Singular Nonlinear H∞ Optimal Control Problem
Schaft, A.J. van der
1996-01-01
The theory of nonlinear H∞ optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for
One Critical Case in Singularly Perturbed Control Problems
Sobolev, Vladimir
2017-02-01
The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.
Singularity problem of control moment gyro cluster with vibration isolators
Directory of Open Access Journals (Sweden)
Cui Yinghui
2016-02-01
Full Text Available As powerful torque amplification actuators, control moment gyros (CMGs are often used in the attitude control of many state-of-the-art high resolution satellites. However, the disturbance generated by the CMGs can not only reduce the attitude stability of a satellite but also deteriorate the performance of optic payloads. Currently, CMG vibration isolators are widely used to target this problem. The isolators can affect the singularity of the CMG system as they are placed between the CMGs and the satellite bus and provide additional freedoms to the CMG system due to their flexibility. The formulation of the output torque of a CMG is studied first considering the dynamic imbalance of its spin rotor and then the deformation angle as a result of the isolator’s flexibility is calculated. With the additional freedoms, the influence of isolator on the singularity problem is studied and a new steering logic to escape from the singular states is proposed.
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Singular nonlinear H-infinity optimal control problem
Maas, W.C.A.; Maas, W.C.A.; van der Schaft, Arjan
1996-01-01
The theory of nonlinear H∞ of optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for
Balder, E.J.
1984-01-01
This note presents a new, quick approach to existence results without convexity conditions for optimal control problems with singular components in the sense of [11.], 438–485). Starting from the resolvent kernel representation of the solutions of a linear integral equation, a version of Fatou's
Edge, E. R.; Powers, W. F.
1976-01-01
Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.
Dissipative control for singular impulsive dynamical systems
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Li Yang
2012-04-01
Full Text Available The aim of this work is to study the dissipative control problem for singular impulsive dynamical systems. We start by introducing the impulse to the singular systems, and give the definition of the dissipation for singular impulsive dynamical systems. Then we discuss the dissipation of singular impulsive dynamical systems, we obtain some sufficient and necessary conditions for dissipation of these systems by solving some linear matrix inequalities (LMIs. By using this method, we design a state feedback controller to make the closed-loop system dissipative. At last, we testify the feasibility of the method by a numerical example.
A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
Energy Technology Data Exchange (ETDEWEB)
Brunovsky, Pavol, E-mail: brunovsky@fmph.uniba.sk [Comenius University Bratislava, Department of Applied Mathematics and Statistics (Slovakia); Cerny, Ales, E-mail: ales.cerny.1@city.ac.uk [City University London, Cass Business School (United Kingdom); Winkler, Michael, E-mail: michael.winkler@uni-due.de [Universitaet Paderborn, Institut fuer Mathematik (Germany)
2013-10-15
We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x{sub 0}={infinity} which is such that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.
Geometric Singularities of the Stokes Problem
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Nejmeddine Chorfi
2014-01-01
Full Text Available When the domain is a polygon of ℝ2, the solution of a partial differential equation is written as a sum of a regular part and a linear combination of singular functions. The purpose of this paper is to present explicitly the singular functions of Stokes problem. We prove the Kondratiev method in the case of the crack. We finish by giving some regularity results.
A numerical method for singular boundary value problem of ordinary differential equation
International Nuclear Information System (INIS)
He Qibing
1992-12-01
A numerical method, regularizing method, is suggested to treat the singular boundary problem of ordinary differential equation that is raised from controlled nuclear fusion science and other fields owing to their singular physical mechanism. This kind of singular boundary problem has been successfully solved by special treatment near the singular points and using difference method. This method overcomes difficulties in numerical calculation due to the singularity. The convergence results and numerical test are also given
THE EXT RACORPOREAL FERTILIZATION TECHNOLOGIES AND THE SINGULARITY PROBLEMS
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S. V. Denysenko
2013-05-01
Full Text Available The peculiarities of modern medicine development connected with the technological and informative singularity are analyzed. The risks of realization of extracorporeal fertilization are examined from positions of development of informative singularity. The warning problems of origin of singularity are discussed on t h e base of t h e newest technologies development.
Singular perturbation for nonlinear boundary-value problems
Directory of Open Access Journals (Sweden)
Rina Ling
1979-01-01
studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular-perturbation type and approximations are constructed by the method of matched asymptotic expansions.
Solutions of dissimilar material singularity and contact problems
International Nuclear Information System (INIS)
Yang, Y.
2003-09-01
Due to the mismatch of the material properties of joined components, after a homogeneous temperature change or under a mechanical loading, very high stresses occur near the intersection of the interface and the outer surface, or near the intersection of two interfaces. For most material combinations and joint geometries, there exists even a stress singularity. These high stresses may cause fracture of the joint. The investigation of the stress situation near the singular point, therefore, is of great interest. Especially, the relationship between the singular stress exponent, the material data and joint geometry is important for choosing a suitable material combination and joint geometry. In this work, the singular stress field is described analytically in case of the joint having a real and a complex eigenvalue. Solutions of different singularity problems are given, which are two dissimilar materials joint with free edges; dissimilar materials joint with edge tractions; joint with interface corner; joint with a given displacement at one edge; cracks in dissimilar materials joint; contact problem in dissimilar materials and logarithmic stress singularity. For an arbitrary joint geometry and material combination, the stress singular exponent, the angular function and the regular stress term can be calculated analytically. The stress intensity factors for a finite joint can be determined applying numerical methods, e.g. the finite element method (FEM). The method to determine more than one stress intensity factor is presented. The characteristics of the eigenvalues and the stress intensity factors are shown for different joint conditions. (orig.)
Modified Differential Transform Method for Two Singular Boundary Values Problems
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Yinwei Lin
2014-01-01
Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.
Adaptive Control of the Chaotic System via Singular System Approach
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Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
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Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
Positive solutions of singular boundary value problem of negative ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Thus we complete the proof of. Theorem 2.2. Acknowledgement. This work is supported in part by the NSF(Youth) of Shandong Province and NNSF of. China. References. [1] Fink A M, Gatica J A, Hernandez G E and Waltman P, Approximation of solutions of singular second order boundary value problems, SIAM J. Math.
A Schwarz alternating procedure for singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)
1994-12-31
The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.
On the Initial Singularity Problem in Two Dimensional Quantum Cosmology
Gamboa, J.
1995-01-01
The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters $(\\alpha, \\beta)$ satisfying the algebraic relation $2\\beta - \\alpha =2$ in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as general solution the temporal singularity. The theory is quantized and we...
More on the initial singularity problem in gravity's rainbow cosmology
Khodadi, M.; Nozari, K.; Sepangi, H. R.
2016-12-01
Using a one-dimensional minisuperspace model with a dimensionless ratio E/E_{Pl}, we study the initial singularity problem at the quantum level for the closed rainbow cosmology with a homogeneous, isotropic classical space-time background. We derive the classical Hamiltonian within the framework of Schutz's formalism for an ideal fluid with a cosmological constant. We characterize the behavior of the system at the early stages of the universe evolution through analyzing the relevant shapes for the potential sector of the classical Hamiltonian for various matter sources, each separately modified by two rainbow functions. We show that for both rainbow universe models presented here, there is the possibility of eliminating the initial singularity by forming a potential barrier and static universe for a non-zero value of the scale factor. We investigate their quantum stability and show that for an energy-dependent space-time geometry with energies comparable with the Planck energy, the non-zero value of the scale factor may be stable. It is shown that under certain constraints the rainbow universe model filled with an exotic matter as a domain wall fluid plus a cosmological constant can result in a non-singular harmonic universe. In addition, we demonstrate that the harmonically oscillating universe with respect to the scale factor is sensitive to E/E_{Pl} and that at high energies it may become stable quantum mechanically. Through a Schrödinger-Wheeler-De Witt equation obtained from the quantization of the classical Hamiltonian, we also extract the wave packet of the universe with a focus on the early stages of the evolution. The resulting wave packet supports the existence of a bouncing non-singular universe within the context of gravity's rainbow proposal.
Complexity, Analysis and Control of Singular Biological Systems
Zhang, Qingling; Zhang, Xue
2012-01-01
Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the ...
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
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Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Existence and regularity of weak solutions for singular elliptic problems
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Brahim Bougherara
2015-11-01
Full Text Available In this article we study the semilinear singular elliptic problem $$\\displaylines{ -\\Delta u = \\frac{p(x}{u^{\\alpha}}\\quad \\text{in } \\Omega \\cr u = 0\\quad \\text{on } \\partial\\Omega,\\quad u>0 \\text{ in } \\Omega, }$$ where $\\Omega$ is a regular bounded domain of $\\mathbb R^{N}$, $\\alpha\\in\\mathbb R$, $p\\in C(\\Omega$ which behaves as $d(x^{-\\beta}$ as $x\\to\\partial\\Omega$ with $d$ the distance function up to the boundary and $0\\leq \\beta 1$.
Strongly oscillating singularities for the interior transmission eigenvalue problem
Bonnet-Ben Dhia, Anne-Sophie; Chesnel, Lucas
2013-10-01
In this paper, we investigate a two-dimensional interior transmission eigenvalue problem for an inclusion made of a composite material. We consider configurations where the difference between the parameters of the composite material and those of the background changes sign on the boundary of the inclusion. In a first step, under some assumptions on the parameters, we extend the variational approach of the T-coercivity to prove that the transmission eigenvalues form at most a discrete set. In the process, we also provide localization results. Then, we study what happens when these assumptions are not satisfied. The main idea is that, due to very strong singularities that can occur at the boundary, the problem may lose Fredholmness in the natural H1 framework. Using Kondratiev theory, we propose a new functional framework where the Fredholm property is restored.
Synchronization and Control of Linearly Coupled Singular Systems
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Fang Qingxiang
2013-01-01
Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.
Hepson, Ozlem Ersoy; Daǧ, Idris
2018-01-01
In this paper, a subdomain Galerkin method is set up to find solutions of singularly perturbed boundary value problems which are used widely in many areas such as chemical reactor theory, aerodynamics, quantum mechanics, reaction-diffusion process, optimal control, etc. A combination of the cubic B-spline base functions as an approximation function is used to build up the presented method over the geometrically graded mesh. Thus finer mesh can be established through the end parts of the problem domain where steep solutions exist.
On the initial singularity problem in rainbow cosmology
Energy Technology Data Exchange (ETDEWEB)
Santos, Grasiele [Dipartimento di Fisica, Università ' ' La Sapienza' ' , P.le A. Moro 2, Roma, 00185 (Italy); Gubitosi, Giulia [Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ United Kingdom (United Kingdom); Amelino-Camelia, Giovanni, E-mail: grasiele.dossantos@icranet.org, E-mail: g.gubitosi@imperial.ac.uk, E-mail: giovanni.amelino-camelia@roma1.infn.it [Dipartimento di Fisica, Università ' ' La Sapienza' ' and Sez. Roma1 INFN, P.le A. Moro 2, Roma, 00185 (Italy)
2015-08-01
It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ('rainbow') spacetime metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbow metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.
Directory of Open Access Journals (Sweden)
Winfried Auzinger
2006-01-01
Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Singularity problems of the power law for modeling creep compliance
Dillard, D. A.; Hiel, C.
1985-01-01
An explanation is offered for the extreme sensitivity that has been observed in the power law parameters of the T300/934 graphite epoxy material systems during experiments to evaluate the system's viscoelastic response. It is shown that the singularity associated with the power law can explain the sensitivity as well as the observed variability in the calculated parameters. Techniques for minimizing errors are suggested.
Topological regularizations of the triple collision singularity in the 3-vortex problem
International Nuclear Information System (INIS)
Hiraoka, Yasuaki
2008-01-01
The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail
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Songlin Wo
2018-01-01
Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.
The analysis of optimal singular controls for SEIR model of tuberculosis
Marpaung, Faridawaty; Rangkuti, Yulita M.; Sinaga, Marlina S.
2014-12-01
The optimally of singular control for SEIR model of Tuberculosis is analyzed. There are controls that correspond to time of the vaccination and treatment schedule. The optimally of singular control is obtained by differentiate a switching function of the model. The result shows that vaccination and treatment control are singular.
Kamenshchik, A. Yu.
2018-03-01
We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. We discuss and compare also different approaches to the problem of crossing of the Big Bang-Big Crunch singularities.
Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems
Burban, Igor
2017-01-01
In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of \\mathbb{k} x,y,z/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
Motion Control of a Quadrotor Aircraft via Singular Perturbations
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Salvador González-Vázquez
2013-10-01
Full Text Available In this paper, a new motion controller for a quadrotor aircraft is introduced. A reformulation of the control inputs of the dynamic model is discussed and then the control algorithm is given in a constructive form. The stability proof of the state space origin of the overall closed-loop system relies on the theory of singularly perturbed systems. Numerical simulations corroborate the viability of the proposed control scheme and the conclusions concerning stability. A set of simulations under practical conditions is also presented, where the system is affected by different types of disturbances and nonlinearities such as noise and actuator saturation.
Propagation of Singularities and Some Inverse Problems in Wave Propagation
National Research Council Canada - National Science Library
Symes, William W
1989-01-01
... in various useful coefficient classes, separation of scales,...We explain the essential role of travel time in the study of these problems, and show how its function may be generalized to multidimensional (i.e. non-layered) problems.
Controllability of switched singular mix-valued logical control networks with constraints
Deng, Lei; Gong, Mengmeng; Zhu, Peiyong
2018-03-01
The present paper investigates the controllability problem of switched singular mix-valued logical control networks (SSMLCNs) with constraints on states and controls. First, using the semi-tenser product (STP) of matrices, the SSMLCN is expressed in an algebraic form, based on which a necessary and sufficient condition is given for the uniqueness of solution of SSMLCNs. Second, a necessary and sufficient criteria is derived for the controllability of constrained SSMLCNs, by converting a constrained SSMLCN into a parallel constrained switched mix-valued logical control network. Third, an algorithm is presented to design a proper switching sequence and a control scheme which force a state to a reachable state. Finally, a numerical example is given to demonstrate the efficiency of the results obtained in this paper.
Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations
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Zdeněk Šmarda
2009-01-01
Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.
B-spline solution of a singularly perturbed boundary value problem arising in biology
International Nuclear Information System (INIS)
Lin Bin; Li Kaitai; Cheng Zhengxing
2009-01-01
We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.
Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent
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Zonghu Xiu
2012-01-01
Full Text Available We consider the existence of multiple solutions of the singular elliptic problem , as , where , , , , , , . By the variational method and the theory of genus, we prove that the above-mentioned problem has infinitely many solutions when some conditions are satisfied.
Directory of Open Access Journals (Sweden)
Huashan Liu
2011-09-01
Full Text Available To deal with the problem of the output feedback tracking (OFT control with bounded torque inputs of robot manipulators, we propose a generalized fuzzy saturated OFT controller based on singular perturbation theory. First, considering the fact that the output toque of joint actuators is limited, a general expression for a class of saturation functions is given to be applied in the control law. Second, to carry out the whole closed‐loop control with only position measurements, linear and nonlinear filters are optionally involved to generate a pseudo signal to surrogate the actual velocity tracking error. As a third contribution, a fuzzy regulator is added to obtain a self‐tuning performance in tackling the disturbances. Moreover, an explicit but strict stability proof of the system based on the stability theory of singularly perturbed systems is presented. Finally, numerical simulations on several sample controllers are implemented to verify the effectiveness of the proposed approach.
Directory of Open Access Journals (Sweden)
Huashan Liu
2011-09-01
Full Text Available To deal with the problem of the output feedback tracking (OFT control with bounded torque inputs of robot manipulators, we propose a generalized fuzzy saturated OFT controller based on singular perturbation theory. First, considering the fact that the output toque of joint actuators is limited, a general expression for a class of saturation functions is given to be applied in the control law. Second, to carry out the whole closed-loop control with only position measurements, linear and nonlinear filters are optionally involved to generate a pseudo signal to surrogate the actual velocity tracking error. As a third contribution, a fuzzy regulator is added to obtain a self-tuning performance in tackling the disturbances. Moreover, an explicit but strict stability proof of the system based on the stability theory of singularly perturbed systems is presented. Finally, numerical simulations on several sample controllers are implemented to verify the effectiveness of the proposed approach.
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem
Stability effects of singularities in force-controlled robotic assist devices
Luecke, Greg R.
2002-02-01
Force feedback is being used as an interface between humans and material handling equipment to provide an intuitive method to control large and bulky payloads. Powered actuation in the lift assist device compensates for the inertial characteristics of the manipulator and the payload to provide effortless control and handling of manufacturing parts, components, and assemblies. The use of these Intelligent Assist Devices (IAD) is being explored to prevent worker injury, enhance material handling performance, and increase productivity in the workplace. The IAD also provides the capability to shape and control motion in the workspace during routine operations. Virtual barriers can be developed to protect fixed objects in the workspace, and regions can be programmed that attract the work piece to a certain position and orientation. However, the robot is still under complete control of the human operator, with the trajectory being determined and commanded using the judgment of the operator to complete a given task. In many cases, the IAD is built in a configuration that may have singular points inside the workspace. These singularities can cause problems when the unstructured trajectory commands from the human cause interaction between the IAD and the virtual walls and fixtures at positions close to these singularities. The research presented here explores the stability effects of the interactions between the powered manipulator and the virtual surfaces when controlled by the operator. Because of the flexible nature of the human decisions determining the real time work piece paths, manipulator singularities that occur in conjunction with the virtual surfaces raise stability issues in the performance around these singularities. We examine these stability issues in the context of a particular IAD configuration, and present analytic results for the performance and stability of these systems in response to the real-time trajectory modification of the human operator.
Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations
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Josef Diblík
2013-01-01
dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived. The method of functions defined implicitly and the topological method (Ważewski's method are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.
Well-posedness of the second-order linear singular Dirichlet problem
Czech Academy of Sciences Publication Activity Database
Lomtatidze, Alexander; Opluštil, Z.
2015-01-01
Roč. 22, č. 3 (2015), s. 409-419 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : singular Dirichlet problem * well-posedness Subject RIV: BA - General Mathematics Impact factor: 0.417, year: 2015 http://www.degruyter.com/view/j/gmj.2015.22.issue-3/gmj-2015-0023/gmj-2015-0023. xml
Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Zamora, M.
2018-01-01
Roč. 70, č. 1 (2018), s. 173-190 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : indefinite singularity * periodic solution * Kepler problem on S^1 Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.963, year: 2016 https://cms.math.ca/10.4153/CJM-2016-050-1
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan; Půža, B.
2015-01-01
Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1
Nonlocal singular problem with integral condition for a second-order parabolic equation
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Ahmed Lakhdar Marhoune
2015-03-01
Full Text Available We prove the existence and uniqueness of a strong solution for a parabolic singular equation in which we combine Dirichlet with integral boundary conditions given only on parts of the boundary. The proof uses a priori estimate and the density of the range of the operator generated by the problem considered.
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan
-, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf
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Marwan Abukhaled
2013-01-01
Full Text Available The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.
Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.
2016-01-01
Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.
Singular Solutions to a (3 + 1-D Protter-Morawetz Problem for Keldysh-Type Equations
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Nedyu Popivanov
2017-01-01
Full Text Available We study a boundary value problem for (3 + 1-D weakly hyperbolic equations of Keldysh type (problem PK. The Keldysh-type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this problem is analogous to a similar one proposed by M. Protter in 1952, but for Tricomi-type equations which, in part, are closely connected with transonic fluid dynamics. We consider a properly defined, in a special function space, generalized solution to problem PK for which existence and uniqueness theorems hold. It is known that it may have a strong power-type singularity at one boundary point even for very smooth right-hand sides of the equation. In the present paper we study the asymptotic behavior of the generalized solutions of problem PK at the singular point. There are given orthogonality conditions on the right-hand side of the equation, which are necessary and sufficient for the existence of a generalized solution with fixed order of singularity.
Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints
Calise, A. J.; Corban, J. E.
1990-01-01
The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.
Interior sound field control using generalized singular value decomposition in the frequency domain.
Pasco, Yann; Gauthier, Philippe-Aubert; Berry, Alain; Moreau, Stéphane
2017-01-01
The problem of controlling a sound field inside a region surrounded by acoustic control sources is considered. Inspired by the Kirchhoff-Helmholtz integral, the use of double-layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers. However, the practical implementation of the Kirchhoff-Helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions. The present study investigates the potential of the Generalized Singular Value Decomposition (GSVD) to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields, respectively. A proper truncation of the singular basis provided by the GSVD factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial Nyquist frequency of the control sources array while leaving the exterior sound field almost unchanged. Proofs of concept are provided through simulations achieved for interior problems by simulations in a free field scenario with circular arrays and in a reflective environment with square arrays.
Symplectic finite element scheme: application to a driven problem with a regular singularity
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.
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Gernot Pulverer
2010-01-01
Full Text Available In this paper, we investigate the singular Sturm-Liouville problem u′′=λg(u, u′(0=0, βu′(1+αu(1=A, where λ is a nonnegative parameter, β≥0, α>0, and A>0. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [0,ρ]⊂[0,1, the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g(u=1/u and for some model problems from the class of singular differential equations (ϕ(u′′+f(t,u′=λg(t,u,u′ discussed in Agarwal et al. (2007. For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied.
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D. K. K. Vamsi
2012-03-01
Full Text Available In this article, we define the Green's matrix for a nonlinear Sturm Liouville problem associated with a pair of dynamic equations on time scales with a singularity at the point of interface. Then using iterative techniques, we obtain eigenvalue intervals for which there exist positive solutions. Then we present iterative schemes for approximating the solutions, and discus an example that illustrates the the results obtained.
Czech Academy of Sciences Publication Activity Database
Ainsworth, M.; Vejchodský, Tomáš
2011-01-01
Roč. 119, č. 2 (2011), s. 219-243 ISSN 0029-599X R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496 Institutional research plan: CEZ:AV0Z10190503 Keywords : a posteriori error estimates * singularly perturbed problems * reaction-diffusion Subject RIV: BA - General Mathematics Impact factor: 1.321, year: 2011 http://www.springerlink.com/content/d384608709584278/
Variational Iteration Method for Singular Perturbation Initial Value Problems with Delays
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Yongxiang Zhao
2014-01-01
Full Text Available The variational iteration method (VIM is applied to solve singular perturbation initial value problems with delays (SPIVPDs. Some convergence results of VIM for solving SPIVPDs are given. The obtained sequence of iterates is based on the use of general Lagrange multipliers; the multipliers in the functionals can be identified by the variational theory. Moreover, the numerical examples show the efficiency of the method.
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Lv Xuezhe
2010-01-01
Full Text Available Abstract The existence and uniqueness of positive solution is obtained for the singular second-order -point boundary value problem for , , , where , , are constants, and can have singularities for and/or and for . The main tool is the perturbation technique and Schauder fixed point theorem.
Numerical static state feedback laws for closed-loop singular optimal control
Graaf, de S.C.; Stigter, J.D.; Straten, van G.
2005-01-01
Singular and non-singular control trajectories of agricultural and (bio) chemical processes may need to be recalculated from time to time for use in closed-loop optimal control, because of unforeseen changes in state values and noise. This is time consuming. As an alternative, in this paper,
Czech Academy of Sciences Publication Activity Database
Čelikovský, Sergej; Papáček, Štěpán; Cervantes-Herrera, A.; Ruiz-León, J.
2010-01-01
Roč. 55, č. 3 (2010), s. 767-772 ISSN 0018-9286 R&D Projects: GA ČR(CZ) GA102/08/0186 Institutional research plan: CEZ:AV0Z10750506; CEZ:AV0Z50200510 Keywords : Photosynthetic factory (PSF) * singular perturbation * optimal control Subject RIV: BC - Control Systems Theory Impact factor: 1.950, year: 2010 http://library.utia.cas.cz/separaty/2010/TR/celikovsky-0342103.pdf
New analytical solution for solving steady-state heat conduction problems with singularities
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Laraqi Najib
2013-01-01
Full Text Available A problem of steady-state heat conduction which presents singularities is solved in this paper by using the conformal mapping method. The principle of this method is based on the Schwarz-Christoffel transformation. The considered problem is a semi-infinite medium with two different isothermal surfaces separated by an adiabatic annular disc. We show that the thermal resistance can be determined without solving the governing equations. We determine a simple and exact expression that provides the thermal resistance as a function of the ratio of annular disc radii.
