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

Staff turnover in hotels : exploring the quadratic and linear relationships.

OpenAIRE

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....

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

Science.gov (United States)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Robust optimal control design using a differential game approach for open-loop linear quadratic descriptor systems

NARCIS (Netherlands)

Musthofa, M.W.; Salmah, S.; Engwerda, Jacob; Suparwanto, A.

This paper studies the robust optimal control problem for descriptor systems. We applied differential game theory to solve the disturbance attenuation problem. The robust control problem was converted into a reduced ordinary zero-sum game. Within a linear quadratic setting, we solved the problem for

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems

NARCIS (Netherlands)

Opmeer, MR; Curtain, RF

2004-01-01

In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show

Genetic algorithm–based varying parameter linear quadratic regulator control for four-wheel independent steering vehicle

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.

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)

Design of Linear-Quadratic-Regulator for a CSTR process

Science.gov (United States)

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.

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

Directory of Open Access Journals (Sweden)

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

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 ...

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

linear-quadratic-linear model

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.

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.

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

Science.gov (United States)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Pareto optimality in infinite horizon linear quadratic differential games

NARCIS (Netherlands)

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

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.)

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

Science.gov (United States)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Bowman, David N. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Asher, Jason C. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Fischer, Sean A. [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA; Cramer, Christopher J. [Department of Chemistry; Supercomputing Institute and Chemical Theory Center; University of Minnesota; Minneapolis; USA; Govind, Niranjan [William R. Wiley Environmental Molecular Sciences Laboratory; Pacific Northwest National Laboratory; P.O. Box 999; Richland; USA

2017-01-01

Threemeso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

Science.gov (United States)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

Science.gov (United States)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

On the equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory

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

Feedback nash equilibria for linear quadratic descriptor differential games

NARCIS (Netherlands)

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

Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

NARCIS (Netherlands)

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

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.

Gain scheduled linear quadratic control for quadcopter

Science.gov (United States)

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.

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)

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.

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.

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....

Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

International Nuclear Information System (INIS)

Rekab, S.; Zenine, N.

2006-01-01

We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

Mixmaster cosmological model in theories of gravity with a quadratic Lagrangian

International Nuclear Information System (INIS)

Barrow, J.D.; Sirousse-Zia, H.

1989-01-01

We use the method of matched asymptotic expansions to examine the behavior of the vacuum Bianchi type-IX mixmaster universe in a gravity theory derived from a purely quadratic gravitational Lagrangian. The chaotic behavior characteristic of the general-relativistic mixmaster model disappears and the asymptotic behavior is of the monotonic, nonchaotic form found in the exactly soluble Bianchi type-I models of the quadratic theory. The asymptotic behavior far from the singularity is also found to be of monotonic nonchaotic type

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

A Fast Condensing Method for Solution of Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...

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...

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

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....

The bounds of feasible space on constrained nonconvex quadratic programming

Science.gov (United States)

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.

Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

OpenAIRE

Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

2015-01-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which imple...

TUNING PARAMETER LINEAR QUADRATIC TRACKING MENGGUNAKAN ALGORITMA GENETIKA UNTUK PENGENDALIAN GERAK LATERAL QUADCOPTER

Directory of Open Access Journals (Sweden)

Farid Choirul Akbar

2016-04-01

Full Text Available Gerakan lateral quadcopter dapat dilakukan apabila quadcopter dapat menjaga kestabilan pada saat hover, sehingga quadcopter dapat melakukan gerak rotasi. Perubahan sudut roll akan mengakibatkan gerak translasi pada sumbu Y, sedangkan perubahan sudut pitch akan mengakibatkan gerak translasi pada sumbu X. Disisi lain, quadcopter merupakan suatu sistem non-linear dan memiliki kestabilan yang rendah sehingga rentan terhadap gangguan. Pada penelitian Tugas Akhir ini dirancang pengendalian gerak rotasi quadcopter menggunakan Linear Quadratic Regulator (LQR dan Linear Quadratic Tracking (LQT untuk pengendalian gerak translasi. Untuk mendapatkan parameter dari LQT digunakan Algoritma Genetika (GA. Hasil tuning GA yang digunakan pada LQT memiliki nilai Qx 700,1884, nilai Qy 700,6315, nilai Rx 0,1568, dan  nilai Ry 0,1579. Respon LQT tersebut memiliki RMSE pada sumbu X dan sumbu Y sebesar 1,99 % serta memiliki time lagging 0,35 detik. Dengan hasil tersebut quadcopter mampu men-tracking trajectory berbentuk segitigaTekni

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.).

Geometric Methods in the Algebraic Theory of Quadratic Forms : Summer School

CERN Document Server

2004-01-01

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes - an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions; - papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension; - a contribution in French by Bruno Kahn which lays out a general fra...

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 time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

Science.gov (United States)

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.

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....

Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

Science.gov (United States)

Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

2016-02-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Linear and quadratic exponential modulation of the solutions of the paraxial wave equation

International Nuclear Information System (INIS)

Torre, A

2010-01-01

A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes

Aspects of Quadratic Gravity

CERN Document Server

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-...

A linear-quadratic model of cell survival considering both sublethal and potentially lethal radiation damage

International Nuclear Information System (INIS)

Rutz, H.P.; Coucke, P.A.; Mirimanoff, R.O.

1991-01-01

The authors assessed the dose-dependence of repair of potentially lethal damage in Chinese hamster ovary cells x-irradiated in vitro. The recovery ratio (RR) by which survival (SF) of the irradiated cells was enhanced increased exponentially with a linear and a quadratic component namely ζ and ψ: RR=exp(ζD+ψD 2 ). Survival of irradiated cells can thus be expressed by a combined linear-quadratic model considering 4 variables, namely α and β for the capacity of the cells to accumulate sublethal damage, and ζ and ψ for their capacity to repair potentially lethal damage: SF=exp((ζ-α)D+ (ψ-β)D 2 ). author. 26 refs.; 1 fig.; 1 tab

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

On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory

OpenAIRE

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...

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

Optimal Quadratic Programming Algorithms

CERN Document Server

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

Quadratic Plus Linear Operators which Preserve Pure States of Quantum Systems: Small Dimensions

International Nuclear Information System (INIS)

Saburov, Mansoor

2014-01-01

A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system

Gain-scheduled Linear Quadratic Control of Wind Turbines Operating at High Wind Speed

DEFF Research Database (Denmark)

Østergaard, Kasper Zinck; Stoustrup, Jakob; Brath, Per

2007-01-01

This paper addresses state estimation and linear quadratic (LQ) control of variable speed variable pitch wind turbines. On the basis of a nonlinear model of a wind turbine, a set of operating conditions is identified and a LQ controller is designed for each operating point. The controller gains...... are then interpolated linearly to get a control law for the entire operating envelope. A nonlinear state estimator is designed as a combination of two unscented Kalman filters and a linear disturbance estimator. The gain-scheduling variable (wind speed) is then calculated from the output of these state estimators...

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Analysis of a monetary union enlargement in the framework of linear-quadratic differential games

NARCIS (Netherlands)

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,

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

CERN Document Server

Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

2017-01-01

This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

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.

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

Science.gov (United States)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

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 application of nonlinear programming to the design of regulators of a linear-quadratic formulation

Science.gov (United States)

Fleming, P.

1983-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

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

Linear quadratic Gaussian controller design for plasma current, position and shape control system in ITER

International Nuclear Information System (INIS)

Belyakov, V.; Kavin, A.; Rumyantsev, E.; Kharitonov, V.; Misenov, B.; Ovsyannikov, A.; Ovsyannikov, D.; Veremei, E.; Zhabko, A.; Mitrishkin, Y.

1999-01-01

This paper is focused on the linear quadratic Gaussian (LQG) controller synthesis methodology for the ITER plasma current, position and shape control system as well as power derivative management system. It has been shown that some poloidal field (PF) coils have less influence on reference plasma-wall gaps control during plasma disturbances and hence they have been used to reduce total control power derivative by means of the additional non-linear feedback. The design has been done on the basis of linear models. Simulation was provided for non-linear model and results are presented and discussed. (orig.)

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)

Quadratic residues and non-residues selected topics

CERN Document Server

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.

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

International Nuclear Information System (INIS)

Aristov, Anatoly I

2011-01-01

We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

Science.gov (United States)

Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

2009-01-01

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

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

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.

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)

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.

Self-Tuning Linear Quadratic Supervisory Regulation of a Diesel Generator using Large-Signal State Estimation

DEFF Research Database (Denmark)

Knudsen, Jesper Viese; Bendtsen, Jan Dimon; Andersen, Palle

2016-01-01

In this paper, a self-tuning linear quadratic supervisory regulator using a large-signal state estimator for a diesel driven generator set is proposed. The regulator improves operational efficiency, in comparison to current implementations, by (i) automating the initial tuning process and (ii...... throughout the operating range of the diesel generator....

Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...

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...

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.

Learning quadratic receptive fields from neural responses to natural stimuli.

Science.gov (United States)

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.

Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

Science.gov (United States)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2017-10-01

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.

Inelastic scattering in a local polaron model with quadratic coupling to bosons

DEFF Research Database (Denmark)

Olsen, Thomas

2009-01-01

We calculate the inelastic scattering probabilities in the wide band limit of a local polaron model with quadratic coupling to bosons. The central object is a two-particle Green's function which is calculated exactly using a purely algebraic approach. Compared with the usual linear interaction term...... a quadratic interaction term gives higher probabilities for inelastic scattering involving a large number of bosons. As an application we consider the problem hot-electron-mediated energy transfer at surfaces and use the delta self-consistent field extension of density-functional theory to calculate...

Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

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.

The Increase in Animal Mortality Risk following Exposure to Sparsely Ionizing Radiation Is Not Linear Quadratic with Dose.

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

Faithfully quadratic rings

CERN Document Server

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

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

Science.gov (United States)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Field equations of the gauge theory of gravitation originate from a quadratic Lagrangian with torsion

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)

Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F{sub N} method

Energy Technology Data Exchange (ETDEWEB)

Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

2017-11-15

One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

Science.gov (United States)

Kendal, W S

2000-04-01

To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

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)

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.

A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

NARCIS (Netherlands)

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

Management of linear quadratic regulator optimal control with full-vehicle control case study

Directory of Open Access Journals (Sweden)

Rodrigue Tchamna

2016-09-01

Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.

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

Students' Understanding of Quadratic Equations

Science.gov (United States)

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…

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

Science.gov (United States)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

A statistical theory of cell killing by radiation of varying linear energy transfer

International Nuclear Information System (INIS)

Hawkins, R.B.

1994-01-01

A theory is presented that provides an explanation for the observed features of the survival of cultured cells after exposure to densely ionizing high-linear energy transfer (LET) radiation. It starts from a phenomenological postulate based on the linear-quadratic form of cell survival observed for low-LET radiation and uses principles of statistics and fluctuation theory to demonstrate that the effect of varying LET on cell survival can be attributed to random variation of dose to small volumes contained within the nucleus. A simple relation is presented for surviving fraction of cells after exposure to radiation of varying LET that depends on the α and β parameters for the same cells in the limit of low-LET radiation. This relation implies that the value of β is independent of LET. Agreement of the theory with selected observations of cell survival from the literature is demonstrated. A relation is presented that gives relative biological effectiveness (RBE) as a function of the α and β parameters for low-LET radiation. Measurements from microdosimetry are used to estimate the size of the subnuclear volume to which the fluctuation pertains. 11 refs., 4 figs., 2 tabs

On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model

International Nuclear Information System (INIS)

Unkel, Steffen; Belka, Claus; Lauber, Kirsten

2016-01-01

The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed

Linear versus quadratic portfolio optimization model with transaction cost

Science.gov (United States)

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.

Quadratic Diophantine equations

CERN Document Server

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.

Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources

International Nuclear Information System (INIS)

Guerrero, Mariana; Carlone, Marco

2010-01-01

Purpose: In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. Methods: The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. Results: In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter β. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusions: The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

Basic concepts of control theory

International Nuclear Information System (INIS)

Markus, L.

1976-01-01

After a philosophical introduction on control theory and its position among various branches of science, mathematical control theory and its connection with functional analysis are discussed. A chapter on system theory concepts follows. After a summary of results and notations in the general theory of ordinary differential equations, a qualitative theory of control dynamical systems and chapters on the topological dynamics, and the controllability of linear systems are presented. As examples of autonomous linear systems, the switching locus for the synthesis of optimal controllers and linear dynamics with quadratic cost optimization are considered. (author)

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

Trends in modern system theory

Science.gov (United States)

Athans, M.

1976-01-01

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

The Theory of Linear Prediction

CERN Document Server

Vaidyanathan, PP

2007-01-01

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vecto

Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints

International Nuclear Information System (INIS)

Zhang Yunong; Li Zhan

2009-01-01

In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

Linear algebra

CERN Document Server

Shilov, Georgi E

1977-01-01

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Diagonalizing quadratic bosonic operators by non-autonomous flow equations

CERN Document Server

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.

Linear contextual modal type theory

DEFF Research Database (Denmark)

Schack-Nielsen, Anders; Schürmann, Carsten

Abstract. When one implements a logical framework based on linear type theory, for example the Celf system [?], one is immediately con- fronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives...... a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. Our main contributions include a mechanically checked proof of soundness and a working implementation....

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.

Employing Theories Far beyond Their Limits - Linear Dichroism Theory.

Science.gov (United States)

Mayerhöfer, Thomas G

2018-05-15

Using linear polarized light, it is possible in case of ordered structures, such as stretched polymers or single crystals, to determine the orientation of the transition moments of electronic and vibrational transitions. This not only helps to resolve overlapping bands, but also assigning the symmetry species of the transitions and to elucidate the structure. To perform spectral evaluation quantitatively, a sometimes "Linear Dichroism Theory" called approach is very often used. This approach links the relative orientation of the transition moment and polarization direction to the quantity absorbance. This linkage is highly questionable for several reasons. First of all, absorbance is a quantity that is by its definition not compatible with Maxwell's equations. Furthermore, absorbance seems not to be the quantity which is generally compatible with linear dichroism theory. In addition, linear dichroism theory disregards that it is not only the angle between transition moment and polarization direction, but also the angle between sample surface and transition moment, that influences band shape and intensity. Accordingly, the often invoked "magic angle" has never existed and the orientation distribution influences spectra to a much higher degree than if linear dichroism theory would hold strictly. A last point that is completely ignored by linear dichroism theory is the fact that partially oriented or randomly-oriented samples usually consist of ordered domains. It is their size relative to the wavelength of light that can also greatly influence a spectrum. All these findings can help to elucidate orientation to a much higher degree by optical methods than currently thought possible by the users of linear dichroism theory. Hence, it is the goal of this contribution to point out these shortcomings of linear dichroism theory to its users to stimulate efforts to overcome the long-lasting stagnation of this important field. © 2018 Wiley-VCH Verlag GmbH & Co. KGa

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....

Finite-Time H∞ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations

Directory of Open Access Journals (Sweden)

Huihong Zhao

2012-01-01

Full Text Available This paper is concerned with the finite-time H∞ filtering problem for linear continuous time-varying systems with uncertain observations and ℒ2-norm bounded noise. The design of finite-time H∞ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time H∞ filtering problem is solved. A numerical example is given to illustrate the performance of the H∞ filter.

