up. The most economic traffic noise parallel barrier which produces significantly high performance, is achieved by covering the top surface of the barrier closed to the receiver by just a QRD with frequency design of 400 Hz and tilting angle of 10 degrees. The average A-weighted insertion loss in this barrier is predicted to be 16.3 dB (A.
Lima, Ricardo
2016-06-16
This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York
Lima, Ricardo; Grossmann, Ignacio E.
2016-01-01
This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York
Directory of Open Access Journals (Sweden)
Liyang Wang
2017-01-01
Full Text Available The application of biped robots is always trapped by their high energy consumption. This paper makes a contribution by optimizing the joint torques to decrease the energy consumption without changing the biped gaits. In this work, a constrained quadratic programming (QP problem for energy optimization is formulated. A neurodynamics-based solver is presented to solve the QP problem. Differing from the existing literatures, the proposed neurodynamics-based energy optimization (NEO strategy minimizes the energy consumption and guarantees the following three important constraints simultaneously: (i the force-moment equilibrium equation of biped robots, (ii frictions applied by each leg on the ground to hold the biped robot without slippage and tipping over, and (iii physical limits of the motors. Simulations demonstrate that the proposed strategy is effective for energy-efficient biped walking.
International Nuclear Information System (INIS)
Hebrard, Elodie
2015-01-01
Forthcoming instruments dedicated to exo-planets detection through the radial velocity method are numerous, and increasingly more accurate. However this method is indirect: orbiting planets are detected and characterised from variations on the spectrum of the host star. We are therefore sensitive to all activity phenomena impacting the spectrum and producing a radial velocity signal (pulsation, granulation, spots, magnetic cycle...). The detection of rocky Earth-like planets around main-sequence stars, and of hot Jupiters into young systems, are currently limited by the intrinsic magnetic activity of the host stars. The radial velocity fluctuations caused by activity (activity jitter) can easily mimic and hide signals from such planets, whose amplitude is of a few m/s and hundreds of m/s, respectively. As a result, the detection threshold of exo-planets is largely set by the stellar activity level. Currently, efforts are invested to overcome this intrinsic limitation. During my PhD, I studied how to take advantage of imaging tomographic techniques (Zeeman-Doppler imaging, ZDI) to characterize stellar activity and magnetic field topologies, ultimately allowing us to filter out the activity jitter. My work is based on spectro-polarimetric observations of a sample of weakly-active M-dwarfs, and young active T Tauri stars. Using a modified version of ZDI, we are able to reconstruct the distribution of active regions, and then model the induced stellar signal allowing us to clean RV curves from the activity jitter. First tests demonstrate that this technique can be efficient enough to recover the planet signal, especially for the more active ones. (author)
Generation and dynamics of quadratic birefringent spatial gap solitons
International Nuclear Information System (INIS)
Anghel-Vasilescu, P.; Dorignac, J.; Geniet, F.; Leon, J.; Taki, A.
2011-01-01
A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe 2 (LGT) crystals. Once irradiated by a cw laser beam of 10 μm wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold.
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares
Orr, Jeb S.
2012-01-01
A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed
Asymptotic behavior for a quadratic nonlinear Schrodinger equation
Directory of Open Access Journals (Sweden)
Pavel I. Naumkin
2008-02-01
Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.
Quadratic electromechanical strain in silicon investigated by scanning probe microscopy
Yu, Junxi; Esfahani, Ehsan Nasr; Zhu, Qingfeng; Shan, Dongliang; Jia, Tingting; Xie, Shuhong; Li, Jiangyu
2018-04-01
Piezoresponse force microscopy (PFM) is a powerful tool widely used to characterize piezoelectricity and ferroelectricity at the nanoscale. However, it is necessary to distinguish microscopic mechanisms between piezoelectricity and non-piezoelectric contributions measured by PFM. In this work, we systematically investigate the first and second harmonic apparent piezoresponses of a silicon wafer in both vertical and lateral modes, and we show that it exhibits an apparent electromechanical response that is quadratic to the applied electric field, possibly arising from ionic electrochemical dipoles induced by the charged probe. As a result, the electromechanical response measured is dominated by the second harmonic response in the vertical mode, and its polarity can be switched by the DC voltage with the evolving coercive field and maximum amplitude, in sharp contrast to typical ferroelectric materials we used as control. The ionic activity in silicon is also confirmed by the scanning thermo-ionic microscopy measurement, and the work points toward a set of methods to distinguish true piezoelectricity from the apparent ones.