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Svatoslav Stanêk
2008-03-01
Full Text Available The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the ÃÂ†-Laplacian. Applications of the existence principle to singular discrete problems are given.
Energy Technology Data Exchange (ETDEWEB)
Dotti, Gustavo; Gleiser, Reinaldo J [Facultad de Matematica, AstronomIa y Fisica (FaMAF), Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba (Argentina)
2009-11-07
The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a (1+1) wave equation partial deriv{sup 2}PSI{sub z} /partial derivt{sup 2} +HPSI{sub z} =0, where H= -partial deriv{sup 2} /partial derivx{sup 2} + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field PSI{sub z} is singular at r{sub s} = -6M/(l - 1)(l +2), with l being the mode harmonic number. The equation PSI{sub z} obeys is also singular, since V has a second-order pole at r{sub s}. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and r{sub s} < 0, but it introduces a non-trivial problem in the naked singular case where M < 0, then r{sub s} > 0, and the singularity appears in the relevant range of r (0 < r < infinity). We solve this problem by developing a new approach to the evolution of the even mode, based on a new gauge invariant function, PSI-circumflex, that is a regular function of the metric perturbation for any value of M. The relation of PSI-circumflex to PSI{sub z} is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that PSI-circumflex and PSI{sub z} obey are related as a supersymmetric pair of quantum Hamiltonians H and H-circumflex. For M < 0,H-circumflex has a regular potential and a unique self-adjoint extension in a domain D defined by a physically motivated boundary condition at r = 0. This allows us to address the issue of evolution of gravitational perturbations in this non-globally hyperbolic background. This formulation is used to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of H-circumflex in D, and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for
Szerszeń, Krzysztof; Zieniuk, Eugeniusz
2016-06-01
The paper presents a strategy for numerical solving of parametric integral equation system (PIES) for 2D potential problems without explicit calculation of singular integrals. The values of these integrals will be expressed indirectly in terms of easy to compute non-singular integrals. The effectiveness of the proposed strategy is investigated with the example of potential problem modeled by the Laplace equation. The strategy simplifies the structure of the program with good the accuracy of the obtained solutions.
Mukhopadhyay, V.; Newsom, J. R.
1982-01-01
A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.
Lebre, Amarino; Santos, António
2003-01-01
These proceedings comprise a large part of the papers presented at the International Conference Factorization, Singular Operators and related problems, which was held from January 28 to February 1, 2002, at the University of th Madeira, Funchal, Portugal, to mark Professor Georgii Litvinchuk's 70 birth day. Experts in a variety of fields came to this conference to pay tribute to the great achievements of Professor Georgii Litvinchuk in the development of vari ous areas of operator theory. The main themes of the conference were focussed around the theory of singular type operators and factorization problems, but other topics such as potential theory and fractional calculus, to name but a couple, were also presented. The goal of the conference was to bring together mathematicians from var ious fields within operator theory and function theory in order to highlight recent advances in problems many of which were originally studied by Profes sor Litvinchuk and his scientific school. A second aim was to sti...
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Reinhardt, Hans-Juergen, E-mail: reinhardt@mathematik.uni-siegen.de [Department of Mathematics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Str. 3, D-57072 Siegen (Germany)
2011-04-01
In this paper singularly perturbed parabolic initial-boundary value problems are considered which, in addition, are illposed. The latter means that at one end of the 1-d spatial domain two conditions (for the solution and its spatial derivative) are given while on the other end the corresponding quantities are to be determined. It is well-known that such problems are illposed in the mathematical sense. Here, in addition, boundary layers may occur which make the problems more difficult. For relatively simple examples numerical experiments have been carried out and numerical results are shown. The Conjugate Gradient Methods is used to find the desired quantities iteratively. It will be explained what has to be done in any iteration step. A regularisation is performed by means of discretization and by determining an optimal final iteration step via a stopping rule.
Full-Order Disturbance-Observer-Based Control for Singular Hybrid System
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Xiuming Yao
2013-01-01
Full Text Available The problem of the disturbance-observer-based control for singular hybrid system with two types of disturbances is addressed in this paper. Under the assumption that the system states are, unavailable, full-order observers (for both system states and the disturbance and a nonlinear control scheme are constructed, such that the composite system can be guaranteed to be stochastically admissible, and the two types of disturbances can be attenuated and rejected, simultaneously. Based on the Lyapunov stability theory, sufficient conditions for the existence of the desired full-order disturbance-observer-based controllers are established in terms of linear matrix inequalities (LMIs. Finally, a numerical example is provided to show the effectiveness of the proposed approaches.
Sayevand, K.; Pichaghchi, K.
2018-04-01
In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.
On the matrix singularity problem in the variational Gaussian wave packet method
Energy Technology Data Exchange (ETDEWEB)
Fabcic, Tomaz; Main, Joerg; Wunner, Guenter [1. Institut fuer Theoretische Physik, Universitaet Stuttgart, 70550 Stuttgart (Germany)
2007-07-01
Variational solutions of the time-dependent Schroedinger equation are often based on Gaussian wave packets (GWP) as trial functions. The equations of motion for the time-dependent Gaussian parameters become ill-conditioned from time to time during the propagation, and this problem increases with the number of propagated GWP, leading to extremely small step sizes of the integration routines. On the other hand a sufficiently large number of GWP is necessary to obtain accurate results. The instabilities of the equations of motion are due to a temporary overcrowding of the set of GWP, making the set of linear equations that has to be solved after each time step of integration nearly singular. We present a novel method to overcome these numerical problems by subjecting the GWP to adequate inequality constraints, rendering the integration process orders of magnitude faster. The power of the method is demonstrated for a two dimensional nonintegrable model potential.
A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems
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Sivakumar K.C.
2013-01-01
Full Text Available For ARnxn and qRn, the linear complementarity problem LCP(A, q is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q. A is called an Ro-matrix if LCP(A,0 has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation.
Singular Integral Operators Associated with Elliptic Boundary Value Problems in Non-smooth Domains
Awala, Hussein
Many boundary value problems of mathematical physics are modelled by elliptic differential operators L in a given domain O. An effective method for treating such problems is the method of layer potentials, whose essence resides in reducing matters to solving a boundary integral equation. This, in turn, requires inverting a singular integral operator, naturally associated with L and O, on appropriate function spaces on ∂O. When the operator L is of second order and the domain O is Lipschitz (i.e., O is locally the upper-graph of a Lipschitz function) the fundamental work of B. Dahlberg, C. Kenig, D. Jerison, E. Fabes, N. Riviere, G. Verchota, R. Brown, and many others, has opened the door for the development of a far-reaching theory in this setting, even though several very difficult questions still remain unanswered. In this dissertation, the goal is to solve a number of open questions regarding spectral properties of singular integral operators associated with second and higher-order elliptic boundary value problems in non-smooth domains. Among other spectral results, we establish symmetry properties of harmonic classical double layer potentials associated with the Laplacian in the class of Lipschitz domains in R2. An array of useful tools and techniques from Harmonic Analysis, Partial Differential Equations play a key role in our approach, and these are discussed as preliminary material in the thesis: • Mellin Transforms and Fourier Analysis; • Calderon-Zygmund Theory in Uniformly Rectifiable Domains; • Boundary Integral Methods. Chapter four deals with proving invertibility properties of singular integral operators naturally associated with the mixed (Zaremba) problem for the Laplacian and the Lame system in infinite sectors in two dimensions, when considering their action on the Lebesgue scale of p integrable functions, for $1 their action on the Lebesgue scale of p integrable functions, for 1 functions). Finally, chapter six, deals with spectral issues
Singular formalism and admissible control of spacecraft with rotating flexible solar array
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Lu Dongning
2014-02-01
Full Text Available This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identities about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a spacecraft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov’s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.
Czech Academy of Sciences Publication Activity Database
Escudero, C.; Hakl, Robert; Peral, I.; Torres, P.J.
2014-01-01
Roč. 37, č. 6 (2014), s. 793-807 ISSN 0170-4214 Institutional support: RVO:67985840 Keywords : singular boundary value problem * epitaxial growth * radial solution Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mma.2836/full
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V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
Numerical solution of singularity-perturbed two-point boundary-value problems
International Nuclear Information System (INIS)
Masenge, R.W.P.
1993-07-01
Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab
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Gai Gongqi
2011-01-01
Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.
Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.
2012-10-01
A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.
Local sensitivity analysis for inverse problems solved by singular value decomposition
Hill, M.C.; Nolan, B.T.
2010-01-01
Local sensitivity analysis provides computationally frugal ways to evaluate models commonly used for resource management, risk assessment, and so on. This includes diagnosing inverse model convergence problems caused by parameter insensitivity and(or) parameter interdependence (correlation), understanding what aspects of the model and data contribute to measures of uncertainty, and identifying new data likely to reduce model uncertainty. Here, we consider sensitivity statistics relevant to models in which the process model parameters are transformed using singular value decomposition (SVD) to create SVD parameters for model calibration. The statistics considered include the PEST identifiability statistic, and combined use of the process-model parameter statistics composite scaled sensitivities and parameter correlation coefficients (CSS and PCC). The statistics are complimentary in that the identifiability statistic integrates the effects of parameter sensitivity and interdependence, while CSS and PCC provide individual measures of sensitivity and interdependence. PCC quantifies correlations between pairs or larger sets of parameters; when a set of parameters is intercorrelated, the absolute value of PCC is close to 1.00 for all pairs in the set. The number of singular vectors to include in the calculation of the identifiability statistic is somewhat subjective and influences the statistic. To demonstrate the statistics, we use the USDA’s Root Zone Water Quality Model to simulate nitrogen fate and transport in the unsaturated zone of the Merced River Basin, CA. There are 16 log-transformed process-model parameters, including water content at field capacity (WFC) and bulk density (BD) for each of five soil layers. Calibration data consisted of 1,670 observations comprising soil moisture, soil water tension, aqueous nitrate and bromide concentrations, soil nitrate concentration, and organic matter content. All 16 of the SVD parameters could be estimated by
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Burkhan T. Kalimbetov
2012-01-01
Full Text Available The regularization method is applied for the construction of algorithm for an asymptotical solution for linear singular perturbed systems with the irreversible limit operator. The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna
2015-06-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
International Nuclear Information System (INIS)
Velichenko, V.V.
1994-01-01
The problem of catastrophe control is discussed. Catastrophe control aims to withdraw responsible engineering constructions out of the catastrophe. The mathematical framework of catastrophes control systems is constructed. It determines the principles of systems filling by the concrete physical contents and, simultaneously, permits to employ modern control methods for the synthesis of optimal withdrawal strategy for protected objects
Vibration control of an elastic strip by a singular force
Indian Academy of Sciences (India)
J. Sound and Vibration 315: 1–21. Han J H, Tani J, Qui J 2006 Active flutter suppression of a lifting surface using piezoelectric actuation and modern control theory. J. Sound and Vibration 291: 706–722. Han J H, Lee I 1999 Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate ...
Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan
2017-03-01
Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
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A New Algorithm Based on the Homotopy Perturbation Method For a Class of Singularly Perturbed Boundary Value Problems
2013-12-01
Full Text Available . In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with leftlayer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The results demonstrate the reliability and efficiency of the proposed method.
A Jacobian singularity based robust controller design for structured uncertainty
Brown, Brandon
Any real system will have differences between the mathematical model response and the response of the true system it represents. These differences can come from external disturbances, incomplete modeling of the dynamics (unstructured uncertainty) or simply incorrect or changing parameter values (structured uncertainty) in the model. Sources of unstructured uncertainty are unavoidable in real systems, so a controller design must always consider robustness to these effects. In many cases, when the sources of structured uncertainty are addressed as another source of unstructured uncertainty, the resulting controller design is conservative. By accurately addressing and designing a controller for the structured uncertainty, large benefits in the controller performance can be generated since the conservative bound is reduced. The classical approach to output shaping of a system involves a feedback loop since this architecture is more robust to differences between the mathematical model and the true system. This dissertation will present an approach to design a feedback controller which is robust to structured uncertainties in a plant, in an accurate and minimal way. The approach begins by identifying a critical set of system parameters which will be proven to represent the full set of system parameters in the Nyquist plane. This critical set is populated by all parameter vectors which satisfy a developed deficiency condition and is the minimal set which will contribute to the Nyquist plane portraits. The invariance of this critical set to control structure is shown explicitly. An improvement of previous work is the addition of a numerical solution technique which guarantees that all critical points are found. The presented approach will allow for the designer set minimum relative stability margins, such as gain and phase margins, which previous work could not compute accurately or with confidence of the results. A robust controller is designed with respect to this
Butuzov, V. F.
2017-06-01
We construct and justify asymptotic expansions of solutions of a singularly perturbed elliptic problem with Dirichlet boundary conditions in the case when the corresponding degenerate equation has a triple root. In contrast to the case of a simple root, the expansion is with respect to fractional (non-integral) powers of the small parameter, the boundary-layer variables have another scaling, and the boundary layer has three zones. This gives rise to essential modifications in the algorithm for constructing the boundary functions. Solutions of the elliptic problem are stationary solutions of the corresponding parabolic problem. We prove that such a stationary solution is asymptotically stable and find its global domain of attraction.
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
International Nuclear Information System (INIS)
Hedrih, K
2008-01-01
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
Energy Technology Data Exchange (ETDEWEB)
Hedrih, K [Faculty of Mechanical Engineering University of Nis, Mathematical Institute SANU, ul. Vojvode Tankosic 3/V/22, 18000-Nis (Serbia)], E-mail: katica@masfak.ni.ac.yu, E-mail: khedrih@eunet.yu
2008-02-15
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task.
HEALTH CARE INFORMATIZATION: PROBLEMS, SOLVED AND UNSOLVED. QUESTION OF EFFICIENCY AND SINGULARITY
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О. P. Mintser
2013-11-01
Full Text Available The considered questions of transformation of basic presentation are in relation to health care informatization. One idea is postulated. Although from the moment of researches beginning in this direction passed more then 50 years, complete clarity in determination to the best strategy of informatization is not defined. New risks are marked. It's related with the origin of technological and informative singularity.
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Rimma M. Safina
2017-04-01
Full Text Available In this paper we consider the first boundary value problem in a rectangular area for a mixed-type equation of the second kind with a singular coefficient. The criterion of the uniqueness of the problem solution is determined. The uniqueness of the problem solution is proved on the basis of completeness of the system of eigenfunctions of the corresponding one-dimensional spectral problem. The solution of the problem is built explicitly as a sum of Fourier–Bessel. There is the problem of the small denominators that appears when justifying the uniform convergence of the constructed series. In this regard, an evaluation of separateness from zero with a corresponding small denominator asymptotic behavior is found. This estimate has allowed to prove the convergence of the series and its derivatives up to the second order, and the existence theorem for the class of regular solutions of this equation.
Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems.
Li, Li; Zhang, Qingling; Zhu, Baoyan
2015-11-01
This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi-Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.
Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.
2018-04-01
We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.
Application of reiteration of Hankel singular value decomposition in quality control
Staniszewski, Michał; Skorupa, Agnieszka; Boguszewicz, Łukasz; Michalczuk, Agnieszka; Wereszczyński, Kamil; Wicher, Magdalena; Konopka, Marek; Sokół, Maria; Polański, Andrzej
2017-07-01
Medical centres are obliged to store past medical records, including the results of quality assurance (QA) tests of the medical equipment, which is especially useful in checking reproducibility of medical devices and procedures. Analysis of multivariate time series is an important part of quality control of NMR data. In this work we proposean anomaly detection tool based on Reiteration of Hankel Singular Value Decomposition method. The presented method was compared with external software and authors obtained comparable results.
International Nuclear Information System (INIS)
Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.
1995-07-01
In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)
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Qiying Wei
2009-01-01
Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.
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George N. Galanis
2005-10-01
Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Energy Technology Data Exchange (ETDEWEB)
Oosterlee, C.W. [Inst. for Algorithms and Scientific Computing, Sankt Augustin (Germany); Washio, T. [C& C Research Lab., Sankt Augustin (Germany)
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
On the W-hair of string black holes and the singularity problem
Ellis, John R.; Nanopoulos, Dimitri V.
1992-01-01
We argue that the infinitely many gauge symmetries of string theory provide an infinite set of conserved (gauge) quantum numbers (W-hair) which characterise black hole states and maintain quantum coherence, even during exotic processes like black hole evaporation/decay. We study ways of measuring the W-hair of spherically-symmetric four-dimensional objects with event horizons, treated as effectively two-dimensional string black holes. Measurements can be done either through the s-wave scattering of light particles off the string black-hole background, or through interference experiments of Aharonov-Bohm type. We also speculate on the role of the extended W-symmetries possessed by the topological field theories that describe the region of space-time around a singularity.
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William Margulies
2004-11-01
Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
Keum, Jung-Hoon; Ra, Sung-Woong
2009-12-01
Nonlinear sliding surface design in variable structure systems for spacecraft attitude control problems is studied. A robustness analysis is performed for regular form of system, and calculation of actuator bandwidth is presented by reviewing sliding surface dynamics. To achieve non-singular attitude description and minimal parameterization, spacecraft attitude control problems are considered based on modified Rodrigues parameters (MRP). It is shown that the derived controller ensures the sliding motion in pre-determined region irrespective of unmodeled effects and disturbances.
Non-linear singular problems in p-adic analysis: associative algebras of p-adic distributions
International Nuclear Information System (INIS)
Albeverio, S; Khrennikov, A Yu; Shelkovich, V M
2005-01-01
We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of p-adic analysis related to p-adic distributions (generalized functions). We construct the p-adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous p-adic distributions. This algebra is embedded in the Colombeau-Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed
The critical slab problem for pure-triplet anisotropic scattering by singular eigenfunction method
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R.G. [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministery of Education, Ankara (Turkey). General Directorate of Secondary Education
2017-12-15
The infinite medium Green function can be written by using the jump condition, found Case's eigenfunctions. Thus, any reactor theory problem which is inplane geometry such the criticality problem as can be investigated by using the proper boundary conditions and suggested flux definitions. By using the criticality equation the critical thicknesses can be calculated as numerically. The selected numerical results can be tabulated.
Analytical methods for an elliptic singular perturbation problem In a circle
N.M. Temme (Nico)
2007-01-01
textabstractWe consider an elliptic perturbation problem in a circle by using the analytical solution that is given by a Fourier series with coefficients in terms of modified Bessel functions. By using saddle point methods we construct asymptotic approximations with respect to a small parameter.
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Gao Feng
2017-01-01
Full Text Available In this paper we address the general fractional calculus of Liouville-Weyl and Liouville-Caputo general fractional derivative types with non-singular power-law kernel for the first time. The Fourier transforms and the anomalous diffusions are discussed in detail. The formulations are adopted to describe complex phenomena of the heat transfer problems.
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
Non-singular orbital elements for special perturbations in the two-body problem
Baù, Giulio; Bombardelli, Claudio; Peláez, Jesús; Lorenzini, Enrico
2015-12-01
Seven spatial elements and a time element are proposed as the state variables of a new special perturbation method for the two-body problem. The new elements hold for zero eccentricity and inclination and for negative values of the total energy. They are developed by combining a spatial transformation into projective coordinates (as in the Burdet-Ferrándiz regularization) with a time transformation in which the exponent of the orbital radius is equal to one instead of two (as commonly done in the literature). By following this approach, we discover a new linearization of the two-body problem, from which the orbital elements can be generated by the variation of parameters method. The geometrical significance of the spatial quantities is revealed by a new intermediate frame which differs from a local vertical local horizontal frame by one rotation in the instantaneous orbital plane. Four elements parametrize the attitude in space of this frame, which in turn defines the orientation of the orbital plane and fixes the departure direction for the longitude of the propagated body. The remaining three elements determine the motion along the radial unit vector and the orbital longitude. The performance of the method, tested using a series of benchmark orbit propagation scenarios, is extremely good when compared to several regularized formulations, some of which have been modified and improved here for the first time.
... niddk.nih.gov Problemas de control de la vejiga (incontinencia urinaria) Información general • La incontinencia urinaria puede ... mujeres tienen algún problema de control de la vejiga en el que accidentalmente se les escapa la ...
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Zamora, M.
2013-01-01
Roč. 20, č. 3 (2013), s. 469-491 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order singular equation * Dirichlet problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0030/gmj-2013-0030. xml ?format=INT
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Zamora, M.
2013-01-01
Roč. 20, č. 3 (2013), s. 469-491 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order singular equation * Dirichlet problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0030/gmj-2013-0030.xml?format=INT
Shen, Jianhe; Han, Maoan
2014-08-01
This paper considers the existence and uniformly valid asymptotic approximation of canard solutions in a second-order nonlinear singularly perturbed boundary value problem with a turning point. We get the main results by constructing the asymptotic solution first and then defining a couple of upper and lower solutions suitably on the basis of the asymptotic solution. Two examples are carried out to illustrate and verify the theoretical results.
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Hans Schonemann
1996-12-01
Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].
Kinematic rate control of simulated robot hand at or near wrist singularity
Barker, K.; Houck, J. A.; Carzoo, S. W.
1985-01-01
A robot hand should obey movement commands from an operator on a computer program as closely as possible. However, when two of the three rotational axes of the robot wrist are colinear, the wrist loses a degree of freedom, and the usual resolved rate equations (used to move the hand in response to an operator's inputs) are indeterminant. Furthermore, rate limiting occurs in close vicinity to this singularity. An analysis shows that rate limiting occurs not only in the vicinity of this singularity but also substantially away from it, even when the operator commands rotational rates of the robot hand that are only a small percentage of the operational joint rate limits. Therefore, joint angle rates are scaled when they exceed operational limits in a real time simulation of a robot arm. Simulation results show that a small dead band avoids the wrist singularity in the resolved rate equations but can introduce a high frequency oscillation close to the singularity. However, when a coordinated wrist movement is used in conjunction with the resolved rate equations, the high frequency oscillation disappears.
Barker, L. K.; Houck, J. A.; Carzoo, S. W.
1984-01-01
An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.
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Xuemei Zhang
2014-01-01
Full Text Available This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.
Sistemas diferenciales-algebraicos: aplicaciones a perturbación singular y control
Etchechoury, María del Rosario
2001-01-01
Los Sistemas Diferenciales Algebraicos (SDA) son también conocidos como sistemas singulares, implícitos, descriptores o sistemas generalizados. Surgen naturalmente como modelos dinámicos de aplicaciones de la ingeniería (tales como redes de circuitos eléctricos [1], sistemas de potencia [2], sistemas mecánicos con restricciones [3], ingeniería aeroespacial [4] y procesos químicos [5]); se utilizan también para modelar sistemas sociales, sistemas económicos, sistemas biológicos; etc. En ...
Analysis of singularity in redundant manipulators
International Nuclear Information System (INIS)
Watanabe, Koichi
2000-03-01
In the analysis of arm positions and configurations of redundant manipulators, the singularity avoidance problems are important themes. This report presents singularity avoidance computations of a 7 DOF manipulator by using a computer code based on human-arm models. The behavior of the arm escaping from the singular point can be identified satisfactorily through the use of 3-D plotting tools. (author)
Infinitesimal Structure of Singularities
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Michael Heller
2017-02-01
Full Text Available Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals and of logic (to the intuitionistic logic. Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer.
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Spectral analysis for differential operators with singularities
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Vjacheslav Anatoljevich Yurko
2004-01-01
Full Text Available Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigen- and associated functions, and investigate the inverse problem of recovering the boundary value problem from its spectral characteristics.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
Deformations of surface singularities
Szilárd, ágnes
2013-01-01
The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...
Multifractal signal reconstruction based on singularity power spectrum
International Nuclear Information System (INIS)
Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning
2016-01-01
Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.
Robust control for fractional variable-order chaotic systems with non-singular kernel
Zuñiga-Aguilar, C. J.; Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Romero-Ugalde, H. M.
2018-01-01
This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen's attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.