Periodic feedback stabilization for linear periodic evolution equations

CERN Document Server

Wang, Gengsheng

2016-01-01

This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

Half-space albedo problem with modified F{sub N} method for linear and quadratic anisotropic scattering

Energy Technology Data Exchange (ETDEWEB)

Tuereci, R.G. [Kirikkale Univ., Kirikkale (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

2017-05-15

One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F{sub N} method.

Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model

OpenAIRE

José Guilherme Couto; Isabel Bravo; Rui Pirraco

2011-01-01

Purpose The purpose of this work was the biological comparison between Low Dose Rate (LDR) and Pulsed Dose Rate (PDR) in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments at our Institution since December 2009. Material and methods In the first phase we studied the influence of the pulse dose and the pulse time in the biological equivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM). In the second phase, the equival...

A computer tool for daily application of the linear quadratic model

International Nuclear Information System (INIS)

Macias Jaen, J.; Galan Montenegro, P.; Bodineau Gil, C.; Wals Zurita, A.; Serradilla Gil, A.M.

2001-01-01

The aim of this paper is to indicate the relevance of the criteria A.S.A.R.A. (As Short As Reasonably Achievable) in the optimization of a fractionated radiotherapy schedule and the presentation of a Windows computer program as an easy tool in order to: Evaluate the Biological Equivalent Dose (BED) in a fractionated schedule; Make comparison between different treatments; Compensate a treatment when a delay has been happened with a version of the Linear Quadratic model that has into account the factor of accelerated repopulation. Conclusions: Delays in the normal radiotherapy schedule are items that have to be controlled as much as possible because it is able to be a very important parameter in order to release a good application of treatment, principally when the tumour is fast growing. It is necessary to evaluate them. ASARA criteria is useful to indicate the relevance of this aspect. Also, computer tools like this one could help us in order to achieve this. (author)

Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....

Rainfall induced landslide susceptibility mapping using weight-of-evidence, linear and quadratic discriminant and logistic model tree method

Science.gov (United States)

Hong, H.; Zhu, A. X.

2017-12-01

Climate change is a common phenomenon and it is very serious all over the world. The intensification of rainfall extremes with climate change is of key importance to society and then it may induce a large impact through landslides. This paper presents GIS-based new ensemble data mining techniques that weight-of-evidence, logistic model tree, linear and quadratic discriminant for landslide spatial modelling. This research was applied in Anfu County, which is a landslide-prone area in Jiangxi Province, China. According to a literature review and research the study area, we select the landslide influencing factor and their maps were digitized in a GIS environment. These landslide influencing factors are the altitude, plan curvature, profile curvature, slope degree, slope aspect, topographic wetness index (TWI), Stream Power Index (SPI), Topographic Wetness Index (SPI), distance to faults, distance to rivers, distance to roads, soil, lithology, normalized difference vegetation index and land use. According to historical information of individual landslide events, interpretation of the aerial photographs, and field surveys supported by the government of Jiangxi Meteorological Bureau of China, 367 landslides were identified in the study area. The landslide locations were divided into two subsets, namely, training and validating (70/30), based on a random selection scheme. In this research, Pearson's correlation was used for the evaluation of the relationship between the landslides and influencing factors. In the next step, three data mining techniques combined with the weight-of-evidence, logistic model tree, linear and quadratic discriminant, were used for the landslide spatial modelling and its zonation. Finally, the landslide susceptibility maps produced by the mentioned models were evaluated by the ROC curve. The results showed that the area under the curve (AUC) of all of the models was > 0.80. At the same time, the highest AUC value was for the linear and quadratic

The quadratic reciprocity law a collection of classical proofs

CERN Document Server

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 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.)

Non-linear variation of the beta function with momentum

International Nuclear Information System (INIS)

Parzen, G.

1983-07-01

A theory is presented for computing the non-linear dependence of the β-functions on momentum. Results are found for the quadratic term. The results of the theory are compared with computed results. A procedure is proposed for computing the strengths of the sextupole correctors to correct the dependence of the β-function on momentum

Overlapping quadratic optimal control of linear time-varying commutative systems

Czech Academy of Sciences Publication Activity Database

Bakule, Lubomír; Rodellar, J.; Rossell, J. M.

2002-01-01

Roč. 40, č. 5 (2002), s. 1611-1627 ISSN 0363-0129 R&D Projects: GA AV ČR IAA2075802 Institutional research plan: CEZ:AV0Z1075907 Keywords : overlapping * optimal control * linear time-varying systems Subject RIV: BC - Control Systems Theory Impact factor: 1.441, year: 2002

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

Science.gov (United States)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

A new formalism for modelling parameters α and β of the linear-quadratic model of cell survival for hadron therapy

Science.gov (United States)

Vassiliev, Oleg N.; Grosshans, David R.; Mohan, Radhe

2017-10-01

We propose a new formalism for calculating parameters α and β of the linear-quadratic model of cell survival. This formalism, primarily intended for calculating relative biological effectiveness (RBE) for treatment planning in hadron therapy, is based on a recently proposed microdosimetric revision of the single-target multi-hit model. The main advantage of our formalism is that it reliably produces α and β that have correct general properties with respect to their dependence on physical properties of the beam, including the asymptotic behavior for very low and high linear energy transfer (LET) beams. For example, in the case of monoenergetic beams, our formalism predicts that, as a function of LET, (a) α has a maximum and (b) the α/β ratio increases monotonically with increasing LET. No prior models reviewed in this study predict both properties (a) and (b) correctly, and therefore, these prior models are valid only within a limited LET range. We first present our formalism in a general form, for polyenergetic beams. A significant new result in this general case is that parameter β is represented as an average over the joint distribution of energies E 1 and E 2 of two particles in the beam. This result is consistent with the role of the quadratic term in the linear-quadratic model. It accounts for the two-track mechanism of cell kill, in which two particles, one after another, damage the same site in the cell nucleus. We then present simplified versions of the formalism, and discuss predicted properties of α and β. Finally, to demonstrate consistency of our formalism with experimental data, we apply it to fit two sets of experimental data: (1) α for heavy ions, covering a broad range of LETs, and (2) β for protons. In both cases, good agreement is achieved.

Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control

Science.gov (United States)

Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

1997-01-01

One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

Introduction to optimal control theory

International Nuclear Information System (INIS)

Agrachev, A.A.

2002-01-01

These are lecture notes of the introductory course in Optimal Control theory treated from the geometric point of view. Optimal Control Problem is reduced to the study of controls (and corresponding trajectories) leading to the boundary of attainable sets. We discuss Pontryagin Maximum Principle, basic existence results, and apply these tools to concrete simple optimal control problems. Special sections are devoted to the general theory of linear time-optimal problems and linear-quadratic problems. (author)

A Quasi-Dynamic Optimal Control Strategy for Non-Linear Multivariable Processes Based upon Non-Quadratic Objective Functions

Directory of Open Access Journals (Sweden)

Jens G. Balchen

1984-10-01

Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.

Linear system theory

Science.gov (United States)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Optimal Operation of Distribution Electronic Power Transformer Using Linear Quadratic Regulator Method

Directory of Open Access Journals (Sweden)

Mohammad Hosein Rezaei

2011-10-01

Full Text Available Transformers perform many functions such as voltage transformation, isolation and noise decoupling. They are indispensable components in electric power distribution system. However, at low frequencies (50 Hz, they are one of the heaviest and the most expensive equipment in an electrical distribution system. Nowadays, electronic power transformers are used instead of conventional power transformers that do voltage transformation and power delivery in power system by power electronic converter. In this paper, the structure of distribution electronic power transformer (DEPT are analized and then paid attention on the design of a linear-quadratic-regulator (LQR with integral action to improve dynamic performance of DEPT with voltage unbalance, voltage sags, voltage harmonics and voltage flicker. The presentation control strategy is simulated by MATLAB/SIMULINK. In addition, the results that are in terms of dc-link reference voltage, input and output voltages clearly show that a better dynamic performance can be achieved by using the LQR method when compared to other techniques.

The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator

Science.gov (United States)

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1985-01-01

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

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)

Black holes in higher dimensional gravity theory with corrections quadratic in curvature

International Nuclear Information System (INIS)

Frolov, Valeri P.; Shapiro, Ilya L.

2009-01-01

Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form C 2 =C αβγδ C αβγδ . The Gauss-Bonnet equation in four-dimensional spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar C 2 correction. An important new feature of the spaces with dimension D>4 is that in the presence of the Weyl curvature-squared term a necessary solution differs from the corresponding 'classical' vacuum Tangherlini metric. This difference is related to the presence of secondary or induced hair. We explore how the Tangherlini solution is modified by 'quantum corrections', assuming that the gravitational radius r 0 is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ordinary differential equation (master equation).

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

Energy Technology Data Exchange (ETDEWEB)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)

2017-06-15

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

Linear network theory

CERN Document Server

Sander, K F

1964-01-01

Linear Network Theory covers the significant algebraic aspect of network theory, with minimal reference to practical circuits. The book begins the presentation of network analysis with the exposition of networks containing resistances only, and follows it up with a discussion of networks involving inductance and capacity by way of the differential equations. Classification and description of certain networks, equivalent networks, filter circuits, and network functions are also covered. Electrical engineers, technicians, electronics engineers, electricians, and students learning the intricacies

Linear–Quadratic Mean-Field-Type Games: A Direct Method

Directory of Open Access Journals (Sweden)

Tyrone E. Duncan

2018-02-01

Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.

Linear spaces: history and theory

OpenAIRE

Albrecht Beutelspracher

1990-01-01

Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.

Time-dependent tumour repopulation factors in linear-quadratic equations

International Nuclear Information System (INIS)

Dale, R.G.

1989-01-01

Tumour proliferation effects can be tentatively quantified in the linear-quadratic (LQ) method by the incorporation of a time-dependent factor, the magnitude of which is related both to the value of α in the tumour α/β ratio, and to the tumour doubling time. The method, the principle of which has been suggested by a numbre of other workers for use in fractionated therapy, is here applied to both fractionated and protracted radiotherapy treatments, and examples of its uses are given. By assuming that repopulation of late-responding tissues is significant during normal treatment strategies in terms of the behaviour of the Extrapolated Response Dose (ERD). Although the numerical credibility of the analysis used here depends on the reliability of the LQ model, and on the assumption that the rate of repopulation is constant throughout treatment, the predictions are consistent with other lines of reasoning which point to the advantages of accelerated hyperfractionation. In particular, it is demonstrated that accelerated fractionation represents a relatively 'foregiving' treatment which enables tumours of a variety of sensitivities and clonogenic growth rates to be treated moderately successfully, even though the critical cellular parameters may not be known in individual cases. The analysis also suggests that tumours which combine low intrinsic sensitivity with a very short doubling time might be bettter controlled by low dose-rate continuous therapy than by almost any form of accelerated hyperfractionation. (author). 24 refs.; 5 figs

A smart rotor configuration with linear quadratic control of adaptive trailing edge flaps for active load alleviation

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...

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

Theory of linear operations

CERN Document Server

Banach, S

1987-01-01

This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.

Linearization instability for generic gravity in AdS spacetime

Science.gov (United States)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

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.

Quadratic prediction of factor scores

NARCIS (Netherlands)

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

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

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

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.

Damped oscillations of linear systems a mathematical introduction

CERN Document Server

Veselić, Krešimir

2011-01-01

The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...

A Genetic-Algorithms-Based Approach for Programming Linear and Quadratic Optimization Problems with Uncertainty

Directory of Open Access Journals (Sweden)

Weihua Jin

2013-01-01

Full Text Available This paper proposes a genetic-algorithms-based approach as an all-purpose problem-solving method for operation programming problems under uncertainty. The proposed method was applied for management of a municipal solid waste treatment system. Compared to the traditional interactive binary analysis, this approach has fewer limitations and is able to reduce the complexity in solving the inexact linear programming problems and inexact quadratic programming problems. The implementation of this approach was performed using the Genetic Algorithm Solver of MATLAB (trademark of MathWorks. The paper explains the genetic-algorithms-based method and presents details on the computation procedures for each type of inexact operation programming problems. A comparison of the results generated by the proposed method based on genetic algorithms with those produced by the traditional interactive binary analysis method is also presented.

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 ...

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.)

Features and stability analysis of non-Schwarzschild black hole in quadratic gravity

International Nuclear Information System (INIS)

Cai, Yi-Fu; Zhang, Hezi; Liu, Junyu; Cheng, Gong; Wang, Min

2016-01-01

Black holes are found to exist in gravitational theories with the presence of quadratic curvature terms and behave differently from the Schwarzschild solution. We present an exhaustive analysis for determining the quasinormal modes of a test scalar field propagating in a new class of black hole backgrounds in the case of pure Einstein-Weyl gravity. Our result shows that the field decay of quasinormal modes in such a non-Schwarzschild black hole behaves similarly to the Schwarzschild one, but the decay slope becomes much smoother due to the appearance of the Weyl tensor square in the background theory. We also analyze the frequencies of the quasinormal modes in order to characterize the properties of new back holes, and thus, if these modes can be the source of gravitational waves, the underlying theories may be testable in future gravitational wave experiments. We briefly comment on the issue of quantum (in)stability in this theory at linear order.

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 ...

LQG/LTR [linear quadratic Gaussian with loop transfer recovery] robust control system design for a low-pressure feedwater heater train

International Nuclear Information System (INIS)

Murphy, G.V.; Bailey, J.M.

1990-01-01

This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs

Groups, matrices, and vector spaces a group theoretic approach to linear algebra

CERN Document Server

Carrell, James B

2017-01-01

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...

Evaluating the Wald entropy from two-derivative terms in quadratic actions

International Nuclear Information System (INIS)

Brustein, Ram; Gorbonos, Dan; Hadad, Merav; Medved, A. J. M.

2011-01-01

We evaluate the Wald Noether charge entropy for a black hole in generalized theories of gravity. Expanding the Lagrangian to second order in gravitational perturbations, we show that contributions to the entropy density originate only from the coefficients of two-derivative terms. The same considerations are extended to include matter fields and to show that arbitrary powers of matter fields and their symmetrized covariant derivatives cannot contribute to the entropy density. We also explain how to use the linearized gravitational field equation rather than quadratic actions to obtain the same results. Several explicit examples are presented that allow us to clarify subtle points in the derivation and application of our method.

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

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)

Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

International Nuclear Information System (INIS)

Kim, Jin Kyu; Kim, Dong Keon

2016-01-01

A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics

Quadratic temporal finite element method for linear elastic structural dynamics based on mixed convolved action

Energy Technology Data Exchange (ETDEWEB)

Kim, Jin Kyu [School of Architecture and Architectural Engineering, Hanyang University, Ansan (Korea, Republic of); Kim, Dong Keon [Dept. of Architectural Engineering, Dong A University, Busan (Korea, Republic of)

2016-09-15

A common approach for dynamic analysis in current practice is based on a discrete time-integration scheme. This approach can be largely attributed to the absence of a true variational framework for initial value problems. To resolve this problem, a new stationary variational principle was recently established for single-degree-of-freedom oscillating systems using mixed variables, fractional derivatives and convolutions of convolutions. In this mixed convolved action, all the governing differential equations and initial conditions are recovered from the stationarity of a single functional action. Thus, the entire description of linear elastic dynamical systems is encapsulated. For its practical application to structural dynamics, this variational formalism is systemically extended to linear elastic multidegree- of-freedom systems in this study, and a corresponding weak form is numerically implemented via a quadratic temporal finite element method. The developed numerical method is symplectic and unconditionally stable with respect to a time step for the underlying conservative system. For the forced-damped vibration, a three-story shear building is used as an example to investigate the performance of the developed numerical method, which provides accurate results with good convergence characteristics.