Asymptotic performance of regularized quadratic discriminant analysis based classifiers
Elkhalil, Khalil
2017-12-13
This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube
International Nuclear Information System (INIS)
Mittelmann, Hans; Peng Jiming; Wu Xiaolin
2009-01-01
In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs.Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n 3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
Separability of diagonal symmetric states: a quadratic conic optimization problem
Directory of Open Access Journals (Sweden)
Jordi Tura
2018-01-01
Full Text Available We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS states. First, we show that separability in the case of DS in $C^d\\otimes C^d$ (symmetric qudits can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT is sufficient and necessary for separability of DS states for $d \\leq 4$. Furthermore, for $d \\geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.
Evolution of universes in quadratic theories of gravity
International Nuclear Information System (INIS)
Barrow, John D.; Hervik, Sigbjoern
2006-01-01
We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Because of the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic Friedmann-Robertson-Walker (FRW) universe acting as a past attractor. This may indicate that there is an isotropization mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated center manifold structure, and show that there exists a set of nonzero measure which has the Kasner solutions as a past attractor. Regarding the late-time behavior, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behavior with phantomlike behavior. New types of anisotropic inflationary behavior are found which do not have counterparts in general relativity
Methods of using the quadratic assignment problem solution
Directory of Open Access Journals (Sweden)
Izabela Kudelska
2012-09-01
Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.
Noise-induced chaos in a quadratically nonlinear oscillator
International Nuclear Information System (INIS)
Gan Chunbiao
2006-01-01
The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system
Application of the linear-quadratic model to myelotoxicity associated with radioimmunotherapy
International Nuclear Information System (INIS)
Wilder, R.B.; DeNardo, G.L.; Sheri, S.; Fowler, J.F.; Wessels, B.W.; DeNardo, S.J.
1996-01-01
The purposes of this study were: To use the linear-quadratic model to determine time-dependent biologically effective doses (BEDs) that were delivered to the bone marrow by multiple infusions of radiolabeled antibodies, and (2) to determine whether granulocyte and platelet counts correlate better with BED than administered radioactivity. Twenty patients with B-cell malignancies that had progressed despite intensive chemotherapy and who had a significant number of malignant cells in their bone marrow were treated with multiple 0.7-3.7 GBq/m 2 intravenous infusions of Lym-1, a murine monoclonal antibody that binds to a tumour-associated antigen, labeled with iodine-131. Granulocyte and platelet counts were measured in order to assess bone marrow toxicity. The cumulative 131 I-Lym-1 radioactivity administered to each patient was calculated. BEDs from multiple 131 I-Lym-1 infusions were summated in order to arrive at a total BED for each patient. There was a weak association between granulocyte and platelet counts and radioactivity. Likewise, there was a weak association between granulocyte and platelet counts and BED. The attempt to take bone marrow absorbed doses and overall treatment time into consideration with the linear-quadratic model did not produce a stronger association than was observed between peripheral blood counts and administered radioactivity. The association between granulocyte and platelet counts and BED may have been weakened by several factors, including variable bone marrow reserve at the start of 131 I-Lym-1 therapy and the delivery of heterogeneous, absorbed doses of radiation to the bone marrow. (orig./MG)
Mismatch management for optical and matter-wave quadratic solitons
International Nuclear Information System (INIS)
Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A.
2007-01-01
We propose a way to control solitons in χ (2) (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM
Quadratic adaptive algorithm for solving cardiac action potential models.
Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing
2016-10-01
An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights
Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.
2018-01-01
Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.
Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces
International Nuclear Information System (INIS)
Oyewumi, K.A.; Bangudu, E.A.
2003-01-01
Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)
A necessary and sufficient condition for a real quadratic extension to have class number one
International Nuclear Information System (INIS)
Alemu, Y.
1990-02-01
We give a necessary and sufficient condition for a real quadratic extension to have class number one and discuss the applicability of the result to find the class number one fields with small discriminant. 9 refs, 3 tabs
Quadratic contributions of softly broken supersymmetry in the light of loop regularization
Energy Technology Data Exchange (ETDEWEB)
Bai, Dong [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Wu, Yue-Liang [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China)
2017-09-15
Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess-Zumino model with soft supersymmetry breaking terms (WZ' model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques. (orig.)
Projection of curves on B-spline surfaces using quadratic reparameterization
Yang, Yijun; Zeng, Wei; Zhang, Hui; Yong, Junhai; Paul, Jean Claude
2010-01-01
Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
Fouha Bay Moving Window Analysis, Benthic Quadrat Surveys at Guam in 2014
National Oceanic and Atmospheric Administration, Department of Commerce — PIRO Fishery Biologist gathered benthic cover data using a 1m2 quadrat with 25 intersecting points every five meters along a transect running from the inner bay to...