Viswanathan, Sasi Prabhakaran
Design, dynamics, control and implementation of a novel spacecraft attitude control actuator called the "Adaptive Singularity-free Control Moment Gyroscope" (ASCMG) is presented in this dissertation. In order to construct a comprehensive attitude dynamics model of a spacecraft with internal actuators, the dynamics of a spacecraft with an ASCMG, is obtained in the framework of geometric mechanics using the principles of variational mechanics. The resulting dynamics is general and complete model, as it relaxes the simplifying assumptions made in prior literature on Control Moment Gyroscopes (CMGs) and it also addresses the adaptive parameters in the dynamics formulation. The simplifying assumptions include perfect axisymmetry of the rotor and gimbal structures, perfect alignment of the centers of mass of the gimbal and the rotor etc. These set of simplifying assumptions imposed on the design and dynamics of CMGs leads to adverse effects on their performance and results in high manufacturing cost. The dynamics so obtained shows the complex nonlinear coupling between the internal degrees of freedom associated with an ASCMG and the spacecraft bus's attitude motion. By default, the general ASCMG cluster can function as a Variable Speed Control Moment Gyroscope, and reduced to function in CMG mode by spinning the rotor at constant speed, and it is shown that even when operated in CMG mode, the cluster can be free from kinematic singularities. This dynamics model is then extended to include the effects of multiple ASCMGs placed in the spacecraft bus, and sufficient conditions for non-singular ASCMG cluster configurations are obtained to operate the cluster both in VSCMG and CMG modes. The general dynamics model of the ASCMG is then reduced to that of conventional VSCMGs and CMGs by imposing the standard set of simplifying assumptions used in prior literature. The adverse effects of the simplifying assumptions that lead to the complexities in conventional CMG design, and
Directory of Open Access Journals (Sweden)
Yuji Liu
2016-11-01
Full Text Available Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard derivative and Riemann-Liouville type Hadamard fractional derivatives with order q in [n-1,n by using the iterative method.
Bladder Control Problems in Women
... be affected than Hispanic/Latina, African American, or Asian American women UI is not a disease. UI ... a UTI, a kidney problem, or diabetes. Urine culture. A health care professional performs a urine culture ...
A semilinear control problem involving homogenization
Directory of Open Access Journals (Sweden)
Carlos Conca
2001-01-01
Full Text Available We consider a control problem involving a semilinear elliptic equation with a uniformly Lipschitz non-linearity and rapidly oscillating coefficients in a bounded domain of $mathbb{R}^N$. The control is distributed on a compact subset interior to the domain. Given an $N-1$ dimensional hypersurface at the interior of the domain not intersecting the control zone, the trace of the solution on the curve has to be controlled. We prove that there exists a limit control as the homogenization parameter converges to zero, which results as the limit of fixed points for controllability problems. We link this limit control with the corresponding homogenized problem.
Singular Perturbations and Time Scales in Modeling and Control of Dynamic Systems,
1980-11-01
separate fluctuations within each of the N clases . ihere dmwtiaL r a-c the mcriz A L exptessed as -ven though transition probabilities an-large as 0.2 A...of t. Y. 3er- Salons , Chairman of the Swtesc Control Comnmfittee. Thus work wsi supported a pans by the U. S. Army Rieanth office wider Coet DAAO29
Discrete Control Processes, Dynamic Games and Multicriterion Control Problems
Directory of Open Access Journals (Sweden)
Dumitru Lozovanu
2002-07-01
Full Text Available The discrete control processes with state evaluation in time of dynamical system is considered. A general model of control problems with integral-time cost criterion by a trajectory is studied and a general scheme for solving such classes of problems is proposed. In addition the game-theoretical and multicriterion models for control problems are formulated and studied.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
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
Singular and degenerate cauchy problems
Carroll, R.W
1976-01-01
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
Preconditioning for Singular Perturbation Problems.
1986-08-01
methods for the solution of (1.1) - see (181, [19]. Almost all iterative methods, including the multigrid methods [14] can be cast in the framework of a...techniques", SIAM J. Numer. Anal., Ser. B. 2, 1 (1964). (14] McCormick, S. F., ed., " Multigrid Methods ", SIAM series on Frontiers of Applied Mathematics 5
Naked singularity, firewall, and Hawking radiation.
Zhang, Hongsheng
2017-06-21
Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.
Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach
Directory of Open Access Journals (Sweden)
Ayman A. El-Badawy
2016-01-01
Full Text Available Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at 90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval. Keywords. Positive solution; singular BVPs; sufficient and necessary conditions; p-Laplacian equations. 1. Introduction. In this paper, we are concerned with higher order singular p-Laplacian boundary value problems. ⎧. ⎨. ⎩.
Solved problems in dynamical systems and control
Tenreiro-Machado, J; Valério, Duarte; Galhano, Alexandra M
2016-01-01
This book presents a collection of exercises on dynamical systems, modelling and control. Each topic covered includes a summary of the theoretical background, problems with solutions, and further exercises.
Singularity is the Future of ICT Research
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
2014-06-01
Jun 1, 2014 ... tech systems, and how in the near future. Artificial Intelligence may impact our lives, AI, Robotics, nanotechnology, mechatronics are collaborative agents of technological singularity. The singularity is already here! Think of modern houses now remotely controlled from far distances, think of e-commerce and.
A numerical method for solving singular De`s
Energy Technology Data Exchange (ETDEWEB)
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Interaction of two singular Lissajous lines in free space.
Chen, Haitao; Gao, Zenghui; Wang, Wanqing
2017-05-20
The interaction of two singular Lissajous lines emergent from a polychromatic vector beam is studied. It is shown that singular Lissajous lines disappear with propagation; meanwhile Lissajous singularities take place. The handedness reversal, the changes in the shape of Lissajous figures, and the degree of polarization of Lissajous singularities, as well as the creation and annihilation of a single singularity, may appear by varying the control parameters. In addition, the transformation of the shape of line h=0, the creation and annihilation of pairs of Lissajous singularities not only with opposite topological charge and same handedness, but also with same degree of polarization, take place with propagation.
Problems in event based engine control
DEFF Research Database (Denmark)
Hendricks, Elbert; Jensen, Michael; Chevalier, Alain Marie Roger
1994-01-01
Physically a four cycle spark ignition engine operates on the basis of four engine processes or events: intake, compression, ignition (or expansion) and exhaust. These events each occupy approximately 180° of crank angle. In conventional engine controllers, it is an accepted practice to sample...... problems on accurate air/fuel ratio control of a spark ignition (SI) engine....
Geodesic fields with singularities
International Nuclear Information System (INIS)
Kafker, A.H.
1979-01-01
The question considered is whether or not a Riemannian metric can be found to make a given curve field on a closed surface into geodesics. Allowing singularities removes the restriction to Euler characteristic zero. The main results are the following: only two types of isolated singularities can occur in a geodesic field on a surface. No geodsic fields exist on a surface with Euler characteristic less than zero. If the Euler characteristic is zero, such a geodesic field can have only removable singularities. Only a limited number of geodesic fields exist on S 2 and RP 2 . A closed geodesic (perhaps made from several curves and singularities) always appears in such a field
Minimal Time Problem with Impulsive Controls
Energy Technology Data Exchange (ETDEWEB)
Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at [University of Graz, Institute for Mathematics and Scientific Computing (Austria); Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at [Austrian Academy of Sciences, Radon Institute of Computational and Applied Mathematics (Austria)
2017-02-15
Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.
Hybrid Predictive Control for Dynamic Transport Problems
Núñez, Alfredo A; Cortés, Cristián E
2013-01-01
Hybrid Predictive Control for Dynamic Transport Problems develops methods for the design of predictive control strategies for nonlinear-dynamic hybrid discrete-/continuous-variable systems. The methodology is designed for real-time applications, particularly the study of dynamic transport systems. Operational and service policies are considered, as well as cost reduction. The control structure is based on a sound definition of the key variables and their evolution. A flexible objective function able to capture the predictive behaviour of the system variables is described. Coupled with efficient algorithms, mainly drawn from the area of computational intelligence, this is shown to optimize performance indices for real-time applications. The framework of the proposed predictive control methodology is generic and, being able to solve nonlinear mixed-integer optimization problems dynamically, is readily extendable to other industrial processes. The main topics of this book are: ●hybrid predictive control (HPC) ...
Remarks on Risk-Sensitive Control Problems
International Nuclear Information System (INIS)
Menaldi, Jose-Luis; Robin, Maurice
2005-01-01
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If u α (θ,x) denotes the optimal cost function, θ being the risk factor, then it is shown that lim { α to 0}α u α (θ,x)=ξ(θ) where ξ(θ) is the average on ]0,θ[ of the optimal cost of the (usual) infinite horizon risk-sensitive control problem
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
Isotopy of Morin singularities
Saji, Kentaro
2015-01-01
We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs.
Ishii, Shihoko
2014-01-01
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...
Singularities in Free Surface Flows
Thete, Sumeet Suresh
Free surface flows where the shape of the interface separating two or more phases or liquids are unknown apriori, are commonplace in industrial applications and nature. Distribution of drop sizes, coalescence rate of drops, and the behavior of thin liquid films are crucial to understanding and enhancing industrial practices such as ink-jet printing, spraying, separations of chemicals, and coating flows. When a contiguous mass of liquid such as a drop, filament or a film undergoes breakup to give rise to multiple masses, the topological transition is accompanied with a finite-time singularity . Such singularity also arises when two or more masses of liquid merge into each other or coalesce. Thus the dynamics close to singularity determines the fate of about-to-form drops or films and applications they are involved in, and therefore needs to be analyzed precisely. The primary goal of this thesis is to resolve and analyze the dynamics close to singularity when free surface flows experience a topological transition, using a combination of theory, experiments, and numerical simulations. The first problem under consideration focuses on the dynamics following flow shut-off in bottle filling applications that are relevant to pharmaceutical and consumer products industry, using numerical techniques based on Galerkin Finite Element Methods (GFEM). The second problem addresses the dual flow behavior of aqueous foams that are observed in oil and gas fields and estimates the relevant parameters that describe such flows through a series of experiments. The third problem aims at understanding the drop formation of Newtonian and Carreau fluids, computationally using GFEM. The drops are formed as a result of imposed flow rates or expanding bubbles similar to those of piezo actuated and thermal ink-jet nozzles. The focus of fourth problem is on the evolution of thinning threads of Newtonian fluids and suspensions towards singularity, using computations based on GFEM and experimental
Prevalence of Multiply Controlled Problem Behavior
Beavers, Gracie A.; Iwata, Brian A.
2011-01-01
We examined articles in the "Journal of Applied Behavior Analysis" in which results of functional analyses indicated that problem behavior was maintained by multiple sources of reinforcement. Data for 88 (16.9%) of 521 subjects reported in 168 studies met the criteria for multiple control. Data for 11 subjects (2.1%) involved a single response…
String theory and cosmological singularities
Indian Academy of Sciences (India)
time' can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities ...
Directory of Open Access Journals (Sweden)
Yuancheng Sun
2016-01-01
Full Text Available For the non-Gaussian singular time-delayed stochastic distribution control (SDC system with unknown external disturbance where the output probability density function (PDF is approximated by the rational square-root B-spline basis function, a robust fault diagnosis and fault tolerant control algorithm is presented. A full-order observer is constructed to estimate the exogenous disturbance and an adaptive observer is used to estimate the fault size. A fault tolerant tracking controller is designed using the feedback of distribution tracking error, fault, and disturbance estimation to let the postfault output PDF still track desired distribution. Finally, a simulation example is included to illustrate the effectiveness of the proposed algorithms and encouraging results have been obtained.
Control problems in very large accelerators
International Nuclear Information System (INIS)
Crowley-Milling, M.C.
1985-06-01
There is no fundamental difference of kind in the control requirements between a small and a large accelerator since they are built of the same types of components, which individually have similar control inputs and outputs. The main difference is one of scale; the large machine has many more components of each type, and the distances involved are much greater. Both of these factors must be taken into account in determining the optimum way of carrying out the control functions. Small machines should use standard equipment and software for control as much as possible, as special developments for small quantities cannot normally be justified if all costs are taken into account. On the other hand, the very great number of devices needed for a large machine means that, if special developments can result in simplification, they may make possible an appreciable reduction in the control equipment costs. It is the purpose of this report to look at the special control problems of large accelerators, which the author shall arbitarily define as those with a length of circumference in excess of 10 km, and point out where special developments, or the adoption of developments from outside the accelerator control field, can be of assistance in minimizing the cost of the control system. Most of the first part of this report was presented as a paper to the 1985 Particle Accelerator Conference. It has now been extended to include a discussion on the special case of the controls for the SSC
Stable computation of generalized singular values
Energy Technology Data Exchange (ETDEWEB)
Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)
1996-12-31
We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
Directory of Open Access Journals (Sweden)
Gabriel Martínez-Niconoff
2012-01-01
Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Numerical Approaches to Spacetime Singularities
Directory of Open Access Journals (Sweden)
Beverly K. Berger
1998-05-01
Full Text Available This review updates a previous review article. Numerical explorationof the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
Mathematical models with singularities a zoo of singular creatures
Torres, Pedro J
2015-01-01
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
Amirjanyan, A. A.; Sahakyan, A. V.
2017-08-01
A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.
Directory of Open Access Journals (Sweden)
Fuyi Xu
2010-04-01
\\end{array}\\right.$$ where $1\\leq k\\leq s\\leq m-2, a_i, b_i\\in(0,+\\infty$ with $0<\\sum_{i=1}^{k}b_{i}-\\sum_{i=k+1}^{s}b_{i}<1, 0<\\sum_{i=1}^{m-2}a_{i}<1, 0<\\xi_1<\\xi_2<\\cdots<\\xi_{m-2}<\\rho(T$, $f\\in C( [0,+\\infty,[0,+\\infty$, $a(t$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results.
Directory of Open Access Journals (Sweden)
Khaled Loukhaoukha
2013-01-01
Full Text Available We present a new optimal watermarking scheme based on discrete wavelet transform (DWT and singular value decomposition (SVD using multiobjective ant colony optimization (MOACO. A binary watermark is decomposed using a singular value decomposition. Then, the singular values are embedded in a detailed subband of host image. The trade-off between watermark transparency and robustness is controlled by multiple scaling factors (MSFs instead of a single scaling factor (SSF. Determining the optimal values of the multiple scaling factors (MSFs is a difficult problem. However, a multiobjective ant colony optimization is used to determine these values. Experimental results show much improved performances of the proposed scheme in terms of transparency and robustness compared to other watermarking schemes. Furthermore, it does not suffer from the problem of high probability of false positive detection of the watermarks.
Propagation of singularities for linearised hybrid data impedance tomography
DEFF Research Database (Denmark)
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2017-01-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non...
Singularities in FLRW spacetimes
het Lam, Huibert; Prokopec, Tomislav
2017-12-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.
Analysis and design of singular Markovian jump systems
Wang, Guoliang; Yan, Xinggang
2014-01-01
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr
Spatio-temporal problems of locomotion control
International Nuclear Information System (INIS)
Smolyaninov, Vladimir V
2000-01-01
The problem of the spatio-temporal construction of legged movements involves structural freedoms due to the multi-link structure of the extremities, kinematic freedoms of the stepping cycle, and interextremity coordination freedoms, whose purposive organization is established by means of appropriate synergies, i.e. additional functional links the brain's control system forms. The main focus of attention in this work is on the kinematic and coordination synergies of the legged movements of humans and animals. The comparative historical analysis of experimental data and modelling metaphors concentrates on obtaining a unified description, whereas the ultimate mathematical metaphor reduces to space-time geometry, with base step synergies as its invariants. Thus, the concept of a synergetic organization for biomechanical movement freedoms is transformed to the geochronometry concept, actually a modification of Minkowskian geometry. To determine the spectrum of possible geochronometries, the consequences of a generalized 'postulate of a constant speed of light' are studied and different models of wave chronometers compared. (reviews of topical problems)
Pursell-Shanks type theorems for fewnomial singularities
International Nuclear Information System (INIS)
Khimshiashvili, G.
2006-04-01
We discuss certain situations in which the analytic isomorphism class of an isolated hypersurface singularity is determined by the Lie algebra of derivations of its moduli algebra. Our main attention is given to singularities defined by polynomials with the number of monomials equal to the number of variables. In this context, we indicate several classes of singularities which are classified by the associated Lie algebras. In particular, it is shown that this takes place for isolated singularities defined by binomials in two variables with the Milnor number not less than 7, which implies that simple singularities with Milnor number not less than 7 can be classified by the associated Lie algebras. Similar results are obtained for several other classes of isolated hypersurfaces singularities. A number of related results and open problems are also presented. (author)
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good Mathematics from Bad Lenses. Rajaram Nityananda. General Article Volume 19 Issue 9 September 2014 pp 787-796. Fulltext. Click here to view fulltext PDF. Permanent link:
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good ... Author Affiliations. Rajaram Nityananda1. Azim Premji University, PES Institute of Technology Campus, Pixel Park, B Block, Electronics City, Hosur Road (Beside NICE Road) Bangalore – 560100 ...
Indian Academy of Sciences (India)
IAS Admin
Standard presentations of optics concentrate on ideal systems made for imaging which bring all rays from a point ... One of the standard topics we study in school is the action of a spherical mirror. Figure 1 shows a set of ..... singularities of smooth maps, and the beauty of the mathematics needed to understand them, Arnold ...
CSIR Research Space (South Africa)
Roux, FS
2013-09-01
Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic...
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2017-01-01
We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...
Singularities in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept
Infinite derivative gravity : non-singular cosmology & blackhole solutions
Mazumdar, Anupam
2017-01-01
Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and
Directory of Open Access Journals (Sweden)
Sheng Liu
2017-01-01
Full Text Available This paper presents a two-time scale control structure for the course keeping of an advanced marine surface vehicle, namely, the fully submerged hydrofoil vessel. The mathematical model of course keeping control for the fully submerged hydrofoil vessel is firstly analyzed. The dynamics of the hydrofoil servo system is considered during control design. A two-time scale model is established so that the controllers of the fast and slow subsystems can be designed separately. A robust integral of the sign of the error (RISE feedback control is proposed for the slow varying system and a disturbance observer based state feedback control is established for the fast varying system, which guarantees the disturbance rejection performance for the two-time scale systems. Asymptotic stability is achieved for the overall closed-loop system based on Lyapunov stability theory. Simulation results show the effectiveness and robustness of the proposed methodology.
Singular potentials in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Aguilera-Navarro, V.C. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Koo, E. Ley [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica
1995-10-01
This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs.
'Footballs', conical singularities, and the Liouville equation
International Nuclear Information System (INIS)
Redi, Michele
2005-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints
Singularities: the Brieskorn anniversary volume
National Research Council Canada - National Science Library
Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M
1998-01-01
...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...
String theory and cosmological singularities
Indian Academy of Sciences (India)
Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics.
Holographic complexity and spacetime singularities
International Nuclear Information System (INIS)
Barbón, José L.F.; Rabinovici, Eliezer
2016-01-01
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
Metric dimensional reduction at singularities with implications to Quantum Gravity
Stoica, Ovidiu Cristinel
2014-08-01
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity.
Belinski, Vladimir
2018-01-01
Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter
2007-01-01
We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....
Light-like big bang singularities in string and matrix theories
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg
2011-01-01
Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.
SIAM symposium on control problems in industry
Energy Technology Data Exchange (ETDEWEB)
NONE
1994-12-31
This symposium focused on industrial control applications that have benefited from recent mathematical and technological developments. The themes featured included: applications of control techniques in aerospace industry, automotive industry, environmental sciences, manufacturing processes, and petroleum industry; optimal shape design in aerospace applications; optimal design of micro-optics; robust control and H-infinity methods.
Take control of font problems in Leopard
Zardetto, Sharon
2009-01-01
Are you suffering from mysterious font problems using Microsoft Office, the Adobe Creative Suite, or other programs in Mac OS X Leopard? Help is at hand, with troubleshooting steps and real-world advice that help you solve problems fast. If you've experienced seemingly inexplicable trouble with characters displaying incorrectly, being unable to type a particular character, fonts missing from Font menus, Font Book crashing, or Character Palette misbehaving, turn to font expert Sharon Zardetto for help. Read this ebook to find the answers to questions such as: Where do fonts belong on my hard
Cosmological models without singularities
International Nuclear Information System (INIS)
Petry, W.
1981-01-01
A previously studied theory of gravitation in flat space-time is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models there exist at the beginning of the universe-in contrast to Einstein's theory-very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal to zero and cosmological constant ALPHA >= O. (author)
Plane waves with weak singularities
International Nuclear Information System (INIS)
David, Justin R.
2003-03-01
We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)
3rd Singularity Theory Meeting of Northeast region & the Brazil-Mexico 2nd Meeting on Singularities
Neto, Aurélio; Mond, David; Saia, Marcelo; Snoussi, Jawad; BMMS 2/NBMS 3; ENSINO; Singularities and foliations geometry, topology and applications
2018-01-01
This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.
Residues and duality for singularity categories of isolated Gorenstein singularities
Murfet, Daniel
2009-01-01
We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.
Spectral asymptotics for nonsmooth singular Green operators
DEFF Research Database (Denmark)
Grubb, Gerd
2014-01-01
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain Ω ⊂ ℝ n , and more generally they appear in the calculus of pseudodifferential boundary problems. In particular, the boundary term in a Krein resolvent formula...... is a singular Green operator. It is well-known in smooth cases that when G is of negative order −t on a bounded domain, its eigenvalues ors-numbers have the behavior (*)s j (G) ∼ cj −t/(n−1) for j → ∞, governed by the boundary dimension n − 1. In some nonsmooth cases, upper estimates (**)s j (G) ≤ Cj −t/(n−1...
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
Study of space shuttle environmental control and life support problems
Dibble, K. P.; Riley, F. E.
1971-01-01
Four problem areas were treated: (1) cargo module environmental control and life support systems; (2) space shuttle/space station interfaces; (3) thermal control considerations for payloads; and (4) feasibility of improving system reusability.
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of `effective naked singularities', which will be quite helpful because general relativity has ...
String theory and cosmological singularities
Indian Academy of Sciences (India)
recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches. Keywords. String theory; cosmological singularities. PACS Nos 11.25.
A hybrid iterative scheme for optimal control problems governed by ...
African Journals Online (AJOL)
A hybrid iterative scheme for optimal control problems governed by some Fredholm Integral Equations. ... Global Journal of Mathematical Sciences ... based on hybrid of perturbation and parametrization methods for obtaining approximate solutions of optimal control problems governed by some Fredholm integral equations.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Statistical analysis of effective singular values in matrix rank determination
Konstantinides, Konstantinos; Yao, Kung
1988-01-01
A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.
Geometric singular perturbation analysis of systems with friction
DEFF Research Database (Denmark)
Bossolini, Elena
This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter...... use a Poincaré compactiﬁcation to study the system near inﬁnity. At inﬁnity, the critical manifold loses hyperbolicity with an exponential rate. We use an adaptation of the blow-up method to recover the hyperbolicity. This enables the identiﬁcation of a new attracting manifold, that organises...... singular, in contrast to the regular stiction solutions that are forward unique. In order to further the understanding of the non-unique dynamics, we introduce a regularization of the model. This gives a singularly perturbed problem that captures the main features of the original discontinuous problem. We...
Singularities of robot mechanisms numerical computation and avoidance path planning
Bohigas, Oriol; Ros, Lluís
2017-01-01
This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves...
Complex collaborative problem-solving processes in mission control.
Fiore, Stephen M; Wiltshire, Travis J; Oglesby, James M; O'Keefe, William S; Salas, Eduardo
2014-04-01
NASA's Mission Control Center (MCC) is responsible for control of the International Space Station (ISS), which includes responding to problems that obstruct the functioning of the ISS and that may pose a threat to the health and well-being of the flight crew. These problems are often complex, requiring individuals, teams, and multiteam systems, to work collaboratively. Research is warranted to examine individual and collaborative problem-solving processes in this context. Specifically, focus is placed on how Mission Control personnel-each with their own skills and responsibilities-exchange information to gain a shared understanding of the problem. The Macrocognition in Teams Model describes the processes that individuals and teams undertake in order to solve problems and may be applicable to Mission Control teams. Semistructured interviews centering on a recent complex problem were conducted with seven MCC professionals. In order to assess collaborative problem-solving processes in MCC with those predicted by the Macrocognition in Teams Model, a coding scheme was developed to analyze the interview transcriptions. Findings are supported with excerpts from participant transcriptions and suggest that team knowledge-building processes accounted for approximately 50% of all coded data and are essential for successful collaborative problem solving in mission control. Support for the internalized and externalized team knowledge was also found (19% and 20%, respectively). The Macrocognition in Teams Model was shown to be a useful depiction of collaborative problem solving in mission control and further research with this as a guiding framework is warranted.