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

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

Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

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

Algebraic Theory of Linear Viscoelastic Nematodynamics

International Nuclear Information System (INIS)

Leonov, Arkady I.

2008-01-01

This paper consists of two parts. The first one develops algebraic theory of linear anisotropic nematic 'N-operators' build up on the additive group of traceless second rank 3D tensors. These operators have been implicitly used in continual theories of nematic liquid crystals and weakly elastic nematic elastomers. It is shown that there exists a non-commutative, multiplicative group N 6 of N-operators build up on a manifold in 6D space of parameters. Positive N-operators, which in physical applications hold thermodynamic stability constraints, do not generally form a subgroup of group N 6 . A three-parametric, commutative transversal-isotropic subgroup S 3 subset of N 6 of positive symmetric nematic operators is also briefly discussed. The special case of singular, non-negative symmetric N-operators reveals the algebraic structure of nematic soft deformation modes. The second part of the paper develops a theory of linear viscoelastic nematodynamics applicable to liquid crystalline polymer. The viscous and elastic nematic components in theory are described by using the Leslie-Ericksen-Parodi (LEP) approach for viscous nematics and de Gennes free energy for weakly elastic nematic elastomers. The case of applied external magnetic field exemplifies the occurrence of non-symmetric stresses. In spite of multi-(10) parametric character of the theory, the use of nematic operators presents it in a transparent form. When the magnetic field is absent, the theory is simplified for symmetric case with six parameters, and takes an extremely simple, two-parametric form for viscoelastic nematodynamics with possible soft deformation modes. It is shown that the linear nematodynamics is always reducible to the LEP-like equations where the coefficients are changed for linear memory functionals whose parameters are calculated from original viscosities and moduli

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.

Estimation of transition doses for human glioblastoma, neuroblastoma and prostate cell lines using the linear-quadratic formalism

Directory of Open Access Journals (Sweden)

John Akudugu

2015-09-01

Full Text Available Purpose: The introduction of stereotactic radiotherapy has raised concerns regarding the use of the linear-quadratic (LQ model for predicting radiation response for large fractional doses. To partly address this issue, a transition dose D* below which the LQ model retains its predictive strength has been proposed. Estimates of D* which depends on the a, β, and D0 parameters are much lower than fractional doses typically encountered in stereotactic radiotherapy. D0, often referred to as the final slope of the cell survival curve, is thought to be constant. In vitro cell survival curves generally extend over the first few logs of cell killing, where D0-values derived from the multi-target formalism may be overestimated and can lead to low transition doses. Methods:  D0-values were calculated from first principles for each decade of cell killing, using experimentally-determined a and β parameters for 17 human glioblastoma, neuroblastoma, and prostate cell lines, and corresponding transition doses were derived.Results: D0 was found to decrease exponentially with cell killing. Using D0-values at cell surviving fractions of the order of 10-10 yielded transition doses ~3-fold higher than those obtained from D0-values obtained from conventional approaches. D* was found to increase from 7.84 ± 0.56, 8.91 ± 1.20, and 6.55 ± 0.91 Gy to 26.84 ± 2.83, 23.95 ± 2.03, and 22.49 ± 2.31 Gy for the glioblastoma, neuroblastoma, and prostate cell lines, respectively. Conclusion: These findings suggest that the linear-quadratic formalism might be valid for estimating the effect of stereotactic radiotherapy with fractional doses in excess of 20 Gy.

Operator approach to linear control systems

CERN Document Server

Cheremensky, A

1996-01-01

Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.

Frequency of micronuclei in hepatocytes following X and fast-neutron irradiations--an analysis by a linear-quadratic model

International Nuclear Information System (INIS)

Ono, K.; Nagata, Y.; Akuta, K.; Abe, M.; Ando, K.; Koike, S.

1990-01-01

The usefulness of the micronucleus assay for investigating the radiation response of hepatocytes was examined. The frequency was defined as the ratio of the total number of micronuclei to the number of hepatocytes examined. The dose-response curves were curvilinear after X rays and linear after neutrons. These dose-response curves were analyzed by a linear-quadratic model, frequency = aD + bD2 + c. The a/b ratio was 3.03 +/- 1.26 Gy following X irradiation. This value is within the range of the alpha/beta ratios reported by others using the clonogenic assay of hepatocytes. While the a/b value for neutrons was 24.3 +/- 11.7 Gy, the maximum relative biological effectiveness of neutrons was 6.30 +/- 2.53. Since the micronucleus assay is simple and rapid, it may be a good tool for evaluating the radiation response of hepatocytes in vivo

Canonical perturbation theory in linearized general relativity theory

International Nuclear Information System (INIS)

Gonzales, R.; Pavlenko, Yu.G.

1986-01-01

Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Linear radial pulsation theory. Lecture 5

International Nuclear Information System (INIS)

Cox, A.N.

1983-01-01

We describe a method for getting an equilibrium stellar envelope model using as input the total mass, the envelope mass, the surface effective temperature, the total surface luminosity, and the composition of the envelope. Then wih the structure of the envelope model known, we present a method for obtaining the raidal pulsation periods and growth rates for low order modes. The large amplitude pulsations observed for the yellow and red giants and supergiants are always these radial models, but for the stars nearer the main sequence, as for all of our stars and for the white dwarfs, there frequently are nonradial modes occuring also. Application of linear theory radial pulsation theory is made to the giant star sigma Scuti variables, while the linear nonradial theory will be used for the B stars in later lectures

Problems of linear electron (polaron) transport theory in semiconductors

CERN Document Server

Klinger, M I

1979-01-01

Problems of Linear Electron (Polaron) Transport Theory in Semiconductors summarizes and discusses the development of areas in electron transport theory in semiconductors, with emphasis on the fundamental aspects of the theory and the essential physical nature of the transport processes. The book is organized into three parts. Part I focuses on some general topics in the theory of transport phenomena: the general dynamical theory of linear transport in dissipative systems (Kubo formulae) and the phenomenological theory. Part II deals with the theory of polaron transport in a crystalline semicon

Quaternion orders, quadratic forms, and Shimura curves

CERN Document Server

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...

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

Energy Technology Data Exchange (ETDEWEB)

Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)

2016-12-15

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

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

Game Theory and its Relationship with Linear Programming Models ...

African Journals Online (AJOL)

Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.

Application of Linear Quadratic Gaussian and Coefficient Diagram Techniques to Distributed Load Frequency Control of Power Systems

Directory of Open Access Journals (Sweden)

Tarek Hassan Mohamed

2015-12-01

Full Text Available This paper presented both the linear quadratic Gaussian technique (LQG and the coefficient diagram method (CDM as load frequency controllers in a multi-area power system to deal with the problem of variations in system parameters and load demand change. The full states of the system including the area frequency deviation have been estimated using the Kalman filter technique. The efficiency of the proposed control method has been checked using a digital simulation. Simulation results indicated that, with the proposed CDM + LQG technique, the system is robust in the face of parameter uncertainties and load disturbances. A comparison between the proposed technique and other schemes is carried out, confirming the superiority of the proposed CDM + LQG technique.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

Directory of Open Access Journals (Sweden)

Xiangrong Li

Full Text Available It is generally acknowledged that the conjugate gradient (CG method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

Science.gov (United States)

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

An enstrophy-based linear and nonlinear receptivity theory

Science.gov (United States)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Hidden conic quadratic representation of some nonconvex quadratic optimization problems

NARCIS (Netherlands)

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

Fluctuations around classical solutions for gauge theories in Lagrangian and Hamiltonian approach

International Nuclear Information System (INIS)

Miskovic, Olivera; Pons, Josep M

2006-01-01

We analyse the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by a quadratic Lagrangian, has the same constraint structure and number of physical degrees of freedom as the original non-perturbed theory, assuming the non-degenerate solution has been chosen. We show that the number of Noether gauge symmetries is the same in both theories, but that the gauge algebra in the fluctuations theory becomes Abelianized. We also show that the fluctuations theory inherits all functionally independent rigid symmetries from the original theory and that these symmetries are generated by linear or quadratic generators according to whether the original symmetry is preserved by the background or is broken by it. We illustrate these results with examples

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning

2014-03-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian

2014-01-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Solving symmetric-definite quadratic lambda-matrix problems without factorization

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1982-01-01

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization

National Research Council Canada - National Science Library

Dennis, John E; El-Alem, Mahmoud; Maciel, Maria C

1995-01-01

.... The normal Component need not be computed accurately. The theory requires a quasi-normal component to satisfy a fraction of Cauchy decrease condition on the quadratic model of the linearized constraints...

(Non-)decoupled supersymmetric field theories

International Nuclear Information System (INIS)

Pietro, Lorenzo Di; Dine, Michael; Komargodski, Zohar

2014-01-01

We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS 4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)

Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

Science.gov (United States)

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.

Scattering theory of the linear Boltzmann operator

International Nuclear Information System (INIS)

Hejtmanek, J.

1975-01-01

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

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)

Linear response theory for quantum open systems

OpenAIRE

Wei, J. H.; Yan, YiJing

2011-01-01

Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

Biologically effective dose distribution based on the linear quadratic model and its clinical relevance

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

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

Science.gov (United States)

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.

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

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

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Introduction to the theory of nonlinear optimization

CERN Document Server

Jahn, Johannes

2007-01-01

This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

Science.gov (United States)

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.

Self-Replicating Quadratics

Science.gov (United States)

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…

Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian

International Nuclear Information System (INIS)

Bel, L.; Zia, H.S.

1985-01-01

We consider those relativistic theories of gravitation which generalize Einstein's theory in the sense that their field equations derive from a scalar Lagrangian which, besides the matter term, contains a linear combination of the Ricci scalar, its square, and the square of the Ricci tensor. Using a generalization of a technique which has been used to deal with some dynamical systems, we regularly and covariantly reduce the corresponding fourth-order differential equations to second-order ones. We examine, in particular, at a low order of approximation, these reduced equations in cosmology, and for static and spherically symmetric interior solutions with constant density

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...

Evaluation of uneven fractionation radiotherapy of cervical lymph node-metastases by linear quadratic model

International Nuclear Information System (INIS)

Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.

1993-01-01

One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

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.

Isobio software: biological dose distribution and biological dose volume histogram from physical dose conversion using linear-quadratic-linear model.

Science.gov (United States)

Jaikuna, Tanwiwat; Khadsiri, Phatchareewan; Chawapun, Nisa; Saekho, Suwit; Tharavichitkul, Ekkasit

2017-02-01

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. 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 (EQD 2 ) was calculated using biological effective dose (BED) based on the LQL model. The software calculation and the manual calculation were compared for EQD 2 verification with pair t -test statistical analysis using IBM SPSS Statistics version 22 (64-bit). 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 D 90% , 0.56% in the bladder, 1.74% in the rectum when determined by D 2cc , and less than 1% in Pinnacle. The difference in the EQD 2 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. 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.

(Non-)decoupled supersymmetric field theories

Energy Technology Data Exchange (ETDEWEB)

Pietro, Lorenzo Di [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel); Dine, Michael [Santa Cruz Institute for Particle Physics and Department of Physics,Santa Cruz CA 95064 (United States); Komargodski, Zohar [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel)

2014-04-10

We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS{sub 4} Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

Science.gov (United States)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Methods in half-linear asymptotic theory

Directory of Open Access Journals (Sweden)

Pavel Rehak

2016-10-01

Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

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.''

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

Science.gov (United States)

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Unitarity condition in covariant quantum field theory with indefinite metric

International Nuclear Information System (INIS)

Slavnov, A.A.

1989-01-01

Conditions that ensure the existence of a unitarity S matrix acting on the subspace of states with positive norm are formulated. A study is made of BRST quantization. The only restriction on the class of theories is that the author assumes asymptotic linearization of the theory, namely, that the asymptotic dynamics is determined by a quadratic Hamiltonian. In field theory this is always the case in the framework of standard perturbation theory. However, in some models, for example, string models, and also outside the framework of perturbation theory, this condition need not be satisfied

Linear {GLP}-algebras and their elementary theories

Science.gov (United States)

Pakhomov, F. N.

2016-12-01

The polymodal provability logic {GLP} was introduced by Japaridze in 1986. It is the provability logic of certain chains of provability predicates of increasing strength. Every polymodal logic corresponds to a variety of polymodal algebras. Beklemishev and Visser asked whether the elementary theory of the free {GLP}-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable [1]. For every positive integer n we solve the corresponding question for the logics {GLP}_n that are the fragments of {GLP} with n modalities. We prove that the elementary theory of the free {GLP}_n-algebra generated by the constants \\mathbf{0}, \\mathbf{1} is decidable for all n. We introduce the notion of a linear {GLP}_n-algebra and prove that all free {GLP}_n-algebras generated by the constants \\mathbf{0}, \\mathbf{1} are linear. We also consider the more general case of the logics {GLP}_α whose modalities are indexed by the elements of a linearly ordered set α: we define the notion of a linear algebra and prove the latter result in this case.

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

Alternative theories of the non-linear negative mass instability

International Nuclear Information System (INIS)

Channell, P.J.

1974-01-01

A theory non-linear negative mass instability is extended to include resistance. The basic assumption is explained physically and an alternative theory is offered. The two theories are compared computationally. 7 refs., 8 figs

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

Quadratic Damping

Science.gov (United States)

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…

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)

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)

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

Science.gov (United States)

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

Bayes linear statistics, theory & methods

CERN Document Server

Goldstein, Michael

2007-01-01

Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...

Graph-based linear scaling electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.; Swart, Pieter J.; Germann, Timothy C.; Bock, Nicolas [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mniszewski, Susan M.; Mohd-Yusof, Jamal; Wall, Michael E.; Djidjev, Hristo [Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Rubensson, Emanuel H. [Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala (Sweden)

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Linear circuits, systems and signal processing: theory and application

International Nuclear Information System (INIS)

Byrnes, C.I.; Saeks, R.E.; Martin, C.F.

1988-01-01

In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

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.

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

On two-primary algebraic K-theory of quadratic number rings with focus on K_2

NARCIS (Netherlands)

Crainic, M.; Østvær, Paul Arne

1999-01-01

We give explicit formulas for the 2-rank of the algebraic K-groups of quadratic number rings. A 4-rank formula for K2 of quadratic number rings given in [1] provides further information about the actual group structure. The K2 claculations are based on 2- and 4-rank formulas for Picard groups of

Linear algebra and group theory for physicists

CERN Document Server

Rao, K N Srinivasa

2006-01-01

Professor Srinivasa Rao's text on Linear Algebra and Group Theory is directed to undergraduate and graduate students who wish to acquire a solid theoretical foundation in these mathematical topics which find extensive use in physics. Based on courses delivered during Professor Srinivasa Rao's long career at the University of Mysore, this text is remarkable for its clear exposition of the subject. Advanced students will find a range of topics such as the Representation theory of Linear Associative Algebras, a complete analysis of Dirac and Kemmer algebras, Representations of the Symmetric group via Young Tableaux, a systematic derivation of the Crystallographic point groups, a comprehensive and unified discussion of the Rotation and Lorentz groups and their representations, and an introduction to Dynkin diagrams in the classification of Lie groups. In addition, the first few chapters on Elementary Group Theory and Vector Spaces also provide useful instructional material even at an introductory level. An author...