Groenwold, A.A.; Wood, D.W.; Etman, L.F.P.; Tosserams, S.
2009-01-01
We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by
Guam Community Coral Reef Monitoring Program, Benthic Quadrat Surveys at Guam in 2013
National Oceanic and Atmospheric Administration, Department of Commerce — Guam community members gathered benthic cover data using a 0.25m2 quadrat with 6 intersecting points at each meter along a 25-meter transect. Members identified...
Integrable quadratic classical Hamiltonians on so(4) and so(3, 1)
International Nuclear Information System (INIS)
Sokolov, Vladimir V; Wolf, Thomas
2006-01-01
We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree
New trace formulae for a quadratic pencil of the Schroedinger operator
International Nuclear Information System (INIS)
Yang Chuanfu
2010-01-01
This work deals with the eigenvalue problem for a quadratic pencil of the Schroedinger operator on a finite closed interval with the two-point boundary conditions. We will obtain new regularized trace formulas for this class of differential pencil.
Fourier transform and mean quadratic variation of Bernoulli convolution on homogeneous Cantor set
Energy Technology Data Exchange (ETDEWEB)
Yu Zuguo E-mail: yuzg@hotmail.comz.yu
2004-07-01
For the Bernoulli convolution on homogeneous Cantor set, under some condition, it is proved that the mean quadratic variation and the average of Fourier transform of this measure are bounded above and below.
Cost Cumulant-Based Control for a Class of Linear Quadratic Tracking Problems
National Research Council Canada - National Science Library
Pham, Khanh D
2007-01-01
.... For instance, the present paper extends the application of cost-cumulant controller design to control of a wide class of linear-quadratic tracking systems where output measurements of a tracker...
International Nuclear Information System (INIS)
Gogala, B.
1983-01-01
The equations of the gauge theory of gravitation are derived from a complex quadratic Lagrangian with torsion. The derivation is performed in a coordinate basis in a completely covariant way. (author)
Use of Quadratic Time-Frequency Representations to Analyze Cetacean Mammal Sounds
National Research Council Canada - National Science Library
Papandreou-Suppappola, Antonia
2001-01-01
.... Analysis of the group delay structure of the mammalian vocal communication signals was matched to the appropriate quadratic time-frequency class for proper signal processing with minimal skewing of the results...
Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid
Brilleslyper, Michael A.
2004-01-01
Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.
DEFF Research Database (Denmark)
Bergami, Leonardo; Poulsen, Niels Kjølstad
2015-01-01
The paper proposes a smart rotor configuration where adaptive trailing edge flaps (ATEFs) are employed for active alleviation of the aerodynamic loads on the blades of the NREL 5 MW reference turbine. The flaps extend for 20% of the blade length and are controlled by a linear quadratic (LQ....... The effects of active flap control are assessed with aeroelastic simulations of the turbine in normal operation conditions, as prescribed by the International Electrotechnical Commission standard. The turbine lifetime fatigue damage equivalent loads provide a convenient summary of the results achieved...
DEFF Research Database (Denmark)
Liu, Xing; Zhou, Binbin; Guo, Hairun
2015-01-01
in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between. lambda = 2.2-2.4 mu m as a resonant dispersive wave. This process relies...... on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation. (C) 2015 Optical Society of America...
International Nuclear Information System (INIS)
Kusakabe, Koichi
2009-01-01
To construct an optimization scheme for an extension of the Kohn-Sham approach, I introduce an operator form of the Coulomb interaction. This form is the sum of quadratic form pairs, which can be redefined in a self-consistent calculation of a multi-reference density functional theory. A detailed derivation of the form is given. A fluctuation term introduced in the extended Kohn-Sham scheme is expressed in this form for regularization. The present procedure also provides an exact derivation of effective negative interactions in charge fluctuation channels. Relevance to high-temperature superconductors is discussed.