Control and Alcohol-Problem Recognition among College Students
Simons, Raluca M.; Hahn, Austin M.; Simons, Jeffrey S.; Gaster, Sam
2015-01-01
Objective: This study examined negative control (ie, perceived lack of control over life outcomes) and need for control as predictors of alcohol-problem recognition, evaluations (good/bad), and expectancies (likely/unlikely) among college students. The study also explored the interaction between the need for control and alcohol consumption in…
Transcendental smallness in singularly perturbed equations of volterra type
International Nuclear Information System (INIS)
Bijura, Angelina M.
2003-11-01
The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important. (author)
Wave-breaking and generic singularities of nonlinear hyperbolic equations
International Nuclear Information System (INIS)
Pomeau, Yves; Le Berre, Martine; Guyenne, Philippe; Grilli, Stephan
2008-01-01
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behaviour of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the numerical results. This shows the power of the analysis by methods using generic concepts of nonlinear science. (open problem)
Resonance scattering and singularities of the scattering function
Energy Technology Data Exchange (ETDEWEB)
Heiss, W.D. [National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch (South Africa); Nazmitdinov, R.G. [Department de Fisica, Universitat de les Illes Balears, Palma de Mallorca (Spain); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation)
2010-05-15
Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel. (authors)
Self-reported impulsivity and inhibitory control in problem gamblers.
Lorains, Felicity K; Stout, Julie C; Bradshaw, John L; Dowling, Nicki A; Enticott, Peter G
2014-01-01
Impulsivity is considered a core feature of problem gambling; however, self-reported impulsivity and inhibitory control may reflect disparate constructs. We examined self-reported impulsivity and inhibitory control in 39 treatment-seeking problem gamblers and 41 matched controls using a range of self-report questionnaires and laboratory inhibitory control tasks. We also investigated differences between treatment-seeking problem gamblers who prefer strategic (e.g., sports betting) and nonstrategic (e.g., electronic gaming machines) gambling activities. Treatment-seeking problem gamblers demonstrated elevated self-reported impulsivity, more go errors on the Stop Signal Task, and a lower gap score on the Random Number Generation task than matched controls. However, overall we did not find strong evidence that treatment-seeking problem gamblers are more impulsive on laboratory inhibitory control measures. Furthermore, strategic and nonstrategic problem gamblers did not differ from their respective controls on either self-reported impulsivity questionnaires or laboratory inhibitory control measures. Contrary to expectations, our results suggest that inhibitory dyscontrol may not be a key component for some treatment-seeking problem gamblers.
Turnpike theory of continuous-time linear optimal control problems
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...
On some control problems of dynamic of reactor
Baskakov, A. V.; Volkov, N. P.
2017-12-01
The paper analyzes controllability of the transient processes in some problems of nuclear reactor dynamics. In this case, the mathematical model of nuclear reactor dynamics is described by a system of integro-differential equations consisting of the non-stationary anisotropic multi-velocity kinetic equation of neutron transport and the balance equation of delayed neutrons. The paper defines the formulation of the linear problem on control of transient processes in nuclear reactors with application of spatially distributed actions on internal neutron sources, and the formulation of the nonlinear problems on control of transient processes with application of spatially distributed actions on the neutron absorption coefficient and the neutron scattering indicatrix. The required control actions depend on the spatial and velocity coordinates. The theorems on existence and uniqueness of these control actions are proved in the paper. To do this, the control problems mentioned above are reduced to equivalent systems of integral equations. Existence and uniqueness of the solution for this system of integral equations is proved by the method of successive approximations, which makes it possible to construct an iterative scheme for numerical analyses of transient processes in a given nuclear reactor with application of the developed mathematical model. Sufficient conditions for controllability of transient processes are also obtained. In conclusion, a connection is made between the control problems and the observation problems, which, by to the given information, allow us to reconstruct either the function of internal neutron sources, or the neutron absorption coefficient, or the neutron scattering indicatrix....
Study of control problems for the stationary MHD equations
Brizitskii, R. V.
2017-10-01
The optimal control problems for the stationary magnetohydrodynamic equations under inhomogeneous mixed boundary conditions for a magnetic field are considered. The role of control in control xs under study is played by normal component of the magnetic field on the part of the boundary. In the capacity of cost fucntionals quadratic tracking–type functionals for a velocity, magnetic field or pressure are taken.
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points....... For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of on-linear equations, for the determination for the equilibrium strategy as well as the equilibrium value function. All known...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
Novel Spreadsheet Direct Method for Optimal Control Problems
Directory of Open Access Journals (Sweden)
Chahid Kamel Ghaddar
2018-01-01
Full Text Available We devise a simple yet highly effective technique for solving general optimal control problems in Excel spreadsheets. The technique exploits Excel’s native nonlinear programming (NLP Solver Command, in conjunction with two calculus worksheet functions, namely, an initial value problem solver and a discrete data integrator, in a direct solution paradigm adapted to the spreadsheet. The technique is tested on several highly nonlinear constrained multivariable control problems with remarkable results in terms of reliability, consistency with pseudo-spectral reported answers, and computing times in the order of seconds. The technique requires no more than defining a few analogous formulas to the problem mathematical equations using basic spreadsheet operations, and no programming skills are needed. It introduces an alternative, simpler tool for solving optimal control problems in social and natural science disciplines.
Cirant, Marco
2016-11-22
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Higher-Order Generalized Invexity in Control Problems
Directory of Open Access Journals (Sweden)
S. K. Padhan
2011-01-01
Full Text Available We introduce a higher-order duality (Mangasarian type and Mond-Weir type for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality are derived for these pair of problems. Also, we establish few examples in support of our investigation.
hp-finite element methods for singular perturbations
Melenk, Jens M
2002-01-01
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Analysis of convergence for control problems governed by evolution ...
African Journals Online (AJOL)
The convergence of a scheme to minimize a class of a system of continuous optimal control problems characterized by a system of evolution equations and a system of linear inequality and equality constraints with multiplier imbedding is considered. The result is applied to some problems and the scheme is found to exhibit ...
Schoenfeld's problem solving theory in a student controlled learning environment
Harskamp, E.; Suhre, C.
2007-01-01
This paper evaluates the effectiveness of a student controlled computer program for high school mathematics based on instruction principles derived from Schoenfeld's theory of problem solving. The computer program allows students to choose problems and to make use of hints during different episodes
Efficient differential evolution algorithms for multimodal optmal control problems
Lopez Cruz, I.L.; Willigenburg, van L.G.; Straten, van G.
2003-01-01
Many methods for solving optimal control problems, whether direct or indirect, rely upon gradient information and therefore may converge to a local optimum. Global optimisation methods like Evolutionary algorithms, overcome this problem. In this work it is investigated how well novel and easy to
Singular traces theory and applications
Sukochev, Fedor; Zanin, Dmitriy
2012-01-01
This text is the first complete study and monograph dedicated to singular traces. For mathematical readers the text offers, due to Nigel Kalton's contribution, a complete theory of traces on symmetrically normed ideals of compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and the deeper mathematical features of singular traces. An application section explores the consequences of these features, which previously were not discussed in general texts on noncommutative geometry.
[Problems of the ectoparasite control in the Mongolian People's Republic].
Ribbeck, R; Splisteser, H; Rauch, H; Hiepe, T
1979-11-01
The co-operation between G.D.R. and M.P.R. in the field of control of ectoparasites in farm animals is described. The problems under the specific conditions of the M.P.R. in the control of the principal parasitoses of economic importance such as hypodermosis, mange, tick infestations, oestrosis, vermipsyllosis, gasterophilosis and wohlfahrtiosis are analysed. The successfully applied hypodermosis control program represents the base for further systematic, state-directed strategic measures in controlling of ectoparasitoses.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
Local and nonlocal space-time singularities
International Nuclear Information System (INIS)
Konstantinov, M.Yu.
1985-01-01
The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established
Method of quadrotor flight control in the target tracking problem
Kotov, K. Yu.; Nesterov, A. A.; Filippov, M. N.; Yan, A. P.
2017-07-01
A problem of control of trajectory motion of a quadrotor vehicle is considered. The choice of the form of required differential equations in the previously proposed method of tracking of a moving target is justified. The workability of the control system in the presence of measurement noise and external perturbations is confirmed by results of experiments with the AR.Drone quadrotor.
ON THE OPTIMAL CONTROL OF A PROBLEM OF ENVIRONMENTAL POLLUTION
Directory of Open Access Journals (Sweden)
José Dávalos Chuquipoma
2016-06-01
Full Text Available This article is studied the optimal control of distributed parameter systems applied to an environmental pollution problem. The model consists of a differential equation partial parabolic modeling of a pollutant transport in a fluid. The model is considered the speed with which the pollutant spreads in the environment and degradation that suffers the contaminant by the presence of a factor biological inhibitor, which breaks the contaminant at a rate that is not dependent on space and time. Using the method of Lagrange multipliers is possible to prove the existence solving the problem of control and obtaining optimality conditions for optimal control.
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Problems of Mathematical Finance by Stochastic Control Methods
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Dissipative Control Systems and Disturbance Attenuation for Nonlinear H∞ Problems
International Nuclear Information System (INIS)
Frankowska, H.; Quincampoix, M.
1999-01-01
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H ∞ problem from contingent formulation of Isaacs' equation
Behavioral Problems in Iranian Epileptic Children; A Case Control Study
Directory of Open Access Journals (Sweden)
Maryam Aludari
2017-12-01
Full Text Available Background Epilepsy is among the most common neurological disorders in childhood, prevalence of which is increasing. Unpredictable and chronic nature of the disease affects physical, social and mental functions of the children and their family. This study was aimed to compare behavioral problems in epileptic children group versus healthy control group. Materials and Methods This study is a case-control one conducted from January 2013 to June 2016 in Tehran, Iran. The epileptic children in age of 7-10 years old that were diagnosed by neurologist referred to the researcher for further process. Their parents were provided with Child Behavior Checklist (CBCL to be completed. For matching by age and gender, the healthy group was sampled after the epilepsy group. Multivariate Analysis of Variance was used for statistical analysis. Results In this study 94 children with epilepsy and 83 healthy children in age of 7-10 years old were studied. The results indicated that there were significantly higher behavioral problems in the children with epilepsy than in control group in nine categories of seclusiveness, physical complaints, anxiety and depression, social problems, thought problems, attention problems, delinquent behaviors, aggressive behaviors, and other problems. Comparison of two generalized and partial epilepsy groups indicated that there was a significant difference only in attention problems (p = 0.024. Conclusion The present study indicates that the children with epilepsy have more behavioral problems as compared to control group. Therefore, educational and psychological interventions are necessary for supporting desirable psychosocial growth and development of such children.
Controlled neural network application in track-match problem
International Nuclear Information System (INIS)
Baginyan, S.A.; Ososkov, G.A.
1993-01-01
Track-match problem of high energy physics (HEP) data handling is formulated in terms of incidence matrices. The corresponding Hopfield neural network is developed to solve this type of constraint satisfaction problems (CSP). A special concept of the controlled neural network is proposed as a basis of an algorithm for the effective CSP solution. Results of comparable calculations show the very high performance of this algorithm against conventional search procedures. 8 refs.; 1 fig.; 1 tab
Clifford wavelets, singular integrals, and Hardy spaces
Mitrea, Marius
1994-01-01
The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.
Propagation of singularities for linearised hybrid data impedance tomography
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2018-02-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.
Brane singularities and their avoidance
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros; Klaoudatou, Ifigeneia
2010-01-01
The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state P = γρ between the 'pressure' P and the 'density' ρ, our results depend crucially on the constant fluid parameter γ. (i) For γ > -1/2, the flat brane solution suffers from a collapse singularity at a finite distance that disappears in the curved case. (ii) For γ < -1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1 < γ ≤ -1/2, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.
The problem of the driverless vehicle specified path stability control
Buznikov, S. E.; Endachev, D. V.; Elkin, D. S.; Strukov, V. O.
2018-02-01
Currently the effort of many leading foreign companies is focused on creation of driverless transport for transportation of cargo and passengers. Among many practical problems arising while creating driverless vehicles, the problem of the specified path stability control occupies a central place. The purpose of this paper is formalization of the problem in question in terms of the quadratic functional of the control quality, the comparative analysis of the possible solutions and justification of the choice of the optimum technical solution. As square value of the integral of the deviation from the specified path is proposed as the quadratic functional of the control quality. For generation of the set of software and hardware solution variants the Zwicky “morphological box” method is used within the hardware and software environments. The heading control algorithms use the wheel steering angle data and the deviation from the lane centerline (specified path) calculated based on the navigation data and the data from the video system. Where the video system does not detect the road marking, the control is carried out based on the wheel navigation system data and where recognizable road marking exits - based on to the video system data. The analysis of the test results allows making the conclusion that the application of the combined navigation system algorithms that provide quasi-optimum solution of the problem while meeting the strict functional limits for the technical and economic indicators of the driverless vehicle control system under development is effective.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains
Kogut, Peter I
2011-01-01
In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu
Impulse control in Kalman-like filtering problems
Directory of Open Access Journals (Sweden)
Michael V. Basin
1998-01-01
Full Text Available This paper develops the impulse control approach to the observation process in Kalman-like filtering problems, which is based on impulsive modeling of the transition matrix in an observation equation. The impulse control generates the jumps of the estimate variance from its current position down to zero and, as a result, enables us to obtain the filtering equations for the Kalman estimate with zero variance for all post-jump time moments. The filtering equations for the estimates with zero variances are obtained in the conventional linear filtering problem and in the case of scalar nonlinear state and nonlinear observation equations.
Sensitivity problems of control system of coal preparation processes
Directory of Open Access Journals (Sweden)
Kaula Roman
2016-01-01
Full Text Available Control of technological processes of coal preparation takes place in the presence of wide disturbances. An important problem is the choice of the controller which is robust for a variety of disturbances. No less important problem in the control process is the tuning of the controller parameters. In the paper the analysis of influence of changes in object model parameters on the course of the controlled value was carried out. For the controller settings, calculated according to model parameters research was carried out on object with other values of parameters. In the studies a sensitivity analysis method was used. The sensitivity analysis for the three methods of tuning PI controller for control systems of coal preparation processes characterized by dynamic properties of the inertial element with time delay was presented. Considerations were performed at various parameters of the object on the basis of the response of the control system for a constant value of the set point. The assessment of the considered tuning methods based on selected indices of control quality was realized.
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
International Nuclear Information System (INIS)
Chen, Yu-Zhu; Li, Wen-Du; Dai, Wu-Sheng
2017-01-01
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
Energy Technology Data Exchange (ETDEWEB)
Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)
2017-12-15
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Singularity Theory and its Applications
Stewart, Ian; Mond, David; Montaldi, James
1991-01-01
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.
Ambient cosmology and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Numerical methods for optimal control problems with state constraints
Pytlak, Radosław
1999-01-01
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
published to study the control problems of nonlinear parabolic equations, for example. [18, 19, 21–24]. ... The extension operator B ∈ L (L2(Q0), L2(0,T ; H)) which is called the controller is introduced as. Bq = { ..... It is well known that the optimality conditions for w is given by the variational inequality. J′(u, w)(v − w) ≥ 0, ...
On The Algorithm for Dynamic Restoring Control Problems with ...
African Journals Online (AJOL)
An algorithm is hereby developed to solve a class of control problems constrained by dynamic restoring type with matrix coefficients numerically. The penalty-multiplier method is evolved to obtain an unconstrained discretized formulation. With the bilinear form expression, an associated operator is constructed via a theorem ...
Problems of Controlled Vocabulary versus Uncontrolled Vocabulary in Subject Indexing
Chao-chen Chen
1998-01-01
This article is mainly to survey the centennial controversy between controlled vocabulary v. uncontrolled vocabulary of subject indexing in the western library and information society. We also discuss the related problems in Chinese information retrieval systems and analyze the factors affecting their performance. [Article content in Chinese
Problems of Controlled Vocabulary versus Uncontrolled Vocabulary in Subject Indexing
Directory of Open Access Journals (Sweden)
Chao-chen Chen
1998-12-01
Full Text Available This article is mainly to survey the centennial controversy between controlled vocabulary v. uncontrolled vocabulary of subject indexing in the western library and information society. We also discuss the related problems in Chinese information retrieval systems and analyze the factors affecting their performance. [Article content in Chinese
Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Directory of Open Access Journals (Sweden)
Li Chen
2012-01-01
stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
SOME PROBLEMS OF AUTOMATIC CONTROL OF DEFECTS OF GLASSWORKS
Directory of Open Access Journals (Sweden)
Rozhkov S.A.
2006-04-01
Full Text Available It is performed analysis of existing systems for checking a quality of glass products with reference to problems of automation of checking of quality of finished products. There are brought results of experimental studies of the model of the system for quality control with the optical sensor.
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
We propose the concept of 'effective naked singularities', which will be quite helpful ... If a pressure gradient force is not sufficiently strong, a body can continue collapsing due to its self-gravity. This phenomenon is called gravitational collapse. .... approaches a self-similar solution, which is called a critical solution, and then it.
Interval matrices: Regularity generates singularity
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří; Shary, S.P.
2018-01-01
Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Abstract. Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of ...
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...
String theory and cosmological singularities
Indian Academy of Sciences (India)
of space and time needs revision near these singularities where quantum effects of gravity become important, it is still not clear what structure could replace space ..... The dimensionful parameter μ is a Lagrange multiplier which ensures that the total number of eigenvalues is fixed. 98. Pramana – J. Phys., Vol. 69, No. 1, July ...
Travelling wave solutions for a singularly perturbed Burgers–KdV ...
Indian Academy of Sciences (India)
Abstract. This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, ...
Removability of singularity for nonlinear elliptic equations with p(x-growth
Directory of Open Access Journals (Sweden)
Yongqiang Fu
2013-09-01
Full Text Available Using Moser's iteration method, we investigate the problem of removable isolated singularities for elliptic equations with p(x-type nonstandard growth. We give a sufficient condition for removability of singularity for the equations in the framework of variable exponent Sobolev spaces.
Removability of singularity for nonlinear elliptic equations with p(x)-growth
Yongqiang Fu; Yingying Shan
2013-01-01
Using Moser's iteration method, we investigate the problem of removable isolated singularities for elliptic equations with p(x)-type nonstandard growth. We give a sufficient condition for removability of singularity for the equations in the framework of variable exponent Sobolev spaces.
THE RIS K OF EDUCATIONAL SINGULARITY RISE: TENDENCIES AND THE FEASIBLE CONSEQUENCES
Directory of Open Access Journals (Sweden)
Yu. V. Voronenko
2013-05-01
Full Text Available There are considered the peculiarities of transition of the system of education from industrial to postindustrial model (informational society. Expert conclusions about the risks of technological and informative singularity are analysed. The prevention problems of technological and informative singularity on the base of newest technologies development, in particular post-graduate medical education are discussed.
Travelling wave solutions for a singularly perturbed Burgers–KdV ...
Indian Academy of Sciences (India)
This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...
Finite element solution of optimal control problems with state-control inequality constraints
Bless, Robert R.; Hodges, Dewey H.
1992-01-01
It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.
Remarks on gauge variables and singular Lagrangians
International Nuclear Information System (INIS)
Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.
1977-01-01
The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 2. Positive Solutions for Higher Order Singular -Laplacian Boundary Value Problems. Guoliang Shi Junhong Zhang ... Guoliang Shi1 Junhong Zhang1. Department of Mathematics, Tianjin University, Tianjin 300072, People's Republic of China ...
Slowly growing solutions of singular linear functional differential systems
Czech Academy of Sciences Publication Activity Database
Pylypenko, V.; Rontó, András
2012-01-01
Roč. 285, 5-6 (2012), s. 727-743 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : functional differential equation * singular Cauchy problem * slowly growing solution Subject RIV: BA - General Mathematics Impact factor: 0.576, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/ mana .201000014/abstract
Fourth order compact finite difference method for solving singularly ...
African Journals Online (AJOL)
A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...
New singularities in nonrelativistic coupled channel scattering. II. Fourth order
International Nuclear Information System (INIS)
Khuri, N.N.; Tsun Wu, T.
1997-01-01
We consider a two-channel nonrelativistic potential scattering problem, and study perturbation theory in fourth order for the forward amplitude. The main result is that the new singularity demonstrated in second order in the preceding paper I also occurs at the same point in fourth order. Its strength is again that of a pole. copyright 1997 The American Physical Society
Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...
African Journals Online (AJOL)
A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...
Singularities and Conjugate Points in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a theorem that when a non-comoving, non-spacelike geodesic in a
Identity and singularity: Metastability and morphogenesis in light of Deleuze
Directory of Open Access Journals (Sweden)
Barison Marcello
2015-01-01
Full Text Available The question of life is inextricably connected with the problem of identification and with the fact that each identification process includes the acquisition of a form. Nevertheless, it appears that at the biological level, that is, for what concerns a morphogenetic description of the status of the living being, the term singularity comes into play right there where you would expect to get into the notion of identity. According to Christian De Duve, the organic form has no identity, but it expresses - and is an expression of - a singularity. Given these observations, this is the object of the paper: to explain in a clear and consistent way how these terms - namely identity and singularity - differ and whether it is possible to ground their distinction in a coherent theoretical manner.
Uniqueness for the inverse backscattering problem for angularly controlled potentials
International Nuclear Information System (INIS)
Rakesh; Uhlmann, Gunther
2014-01-01
We consider the problem of recovering a smooth, compactly supported potential on R 3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives, then the two potentials are identical. In particular, if two potentials differ by a finite linear combination of spherical harmonics with radial coefficients and have the same backscattering data then the two potentials are identical. (paper)
On psichological problem of NPP operation and control
International Nuclear Information System (INIS)
Mashin, V.A.
1994-01-01
The role of psichological factor as a reserve for increasing NPP safety connected with human factor is discussed. It is emphasized that the process of NPP personnel professional training should not be restricted by formation of a certain set of knowledge, skills and experience. It is necessary to initiate ability for constant self-developing. Control for assurance of effective interaction of the whole NPP personnel is an important problem
Problems of rodent control in rural tropical areas.
Barnes, A M
1975-01-01
Rodent control strategies, techniques, and research needs in rural tropical environments are reviewed and discussed with special reference to Mastomys natalensis, the possible reservoir of Lassa fever in West Africa.Public health rodent problems are far more serious and widespread in rural tropical areas than in developed countries. In the latter, only the commensal rodents constitute a major problem, whereas in rural tropical areas, native semidomestic species also serve as disease reservoirs and sources of infection to man. The success of rodent control programmes in developed countries depends in large part on the willingness and ability of people and governments to spend relatively large sums on research and control, on an acquired intolerance of people to rats and disease, and on a substantial economic base. These prerequisites are not usually to be found in rural tropical areas. Consequently, the rodent control techniques and programme organizations of developed countries are not directly applicable to such areas, even though the principles are the same. For this reason, it is suggested that a well-funded, integrated research and control programme should be undertaken in a known Lassa fever area, stressing public education, personnel training, and environmental management as well as rodenticidal approaches.
Laplacian growth, elliptic growth, and singularities of the Schwarz potential
Lundberg, Erik
2011-04-01
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or 'Hele-Shaw') problem in the plane. The guiding principle in this connection is the fact that 'non-physical' singularities in the 'oil domain' of the Schwarz function are stationary, and the 'physical' singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by Khavinson and Shapiro (1989 Technical Report TRITA-MAT-1989-36 Royal Institute of Technology, Stockholm). An extension is also given for the so-called elliptic growth problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how {C}^n-techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing 'globalizing families'.