A local homology theory for linearly compact modules

International Nuclear Information System (INIS)

Nguyen Tu Cuong; Tran Tuan Nam

2004-11-01

We introduce a local homology theory for linearly modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties of local homology modules are shown such as: the vanishing and non-vanishing, the noetherianness of local homology modules. By using duality, we extend some well-known results in theory of local cohomology of A. Grothendieck. (author)

Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation

International Nuclear Information System (INIS)

Baker, C.M.J.; Buchan, A.G.; Pain, C.C.; Tollit, B.; Eaton, M.D.; Warner, P.

2012-01-01

This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution’s coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution’s convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.

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)

Study on TVD parameters sensitivity of a crankshaft using multiple scale and state space method considering quadratic and cubic non-linearities

Directory of Open Access Journals (Sweden)

R. Talebitooti

Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.

Coarse-graining free theories with gauge symmetries: the linearized case

International Nuclear Information System (INIS)

Bahr, Benjamin; Dittrich, Bianca; He Song

2011-01-01

Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties in both canonical and covariant quantization approaches. We discuss here the method of perfect actions, which attempts to restore gauge symmetries by mirroring exactly continuum physics on a lattice via a coarse graining process. Analytical results can only be obtained via a perturbative approach, for which we consider the first step, namely the coarse graining of the linearized theory. The linearized gauge symmetries are exact also in the discretized theory; hence, we develop a formalism to deal with gauge systems. Finally, we provide a discretization of linearized gravity as well as a coarse graining map and show that with this choice the three-dimensional (3D) linearized gravity action is invariant under coarse graining.

Three caveats for linear stability theory: Rayleigh-Benard convection

International Nuclear Information System (INIS)

Greenside, H.S.

1984-06-01

Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold

A nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term

International Nuclear Information System (INIS)

Wang, Xiao-Lu; Fan, Xiang-Yu; Nie, Ren-Shi; Huang, Quan-Hua; He, Yong-Ming

2013-01-01

Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log–log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately. (paper)

Rescuing Quadratic Inflation

CERN Document Server

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.

Combining support vector machines with linear quadratic regulator adaptation for the online design of an automotive active suspension system

International Nuclear Information System (INIS)

Chiou, J-S; Liu, M-T

2008-01-01

As a powerful machine-learning approach to pattern recognition problems, the support vector machine (SVM) is known to easily allow generalization. More importantly, it works very well in a high-dimensional feature space. This paper presents a nonlinear active suspension controller which achieves a high level performance by compensating for actuator dynamics. We use a linear quadratic regulator (LQR) to ensure optimal control of nonlinear systems. An LQR is used to solve the problem of state feedback and an SVM is used to address the question of the estimation and examination of the state. These two are then combined and designed in a way that outputs feedback control. The real-time simulation demonstrates that an active suspension using the combined SVM-LQR controller provides passengers with a much more comfortable ride and better road handling

Formulated linear programming problems from game theory and its ...

African Journals Online (AJOL)

Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.

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)

Non-chaotic behaviour for a class of quadratic jerk equations

International Nuclear Information System (INIS)

Malasoma, J.-M.

2009-01-01

It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

Connection dynamics of a gauge theory of gravity coupled with matter

International Nuclear Information System (INIS)

Yang, Jian; Banerjee, Kinjal; Ma, Yongge

2013-01-01

We study the coupling of the gravitational action, which is a linear combination of the Hilbert–Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory (PGT) with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity (LQG) can be employed to quantize this PGT with non-zero torsion. Moreover, the Barbero–Immirzi parameter in LQG acquires its physical meaning as the coupling parameter between the Hilbert–Palatini term and the quadratic torsion term in this gauge theory of gravity. (paper)

Measurement of quadratic electrogyration effect in castor oil

Science.gov (United States)

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.

A Note on 5-bit Quadratic Permutations’ Classification

OpenAIRE

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...

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

Newton's method for solving a quadratic matrix equation with special coefficient matrices

International Nuclear Information System (INIS)

Seo, Sang-Hyup; Seo, Jong Hyun; Kim, Hyun-Min

2014-01-01

We consider the iterative method for solving a quadratic matrix equation with special coefficient matrices which arises in the quasi-birth-death problem. In this paper, we show that the elementwise minimal positive solvents to quadratic matrix equations can be obtained using Newton's method. We also prove that the convergence rate of the Newton iteration is quadratic if the Fréchet derivative at the elementwise minimal positive solvent is nonsingular. However, if the Fréchet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.(This is summarized a paper which is to appear in Honam Mathematical Journal.)

Selective Linear or Quadratic Optomechanical Coupling via Measurement

Directory of Open Access Journals (Sweden)

Michael R. Vanner

2011-11-01

Full Text Available The ability to engineer both linear and nonlinear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical-displacement coupling can be achieved using the optomechanical interaction that is linearly proportional to the mechanical position. The resulting square-displacement measurement strength is compared to that attainable in the dispersive case that has a direct interaction with the mechanical-displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.

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.

Gravitation SL(2,C) gauge theory and conservation laws

CERN Document Server

Carmeli, Moshe; Nissani, Noah

1990-01-01

This monograph gives a comprehensive presentation of the SL(2,C) Gauge Theory of Gravitation along with some recent developments in the problem of Conservation Laws in General Relativity. Emphasis is put on quadratic Lagrangians which yield the Einstein field equations, as compared with Hilbert's original linear Langrangian, thus gravitation follows the other Gauge Fields all of which are derived from nonlinear Lagrangians.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

International Nuclear Information System (INIS)

Hack, Thomas-Paul; Schenkel, Alexander

2012-05-01

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Physik

2012-05-15

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

Stationary stochastic processes theory and applications

CERN Document Server

Lindgren, Georg

2012-01-01

Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...

The linearization method in hydrodynamical stability theory

CERN Document Server

Yudovich, V I

1989-01-01

This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

On the classification of elliptic foliations induced by real quadratic fields with center

Science.gov (United States)

Puchuri, Liliana; Bueno, Orestes

2016-12-01

Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.

A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

Science.gov (United States)

Martin, C. J.; Lee, Y. M.

1972-01-01

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Renormalization of gauge theories without cohomology

International Nuclear Information System (INIS)

Anselmi, Damiano

2013-01-01

We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

A new accurate quadratic equation model for isothermal gas chromatography and its comparison with the linear model

Science.gov (United States)

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

The gas holdup time (tM) is a dominant parameter in gas chromatographic retention models. The difference equation (DE) model proposed by Wu et al. (J. Chromatogr. A 2012, http://dx.doi.org/10.1016/j.chroma.2012.07.077) excluded tM. In the present paper, we propose that the relationship between the adjusted retention time tRZ′ and carbon number z of n-alkanes follows a quadratic equation (QE) when an accurate tM is obtained. This QE model is the same as or better than the DE model for an accurate expression of the retention behavior of n-alkanes and model applications. The QE model covers a larger range of n-alkanes with better curve fittings than the linear model. The accuracy of the QE model was approximately 2–6 times better than the DE model and 18–540 times better than the LE model. Standard deviations of the QE model were approximately 2–3 times smaller than those of the DE model. PMID:22989489

The quadratic-form identity for constructing the Hamiltonian structure of integrable systems

International Nuclear Information System (INIS)

Guo Fukui; Zhang Yufeng

2005-01-01

A usual loop algebra, not necessarily the matrix form of the loop algebra A-tilde n-1 , is also made use of for constructing linear isospectral problems, whose compatibility conditions exhibit a zero-curvature equation from which integrable systems are derived. In order to look for the Hamiltonian structure of such integrable systems, a quadratic-form identity is created in the present paper whose special case is just the trace identity; that is, when taking the loop algebra A-tilde 1 , the quadratic-form identity presented in this paper is completely consistent with the trace identity

Inference for the jump part of quadratic variation of Itô semimartingales

DEFF Research Database (Denmark)

Veraart, Almut

Recent research has focused on modelling asset prices by Itô semimartingales. In such a modelling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference...... of realised variance and realised multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realised variance and realised multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump...

Inference for the jump part of quadratic variation of Itô semimartingales

DEFF Research Database (Denmark)

Veraart, Almut

2010-01-01

Recent research has focused on modeling asset prices by Itô semimartingales. In such a modeling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference...... of realized variance and realized multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realized variance and realized multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump...

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Einstein-aether theory with a Maxwell field: General formalism

Energy Technology Data Exchange (ETDEWEB)

Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru [Department of General Relativity and Gravitation, Institute of Physics, Kazan Federal University, Kremlevskaya str. 18, Kazan 420008 (Russian Federation); Lemos, José P.S., E-mail: joselemos@ist.utl.pt [Centro Multidisciplinar de Astrofísica-CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)

2014-11-15

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.

A geometric formulation of exceptional field theory

Energy Technology Data Exchange (ETDEWEB)

Bosque, Pascal du [Arnold Sommerfeld Center for Theoretical Physics,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805 München (Germany); Hassler, Falk [Department of Physics and Astronomy, University of North Carolina, Phillips Hall, CB #3255, 120 E. Cameron Ave., Chapel Hill, NC 27599-3255 (United States); City University of New York, The Graduate Center, 365 Fifth Avenue, New York, NY 10016 (United States); Department of Physics, Columbia University, Pupin Hall, 550 West 120th St., New York, NY 10027 (United States); Lüst, Dieter [Arnold Sommerfeld Center for Theoretical Physics,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805 München (Germany); Malek, Emanuel [Arnold Sommerfeld Center for Theoretical Physics,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany)

2017-03-01

We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with SL(5)×ℝ{sup +}-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the SL(5)×ℝ{sup +}-structure is not locally flat.

Repair-dependent cell radiation survival and transformation: an integrated theory

International Nuclear Information System (INIS)

Sutherland, John C

2014-01-01

The repair-dependent model of cell radiation survival is extended to include radiation-induced transformations. The probability of transformation is presumed to scale with the number of potentially lethal damages that are repaired in a surviving cell or the interactions of such damages. The theory predicts that at doses corresponding to high survival, the transformation frequency is the sum of simple polynomial functions of dose; linear, quadratic, etc, essentially as described in widely used linear-quadratic expressions. At high doses, corresponding to low survival, the ratio of transformed to surviving cells asymptotically approaches an upper limit. The low dose fundamental- and high dose plateau domains are separated by a downwardly concave transition region. Published transformation data for mammalian cells show the high-dose plateaus predicted by the repair-dependent model for both ultraviolet and ionizing radiation. For the neoplastic transformation experiments that were analyzed, the data can be fit with only the repair-dependent quadratic function. At low doses, the transformation frequency is strictly quadratic, but becomes sigmodial over a wider range of doses. Inclusion of data from the transition region in a traditional linear-quadratic analysis of neoplastic transformation frequency data can exaggerate the magnitude of, or create the appearance of, a linear component. Quantitative analysis of survival and transformation data shows good agreement for ultraviolet radiation; the shapes of the transformation components can be predicted from survival data. For ionizing radiations, both neutrons and x-rays, survival data overestimate the transforming ability for low to moderate doses. The presumed cause of this difference is that, unlike UV photons, a single x-ray or neutron may generate more than one lethal damage in a cell, so the distribution of such damages in the population is not accurately described by Poisson statistics. However, the complete

Azerbaijan Technical University’s Experience in Teaching Linear Electrical Circuit Theory

Directory of Open Access Journals (Sweden)

G. A. Mamedov

2006-01-01

Full Text Available An experience in teaching linear electrical circuit theory at the Azerbaijan Technical University is presented in the paper. The paper describes structure of the Linear Electrical Circuit Theory course worked out by the authors that contains a section on electrical calculation of track circuits, information on electro-magnetic compatibility and typical tests for better understanding of the studied subject.

An algorithm for the solution of dynamic linear programs

Science.gov (United States)

Psiaki, Mark L.

1989-01-01

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

Science.gov (United States)

Freed, Alan D.; Leonov, Arkady I.

2002-01-01

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Saburov, Mansoor; Qaralleh, Izzat

2013-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ (s) -QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ (s) -QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.

Relativistic quantum vorticity of the quadratic form of the Dirac equation

International Nuclear Information System (INIS)

Asenjo, Felipe A; Mahajan, Swadesh M

2015-01-01

We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)

Fundamentals of number theory

CERN Document Server

LeVeque, William J

1996-01-01

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

International Nuclear Information System (INIS)

Marcos, B.

2008-01-01

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

A program package for solving linear optimization problems

International Nuclear Information System (INIS)

Horikami, Kunihiko; Fujimura, Toichiro; Nakahara, Yasuaki

1980-09-01

Seven computer programs for the solution of linear, integer and quadratic programming (four programs for linear programming, one for integer programming and two for quadratic programming) have been prepared and tested on FACOM M200 computer, and auxiliary programs have been written to make it easy to use the optimization program package. The characteristics of each program are explained and the detailed input/output descriptions are given in order to let users know how to use them. (author)

Design of Linear - and Minimum-phase FIR-equalizers

DEFF Research Database (Denmark)

Bysted, Tommy Kristensen; Jensen, K.J.; Gaunholt, Hans

1996-01-01

an error function which is quadratic in the filtercoefficients. The advantage of the quadratic function is the ability to find the optimal coefficients solving a system of linear equations without iterations.The transformation to a minimum-phase equalizer is carried out by homomorphic deconvolution...

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

Science.gov (United States)

Brooke, D.; Vondrasek, D. V.

1978-01-01

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

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...

When is quasi-linear theory exact. [particle acceleration

Science.gov (United States)

Jones, F. C.; Birmingham, T. J.

1975-01-01

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Wigner's little group as a gauge generator in linearized gravity theories

International Nuclear Information System (INIS)

Scaria, Tomy; Chakraborty, Biswajit

2002-01-01

We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

Directory of Open Access Journals (Sweden)

V. V. Zozulya

2013-01-01

Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

Theories of quantum dissipation and nonlinear coupling bath descriptors

Science.gov (United States)

Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

2018-03-01

The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

Linear and quadratic models of point process systems: contributions of patterned input to output.

Science.gov (United States)

Lindsay, K A; Rosenberg, J R

2012-08-01

In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike. Copyright © 2012 Elsevier Ltd. All rights reserved.

Exploring linear algebra labs and projects with Mathematica

CERN Document Server

Arangala, Crista

2014-01-01

Matrix Operations Lab 0: An Introduction to Mathematica Lab 1: Matrix Basics and Operations Lab 2: A Matrix Representation of Linear Systems Lab 3: Powers, Inverses, and Special Matrices Lab 4: Graph Theory and Adjacency Matrices Lab 5: Permutations and Determinants Lab 6: 4 x 4 Determinants and Beyond Project Set 1 Invertibility Lab 7: Singular or Nonsingular? Why Singularity Matters Lab 8: Mod It Out, Matrices with Entries in ZpLab 9: It's a Complex World Lab 10: Declaring Independence: Is It Linear? Project Set 2 Vector Spaces Lab 11: Vector Spaces and SubspacesLab 12: Basing It All on Just a Few Vectors Lab 13: Linear Transformations Lab 14: Eigenvalues and Eigenspaces Lab 15: Markov Chains, An Application of Eigenvalues Project Set 3 Orthogonality Lab 16: Inner Product Spaces Lab 17: The Geometry of Vector and Inner Product SpacesLab 18: Orthogonal Matrices, QR Decomposition, and Least Squares Regression Lab 19: Symmetric Matrices and Quadratic Forms Project Set 4 Matrix Decomposition with Applications L...

Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

CERN Document Server

Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

2016-01-01

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

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.

Linear control theory for gene network modeling.