Lin, Nan; Zhu, Yun; Fan, Ruzong; Xiong, Momiao
2017-10-01
Investigating the pleiotropic effects of genetic variants can increase statistical power, provide important information to achieve deep understanding of the complex genetic structures of disease, and offer powerful tools for designing effective treatments with fewer side effects. However, the current multiple phenotype association analysis paradigm lacks breadth (number of phenotypes and genetic variants jointly analyzed at the same time) and depth (hierarchical structure of phenotype and genotypes). A key issue for high dimensional pleiotropic analysis is to effectively extract informative internal representation and features from high dimensional genotype and phenotype data. To explore correlation information of genetic variants, effectively reduce data dimensions, and overcome critical barriers in advancing the development of novel statistical methods and computational algorithms for genetic pleiotropic analysis, we proposed a new statistic method referred to as a quadratically regularized functional CCA (QRFCCA) for association analysis which combines three approaches: (1) quadratically regularized matrix factorization, (2) functional data analysis and (3) canonical correlation analysis (CCA). Large-scale simulations show that the QRFCCA has a much higher power than that of the ten competing statistics while retaining the appropriate type 1 errors. To further evaluate performance, the QRFCCA and ten other statistics are applied to the whole genome sequencing dataset from the TwinsUK study. We identify a total of 79 genes with rare variants and 67 genes with common variants significantly associated with the 46 traits using QRFCCA. The results show that the QRFCCA substantially outperforms the ten other statistics.
Quadratic Hierarchy Flavor Rule as the Origin of Dirac CP-Violating Phases
Lipmanov, E. M.
2007-01-01
The premise of an organizing quadratic hierarchy rule in lepton-quark flavor physics was used earlier for explanation of the hierarchy patterns of four generic pairs of flavor quantities 1) charged-lepton and 2) neutrino deviations from mass-degeneracy, 3) deviations of lepton mixing from maximal magnitude and 4) deviations of quark mixing from minimal one. Here it is shown that the quadratic hierarchy equation that is uniquely related to three flavor particle generations may have yet another...
Electron laser acceleration in vacuum by a quadratically chirped laser pulse
International Nuclear Information System (INIS)
Salamin, Yousef I; Jisrawi, Najeh M
2014-01-01
Single MeV electrons in vacuum subjected to single high-intensity quadratically chirped laser pulses are shown to gain multi-GeV energies. The laser pulses are modelled by finite-duration trapezoidal and cos 2 pulse-shapes and the equations of motion are solved numerically. It is found that, typically, the maximum energy gain from interaction with a quadratic chirp is about half of what would be gained from a linear chirp. (paper)
Institute of Scientific and Technical Information of China (English)
XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian
2007-01-01
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Energy Technology Data Exchange (ETDEWEB)
Szederkenyi, Gabor; Hangos, Katalin M
2004-04-26
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Szederkényi, Gábor; Hangos, Katalin M.
2004-04-01
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
International Nuclear Information System (INIS)
Szederkenyi, Gabor; Hangos, Katalin M.
2004-01-01
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities
On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory
Taras Bodnar; Nestor Parolya; Wolfgang Schmid
2012-01-01
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization prob...
Decay constants for pulsed monoenergetic neutron systems with quadratically anisotropic scattering
International Nuclear Information System (INIS)
Sjoestrand, N.G.
1977-06-01
The eigenvalues of the time-dependent transport equation for monoenergetic neutrons have been studied numerically for various combinations of linearly and quadratically anisotropic scattering assuming a space dependence of e β . The results, presented in the form of tables and graphs, show that quadratic anisotropy leads to a more complicated eigenvalue spectrum. However, no drastic changes occur in comparison to purely linear anistropy.(author)
International Nuclear Information System (INIS)
Zhitnikov, V.V.; Ponomarev, V.N.
1986-01-01
An attempt is made to compare the solution of field equations, corresponding to quadratic equations for the fields (g μν , Γ μν α ) in gauge gravitation theory (GGT) with general relativity theory solutions. Without restrictions for a concrete type of metrics only solutions of equations, for which torsion turns to zero, are considered. Equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory is proved using the Newman-Penrose formalism
Exponential quadratic operators and evolution of bosonic systems coupled to a heat bath
International Nuclear Information System (INIS)
Ni Xiaotong; Liu Yuxi; Kwek, L. C.; Wang Xiangbin
2010-01-01
Using exponential quadratic operators, we present a general framework for studying the exact dynamics of system-bath interaction in which the Hamiltonian is described by the quadratic form of bosonic operators. To demonstrate the versatility of the approach, we study how the environment affects the squeezing of quadrature components of the system. We further propose that the squeezing can be enhanced when parity kicks are applied to the system.