Laplacian growth, elliptic growth, and singularities of the Schwarz potential
International Nuclear Information System (INIS)
Lundberg, Erik
2011-01-01
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or 'Hele-Shaw') problem in the plane. The guiding principle in this connection is the fact that 'non-physical' singularities in the 'oil domain' of the Schwarz function are stationary, and the 'physical' singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by Khavinson and Shapiro (1989 Technical Report TRITA-MAT-1989-36 Royal Institute of Technology, Stockholm). An extension is also given for the so-called elliptic growth problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how C n -techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing 'globalizing families'.
Singularities formation, structure, and propagation
Eggers, J
2015-01-01
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Historical developments in singular perturbations
O'Malley, Robert E
2014-01-01
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Energy conditions and spacetime singularities
International Nuclear Information System (INIS)
Tipler, F.J.
1978-01-01
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstra......This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Fundamental solutions of singular SPDEs
Energy Technology Data Exchange (ETDEWEB)
Selesi, Dora, E-mail: dora@dmi.uns.ac.rs [Department of Mathematics and Informatics, University of Novi Sad (Serbia)
2011-07-15
Highlights: > Fundamental solutions of linear SPDEs are constructed. > Wick-convolution product is introduced for the first time. > Fourier transformation maps Wick-convolution into Wick product. > Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. > Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P({omega}, D) Lozenge u(x, {omega}) = A(x, {omega}) are considered, where A is a singular generalized stochastic process and P({omega}, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A Lozenge I{sup Lozenge (-1)}, where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.
Why the Singularity Cannot Happen
Modis, Theodore
2012-01-01
The concept of a Singularity as described in Ray Kurzweil's book cannot happen for a number of reasons. One reason is that all natural growth processes that follow exponential patterns eventually reveal themselves to be following S-curves thus excluding runaway situations. The remaining growth potential from Kurzweil's ''knee'', which could be approximated as the moment when an S-curve pattern begins deviating from the corresponding exponential, is a factor of only one order of magnitude grea...
Fundamental solutions of singular SPDEs
International Nuclear Information System (INIS)
Selesi, Dora
2011-01-01
Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
Pfister, Gerhard; Schulze, Mathias
2017-01-01
This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra. Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists. The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
Flavour from partially resolved singularities
Energy Technology Data Exchange (ETDEWEB)
Bonelli, G. [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy)]. E-mail: bonelli@sissa.it; Bonora, L. [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy); Ricco, A. [International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Beirut 2-4, 34014 Trieste (Italy)
2006-06-15
In this Letter we study topological open string field theory on D-branes in a IIB background given by non-compact CY geometries O(n)-bar O(-2-n) on P{sup 1} with a singular point at which an extra fiber sits. We wrap N D5-branes on P{sup 1} and M effective D3-branes at singular points, which are actually D5-branes wrapped on a shrinking cycle. We calculate the holomorphic Chern-Simons partition function for the above models in a deformed complex structure and find that it reduces to multi-matrix models with flavour. These are the matrix models whose resolvents have been shown to satisfy the generalized Konishi anomaly equations with flavour. In the n=0 case, corresponding to a partial resolution of the A{sub 2} singularity, the quantum superpotential in the N=1 unitary SYM with one adjoint and M fundamentals is obtained. The n=1 case is also studied and shown to give rise to two-matrix models which for a particular set of couplings can be exactly solved. We explicitly show how to solve such a class of models by a quantum equation of motion technique.
PID controller tuning using metaheuristic optimization algorithms for benchmark problems
Gholap, Vishal; Naik Dessai, Chaitali; Bagyaveereswaran, V.
2017-11-01
This paper contributes to find the optimal PID controller parameters using particle swarm optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm. The algorithms were developed through simulation of chemical process and electrical system and the PID controller is tuned. Here, two different fitness functions such as Integral Time Absolute Error and Time domain Specifications were chosen and applied on PSO, GA and SA while tuning the controller. The proposed Algorithms are implemented on two benchmark problems of coupled tank system and DC motor. Finally, comparative study has been done with different algorithms based on best cost, number of iterations and different objective functions. The closed loop process response for each set of tuned parameters is plotted for each system with each fitness function.
Teamwork and problem solving in the control room
International Nuclear Information System (INIS)
Nygard, F.I.; Dedon, J.M.; Fuld, R.B.
1989-01-01
The importance of teamwork and communications in the control room of a nuclear power plant has been the subject of significant attention during the 10 yr since the Three Mile Island accident. The ability to conduct effective problem solving, especially under unexpected conditions, requires that the control room crew be well trained in techniques that produce synergism and avoid ambiguous or conflicting interactions. This paper describes the foundations of a training program developed and conducted by Combustion Engineering to produce a winning team in the control room. The complete licensed operations staffs of three utilities, Florida Power ampersand Light, Louisiana Power ampersand Light, and Omaha Public Power District, have completed this program. Thus, the results of the experience of ∼150 licensed operators is reported
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
(1.4). The singular or nonsingular fourth-order boundary value problems (1.4) have been exten- sively studied by many authors [1,2,6,7,10,13–15]. Shi and Chen [10,11] gave the sufficient and necessary conditions for the existence of positive solutions to superlinear problem (1.4) by the fixed point theorem in cones when 1 ...
Günüşen, Neslihan Partlak; Serçekuş, Pınar; Edeer, Aylin Durmaz
2014-06-01
The purpose of this study is to compare the locus of control and problem-solving skills of nursing students studying with the problem-based learning method with those of nursing students studying with the traditional method. This is a descriptive and comparative study. For data collection, the Problem-Solving Skills Inventory and the Locus of Control Scale were used. The study sample included 680 nursing students. It was determined that the problem-based learning method was more effective in the development of problem-solving skills and internal locus of control than was the traditional method. © 2014 NANDA International.
Mayer control problem with probabilistic uncertainty on initial positions
Marigonda, Antonio; Quincampoix, Marc
2018-03-01
In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on Rn endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on Rd and by a vector-valued measure on Rd, respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton-Jacobi-Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
where zd ∈ S is a desired state and δ > 0 is fixed. An optimal control problem about the extended Fisher–Kolmogorov equation is min J (u, w),. (3.3) where (u, w) satisfies (3.1). Let X = W(0,T ; V ) × L2(Q0) and Y = L2(0,T ; V ) × H. We define an operator e = e(e1,e2) : X → Y, where e1 = (2)−1(ut + k2u − u + u3 − u − Bw) and.
Experience with control valve cavitation problems and their solutions
International Nuclear Information System (INIS)
Ozol, J.
1988-01-01
Pressure reduction in control valves can induce cavitation, which has three effects on the control valve. Firstly, it modifies or changes the hydraulic performance of the control valve. Since control valves are designed for noncavitating conditions, the result is usually reduced stability of the control valve or, in extreme cavitating conditions known as supercavitation, the valve may limit the flow rate and thus be undersized. Secondly, cavitation can cause material damage to valve parts, trim, or valve body, or erodes downstream piping; consequently, the valve or piping leaks. Thirdly, cavitation causes noise and vibration, which may cause major damage or destruction to equipment such as valve positioners, actuators, pipe supports and sometimes to other downstream valves. The purpose of this paper is twofold: (1) It describes the I.S.A. valve sizing equations and how they relate to cavitation. (2) It describes experiences with these three problems, and discusses corrective actions and practical approaches to their solution. This paper discusses thirteen cavitation experiences
Problems and achievements of cotton (Gossypium Hirsutum L. weeds control
Directory of Open Access Journals (Sweden)
T. Barakova
2017-09-01
Full Text Available Abstract. Weed control in the cultivation of cotton is critical to the yield and quality of production. The influence of economically important weeds was studied. Chemical control is the most effective method of weed control in cotton but much of the information on it relates to primary weed infestation. Problems with primary weed infestation in cotton have been solved to a significant extent. The question of secondary weed infestation with annual and perennial graminaceous weeds during the period of cotton vegetation is also determined largely by the use of antigraminaceous herbicides. The data related to herbicides to effectively control secondary germinated broadleaf weeds in conventional technology for cotton growing are quite scarce, even globally. We are still seeking effective herbicides for control of these weeds in cotton crops. Studies on their influence on the sowing characteristics of cotton seed and the quality of cotton fiber are still insufficient. In the scientific literature there is not enough information on these questions. The combinations of herbicides, as well as their tank mixtures with fertilizers or plant growth regulators are more efficient than autonomous application. Often during their combined application higher synergistic effect on yield is produced. There is information about cotton cultivars resistant to glyphosate. These cultivars are GMO and they are banned within the European Union, including Bulgaria.
On important precursor of singular optics (tutorial)
Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.
2018-01-01
The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].
Lecture notes on mean curvature flow, barriers and singular perturbations
Bellettini, Giovanni
2013-01-01
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
Optimal Control Approaches to the Aggregate Production Planning Problem
Directory of Open Access Journals (Sweden)
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
A technical overview of air pollution problems and its control
International Nuclear Information System (INIS)
Rusheed, A.
1997-01-01
Air pollution is a well known phenomenon experienced in every day life. The air we breathe consist of gases and aerosol particles on which pollutants such as toxic elements and bacteria reside. These microscopic particles are transported to long distances from the source of origin the direction and magnitude of which depends upon the prevailing meteorological conditions. In order to assess the impact of air pollution, systematic studies are carried out which consist of: 1) sampling of air, 2) measurement of pollutants, 3) identification of pollutant source and 4) adoption of control methods. Each of these topics are fairly exhaustive and their understanding requires accurate scientific approach. An overview of these topic has been presented in this talk. Air samples are best collected by filtering air through suitable medium and analyses are carried out by diverse analytical techniques. Source identifications is a very important step which is done either by emission modeling or receptor modeling techniques. A general survey of these techniques, especially receptor modeling is presented in this talk. The control of air pollution is carried out by using carried devices and the processes especially developed for this purpose. Air pollution has given rise to a number of global problems such as depletion of stratospheric ozone, acid rain and greenhouse effect, which are being tackled on international scale. These problems have been discussed very briefly and a summary of international efforts has been presented. (author)
Directory of Open Access Journals (Sweden)
A. S. Koval
2010-01-01
Full Text Available The paper considers problems concerning electromechanical interaction in elevators with an adjustable asynchronous electric drive equipped with the vector control systems under direct torque control and direct torque control with pulse-width modulator. A mathematical description of electromechanical elevator system with due account of nonlinearity of the worm gear is given in the paper. The paper presents a simplified circuit design of a control system with a fuzzy speed controller. It has been established that the factor of electromechanical interaction in electromechanical system with the adjustable asynchronous electric drive and an fuzzy speed controller is within the range which corresponds to existence of the essential electromechanical interaction.
Symmetry generators in singular theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1989-01-01
It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
The geometry of warped product singularities
Stoica, Ovidiu Cristinel
In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
DEKOMPOSISI NILAI SINGULAR PADA SISTEM PENGENALAN WAJAH
Beni Utomo
2012-01-01
Dekomposisi Nilai Singular atau Singular Value Decomposition (SVD)merupakan salah satu cara untuk menyatakan Principal Component Analysis (PCA).PCA sendiri merupakan suatu proses untuk menemukan kontributor-kontributorpenting dari suatu data berdasarkan besaran statistika deviasi standart dan variansi.SVD merupakan proses untuk mendapatkan matriks diagonal yang elementak nolnya merupakan nilai singular yang akarnya merupakan eigenvalue.SVD atas matriks kovarian C berbentuk C = U?V T dengan ma...
Box graphs and singular fibers
International Nuclear Information System (INIS)
Hayashi, Hirotaka; Lawrie, Craig; Morrison, David R.; Schäfer-Nameki, Sakura
2014-01-01
We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E 6 , E 7 and E 8
Spacetime averaging of exotic singularity universes
International Nuclear Information System (INIS)
Dabrowski, Mariusz P.
2011-01-01
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
Diversity Controlling Genetic Algorithm for Order Acceptance and Scheduling Problem
Directory of Open Access Journals (Sweden)
Cheng Chen
2014-01-01
Full Text Available Selection and scheduling are an important topic in production systems. To tackle the order acceptance and scheduling problem on a single machine with release dates, tardiness penalty, and sequence-dependent setup times, in this paper a diversity controlling genetic algorithm (DCGA is proposed, in which a diversified population is maintained during the whole search process through survival selection considering both the fitness and the diversity of individuals. To measure the similarity between individuals, a modified Hamming distance without considering the unaccepted orders in the chromosome is adopted. The proposed DCGA was validated on 1500 benchmark instances with up to 100 orders. Compared with the state-of-the-art algorithms, the experimental results show that DCGA improves the solution quality obtained significantly, in terms of the deviation from upper bound.
Block factorization of step response model predictive control problems
DEFF Research Database (Denmark)
Kufoalor, D. K.M.; Frison, Gianluca; Imsland, L.
2017-01-01
implemented in the HPMPC framework, and the performance is evaluated through simulation studies. The results confirm that a computationally fast controller is achieved, compared to the traditional step response MPC scheme that relies on an explicit prediction formulation. Moreover, the tailored condensing......By introducing a stage-wise prediction formulation that enables the use of highly efficient quadratic programming (QP) solution methods, this paper expands the computational toolbox for solving step response MPC problems. We propose a novel MPC scheme that is able to incorporate step response data...... algorithm exhibits superior performance and produces solution times comparable to that achieved when using a condensing scheme for an equivalent (but much smaller) state-space model derived from first-principles. Implementation aspects necessary for high performance on embedded platforms are discussed...
Using Model Checking for Analyzing Distributed Power Control Problems
DEFF Research Database (Denmark)
Brihaye, Thomas; Jungers, Marc; Lasaulce, Samson
2010-01-01
Model checking (MC) is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control ( PC) problem can be modeled by a timed game between a given transmitter and its environment, the authors...... wanted to know whether this approach can be applied to distributed PC. It turns out that it can be applied successfully and allows one to analyze realistic scenarios including the case of discrete transmit powers and games with incomplete information. The proposed methodology is as follows. We state some...... objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired...
Using Model Checking for Analyzing Distributed Power Control Problems
Directory of Open Access Journals (Sweden)
Thomas Brihaye
2010-01-01
Full Text Available Model checking (MC is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control (PC problem can be modeled by a timed game between a given transmitter and its environment, the authors wanted to know whether this approach can be applied to distributed PC. It turns out that it can be applied successfully and allows one to analyze realistic scenarios including the case of discrete transmit powers and games with incomplete information. The proposed methodology is as follows. We state some objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired properties are verified and determine a winning strategy.
Spectral singularities and zero energy bound states
Energy Technology Data Exchange (ETDEWEB)
Heiss, W.D. [National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch, 7602 Matieland (South Africa); Nazmitdinov, R.G. [Department de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2011-08-15
Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled. (authors)
Wang, S. S.; Choi, I.
1983-01-01
The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be different from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites. Previously announced in STAR as N84-13221
Relaxation periodic solutions of one singular perturbed system with delay
Kashchenko, A. A.
2017-12-01
In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.
Quantum gravity removes classical singularities and shortens the life of black holes
International Nuclear Information System (INIS)
Frolov, V.P.; Vilkovisky, G.A.
1982-01-01
One of the fundamental problems in classical General Relativity is what is to be done with singularities which inevitably arise in the theoretical description of the massive body (or total Universe) collapse. Although the singularities arising as a result of the gravitational collapse are believed to be hidden under event horizons and thus are not visible to an external observer, their very existence means the crisis of the classical gravitational physics. It is generally believed that the proper account of quantum effects may cure this disease. The aim of the present work is to show that it really happens, and quantum gravity does remove classical singularities. (Auth.)
Quantum transitions through cosmological singularities
Energy Technology Data Exchange (ETDEWEB)
Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)
2017-07-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Directory of Open Access Journals (Sweden)
Elvio Alccinelli
2001-07-01
Full Text Available En este artículo pretendemos mostrar que le conjunto de las economías singulares, si bien pequeño desde el punto de vista de la topología y/o desde el punto de vista de la teoría de la medida, tiene importantes efectos en el desarrollo de los regímenes económicos. Es el responsable de los cambios abruptos en los estados de equilibrio y de la multiplicidad de tales estados. Permite además establecer a partir de los tipos de singularidades posibles, una partición del conjunto de economías según tenga lugar uno u otro tipo de singularidad cuya presencia o no, caracteriza el comportamiento posible de la economía en cuestión.
Vector fields on singular varieties
Brasselet, Jean-Paul; Suwa, Tatsuo
2009-01-01
Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
On the singular values decoupling in the Singular Spectrum Analysis of volcanic tremor at Stromboli
Directory of Open Access Journals (Sweden)
R. Carniel
2006-01-01
Full Text Available The well known strombolian activity at Stromboli volcano is occasionally interrupted by rarer episodes of paroxysmal activity which can lead to considerable hazard for Stromboli inhabitants and tourists. On 5 April 2003 a powerful explosion, which can be compared in size with the latest one of 1930, covered with bombs a good part of the normally tourist-accessible summit area. This explosion was not forecasted, although the island was by then effectively monitored by a dense deployment of instruments. After having tackled in a previous paper the problem of highlighting the timescale of preparation of this event, we investigate here the possibility of highlighting precursors in the volcanic tremor continuously recorded by a short period summit seismic station. We show that a promising candidate is found by examining the degree of coupling between successive singular values that result from the Singular Spectrum Analysis of the raw seismic data. We suggest therefore that possible anomalies in the time evolution of this parameter could be indicators of volcano instability to be taken into account e.g. in a bayesian eruptive scenario evaluator. Obviously, further (and possibly forward testing on other cases is needed to confirm the usefulness of this parameter.
Directory of Open Access Journals (Sweden)
Alexander N. Kvitko
2017-01-01
Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.
Cold atoms in singular potentials
International Nuclear Information System (INIS)
Denschlag, J. P.
1998-09-01
We studied both theoretically and experimentally the interaction between cold Li atoms from a magnetic-optical trap (MOT) and a charged or current-carrying wire. With this system, we were able to realize 1/r 2 and 1/r potentials in two dimensions and to observe the motion of cold atoms in both potentials. For an atom in an attractive 1/r 2 potential, there exist no stable trajectories, instead there is a characteristic class of trajectories for which atoms fall into the singularity. We were able to observe this falling of atoms into the center of the potential. Moreover, by probing the singular 1/r 2 potential with atomic clouds of varying size and temperature we extracted scaling properties of the atom-wire interaction. For very cold atoms, and very thin wires the motion of the atoms must be treated quantum mechanically. Here we predict that the absorption cross section for the 1/r 2 potential should exhibit quantum steps. These quantum steps are a manifestation of the quantum mechanical decomposition of plane waves into partial waves. For the second part of this work, we realized a two dimensional 1/r potential for cold atoms. If the potential is attractive, the atoms can be bound and follow Kepler-like orbits around the wire. The motion in the third dimension along the wire is free. We were able to exploit this property and constructed a novel cold atom guide, the 'Kepler guide'. We also demonstrated another type of atom guide (the 'side guide'), by combining the magnetic field of the wire with a homogeneous offset magnetic field. In this case, the atoms are held in a potential 'tube' on the side of the wire. The versatility, simplicity, and scaling properties of this guide make it an interesting technique. (author)
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at ...
Building Reproducible Science with Singularity Containers
CERN. Geneva
2018-01-01
Michael Bauer first began working with containers at GSI national lab in Darmstadt, Germany, in 2017 while taking a semester off of school at the University of Michigan. Michael met Greg Kurtzer, project lead of Singularity, during his time at GSI and he began contributing heavily to the Singularity project. At the start of summer 2017, Greg hired Michael to work at the ...
Singularities in the nonisotropic Boltzmann equation
International Nuclear Information System (INIS)
Garibotti, C.R.; Martiarena, M.L.; Zanette, D.
1987-09-01
We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces...
Reasons for singularity in robot teleoperation
DEFF Research Database (Denmark)
Marhenke, Ilka; Fischer, Kerstin; Savarimuthu, Thiusius Rajeeth
2014-01-01
In this paper, the causes for singularity of a robot arm in teleoperation for robot learning from demonstration are analyzed. Singularity is the alignment of robot joints, which prevents the configuration of the inverse kinematics. Inspired by users' own hypotheses, we investigated speed and delay...
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
in terms of the incompleteness of non-space-like geodesics in spacetime. It is possible that such ... outside. The above discussion does not imply the absence of singularity-free solutions to Einstein's equations. ..... spherical collapse also turns out to be a stable feature as implied by the singularity theorems discussed above.
The Geometry of Black Hole Singularities
Directory of Open Access Journals (Sweden)
Ovidiu Cristinel Stoica
2014-01-01
Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.
Nietzsche, immortality, singularity and eternal recurrence | Olivier ...
African Journals Online (AJOL)
Moreover, once anything has existed, it is in a certain sense, for Nietzsche, necessary despite its temporal singularity. Therefore, to be able to rise to the task of affirming certain actions or experiences in one's own life, bestows on it not merely this kind of necessary singularity, but what he thought of as 'eternal recurrence' –
Debbarma, Sanjoy; Saikia, Lalit Chandra; Sinha, Nidul
2014-03-01
Present work focused on automatic generation control (AGC) of a three unequal area thermal systems considering reheat turbines and appropriate generation rate constraints (GRC). A fractional order (FO) controller named as I(λ)D(µ) controller based on crone approximation is proposed for the first time as an appropriate technique to solve the multi-area AGC problem in power systems. A recently developed metaheuristic algorithm known as firefly algorithm (FA) is used for the simultaneous optimization of the gains and other parameters such as order of integrator (λ) and differentiator (μ) of I(λ)D(µ) controller and governor speed regulation parameters (R). The dynamic responses corresponding to optimized I(λ)D(µ) controller gains, λ, μ, and R are compared with that of classical integer order (IO) controllers such as I, PI and PID controllers. Simulation results show that the proposed I(λ)D(µ) controller provides more improved dynamic responses and outperforms the IO based classical controllers. Further, sensitivity analysis confirms the robustness of the so optimized I(λ)D(µ) controller to wide changes in system loading conditions and size and position of SLP. Proposed controller is also found to have performed well as compared to IO based controllers when SLP takes place simultaneously in any two areas or all the areas. Robustness of the proposed I(λ)D(µ) controller is also tested against system parameter variations. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel
2008-01-01
An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...
Singularity: Scientific containers for mobility of compute.
Directory of Open Access Journals (Sweden)
Gregory M Kurtzer
Full Text Available Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and software engineers and researchers alike, and integrates seamlessly into common workflows for both of these groups. As its primary use case, Singularity brings mobility of computing to both users and HPC centers, providing a secure means to capture and distribute software and compute environments. This ability to create and deploy reproducible environments across these centers, a previously unmet need, makes Singularity a game changing development for computational science.
Biclustering via Sparse Singular Value Decomposition
Lee, Mihee
2010-02-16
Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.
Singularity fitting in hydrodynamical calculations II
International Nuclear Information System (INIS)
Richtmyer, R.D.; Lazarus, R.B.
1975-09-01
This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self-similar solutions for γ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary-value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of γ; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows
Singular perturbation in the physical sciences
Neu, John C
2015-01-01
This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and p...
Grogan, Robert L.
1994-01-01
The feasibility of utilizing a neural network to solve the constrained flight control allocation problem is investigated for the purposes of developing guidelines for the selection of a neural network structure as a function of the control allocation problem parameters. The control allocation problem of finding the combination of several flight controls that generate a desired body axis moment without violating any control constraint is considered. Since the number of controls,...
Distributed Systems for Problems in Robust Control and Visual Tracking
National Research Council Canada - National Science Library
Tannenbaum, Allen
2000-01-01
.... A key application is in controlled active vision, including visual tracking, the control of autonomous vehicles, motion planning, and the utilization of visual information in guidance and control...
32 CFR 1602.22 - Singular and plural.
2010-07-01
....22 Singular and plural. Words importing the singular number shall include the plural number, and words importing the plural number shall include the singular, except where the context clearly indicates...
DEFF Research Database (Denmark)
Wang, W.; Duan, Z.H.; Hanson, Steen Grüner
2006-01-01
By controlling the irradiance of an extended quasimonochromatic, spatially incoherent source, an optical field is generated that exhibits spatial coherence with phase singularities, called coherence vortices. A simple optical geometry for direct visualization of coherence vortices is proposed, an...