Science.gov (United States)

Shin, Yong-Jun; Bleris, Leonidas

2010-09-16

Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

An experimental test of the linear no-threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

There is a substantial body of quantitative information on radiation-induced cancer at high dose, but there are no data at low dose. The usual method for estimating effects of low-level radiation is to assume a linear no-threshold dependence. if this linear no-threshold assumption were not used, essentially all fears about radiation would disappear. Since these fears are costing tens of billions of dollars, it is most important that the linear no-threshold theory be tested at low dose. An opportunity for possibly testing the linear no-threshold concept is now available at low dose due to radon in homes. The purpose of this paper is to attempt to use this data to test the linear no-threshold theory

High peer popularity longitudinally predicts adolescent health risk behavior, or does it?: an examination of linear and quadratic associations.

Science.gov (United States)

Prinstein, Mitchell J; Choukas-Bradley, Sophia C; Helms, Sarah W; Brechwald, Whitney A; Rancourt, Diana

2011-10-01

In contrast to prior work, recent theory suggests that high, not low, levels of adolescent peer popularity may be associated with health risk behavior. This study examined (a) whether popularity may be uniquely associated with cigarette use, marijuana use, and sexual risk behavior, beyond the predictive effects of aggression; (b) whether the longitudinal association between popularity and health risk behavior may be curvilinear; and (c) gender moderation. A total of 336 adolescents, initially in 10-11th grades, reported cigarette use, marijuana use, and number of sexual intercourse partners at two time points 18 months apart. Sociometric peer nominations were used to examine popularity and aggression. Longitudinal quadratic effects and gender moderation suggest that both high and low levels of popularity predict some, but not all, health risk behaviors. New theoretical models can be useful for understanding the complex manner in which health risk behaviors may be reinforced within the peer context.

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....

An introduction to linear algebra

CERN Document Server

Mirsky, L

2003-01-01

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.

Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

DEFF Research Database (Denmark)

Yan, Wei

2015-01-01

We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizsa¨cker kinetic energy, and the exchange-correlation Coulomb...... energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear...... response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately....

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)

Effective description of higher-order scalar-tensor theories

Energy Technology Data Exchange (ETDEWEB)

Langlois, David [APC—Astroparticule et Cosmologie, Université Paris Diderot Paris 7, 75013 Paris (France); Mancarella, Michele; Vernizzi, Filippo [Institut de physique théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette (France); Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr [Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours (France)

2017-05-01

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.

Optimization for decision making linear and quadratic models

CERN Document Server

Murty, Katta G

2010-01-01

While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.

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.

Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems

Directory of Open Access Journals (Sweden)

Bambang Riyanto

2005-11-01

Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.

Decentralized linear quadratic power system stabilizers for multi ...

Indian Academy of Sciences (India)

Introduction. Modern excitation systems considerably enhance the overall transient stability of power systems ..... to the local bus rather than the angle δ measured with respect to the remote bus. ... With this in view, the linear and nonlinear per-.

Extensions of linear-quadratic control, optimization and matrix theory

CERN Document Server

Jacobson, David H

1977-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

New results for time reversed symplectic dynamic systems and quadratic functionals

Directory of Open Access Journals (Sweden)

Roman Simon Hilscher

2012-05-01

Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.

Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory

International Nuclear Information System (INIS)

Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.

2017-11-01

This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.

Linear control theory for gene network modeling.

Directory of Open Access Journals (Sweden)

Yong-Jun Shin

Full Text Available Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain and linear state-space (time domain can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.

Plane answers to complex questions the theory of linear models

CERN Document Server

Christensen, Ronald

1987-01-01

This book was written to rigorously illustrate the practical application of the projective approach to linear models. To some, this may seem contradictory. I contend that it is possible to be both rigorous and illustrative and that it is possible to use the projective approach in practical applications. Therefore, unlike many other books on linear models, the use of projections and sub­ spaces does not stop after the general theory. They are used wherever I could figure out how to do it. Solving normal equations and using calculus (outside of maximum likelihood theory) are anathema to me. This is because I do not believe that they contribute to the understanding of linear models. I have similar feelings about the use of side conditions. Such topics are mentioned when appropriate and thenceforward avoided like the plague. On the other side of the coin, I just as strenuously reject teaching linear models with a coordinate free approach. Although Joe Eaton assures me that the issues in complicated problems freq...

Solving the transport equation with quadratic finite elements: Theory and applications

International Nuclear Information System (INIS)

Ferguson, J.M.

1997-01-01

At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids

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.

A simple theory of linear mode conversion

International Nuclear Information System (INIS)

Cairns, R.A.; Lashmore-Davies, C.N.; Woods, A.M.

1984-01-01

A summary is given of the basic theory of linear mode conversion involving the construction of differential equations for the mode amplitudes based on the properties of the dispersion relation in the neighbourhood of the mode conversion point. As an example the transmission coefficient for tunneling from the upper hybrid resonance through the evanescent region to the adjacent cut-off is treated. 7 refs, 3 figs

Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.

1995-01-01

The study is continued on noncommutative integration of linear partial differential equations in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of, where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation

Fitness analysis method for magnesium in drinking water with atomic absorption using quadratic curve calibration

Directory of Open Access Journals (Sweden)

Esteban Pérez-López

2014-11-01

Full Text Available Because of the importance of quantitative chemical analysis in research, quality control, sales of services and other areas of interest , and the limiting of some instrumental analysis methods for quantification with linear calibration curve, sometimes because the short linear dynamic ranges of the analyte, and sometimes by limiting the technique itself, is that there is a need to investigate a little more about the convenience of using quadratic curves for analytical quantification, which seeks demonstrate that it is a valid calculation model for chemical analysis instruments. To this was taken as an analysis method based on the technique and atomic absorption spectroscopy in particular a determination of magnesium in a sample of drinking water Tacares sector Northern Grecia, employing a nonlinear calibration curve and a curve specific quadratic behavior, which was compared with the test results obtained for the same analysis with a linear calibration curve. The results show that the methodology is valid for the determination referred to, with all confidence, since the concentrations are very similar, and as used hypothesis testing can be considered equal.

A quantum-mechanical perspective on linear response theory within polarizable embedding

DEFF Research Database (Denmark)

List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob

2017-01-01

We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole...

[The enigma of the biological interpretation of the linear-quadratic model finally resolved? A summary for non-mathematicians].

Science.gov (United States)

Bodgi, L; Canet, A; Granzotto, A; Britel, M; Puisieux, A; Bourguignon, M; Foray, N

2016-06-01

The linear-quadratic (LQ) model is the only mathematical formula linking cellular survival and radiation dose that is sufficiently consensual to help radiation oncologists and radiobiologists in describing the radiation-induced events. However, this formula proposed in the 1970s and α and β parameters on which it is based remained without relevant biological meaning. From a collection of cutaneous fibroblasts with different radiosensitivity, built over 12 years by more than 50 French radiation oncologists, we recently pointed out that the ATM protein, major actor of the radiation response, diffuses from the cytoplasm to the nucleus after irradiation. The evidence of this nuclear shuttling of ATM allowed us to provide a biological interpretation of the LQ model in its mathematical features, validated by a hundred of radiosensitive cases. A mechanistic explanation of the radiosensitivity of syndromes caused by the mutation of cytoplasmic proteins and of the hypersensitivity to low-dose phenomenon has been proposed, as well. In this review, we present our resolution of the LQ model in the most didactic way. Copyright © 2016 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

Science.gov (United States)

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.

Advanced number theory with applications

CERN Document Server

Mollin, Richard A

2009-01-01

Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...

A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

OpenAIRE

Giang, Phan H.; Shenoy, Prakash P.

2013-01-01

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic l...

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.

Extending the Scope of Robust Quadratic Optimization

NARCIS (Netherlands)

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

Primer on theory and operation of linear accelerators in radiation therapy

International Nuclear Information System (INIS)

Karzmark, C.J.; Morton, R.J.

1981-12-01

This primer is part of an educational package that also includes a series of 3 videotapes entitled Theory and Operation of Linear Accelerators in Radiation Therapy, Parts I, II, and III. This publication provides an overview of the components of the linear accelerator and how they function and interrelate. The auxiliary systems necessary to maintain the operation of the linear accelerator are also described

Partial Stator Overlap in a Linear Generator for Wave Power: An Experimental Study

Directory of Open Access Journals (Sweden)

Anna E. Frost

2017-11-01

Full Text Available This paper presents a study on how the power absorption and damping in a linear generator for wave energy conversion are affected by partial overlap between stator and translator. The theoretical study shows that the electrical power as well as the damping coefficient change quadratically with partial stator overlap, if inductance, friction and iron losses are assumed independent of partial stator overlap or can be neglected. Results from onshore experiments on a linear generator for wave energy conversion cannot reject the quadratic relationship. Measurements were done on the inductance of the linear generator and no dependence on partial stator overlap could be found. Simulations of the wave energy converter’s operation in high waves show that entirely neglecting partial stator overlap will overestimate the energy yield and underestimate the peak forces in the line between the buoy and the generator. The difference between assuming a linear relationship instead of a quadratic relationship is visible but small in the energy yield in the simulation. Since the theoretical deduction suggests a quadratic relationship, this is advisable to use during modeling. However, a linear assumption could be seen as an acceptable simplification when modeling since other relationships can be computationally costly.

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.

Linearized analysis of (2+1)-dimensional Einstein-Maxwell theory

International Nuclear Information System (INIS)

Soda, Jiro.

1989-08-01

On the basis of previous result by Hosoya and Nakao that (2+1)-dimensional gravity reduces the geodesic motion in moduli space, we investigate the effects of matter fields on the geodesic motion using the linearized theory. It is shown that the transverse-traceless parts of energy-momentum tensor make the deviation from the geodesic motion. This result is important for the Einstein-Maxwell theory due to the existence of global modes of Maxwell fields on torus. (author)

Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics A Tribute to Michael K Sain

CERN Document Server

Won, Chang-Hee; Michel, Anthony N

2008-01-01

This volume - dedicated to Michael K. Sain on the occasion of his seventieth birthday - is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. Written by experts in their respective fields, the chapters are thematically organized into four parts: Part I focuses on statistical control theory, where the cost function is viewed as a random variable and performance is shaped through cost cumulants. In this respect, statistical control generalizes linear-quadratic-Gaussian and H-infinity control. Part II addresses algebraic systems th

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (CDC VERSION)

Science.gov (United States)

Armstrong, E. S.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

Science.gov (United States)

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

Science.gov (United States)

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example

A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games

NARCIS (Netherlands)

Engwerda, Jacob

2015-01-01

This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to

Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid

Directory of Open Access Journals (Sweden)

Dwi Riana Aryani

2017-11-01

Full Text Available A hybrid alternate current/direct current (AC/DC microgrid consists of an AC subgrid and a DC subgrid, and the subgrids are connected through the interlink bidirectional AC/DC converter. In the stand-alone operation mode, it is desirable that the interlink bidirectional AC/DC converter manages proportional power sharing between the subgrids by transferring power from the under-loaded subgrid to the over-loaded one. In terms of system security, the interlink bidirectional AC/DC converter takes an important role, so proper control strategies need to be established. In addition, it is assumed that a battery energy storage system is installed in one subgrid, and the coordinated control of interlink bidirectional AC/DC converter and battery energy storage system converter is required so that the power sharing scheme between subgrids becomes more efficient. For the purpose of designing a tracking controller for the power sharing by interlink bidirectional AC/DC converter in a hybrid AC/DC microgrid, a droop control method generates a power reference for interlink bidirectional AC/DC converter based on the deviation of the system frequency and voltages first and then interlink bidirectional AC/DC converter needs to transfer the power reference to the over-loaded subgrid. For efficiency of this power transferring, a linear quadratic regulator with exponential weighting for the current regulation of interlink bidirectional AC/DC converter is designed in such a way that the resulting microgrid can operate robustly against various uncertainties and the power sharing is carried out quickly. Simulation results show that the proposed interlink bidirectional AC/DC converter control strategy provides robust and efficient power sharing scheme between the subgrids without deteriorating the secure system operation.

A generalized linear-quadratic model incorporating reciprocal time pattern of radiation damage repair

International Nuclear Information System (INIS)

Huang, Zhibin; Mayr, Nina A.; Lo, Simon S.; Wang, Jian Z.; Jia Guang; Yuh, William T. C.; Johnke, Roberta

2012-01-01

Purpose: It has been conventionally assumed that the repair rate for sublethal damage (SLD) remains constant during the entire radiation course. However, increasing evidence from animal studies suggest that this may not the case. Rather, it appears that the repair rate for radiation-induced SLD slows down with increasing time. Such a slowdown in repair would suggest that the exponential repair pattern would not necessarily accurately predict repair process. As a result, the purpose of this study was to investigate a new generalized linear-quadratic (LQ) model incorporating a repair pattern with reciprocal time. The new formulas were tested with published experimental data. Methods: The LQ model has been widely used in radiation therapy, and the parameter G in the surviving fraction represents the repair process of sublethal damage with T r as the repair half-time. When a reciprocal pattern of repair process was adopted, a closed form of G was derived analytically for arbitrary radiation schemes. The published animal data adopted to test the reciprocal formulas. Results: A generalized LQ model to describe the repair process in a reciprocal pattern was obtained. Subsequently, formulas for special cases were derived from this general form. The reciprocal model showed a better fit to the animal data than the exponential model, particularly for the ED50 data (reduced χ 2 min of 2.0 vs 4.3, p = 0.11 vs 0.006), with the following gLQ parameters: α/β = 2.6-4.8 Gy, T r = 3.2-3.9 h for rat feet skin, and α/β = 0.9 Gy, T r = 1.1 h for rat spinal cord. Conclusions: These results of repair process following a reciprocal time suggest that the generalized LQ model incorporating the reciprocal time of sublethal damage repair shows a better fit than the exponential repair model. These formulas can be used to analyze the experimental and clinical data, where a slowing-down repair process appears during the course of radiation therapy.

Comparison of Linear Induction Motor Theories for the LIMRV and TLRV Motors

Science.gov (United States)

1978-01-01

The Oberretl, Yamamura, and Mosebach theories of the linear induction motor are described and also applied to predict performance characteristics of the TLRV & LIMRV linear induction motors. The effect of finite motor width and length on performance ...

On the buckling of magnetothermoviscoelastic plate and an associated quadratic operator bundle

International Nuclear Information System (INIS)

El-Sayed, M.A.

1987-10-01

The paper is devoted to the application of the theory of quadratic self-adjoint operator bundles to investigate the problem of oscillations and stability of an isotropic homogeneous, thermoviscoelastic ferromagnetic plate of arbitrary shape, small constant thickness and infinite electric conductivity, placed in a transverse uniform constant magnetic field and clamped along its whole boundary. 14 refs

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

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

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

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

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...

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

The maximally achievable accuracy of linear optimal regulators and linear optimal filters

NARCIS (Netherlands)

Kwakernaak, H.; Sivan, Raphael

1972-01-01

A linear system with a quadratic cost function, which is a weighted sum of the integral square regulation error and the integral square input, is considered. What happens to the integral square regulation error as the relative weight of the integral square input reduces to zero is investigated. In

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.))

Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

Directory of Open Access Journals (Sweden)

J. M. Shao

2016-02-01

Full Text Available Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy just correspond to the absorptions of left-handed (σ− and right-handed (σ+ polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ− are decided by the magnitude of the quadratic term and the magnetic field.

Linear and nonlinear instability theory of a noble gas MHD generator

International Nuclear Information System (INIS)

Mesland, A.J.