Energy Technology Data Exchange (ETDEWEB)
Banasek, J. T., E-mail: jtb254@cornell.edu; Engelbrecht, J. T.; Pikuz, S. A.; Shelkovenko, T. A.; Hammer, D. A. [Cornell University, Ithaca, New York 14850 (United States)
2016-11-15
We have shown that Zeeman splitting of the sodium (Na) D-lines at 5890 and 5896 Å can be used to measure the magnetic field (B-field) produced in high current pulsed power experiments. We have measured the B-field next to a return current conductor in a hybrid X-pinch experiment near a peak current of about 500 kA. Na is deposited on the conductor and then is desorbed and excited by radiation from the hybrid X-pinch. The D-line emission spectrum implies B-fields of about 20 T with a return current post of 4 mm diameter or up to 120 T with a return current wire of 0.455 mm diameter. These measurements were consistent or lower than the expected B-field, thereby showing that basic Zeeman splitting can be used to measure the B-field in a pulsed-power-driven high-energy-density (HED) plasma experiment. We hope to extend these measurement techniques using suitable ionized species to measurements within HED plasmas.
Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong
2018-05-19
In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.
Directory of Open Access Journals (Sweden)
Benjamin M Haley
Full Text Available The US government regulates allowable radiation exposures relying, in large part, on the seventh report from the committee to estimate the Biological Effect of Ionizing Radiation (BEIR VII, which estimated that most contemporary exposures- protracted or low-dose, carry 1.5 fold less risk of carcinogenesis and mortality per Gy than acute exposures of atomic bomb survivors. This correction is known as the dose and dose rate effectiveness factor for the life span study of atomic bomb survivors (DDREFLSS. It was calculated by applying a linear-quadratic dose response model to data from Japanese atomic bomb survivors and a limited number of animal studies.We argue that the linear-quadratic model does not provide appropriate support to estimate the risk of contemporary exposures. In this work, we re-estimated DDREFLSS using 15 animal studies that were not included in BEIR VII's original analysis. Acute exposure data led to a DDREFLSS estimate from 0.9 to 3.0. By contrast, data that included both acute and protracted exposures led to a DDREFLSS estimate from 4.8 to infinity. These two estimates are significantly different, violating the assumptions of the linear-quadratic model, which predicts that DDREFLSS values calculated in either way should be the same.Therefore, we propose that future estimates of the risk of protracted exposures should be based on direct comparisons of data from acute and protracted exposures, rather than from extrapolations from a linear-quadratic model. The risk of low dose exposures may be extrapolated from these protracted estimates, though we encourage ongoing debate as to whether this is the most valid approach. We also encourage efforts to enlarge the datasets used to estimate the risk of protracted exposures by including both human and animal data, carcinogenesis outcomes, a wider range of exposures, and by making more radiobiology data publicly accessible. We believe that these steps will contribute to better estimates
Comments on a time-dependent version of the linear-quadratic model
International Nuclear Information System (INIS)
Tucker, S.L.; Travis, E.L.
1990-01-01
The accuracy and interpretation of the 'LQ + time' model are discussed. Evidence is presented, based on data in the literature, that this model does not accurately describe the changes in isoeffect dose occurring with protraction of the overall treatment time during fractionated irradiation of the lung. This lack of fit of the model explains, in part, the surprisingly large values of γ/α that have been derived from experimental lung data. The large apparent time factors for lung suggested by the model are also partly explained by the fact that γT/α, despite having units of dose, actually measures the influence of treatment time on the effect scale, not the dose scale, and is shown to consistently overestimate the change in total dose. The unusually high values of α/β that have been derived for lung using the model are shown to be influenced by the method by which the model was fitted to data. Reanalyses of the data using a more statistically valid regression procedure produce estimates of α/β more typical of those usually cited for lung. Most importantly, published isoeffect data from lung indicate that the true deviation from the linear-quadratic (LQ) model is nonlinear in time, instead of linear, and also depends on other factors such as the effect level and the size of dose per fraction. Thus, the authors do not advocate the use of the 'LQ + time' expression as a general isoeffect model. (author). 32 refs.; 3 figs.; 1 tab
Energy Technology Data Exchange (ETDEWEB)
Huhta, A.P.; Korpela, L. [Finnish Forest Research Institute, Helsinki (Finland)
2006-05-15
This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m{sup 2}), each containing eight quadrats (a 1m{sup 2}), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)
International Nuclear Information System (INIS)
Huhta, A.P.; Korpela, L.
2006-05-01
This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m 2 ), each containing eight quadrats (a 1m 2 ), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)
Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu
2017-06-21
For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.
Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras
Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal
2017-03-01
Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.
International Nuclear Information System (INIS)
Dakaloyannis, C.
2006-01-01
Full text: (author)The two dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar as the classical ones multiplied by a quantum coefficient -n 2 plus a quantum deformation of order n 4 and n 6 . The systems inside the classes are transformed using Stackel transforms in the quantum case as in the classical case and general form is discussed. The idea of the Jacobi Hamiltonian corresponding to the Jacobi metric in the classical case is discussed