Minimal solution for inconsistent singular fuzzy matrix equations
Directory of Open Access Journals (Sweden)
M. Nikuie
2013-10-01
Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.
Han, Lanshan; Camlibel, M. Kanat; Pang, Jong-Shi; Heemels, W. P. Maurice H.
2012-01-01
This paper presents a numerical scheme for solving the continuous-time convex linear-quadratic (LQ) optimal control problem with mixed polyhedral state and control constraints. Unifying a discretization of this optimal control problem as often employed in model predictive control and that obtained
Sutrisno; Widowati; Tjahjana, R. H.
2017-10-01
In this paper, we formulate a hybrid mathematical model of supplier selection problem integrated with inventory control problem of a single product inventory system with piecewise holding cost. This model will be formulated in a piecewise affine (PWA) form that can be converted into mixed logical dynamic (MLD) form. By using this MLD model, we solve the supplier selection problem and control this inventory system so that the stock level tracks a desired level as the reference trajectory as closed as possible with minimal total cost. We use model predictive control for hybrid system to solve the problem. From the numerical experiment results, the optimal supplier was selected at each time period and the evolution of the stock level tracks the desired level well.
Formation of current singularity in a topologically constrained plasma
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Huang, Yi-Min [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China.; Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
2016-02-01
Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.
Singular symmetric functionals and Banach limits with additional invariance properties
International Nuclear Information System (INIS)
Dodds, P G; Pagter, B de; Sedaev, A A; Semenov, E M; Sukochev, F A
2003-01-01
For symmetric spaces of measurable functions on the real half-line, we study the problem of existence of positive linear functionals monotone with respect to the Hardy-Littlewood semi-ordering, the so-called symmetric functionals. Two new wide classes of symmetric spaces are constructed which are distinct from Marcinkiewicz spaces and for which the set of symmetric functionals is non-empty. We consider a new construction of singular symmetric functionals based on the translation-invariance of Banach limits defined on the space of bounded sequences. We prove the existence of Banach limits invariant under the action of the Hardy operator and all dilation operators. This result is used to establish the stability of the new construction of singular symmetric functionals for an important class of generating sequences
Sediment problems in reservoirs. Control of sediment deposits
Energy Technology Data Exchange (ETDEWEB)
Jacobsen, Tom
1997-12-31
When a reservoir is formed on a river, sediment will deposit in the reservoir. Such processes are unfortunate, for instance, for the implementation of hydroelectric energy. This thesis studies the problem of reservoir sedimentation and discusses methods of removing the sediments. Various aspects of reservoir sedimentation are discussed. Anthropogenic impacts seem to greatly affect the erosion processes. Temporal distribution is uneven, mainly because of the very large flood events. A world map showing the Reservoir Capacity: Annual Sediment Inflow ratio for reservoirs with volume equal to 10% of annual inflow has been prepared. The map shows that sedimentation is severe in the western parts of North and South America, eastern, southern and northern Africa, parts of Australia and most of Asia. The development of medium-sized reservoirs is difficult, as they are too large for conventional flushing technique and too small to store the sediment that accumulates during their economic lifetime. A computer model, SSIIM, was used with good results in a case study of two flood drawdown trials in Lake Roxburg, New Zealand. Two techniques have been developed that permits controlled suction of sediment and water into a pipe: the Slotted Pipe Sediment Sluicer (SPSS) and the Saxophone Sediment Sluicer (SSS). The techniques exploit the inflow pattern in through a slot in a pipe. An equation describing this inflow pattern was derived and verified experimentally. The SPSS is fixed near the reservoir bed, and sediment that deposits on top of it is removed in the sluicing process. The SSS sluices sediment from the surface of the sediment deposits. Some technical and economic conditions affecting the economics of sediment removal from reservoirs have been identified and studied. 79 refs., 112 figs., 14 tabs.
Le probleme du controle de la liquidité en France. (The problem of controlling liquidity in France
Directory of Open Access Journals (Sweden)
H. FOURNIER
2014-07-01
Full Text Available The idea of liquidity in France finds expression in more or less the same way as in the other western countries. It is normal practice to distinguish between the “liquidity of the economy” on the one hand, and the “liquidity of the banking system” on the other. The former corresponds to the money supply, while the latter comprises the banks’ holdings of notes and coin and their balances on sight accounts with the Bank of France, together with the total amount of the items which they can put into the Bank of France. The methods of influencing liquidity are also similar to those employed in other countries. However, to make them easier to understand, the present article first recalls certain special features of France’s monetary institutions, namely the banks, the specialised institutions and the Treasury. The author then examines the duel problems of controlling the liquidity of the economy and bank liquidity.JEL: E51, E52, E58, G21
To the problem of electron temperature control in plasma
International Nuclear Information System (INIS)
Galechyan, G.A.; Anna, P.R.
1995-01-01
One of the main problems in low temperature plasma is control plasma parameters at fixed values of current and gas pressure in the discharge. It is known that an increase in the intensity of sound wave directed along the positive column to values in excess of a definite threshold leads to essential rise of the temperature of electrons. However, no less important is the reduction of electron temperature in the discharge down to the value less than that in plasma in the absence external influence. It is known that to reduce the electron temperature in the plasma of CO 2 laser, easily ionizable admixture are usually introduced in the discharge area with the view of increasing the overpopulation. In the present work we shall show that the value of electron temperature can be reduced by varying of sound wave intensity at its lower values. The experiment was performed on an experimental setup consisted of the tube with length 52 cm and diameter 9.8 cm, two electrodes placed at the distance of 27 cm from each other. An electrodynamical radiator of sound wave was fastened to one of tube ends. Fastened to the flange at the opposite end was a microphone for the control of sound wave parameters. The studies were performed in range of pressures from 40 to 180 Torr and discharge currents from 40 to 110 mA. The intensity of sound wave was varied from 74 to 92 dB. The measurement made at the first resonance frequency f = 150 Hz of sound in the discharge tube, at which a quarter of wave length keep within the length of the tube. The measurement of longitudinal electric field voltage in plasma of positive column was conducted with the help of two probes according to the compensation method. Besides, the measurement of gas temperature in the discharge were taken. Two thermocouple sensors were arranged at the distance of 8 cm from the anode, one of them being installed on the discharge tube axis, the second-fixed the tube wall
To the problem of electron temperature control in plasma
Energy Technology Data Exchange (ETDEWEB)
Galechyan, G.A. [Institute of Applied Problem of Physics, Yerevan (Armenia); Anna, P.R. [Raritan Valley Community College, Somerville, NJ (United States)
1995-12-31
One of the main problems in low temperature plasma is control plasma parameters at fixed values of current and gas pressure in the discharge. It is known that an increase in the intensity of sound wave directed along the positive column to values in excess of a definite threshold leads to essential rise of the temperature of electrons. However, no less important is the reduction of electron temperature in the discharge down to the value less than that in plasma in the absence external influence. It is known that to reduce the electron temperature in the plasma of CO{sub 2} laser, easily ionizable admixture are usually introduced in the discharge area with the view of increasing the overpopulation. In the present work we shall show that the value of electron temperature can be reduced by varying of sound wave intensity at its lower values. The experiment was performed on an experimental setup consisted of the tube with length 52 cm and diameter 9.8 cm, two electrodes placed at the distance of 27 cm from each other. An electrodynamical radiator of sound wave was fastened to one of tube ends. Fastened to the flange at the opposite end was a microphone for the control of sound wave parameters. The studies were performed in range of pressures from 40 to 180 Torr and discharge currents from 40 to 110 mA. The intensity of sound wave was varied from 74 to 92 dB. The measurement made at the first resonance frequency f = 150 Hz of sound in the discharge tube, at which a quarter of wave length keep within the length of the tube. The measurement of longitudinal electric field voltage in plasma of positive column was conducted with the help of two probes according to the compensation method. Besides, the measurement of gas temperature in the discharge were taken. Two thermocouple sensors were arranged at the distance of 8 cm from the anode, one of them being installed on the discharge tube axis, the second-fixed the tube wall.
Topology of singular fibers of differentiable maps
Saeki, Osamu
2004-01-01
The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.
Quantization function for attractive, singular potential tails
International Nuclear Information System (INIS)
Raab, Patrick N.
2010-01-01
The interaction between atoms and molecules with each other are deep potential wells with attractive, singular tails. Bound state energies are determined by a quantization function according to a simple quantization rule. This function is dominantly determined by the singular potential tail for near-threshold states. General expressions for the low- and high-energy contributions of the singular potential tail to the quantization function, as well as the connection to the scattering length are presented in two and three dimensions. Precise analytical expressions for the quantization function are determined for the case of potential tails proportional to -1/r 4 and -1/r 6 for three dimensions. (orig.)
DEKOMPOSISI NILAI SINGULAR PADA SISTEM PENGENALAN WAJAH
Directory of Open Access Journals (Sweden)
Beni Utomo
2012-11-01
Full Text Available Dekomposisi Nilai Singular atau Singular Value Decomposition (SVDmerupakan salah satu cara untuk menyatakan Principal Component Analysis (PCA.PCA sendiri merupakan suatu proses untuk menemukan kontributor-kontributorpenting dari suatu data berdasarkan besaran statistika deviasi standart dan variansi.SVD merupakan proses untuk mendapatkan matriks diagonal yang elementak nolnya merupakan nilai singular yang akarnya merupakan eigenvalue.SVD atas matriks kovarian C berbentuk C = U?V T dengan matriks U dan Vmemuat eigenvektor yang sudah terurut dari nilai variansi terbesar ke nilai variansiterkecilnya. Variansi terbesar memiliki arti eigenvektor menangkap ciri-ciri yangpaling banyak berubah. Sifat inilah yang dipakai untuk membentuk eigenface.
International Nuclear Information System (INIS)
Zhuchkov, A.A.; Kul'shin, A.V.; Al'masri, Kh.F.
2013-01-01
Problems of approaching the final state of a liquid with given parameters and forecasting the state of the liquid under mixing have been studied in detail with the use of fuzzy sets. Algorithms include the stages of fuzzification, rule construction, and defuzzification. It is important to ensure a small number of variables for the creation of appropriate fuzzy controller. Methods for increasing efficiency have been discussed (specification of the importance of rules, membership functions, and choice between Mamdani and Surgeno). A simulator of automated control systems of nuclear power plants has been used for some problems. Errors of the fuzzy solution are compared to the ideal errors. The possibility of decreasing these errors, as well as software implementations of the fuzzy approach, have been discussed [ru
Singular boundary perturbations of distributed systems
DEFF Research Database (Denmark)
Pedersen, Michael
1990-01-01
Some problems arising in real-life control applications are addressed--namely, problems concerning non-smooth control inputs on the boundary of the spatial domain. The classical variational approach is extended, and sufficient conditions are given for the solutions to continuous functions of time...
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://www. science direct.com/ science /article/pii/S0377042716302631?via%3Dihub
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://www.sciencedirect.com/science/article/pii/S0377042716302631?via%3Dihub
Exact Controllability and Perturbation Analysis for Elastic Beams
International Nuclear Information System (INIS)
Moreles, Miguel Angel
2004-01-01
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials
Directory of Open Access Journals (Sweden)
Maria eHuber
2015-07-01
Full Text Available The aims of the present multi-center study were to investigate the extent of mental health problems in adolescents with a hearing loss and cochlear implants (CIs in comparison to normal hearing (NH peers and to investigate possible relations between the extent of mental health problems of young CI users and hearing variables, such as age at implantation, or functional gain of CI. The survey included 140 adolescents with CI (mean age = 14.7, SD = 1.5 years and 140 NH adolescents (mean age = 14.8, SD = 1.4 years, their parents and teachers. Participants were matched by age, gender and social background. Within the CI group, 35 adolescents were identified as risk cases due to possible and manifest additional handicaps, and 11 adolescents were non-classifiable. Mental health problems were assessed with the Strengths and Difficulties Questionnaire (SDQ in the versions Self, Parent, and Teacher. The CI group showed significantly more Peer Problems than the NH group. When the CI group was split into a risk-group (35 risk cases and 11 non-classifiable persons and a non-risk group (n = 94, increased peer problems were perceived in both CI subgroups by adolescents themselves. However, no further differences between the CI non-risk group and the NH group were observed in any rater. The CI-risk group showed significantly more hyperactivity compared to the NH group and more hyperactivity and conduct problems compared to the CI non-risk group. Cluster analyses confirmed that there were significantly more adolescents with high problems in the CI-risk group compared to the CI non-risk group and the NH group. Adolescents with CI, who were able to understand speech in noise had significantly less difficulties compared to constricted CI users. Parents, teachers, and clinicians should be aware that CI users with additionally special needs may have mental health problems. However, peer problems were also experienced by CI adolescents without additional handicaps
An approach to the multi-axis problem in manual control. [optimal pilot model
Harrington, W. W.
1977-01-01
The multiaxis control problem is addressed within the context of the optimal pilot model. The problem is developed to provide efficient adaptation of the optimal pilot model to complex aircraft systems and real world, multiaxis tasks. This is accomplished by establishing separability of the longitudinal and lateral control problems subject to the constraints of multiaxis attention and control allocation. Control solution adaptation to the constrained single axis attention allocations is provided by an optimal control frequency response algorithm. An algorithm is developed to solve the multiaxis control problem. The algorithm is then applied to an attitude hold task for a bare airframe fighter aircraft case with interesting multiaxis properties.
Quantum singular-value decomposition of nonsparse low-rank matrices
Rebentrost, Patrick; Steffens, Adrian; Marvian, Iman; Lloyd, Seth
2018-01-01
We present a method to exponentiate nonsparse indefinite low-rank matrices on a quantum computer. Given access to the elements of the matrix, our method allows one to determine the singular values and their associated singular vectors in time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and nonsquare matrices via matrix embedding. Moreover, our method preserves the phase relations between the singular spaces allowing for efficient algorithms that require operating on the entire singular-value decomposition of a matrix. As an example of such an algorithm, we discuss the Procrustes problem of finding a closest isometry to a given matrix.
A Singular Finite Element on the Mixed-Mode Bimaterial Interfacial Cracks
Yao, W. A.; Hu, X. F.
2012-07-01
A singular finite element is presented to study the mixed-mode Dugdale-model-based bimaterial interfacial cracks. Firstly, the bimaterial interfacial crack problem is led into the symplectic space, and the symplectic dual equation is obtained and solved analytically. The cohesive stresses of the Dugdale model are treated as special solutions. Subsequently, the analytical solution is employed to develop a novel singular finite element, which depicts accurately the characteristic of displacements and singular stress fields near the crack tip. Finally, combining the singular finite element and conventional finite element method, the length of plastic zone, crack tip opening, and/or sliding displacement can be solved by iteration. Numerical examples are given to illustrate the validity of the present method.
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I
International Nuclear Information System (INIS)
Gaiotto, D.; Teschner, J.
2012-03-01
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S 4 . (orig.)
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I
Energy Technology Data Exchange (ETDEWEB)
Gaiotto, D. [Institute for Advanced Study (IAS), Princeton, NJ (United States); Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-03-15
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S{sup 4}. (orig.)
Energy conditions of non-singular black hole spacetimes in conformal gravity
Energy Technology Data Exchange (ETDEWEB)
Toshmatov, Bobir [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic); Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany); Ahmedov, Bobomurat [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Abdujabbarov, Ahmadjon [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Tashkent University of Information Technologies, Tashkent (Uzbekistan); Stuchlik, Zdenek [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)
2017-08-15
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)
Huber, Maria; Burger, Thorsten; Illg, Angelika; Kunze, Silke; Giourgas, Alexandros; Braun, Ludwig; Kröger, Stefanie; Nickisch, Andreas; Rasp, Gerhard; Becker, Andreas; Keilmann, Annerose
2015-01-01
The aims of the present multi-center study were to investigate the extent of mental health problems in adolescents with a hearing loss and cochlear implants (CIs) in comparison to normal hearing (NH) peers and to investigate possible relations between the extent of mental health problems of young CI users and hearing variables, such as age at implantation, or functional gain of CI. The survey included 140 adolescents with CI (mean age = 14.7, SD = 1.5 years) and 140 NH adolescents (mean age = 14.8, SD = 1.4 years), their parents and teachers. Participants were matched by age, gender and social background. Within the CI group, 35 adolescents were identified as “risk cases” due to possible and manifest additional handicaps, and 11 adolescents were non-classifiable. Mental health problems were assessed with the Strengths and Difficulties Questionnaire (SDQ) in the versions “Self,” “Parent,” and “Teacher.” The CI group showed significantly more “Peer Problems” than the NH group. When the CI group was split into a “risk-group” (35 “risk cases” and 11 non-classifiable persons) and a “non-risk group” (n = 94), increased peer problems were perceived in both CI subgroups by adolescents themselves. However, no further differences between the CI non-risk group and the NH group were observed in any rater. The CI risk-group showed significantly more hyperactivity compared to the NH group and more hyperactivity and conduct problems compared to the CI non-risk group. Cluster analyses confirmed that there were significantly more adolescents with high problems in the CI risk-group compared to the CI non-risk group and the NH group. Adolescents with CI, who were able to understand speech in noise had significantly less difficulties compared to constricted CI users. Parents, teachers, and clinicians should be aware that CI users with additionally special needs may have mental health problems. However, peer problems were also experienced by CI
Directory of Open Access Journals (Sweden)
M. E. Haji Abadi
2013-09-01
Full Text Available In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the Pdf estimation problem can be reformulated as the optimal control problem. Finally, the proposed method is applied to estimate the Pdf of the hourly electricity prices of New England and Ontario electricity markets. Obtained results show the efficiency of the proposed method.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
Technological Singularity: What Do We Really Know?
Directory of Open Access Journals (Sweden)
Alexey Potapov
2018-04-01
Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.
Topological Signals of Singularities in Ricci Flow
Directory of Open Access Journals (Sweden)
Paul M. Alsing
2017-08-01
Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.
Approximate Uniqueness Estimates for Singular Correlation Matrices.
Finkbeiner, C. T.; Tucker, L. R.
1982-01-01
The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)
Finite conformal quantum gravity and spacetime singularities
Modesto, Leonardo; Rachwał, Lesław
2017-12-01
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.
Low-cost control problems on perforated and non-perforated domains
Indian Academy of Sciences (India)
We study the homogenization of a class of optimal control problems whose state equations are given by second order elliptic boundary value problems with oscillating coefficients posed on perforated and non-perforated domains. We attempt to describe the limit problem when the cost of the control is also of the same order ...
Stability of the turnpike phenomenon in discrete-time optimal control problems
Zaslavski, Alexander J
2014-01-01
The structure of approximate solutions of autonomous discrete-time optimal control problems and individual turnpike results for optimal control problems without convexity (concavity) assumptions are examined in this book. In particular, the book focuses on the properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals; these results apply to the so-called turnpike property of the optimal control problems. By encompassing the so-called turnpike property the approximate solutions of the problems are determined primarily by the objective function and are fundamentally independent of the choice of interval and endpoint conditions, except in regions close to the endpoints. This book also explores the turnpike phenomenon for two large classes of autonomous optimal control problems. It is illustrated that the turnpike phenomenon is stable for an optimal control problem if the corresponding infinite horizon optimal control problem possesses an asymp...
Singularity analysis, Hadamard products, and tree recurrences
Fill, James Allen; Flajolet, Philippe; Kapur, Nevin
2005-02-01
We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relations.
Observational constraints on cosmological future singularities
Energy Technology Data Exchange (ETDEWEB)
Beltran Jimenez, Jose [Aix Marseille Univ, Universite de Toulon CNRS, CPT, Marseille (France); Lazkoz, Ruth [Euskal Herriko Unibertsitatea, Fisika Teorikoaren eta Zientziaren Historia Saila, Zientzia eta Teknologia Fakultatea, Bilbao (Spain); Saez-Gomez, Diego [Faculdade de Ciencias da Universidade de Lisboa, Departamento de Fisica, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Salzano, Vincenzo [University of Szczecin, Institute of Physics, Szczecin (Poland)
2016-11-15
In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H(z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means ∝2.8 Gyrs from the present time. (orig.)
Removal of apparent singularity in grid computations
International Nuclear Information System (INIS)
Jakubovics, J.P.
1993-01-01
A self-consistency test for magnetic domain wall models was suggested by Aharoni. The test consists of evaluating the ratio S = var-epsilon wall /var-epsilon wall , where var-epsilon wall is the wall energy, and var-epsilon wall is the integral of a certain function of the direction cosines of the magnetization, α, β, γ over the volume occupied by the domain wall. If the computed configuration is a good approximation to one corresponding to an energy minimum, the ratio is close to 1. The integrand of var-epsilon wall contains terms that are inversely proportional to γ. Since γ passes through zero at the centre of the domain wall, these terms have a singularity at these points. The integral is finite and its evaluation does not usually present any problems when the direction cosines are known in terms of continuous functions. In many cases, significantly better results for magnetization configurations of domain walls can be obtained by computations using finite element methods. The direction cosines are then only known at a set of discrete points, and integration over the domain wall is replaced by summation over these points. Evaluation of var-epsilon wall becomes inaccurate if the terms in the summation are taken to be the values of the integrand at the grid points, because of the large contribution of points close to where γ changes sign. The self-consistency test has recently been generalised to a larger number of cases. The purpose of this paper is to suggest a method of improving the accuracy of the evaluation of integrals in such cases. Since the self-consistency test has so far only been applied to two-dimensional magnetization configurations, the problem and its solution will be presented for that specific case. Generalisation to three or more dimensions is straight forward
Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco
2014-11-01
We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.
Machine vision for timber grading singularities detection and applications
Hittawe, Mohamad Mazen; Sidibé, Désiré; Beya, Ouadi; Mériaudeau, Fabrice
2017-11-01
This article deals with machine vision techniques applied to timber grading singularities. Timber used for architectural purposes must satisfy certain mechanical requirements, and, therefore, must be mechanically graded to ensure the manufacturer that the product complies with the requirements. However, the timber material has many singularities, such as knots, cracks, and presence of juvenile wood, which influence its mechanical behavior. Thus, identifying those singularities is of great importance. We address the problem of timber defects segmentation and classification and propose a method to detect timber defects such as cracks and knots using a bag-of-words approach. Extensive experimental results show that the proposed methods are efficient and can improve grading machines performances. We also propose an automated method for the detection of transverse knots, which allows the computation of knot depth ratio (KDR) images. Finally, we propose a method for the detection of juvenile wood regions based on tree rings detection and the estimation of the tree's pith. The experimental results show that the proposed methods achieve excellent results for knots detection, with a recall of 0.94 and 0.95 on two datasets, as well as for KDR image computation and juvenile timber detection.
Singular Hopf bifurcation in a differential equation with large state-dependent delay.
Kozyreff, G; Erneux, T
2014-02-08
We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.
Common Occupational Health Problems In Disease Control In Nigeria
African Journals Online (AJOL)
This article reviews some common occupational health problems among health workers due to exposure to hazardous or pathogenic biological, chemical and physical agents in the line of duty. Highlighted biological agents are pathogenic viruses, bacteria etc; chemical agents are laboratory reagents, mercury and ...
Are Marketing Students in Control in Problem-Based Learning?
Geitz, Gerry; Joosten-ten Brinke, Desirée; Kirschner, Paul A.
2016-01-01
This study investigated to what extent self-efficacy, learning behavior, and performance outcomes relate to each other and how they can be positively influenced by students asking for and seeking feedback within a problem-based learning (PBL) environment in order to meet today's requirements of marketing graduates. An experimental…
Are marketing students in control in problem-based learning?
Geitz, Gerry; Joosten-ten Brinke, Desirée; Kirschner, Paul A.
2018-01-01
This study investigated to what extent self-efficacy, learning behavior, and performance outcomes relate to each other and how they can be positively influenced by students asking for and seeking feedback within a problem-based learning (PBL) environment in order to meet today’s requirements of
The Library Space Problem, Future Demand, and Collection Control.
Lee, Hur-Li
1993-01-01
Outlines a model for determining library collection use, incorporating prediction of future demand and cost analysis to assist collection development librarians determine whether weeding or remote storage is the most economically feasible way to address the space problem in libraries. (13 references) (EA)
A hybrid iterative scheme for optimal control problems governed by ...