1982-01-01

This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (DEC VAX VERSION)

Science.gov (United States)

Frisch, H.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.; Texas Univ., Austin

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any kind of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated - which need not be the same for all particle species in a plasma - are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. (orig.)

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any king of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated --- which need not be the same for all particle species in a plasma --- are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. 11 refs

Linear kinetic theory and particle transport in stochastic mixtures

Energy Technology Data Exchange (ETDEWEB)

Pomraning, G.C. [Univ. of California, Los Angeles, CA (United States)

1995-12-31

We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

Linear response theory an analytic-algebraic approach

CERN Document Server

De Nittis, Giuseppe

2017-01-01

This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about...

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

Spectral theory of linear operators and spectral systems in Banach algebras

CERN Document Server

Müller, Vladimir

2003-01-01

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...

Study of load change control in PWRs using the methods of linear optimal control

International Nuclear Information System (INIS)

Yang, T.

1983-01-01

This thesis investigates the application of modern control theory to the problem of controlling load changes in PWR power plants. A linear optimal state feedback scheme resulting from linear optimal control theory with a quadratic cost function is reduced to a partially decentralized control system using mode preservation techniques. Minimum information transfer among major components of the plant is investigated to provide an adequate coordination, simple implementation, and a reliable control system. Two control approaches are proposed: servo and model following. Each design considers several information structures for performance comparison. Integrated output error has been included in the control systems to accommodate external and plant parameter disturbances. In addition, the cross limit feature, specific to certain modern reactor control systems, is considered in the study to prevent low pressure reactor trip conditions. An 11th order nonlinear model for the reactor and boiler is derived based on theoretical principles, and simulation tests are performed for 10% load change as an illustration of system performance

Theory of linear operators in Hilbert space

CERN Document Server

Akhiezer, N I

1993-01-01

This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

Science.gov (United States)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

Science.gov (United States)

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.

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

A convex optimization approach for solving large scale linear systems

Directory of Open Access Journals (Sweden)

Debora Cores

2017-01-01

Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

Robustness analysis of the Zhang neural network for online time-varying quadratic optimization

International Nuclear Information System (INIS)

Zhang Yunong; Ruan Gongqin; Li Kene; Yang Yiwen

2010-01-01

A general type of recurrent neural network (termed as Zhang neural network, ZNN) has recently been proposed by Zhang et al for the online solution of time-varying quadratic-minimization (QM) and quadratic-programming (QP) problems. Global exponential convergence of the ZNN could be achieved theoretically in an ideal error-free situation. In this paper, with the normal differentiation and dynamics-implementation errors considered, the robustness properties of the ZNN model are investigated for solving these time-varying problems. In addition, linear activation functions and power-sigmoid activation functions could be applied to such a perturbed ZNN model. Both theoretical-analysis and computer-simulation results demonstrate the good ZNN robustness and superior performance for online time-varying QM and QP problem solving, especially when using power-sigmoid activation functions.

On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables

KAUST Repository

Al-Naffouri, Tareq Y.

2015-10-30

© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.

Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

1995-01-01

The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

Estimation of stature from sternum - Exploring the quadratic models.

Science.gov (United States)

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.

Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

Science.gov (United States)

Bianchi, Eugenio; Hackl, Lucas; Yokomizo, Nelson

2018-03-01

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate h KS given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian. The derivation takes into account the case of time-dependent Hamiltonians with Floquet instabilities. We show that the entanglement entropy S A of a Gaussian state grows linearly for large times in unstable systems, with a rate Λ A ≤ h KS determined by the Lyapunov exponents and the choice of the subsystem A. We apply our results to the analysis of entanglement production in unstable quadratic potentials and due to periodic quantum quenches in many-body quantum systems. Our results are relevant for quantum field theory, for which we present three applications: a scalar field in a symmetry-breaking potential, parametric resonance during post-inflationary reheating and cosmological perturbations during inflation. Finally, we conjecture that the same rate Λ A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.

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...

Comparisons of perturbation and integral equation theories for the angular pair correlation function in molecular fluids

International Nuclear Information System (INIS)

Murad, S.; Gubbins, K.E.; Gray, C.G.

1983-01-01

We compare several recently proposed theories for the angular pair correlation function g(rω 1 ω 2 ), including first- and second-order perturbation theory (the u-expansion), a Pade approximant to this series, first-order f-expansion, the single superchain, generalized mean field, linearized hypernetted chain, and quadratic hypernetted chain approximations. Numerical results from these theories are compared with available computer simulation data for four model fluids whose intermolecular pair potential is of the form u 0 +usub(a), where u 0 is a hard-sphere of Lennard-Jones model, while usub(a) is a dipole-dipole or quadrupole-quadrupole interaction; we refer to these model fluids as HS+μμ, HS+QQ, LJ+μμ, and LJ+QQ. Properties studied include the angular pair correlation function and its spherical harmonic components, the thermodynamic properties, and the angular correlation parameters G 1 and G 2 that are related to the dielectric and Kerr constants. The second-order perturbation theory is superior to the integral equation theories for the thermodynamic harmonics of g(rω 1 ω 2 ) and for the thermodynamic properties themselves at moderate multipole strengths. For other harmonics and properties, the integral equation theories are better, with the quadratic hypernetted chain approximation being the best overall. (orig.)

Turnpike theory of continuous-time linear optimal control problems

CERN Document Server

Zaslavski, Alexander J

2015-01-01

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems.  The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands.  Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...

Linear conversion theory on the second harmonic emission from a plasma filament

International Nuclear Information System (INIS)

Tan Weihan; Gu Min

1989-01-01

The linear conversion theory of laser produced plasma filaments is studied. By calculations for the energy flux of the second harmonic emission on the basis of the planar wave-plasma interaction model, it has been found that there exists no 2ω 0 harmonic emission in the direction perpendicular to the incident laser, in contradiction with the experiments. A linear conversion theory is proposed on the second harmonic emission from a plasma filament and discovered the intense 2ω 0 harmonic emission in the direction perpendicular to the incident laser, which is in agreement with the experiments. (author)

Janus field theories from non-linear BF theories for multiple M2-branes

International Nuclear Information System (INIS)

Ryang, Shijong

2009-01-01

We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

Linearized propulsion theory of flapping airfoils revisited

Science.gov (United States)

Fernandez-Feria, Ramon

2016-11-01

A vortical impulse theory is used to compute the thrust of a plunging and pitching airfoil in forward flight within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick that considered the leading-edge suction and the projection in the flight direction of the pressure force. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains a new term that generalizes the leading-edge suction term and depends on Theodorsen function C (k) and on a new complex function C1 (k) of the reduced frequency k. The main qualitative difference with Garrick's theory is that the propulsive efficiency tends to zero as the reduced frequency increases to infinity (as 1 / k), in contrast to Garrick's efficiency that tends to a constant (1 / 2). Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as k -> ∞ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining non-dimensional parameters. The present analytical results are in good agreement with experimental data and numerical results for small amplitude oscillations. Supported by the Ministerio de Economia y Competitividad of Spain Grant No. DPI2013-40479-P.

Symmetric linear systems - An application of algebraic systems theory

Science.gov (United States)

Hazewinkel, M.; Martin, C.

1983-01-01

Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

Covariant quantization of Lagrangians with quadratic dependent fields and derivative couplings

International Nuclear Information System (INIS)

Lam, C.S.; Wang, K.

1977-01-01

A covariant path-integral formula is derived for Lagrangians with quadratic dependent fields and derivative couplings. It differs from the naive one by a factor which can be viewed graphically as due to the coupling with ghost fields. These path integrals can be shown to be unitary and to satisfy equations of motion if and only if this extra factor is present. Applications of this formula to gauge and other field theories are discussed

Linear response theory of activated surface diffusion with interacting adsorbates

Energy Technology Data Exchange (ETDEWEB)

Marti' nez-Casado, R. [Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ (United Kingdom); Sanz, A.S.; Vega, J.L. [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); Rojas-Lorenzo, G. [Instituto Superior de Tecnologi' as y Ciencias Aplicadas, Ave. Salvador Allende, esq. Luaces, 10400 La Habana (Cuba); Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain); Miret-Artes, S., E-mail: s.miret@imaff.cfmac.csic.es [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain)

2010-05-12

Graphical abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed. - Abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.

Linear-response theory of Coulomb drag in coupled electron systems

DEFF Research Database (Denmark)

Flensberg, Karsten; Hu, Ben Yu-Kuang; Jauho, Antti-Pekka

1995-01-01

We report a fully microscopic theory for the transconductivity, or, equivalently, the momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which...

Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm.

Science.gov (United States)

Liang, Lihua; Yuan, Jia; Zhang, Songtao; Zhao, Peng

2018-01-01

This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller.

Linear theory of equatorial spread F

International Nuclear Information System (INIS)

Hudson, M.K.; Kennel, C.F.

1975-01-01

A fluid dispersion relation for the drift and interchange (Rayleigh-Taylor) modes in a collisional plasma forms the basis for a linear theory of equatorial spread F. The collisional drift mode growth rate will exceed the growth rate of the Rayleigh-Taylor mode at short perpendicular wavelengths and density gradient scale lengths, and the drift mode can grow on top side as well as on bottom side density gradients. However, below the F peak, where spread F predominates, it is concluded that both the drift and the Rayleigh-Taylor modes contribute to the total spread F spectrum, the Rayleigh-Taylor mode dominating at long and the drift mode at short perpendicular wavelengths above the ion Larmor radius

Stochastic linear programming models, theory, and computation

CERN Document Server

Kall, Peter

2011-01-01

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

Fast numerical algorithm for the linear canonical transform.

Science.gov (United States)

Hennelly, Bryan M; Sheridan, John T

2005-05-01

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an N log N algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

Linearly Polarized IR Spectroscopy Theory and Applications for Structural Analysis

CERN Document Server

Kolev, Tsonko

2011-01-01

A technique that is useful in the study of pharmaceutical products and biological molecules, polarization IR spectroscopy has undergone continuous development since it first emerged almost 100 years ago. Capturing the state of the science as it exists today, "Linearly Polarized IR Spectroscopy: Theory and Applications for Structural Analysis" demonstrates how the technique can be properly utilized to obtain important information about the structure and spectral properties of oriented compounds. The book starts with the theoretical basis of linear-dichroic infrared (IR-LD) spectroscop

Quadratic genetic modifications: a streamlined route to cosmological simulations with controlled merger history

Science.gov (United States)

Rey, Martin P.; Pontzen, Andrew

2018-02-01

Recent work has studied the interplay between a galaxy's history and its observable properties using `genetically modified' cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping its cosmological environment fixed. Applications to date altered linear properties of the initial conditions, such as the mean overdensity of specified regions; we extend the formulation to include quadratic features, such as local variance, that determines the overall importance of smooth accretion relative to mergers in a galaxy's history. We introduce an efficient algorithm for this new class of modification and demonstrate its ability to control the variance of a region in a one-dimensional toy model. Outcomes of this work are twofold: (i) a clarification of the formulation of genetic modifications and (ii) a proof of concept for quadratic modifications leading the way to a forthcoming implementation in cosmological simulations.

Non normal and non quadratic anisotropic plasticity coupled with ductile damage in sheet metal forming: Application to the hydro bulging test

International Nuclear Information System (INIS)

Badreddine, Houssem; Saanouni, Khemaies; Dogui, Abdelwaheb

2007-01-01

In this work an improved material model is proposed that shows good agreement with experimental data for both hardening curves and plastic strain ratios in uniaxial and equibiaxial proportional loading paths for steel metal until the final fracture. This model is based on non associative and non normal flow rule using two different orthotropic equivalent stresses in both yield criterion and plastic potential functions. For the plastic potential the classical Hill 1948 quadratic equivalent stress is considered while for the yield criterion the Karafillis and Boyce 1993 non quadratic equivalent stress is used taking into account the non linear mixed (kinematic and isotropic) hardening. Applications are made to hydro bulging tests using both circular and elliptical dies. The results obtained with different particular cases of the model such as the normal quadratic and the non normal non quadratic cases are compared and discussed with respect to the experimental results

Introduction to generalized linear models

CERN Document Server

Dobson, Annette J

2008-01-01

Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...

Gaussian-2 theory: Use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Moller--Plesset zero-point energies

International Nuclear Information System (INIS)

Curtiss, L.A.; Raghavachari, K.; Pople, J.A.

1995-01-01

The performance of Gaussian-2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero-point energies. A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)]. The use of geometries optimized at the QCISD level rather than the second-order Moller--Plesset level (MP2) and the use of scaled MP2 zero-point energies rather than scaled Hartree--Fock (HF) zero-point energies have also been examined. The set of 125 energies used for validation of G2 theory [J. Chem. Phys. 94, 7221 (1991)] is used to test out these variations of G2 theory. Inclusion of higher levels of correlation treatment has little effect except in the cases of multiply-bonded systems. In these cases better agreement is obtained in some cases and poorer agreement in others so that there is no improvement in overall performance. The use of QCISD geometries yields significantly better agreement with experiment for several cases including the ionization potentials of CS and O 2 , electron affinity of CN, and dissociation energies of N 2 , O 2 , CN, and SO 2 . This leads to a slightly better agreement with experiment overall. The MP2 zero-point energies gives no overall improvement. These methods may be useful for specific systems

Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

International Nuclear Information System (INIS)

Zavaljevski, N.

1985-01-01

Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

A dynamical theory for linearized massive superspin 3/2

International Nuclear Information System (INIS)

Gates, James S. Jr.; Koutrolikos, Konstantinos

2014-01-01

We present a new theory of free massive superspin Y=3/2 irreducible representation of the 4D, N=1 Super-Poincaré group, which has linearized non-minimal supergravity (superhelicity Y=3/2) as it’s massless limit. The new results will illuminate the underlying structure of auxiliary superfields required for the description of higher massive superspin systems

System theory as applied differential geometry. [linear system

Science.gov (United States)

Hermann, R.

1979-01-01

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Linear time relational prototype based learning.

Science.gov (United States)

Gisbrecht, Andrej; Mokbel, Bassam; Schleif, Frank-Michael; Zhu, Xibin; Hammer, Barbara

2012-10-01

Prototype based learning offers an intuitive interface to inspect large quantities of electronic data in supervised or unsupervised settings. Recently, many techniques have been extended to data described by general dissimilarities rather than Euclidean vectors, so-called relational data settings. Unlike the Euclidean counterparts, the techniques have quadratic time complexity due to the underlying quadratic dissimilarity matrix. Thus, they are infeasible already for medium sized data sets. The contribution of this article is twofold: On the one hand we propose a novel supervised prototype based classification technique for dissimilarity data based on popular learning vector quantization (LVQ), on the other hand we transfer a linear time approximation technique, the Nyström approximation, to this algorithm and an unsupervised counterpart, the relational generative topographic mapping (GTM). This way, linear time and space methods result. We evaluate the techniques on three examples from the biomedical domain.

Non-linear electrodynamics in Kaluza-Klein theory

International Nuclear Information System (INIS)

Kerner, R.