African Journals Online (AJOL)
MRT
homotopy perturbation method (HPM), which was proposed first by J. Huan He in 1998 (He, 1998), has been extended and improved by many scientist and engineers as an applicable tool for obtaining approximate solution in a wide range of problems in applied mathematics. Because this method continuously deforms the ...
Fuzzy Adaptive Control for Intelligent Autonomous Space Exploration Problems
Esogbue, Augustine O.
1998-01-01
The principal objective of the research reported here is the re-design, analysis and optimization of our newly developed neural network fuzzy adaptive controller model for complex processes capable of learning fuzzy control rules using process data and improving its control through on-line adaption. The learned improvement is according to a performance objective function that provides evaluative feedback; this performance objective is broadly defined to meet long-range goals over time. Although fuzzy control had proven effective for complex, nonlinear, imprecisely-defined processes for which standard models and controls are either inefficient, impractical or cannot be derived, the state of the art prior to our work showed that procedures for deriving fuzzy control, however, were mostly ad hoc heuristics. The learning ability of neural networks was exploited to systematically derive fuzzy control and permit on-line adaption and in the process optimize control. The operation of neural networks integrates very naturally with fuzzy logic. The neural networks which were designed and tested using simulation software and simulated data, followed by realistic industrial data were reconfigured for application on several platforms as well as for the employment of improved algorithms. The statistical procedures of the learning process were investigated and evaluated with standard statistical procedures (such as ANOVA, graphical analysis of residuals, etc.). The computational advantage of dynamic programming-like methods of optimal control was used to permit on-line fuzzy adaptive control. Tests for the consistency, completeness and interaction of the control rules were applied. Comparisons to other methods and controllers were made so as to identify the major advantages of the resulting controller model. Several specific modifications and extensions were made to the original controller. Additional modifications and explorations have been proposed for further study. Some of
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....
Fuzzy Self-Organising Control Of A Pendulum Problem
DEFF Research Database (Denmark)
Olivares, Manuel; Jantzen, Jan
1999-01-01
In a cart-ball balancer the control objective is to balance a ball on a curved track. This simulation study in Simulink tries to stabilise the system with a nonlinear adaptive controller. A simplified adjustment mechanism is implemented, and test results show that the adjustment mechanism works, ...
Counselling problem drinkers in medical wards: a controlled study.
Chick, J; Lloyd, G; Crombie, E
1985-01-01
Seven hundred and thirty one men admitted to medical wards were interviewed to identify problem drinkers who had not received previous treatment for alcoholism and who had some social support. One hundred and sixty one met the diagnostic criteria; 156 agreed to a follow up interview and were allocated to one of two groups. One group received a session of counselling about their drinking habits from a nurse while the other received only routine medical care. Both groups reported a reduction in...
The effect of high and low assertiveness on locus of control and health problems.
Williams, J M; Stout, J K
1985-03-01
The effect of high and low assertiveness on locus of control and health problems was examined with 78 direct-service workers in mental health and mental retardation settings in northeastern Pennsylvania. The direct-service workers completed the Rathus (1973) Assertiveness Schedule, the Rotter (1966) Internal-External Locus of Control Scale, and a health-problems inventory. Highly assertive individuals were found to be more internally controlled and to experience fewer health problems than were individuals low in assertiveness.
Discrete-time entropy formulation of optimal and adaptive control problems
Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.
1992-01-01
The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.
Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential
Directory of Open Access Journals (Sweden)
K. Atifi
2017-01-01
Full Text Available A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient. Some numerical experiments are given.
Abdulhameed, M.; Vieru, D.; Roslan, R.
2017-10-01
This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological
Solving the optimal attention allocation problem in manual control
Kleinman, D. L.
1976-01-01
Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.
On the problem of quantum control in infinite dimensions
Mendes, R. Vilela; Man'ko, Vladimir I.
2010-01-01
In the framework of bilinear control of the Schr\\"odinger equation with bounded control operators, it has been proved that the reachable set has a dense complemement in ${\\cal S}\\cap {\\cal H}^{2}$. Hence, in this setting, exact quantum control in infinite dimensions is not possible. On the other hand it is known that there is a simple choice of operators which, when applied to an arbitrary state, generate dense orbits in Hilbert space. Compatibility of these two results is established in this...
General problems of dynamics and control of vibratory gyroscopes
CSIR Research Space (South Africa)
Shatalov, MY
2008-05-01
Full Text Available resonator gyroscope. The foundations of feedback control in the gyroscopes are considered and classification of the main operational regimes is given in terms of the integral manifolds and new classes of nonlinear parametric excitation forces are added...
The Accountable Animal : Naturalising the management control problem
P.I. Eskenazi (Philip)
2015-01-01
markdownabstract__Abstract__ In this dissertation we investigate two themes around the topic of social relations in management control structures. We use developments in neuroscience and eye-tracking to supplement the traditional psychological and economic perspective on management
Null controllability of a nonlinear population dynamics problem
Traore, Oumar
2006-01-01
We establish a null controllability result for a nonlinear population dynamics model. In our model, the birth term is nonlocal and describes the recruitment process in newborn individuals population. Using a derivation of Leray-Schauder fixed point theorem and Carleman inequality for the adjoint system, we show that for all given initial density, there exists an internal control acting on a small open set of the domain and leading the population to extinction.
Uncertainty Quantification in Control Problems for Flocking Models
Directory of Open Access Journals (Sweden)
Giacomo Albi
2015-01-01
Full Text Available The optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given. The use of a selective model predictive control permits steering of the system towards the desired state even in unstable regimes.
Luo, Jianhua; Mou, Zhiying; Qin, Binjie; Li, Wanqing; Ogunbona, Philip; Robini, Marc C; Zhu, Yuemin
2017-12-09
Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.
Multiple curved descending approaches and the air traffic control problem
Hart, S. G.; Mcpherson, D.; Kreifeldt, J.; Wemple, T. E.
1977-01-01
A terminal area air traffic control simulation was designed to study ways of accommodating increased air traffic density. The concepts that were investigated assumed the availability of the microwave landing system and data link and included: (1) multiple curved descending final approaches; (2) parallel runways certified for independent and simultaneous operation under IFR conditions; (3) closer spacing between successive aircraft; and (4) a distributed management system between the air and ground. Three groups each consisting of three pilots and two air traffic controllers flew a combined total of 350 approaches. Piloted simulators were supplied with computer generated traffic situation displays and flight instruments. The controllers were supplied with a terminal area map and digital status information. Pilots and controllers also reported that the distributed management procedure was somewhat more safe and orderly than the centralized management procedure. Flying precision increased as the amount of turn required to intersect the outer mark decreased. Pilots reported that they preferred the alternative of multiple curved descending approaches with wider spacing between aircraft to closer spacing on single, straight in finals while controllers preferred the latter option. Both pilots and controllers felt that parallel runways are an acceptable way to accommodate increased traffic density safely and expeditiously.
Brief telephone interventions for problem gambling: a randomized controlled trial.
Abbott, Max; Hodgins, David C; Bellringer, Maria; Vandal, Alain C; Palmer Du Preez, Katie; Landon, Jason; Sullivan, Sean; Rodda, Simone; Feigin, Valery
2018-05-01
Problem gambling is a significant public health issue world-wide. There is substantial investment in publicly funded intervention services, but limited evaluation of effectiveness. This study investigated three brief telephone interventions to determine whether they were more effective than standard helpline treatment in helping people to reduce gambling. Randomized clinical trial. National gambling helpline in New Zealand. A total of 462 adults with problem gambling. INTERVENTIONS AND COMPARATOR: (1) Single motivational interview (MI), (2) single motivational interview plus cognitive-behavioural self-help workbook (MI + W) and (3) single motivational interview plus workbook plus four booster follow-up telephone interviews (MI + W + B). Comparator was helpline standard care [treatment as usual (TAU)]. Blinded follow-up was at 3, 6 and 12 months. Primary outcomes were days gambled, dollars lost per day and treatment goal success. There were no differences across treatment arms, although participants showed large reductions in gambling during the 12-month follow-up period [mean reduction of 5.5 days, confidence interval (CI) = 4.8, 6.2; NZ$38 lost ($32, $44; 80.6%), improved (77.2%, 84.0%)]. Subgroup analysis revealed improved days gambled and dollars lost for MI + W + B over MI or MI + W for a goal of reduction of gambling (versus quitting) and improvement in dollars lost by ethnicity, gambling severity and psychological distress (all P gambling severity than TAU or MI at 12 months and also better for those with higher psychological distress and lower self-efficacy to MI (all P problem gambling in New Zealand, brief telephone interventions are associated with changes in days gambling and dollars lost similar to more intensive interventions, suggesting that more treatment is not necessarily better than less. Some client subgroups, in particular those with greater problem severity and greater distress, achieve better outcomes when they receive more
Comments on `A discrete optimal control problem for descriptor systems'
DEFF Research Database (Denmark)
Ravn, Hans
1990-01-01
In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates that there ...... that there is not an `if and only if' correspondence between stationarity conditions and minimization of the Hamiltonian. In replying, Lin and Yang acknowledge this and also give a version of theorem two in the context of their response to achieve a balance...
Conical flow near singular rays. [shock generation in ideal gas
Zahalak, G. I.; Myers, M. K.
1974-01-01
The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.
Safety problems in vehicles with adaptive cruise control system
Directory of Open Access Journals (Sweden)
Yadav Arun K.
2017-06-01
Full Text Available In today’s world automotive industries are still putting efforts towards more autonomous vehicles (AVs. The main concern of introducing the autonomous technology is safety of driver. According to a survey 90% of accidents happen due to mistake of driver. The adaptive cruise control system (ACC is a system which combines cruise control with a collision avoidance system. The ACC system is based on laser and radar technologies. This system is capable of controlling the velocity of vehicle automatically to match the velocity of car, bus or truck in front of vehicle. If the lead vehicle gets slow down or accelerate, than ACC system automatically matches that velocity. The proposed paper is focusing on more accurate methods of detecting the preceding vehicle by using a radar and lidar sensors by considering the vehicle side slip and by controlling the distance between two vehicles. By using this approach i.e. logic for calculation of former vehicle distance and controlling the throttle valve of ACC equipped vehicle, an improvement in driving stability was achieved. The own contribution results with fuel efficient driving and with more safer and reliable driving system, but still some improvements are going on to make it more safe and reliable.
Singularities in Structural Optimization of the Ziegler Pendulum
Directory of Open Access Journals (Sweden)
O. N. Kirillov
2011-01-01
Full Text Available Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.
Directory of Open Access Journals (Sweden)
Nikita Agarwal
2017-07-01
Full Text Available In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems with the optimal control of the corresponding homogenized problem.
Severe Self-Injurious Behavior: The Problem of Clinical Control
Romanczyk, Raymond G.; Goren, Elizabeth R.
1975-01-01
The long-term treatment program and follow-up of a case of chronic, severe, multiple self-injurious behavior is presented. Contingent electric shock and differential reinforcement of other behavior were the primary techniques utilized. Total suppression was achieved in the laboratory setting, but extending control to the natural environment proved…
Problems Of Resource Control In Nigeria And The Way Forward ...
African Journals Online (AJOL)
In recent times, the issues of Resources Control in Nigeria have generated a lot of controversies. In discussing these issues, this paper focuses primarily on Crude Oil and its allied products from an historic standpoint, the issues of Federalism, Inter-governmental Relations in Nigeria, Fiscal federalism and the distribution of ...
Solving nonconvex SDP problems of structural optimization with stability control
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Stingl, M.
2004-01-01
Roč. 19, č. 5 (2004), s. 595-609 ISSN 1055-6788 R&D Projects: GA AV ČR IAA1075005 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : structural optimization * stability control * nonconvex semidefinite programming Subject RIV: BA - General Mathematics Impact factor: 0.273, year: 2004
Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle
Adams, Richard J.
1993-01-01
High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.
Singularity hypotheses a scientific and philosophical assessment
Moor, James; Søraker, Johnny; Steinhart, Eric
2012-01-01
Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.
Phantom cosmology without Big Rip singularity
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)
2012-03-23
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Holographic subregion complexity for singular surfaces
Energy Technology Data Exchange (ETDEWEB)
Bakhshaei, Elaheh [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Mollabashi, Ali [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)
2017-10-15
Recently holographic prescriptions were proposed to compute the quantum complexity of a given state in the boundary theory. A specific proposal known as 'holographic subregion complexity' is supposed to calculate the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cut-off, due to the singularities of a family of surfaces including a kink in (2 + 1) dimensions and cones in even dimensional field theories. We also find examples of new divergent terms such as squared logarithm and negative powers times the logarithm of the UV cut-off parameter. (orig.)
Anger, perceived control and school behavior among students with learning problems.
Smith, D C; Adelman, H S; Nelson, P; Taylor, L
1988-07-01
With regard to students with learning problems, findings indicate that the more severe the learning problem, the greater the tendency toward anger in response to conflicts at school. The relationship between learning problem severity and perceptions of control at school was not significant, but anger was negatively correlated to perceived control. None of the variables were significantly related to misbehavior. A stepwise regression analysis indicated perceived control as the most potent single variable accounting for the variance in anger scores. Overall, findings highlight implications for work focused on reactions to learning problems and factors associated with their cause and correction.
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
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 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......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...... 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....
EFPA’s New Research Controls: Problems Remain.
1981-07-14
by the National Academy of Sciencies and the Office of Technology Assessment reinforced this finding. These critics of EPA’s research program...lack of peer (experts inside and outside of EPA) review of research plans and results. As a result of these criticisms, the Congress directed EPA to...NEW RESEARCH CONTROLS In response to the congressional directives , EPA presented a report to the President and the Congress entitled "The Planning and
Kim, Geunyoung; Walden, Tedra; Harris, Vicki; Karrass, Jan; Catron, Thomas
2007-01-01
The present study examined the role of emotion and emotion control in children's externalizing problems. Third- to sixth-grade children were administered a self-report measure of positive emotion, negative emotion, and emotion control. Peer- and teacher-reported adjustment problems were assessed. Structural equations modeling revealed that…
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...... the classical one, for systems with many states. A number of parallel implementations of the alternative version has been proposed and tested....
Singular vectors for the WN algebras
Ridout, David; Siu, Steve; Wood, Simon
2018-03-01
In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.
Controlling sign problems in spin models using tensor renormalization
Energy Technology Data Exchange (ETDEWEB)
Denbleyker, Alan [Iowa U.; Liu, Yuzhi [Colorado U.; Meurice, Y. [Iowa U.; Qin, M. P. [Beijing, Inst. Phys.; Xiang, T. [Beijing, Inst. Phys.; Xie, Z. Y. [Beijing, Inst. Phys.; Yu, J. F. [Beijing, Inst. Phys.; Zou, Haiyuan [Iowa U.
2014-01-09
We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
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...
Wang, S. S.; Choi, I.
1983-01-01
The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be diferent from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites.
Constructing Current Singularity in a 3D Line-tied Plasma
Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.
2018-01-01
We revisit Parker’s conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.
Inverse problems of geophysics
International Nuclear Information System (INIS)
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Burman, Erik; Hansbo, Peter; Larson, Mats G.
2018-03-01
Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.
Ensuring Well-Posedness by Analogy; Stokes Problem and Boundary Control for the Wave Equation
Glowinski, R.
1992-12-01
In this article we give a comparative discussion of the finite element approximation of two partial differential equation problems. These two problems which are apparantly quite unrelated are the Stokes problem for incompressible viscous flow and an exact boundary controllability problem for the wave equation. We show that straightforward discrete approximations to these problems yield approximate problems which are ill-posed. The analysis of the ill-posedness of the above problems shows an identical cause, namely the strong damping of the high frequency modes, beyond a critical wave number. From this analogy, a well-known cure for the discrete Stokes problem, i.e., using more accurate approximations for velocity than for pressure, provides a simple way to eliminate the ill-posedness of the discrete exact boundary controllability problem. Numerical examples concerning the control problem testify about the soundness of the new approach. To conclude this paper one takes advantage of the previous analysis to give a brief discussion of the wavelet approximation of the Stokes problem, for Dirichlet boundary conditions.
Swamp Buffalo in South Kalimantan : Problem, Disease and Control
Directory of Open Access Journals (Sweden)
Lily Natalia
2006-12-01
Full Text Available In recent years, several studies have been carried out to evaluate and investigate the important diseases of swamp buffaloes (Bubalus carabanensis in Kalimantan . More attention has been focused on the case of acute infectious diseases and sudden death in the buffaloes . Fasciolosis black disease, acute enteritis, especially fatal enterotoxaemia haemorrhagic septicaemia . and trypanosomiasis (Surra, are some of the important diseases found in these animals . Black disease caused by toxigenic Clostridium novyi occurs in the presence of the organism in the liver and the degree of liver fluke Fasciola gigantica infestation . In regions where black disease is enzootic, Cl. novvi can be isolated from livers of normal healthy animals . In Hulu Sungai Utara district, South Kalimantan, the prevalence of fasciolosis caused by Fasciola gigantica in swamp buffalo was 77% in 1991 . A gross sudden change in diet due to seasonal changes could induce rumen and intestinal stasis, which provide a favourable environment for the rapid proliferation of commensal toxigenic Clostridium perfringens in the small intestine . Subsequent absorption of the toxin produced through the gut wall and its generalized dissemination culminated in a fatal enterotoxaemia . Haemorrhagic septicaemia (HS is an acute, fatal disease affecting swamp buffalo, and caused by Pasteurella multocida B : 2 . The swamp buffalo is particularly susceptible for HS, and the reported greatest losses of swamp buffalo in Kalimantan due to HS is recorded in 1980s. The clinical signs of Surra in swamp buffalo were also found in certain areas in Danau Panggang area . Hulu Sungai Utara district . Vaccination is the accepted method for controlling Black disease, enterotoxaemia and HS. Multi component vaccine, alum adjuvant containing at least 5 types of clostridial toxoids and P. multocida B2 bacterin have been used and provide good protection to the animals . Control and treatment of liver fluke infestation
Singular Linear Differential Equations in Two Variables
Braaksma, B.L.J.; Put, M. van der
2008-01-01
The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating ...
Supersymmetric quantum mechanics under point singularities
International Nuclear Information System (INIS)
Uchino, Takashi; Tsutsui, Izumi
2003-01-01
We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature
Classical resolution of singularities in dilaton cosmologies
Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK
2005-01-01
For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to
Mobile communications technology: The singular factor responsible ...
African Journals Online (AJOL)
This paper investigated the factors responsible for the growth of Internet usage on the African continent. The principal finding was that increasing growth of Internet usage is also down to one singular factor: mobile communications technology. The proliferation of mobile phone usage in Africa has resulted in the sustained ...
Polynomial computation of Hankel singular values
Kwakernaak, H.
1992-01-01
A revised and improved version of a polynomial algorithm is presented. It was published by N.J. Young (1990) for the computation of the singular values and vectors of the Hankel operator defined by a linear time-invariant system with a rotational transfer matrix. Tentative numerical experiments
Ray tracing in anisotropic media with singularities
Czech Academy of Sciences Publication Activity Database
Vavryčuk, Václav
2001-01-01
Roč. 145, č. 1 (2001), s. 265-276 ISSN 0956-540X R&D Projects: GA ČR GA205/00/1350 Institutional research plan: CEZ:AV0Z3012916 Keywords : anisotropic media * ray tracing * singularities Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.366, year: 2001
Inverting dedevelopment: geometric singularity theory in embryology
Bookstein, Fred L.; Smith, Bradley R.
2000-10-01
The diffeomorphism model so useful in the biomathematics of normal morphological variability and disease is inappropriate for applications in embryogenesis, where whole coordinate patches are created out of single points. For this application we need a suitable algebra for the creation of something from nothing in a carefully organized geometry: a formalism for parameterizing discrete nondifferentiabilities of invertible functions on Rk, k $GTR 1. One easy way to begin is via the inverse of the development map - call it the dedevelopment map, the deformation backwards in time. Extrapolated, this map will inevitably have singularities at which its derivative is zero. When the dedevelopment map is inverted to face forward in time, the singularities become appropriately isolated infinities of derivative. We have recently introduced growth visualizations via extrapolations to the isolated singularities at which only one directional derivative is zero. Maps inverse to these create new coordinate patches directionally rather than radically. The most generic singularity that suits this purpose is the crease f(x,y) equals (x,x2y+y3), which has already been applied in morphometrics for the description of focal morphogenetic phenomena. We apply it to embryogenesis in the form of its analytic inverse, and demonstrate its power using a priceless new data set of mouse embryos imaged in 3D by micro-MR with voxels smaller than 100micrometers 3.
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
the framework of a general spacetime without any symmetry conditions, in terms of the overall behaviour of .... We now outline the basic idea and the chain of logic behind the proof of a typical singularity theorem ..... a detailed investigation of the dynamics of gravitational collapse within the frame- work of Einstein's theory.
Analysis of the problems, which have the users employing software packages in the production control
International Nuclear Information System (INIS)
Vortherms, B.; Moeller, C.
1977-08-01
The use of EDP is particularly effective in the dispositive area of enterprises. The realization of adequate systems, however, is involving considerable problems. This study is analyzing such problems of production control which have been obtained by investigations carried out in several enterprises. The problems of production control, the procedure in carrying out investigations and the prevalence of EDP in enterprises are demonstrated. The problems found out and their causes are then systematized and analyzed. The solution proposals derived are orientation aids for an optimum use of EDP. (orig.) [de
On the formulation and numerical simulation of distributed-order fractional optimal control problems
Zaky, M. A.; Machado, J. A. Tenreiro
2017-11-01
In a fractional optimal control problem, the integer order derivative is replaced by a fractional order derivative. The fractional derivative embeds implicitly the time delays in an optimal control process. The order of the fractional derivative can be distributed over the unit interval, to capture delays of distinct sources. The purpose of this paper is twofold. Firstly, we derive the generalized necessary conditions for optimal control problems with dynamics described by ordinary distributed-order fractional differential equations (DFDEs). Secondly, we propose an efficient numerical scheme for solving an unconstrained convex distributed optimal control problem governed by the DFDE. We convert the problem under consideration into an optimal control problem governed by a system of DFDEs, using the pseudo-spectral method and the Jacobi-Gauss-Lobatto (J-G-L) integration formula. Next, we present the numerical solutions for a class of optimal control problems of systems governed by DFDEs. The convergence of the proposed method is graphically analyzed showing that the proposed scheme is a good tool for the simulation of distributed control problems governed by DFDEs.
Regularity versus singularities for elliptic problems in two dimensions
Beck, Lisa
2009-01-01
In two dimensions every weak solution to a nonlinear elliptic system $\\rm{div} a(x,u,Du)=0$ has H\\"older continuous first derivatives provided that standard continuity, ellipticity and growth assumptions hold with a growth exponent $p \\geq 2$. We give an example showing that this result cannot be extended to the subquadratic case, i.e. that weak solutions are not necessarily continuous if $1< p
Generalized Parton Distributions and their Singularities
Energy Technology Data Exchange (ETDEWEB)
Anatoly Radyushkin
2011-04-01
A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function $f(\\beta)/\\beta$ rather than with the usual parton density $f(\\beta)$. This results in a non-integrable singularity at $\\beta=0$ exaggerated by the fact that $f(\\beta)$'s, on their own, have a singular $\\beta^{-a}$ Regge behavior for small $\\beta$. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs $H(x,\\xi)$ that are finite and continuous at the "border point'' $x=\\xi$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $\\beta=0$ singularities is proposed that is based on the separation of the initial single DD $f(\\beta, \\alpha)$ into the "plus'' part $[f(\\beta,\\alpha)]_{+}$ and the $D$-term. It is demonstrated that the "DD+D'' separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution $f(x)=H(x,0)$ and the border function $H(x,x)$ with the $D$-term function $D(\\alpha)$.