1987-01-01

The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

Calculation of the interfacial tension of the methane-water system with the linear gradient theory

DEFF Research Database (Denmark)

Schmidt, Kurt A. G.; Folas, Georgios; Kvamme, Bjørn

2007-01-01

The linear gradient theory (LGT) combined with the Soave-Redlich-Kwong (SRK EoS) and the Peng-Robinson (PR EoS) equations of state has been used to correlate the interfacial tension data of the methane-water system. The pure component influence parameters and the binary interaction coefficient...... for the mixture influence parameter have been obtained for this system. The model was successfully applied to correlate the interfacial tension data set to within 2.3% for the linear gradient theory and the SRK EoS (LGT-SRK) and 2.5% for the linear gradient theory and PE EoS (LGT-PR). A posteriori comparison...... of data not used in the parameterisation were to within 3.2% for the LGT-SRK model and 2.7% for the LGT-PR model. An exhaustive literature review resulted in a large database for the investigation which covers a wide range of temperature and pressures. The results support the success of the linear...

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.

Calculus of variations and optimal control theory a concise introduction

CERN Document Server

Liberzon, Daniel

2011-01-01

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the h...

The spin polarized linear response from density functional theory: Theory and application to atoms

Energy Technology Data Exchange (ETDEWEB)

Fias, Stijn, E-mail: sfias@vub.ac.be; Boisdenghien, Zino; De Proft, Frank; Geerlings, Paul [General Chemistry (ALGC), Vrije Universiteit Brussel (Free University Brussels – VUB), Pleinlaan 2, 1050 Brussels (Belgium)

2014-11-14

Within the context of spin polarized conceptual density functional theory, the spin polarized linear response functions are introduced both in the [N, N{sub s}] and [N{sub α}, N{sub β}] representations. The mathematical relations between the spin polarized linear response functions in both representations are examined and an analytical expression for the spin polarized linear response functions in the [N{sub α}, N{sub β}] representation is derived. The spin polarized linear response functions were calculated for all atoms up to and including argon. To simplify the plotting of our results, we integrated χ(r, r′) to a quantity χ(r, r{sup ′}), circumventing the θ and ϕ dependence. This allows us to plot and to investigate the periodicity throughout the first three rows in the periodic table within the two different representations. For the first time, χ{sub αβ}(r, r{sup ′}), χ{sub βα}(r, r{sup ′}), and χ{sub SS}(r, r{sup ′}) plots have been calculated and discussed. By integration of the spin polarized linear response functions, different components to the polarisability, α{sub αα}, α{sub αβ}, α{sub βα}, and α{sub ββ} have been calculated.

Quantum optimal control theory in the linear response formalism

International Nuclear Information System (INIS)

Castro, Alberto; Tokatly, I. V.

2011-01-01

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.

Solution of the Chew-Low equations in the quadratic approximation

International Nuclear Information System (INIS)

Gerdt, V.P.; Zharkov, A.Yu.

1982-01-01

Within the framework of the iteration scheme for constructing the general solution of the Chew-Low equations as suggested earlier the second order power contributions are found. In contrast to the linear approximation obtained before the quadratic approximation includes an infinite number of poles on the complex plane of the uniformizing variable w. It is shown that taking into account the second order corrections in the general solution allows us to select the class of solutions possessing the Born pole at w=0. The most cumbersome part of analytical computations has been carried out by computer using the algebraic system REDUCE-2

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

Science.gov (United States)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Generation companies decision-making modeling by linear control theory

International Nuclear Information System (INIS)

Gutierrez-Alcaraz, G.; Sheble, Gerald B.

2010-01-01

This paper proposes four decision-making procedures to be employed by electric generating companies as part of their bidding strategies when competing in an oligopolistic market: naive, forward, adaptive, and moving average expectations. Decision-making is formulated in a dynamic framework by using linear control theory. The results reveal that interactions among all GENCOs affect market dynamics. Several numerical examples are reported, and conclusions are presented. (author)

A non-self-adjoint quadratic eigenvalue problem describing a fluid-solid interaction Part II : analysis of convergence

NARCIS (Netherlands)

Bourne, D.P.; Elman, H.; Osborn, J.E.

2009-01-01

This paper is the second part of a two-part paper treating a non-self-adjoint quadratic eigenvalue problem for the linear stability of solutions to the Taylor-Couette problem for flow of a viscous liquid in a deformable cylinder, with the cylinder modelled as a membrane. The first part formulated

A high-performance Riccati based solver for tree-structured quadratic programs

DEFF Research Database (Denmark)

Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz

2017-01-01

the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...

Classical theory of algebraic numbers

CERN Document Server

Ribenboim, Paulo

2001-01-01

Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...

Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model

Directory of Open Access Journals (Sweden)

José Guilherme Couto

2011-09-01

Full Text Available Purpose: The purpose of this work was the biological comparison between Low Dose Rate (LDR and Pulsed DoseRate (PDR in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments atour Institution since December 2009. Material and methods: In the first phase we studied the influence of the pulse dose and the pulse time in the biologicalequivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM. In the second phase,the equivalent dose in 2 Gy/fraction (EQD2 for the tumor, rectum and bladder in treatments performed with both techniqueswas evaluated and statistically compared. All evaluated patients had stage IIB cervical cancer and were treatedwith External Beam Radiotherapy (EBRT plus two Brachytherapy (BT applications. Data were collected from 48 patients(26 patients treated with LDR and 22 patients with PDR. Results: In the analyses of the influence of PDR parameters in the biological equivalence between LDR and PDRtreatments (Phase 1, it was calculated that if the pulse dose in PDR was kept equal to the LDR dose rate, a small therapeuticloss was expected. If the pulse dose was decreased, the therapeutic window became larger, but a correction inthe prescribed dose was necessary. In PDR schemes with 1 hour interval between pulses, the pulse time did not influencesignificantly the equivalent dose. In the comparison between the groups treated with LDR and PDR (Phase 2 weconcluded that they were not equivalent, because in the PDR group the total EQD2 for the tumor, rectum and bladderwas smaller than in the LDR group; the LQM estimated that a correction in the prescribed dose of 6% to 10% was ne -cessary to avoid therapeutic loss. Conclusions: A correction in the prescribed dose was necessary; this correction should be achieved by calculatingthe PDR dose equivalent to the desired LDR total dose.

Biological equivalence between LDR and PDR in cervical cancer: multifactor analysis using the linear-quadratic model.

Science.gov (United States)

Couto, José Guilherme; Bravo, Isabel; Pirraco, Rui

2011-09-01

The purpose of this work was the biological comparison between Low Dose Rate (LDR) and Pulsed Dose Rate (PDR) in cervical cancer regarding the discontinuation of the afterloading system used for the LDR treatments at our Institution since December 2009. In the first phase we studied the influence of the pulse dose and the pulse time in the biological equivalence between LDR and PDR treatments using the Linear Quadratic Model (LQM). In the second phase, the equivalent dose in 2 Gy/fraction (EQD(2)) for the tumor, rectum and bladder in treatments performed with both techniques was evaluated and statistically compared. All evaluated patients had stage IIB cervical cancer and were treated with External Beam Radiotherapy (EBRT) plus two Brachytherapy (BT) applications. Data were collected from 48 patients (26 patients treated with LDR and 22 patients with PDR). In the analyses of the influence of PDR parameters in the biological equivalence between LDR and PDR treatments (Phase 1), it was calculated that if the pulse dose in PDR was kept equal to the LDR dose rate, a small the-rapeutic loss was expected. If the pulse dose was decreased, the therapeutic window became larger, but a correction in the prescribed dose was necessary. In PDR schemes with 1 hour interval between pulses, the pulse time did not influence significantly the equivalent dose. In the comparison between the groups treated with LDR and PDR (Phase 2) we concluded that they were not equivalent, because in the PDR group the total EQD(2) for the tumor, rectum and bladder was smaller than in the LDR group; the LQM estimated that a correction in the prescribed dose of 6% to 10% was ne-cessary to avoid therapeutic loss. A correction in the prescribed dose was necessary; this correction should be achieved by calculating the PDR dose equivalent to the desired LDR total dose.

Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy

International Nuclear Information System (INIS)

McAneney, H; O'Rourke, S F C

2007-01-01

The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was concerned with the case of exponential re-growth between treatments. Here we also consider the restricted exponential model. This has been successfully used by Panetta and Adam (1995 Math. Comput. Modelling 22 67) in the case of chemotherapy treatment planning.Treatment schedules investigated include standard fractionation of daily treatments, weekday treatments, accelerated fractionation, optimized uniform schedules and variation of the dosage and α/β ratio, where α and β are radiobiological parameters for the tumour tissue concerned. Parameters for these treatment strategies are extracted from the literature on advanced head and neck cancer, prostate cancer, as well as radiosensitive parameters. Standardized treatment protocols are also considered. Calculations based on the present analysis indicate that even with growth laws scaled to mimic initial growth, such that growth mechanisms are comparable, variation in survival fraction to orders of magnitude emerged. Calculations show that the logistic and exponential models yield similar results in tumour eradication. By comparison the Gompertz model calculations indicate that tumours described by this law result in a significantly poorer prognosis for tumour eradication than either the exponential or logistic models. The present study also shows that the faster the tumour growth rate and the higher the repair capacity of the cell line, the greater the variation in outcome of the survival fraction. Gaps in treatment, planned or unplanned, also accentuate the differences of the survival fraction given alternative growth

Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

Science.gov (United States)

Gasbarro, Andrew

2018-03-01

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ2/d.o.f. = 0.5 compared to Χ2/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ2/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

Linear spin-wave theory of incommensurably modulated magnets

DEFF Research Database (Denmark)

Ziman, Timothy; Lindgård, Per-Anker

1986-01-01

Calculations of linearized theories of spin dynamics encounter difficulties when applied to incommensurable magnetic phases: lack of translational invariance leads to an infinite coupled system of equations. The authors resolve this for the case of a `single-Q' structure by mapping onto the problem......: at higher frequency there appear bands of response sharply defined in frequency, but broad in momentum transfer; at low frequencies there is a response maximum at the q vector corresponding to the modulation vector. They discuss generalizations necessary for application to rare-earth magnets...

Checking the foundation: recent radiobiology and the linear no-threshold theory.

Science.gov (United States)

Ulsh, Brant A

2010-12-01

The linear no-threshold (LNT) theory has been adopted as the foundation of radiation protection standards and risk estimation for several decades. The "microdosimetric argument" has been offered in support of the LNT theory. This argument postulates that energy is deposited in critical cellular targets by radiation in a linear fashion across all doses down to zero, and that this in turn implies a linear relationship between dose and biological effect across all doses. This paper examines whether the microdosimetric argument holds at the lowest levels of biological organization following low dose, low dose-rate exposures to ionizing radiation. The assumptions of the microdosimetric argument are evaluated in light of recent radiobiological studies on radiation damage in biological molecules and cellular and tissue level responses to radiation damage. There is strong evidence that radiation initially deposits energy in biological molecules (e.g., DNA) in a linear fashion, and that this energy deposition results in various forms of prompt DNA damage that may be produced in a pattern that is distinct from endogenous (e.g., oxidative) damage. However, a large and rapidly growing body of radiobiological evidence indicates that cell and tissue level responses to this damage, particularly at low doses and/or dose-rates, are nonlinear and may exhibit thresholds. To the extent that responses observed at lower levels of biological organization in vitro are predictive of carcinogenesis observed in vivo, this evidence directly contradicts the assumptions upon which the microdosimetric argument is based.

Mean-Variance Portfolio Selection Problem with Stochastic Salary for a Defined Contribution Pension Scheme: A Stochastic Linear-Quadratic-Exponential Framework

Directory of Open Access Journals (Sweden)

Charles Nkeki

2013-11-01

Full Text Available This paper examines a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a defined contribution (DC pension plan. The utility function is assumed to be quadratic. It was assumed that the flow of contributions made by the PPM are invested into a market that is characterized by a cash account, an inflation-linked bond and a stock. In this paper, inflationlinked bond is traded and used to hedge inflation risks associated with the investment. The aim of this paper is to maximize the expected final wealth and minimize its variance. Efficient frontier for the three classes of assets (under quadratic utility function that will enable pension plan members (PPMs to decide their own wealth and risk in their investment profile at retirement was obtained.

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.))

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 ...

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

Science.gov (United States)

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

Linear canonical transforms theory and applications

CERN Document Server

Kutay, M; Ozaktas, Haldun; Sheridan, John

2016-01-01

This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

UV / IR mixing in noncommutative field theory via open string loops

International Nuclear Information System (INIS)

Kiem, Youngjai; Lee, Sangmin

2000-01-01

We explicitly evaluate one-loop (annulus) planar and nonplanar open string amplitudes in the presence of the background NS-NS two-form field. In the decoupling limit of Seiberg and Witten, we find that the nonplanar string amplitudes reproduce the UV/IR mixing of noncommutative field theories. In particular, the investigation of the UV regime of the open string amplitudes shows that certain IR closed string degrees of freedom survive the decoupling limit as previously predicted from the noncommutative field theory analysis. These degrees of freedom are responsible for the quadratic, linear and logarithmic IR singularities when the D-branes embedded in space-time have the codimension zero, one and two, respectively. The analysis is given for both bosonic and supersymmetric open strings

Linear collider: a preview

Energy Technology Data Exchange (ETDEWEB)

Wiedemann, H.

1981-11-01

Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.

Linear collider: a preview

International Nuclear Information System (INIS)

Wiedemann, H.

1981-11-01

Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center

Agreement of quadratic and CRE models in predicting the late effects of continuous low dose-rate radiotherapy; and reply

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.)

Background field method in gauge theories and on linear sigma models

International Nuclear Information System (INIS)

van de Ven, A.E.M.

1986-01-01

This dissertation constitutes a study of the ultraviolet behavior of gauge theories and two-dimensional nonlinear sigma-models by means of the background field method. After a general introduction in chapter 1, chapter 2 presents algorithms which generate the divergent terms in the effective action at one-loop for arbitrary quantum field theories in flat spacetime of dimension d ≤ 11. It is demonstrated that global N = 1 supersymmetric Yang-Mills theory in six dimensions in one-loop UV-finite. Chapter 3 presents an algorithm which produces the divergent terms in the effective action at two-loops for renormalizable quantum field theories in a curved four-dimensional background spacetime. Chapter 4 presents a study of the two-loop UV-behavior of two-dimensional bosonic and supersymmetric non-linear sigma-models which include a Wess-Zumino-Witten term. It is found that, to this order, supersymmetric models on quasi-Ricci flat spaces are UV-finite and the β-functions for the bosonic model depend only on torsionful curvatures. Chapter 5 summarizes a superspace calculation of the four-loop β-function for two-dimensional N = 1 and N = 2 supersymmetric non-linear sigma-models. It is found that besides the one-loop contribution which vanishes on Ricci-flat spaces, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for superstrings are discussed. Chapters 6 and 7 treat the details of these calculations

Linear representation of algebras with non-associative operations which are satisfy in the balanced functional equations

International Nuclear Information System (INIS)

Ehsani, Amir

2015-01-01

Algebras with a pair of non-associative binary operations (f, g) which are satisfy in the balanced quadratic functional equations with four object variables considered. First, we obtain a linear representation for the operations, of this kind of binary algebras (A,f,g), over an abelian group (A, +) and then we generalize the linear representation of operations, to an algebra (A,F) with non-associative binary operations which are satisfy in the balanced quadratic functional equations with four object variables. (paper)

On Optimal Feedback Control for Stationary Linear Systems

International Nuclear Information System (INIS)

Russell, David L.

2010-01-01

We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

Asymptotic performance of regularized quadratic discriminant analysis based classifiers

KAUST Repository

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.

Joint shape segmentation with linear programming

KAUST Repository

Huang, Qixing

2011-01-01

We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms single-shape segmentation techniques. © 2011 ACM.

Elementary number theory

CERN Document Server

Kraft, James S

2014-01-01

Introduction. Divisibility. Linear Diophantine Equations. Unique Factorization. Applications of Unique Factorization. Congruences. Fermat, Euler, Wilson. Cryptographic Applications. Order and Primitive Roots. More Cryptographic Applications. Quadratic Reciprocity. Primality and Factorization. Sums of Squares. Arithmetic Functions. Continued Fractions. Recent Developments. Appendices. Index.

Experimental determination of the anisotropy function for the Model 200 103Pd 'light seed' and derivation of the anisotropy constant based upon the linear quadratic model

International Nuclear Information System (INIS)

Yue Ning; Nath, Ravinder

2002-01-01

Since the publication of the AAPM Task Group 43 report in 1995, Model 200 103 Pd seed, which has been widely used in prostate seed implants and other brachytherapy procedures, has undergone some changes in its internal geometry resulting from the manufacturer's transition from lower specific activity reactor-produced 103 Pd ('heavy seeds') to higher specific activity accelerator-produced radioactive material ('light seeds'). Based on previously reported theoretical calculations and measurements, the dose rate constants and the radial dose functions of the two types of seeds are nearly the same and have already been reported. In this work, the anisotropy function of the 'light seed' was experimentally measured and an averaging method for the determination of the anisotropy constant from distance-dependent values of anisotropy factors is presented based upon the continuous low dose rate irradiation linear quadratic model for cell killing. The anisotropy function of Model 200 103 Pd 'light seeds' was measured in a Solid Water trade mark sign phantom using 1x1x1 mm micro LiF TLD chips at radial distances of 1, 2, 3, 4, 5, and 6 cm and at angles from 0 to 90 deg. with respect to the longitudinal axis of the seeds. At a radial distance of 1 cm, the measured anisotropy function of the 103 Pd 'light seed' is considerably lower than that of the 103 Pd 'heavy seed' reported in the TG 43 report. Our measured values at all radial distances are in excellent agreement with the results of a Monte Carlo simulation reported by Weaver, except for points along and near the seed longitudinal axis. The anisotropy constant of the 103 Pd 'light seed' was calculated using the linear quadratic biological model for cell killing in 30 clinical implants. For the model 200 ''light seed,'' it has a value of 0.865. However, our biological model calculations lead us to conclude that if the anisotropy factors of an interstitial brachytherapy seed vary significantly over radial distances anisotropy

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task

Directory of Open Access Journals (Sweden)

Ken eKinjo

2013-04-01

Full Text Available Linearly solvable Markov Decision Process (LMDP is a class of optimal control problem in whichthe Bellman’s equation can be converted into a linear equation by an exponential transformation ofthe state value function (Todorov, 2009. In an LMDP, the optimal value function and the correspondingcontrol policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunctionproblem in a continuous state using the knowledge of the system dynamics and the action, state, andterminal cost functions.In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in whichthe dynamics of the body and the environment have to be learned from experience. We first perform asimulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynam-ics model on the derived the action policy. The result shows that a crude linear approximation of thenonlinear dynamics can still allow solution of the task, despite with a higher total cost.We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robotplatform. The state is given by the position and the size of a battery in its camera view and two neck jointangles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servocontroller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state costfunctions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics modelperformed equivalently with the optimal linear quadratic controller (LQR. In the non-quadratic task, theLMDP controller with a linear dynamics model showed the best performance. The results demonstratethe usefulness of the LMDP framework in real robot control even when simple linear models are usedfor dynamics learning.

Non-linear theory of elasticity and optimal design

CERN Document Server

Ratner, LW

2003-01-01

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

International Nuclear Information System (INIS)

Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

1983-01-01

In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

Science.gov (United States)

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…

Linear extended neutron diffusion theory for semi-in finites homogeneous means

International Nuclear Information System (INIS)

Vazquez R, R.; Vazquez R, A.; Espinosa P, G.

2009-10-01

Originally developed for heterogeneous means, the linear extended neutron diffusion theory is applied to the limit case of monoenergetic neutron diffusion in a semi-infinite homogeneous mean with a neutron source, located in the coordinate origin situated in the frontier of dispersive material. The monoenergetic neutron diffusion is studied taking into account the spatial deviations in the neutron flux to the interfacial current caused by the neutron source, as well as the influence of the spatial deviations in the absorption rate. The developed pattern is an unidimensional model for an energy group obtained of application of volumetric average diffusion equation in the moderator. The obtained results are compared against the classic diffusion theory and qualitatively against the neutron transport theory. (Author)

Neural network for solving convex quadratic bilevel programming problems.

Science.gov (United States)

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.

ONETEP: linear-scaling density-functional theory with plane-waves

International Nuclear Information System (INIS)

Haynes, P D; Mostof, A A; Skylaris, C-K; Payne, M C

2006-01-01

This paper provides a general overview of the methodology implemented in onetep (Order-N Electronic Total Energy Package), a parallel density-functional theory code for largescale first-principles quantum-mechanical calculations. The distinctive features of onetep are linear-scaling in both computational effort and resources, obtained by making well-controlled approximations which enable simulations to be performed with plane-wave accuracy. Titanium dioxide clusters of increasing size designed to mimic surfaces are studied to demonstrate the accuracy and scaling of onetep

Portfolio optimization using fuzzy linear programming

Science.gov (United States)

Pandit, Purnima K.

2013-09-01

Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

Distribution Locational Marginal Pricing through Quadratic Programming for Congestion Management in Distribution Networks

DEFF Research Database (Denmark)

Huang, Shaojun; Wu, Qiuwei; Oren, Shmuel S.

2015-01-01

) calculates dynamic tariffs and publishes them to the aggregators, who make the optimal energy plans for the flexible demands. The DLMP through QP instead of linear programing as studied in previous literatures solves the multiple solution issue of the ag- gregator optimization which may cause......This paper presents the distribution locational mar- ginal pricing (DLMP) method through quadratic programming (QP) designed to alleviate the congestion that might occur in a distribution network with high penetration of flexible demands. In the DLMP method, the distribution system operator (DSO...

Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

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

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.

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...

Linear kinetic theory and particle transport in stochastic mixtures

International Nuclear Information System (INIS)

Pomraning, G.C.

1994-03-01

The primary goal in this research is to develop a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. The statistics considered correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components of the mixture. The mixing statistics studied are Markovian as well as more general statistics, such as renewal processes. A further goal of this work is to demonstrate the applicability of the formalism to real world engineering problems. This three year program was initiated June 15, 1993 and has been underway nine months. Many significant results have been obtained, both in the formalism development and in representative applications. These results are summarized by listing the archival publications resulting from this grant, including the abstracts taken directly from the papers

Linear algebra and analytic geometry for physical sciences

CERN Document Server

Landi, Giovanni

2018-01-01

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers m...

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles.

Science.gov (United States)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J

2017-09-29

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

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

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

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.

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Directory of Open Access Journals (Sweden)

2007-01-01

Full Text Available Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

A test of the linear-no threshold theory of radiation carcinogenesis

International Nuclear Information System (INIS)

Cohen, B.L.

1990-01-01

It has been pointed out that, while an ecological study cannot determine whether radon causes lung cancer, it can test the validity of a linear-no threshold relationship between them. The linear-no threshold theory predicts a substantial positive correlation between the average radon exposure in various counties and their lung cancer mortality rates. Data on living areas of houses in 411 counties from all parts of the United States exhibit, rather, a substantial negative correlation with the slopes of the lines of regression differing from zero by 10 and 7 standard deviations for males and females, respectively, and from the positive slope predicted by the theory by at least 16 and 12 standard deviations. When the data are segmented into 23 groups of states or into 7 regions of the country, the predominantly negative slopes and correlations persist, applying to 18 of the 23 state groups and 6 of the 7 regions. Five state-sponsored studies are analyzed, and four of these give a strong negative slope (the other gives a weak positive slope, in agreement with our data for that state). A strong negative slope is also obtained in our data on basements in 253 counties. A random selection-no charge study of 39 high and low lung cancer counties (+4 low population states) gives a much stronger negative correlation. When nine potential confounding factors are included in a multiple linear regression analysis, the discrepancy with theory is reduced only to 12 and 8.5 standard deviations for males and females, respectively. When the data are segmented into four groups by population, the multiple regression vs radon level gives a strong negative slope for each of the four groups. Other considerations are introduced to reduce the discrepancy, but it remains very substantial

Application of a quadratic method of programming to a particular problem of a rational development of a waterflooded field

Energy Technology Data Exchange (ETDEWEB)

Korotkov, S F; Khalitov, N T

1965-01-01

he quadratic method of programming is used to solve the following type of problem. A circular reservoir is subjected to a peripheral waterflood. The reservoir is drained by wells arranged in 3 concentric circles. The objective is to control the operation of producing wells, that a maximum quantity of water-free oil will be produced. The wells are flowed so that bottomhole pressure is above the bubble point. A quadratic equation is used to express the essential features of the problem; a system of linear equations is used to express the boundary conditions. The problem is solved by means of the Wolf algorithm method. The method is demonstrated by an illustrative example.

H 2 guaranteed cost control of discrete linear systems

Directory of Open Access Journals (Sweden)

Colmenares W.

2000-01-01

Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

Low photon count based digital holography for quadratic phase cryptography.

Science.gov (United States)

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.

On the non-linear scale of cosmological perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-04-15

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-04-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

CERN Document Server

Blas, Diego; Konstandin, Thomas

2013-01-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

Linear-quadratic dose kinetics or dose-dependent repair/misrepair

International Nuclear Information System (INIS)

Braby, L.A.; Nelson, J.M.

1992-01-01

Models for the response of cells exposed to low (LET) linear energy transfer radiation can be grouped into three general types on the basis of assumptions about the nature of the interaction which results in the shoulder of the survival curve. The three forms of interaction are 1) sublethal damage becoming lethal, 2) potentially lethal damage becoming irreparable, and 3) potentially lethal damage ''saturating'' a repair system. The effects that these three forms of interaction would have on the results of specific types of experiments are investigated. Comparisons with experimental results indicate that only the second type is significant in determining the response of typical cultured mammalian cells. (author)

Fitness of the analysis method of magnesium in drinking water using atomic absorption with quadratic calibration curve

International Nuclear Information System (INIS)

Perez-Lopez, Esteban

2014-01-01

The quantitative chemical analysis has been importance in research. Also, aspects like: quality control, sales of services and other areas of interest. Some instrumental analysis methods for quantification with linear calibration curve have presented limitations, because the short liner dynamic ranges of the analyte, or sometimes, by limiting the technique itself. The need has been to investigate a little more about the convenience of using quadratic calibration curves for analytical quantification, with which it has seeked demonstrate that has been a valid calculation model for chemical analysis instruments. An analysis base method is used on the technique of atomic absorption spectroscopy and in particular a determination of magnesium in a drinking water sample of the Tacares sector North of Grecia. A nonlinear calibration curve was used and specifically a curve with quadratic behavior. The same was compared with the test results obtained for the equal analysis with a linear calibration curve. The results have showed that the methodology has been valid for the determination referred with all confidence, since the concentrations have been very similar and, according to the used hypothesis testing, can be considered equal. (author) [es

Robustness of Linear Systems towards Multi-Dissipative Pertubations

DEFF Research Database (Denmark)

Thygesen, Uffe Høgsbro; Poulsen, Niels Kjølstad

1997-01-01

We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several...... robustness analysis questions to linear matrix inequalities: robust stability, robust H2 performance and robust performance in presence of disturbances with finite signal-to-noise ratios...

A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation

Czech Academy of Sciences Publication Activity Database

Duarte-Mermoud, M.A.; Ordonez-Hurtado, R.H.; Zagalak, Petr

2012-01-01

Roč. 43, č. 11 (2012), s. 2015-2029 ISSN 0020-7721 R&D Projects: GA ČR(CZ) GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Switched linear systems * Lyapunov function * particle swarm optimization Subject RIV: BC - Control Systems Theory Impact factor: 1.305, year: 2012 http://library.utia.cas.cz/separaty/2012/AS/zagalak-0382169.pdf

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

Energy Technology Data Exchange (ETDEWEB)

Shalchi, A. [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada); Negrea, M.; Petrisor, I. [Department of Physics, University of Craiova, Association Euratom-MEdC, 13A.I.Cuza Str, 200585 Craiova (Romania)

2016-07-15

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

International Nuclear Information System (INIS)

Shalchi, A.; Negrea, M.; Petrisor, I.

2016-01-01

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.

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 Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

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.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

Science.gov (United States)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes: Analytic part

International Nuclear Information System (INIS)

Baekler, Peter; Hehl, Friedrich W.; Nester, James M.

2011-01-01

We propose a cosmological model in the framework of the Poincare gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in both curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar R and the curvature pseudoscalar X linearly and quadratically (including an RX term) and (ii) pieces quadratic in the torsion vector V and the torsion axial vector A (including a VA term). We show generally that in quadratic PG models we have nearly the same number of parity conserving terms ('world') and of parity violating terms ('shadow world'). This offers new perspectives in cosmology for the coupling of gravity to matter and antimatter. Our specific model generalizes the fairly realistic ''torsion cosmologies'' of Shie-Nester-Yo (2008) and Chen et al. (2009). With a Friedman type ansatz for an orthonormal coframe and a Lorentz connection, we derive the two field equations of PG in an explicit form and discuss their general structure in detail. In particular, the second field equation can be reduced to first order ordinary differential equations for the curvature pieces R(t) and X(t). Including these along with certain relations obtained from the first field equation and curvature definitions, we present a first order system of equations suitable for numerical evaluation. This is deferred to the second, numerical part of this paper.

A Quadratic Spring Equation

Science.gov (United States)

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]…

Natural excitation orbitals from linear response theories : Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

NARCIS (Netherlands)

Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.

2017-01-01

Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In

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...

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.

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

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...

Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2003-01-01

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

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.

On Convex Quadratic Approximation

NARCIS (Netherlands)

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

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

Science.gov (United States)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

Directory of Open Access Journals (Sweden)

Wang Peng

2016-01-01

Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

Quadratic obstructions to small-time local controllability for scalar-input systems

Science.gov (United States)

Beauchard, Karine; Marbach, Frédéric

2018-03-01

We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.

Linear theory of density perturbations in a neutrino+baryon universe

International Nuclear Information System (INIS)

Wasserman, I.

1981-01-01

Various aspects of the linear theory of density perturbations in a universe containing a significant population of massive neutrinos are calculated. Because linear perturbations in the neutrino density are subject to nonviscous damping on length scales smaller than the effective neutrino Jeans length, the fluctuation spectrum of the neutrino density perturbations just after photon decoupling is expected to peak near the maximum neutrino Jeans mass. The gravitational effects of nonneutrino species are included in calculating the maximum neutrino Jeans mass, which is found to be [M/sub J/(t)]/sub max/approx.10 17 M/sub sun//[m/sub ν/(eV)] 2 , about an order of magnitude smaller than is obtained when nonneutrino species are ignored. An explicit expression for the nonviscous damping of neutrino density perturbations less massive than the maximum neutrino Jeans mass is derived. The linear evolution of density perturbations after photon decoupling is discussed. Of particular interest is the possibility that fluctuations in the neutrino density induce baryon density perturbations after photon decoupling and that the maximum neutrino Jeans determines the characteristic bound mass of galaxy clusters

Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

Science.gov (United States)

Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David

2011-09-01

Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that

Classes and Theories of Trees Associated with a Class Of Linear Orders