Thomas, Shane A; Merkouris, Stephanie S; Browning, Colette J; Radermacher, Harriet; Feldman, Susan; Enticott, Joanne; Jackson, Alun C
2015-11-24
International prevalence rates for problem gambling are estimated at 2.3%. Problem gambling is a serious global public health concern due to adverse personal and social consequences. Previous research evaluating the effectiveness of psychological interventions for the treatment of problem gambling has been compromised by methodological limitations, including small sample sizes and the use of waitlist control groups. This article describes the study protocol for a pragmatic randomised controlled trial (RCT) evaluating the effectiveness of cognitive-behavioural therapy (CBT), behaviour therapy (BT), motivational interviewing (MI) against a non-directive supportive therapy (NDST) control, in treating problem gambling. This study was a mixed-methods design, with a parallel group, pragmatic RCT as the primary component, and embedded qualitative studies conducted alongside. A total of 297 participants were recruited from the community in Victoria, Australia. Individuals aged 18 years and over, could communicate in English and wished to receive treatment for a gambling problem were eligible. Participants were randomly allocated in to 1 of the 4 psychological interventions: CBT, BT, MI and NDST. Repeated measures were conducted at pretreatment and post-treatment, and 6 and 12 months post-treatment. The statistical analysis will use an intention-to-treat approach. Multilevel mixed modelling will be used to examine changes in the primary outcome measures: gambling symptom severity, using the Gambling Symptom Assessment Scale, and gambling behaviours (frequency, time and expenditure). Secondary outcomes are depression, anxiety, stress and alcohol use. Individual semistructured qualitative interviews were conducted at pretreatment and post-treatment and 12 months post-treatment for a subset of participants (n=66). This study was approved by the Victorian Department of Justice, Monash University and the University of Melbourne Human Research Ethics Committees. Findings
São Carlos Workshop on Real and Complex Singularities
Ruas, Maria
2007-01-01
The São Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains papers presented at the eighth workshop, held at the IML, Marseille, July 19–23, 2004. The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities. This is reflected by the contributions in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.
A Note on Inclusion Intervals of Matrix Singular Values
Cui, Shu-Yu; Tian, Gui-Xian
2012-01-01
We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.
Periodic solutions to singular second order differential equations: the repulsive case
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Torres, P.J.; Zamora, M.
2012-01-01
Roč. 39, č. 2 (2012), s. 199-220 ISSN 1230-3429 Institutional support: RVO:67985840 Keywords : singular nonlinear boundary value problem * positive solutions * periodic solutions Subject RIV: BA - General Mathematics Impact factor: 1.099, year: 2012
Stability bound analysis of singularly perturbed systems with time-delay
Directory of Open Access Journals (Sweden)
Sun Fengqi
2013-01-01
Full Text Available This paper considers the stability bound problem of singularly perturbed systems with time-delay. Some stability criteria are derived by constructing appropriate Lyapunov-Krasovskii functionals. The proposed criteria are less conservative than the existing ones. Two numerical examples are given to illustrate the advantages and effectiveness of the proposed methods.
Direct and Inverse Kinematic of 3DOF Parallel Mechanism with Singularity Analysis
Bałchanowski, J.
This paper presents the structure and geometry of a new translational parallel mechanism. Relations for the analysis of the direct and inverse kinematics problems are derived. An analytical procedure for determining the system's singular positions is presented and illustrated with examples.
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2016-01-01
Full Text Available In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.
Solving quantum optimal control problems using Clebsch variables and Lin constraints
Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.
2018-01-01
Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.
International Nuclear Information System (INIS)
1964-01-01
The development of nuclear reactors is closely associated with the progress made in the solution of control problems. To survey the present state of the subject the International Atomic Energy Agency convened a symposium devoted to ''Physics and Material Problems in Reactor Control Rods''. The Symposium was held in Vienna from 11 to 15 November 1963 and was attended by more than 100 participants representing 21 of the Agency's Member States and two international organizations. Problems discussed in the 34 papers presented at 8 sessions covered many special aspects of theoretical and experimental physics, engineering, metallurgy, etc. The first session of the Symposium was devoted to different theoretical methods used for the determination of control rod effectiveness in a multi- regioned reactor, and in natural-uranium heavy-water moderated cores. Homogeneous and heterogeneous approaches were discussed and applicability of proposed methods for various forms of control elements considered. During the two following sessions a number of theoretical problems and mathematical models were examined together with various control rod experiments and measurements in exponential and critical assemblies and at commercial nuclear power stations. The next session dealt with the connection between physics and technology of control rods, the latter being the subject of the remainder of the Symposium. Testing and actual operating experience of control rods were also treated in some of the presented papers. The session on engineering aspects of control rod systems included presentation of research results in a marine control station, the design of large graphite reactor control drives and the description of different mechanisms for rapid insertion of control absorbers. Finally, the methods of fast reactor control were discussed, followed by the presentation of various ''unconventional'' methods of reactivity control, such as hydraulic ball, fluidized bed, gas pressure and soluble
Leeman, Robert F.; Toll, Benjamin A.; Taylor, Laura A.; Volpicelli, Joseph R.
2009-01-01
Trait disinhibition is associated with problem drinking and alcohol drinking itself can bring about a state of disinhibition. It is unclear however, if expectancies of alcohol-induced disinhibition are unique predictors of problem drinking. Impaired control (i.e., difficulty in limiting alcohol consumption) may be related to disinhibition expectancies in that both involve issues of control related to alcohol use. Data from a prospective survey of undergraduates assessed during freshman (N = 337) and senior year (N = 201) were analyzed to determine whether subscales of the Drinking-Induced Disinhibition Scale and the Impaired Control Scale predicted unique variance in heavy episodic drinking and alcohol-related problems. In Time 1 cross-sectional models, dysphoric disinhibition expectancies predicted alcohol-related problems and impaired control predicted both alcohol-related problems and heavy episodic drinking. In prospective models, Time 1 impaired control predicted Time 2 alcohol-related problems and Time 1 euphoric/social disinhibition expectancies predicted Time 2 heavy episodic drinking. These findings suggest that expectancies of alcohol-induced disinhibition and impaired control predict unique variance in problem drinking cross-sectionally and prospectively and that these phenomena should be targeted in early intervention efforts. PMID:20025361
A Simple Proof of the Theorem Concerning Optimality in a One-Dimensional Ergodic Control Problem
International Nuclear Information System (INIS)
Fujita, Y.
2000-01-01
We give a simple proof of the theorem concerning optimality in a one-dimensional ergodic control problem. We characterize the optimal control in the class of all Markov controls. Our proof is probabilistic and does not need to solve the corresponding Bellman equation. This simplifies the proof
Computer difference scheme for a singularly perturbed convection-diffusion equation
Shishkin, G. I.
2014-08-01
The Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation with a perturbation parameter ɛ (that takes arbitrary values from the half-open interval (0, 1]) is considered. For this problem, an approach to the construction of a numerical method based on a standard difference scheme on uniform meshes is developed in the case when the data of the grid problem include perturbations and additional perturbations are introduced in the course of the computations on a computer. In the absence of perturbations, the standard difference scheme converges at an (δ st ) rate, where δ st = (ɛ + N -1)-1 N -1 and N + 1 is the number of grid nodes; the scheme is not ɛ-uniformly well conditioned or stable to perturbations of the data. Even if the convergence of the standard scheme is theoretically proved, the actual accuracy of the computed solution in the presence of perturbations degrades with decreasing ɛ down to its complete loss for small ɛ (namely, for ɛ = (δ-2max i, j |δ a {/i j }| + δ-1 max i, j |δ b {/i j }|), where δ = δ st and δ a {/i j }, δ b {/i j } are the perturbations in the coefficients multiplying the second and first derivatives). For the boundary value problem, we construct a computer difference scheme, i.e., a computing system that consists of a standard scheme on a uniform mesh in the presence of controlled perturbations in the grid problem data and a hypothetical computer with controlled computer perturbations. The conditions on admissible perturbations in the grid problem data and on admissible computer perturbations are obtained under which the computer difference scheme converges in the maximum norm for ɛ ∈ (0, 1] at the same rate as the standard scheme in the absence of perturbations.
Sain, M. K.; Antsaklis, P. J.; Gejji, R. R.; Wyman, B. F.; Peczkowski, J. L.
1981-01-01
Zames (1981) has observed that there is, in general, no 'separation principle' to guarantee optimality of a division between control law design and filtering of plant uncertainty. Peczkowski and Sain (1978) have solved a model matching problem using transfer functions. Taking into consideration this investigation, Peczkowski et al. (1979) proposed the Total Synthesis Problem (TSP), wherein both the command/output-response and command/control-response are to be synthesized, subject to the plant constraint. The TSP concept can be subdivided into a Nominal Design Problem (NDP), which is not dependent upon specific controller structures, and a Feedback Synthesis Problem (FSP), which is. Gejji (1980) found that NDP was characterized in terms of the plant structural matrices and a single, 'good' transfer function matrix. Sain et al. (1981) have extended this NDP work. The present investigation is concerned with a study of FSP for the unity feedback case. NDP, together with feedback synthesis, is understood as a Total Synthesis Problem.
Directory of Open Access Journals (Sweden)
D. Agus Harjito
2009-05-01
Full Text Available This study investigates the substitution relationship (substitutability between debt policy, insider ownership, and dividend policy as the agency problem control mechanism in Malaysia. If the substitution relationship exists between the agency control mechanisms, the agency problem can be reduced through this relationship. Reducing the agency problem as a result can increase the firm value proxied by Tobin’s Q. This study employs 396 firms sample listed on Malaysian Bourse from 2001 to 2004. To achieves the objectives, this study uses two-stage least square method. The results of this study indicate that the substitutability between debt policy, insider ownership, and dividend policy as agency problem control mechanism does not fully exist in Malaysia. Apparently the substitutability only exists for debt policy and dividend. There is no substitution between debt policy and insider ownership as well as between dividend policy and insider ownership. Key words: debt policy, insider ownership, dividend policy, agency problem, firm value
Singularities and the geometry of spacetime
Hawking, Stephen
2014-11-01
The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove
On the application of deterministic optimization methods to stochastic control problems
Kramer, L. C.; Athans, M.
1974-01-01
A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.
Control of stochastic sensitivity in a stabilization problem for gas discharge system
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Ural Federal University, Lenina, 51, Ekaterinburg, 620000 (Russian Federation)
2015-11-30
We consider a nonlinear dynamic stochastic system with control. A problem of stochastic sensitivity synthesis of the equilibrium is studied. A mathematical technique of the solution of this problem is discussed. This technique is applied to the problem of the stabilization of the operating mode for the stochastic gas discharge system. We construct a feedback regulator that reduces the stochastic sensitivity of the equilibrium, suppresses large-amplitude oscillations, and provides a proper operation of this engineering device.
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
... )) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a `big' subset of the true initial data set ...
Kalmar, Boldizsar
2006-01-01
We give a Pontryagin-Thom-Szucs type construction for non-positive codimensional singular maps, and obtain results about cobordism and bordism groups of -1 codimensional stable maps with prescribed singular fibers.
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Citrus Quality Control: An NMR/MRI Problem-Based Experiment
Erhart, Sarah E.; McCarrick, Robert M.; Lorigan, Gary A.; Yezierski, Ellen J.
2016-01-01
An experiment seated in an industrial context can provide an engaging framework and unique learning opportunity for an upper-division physical chemistry laboratory. An experiment that teaches NMR/MRI through a problem-based quality control of citrus products was developed. In this experiment, using a problem-based learning (PBL) approach, students…
Maaskant, A.M.; van Rooij, F.B.; Overbeek, G.J.; Oort, F.J.; Arntz, M.; Hermanns, J.M.A.
The present randomized controlled trial examined the effectiveness of Parent Management Training Oregon for foster parents with foster children (aged 4–12) with severe externalizing behavior problems in long-term foster care arrangements. Foster children’s behavior problems are challenging for
Problem based learning in continuing medical education: a review of controlled evaluation studies
Smits, P. B. A.; Verbeek, J. H. A. M.; de Buisonjé, C. D.
2002-01-01
Reviews of undergraduate medical education cautiously support the short term and long term outcomes of problem based learning compared with traditional learning. The effectiveness of problem based learning in continuing medical education, however, has not been reviewed. This review of controlled
Teaching Third Graders about Real-Life Mathematical Problem Solving: A Randomized Controlled Study
Fuchs, Lynn S.; Fuchs, Douglas; Finelli, Robin; Courey, Susan J.; Hamlett, Carol L.; Sones, Estelle M.; Hope, Susan K.
2006-01-01
The purpose of this study was to assess the effects of schema-broadening instruction (SBI), with and without explicit instruction in strategies for tackling the complexities involved in real-life (RL) math problems, on the math problem solving of third-grade students. Teachers (n = 30) were assigned randomly to 3 16-week conditions: control, SBI,…
Health and Sleep Problems in Cornelia de Lange Syndrome: A Case Control Study
Hall, S. S.; Arron, K.; Sloneem, J.; Oliver, C.
2008-01-01
Background: Self-injury, sleep problems and health problems are commonly reported in Cornelia de Lange Syndrome (CdLS) but there are no comparisons with appropriately matched participants. The relationship between these areas and comparison to a control group is warranted. Method: 54 individuals with CdLS were compared with 46 participants with…
Scheifes, A.; Stolker, J. J.; Egberts, A. C. G.; Nijman, H. L. I.; Heerdink, E. R.
2011-01-01
Background: Behavioural problems are common in people with intellectual disability (ID) and are often treated with antipsychotics. Aim: To establish the frequency and characteristics of people with ID included in randomised controlled trials (RCTs) on antipsychotic treatment for behavioural problems, and to investigate the quality of these RCTs.…
Construction of multiple trade-offs to obtain arbitrary singularities of adaptive dynamics.
Kisdi, Éva
2015-04-01
Evolutionary singularities are central to the adaptive dynamics of evolving traits. The evolutionary singularities are strongly affected by the shape of any trade-off functions a model assumes, yet the trade-off functions are often chosen in an ad hoc manner, which may unjustifiably constrain the evolutionary dynamics exhibited by the model. To avoid this problem, critical function analysis has been used to find a trade-off function that yields a certain evolutionary singularity such as an evolutionary branching point. Here I extend this method to multiple trade-offs parameterized with a scalar strategy. I show that the trade-off functions can be chosen such that an arbitrary point in the viability domain of the trait space is a singularity of an arbitrary type, provided (next to certain non-degeneracy conditions) that the model has at least two environmental feedback variables and at least as many trade-offs as feedback variables. The proof is constructive, i.e., it provides an algorithm to find trade-off functions that yield the desired singularity. I illustrate the construction of trade-offs with an example where the virulence of a pathogen evolves in a small ecosystem of a host, its pathogen, a predator that attacks the host and an alternative prey of the predator.
Fully stable cosmological solutions with a non-singular classical bounce
Ijjas, Anna; Steinhardt, Paul J.
2017-01-01
We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order L4 Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.
Shocks and finite-time singularities in Hele-Shaw flow
Energy Technology Data Exchange (ETDEWEB)
Teodorescu, Razvan [Los Alamos National Laboratory; Wiegmann, P [UNIV OF MONTREAL; Lee, S-y [UNIV OF CHICAGO
2008-01-01
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.
Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations
International Nuclear Information System (INIS)
Civalek, Omer; Acar, Mustafa Hilmi
2007-01-01
The method of discrete singular convolution (DSC) is used for the bending analysis of Mindlin plates on two-parameter elastic foundations for the first time. Two different realizations of singular kernels, such as the regularized Shannon's delta (RSD) kernel and Lagrange delta sequence (LDS) kernel, are selected as singular convolution to illustrate the present algorithm. The methodology and procedures are presented and bending problems of thick plates on elastic foundations are studied for different boundary conditions. The influence of foundation parameters and shear deformation on the stress resultants and deflections of the plate have been investigated. Numerical studies are performed and the DSC results are compared well with other analytical solutions and some numerical results
Pieper, M.J.; Francke, A.L.; Steen, J.T. van der; Scherder, E.J.; Twisk, J.W.R.; Kovach, C.R.; Achterberg, W.P.
2016-01-01
OBJECTIVE: To investigate whether implementation of a stepwise multidisciplinary intervention ('STA OP!' ['STAND UP!']) is effective in reducing behavioural problems and depressive symptoms in nursing home residents with advanced dementia. DESIGN: Cluster randomised controlled trial. METHOD: We
On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems
International Nuclear Information System (INIS)
Diaz, J. I.; Henry, J.; Ramos, A. M.
1998-01-01
We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem
Visual problem solving and self-regulation in training air traffic control
Van Meeuwen, Ludo
2013-01-01
Van Meeuwen, L. W. (2013). Visual problem solving and self-regulation in training air traffic control (Unpublished doctoral dissertation). Centre for Learning Sciences and Technologies, Open Universiteit, Heerlen, The Netherlands.
Visual Problem Solving and Self‐regulation in Training Air Traffic Control
Meeuwen van, Ludo
2015-01-01
Van Meeuwen, L. W. (2013). Visual problem solving and self-regulation in training air traffic control (Unpublished doctoral dissertation). Centre for Learning Sciences and Technologies, Open Universiteit, Heerlen, The Netherlands.
Belmiloudi, Aziz
2006-01-01
We formulate and study robust control problems for a two-dimensional time-dependent Ginzburg-Landau model with Robin boundary conditions on phase-field parameter, which describes the phase transitions taking place in superconductor films with variable thickness. The objective of such study is to control the motion of vortices in the superconductor films by taking into account the influence of noises in data. Firstly, we introduce the perturbation problem of the nonlinear ...
Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
2017-05-01
A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
A Path-following Method for Solving BMI Problems in Control
1999-06-01
University Stanford, CA 94305-9510, USA Abstract—In this paper we present a path-following ( homotopy ) method for (locally) solving bilinear matrix inequality...programming (SDP), robust control, low-authority control. 1 Introduction Promising new methods for the analysis and design of ro- bust controllers for...following ( homotopy ) method for (locally) solving BMI problems in control. The method is very easy to implement: the BMI is linearized using a first
Singular electrostatic energy of nanoparticle clusters
Qin, Jian; Krapf, Nathan W.; Witten, Thomas A.
2016-02-01
The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation h has a singular logarithmic dependence on h . We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact c (h ) , together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.
Further holographic investigations of big bang singularities
Energy Technology Data Exchange (ETDEWEB)
Engelhardt, Netta [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States); Hertog, Thomas [Institute for Theoretical Physics, KU Leuven,3001 Leuven (Belgium); Horowitz, Gary T. [Department of Physics, UCSB,Santa Barbara, CA 93106 (United States)
2015-07-09
We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves N=4 super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.
Further holographic investigations of big bang singularities
Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T.
2015-07-01
We further explore the quantum dynamics near past cosmological singularities in anisotropic Kasner-AdS solutions using gauge/gravity duality. The dual description of the bulk evolution involves super Yang-Mills on the contracting branch of an anisotropic de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlator between two points separated in a direction with negative Kasner exponent p always exhibits a pole at horizon scales, in any dimension, which we interpret as a dual signature of the classical bulk singularity. This indicates that the geodesic approximation selects a non-normalizable Yang-Mills state.
Singular tachyon kinks from regular profiles
International Nuclear Information System (INIS)
Copeland, E.J.; Saffin, P.M.; Steer, D.A.
2003-01-01
We demonstrate how Sen's singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important role in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action, we are able circumvent the results of a recent paper which derived two conditions on the asymptotic tachyon potential such that the singular kink could be recovered in the large amplitude limit of periodic solutions. We show that this is explained by the non-commuting nature of two limits, and that Sen's solution is recovered if the order of the limits is chosen appropriately
Method of rotations for bilinear singular integrals
Czech Academy of Sciences Publication Activity Database
Diestel, G.; Grafakos, L.; Honzík, Petr; Zengyan, S.; Terwilleger, E.
2011-01-01
Roč. 3, - (2011), s. 99-107 ISSN 1938-9787. [Analysis, Mathematical Physics and Applications. Ixtapa, 01.03.2010-05.03.2010] R&D Projects: GA AV ČR KJB100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : bilinear singular integrals * bilinear Hilbert transform * Fourier multipliers Subject RIV: BA - General Mathematics http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.cma/1298670006&page=record
Non-singular spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Guardiola, R.
1990-01-01
A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)
Space-time singularities in Weyl manifolds
Energy Technology Data Exchange (ETDEWEB)
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
The technological singularity and exponential medicine
Iraj Nabipour; Majid Assadi
2016-01-01
The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested th...
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
Directory of Open Access Journals (Sweden)
D. A. Fetisov
2015-01-01
Full Text Available State-feedback linearization is widely used to solve various problems of the control theory. An affine system is said to be state-feedback linearizable if there are a smooth change of variables in the space of states and an invertible change of controls, which transform the system to the system of a regular canonical form. However if a system is not state-feedback linearizable it yet can be orbitally feedback linearized, i.e. the system can be transformed to a regular canonical form after a change of the independent variable.The article solves the following terminal problem for multi-dimensional stationary affine systems: for given two states, find controls and a time T such that the corresponding trajectory of the system joins these states for the time T. We make an integrable change of the independent variable depending on controls. As a result, we obtain a non-stationary affine system, its dimension being one less than dimension of the original system. The new terminal problem with the restriction on controls is formulated for the transformed system. We prove the relation between solutions of the original terminal problem and solutions of the terminal problem for the transformed system. It is shown that to solve the original terminal problem it is sufficient to solve terminal problem for the transformed system. Then, we check whether the transformed system can be state-feedback linearized. For this purpose, we check the necessary and sufficient conditions of state-feedback linearization for non-stationary affine systems. If the conditions are met then we transform the system to a regular canonical form for which the concept of inverse dynamics problems can be used to solve terminal problems. However, due to the restriction on controls an additional check is necessary whether the found controls meet the restriction.An example of the terminal problem for the five-dimensional affine system with two controls is given. We prove that the system in
Directory of Open Access Journals (Sweden)
Eko Sujadi
2016-03-01
Full Text Available Problem focused coping need to be possessed by every individual. The purposes of this research were to described locus of control, the effectiveness of interpersonal communication, problem focused coping,the correlation between locus of control with problem focused coping, andthe correlationbetween the effectiveness of interpersonal communication with problem focused coping.This research was descriptive & correlation research by using quantitative approach. Data were collected through a Likert scale questionaire and locus of controlby using inventory Rotters Internal-External Locus of Control (I-E Scale, which was the validity and reliability has been tested. The data were analyzed by percentage technique and product moment correlation. The finding of research are: 1locus of control were in the middle range between internal locus of control and external locus of control with an average as big as 11.46, 2 the general level of effectiveness of interpersonal communication is in high category, 3 the general level of problem focused coping is in high category, 4 there is correlation between locus of control withproblem focused coping, and 5 there is correlation betweeneffectiveness of interpersonal communicationwithproblem focused coping.
Boukraa, S.; Hassani, S.; Maillard, J.-M.
2012-12-01
Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard-Fuchs systems of two-variables ‘above’ Calabi-Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ(n), corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ(3) and χ(4), that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ(n)s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi-Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non-holonomic anisotropic full
International Nuclear Information System (INIS)
Boukraa, S; Hassani, S; Maillard, J-M
2012-01-01
Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard–Fuchs systems of two-variables ‘above’ Calabi–Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ (n) , corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ (3) and χ (4) , that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ (n) s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi–Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non
Sleep problems and suicide attempts among adolescents: a case-control study.
Koyawala, Neel; Stevens, Jack; McBee-Strayer, Sandra M; Cannon, Elizabeth A; Bridge, Jeffrey A
2015-01-01
This study used a case-control design to compare sleep disturbances in 40 adolescents who attempted suicide with 40 never-suicidal adolescents. Using hierarchical logistic regression analyses, we found that self-reported nighttime awakenings were significantly associated with attempted suicide, after controlling for antidepressant use, antipsychotic use, affective problems, and being bullied. In a separate regression analysis, the parent-reported total sleep problems score also predicted suicide attempt status, controlling for key covariates. No associations were found between suicide attempts and other distinct sleep problems, including falling asleep at bedtime, sleeping a lot during the day, trouble waking up in the morning, sleep duration, and parent-reported nightmares. Clinicians should be aware of sleep problems as potential risk factors for suicide attempts for adolescents.
Zemlyanova, A. Y.
2013-03-08
A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.